cxum-afxazeTis mecnierebaTa akademia Tskhum-Abkhazian Academy of Sciences
eZRvneba gamoCenili maTematikosisa da meqanikosis, akademikos ilia vekuas dabadebidan 110 wlisTavs Dedicated to the 110th Anniversary of Outstanding Mathematician and Mechanist, Academician Ilia Vekua Tskhum-Abkhazian Academy of Sciences
PROCEEDINGS
XIII-XIV
Publishing House “SAARI” Tbilisi, 2017 cxum-afxazeTis mecnierebaTa akademia
S r o m e b i
XIII-XIV
gamomcemloba `saari~ Tbilisi, 2017 mTavari redaqtori oTar Jordania redaqtorebi: Temur CilaCava, meri gabedava, nona (nazi) uSveriZe pasuxismgebeli mdivani: irma zaqaraia
saredaqcio sabWo maria kornelia barliba, rumineTi (kulturologia), badri gogia, safrangeTi (istoria), tania kapiki, saberZneTi (turizmi), anzor miqaia, aSS (qimia), henrik pa- procki, poloneTi (Teologia), liubov soloviova, ruseTi (eTnologia), daviT yolbaia, poloneTi (istoria), maria koniuSkeviCi, belorusi (filologia).
saredaqcio kolegia WiaTurisa da saCxeris mitropoliti danieli (daTuaSvili), zoia adamia, diana alania, ekaterine bakaraZe, meri gabedava, nugzar ebanoiZe, eka vardoSvili, anzor ToTaZe, guCa kvaracxelia, medea kvaracxelia, paata koRuaSvili, maia marRania, antonina msxilaZe, nodar naTaZe, qeTevan pavliaSvili, oTar Jordania, avTandil silagaZe, nona (nazi) uSveriZe, gulnara qarCava, malxaz Rvinjilia, manana Selia, vaJa Sengelia, Temur CilaCava, nodar CxartiSvili, givi cincaZe, marat cicqiSvili, mineda Wanturia, nodar WiTanava, gulnaz xuxua, marina jaiani, liliana janaSia, levan jinjixaZe, jemal jinjixaZe.
Editor-in-Chief: Otar Zhordania Editors: Temur Chilachava, Meri Gabedava, Nona (Nazi) Ushveridze Executive Secretarie: Irma Zakaraia
EDITORIAL COUNCIL Maria Cornelia Barliba, Romania (Culture Studies), Badri Gogia, France (History), Tania Kapiki, Greece (Tourism), David Kolbaia, Poland (History), Anzor Mikaia, USA (Chemistry), Henrik Paprotsky, Poland (Theology), Lubov Soloviova, Russia (Ethnology), Sergi Volkov, Ukraine (Chemistry), Maria Koniushkevich, Belorus (Philology).
EDITORIAL BOARD Metropolitan Daniel (Datuashvili) of Chiatura and Sachkhere Eparchy, Zoia Adamia, Diana Alania, Ekaterine Bakaradze, Meri Gabedava, Mineda Chanturia, Temur Chilachava, Nodar Chitanava, Nodar Chkhartishvili, Nugzar Ebanoidze, Malkhaz Ghvindjilia, Marina Jaiani, Liliana Janashia, Jemal Jinjikhadze, Levan Jinjikhadze, Gulnara Karchava, Gulnaz khukhua, Gucha Kvaratskhelia, Medea Kvaratskhelia, Paata Koghuashvili, Maia Marghania, Antonina Mskhiladze, Nodar Natadze, Ketevan Pavliashvili, Avtandil Silagadze, Manana Shelia, Vazha Shengelia, Anzor Totadze, Givi Tsintsadze, Marat Tsitskishvili, Nonna (Nazi) Ushveridze, Eka Vardoshvili, Otar Zhordania.
Address: Tskhum-Abkhazian Academy of misamarTi: cxum-afxazeTis mecnierebaTa Sciences, 15a Tamarashvili st. 0186, Tbilisi, akademia, 0186, saqarTvelo, Tbilisi, Georgia. m. TamaraSvilis q. 15a. www.taas.ge; [email protected]; Tel. 2 18 39 42
cxum-afxazeTis mecnierebaTa akademia uak (UDC) 908(479.224) Tskhum-Abkhazian Academy of Sciences c-998
krebuli daibeWda afxazeTis mecnierTa mxardaWeris programis dafinansebiT. This Volume of the Proceedings was Financed and Published Thanks to the Supporting Programme for Scientists from Abkhazia.
ISSN 2233-3363 akademikosi ilia vekua ACADEMICIAN ILIA VEKUA (23.04.1907 - 2.12.1977) cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
ilia vekua _ 110 ILIA VEKUA _ 110
Temur CilaCava
akademikos ilia vekuas cxovreba da moRvaweoba
Cven samar T li a nad vama yobT qarTu li maTe ma ti ku ri, fizi o logi u ri da fsiqo lo gi u ri skole bis msoflio aRia re biT. udide si madli e re biT da pati vis ce miT movix se ni ebT maT fuZem deb lebs niko loz musxe liS vils, ivane beri taS vils, dimit ri uzna Zes. am skoleb Tan mrava li saxel gan T q mu li mecni e re bis saxe lia dakav Si re bu li. maT ricxvs uTuod mie kuT v ne ba akade mi ko si ilia veku a. gansa kuT re bu li niWis, Sromis moy va re o bis, axalgaz r do bis mizid vi sa da gata ce bis unaris wyalo biT, man didi wvlili Sei ta na maTe ma ti kis da meqa ni kis mecni e re ba Ta ganvi Ta re ba Si, SeZlo pers peqti u li mimar Tu le be bis aRmo Ce na, Tavad gaxda axali samec ni e ro skolis meTa u ri. 1907 wlis 23 aprils afxaze Tis sofel SeSe le Tis mkvidr nes tor veku as da mis meuR les liza (memu) abSi la vas See Zi naT vaJi, ro melsac ilia daar q ves. nestor veku as ojaxis siyr mis Svils wilad xvda gamx da ri yo me-20 sau ku nis erT -er Ti udide si maTe ma ti ko si. am qarTul -afxa zur tradi ci ul ojaxSi cxovrob d nen erTi az riT _ yofi liy v nen Sromis moy va re ni, simar T li saT vis mebr Zol ni da hqono daT swavlis survi li. maTi welga u mar Ta vi SromiT mowe uli Wirna xu li iyo nestor veku as mraval ricxo va ni ojaxis arse bobis mTava ri wyaro. ilia saTu Tad mosiy va ru le, didad mzrunve li Zma iyo Tavi si umc ro si Zmis vasos da debis maros, vera sa da cocos mimarT. Svi liSvi le bis aRz r di sa da ganaT le bi saT vis didad zrunav da ilias babua Tedo veku a. man Tavi si sakar mi da mo miwa gamo yo imisaT vis, rom sofel SeSe leT Si, SvilTan erTad aeSene bi na pirve li skola. sare cel ze mijaW vul ma Tedom Tavis vaJs, nestors uander Za, yove li Rone exma ra, raTa SviliS vi le bi saT vis mie ca swavla- ga naTle ba, radgan mas swamda, rom ganaT le bas mokle bu li adami a nis cxovre ba uRimRa mo iqne bo da. pata ra ilia jer swavlob da SeSe le Tis skola Si, mere muxuris, xolo 1925 wels warma te biT daam Tav ra zugdi dis pirve li saSu a lo skola. imave wlis Semod go ma ze ilia vekua Cai ricxa Tbili sis 6 Temur CilaCava saxel m wi fo univer si te tis fizi ka- ma Te ma ti kis fakul tet ze. misi arCe va ni ar iyo SemTx ve vi Ti. skolis wlebSi ve maTe ma ti ka mas izi davda Tavi si si zustiT da msjelo ba Ta Sina ga ni logi ku ri Tan mimdev ro biT. TiTqos yvela fe ri kargad daiwyo, magram 1926 wels ilias ojaxs Tavs daaty da didi ubedu re ba. ormoc da oTxi wli sa garda ec va la deda, qalba to ni liza. dedis gardac va le biT ga mowve ul ma didma suli er ma tramvam da mate ri a lur ma siZne le eb ma ilias ver aaRebi nes xeli univer si tet Si swavlis gagr Ze le bis survil ze. 1932 wels mamis gardac va le bis Semdeg iliam Tbilis Si Camo iyvana Zma, debi da patronobda maT. es is dro iyo, rodesac Tbi lisis saxel m wi fo univer si te tis fizi ka- ma Te ma ti kis fakul tet ze samec ni e ro da peda go gi ur moRva we o bas eweod nen niko loz musxe liSvi li, gior gi niko la Ze, and ria razma Ze, arCil xara Ze. XX s. 20-iani wlebis dasas rul sa da 30-ia ni wlebis dasawyis Si saqar T ve lo Si gaix s na ramde ni me umaRle si saswav le be li (maga li Tad, 1932 wels, soxu mis agro pe da go gi u ri ins ti tu ti, rome lic 1933 wels gada keT da peda go gi ur ins ti tu tad ), maT Soris, teqni ku ri profi lis, ris gamoc aucile be li gaxda kvali fi ci u ri maTe ma ti kuri kadre bis gegmi u ri momza de ba. niko loz musxe liS vi lis Taos no biT, qarT vel axalgaz r da ma Tema ti kos Ta didi jgufi, univer si te tis warma te biT damTav re bis Semdeg, aspi ran tu ris gasav le lad gaig zav na moskov sa da lenin g radis (sankt - pe ter bur gis) samec ni e ro cent reb Si. axlad fexad g mul qarTu li maTe ma ti ku ri skoli saT vis es iyo mZime danak li sis wlebi. ulmo bel ma sikv dil ma gamos ta ca mas ori gamo Ce ni li mecni e ri, maTe ma ti ku ri skolis fuZem deb le bi _ and ria razma Ze da gior gi niko la Ze. 1930 wlis oqtom ber Si ilia vekua Cairicxa mecni e re ba Ta akade miis aspi ran tu ra Si, rome lic maSin lenin g rad Si iyo. mecni e re ba Ta akade mi is fizi ka- ma Te ma ti kis ins ti tut sa da lenin g ra dis saxel m wifo univer si tet Si muSa ob d nen gamo Ce ni li maTe ma ti ko se bi, saxel ganT q mu li sank t - pe ter bur gis maTe ma ti ku ri skolis tradi ci e bis saxe lo va ni gamg r Ze le be li: ivane vinog ra do vi, niko loz giun te ri, niko loz koCi ni, and rei krilo vi, vladi mir smirno vi da sxva. maTi sain te re so speckur se bi exebo da Teo ri u li da gamo ye ne biTi maTe ma ti kis mTel rig aqtu a lur mimar Tu le bebs. isini gani xilav d nen didi mecni e ru li mniSv ne lo bis axal proble mebs, xelm ZRva ne lob d nen saswav lo- sa mec ni e ro semi na rebs. im wlebSi lenin grad Si xSirad Cadi o da niko loz musxe liS vi li, igi kiTxulob da 7 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV leqci ebs dreka do bis maTe ma ti ku ri Teo ri a Si da xelm ZR va ne lob da aspi ran te bis muSa o bas. ra Tqma unda, aseTi gacxove le bu li samec ni e ro muSa o ba le ning ra di sa ken izidav da bevr axalgaz r da maTe ma ti koss. ilia veku asTan erTad, peter bur g Si, aspi ran tu ra Si warma te biT swavlob d nen a. gorgi Ze, d. doli Ze, i. mecxva riS vi li, a. ruxa Ze da sxvebi. maTe ma ti ku ri anali zi sa da ricxv Ta anali zu ri Teo ri is faqiz sakiTxeb Tan erTad, peter bur gis maTe ma ti ku ri skolis yuradRe bis cent r Si iyo uwyve ti gare mos meqa ni kis maTe ma ti kur aspeq teb Tan dakav Si re bu li proble me bic. ukve ocia ni wlebi dan dreka do bis Teo ri a Si maTe ma ti ku ri me Tode bis ganvi Ta re ba ze did zegav le nas axden da niko loz musxe liSvi lis Srome bi. mis mier wamo ye ne bu li promle me bi gaxda bevri axalgaz r da maTe ma ti ko sis kvlevis saga ni. Tavis pirvel origi na lur samec ni e ro gamok v le veb Si (a. ruxa Zes Tan erTad) ilia veku am daa mu Sa va dreka di Zelebi sa da Rero e bis grexvi sa da Runvis amo cane bi. aspi ran tu ra Si ilia veku as xelm ZR va ne li iyo akade mi ko si and rei krilo vi, v. a. steklo vis saxe lo bis fizi ka- ma Te ma ti ku ri in sti tu tis direq to ri. ilia vekua Tanda Tan Caer To akade mi kos v. smirno vis jgufis muSa o ba Si. v. smirno vi xelm ZRa ne lob da seis mo logi u ri ins ti tu tis Teo ri ul ganyo fi le bas. es ins ti tu ti maSin Sedi o da fizi ka- ma Te ma ti ku ri ins ti tu tis Semad gen lo ba Si. am peri ods ekuTv nis ilia veku as gamok v le ve bi, romle bic exe ba or para le lur sibr tyes Soris moTav se bul usasru lo fena Si dreka di talRe bis gavr ce le bis Teo ri as. peter bur g Si muSa o bis sami wlis ganmavlobaSi ilia vekua Camo yalib da rogorc maTe ma ti ko si, seri o zu li maTe ma ti ku ri gamok v leve bis avto ri. 1933 wels ilia vekua da sxva qarT ve li maTe ma ti ko se bi, rom lebmac moskov sa da peter bur g Si daam Tav res aspi ran tu ra, Tbi lisSi dabrun d nen. maT wina Se iyo metad aqtu a lu ri da Zneli amo cana: gae Sa laT samec ni e ro muSa o ba da aemaRle bi naT swavle bis done maTe ma ti kis im dargeb Si, romleb Sic mwvaved igr Z no bo da ad gilob ri vi speci a lis te bis nakle bo ba. 1933 wlis Semod go ma ze ilia vekua, Ziri Ta dad, muSa ob da Tbi lisis saxel m wi fo univer si te tis fizi ka- ma Te ma ti kis fakul te tis mecni er - Ta nam S rom lad. igi maSin ve gaxda maTe ma ti ki sa da meqa ni kis proble me bis mudmiv moq me di samec ni e ro-kvleviTi semi na ris aqti uri mona wi le. semi na ris sxdomeb ze mas xSirad hqonda moxse ne be bi 8 Temur CilaCava kerZo warmo e bu li a ni dife ren ci a lu ri ganto le be bis Teo ri is sa kiTxebze, fizi kis ganyo fi le bis ufros kur sel TaT vis kiTxulob da leqci ebs maTe ma ti kis rCeul Temebze. es leqci e bi moi cav d nen Tana med ro ve maTe ma ti kis iseT dargebs, rogo ri caa kerZo warmo ebu li a ni dife ren ci a lu ri ganto le be bi, vari a ci u li aRricx va, tenzo ru li anali zi, speci a lu ri funq ci e bi da sxva. 1937 wlis Semod go maze ma Te ma ti ku ri ganyo fi le bis mesa me kursis studen taT vis ilia veku am daiwyo Cveu leb ri vi dife ren ci alu ri ganto le be bis saleq cio kursis kiTxva. ilia veku as leqci e bi gans x vav de bo da sxvaTa leqci e bi sa gan, igi sagans gadmo cem da am darg Si uaxle si mecni e ru li miRwe ve bis gaTva lis wi ne biT. leqci e bis kiTxvi sas misi metyve le ba da qceva Tavi su fa li iyo yovel g va ri artis tiz mi sa gan. maTe ma ti ku ri faq tebis erTi a no bi dan arse bo bi sa da mTava ris mkafi od gamo yo fis unari, am faqte bis Sina ga ni logi kis naTlad warmo Ce na saSu a le bas aZlev da mas msmene lis Tvalwin gae Sa la sagnis mTeli sila ma ze. didi momTxov ne lo bis miu xe da vad, mosw re ba im discip li neb Si, romleb sac ilia vekua kiTxulob da, Zalze maRa li iyo. albaT amitom, 1935 wlis nakadis student-maTematikosebma spe cialobad airCies maTematikuri analizisa da gamoyenebiTi maTema tikis ilia vekuas samecniero interesebis areSi Semavali dargebi, kerZod, maTematikuri fizikis gantolebebi, funqcionaluri anali zi, uwyveti garemos meqanika, Teoriuli geofizika da sxva. samec ni e ro xaris xe bis miniWebas saqar T ve lo Si mxolod 30-iani wlebis meo re naxev ri dan mieq ca gansa kuT re bu li yuradRe ba. 1937 wels ilia veku am peter bur g Si Sesru le bul namu Se var Ta safuZ velze daic va sakan di da to disertacia Tema ze: `dreka di rxeve bis gavr ce le ba usasru lo fena Si~ . Teo ri u li da gamo ye ne bi Ti maTe ma tikis mimar Tu le bebs Soris ilia veku as gansa kuT re biT ainte re sebda elifsu ri tipis kerZo warmo e bu li a ni dife ren ci a lu ri gan tole be bis Teo ri a. funq ci o na lu rad inva ri an tul amonax s n Ta simrav li sa da bi harmo ni u li ganto le bis zoga di amonax s nis arsi sa da rolis ana lizma, jer kidev peter bur g Si yofni sas, ilia vekua miiy va na im az ramde, rom elifsu ri ganto le be bis sakma ri sad farTo klasi saT vis moe Zeb na amonax s n Ta zoga di warmod ge ne bi da, rac mTava ri a, am warmod ge ne bis saSu a le biT Seeq m na sasazR v ro amoca na Ta amoxs nis axali meTo de bi. elifsu ri ganto le be bis zogi er Ti kerZo klasis zoga di amonax s ne bi maTe ma ti ka Si adrec iyo cnobi li, magram ma Tema ti ko se bis damo ki de bu le ba misad mi sakma od skepti ku ri iyo. 9 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV speci a lis teb ma maSin ar icodnen rogor gamo e ye ne bi naT es zoga di amonax s ne bi maTe ma ti ku ri fizi kis Ziri Ta di amoca ne bis amoxs ni saTvis. iseTi didi maTe ma ti ko se bi, rogo rebic iyv nen: daviT hilber ti da misi mowa fe rihard kuran ti, Tavi anT maTe ma ti ku ri fizi kis or tomi an monog ra fi a Si eWvs gamoT q vam d nen elifsu ri ganto le be bis amonax s ne bis zoga di komp leq su ri warmod ge ne bis gamo ye ne bis Se saZleb lo ba ze. dRes maTe ma ti kur samya ro Si sayo vel Ta od miRe bu li a, rom skepti ciz mis daZle va ganu yof lad dakav Si re bu lia ilia veku as saxel Tan. ilia veku as mier 1936 wels dawyebu li inten si u ri ga mokv le ve bi 40-ian wlebSi dasrul da ori cvladis elifsu ri ti pis wrfiv kerZo warmo e bu li an ganto le ba Ta mwyobri anali zu ri Teo ri is Seqm niT. mis mier agebu li elifsu ri ganto le be bis amo naxs ne bis zoga di komp leq su ri warmod ge ne bi Zalze mosa xer xe be li aRmoC n d a rogorc am amonax s ne bis axali Tvisob ri vi da struqtu ruli bune bis dasad ge nad, ise sasazR v ro amoca ne bis farTo kla sis amosax s ne lad. elifsur ganto le ba Ta Teo ri a Si ilia veku as Sede ge bi da me Tode bi farTod gamo i ye ne ba uwyve ti gare mos meqa ni ka Si, kerZod, dreka di garse bis Teo ri a Si. yvela zemoxsenebul Sedegs ilia vekua 1937 wlidan Tanmim dev rulad aqvey neb da sxvadas x va peri o dul gamo ce ma Si. Semd gom Si, am Sede ge bis didi nawi li gamoq vey n da monog ra fi a Si `elif su ri gan tole be bis amoxs ne bis axali meTo de bi~, risT vi sac mis avtors 1950 wels saxel m wi fo premia mie ni Wa. ilia veku as inten si u ri Semoq me de bi Ti Sromis Sede gi a no ba da misi samec ni e ro idee bis nayo fi e re ba yovel T vis izidav da axal gazr da maTe ma ti ko sebs. amitom ar aris gasak vi ri, rom igi maSin, ormo ci an wlebSi, garSe mor ty mu li iyo mraval ricxo va ni mowa fi Ta da mimdev riT. ilia vekua iyo yuradRe bi a ni, amasTa na ve momTxov ni da samec ni ero Sede ge bis Sefa se bi sas princi pu li. am Tvise be bis gamo uyvar daT da pativs scemd nen mas misi mowa fe e bi. mecnierTa warmatebebi didaa damokidebuli samecniero dawese bulebebisa da umaRlesi saswavleblebis muSaobis swor organiza ciaze. dRes Cven buneb ri vad migvaCnia, rom mecni e re bi sa da umaRle si ganaT le bis orga ni za to re bi gamo Ce ni li mecni e re bi unda iyv nen. XX s. 40-ian wlebSi ilia vekua gvevli ne ba saqar T ve lo Si mecni ere bi sa da umaRle si ganaT le bis did orga ni za to rad. omis wlebSi 10 Temur CilaCava is iyo jer saxel m wi fo univer si te tis fizi ka- ma Te ma ti kis fakul tetis deka ni, Semdeg _ univer si te tis proreq to ri. para le lu rad igi saTa ve Si edga geo met ri is kaTed ras univer si tet Si da Teo ri uli meqa ni kis kaTed ras amier kav ka si is mimos v lis gzebis inJi ner Ta ins ti tut Si. mas didi orga ni za to ru li muSa o ba moux da, raTa omiT gamow ve u li siZne le ebs ar See fer xe bi naT saswav lo proce si. ilia veku as samec ni e ro miRwe veb ma didi aRia re ba moi po ves. 1944 wels igi airCi es saqar T ve los mecni e re ba Ta akade mi is wevr - kores pon den tad, xolo 1946 wels _ sabWo Ta kavSi ris mecni e re ba Ta akade mi is wevr - ko res pon den tad da saqar T ve los mecni e re ba Ta akade mi is akade mi ko sad. Tavi si unariT, swored See fa se bi na mecni e re bis ganvi Ta re bis pers peq ti ve bi, samec ni e ro -or ga ni za ci u li sakiTxe bis gadawy ve ti sas urye vi princi pu lo biT, ilia veku am didi avto ri te ti moi po va akade mi is koleq tiv Si. miu xe da vad imisa, rom saor ga ni za cio mu Sao ba mas did dros arT mev da, igi mecni e re bas ar eTiSe bo da da mudam iyo misi ganvi Ta re bis wina xazze, warma te biT amuSa veb da princi pu li mniSv ne lo bis proble mebs. didi mecni e ris Semoq me de bi Ti gza ar yofi la ia-var diT mo feni li. ilia veku as cxovre bis gzaze ara erTxel Sexved ria seri ozu li wina aR m de go be bi da siZne le e bi. erTi Sexed viT ucna u ri a, rom es didi mecni e ri swored misi cxovre bis mZime peri o deb Si aR wevda udides Semoq me de biT warma te bebs, rac mis brwyinva le niWsa da nebis yo fis gansa kuT re bul siZli e re ze metyve lebs. 1951 wlis Semodgomis miwuruls ilia vekua gaemgzavra ojaxiT (meuRle Tamarsa da qaliSvil lamarasTan erTad) moskovSi da da iwyo muSaoba cetraluri hidroaerodinamikuri institutis ( ) ganyofilebis gamged. paralelurad igi iyo moskovis fizika-teq nikuri institutis Teoriuli meqanikis kaTedris gamge. am ЦАГИ orive dawesebulebas maSin xelmZRvanelobda akademikosi sergei xristi anoviCi, romelsac ekuTvnis ilia vekuas miwvevis iniciativa. am pe riod Si ilia veku as samec ni e ro inte re se bi ar Semo i far g le bo da mxolod gamo ye ne bi Ti xasi a Tis proble me biT. 1952 wels ilia vekua airCi es m. lomo no so vis saxe lo bis mos kovis saxel m wi fo univer si te tis dife ren ci a lu ri kaTed ris pro feso rad, xolo 1953 wels _ v. steklo vis saxe lo bis maTe ma ti ku ri ins ti tu tis ufros mecni er - Ta nam S rom lad. is warma te biT agr Ze lebda pirve li rigis organto le bi a ni elifsu ri siste mis Teo riis sakiTxe bis kvlevas, rome lic jer kidev Tbilis Si daiwyo. swored Tbilis Si dai we ra da 1952 wels Jurnal « 11 Математический cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
-Si gamoq vey n da misi funda men tu ri naSro mi `pirve li ri gis dife ren ci a lur ganto le ba Ta siste me bi da sasazR v ro amoca neсборник»bi da maTi gamo ye ne ba gars Ta Teo ri a Si~. farTov de bo da ilia vekuas mowa fe e bi sa da Tanamoazreebis wre. XX s. 50-ia ni wlebis SuaxanebSi misi xelm ZR va ne lo biT univer sitet sa da v. steklo vis saxe lo bis maTe ma ti kis ins ti tut Si mu Saob da bevri niWi e ri axalgaz r da maTe ma ti ko si qveynis sxvadas x va kuTxidan da sazRvar ga re Ti dan. amave peri od Si, m. lavren ti ev Tan da s. sobo lev Tan erTad, ilia vekua saTa ve Si edga samec ni e ro- kvlevi Ti semi na re bis muSa o bas funq ci a Ta Teo ri a Si (v. steklo vis saxe lo bis maTe ma ti kis ins ti tut Si) da kerZo warmo e bu li a ni di feren ci a lu ri ganto le be bis Teo ri a Si (mosko vis saxel m wi fo uni versi tet Si). ilia veku as cxovre bis mosko vis xana aRiniS na misi mecni e ru li miRwe ve bis msoflio aRia re biT. misi Sede ge bi Sevi da saxel gan T q muli mecni e re bis monog ra fi eb sa da mimo xil veb Si. igi warma te biT gamo vi da samec ni e ro moxse ne be biT helsin k Si gamar Tul funq ci a Ta Teo ri is samec ni e ro konfe ren ci a ze 1957 wels da maTe ma ti kos Ta saer Ta So ri so kong res ze edinbur g Si 1958 wels. daamyara pira di urTi er To be bi maTe ma ti ku ri anali zis sazRvar ga re Tis did speci alis tebTan. orive misi monog ra fia iTarg m na ing li sur, germa nul da Cinur enebze, xolo calke u li Srome bi _ espa nur, itali ur, rumi nul da sxva enebze. 1955 wels v. steklo vis saxe lo bis maTe ma ti kis ins ti tu tis di reqtor ma akad. ivane vinog ra dov ma ilia vekua miiw via Tavis mo adgi led. ilia veku am am post ze Secva la akade mi ko si mstislav keldi Si. ilia veku as samec ni e ro -or ga ni za to rul ma moRva we o bam Semd gomi aRia re ba pova. mecni e re ba Ta akade mi is teqni kur mecni e re ba Ta ganyo fi le bis wevr - ko res pon dents 1954 wels irCe ven fizi ka- ma Te mati kur mecni e re ba Ta biu ros wevrad, xolo 1958 wels _ sabWoTa kavSi ris mecni e re ba Ta akade mi is namd vil wevrad. akade mi kos m. lavren ti e vis sai ni ci a ti vo jgufTan erTad ilia vekua mona wi le ob da mecni e re ba Ta akade mi is cimbi ris ganyo fi le bis proeq tis Seqm na Si. kerZod, 1957 wels Seiq m na sabWo Ta kavSi ris mecni e re ba Ta akade mi is cimbi ris ganyo fi le ba da damt kic da saor gani za cio komi te ti akad. m. lavri en ti e vis meTa u ro biT. cimbiris ganyofilebas daemqvemdebara yvela akademiuri samec niero-kvleviTi instituti, romlebic teritoriulad cimbirsa da Soreul aRmosavleTSi mdebareobda. 1957 wels, novosibirskis 12 Temur CilaCava maxloblad, obis wyalsacavis Tvalwarmtac napirze daiwyo akadem qalaqis mSenebloba. igi unda gamxdariyo mecnierebaTa akademiis cimbiris ganyofilebis centri. novo si bir s k Si moskov idan da lenin g ra di dan samu Sa od gada- vidnen gamo Ce ni li mecni e re bi. maT gayvnen TavianTi samec ni e ro koleq ti ve bi, romelTa safuZ vel zec Seiq m na cimbi ris ganyo fi le bis axali samec ni e ro- k v le vi Ti ins ti tu te bi. 1958 wlis mart Si arCeul iqna ssrk mecni e re ba Ta akade mi is cimbi ris ganyo fi le bis prezi di u mi m. lavren ti e vis meTa u ro biT, romlis Semad gen lo ba Si Sedioda ilia veku ac. akadem qa laq Si samec ni e ro- k v le vi Ti ins ti tu te bi ver ganvi Tarde bo da da ver gafar Tov de bo da axalgaz r du li Zale bis mud mivi mozRva ve bis gare Se. amitom mTavar amoca nad iqca umaRle si mecni e ru li kvali fi ka ci is kadre bis momza de ba adgil ze. 1959 wlis 9 ianvars minis t r Ta sabWom mii Ro gadawy ve ti le ba akadem qa laqSi novo si bir s kis saxel m wi fo univer s ti te tis gaxs nis Sesa xeb, romlis reqto rad daniS nes ilia veku a. Canafiqris mixedviT, novosibirskis universiteti unda gamxda riyo axali tipis umaRlesi saswavlebeli. axladdaniSnul reqtors uamravi saqme hqonda mosagvarebeli: unda uzrunveleyo universi tetis profesor-maswavlebelTa Semadgenlobis dakompleqteba, mi si xelmZRvanelobiT unda warmarTuliyo muSaoba axali saswavlo gegmebisa da programebis Sedgenaze, unda mieRo studentTa pir veli kontingenti da, rac aranakleb mniSvnelovani iyo, yofiliyo mSeneblebTan mudmiv kontaqtSi, raTa 1959 wlis 1 oqtom b ri saT vis damTarebuliyo saskolo Senobis mSenebloba, sadac droebiT dai debda binas jer kidev mxolod dadgenilebebiT arsebuli univer siteti. yvela am amocanis gadawyveta ilia vekuasagan moiTxovda Zalebisa da energiis srul daZabvas. es iyo misi organizatoruli niWis didi gamocda. novo si bir s kis univer si te tis reqto ro bas Tan erTad ilia ve kua xelm ZR va ne lob da ssrk mecni e re ba Ta akade mi is cimbi ris ganyo file bis hidro di na mi kis ins ti tu tis Teo ri ul ganyo fi le bas, iyo oTxi samec niero sabWo s Sevri Tu xelmZRvaneli; is rogorc red kole gi is wevri aqti urad mona wi le o bda `cimbi ris maTe ma ti ku ri Jurna lis~ gamocemaSi. administratiul-organizatoruli muSaobiT didi datvirTvis miuxedavad, ilia vekua mudam poulobda dros samecniero-kvleviTi saqmianobisaTvis. misi samecniero moRvaweobis cimbiris periodSi igi sul ufro farTod erTveba Tanamedrove maTematikisa da myari 13 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV tanis meqanikis axali dargebis damuSavebaSi, amasTan, misi kvlevis obieqtad aqac principuli mniSvnelobis problemebi gvevlineba. 1964 wlis damle vi saT vis ilia veku as mowa fe Ta raodenoba fi zika- ma Te ma ti kis mecni e re ba Ta aTamde doqto rsa da ocamde mec- nierebaTa kandidats iTvlida. maT Soris iyvnen rogorc sabWoTa kavSi ris warmomadgenlebi, aseve mecni e re bi germa ni i dan, polo ne Tidan, Cine Ti dan, kore i dan da sxva. Tavi si 60 wlis iubilesaTvis msofli o Si saxel gan T q mu li mec nie ri, saxel m wi fo premi e bis lau re a ti, sabWo Ta kavSi ris mecni e reba Ta akade mi is akade mi ko si ilia vekua kvlav samSob lo Si a. 1964 wlis noeb ri dan ilia vekua saqar T ve los mecni e re ba Ta akade mi is vice- p re zi den ti a, xolo 1965 wlis dekem b ri dan _ Tbi lisis saxel m wi fo univer si te tis reqto ri. mTel siTbosa da Cinebuli organizatoris mdidar SesaZleb lobebs ilia vekua axmarda Tavis alma mater _ mSobli ur univer si tets, misi didi niWis pirveli aRmafrenis mowmes. Tbilisis saxel mwifo universiteti daarsebidanve iqca saqarTveloSi umaRlesi ganaTlebis, mecnierebisa da kulturis kerad. pirvel xanebSi mas saTaveSi edgnen didi, saxelganTqmuli mecnierebi petre meli qiS vi li da ivane java xiS vi li. isini uaRresad dainteresebuli iyvnen mec nierebis ganviTarebiT, saqarTvelos mosaxleobis farTo wreebSi kulturisa da ganaTlebis gavrcelebiT. kvleviTi muSaobisaTvis da leqciebis wasakiTxad isini xSirad iwvevdnen gamoCenil ucxoel specialistebs. SemoRebuli iyo ufrosi kursis gamorCeuli niWis studentebisa da axalgazrda specialistebis mivlineba msoflios msxvil samecniero centrebSi. yovelive amis Sedegad Camoyalibda kargi tradiciebi, romlebmac Tbilisis saxelmwifo universite ti sabWoTa kavSiris saukeTeso umaRles saswav le bel Ta rigebSi moaqcia. saqar T ve los umaRle si saswav leb le bis umrav le so ba swored univer si tet Si dai ba da. saqar T ve los mecni e re ba Ta akade mia 1941 wels misi samec ni e ro qveda na yo fe bis baza ze Camo ya lib da. 1968 wels saze i mo viTa re ba Si aRiniS na Tbili sis saxel m wi fo univer si te tis daar se bis 50 wlisTa vi. univer si te ti sa da misi reqto ri sad mi didi pati vis ce mis niSnad, dResas wa ul ze dasas w re bad Tbilis Si msofli os mrava li didi univer si te tis warmo mad ge nelma moi ya ra Tavi. 1972 wels, xandaz mu lo bis gamo, niko musxe liS vil ma gadawy vita dae to ve bi na saqar T ve los mecni e re ba Ta akade mi is prezi den tis posti, romel ze dac mas ucv le lad irCev d nen 1941 wlidan. 14 Temur CilaCava n. musxe liS vi lis wina da de biT akade mi am prezi den tad airCia ilia veku a. janm r Te lo bis gau a re se bis miu xe da vad, is unari a nad xelm ZRva ne lob da akade mi is muSa o bas. did samec ni e ro -or ga ni za to rul muSa o bas Tan erTad, ilia vekua warma te biT agr Ze leb da moskov sa da novo si bir s k Si dawye bul gamok v le vebs gars Ta maTe ma ti kur Teo ri a Si, amasTan erTad, igi amuSa veb da meur ne o bis T vis mniSv ne lo van samSe neb lo meqa ni kis amoca ne bis ricxvi Ti amoxs ne bis meTo debs. am mimar Tu le biT mi Rebu li Sede ge bis Sesa xeb man moxse ne be bi wai kiTxa saer Ta So ri so simpo zi u meb ze iuvias ki u li a Si (1972, fine Ti), darm S tad Si (1976, germa ni a) da sxva Tavy ri lo beb ze. mrava li wlis ganmav lo ba Si moRva we ob da ra novo si bir s kis (1959-1965) da Tbili sis (1966-1972) univer si te te bis reqto rad, ag reTve, saqar T ve los mecni e re ba Ta akade mi is (1972-1977) prezi den tad, akade mi ko si ilia vekua, ganur Cev lad erovne bi sa, yovel m x riv zrunav da da xels uwyobda axali samec ni e ro kadre bis, maT Soris afxazebis aRz r dasa da ganvi Ta re bas. akade mi kos ilia veku as uSua lo mona wi le o biT afxazeT Si gaixs nal axali samec ni e ro cent re bi, romle bic amza deb d nen kadrebs avtonomiuri respub li ki saT vis. saqar T ve los mecni e re ba Ta akade miaSi ilia veku as prezi den tobis dros gansa kuT re bu li mxarda We ra hqonda birT vu li fizi kis darg Si momuSave, tradi ci u lad Zlier, soxu mis fizi ka- teq ni kis ins ti tuts, rome lic dRes ilia vekuas saxels atarebs. 1974 wels uSua lod ilia veku as Taos no biT soxum Si gaix s na saqar T ve los mecni e re ba Ta akade mi is a. naTiS vi lis saxe lo bis eq spe ri men ta lu ri morfo lo gi is ins ti tu tis soxu mis fili a li (ge ronto lo gi is labo ra to ri a). samec ni e ro labo ra to ri a, romlis Ziri Tad Semad gen lo ba Si mxolod adgi lob ri vi kadre bi iyo, swav lobda dRegr Zel Ta feno mens. labo ra to ria awyobda saer Ta So ri so eqs pe di ci ebs, romleb Sic, mona wi le ob d nen mecni e re bi ameri kis Seer Te bu li State bi dan, iaponi i dan, ruse Ti dan. Seswav lil iqna saqarTvelos sxvadasxva kuTxe, maT Soris, afxaze Ti (durifSis, atara abxazka i as da sxva eqs pe di ci e bi), aWa ra da sameg re lo. ilia vekua gansa kuT re bu l yuradRe bas iCenda afxaze Tis ad- gilobrivi kadre bis momza de bi sadmi. cnobi lia misi Tanad go ma da mxarda We ra, sofel bedi i dan Camo su li erovnebiT afxazi axal gazr disadmi, ipoli te baRba i a sad mi, novo si bir s kis univer si te tis reqto ro bis dros. Semd gomSi i. baRbaia muSa ob da afxaze Tis sa xelm wi fo univer si tetis docen tad da emsaxureboda axalgazrda kadrebis aRzrdis saqmes. 15 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
ilia vekuas Tbili sis univer si te tis reqto ro bis peri od Si sakmao rao de no biT iyo gamo yo fili limi te bi afxaze Tis mkvidr TaTvis. am peri od Si bevri afxazi swavlob da da samec ni e ro kva- lifikacias imaRlebda TbilisSi. samwuxarod, XX s. 70-ni wlebis meo re naxev ri dan es naka di sagr Z nob lad Semcir da da afxazi axal gazr de bi ganaTlebis misaRebad midi od nen ruseT Si. ilia vekuas miaC n da, rom saqar T ve los momavali warmoudgene- lia ekono mi ku rad Zlie ri, ganvi Ta re bu li regi o ne bis gare Se. ne bismi e ri regi o nis ganvi Ta re ba ki sabo loo jamSi damo ki de bu lia adgil ze arse bu l kvali fi ci ur kadreb ze. ilia vekua bavS vo bi dan ve iyo ra aRz r di li Zmur qarTul da afxazur kultu ra Ta mdidar tradi ci eb ze, Semd gom Si, Tavis sa mecni e ro, peda go gi u r da sazo ga do eb riv moRva we o ba Si xelm ZR va nelob da xalx Ta Soris WeSma ri ti megob ro bis urye vi princi piT. qarT ve li da afxazi xalxi, erT na i rad Rrmad pativs scemen Tavis Rirse ul Svils, akade mi kos ilia veku as, romel mac saxe li gauT qva msofli o Si pata ra, magram misT vis Zali an sayva rel mSobli ur afxazeTs. afxaze Tis sazo ga do e bam didi pati vi mia go Tavis geni a lur Svils da 1967 wels sazeimod aRniS na ilia veku as dabadebis 60 wlisTa vi. yvelas uxaro da, rom afxaze Tis erT -erT sofel Si daba debul ma kacma miaR wia mecni e re bis umaRles mwverva lebs da mTel msofli o Si gauT q va saxe li misT vis usayvar les kuTxes. Cven, qarT ve leb ma da afxazeb ma, bevri unda viswav loT ilia ve kuas keTil So bi lu ri, didbu ne bo va ni xasi a Ti sa gan, romel mac yve la Tavis arake Til mo sur nes apatia da Seun do, xolo zog SemTx ve vaSi _ daa wi na u ra kide c. es aris saxal xo diplo ma ti is unika lu ri maga li Ti. ilia vekua garda icva la 1977 wlis 2 dekembers. is dakrZalu- lia Tbilis Si, mTawmin dis panTe on Si, Tavisi maswav leb li sa da Ta namo az ris niko musxe liS vi lis gverdiT.
16 Temur CilaCava
ACADEMICIAN ILIA VEKUA
The outstanding mathematician and mechanist Ilia Vekua was born on April 23, 1907 in Abkhazian village Shesheleti (West Georgia). After finishing a secondary school in the West-Georgian town Zugdidi in 1925, he moved to Tbilisi, the capital of Georgia, where he entered the faculty of physics and mathematics of Tbilisi State University. He graduated the university with ho- nors in 1930 and, following the recommendation of Academician Niko Mus- khelishvili, left Tbilisi for Leningrad (now Sankt Petersburg) to continue his education there as a post-graduate student at the USSR Academy of Sciences. His initial research was conducted under the supervision of the well-known mathematician A. N. Krylov. In Leningrad Ilia Vekua published papers on pro- blems of torsion and bending of elastic bars. He also worked on the theory of propagation of electric waves in an infinite layer with parallel plane boundaries and obtained the results whichsubsequently formed the basis of his thesis for the Candidate of Science degree. After finishing the post-graduate course in 1933, Ilia Vekua returned to Tbi- lisi to work at his alma mater. He wholly devoted himself to scientific, educa- tional and organizational activities. Ilia Vekua became an active participant in the famous seminar guided by Niko Muskhelishvili. He delivered lectures on mathematical physics, calculus of variations, differential and integral equations and was one of the founders of the Mathematical Institute of the Georgian Branch of theUSSR Academy of Sciences (now A. Razmadze Mathematical Institute). In 1937 Ilia Vekua defended the degree of candidate on the subject “Propaga- tion of elastic waves in an infinite lager” and in 1939 the degree of doctor on the subject “A complex representation of solutions of elliptic differential equations and its application to boundary value problems”. In 1946 I. Vekua was elected as an academician of the Georgia Academy of sciences and in 28 March 1958 was elected as an academician of the USSR Academy of sciences. In 1948 I. Vekua published the first monograph “New methods of solution of elliptic equations” (Russian) and received Stalin Prize for it in 1950. In 1951, Ilia Vekua moved to Moscow where he was officially invited for permanent residence and work. Together with his outstanding colleagues and friends M. A. Lavrent’ev, I. G. Petrovskii, and S. L. Sobolev, he directed the research seminars at V. A. Steklov Mathematical Institute and M.V. Lomonosov Moscow University. Ilia Vekua was the founding Rector (1959-1964) of Novosibirsk University. When living in Siberia, Ilia Vekua simultaneously combined several duties: he headed the theoretical department at the Hydrodynamics Institute of the Siberian 17 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Branch of the USSR Academy of Sciences, the mathematical physics chair of Novosibirsk University, and supervised the work of several scientific seminars. After the USSR National Committee on Theoretical and Applied Mechanics was formed in 1956, Ilia Vekua became its permanent member. From 1963 he was member of the National Committee of Soviet Mathematicians. In 1959 I. Vekua published the scientific work “Generalized analytic functions” (Russian) and received Lenin Prize for it in 1963. At the end of 1964 Ilia Vekua returned to Tbilisi, where he was elected vice- president of the Georgian Academy of Sciences (1964-1965) and head of the higher mathematics chair at Tbilisi State University (1966-1972). On his initia- tive and under his guidance the department of mechanics was organized (1964) at A. Razmadze Mathematical Institute, and the problem laboratory of applied mathematics was founded (1966) at Tbilisi State University, which shortly was reorganized into the Institute of Applied Mathematics (1968). The latter institute is named after Ilia Vekua as he was its founder and remained its director and scientific leader (1968-1977) till the last days of his life. Throughout 1972-1977, Ilia Vekua was the president of the Georgian Academy of Sciences. In 1982 Ilia Vekua’s research work was published “Some General methods of contacting various versions of the shell theory” (Russian) and he was awarded State Prize in 1984. Ilia Vekua’s research works cover various fields of mathematics and mecha- nics. Many of them are devoted to the theory of partial differential equations in which Ilia Vekua took a great interest. In the analytical theory of linear differential equations of elliptic type with two independent variables, an important part was played by formulas of gene- ral representation of solutions by means of analytic functions of one complex variable. These formulas made it possible to widen considerably the field of application of the methods of the classical theory of analytic functions of a complex variable. Based on these studies, Ilia Vekua developed new methods for solving boundary value problems which enabled him to investigate a vast class of boundary value problems formulated in nonclassical sense. The method he proposed for reducing boundary value problems to singular integral equa- tions is one of the most powerful means for studies in this field. Special mention should be made of a general boundary value problem for elliptic equations, which Ilia Vekua formulated and studied most completely. The well known boundary value problems of Dirichlet, Neumann and Poincaré are particular ca- ses of this problem. Ilia Vekua derived the formulas of integral representation of holomorphic functions, which in the mathematical literature are named after him, and used them as an important tool in investigating the problem. Ilia Vekua is one of the founders of the theory of generalized analytic functions. 18 Temur CilaCava
Ilia Vekua worked out several versions of the mathematical theory of elastic shells. In spite of his grave illness, Ilia Vekua continued to pursue his scientific, teaching and organizational activities till the last days of his life. His last mono- graphs were published posthumously. In September 1976, at Ilia Vekua’s sugges- tion, the IUTAM’s General Assembly decided to organize the 3rd International Symposium on the Theory of Shells in Tbilisi, Georgia. Ilia Vekua was appointed chairman both of the international scientific com- mittee and of the national organizing committee. I. Vekua died on December 2, 1977 and is buried in the Mtatsminda Pantheon of Writers and Public Figures in Tbilisi, near academician N. Muskhelishvili. Preparations for the symposium were underway when the whole scientific world was deeply saddened by theun- timely demise of Ilia Vekua. IUTAM symposia, which held in Tbilisi on August 22-28, 1978, and on April 23-28, 2008 were dedicated to his memory.*
* Based on the article from Georgian Electronic Scientific Journal: Computer Science and Telecommunications 2007|No. 2(13) 19 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Tengiz meunargia
eZRvneba akademikos ilia vekuas 110 wlisTavs
gardacvalebamde ramde ni me dRiT adre, umZi me si avadm yo fo biT Sepyro bil ma baton ma iliam, udide si Zalis x me vis Sede gad SeZlo daem Tav re bi na muSa o ba or monog ra fi a ze: pirve li, `tenzo ruli anali zi sa da kova ri an t Ta Teo ri is safuZ v le bi~ da meo re, `gars Ta Teo ri is sxvadas x va vari an tis agebis zogi er Ti zoga di me Todi~. orive monog ra fia gamos ca gamom cem lo ba Москва, «Наука», Главная Редакция, Физико-Математической Литературы _ pirve li 1978 wels, xolo meo re _ 1982 wels, romel sac mie ni Wa saxel m wi fo pre mia, Semd gom ki ing li sur enaze gamo i ca ucxoeT Si 1985 wels _ Pitman Advanced Publishing Program, Boston-London-Melburne. pirvel monog ra fi a Si gadmo ce mu lia tenzo ru li aRricx vis zogi er Ti gamo ye ne ba geo met ri u li xasi a Tis amoca ne bi saT vis, ase ve, dreka di garse bis zogad Teo ri a Si. wign Si mniSv ne lo va ni adgi li eTmo ba zeda pir Ta Teo ri is sakiTxebs. gars Ta Teo ri is agebi sas saWi ro xdeba garsis formis ganm sazR v re li gark ve ul zeda pir Tan (romel sac, Cveu leb riv garsis Sua zeda pi ri ewode ba) dakav Si re buli koor di nat Ta siste me bis speci a lu ri klasis gamo ye ne ba. amis gamo zeda pir Ta Teo ri as Tan erTad warmo i So ba tenzo ru li anali zis gamo ye ne bis aucileb lo bac. amasTan, geo met ri u li amoca ne bis ganxil vis dros avto ri axerxebs iseTi safuZ v lis Seqm nas, rome lic tenzo ru li anali zis forma lu ri kons t ruq ci e bis konk re tu li da Sina ar sob ri vi gaaz re bis saSu a le bas iZle va. tenzo ru li anali ziT sargeb lo bis aucileb lo ba warmo i So ba yvela iseT SemTx ve va Si, roca rai me fizi ku ri movle nis Sesas wavlad gamo ye ne bu lia koor di nat Ta meTo di, rome lic saSu a le bas iZle va ganxor ci el des mode le bis (geo met ri u li agebu le bis, logi ku ri sqeme bis da sxva) para met ri za cia iseTi koor di nat Ta siste me bis saSu a le biT, romel TaT vi sac SesaZ le be lia ama Tu im maTe ma ti ku ri opera ci is Cata re ba. rac ufro meti sxvadas x va ope raci is ganxor ci e le baa SesaZ le be li mode lis para met reb ze, miT ufro mdida ria da Sina ar sob ri vi Sesa ba mi si maTe ma ti ku ri Teo ri a. Semdeg, avto ri wers: `gansa xil ve li mode lis ganm sazR v rel pa ramet reb ze (koor di na teb ze) ganxor ci e le bu li opera ci e bis Sede gad unda mivi RoT obieq tu ri Sina ar sis dask v ne bi, romle bic axa sia Te ben Sesas wav li movle nis Tvise bebs, gamo ye ne bu li para met ri zaci is xerxi sa gan damo u ki deb lad. 20 Tengiz meunargia
modelis parametrizacia, sazogadod, SeiZleba ganxorciel- des sxvadasxva saSualebiT. Tu, magaliTad, modeli ganisazRvre- ba n sxvadasxva x1 , x 2 ,, x n ricxvTa dasaxelebiT, vawarmoebT ra maTze raime urTierTcalsaxa x i' = ϕ i' (x1 , x 2 ,, x n ) (i'= 1,2,,n) saxis gardaqmnas, miviRebT modelis axal parametrizacias x1' , x 2' ,, x n' ricxvebis saSualebiT, romelic principulad tol- fasia adre ganxilulisa. modelis sxvadasxva SesaZlebel para- metrizaciebTan dakavSirebiT bunebrivad warmoiSveba amocana: rogor gamovavlinoT im daskvnebis obieqturi xasiaTi, romel- nic miiRebian modelis raime kerZo parametrizaciis gamoyenebis safuZvelze. rea lu ri Sina ar sis mqone sabo loo dask v ne bi unda gamo i sa xe bodes koor di nat Ta siste mis arCe vi sa gan inva ri an tu li formiT. aseTi mizne bi saT vis umjo be si a, roca es SesaZ le be li a, sakiTxis gaSu qe ba warmo eb des zoga di, koor di nat Ta siste mis speci a li za cii sa gan damo u ki de be li saxiT, maSin Sede ge bi gamo sa xu li iqne ba iseTi formiT, rome lic gagvi ad vi lebs erTi koor di na te bi dan me ore ze gadas v las, xolo im Tana far do bebs, romel nic gamo sa xa ven obieq tur kanon zo mi e re bebs, cxadi a, koor di nat Ta gardaq m ni sa gan inva ri an tu li saxe eqne baT. `magram es srule biT ar niSnavs imas, rom, _ agr Ze lebs bato ni ilia, _ konk re tu li amoca ne bis amoxs ni sas koor di nat Ta siste mis SerCe vas aravi Ta ri mniSv n lo ba ar aqvs~. xSirad koor di nat Ta sis temis xei ri a ni Ser Ce vis wyalo biT sagr Z nob lad martiv de ba gamoT vle bi, Tana far do be bi Rebu lo ben martiv sa da Tvalsa Ci no struq turas. es ki aadvi lebs Sesas wav li obieq tis saZi e be li Tvise be bis dadge nas. amasTan dakav Si re biT mniSv ne lo va nia krite ri u me bi, romel nic speci a lur koor di nat Ta siste meb Si Sedge ni li ama Tu im gamo sa xu le bis inva ri an tu lo bis gamov li ne bis saSu a le bas mogv cems, rac tenzo ru li anali zis erT -er Ti mTava ri amoca na Ta ga ni a. tenzo ru li anali zi SeiZ le ba aigos metri kis mqone rima nis zoga di mraval sa xe o be bis baza ze. `miu xe da vad amisa, Cven vamjo bi nebT, _ wers bato ni ilia, _ daviwyoT samgan zo mi le bi a ni evk li des sivr cis veqto ru li vele bis sxvadas xva dife ren ci a lu ri Tvise bebis Seswav liT. es saSu a le bas gvaZlevs ganva vi Ta roT tenzo ru li anali zi Tvalsa Ci no geo met ri u li warmod ge ne bis gamo ye ne biT~. ganzo ga do e ba ni ufro zoga di saxis mraval sa xe o ba Ta SemTx ve vi saTvis Zneli gansa xor ci e le be li araa. wign Si gansa kuT re bu li
21 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV yuradRe ba eTmo ba tenzo rul analizs rima nis organ zo mi le bi a ni mraval sa xe o be bi saT vis, faqti u rad, samgan zo mi le bi a ni evk li du ri sivr cis zeda pi re bi saT vis. es gza imiTaa gamar T le bu li, rom ten zoru li anali zis dakav Si re ba umarti ves, magram aratrivi a lur mraval sa xe o bas Tan, rogo ri caa rima nis mraval sa xe o ba, saSu a le bas iZle va gavi az roT zoga di Teo ria geo met ri u lad Tvalsa Ci no war modge ne bis safuZ vel ze. tenzorul analizs mravalricxovani gamoyeneba aqvs geomet riaSi, fizikasa da meqanikaSi. wignSi gadmocemulia zogierTi ga moyeneba zedapirTa TeoriaSi. magaliTad, zedapirze izometriuli koordinatebis ganxilvasTan dakavSirebiT mocemulia beltramis diferencialur gantolebaTa sistemis homeomorfizmebis agebis axali meTodebi. rogorc cnobilia, am problebas kvazikonformul asaxvaTa TeoriaSi centraluri adgili ukavia. sazogadod, izomet riul koordinatebs wignSi SedarebiT didi adgili eTmoba da es ga keTebulia savsebiT Segnebulad. `isini saSualebas gvaZleven far Tod gamoviyenoT kompleqsuri cvladis funqciaTa Teoriis apara ti geometriisa da uwyveti tanis meqanikis amocanebis Sesaswavlad, _ wers batoni ilia. wignSi ganxilulia zedapiris konformulad invariantuli tenzoruli formebi da agebulia kovariantebis Te oria, romelTac didi gamoyeneba aqvT, kerZod garsebis TeoriaSi. meo re wign Si `gars Ta sxvadas x va vari an tis agebis zogi er Ti zoga di meTo di~, avto ri gvTava zobs gars Ta Teo ri is sxvadas x va vari an tis agebis ram de ni me meTods. yove li vari an ti saT vis miRe bulia ori damo u ki de be li cvladis mimarT kerZo warmo e bu li a ni dife ren ci a lu r ganto le ba Ta siste ma da masTan Tavse ba di sasazR vro piro be bi. am ganto le be bis gamoy va ni sas avto ri sargeb lobs samgan zo mi le bi a ni amoca nis organ zo mi le bi an ze dayva nis sxvadas xva xerxiT. aseTi dayva na ara marto mniSv ne lov nad amarti vebs ma Tema ti kur amoca nas, amci rebs ra damo u ki de bel cvladTa ricxvs erTiT, aramed xSirad pasu xobs amoca nis dama xa si a Te bel meqa ni kur da geo met ri ul bune bas. radgan garsis erTi ganzomileba-sisqe-gacilebiT mcirea mis danarCen ganzomilebebTan SedarebiT, amitom xSirad es garemoe ba iZleva saSualebas garsi ganvixiloT rogorc organzomilebiani sxeuli, romelsac miuxedavad amisa, mainc gaaCnia mniSvnelovani wi naaRmdegobis unari, e.i. gare datvirTvis (romlis sidide ar aWar bebs kritikul mniSvnelobas) zemoqmedebis Sedegad deformirebu li garsi ar kargavs mdgradobas da simtkices, da inarCunebs unars, rom Seasrulos Tavisi funqcia, rogorc ama Tu im konstruqciis 22 Tengiz meunargia elementma, magram, samganzomilebiani sxeulebisagan gansxvavebiT, romelTa yvela ganzomileba erTi da igive rigisaa, garsebs gaaC niaT TavianTi gansakuTrebuli Tvisebebi, isini mdgomareoben ima Si, rom sisqis simciris gamo, garsebs deformaciis Zalebis mimarT sxvadasxva mimarTulebiT winaaRmdegobis gawevis sxvadasxva unari gaaCniaT. cxadia, ganivi mimarTulebiT winaaRmdegobis gawevis una ri ufro sustia, vidre gaswvrivi mimarTulebiT. es Tviseba gansa kuTrebuli sicxadiT vlindeba Txeli garsebis SemTxvevaSi. Tu ori erTi da igive sididis ZalTa sistema moqmedebs garsze gaswvrivi da ganivi mimarTulebiT, masTan gaswvrivi mimarTulebiT Zalebi iw veven usasrulod mcire deformacias, maSin ganivi mimarTulebiT am ZalTa moqmedebam SeiZleba gamoiwvios sasruli rigis deforma cia. amitom garsebSi (gansakuTrebiT TxelSi) mRunavi deformaci ebi Cveulebriv Warboben deformaciebs gaswvrivi mimarTulebiT. unda aRiniSnos, rom garsis Runva SeiZleba gamoiwvios ara marto ganivma Zalebma, aramed im Zalebmac, romlebic moqmedeben gaswvri vi mimarTulebiT. Tu am garemoebebs miviRebT mxedvelobaSi, didi sifrTxilea saWiro, rodesac garsebis gamosaTvlelad gamoiyeneba hukis ganzogadoebuli kanoni, _ wers batoni ilia. Cveu leb riv, roca iyene ben hukis kanons, erT g va ro va ni izot ropu li dreka di sxeu li saT vis, uSve ben, rom ori sidi diT toli Zala, romle bic moqme de ben sxvadas x va mimar Tu le biT, iwve ven er Tna ir defor ma ci ebs am mimar Tu le biT, rogorc zemoT iyo naTq vami, garsis SemTx ve va Si es Tvise ba sazo ga dod ar srulde ba. miu xeda vad amisa, arse bobs praqti ka Si gamo ye ne bu li sakma ri sad sqeli firfi te bis erTi klasi, romel Ta mimarT hukis kano nis gamo ye ne bas ar mivya varT garsis daZa bul - de for mi re bu li mdgoma re o bis arse bi Tad gans x va ve bul sura Tam de, rac sinam d vi le Si daim zi re ba. amitom bato ni ilia gani xi lavs garse bis im klass, romel Ta mimarT hukis kano nis gamo ye ne ba SesaZ le be lia da agebs arawi na aR m de gob rivi Teo ri is ramde ni me vari ants aseTi saxis garse bis gasaT v le lad. am sakiTxebs eZRvneba am wignis I da II Tavebi. mesa me TavSi bato ni ilia gani xi lavs stati ku rad gansazR v re bad amoca nebs. aq srule biT ar gamo i ye ne ba sxeu lis Zabvi sa da defor ma ci is velebs Soris kavSi ri. garsis wonas wo ro bis amoca na amoix s ne ba mxolod Zabvis kompo nen teb Si Cawe ri li ganto le ba Ta siste mis saSu a le biT da amde nad, gani sazR v re ba garsis mxolod daZa bu li mdgoma re oba. statikurad gansazRvrebadi amocanebis ganxilvisas aucilebe lia zogierTi daSvebis miReba garsSi Zabvebis ganawilebis Sesaxeb. 23 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV es daSvebani, cxadia, ar SeiZleba iyvnen savsebiT xelovnurni. isini unda gamosaxavdnen garsis gansaxilveli klasis ama Tu im meqanikur Tvisebas, Tundac intuiciur doneze. statikurad gansazRvreba di amocanebis klasikur magaliTs warmoadgens garsebis umomento Teoria. umomento TeoriaSi miRebulia Semdegi daSvebebi: Zabvebi, romlebic moqmedeben kveTis farTobebze, statikurad ekvivalen turia nakrebi Zalebis, xolo maTi momentebi imdenad umniSvneloa, rom SeiZleba maTi ugulebelyofa. es daSve ba bevr SemTx ve va Si rea liz de ba didi sizus tiT, magram is mainc moi cavs garse bis Zalze viwro klass. umomen to daZa bu li mdgoma re o ba xorci el de ba speci a lu ri gare datvir T ve bi sa da kine ma ti ku ri kavSi re bi saT vis. garse bis napi re bi (kide e bi, gverdi Ti zeda pi re bi) ar unda iyv nen SezRudu li yvela iseTi fizi ku ri an kine ma ti ku ri piro be biT, romle bic uzrun vel yo fen samgan zo mile bi a ni amoca ne bis calsa xad amoxs na do bas. maT unda mie ni WoT gark ve u li Tavi suf le ba, raTa gars ma SeZlos Segu e ba im moTxov nile beb Tan, rome lic saWi roa umomen to daZa bu li mdgoma re o bis sare a li za ci od. maga li Tad, amozne qi li garse bi saT vis wonas wo robis umomen to mdgoma re o bis rea li za ci i saT vis aucile be lia da sakma ri si, rom gare datvi rTe bi sa da kine ma ti ku ri kavSi re bis reaq ci is Zale bis muSa o ba gada ad gi le beb ze, romle bic daSve bu lia garsis Sua zeda pi ris usasru lo mcire Runvis dros, udri des nuls. saxel dobr, Tu amozne qi li garsi Cake ti li a, maSin misi Sua zeda pi ri warmo ad gens ovalo ids, rome lic xisti a. maSa sa da me ova loi dis usasru lo mcire Runva Ta klasi, _ wers bato ni ilia, _ amoi wu re ba moZra o be biT, ese igi trivi a lu ri Runve biT, romle bic gamo i sa xe bi an formu liT
U = C × r + C 0 , C C sadac r garsis Sua zedapiris radius-veqtoria, da 0 mudmivi veqtoruli velebia. am SemTxvevaSi umomento daZabuli mdgomare- obis realizaciis pirobebi emTxvevian absoluturad xisti sxeu- lis wonasworobis eqvs pirobas. umetes SemTxvevaSi praqtikaSi gamoyenebuli garsebis gaanga riSebis dros ganivi kveTis farTobebze moqmedi Zabvis momentebis ugulebelyofa ar SeiZleba, _ wers batoni ilia, _ zogjer isini sWarboben kidevac nakreb Zalebs-Zabvebs. Semdeg, batoni ilia umo mento Teoriis meTodebs avrcelebs ufro zogadi sasazRvro pi robebisaTvis. am miznisaTvis drekadi garsebis gasaTvlelad gamo yenebuli aqvs ZabvaTa velis e.w. `normirebul momentTa~ meTodi, romelsac mivyavarT umomento Teoriis gantolebaTa sistemamde 24 Tengiz meunargia da zedapiris usasrulo mcire Runvamde. SevniSnavT, rom amozne qili garsebisaTvis am amocanas mivyavarT koSi-rimanis ganzogade bul gantolebamde da SeiZleba ganzogadebul analizur funqcia Ta Teoriis meTodebis gamoyeneba. meoTxe TavSi gansazRvrulia ara marto Zabvebi, rogorc es keTdeboda mesame TavSi, aramed garsebis deformaciebic. Sedegad miRebulia gantolebaTa sistema da sasazRvro pirobebi, romlebic iZlevian saSualebas ganisazRvros gadaadgilebis veli. SevniSnavT, rom amozneqili garsebis SemTxvevaSi fizikuri sasazRvro amocanis amosaxsnelad da Zabvis tangencialuri velis gansasazRvravad, xo lo Semdeg gadaadgilebis velis sapovnelad gveqneba koSi-rimanis ganzogadebuli gantoleba Sesabamisi sasazRvro pirobebiT. aRv niSnavT, agreTve, rom fizikur da kinematikur amocanebs mivyavarT ganzogadebul analizur funqciaTa Teoriis urTierTSeuRlebul sasazRvro amocanamde, rac mniSvnelovan wilad aadvilebs am amo canebis amonaxsnebis arsebobisa da maTi erTaderTobis sakiTxebs. me-5 TavSi Seswav li lia garsis neit ra lu ri zeda pi ris arse bobis sakiTxi. neit ra lu ri zeda pi ris qveS igulis x me ba zeda pi ri, rome lic garsis defor ma ci is dros ganic dis mxolod usasru los mcire Runvas, kerZod rCeba xisti. pirvel da meore TavebSi SemoTavazebuli meTodebi saSuale- bas iZleva drekadi garsebis wonasworobis amocanebi miyvanil iqnas ori damoukidebeli cvladis elifsur gantolebaTa sistemamde. am gantolebaTa rigi ganisazRvreba amocanis amonaxsnis miaxloebis xa- risxiT x 3 koordinatis mimarT. pirvel TavSi naCvenebia, rom Tu miaxloebebi gamoisaxebian x 3 koordinatis mimarT N xarisxis po- linomis saSualebiT, maSin erT-erTi ganxilul variantSi (§8) Sesa- bamisi elifsuri sistemis rigi udris 6N + 6 . meore variantSi (§7) gamonakliss Seadgenen N = 0,1,2; maSin es sistemebi daiSlebian ufro dabali rigis urTierTdamoukidebel sistemebad. kerZod, N = 0,1- Tvis miiReba garsis umomento mdgomareobis gantolebaTa sistema da agreTve, zedapiris usasrulod mcire Runvis gantolebaTa sis- tema, zogad SemTxvevaSi (N > 2) ki _ 6N + 6 rigis urTierTSebmul Zalze rTuli struqturis gantolebaTa sistema, rac cxadia, arTu- lebs mis praqtikul gamoyenebas, _ aRniSnavs batoni ilia. I da II TavebSi gadmocemulia ramdenime saxeSecvlili meTo- di, sadac batoni ilia specialurad Semoifargleba N = 1 rigis miaxloebis agebiT. es meTodi iZleva saSualebas me-12 rigis gan- tolebaTa sistemis nacvlad aigos me-10 rigis elifsuri siste- ma, romelic Tavsebadia xuT sasazRvro pirobasTan. magaliTad, 25 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV garsis sazRvarze SeiZleba nebismieri xuTi fizikuri sasazRvro pirobis dasaxeleba: normaluri da mxebi Zabvebi, gadamWreli Za- lebi, mRunavi da mgrexavi momentebi. rogorc ukve zemoT iyo aRniSnuli, miRebul gantolebaTa sistemebis maRali rigi, rasakvirvelia, aZnelebs maT praqtikul gamoyenebas, amitom garsebis wonasworobis amocanebis iseTi kla- sis gamoyofas, romelic SesaZlebelia amoixsnas I rigis ganto- lebaTa sistemis an II rigis kerZo warmoebuliani gantolebebis saSualebiT aqvs Zalze didi praqtikuli mniSvneloba. amas garda, im faqts, rom membranuli (umomento) Teoriis gantolebebi mWidrod aris dakavSirebuli zedapiris usasrulo mcire Runvis gantolebebTan, aqvs didi mniSvneloba ganxiluli amocanebis fizikuri da geometriuli bunebis Sesaswavlad. mem- branuli Teoriis gantolebis SedarebiT martivi da xelsayreli saxe gamoyofs mas drekadi garsebis zogadi Teoriis sxva nawile- bisgan, romelTa nebismieri varianti warmoadgens maRali rigis rTuli struqturis mqone gantolebebs. aRsaniSnavia agreTve, is faqti, rom garsebis wonasworobis zogadi Teoriis gantolebebi yovelTvis elifsuria, damoukideblad imisa, Tu ra geometriuli formisaa esa Tu is garsi. rac Seexeba membranuli Teoriis ganto- lebebs, isini mWidrod arian dakavSirebulni garsis geometriul formasTan. es vlindeba imaSi, rom am gantolebaTa tipi ganisazR- vreba Sua zedapiris mTavari (gausis) simrudis niSnis mixedviT. Tu K > 0 (Sesabamisad K < 0 an K = 0 , maSin gveqneba elifsuri (Sesabamisad, hiperboluri an paraboluri) tipis gantolebebi. Semdeg, batoni ilia aRniSnavs, rom `SemTxveva K > 0 xor- cieldeba amozneqili garsebisaTvis da es warmoadgens membranu- li Teoriis gansakuTrebiT mniSvnelovan mxares. am SemTxvevaSi gantolebaTa sistema miiyvaneba koSi-rimanis ganzogadoebul gan- tolebebamde da amozneqili garsebis umomento Teoriis amocane- bis amosaxsnelad gamoiyeneba ganzogadebuli analizur funqciaTa Teoriis aparati.
26 Tengiz meunargia
Tengiz Meunargia
IT IS DEVOTED TO THE 110 ANNIVERSARY OF THE ACADEMICIAN ILIYA VEKUA
Summary
Shortly before death Ilya Vekua has finished work on two monographs: the first “The tensor analysis and bases of the theory of covariants”, the second “About some the general methods of creation of various versions of the theory of shells”. In the first monograph some applications of tensor calculation for pro- blems of geometrical character and also in the general theory of elastic shells are considered. In the second monograph the author offers several methods of crea- tion of various versions of the theory of shells.
27 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
gamoyenebiTi maTematika APPLIED MATHEMATICS
Sandra Pinelas, Ilia Tavkhelidze
SOME REMARKS ABOUT BULK LINKS WHICH APPEAR AFTER CUTTING OF GENERALALIZED MOBIUS-LISTING’S n BODIES GML6
Abstract For more than a hundred years the Möbius sheet and its “mysterious” prop- erty attracts the attention of mathematicians. After a complete cut of this surface, one object appears, but already with a fourfold wrap. The generalization of this phenomenon to figures of a more complex configuration led to an “unexpected” result: after the cut of the generalized Möbius-Listing body, more than two geo- metric shapes may appear. In this paper, we consider all possible cases of a com- plete cut of the generalized Möbius-Listing body with a regular hexagon in the radial section. The authors have since 1999 tried to understand the possibility of applying the methods of exploring (cylindrical shells, (Vekua, 1985) of I. Vekua to the “shells” whose middle surface is the Möbius sheet. However, the impos- sibility of using the standard analysis methods (one-sided surface) on the one hand and the pre-wave original geometric properties (structure of the boundary condition) on the other hand, made the authors to make the main emphasis on the study of the geometric properties of objects of this configuration. Notations In this article we use notations whose are simmilar to the notations in pre- viouse articles (Tavkhelidze, Caratelli Gielis, Ricci, Rogava, Transirico, 2017: 129-158; Tavkhelidze, Ricci, 2017: 158-185): X; Y; Z denote, as usual, the Cartesian coordinates, τ ,ψ ,θ - are space values (local coordinates or parameters in parallelo- gram): * * 1. τ ∈[τ * ,τ ], whereτ * ≤τ usually are non − negative constants; 2. ψ ∈[0,2π ]; 3. θ ∈[0,2πh], where h ∈ R (Real);
Pm ≡ A0 A1 Am−1 - denotes an “Plane figure with m -symmetry”, in particular Pm is a “regular polygon” and m is the number of its angles or vertices. In the general case the edges of “regular polygons” are not always
28 sandra pinelasi, ilia TavxeliZe
straight lines ( Ai Ai+1 may be, for example: edge of epicycloid, or edge of hypo- cycloid, or part of lemniscate of Bernoulli, and so on). Wide class of Pm may be reprezented by Gielis superformula (1) (see e.g. Fig. 1 c, and.i.); 1 − n2 n3 n m ψ m ψ 1 cos 1 sin 2 4 4 p(τ ,ψ ) ≡ + , (1) a b
′ ′ ′ PRPRmm ≡ A0 A1 Am−1 A0 A1 Am−1 denotes an orthogonal prism, whose ′ ′ ′ ends A0 A1 Am−1 and A0 A1 Am=1 are “Plane m-symmetric figures”P m ; ≡ ′ ′ ≡ -PR PR22 A0 A1 A0 A1 is a rectangle, if P2 A0 A1 is a segment of straight line; but also PR2 maybe a cylinder with cross section P2 (ellipse, or lemniscate of Bernoulli and so on); - PR ∞ - is an orthogonal cylinder, whose cross section is a P∞ -circle. The OO' -axis of symmetry (middle line) of the prism PRm is trans- n formed into a “Basic line” of the GTRm body; In the article, just in case, we give a verbal definition of the Generalized Möbius Listing’s body and, without loss of generality, we shall use one of the for me of its analytic representation given in (Tavkhelidze, Ricci, 2006: 191-212; Tavkhelidze, 2009: 177-190; Tavkhelidze, Cassisa, Gielis, Ricci, 2013: 11-38; Tavkhelidze, Caratelli Gielis, Ricci, Rogava, Transirico, 2017: 129-158; Tavkhe- lidze, Ricci, 2017: 158-185). n Definition 1.(Generalized Möbius Listing’s body) - shortly GMLm - is obtained by identifying the opposite ends of the prism PRm in such a way that: A) For any integer n ∈ Z and i = 11, ,...,m,m each vertex Ai coincides with A′ ≡ A′ , and each edge A A + coincides with the edge i+n modm (i+n) i i 1 A′ A′ ≡ A′ A′ i+n i+n+1 modm (i+n) modm (i+n+1) correspondingly; B) The integer n ∈ Z denotes the number of rotations of the end of the prism with respect to the axis OO' before the identification. Ifn > 0, the rotations are counter-clockwise, and if n < 0 then rotations are clockwise. Some particular n examples of GMLm and its graphical realizations can be found in (Tavkhelidze, Ricci, 2006: 191-212; Tavkhelidze., Cassisa, Gielis Ricci: 2013: 11-38; Tavkhe- lidze, Caratelli, Gielis, Ricci, Rogava, Transirico, 2017: 129-158; Tavkhelidze, Ricci, 2017: 158-185). 29 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
nθ τ θ θ + θ 1 + τ ψ ψ + θ θ X ( , ) = R( ) r( )1 cos r2 ( , )cos( g( )) cos( ) m1 nθ τ θ θ + θ 1 + τ ψ ψ + θ θ Y ( , ) = R( ) r1( )cos r2 ( , )cos( g( )) sin( ) m1 (2) nθ τ θ θ 1 + τ ψ ψ + θ Z( , ) = r1( )sin r2 ( , )sin( g( )), m1
According to the above notation in (Tavkhelidze, Caratelli, Gielis, Ricci, Rogava, Transirico, 2017: 129: 158): Function R(θ ) _ defines the “shape of plane basic line”of the initil vir- tual surface and in this article we believe that R(θ ) ≡ R ≡ const. > 0 (this means that basic line is circle, i.e. initial surfase is a classical torus. )
Function r1(θ ) _ defines the “shape of the radial cross section of the pipe that wraps the initial virtual surface” ;
Function r2 (τ ,ψ ) _ defines the “shape of the radial cross section” of the body; Function g(θ ) _ defines the “rule of twisting around basic surface” (or rotation at the end of the prism Pm along the middle line OO′ ), and it may be an arbitrary sufficiently smooth function
g(θ ) :[0,2hπ ] → [0,2hπ ] (3)
But in this article we believe that rule of twisting around the basic line is regular and this means that in formula (3) nθ g(θ ) ≡ , 6 were n, according to the Definition1, denotes the number of rotations of the end of the prism with respect to the axis OO′ before the identification, and nu- mer 6 is a number of simmetry of the initial prisme; µ The number in (5) defines the“Characteristic of twisting” n /m , when m ∈ N and n ∈ Z µ ≡ 1 1 1 1 (4) n1 when m1 = ∞ and n1 ∈ Z (or n1 ∈ R (Real))
n In this article we believe that the basic lines of these GML6{µ} bodies, are always “torus lines” with characteristic µ ≡ n1 , but before cutting basic line m GMLn {0}≡ GMLn 1 of 6 6 always is a circle! 30 sandra pinelasi, ilia TavxeliZe
According to these restrictions the analytic representations (2) of the corre- GMLn {µ} sponding 6 bodies or surfaces have following form
n θ nθ τ θ + 1 + τ ψ ψ + θ X ( , ) = R r1 cos p( , )cos cos( ) m1 6 n θ nθ (5) τ θ + 1 + τ ψ ψ + θ Y ( , ) = R r1 cos p( , )cos sin( ) m1 6 n θ nθ τ θ 1 + τ ψ ψ + Z( , ) = r1 sin p( , )sin , m1 6
More precise information about the analytic representation of these bodies can be found in (Tavkhelidze, Ricci, 2006: 191-212; Tavkhelidze, Cassisa, Gielis, Ricci, 2013: 11-38) and (Tavkhelidze, Caratelli Gielis, Ricci, Rogava, Transirico, 2017: 129-158).
n Part II. Generalized Möbius-Listing’s Bodies GML6 and the corre- sponding sets of bulky knots and bulky links Based on analytical representation (5), and on the definition of operation of cutting defined earlier by the author, some basic questions to be answered appear, for example: n 1. How many objects appear after cutting of the GMLm surfaces or bodies? 2. What type of the GML? surfaces or bodies appear after cutting (first time this ? question for Möbius stripe was formulated by Sosinski see e.g. (Sossinsky, 2002)? 3. What is a link-structure of the surfaces or bodies, which appear after cutting? 4. What are shapes of radial cross sections of the bodies those appear after n cutting of GMLm surfaces or bodies? 5. How many different combinations of shapes of the bodies appear after cutting for specific number m? n 6. What are differential geometric characteristics of GMLm surfaces or bodies?
At this stage, we unfortunately do not have answers to all these questions raised in the case of arbitrary values of m, however, some particular cases discussed in the previous file papers (see e.g. (Tavkhelidze, 2011: 177-190; Tavkhelidze, Ricci, 2017: 158-185) by the author and his colleagues. A tabulation of knots and links of small complexity (thread structure with- out interiorgeometry) classifications is well known (see e.g. (Doll, Hoste, 1981: 747-761; Kupenberg, 1994: 41-50) or (Weisstein, 2003). In this part of article, we use the analytic representation (5) for study bulky knots and links which ap- n pear after acutting process of the Generalized Möbius - Listing’s bodies GML6 31 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV along “parallel” lines of their “Ribs”. In previous articles (Tavkhelidze, 2011: n 177-190) a set of Generalized Möbius Listing’s surfaces- shortly GMLm which n are a particular cases of the GTRm bodies (surfaces), have been defined and- n was considered cases, when the GMLm surface (with radial cross section regular simple star) was affected by a “k-times cutting” along its basic line. Also, based on the previous results, see e.g. (Tavkhelidze, Cassisa, Gielis, Ricci, 2013: 11- n 138;), and (Tavkhelidze, Ricci, 2017: 58-185) we studied the cases when GML2 GMLn n GMLn 3 GML4 and 5 are bodies, whose radial cross section is givenby a plane 2,3,4 or 5-symmetric convex figure with correspondingly 2,3,4 or 5 verti- ces. Now, based on the importance of the practical applications for each specific n concret meaning of the number of simmetry, we consider the case when GML6 is a body, whose radial cross section is given by regularhexagon. n Definition 2. Basic line of the GML6 body is a continuous closed, in the general case, the spatial, line on which transforms the axis of symmetry OO′ of the prism, after identifying the ends of the prism; This line is represented by (5) when the arguments τ = 0 and ψ = 0 . n Definition3. Rib of the GML6 is a continuous closed line, in which are situated only the vertices of the radial cross sections (plane figures) of this body. GMLn Definition 4. Side of the 6 - is a continuous closed surface, in which are situated only the sides of the radial cross section (plane figures) of this body.
Remark 1. It is clear, that this analytic representation (5) when r1 = const. = 0 and p(τ,ψ) ≡ 0 describe a “torus lines” lying on the surface of a torus and:
n1 a. if ν ≡ ∈ Z (integer`56=), then this line make n1coils after one circum- m1 ventaround torus;
n1 b. if ν ≡ ∈ Q (rational number), then this line make n1 coils after m1 m1 circumvent aroundtorus; n c. if ν ≡ 1 ∈ R \ Q (irrational number), then this line make infinite coils m1 after infinite circumvent around torus without self-intersections ; • each meaning of parameter define corresponding element of fundamental group of torus (Weisstein , 2003); GMLn d. each rib of the m bodies is a torus line with characteristic rational n ∈ Q . m 32 sandra pinelasi, ilia TavxeliZe
n Definition 5.We call Slit-surface or s-surface of the GMLm body a surface
k n GML such that: 2 m 1. Its basic line is strictly contained into the n body and it is “parallel” GMLm to thebasic line and ribs of this body;
2. Its radial cross section is a straight line; n 3. The line of intersection of the k with the n body, which GML2 GMLm m n is situatedon the side of this body, is “parallel” to the rib line of the GMLm body; This restriction defines the number of rotation k (of surface) which strictly depends to the number of rotation n - of the body;
Definition 6. For s-surfaces, without loss of generality, we will use the fol- lowing notations:
n k n 1. S1, j -surface of the GML body is a slit-surface GML such that the 6 2 6 ends of the straight line (radial cross section) are situated on the sides with the numbers 1 (or A0A1) and j (or Aj−1Aj ) where j = 2,3,4;correspondingly of the plane figures (6 symmetric polygon, hexagon) of the radial cross section of the n GML6 body; n 2. SB-surface of the GMLn body is such S slit-surface GMLk , 6 1;4 2 6 whose radial cross section (straight line) contains the center of symmetry and
n does not containvertices of the radial cross section of the GML6 body ; n 3. VS -surface of the GMLn body is a slit-surface GMLk , whose ra- 0, j 6 2 6 dial cross section (straight line) is situated on the edges with the numbers j (where
n j = 2, 3) and contains vertex number 0 of the radial cross section of the GML6 body ;
n k n 4. V0,2 -surface of the GML body is a slit-surface GML , whose ra- 6 2 6 dial cross sections (straight line) contain correspondingly vertexes numbers 0 and
2 of the radial cross section of hexagon.
33 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
n 5. VB -surface of the GMLn body is a slit-surface GMLk , whose ra- 0,3 6 2 6 dial cross sections (straight line) contain correspondingly vertexes numbers 0 and
3 and center of simmetry of the radial cross section of hexagon. Remark 2. According to the regularity of hexagon it is clear that previous designations are sufficient and do not limit the generality; In the future we will have to consider several cases separately and therefore it is necessary to introduce the following notation:
1. A ≡ |A0A1| - full length of the side of the regular polygon (radial cross sec-
n tion of GML6 body);
b1 ≡ C1 A 2 2 2 2. j j 1 and bj ≡ C j A1 b2≡ |C 2 A1|, where j=2,3 or 4 and points
1 2 1 2 C j ∈ A0 A1 and C j ∈ Aj−1Aj are correspondingly ends of straight line C jC j (line n is a radial cross section of the corresponding slit-surface GMLk ; 2 6 n Definition 7. A domain, part of the GML6{µ} body (having similar struc- k ture to the GML? {?}body, usually radial cross section is not symmetric figures), whose two opposite parallels to the side-surfaces (see Def. 2) are slit-surfaces, is called a “Slit zone” or shortly an “s-zone”. • “Thickness” of the slit-zone is the distance between two opposite parallel slit-surfaces (distance between two opposite parallel straight line in the radial cross sec- tion of the slit-zone); • If the thickness of the slit-zone is zero, then it coincides with a slit-surface. Without loss of generality, in this article we assume that the “-thickness of the slit-zone is very small with respect to the size of the body.
n Definition 8. The “process of cutting” or shortly the “cutting” of a GML6 body is always realized along some s-surface and produces the vanishing (i.e. elimination) of the corresponding s-zone (which possibly reduces to a slit-sur- face). n S1, j • If a GML6 body is cut along an S1, j -surface ( → ), where j = 2,3, or
4then the corresponding vanishing zone is called an S1, j -slit , and such cutting process is called an S1, j -zone-slit; n SBSB • If a GML6 body is cut along its SB-surface ( → ), then the correspond- ingvanishing zone is called a SB-slit, and such cutting process is called an SB
-zone-slit(this is a one of the S1,4-surface ); 34 sandra pinelasi, ilia TavxeliZe
VS n SB 0, j • If GML6 body is cut along its VS 0, j -surface ( → ), where j = 2,3, then
the corresponding vanishing zone is called a VS 0, j -slit, and such cutting process
is called an VS 0, j -zone-slit; n V0,2 • If GML6 body is cut along its V0,2 -surface ( →V0,2), then the cor- responding vanishing zone is called a V0,2 -slit, and such cutting process is called
an V0,2 -zone-slit; VB n SB 0,3 • If a GML6 body is cut along its VB0,3 -surface ( → ), then thecorre-
sponding vanishing zone is called a VB0,3 -slit, and such cutting process is called
an VB0,3 -zone-slit;
Remark 3.a. For the completeness review of all cases of S1, j -zone-slit when j = 2,3 or 4 sometime should be considered separatelysome different variants: 1 2 1 2 1 2 I. bj + bj < A ; II. bj + bj = A ; III. bj + bj > A ; 1 2 b. IV. We consider separately the case when the line C3C3 contains a center of symmetry of hexagon and correspondingly we have a SB -zone-slit. Using the technique described in (Tavkhelidze, 2011: 177-190; Tavkhelidze, Cassisa, Gielis, Ricci, 2013: 11-38) or in (Tavkhelidze I., Ricci, 2017: 158-185) we obtain the following theorems: Theorem 1.If the number of twisting is n = 6ω , where ω ∈ Z (ω is a number of full rotations of radial cross section of a body around of basic line) and n the GML6 body is cut along some of its slit-surfaces, then an object “bulk link- 2 2” {(2ω) 1} (according to the classic tabulation of the links of small complexity Doll, Hoste, 1991: 747-761; Kupenberg , 1994: 41-50; Weisstein , 2003) ) of the two bulk link-1 appears; But both components of this bulk link-2have 7 different geometric structure, more precisely:
n A. - after an S1, j -zone-slit for each j = 2,3 or 4 of the GML6 body, appears
2 ( j+1)ω (9− j )ω an object bulk link-2 {(2ω) 1}of the GML( j+1) {ω}and GML(9− j ) {0}(see def. 6) bodies,whose radial cross section are correspondingly (j + 1) and (9− j) angular
planefigures , i.e. for each naturalω = 0; 1; 2; …;
ω ) ω j ) j − 9 − ( 9 ( ω ) 6ω 1 ) ω+ 1 j + ( j ( S1, j 2 2 2 j , j 1 , S 1 S ( j+ω 16 ω )ω6 (9− j )ω } } ν { ν { ) j ) j − 9 − ( 9 ( GML GML and and GML} } µ µ { { ) 61 ) + 1 j + ( j ( →GML GML linkthe the −of2of{( } } 1 ) 21 ) ωω ω 2 )12 }{( {(2 of 2 − − thelink link GML→ → ( j +16 )6 {µ}GML GML and GML(9− j ) {ν} (6)
When j=2 or 3 then always µ = ω and ν = 0 in formula (6); When j=4 there are two fundamentally different subcases, that are as- sociated with finding a center of symmetry figures after the cut; more precisely - If center of symmetry of the radial cross section (initial hexagon) after cutting remains in: 35 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
• a. one of the fife-angular part of domain, thenthis figurehas a charasteristic 0 and other equal to ω , i.e. in formula (6) _ µ = 0 and ν = ω or µ = ω and ν = 0 ; • b. the cutting line (SB-slit), then in formula (6) - both element have char- acteristic µ= ν =ω . n B. - after an VS 0, j -zone-slit for each j = 2; 3;of the GML6 body, appears
2 ( j+1)ω (8− j )ω an object bulk link-2 {(2ω) 1} of the GML( j+1) {ω}and GML(8− j ) {0} bodies, whose radial cross section are correspondingly (j + 1) and (8− j) angular plane figures , i.e. for each natural ω = 0; 1; 2; …and j = 2,3;
ω ) j ω ) j − 9 − ( 9 ( 6ω6ω6ω6VS ωω ) 0VS1 ω ,) + jVS1 j 0+ ( , j j0VS ( , j 0, j 2 22 2 2 2 j , (1 j j, S +1 (S 1j)(+ωj1+()ω 1j6 )+ω 6 1)ω (8−(8j()−8ω−j()8ωj−)ωj )ω } } ν { ν { ) j ) j − 9 − ( 9 ( GML GML GMLGMLGMLand GML6and 6} 6} µ { 6µ { ) 1 ) + 1 j →+ ( j ( →link→link→GML linkGML −link−2{(−the 2the −{(22{( ofω22of} {( 2ω)1 } 1ω) 1 2})) 1)ω of }12 ω })of 2 1{(of the}2 {( ofthe2 − the− theGMLlink GMLlink GML→ GML→ ( j +( 1j)(+ j1+ {()1ωj6 )+{6 1}ω{)ω}{ω}andGML GML }andandandGMLGMLGMLGML(8−(8j()−8−j{()8j0−){}j0{)(7)0}{}0}
n C. - after an V0,2 -zone-slit of the GML6 body, appears an object bulk link-2 2 3ω 5ω {(2ω) 1} of the GML3 {ω}and GML5 {0} bodies, whose radial cross section are correspondingly 3and 4angular plane figures , i.e. for each natural ω = 0; 1; 2; …;
ω ) ω j ) j − 9 − ( 9 ( 6ω ) ω 1 ) + 1 j + ( j ( V0,2 2 2 2 j , j 1 , S 1 S 3ω 6 ω 6 5ω } } ν { ν { ) j ) j − 9 − ( 9 ( GML GML and and GML} } µ { µ 6{ ) 1 ) + 1 j + ( j ( →GML GML linkthe the −of2of{( } } 1 ) 1 2) ωω ω 2 )2 1{(}{(2 of 2 − − thelink link → GML→ 3 6 [6 ω] GML GML and GML5 [0] (8)
n D. after an VB0,3 -zone-slit of the GML6 body, appears an object bulk link- 2 4ω 2 {(2ω) 1} of the two identic GML4 {ω} bodies, whose radial cross section are 4angular plane figures , i.e. for each natural ω = 0; 1; 2; …;
ω ) ω j ) j − 9 − ( 9 ( 6ω ω) ω 1 ) + 1 j + ( j ( V0,3 2 2 2 j , j 1 , S 1 S ω 6 ω 6 4ω (9) } } ν { ν { ) j ) j − 9 − ( 9 ( GML GML and and GML} } µ µ { 6{ ) 1 ) + 1 j + ( j ( →GML GML linkthe the −of2of{( } } 1 ) 1 2) ωω ω 2 )2 1{(}{(2 of2 − − thelink link → the→ GML6 6 4GML GML {ω}
S1,2 S1,3 S1,4
VS 0,2 VS 0,3 V0,2 VB 0,3
Tab.1 36 sandra pinelasi, ilia TavxeliZe
Sketch of the proof. We draw a straight lines connecting the center of sym- metry with the corresponding vertices, so we obtain a star like hexagram, and n this case of GML6 ,generalized Möbius-Listing’s surfaces, has been studied in (see. f.e. (Tavkhelidze, 2011: 177-190 or Tavkhelidze, Ricci, 2017: 158-185). Slit surface forbulky link is converted in a corresponding slit-line, but in this situation we know all possiblevariants that appear after cutting. But after we return to the considering case and we count separately how many rotation make some vertices of new bodies that appear after cutting! All possible cases and corresponding shapes of the radial cross sections after the cutting process are given in the table 1.
Theorem 2. If n ≡ 6ω +q is a number of twisting, where ω is an arbitrary n integer number and q= 1 or 5, and the GML6 body is cut along some of its slit- surfaces, then 12 different cases from a geometric forms of the radial cross sec- tions appear and each thiscase generates four possible twist of the GML bodies which appear after cutting. Moorprecisely following results hold: Case A. Taking into account remark 3 we have three different subcases:
1 2 • Case A.I if b2 + b2 < A(see remark 3.I), after an S1,2-zone-slit of
n 2(6ω +q) the GML6 body appears an object bulk link-2, of GML12 {0} and GML3(6(ω +1)+(q−1)) ω + q bodies. The first one has the same structure {(0) } as 3 { 6 } 1 a initial body before cutting. Alsotheir radial cross sections are twelwe and three
angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ωω+ +ω +ω +SωS+ S S S ( (ω +ω( +(ω)( +ω)ω++) )) ( ω( + ω( +(+ω( +ωω+)+++)++)))qqqqq GMLGMLGMLGML6 6GMLq6 q6q61q,21q,→2→1,2link→1,link21,→2link→−link−link22−of of −2−theof 22theof ofof thetheGMLtheGMLGML12GMLGML12 122q 212 12{q02{}q022{}qq0and{}0and}andandGMLGMLGML18GMLGML18 318q 18 31815 q 315q3ω3q15q15+ω15 ω+ωω+ (10)++ 6 6 6 6 6 12 12 12 12 12 3 3 3 33 66666 1 2 • Case A.II if b2 + b2 = A (see remark 3.II), after an S1,2-zone-slit
n (6ω +q) of the GML6 body appears an object bulk link-2, of GML6 {0}and
3(6(ω +1)+(q−1)) q GML ω + bodies. The first one has the same structure {(0) } 3 { 6 } 1 as a initial body before cutting. Alsotheir radial cross sections are six and three
angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) ( ω + + ) q GML6 q 1,2 →link − 2ofof the GML 6 q {0} and GML18 3q 15 ω + (11) 6 6 3 6
1 2 • Case A.III if b2 + b2 > A (see remark 3.III), after an S1,2-zone-slit 37 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
n (6ω +q) of the GML5 body appears an object bulk link-3, of GML6 {0}and
( (ω + )+( − )) 5(6(ω +1)+(q−1)) q GML3 6 1 q 1 ω + q and GML ω + bodies. The first one 3 { 6 } 5 { 6 }
has the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections are six, three and five angular plane figures, i.e. for each natural ω= 0, 1, 2,. . .
ω + S ( ω + ) ( ω + + ) q ( ω + + ) q GML6 q 1,2 →link − 3 ofGML 6 q {0},GML18 3q 15 ω + and GML 30 5q 25 ω + 6 6 3 6 5 6 6ω +q S1,2 (6ω +q) (18 ω +3q+15 ) q (30 ω +5q+25 ) q GML →link − 3 ofGML {0},GML ω + and GML 30 25 ω + (12) 6 6 3 6 5 6 Case B. Taking into account remark 3 we have three different subcases: 1 2 • Case B.I if b3 + b3 < A (see remark 3.I), after an S1,3-zone-slit of the
n (6ω +q) GML6 body appears an object bulk link-3, of GML6 {0} and two bodies
4(6(ω +1)+(q−1)) q GML ω + . The first one has the same structure {(0)1} as a ini- 4 { 6 } tial body before cutting. Alsotheir radial cross sections are five six and four angu- lar plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) ( ω + + ) q GML6 q 1,3 →link − 3 of the GML 6 q {0}, and two GML 24 4q 20 ω + 6 6 4 6 ω + S ( ω + ) (24ω + +20 ) q GML6 q 1,3 →link − 3 of the GML 6 q {0}, and two GML 24 4q 20 ω + (13) 6 6 4 6
1 2 n • Case B.II if b3 + b3 = A (see remark 3.II), after an S13-zone-slit of the GML6 body appears an object bulk link-3, of GML(6ω +q){0}, GML3(6(ω +1)+(q−1)) ω + q 6 3 { 6 } 4(6(ω +1)+(q−1)) q and GML ω + bodies. The first one has the same structure {(0) } 4 { 6 } 1 as a initial body before cutting. Alsotheir radial cross sections are six, three and four angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) (18ω + +15) q ( ω + + ) q GML6 q 1,3 →link − 3 ofGML 6 q {0},GML18 3q 15 ω + and GML 24 4q 20 ω + 6 6 3 6 5 6 ω + S ( ω + ) ( ω + + ) q (24ω + +20 ) q GML6 q 1,3 →link − 3 ofGML 6 q {0},GML18 3q 15 ω + and GML 24 4q 20 ω + (14) 6 6 3 6 5 6 1 + 2 > • Case B.III if b3 b3 A (see remark 3.III), after an S1,3-zone-slit of the n (6ω +q) GML6 body appears an object bulk link-4, of GML6 {0}, two similar bodies
3(6(ω +1)+(q−1)) 6(6(ω +1)+(q−1)) q GML ω + q and GML ω + bodies. The first one 3 { 6 } 6 { 6 } 38 sandra pinelasi, ilia TavxeliZe
has the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections correspondingly are five, two times three and six angular plane figures, i.e. for each natural ω= 0,1,2,. . .
6ω +q S1,3 (6ω +q) GML6 →link − 4 of the GML6 {0},
(18ω + +15) q (36ω + +30 ) q two GML18 3q 15 ω + and GML 36 6q 30 ω + (15) 3 6 6 6
Case C. Taking into account remark 3 we have two different subcases: n • Case C.I after an S1,4 -zone-slit of the GML6 body appears an ob- (6ω +q) GML3(6(ω +1)+(q−1)) ω + 0.2q ject bulk link-4, of GML6 {0}, 3 { 6 }, GML4(6(ω +1)+(q−1)) ω + 0.2q GML5(6(ω +1)+(q−1)) ω + 0.2q 4 { 6 }and 5 { 6 } bodies. The first one has the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections correspondingly are six, three, four and fife angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) (18ω + +15) q GML6 q 1,3 →link − 4 of the GML 6 q {0}, GML18 3q 15 ω + 6 6 3 6 (16) ( ω + + ) q ( ω + +25) q GML2424 4q 20 ω + and GML30 5q 25 ω + 4 6 5 6
n • Case C. II after an SB-zone-slit of the GML6 body (see remark 3 ), appears
( (ω + )+( − )) an object bulk link-1 (bulk-knot), of GML4 6 1 q 1 ω + q body (Möbius 4 { 6 } strip phenomenon). Which radial cross section isfour angular plane figure, i.e. for each natural ω= 0,1,2,. . .
ω + ( ω + + ) q GML6 q SBSB →link −1 of the GML2424 4q 20 ω + (17) 6 4 6
n • Case D. I after an VS0,2-zone-slit of the GML6 body, appears an
(6ω +q) 3(6(ω +1)+(q−1)) q object bulk link-3, of GML6 {0}, GML ω + and 3 { 6 } GML4(6(ω +1)+(q−1)) ω + q bodies. Which radial cross sections are six, three and 4 { 6 } four angular plane figures, i.e. for each natural ω = 0,1,2,. . . 39 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
ω + VSVS ( ω + ) ( ω + + ) q ( ω + + ) q GML6 q 0,2 →link − 3 ofGML 6 q {0},GML18 3q 15 ω + ,GML 24 4q 20 ω + 6 6 3 6 4 6 ω + VS ( ω + ) ( ω + + ) q ( ω + + ) q GML6 q 0,2 →link − 3 ofGML 6 q {0},GML18 3q 15 ω + ,GML2424 4q 20 ω + (18) 6 6 3 6 4 6
n • Case D.II after an VS0,3-zone-slit of the GML6 body, appears an ob- (6ω +q){ } GML3(6(ω +1)+(q−1)) ω + q ject bulk link-4, of GML6 0 , two bodies 3 { 6 } and ( (ω + )+( − )) GML5 6 1 q 1 ω + q bodies. Which radial cross sections are six, fife ant 5 { 6 } two times three angular plane figures, i.e. for each natural ω = 0,1,2,. . .
6ω +q VS 0,3 (6ω +q) GML6 →link − 4 of the GML6 {0}, (19) q q (18 ω +3q+15 ) ω + (30ω +5q+25 ) ω + two GML3 and GML5 6 6
n • Case E. after an V0,2-zone-slitof the GML6 body, appears an object bulk
(6ω +q) link-3, of GML {0}and two GML3(6(ω +1)+(q−1)) ω + q bodies. Which radial 6 3 { 6 } cross sections are correspondingly six and three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + V ( ω + ) ( ω + + ) q GML6 q 0,2 →link − 3 of the GML 6 q {0}and two GML18 3q 15 ω + 6 6 3 6 ω + V ( ω + ) (18ω + +15) q GML6 q 0,2 →link − 3 of the GML 6 q {0}and two GML18 3q 15 ω + (20) 6 6 3 6
n • Case F. after an VB0,3-zone-slit of the GML6 body, appears an object bulk link-1 (or bulk knot), of GML3(6(ω +1)+(q−1)) ω + q bodies (Möbius strip phe- 3 { 6 } nomenon). Which radial cross section is are three angular plane figure, i.e. for each natural ω= 0,1,2,. . .
ω + VBVB (18ω + +15) q GML6 q 0,3 →link −1 of the GML18 3q 15 ω + (21) 6 3 6 Sketch of the proof. proof absolutely similar to previous theorem and its n based on the corresponding results for the surfaces GML6 (see. f.e. (Tavkhe- lidze, Ricci, 2006: 191-122 or Tavkhelidze, Ricci, 2017: 158-185). All possible cases and corresponding shapes of the radial cross sections after the cutting pro- cess are given in the table 2. 40 sandra pinelasi, ilia TavxeliZe
1 2 1 2 S 1 2 S1,2 - b + b < A S - + = 1,2 - b2 + b2 > A S 2 2 1,2 b2 b2 A 1,4
1 2 1 2 S 1 2 S - b + b < A S - + = 1,3 - b2 + b2 > A SB 1,3 3 3 1,3 b2 b2 A
VS0,2 VS0,3 V0,2 VB0,3
Tab. 2
Theorem 3. If n ≡ 6ω +2q is a number of twisting, where ω is an arbitrary n integer number and q= 1 or2, and the GML6 body is cut along some of its slit- surfaces, then 10 different cases from a geometric forms of the radial cross sec- tions appear and each thiscase generates four possible twist of the GML bodies which appear after cutting. Moorprecisely following results hold: n • Case A. after an S1,2-zone-slit of the GML6 body appears an object bulk
( ω + ) link-2, of GML3 3 q {0}and GML3(3(ω +1)+(q−1)) ω + q bodies. The first one 9 3 { 3 }
has the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections are nine and three angular plane figures, i.e. for each natural ω = 0, 1, 2,. . .
ω + S ( ω + ) ( ω + + ) q GML6 q 1,2 →link − 2 of the GML 9 3q {0} and GML 9 3q 6 ω + 6 9 3 3 ω + S ( ω + ) ( ω + + ) q GML6 q 1,2 →link − 2 of the GML 9 3q {0} and GML 9 3q 6 ω + (22) 6 9 3 3 41 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Case B. Taking into account remark 3 we have three different subcases: 1 2 • Case B.I if b3 + b3 < A (see remark 3.I), after an S1,3-zone-slit of the n 2(3ω +q) GML6 body appears an object bulk link-2, of GML6 {0}and two bodies GML4(3(ω +1)+(q−1)) ω + q . The first one has the same structure {(0) } as a ini- 4 { 3 } 1 tial body before cutting. Alsotheir radial cross sections are six and four angular plane figures, i.e. for each natural ω= 0, 1, 2,. . .
ω + S ( ω + ) ( ω + + ) q GML6 q 1,3 →link − 2 of the GML 6 2q {0}, and GML12 4q 8 ω + 6 6 4 3 ω + S ( ω + ) (12ω + + ) q GML6 q 1,3 →link − 2 of the GML 6 2q {0}, and GML12 4q 8 ω + (23) 6 6 4 3 1 + 2 = • Case B.II if b3 b3 A (see remark 3.II), after an S13-zone-slit n (3ω +q) of the GML6 body appears an object bulk link-2, of GML3 {0}and
4(3(ω +1)+(q−1)) q GML ω + bodies. The first one has the same structure {(0) } 4 { 3 } 1 as a initial body before cutting. Alsotheir radial cross sections are six and three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) ( ω + + ) q GML6 q 1,3 →link − 2 of the GML 3 q {0} and GML12 4q 8 ω + 6 3 4 3 ω + S ( ω + ) (12ω + + ) q GML6 q 1,3 →link − 2 of the GML 3 q {0} and GML12 4q 8 ω + (24) 6 3 4 3 1 + 2 > • Case B.III if b3 b3 A (see remark 3.III), after an S1,3-zone- n (3ω +q) slit of the GML6 body appears an object bulk link-3, of GML3 {0},
3(3(ω +1)+(q−1)) 6(3(ω +1)+(q−1)) q GML ω + q and GML ω + bodies. The first one 3 { 3 } 6 { 3 }
has the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections correspondingly are five, two times three and six angular plane figures, i.e. for each natural ω= 0,1,2,. . .
6ω +q S1,3 (3ω +q) GML6 →link − 3 of the GML3 {0}, (25) ( ω + + ) q ( ω + + ) q GML 9 3q 6 ω + and GML18 6q 12 ω + 3 3 6 3 Case C. Taking into account remark 3 we have two different subcases: n • Case C.I after an S1,4 -zone-slit of the GML6 body appears an ob-
( ω + ) ject bulk link-3, of GML 3 q {0}, GML3(3(ω +1)+(q−1)) ω + q and 3 3 { 3 } GML5(3(ω +1)+(q−1)) ω + q bodies. The first one has the same structure {(0) } as 5 { 3 } 1
42 sandra pinelasi, ilia TavxeliZe
a initial body before cutting. Alsotheir radial cross sections correspondingly are six, three, four and five angular plane figures, i.e. for each natural ω= 0,1,2,. . .
6ω +q S1,4 (3ω +q) GML6 →link − 3 of the GML3 {0}, (26) ( ω + + ) q (15ω + +10) q GML 9 3q 6 ω + and GML15 6q 10 ω + 3 3 6 3 n • Case C. II after an SB-zone-slit of the GML6 body (see remark 3), appears
( (ω + )+( − )) an object bulk link-2, of two GML4 3 1 q 1 ω + q bodies. Which radial 4 { 3 } cross section arefour angular plane figures, i.e. for each natural ω = 0,1,2,. . .
ω + ( ω + + ) q GML6 q SBSB →link − 2 of the two GML12 4q 8 ω + (27) 6 4 3 n • Case D. I after an VS0,2-zone-slit of the GML6 body, appears an object bulk
2(3ω +q) 3(3(ω +1)+(q−1)) q link-2, of GML {0} and GML ω + bodies. Which radial 6 3 { 3 } cross sections are six and three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + VSVS ( ω + ) ( ω + + ) q GML6 q 0,2 →link − 2 ofof the GML 6 2q {0} and GML 9 3q 6 ω + 6 6 3 6 ω + VS ( ω + ) ( ω + + ) q GML6 q 0,2 →link − 2 of the GML 6 2q {0} and GML 9 3q 6 ω + (28) 6 6 3 6 n • Case D.II after an VS0,3-zone-slit of the GML6 body, appears an ob- ( ω + ) ject bulk link-4, of GML 3 q {0}, two bodies GML3(3(ω +1)+(q−1)) ω + q and 3 3 { 3 } ( (ω + )+( − )) GML5 3 1 q 1 ω + q bodies. Which radial cross sections are six, fife ant 5 { 3 } two times three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
6ω +q VSVS 0,3 (3ω +q) GML6 →link − 3 of of the GML3 {0}, (29) q q (9ω +3q+6) ω + (15ω +5q+10 ) ω + GML3 and GML5 3 3 n • Case E. after an V0,2-zone-slit of the GML6 body, appears an object bulk
(3ω +q) 3(3(ω +1)+(q−1)) q link-2, of { } and GML ω + bodies. Which radial GML3 0 3 { 3 } cross sections are correspondingly three angular plane figures, i.e. for each natu- ral ω= 0,1,2,. . .
ω + V ( ω + ) ( ω + + ) q GML6 q 0,2 →link − 2 of the GML 3 q {0}and GML 9 3q 6 ω + (30) 6 3 3 3 43 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
n • Case F. after an VB0,3-zone-slit of the GML6 body, appears an object bulk link-2 of GML3(3(ω +1)+(q−1)) ω + q bodies. Which radial cross section is are 3 { 3 } three angular plane figure, i.e. for each natural ω= 0,1,2,. . .
ω + VSVB ( ω + + ) q GML6 q 0,3 →link − 2 of the GML 9 3q 6 ω + (31) 6 3 3 Sketch of the proof. proof absolutely similar to previous theorem and its n based on the corresponding results for the surfaces GML6 (see. f.e. (Tavkhe- lidze, Ricci, 2006: 191-212 or Tavkhelidze, Ricci, 2017: 158-185). All possible cases and corresponding shapes of the radial cross sections after the cutting pro- cess are given in the table 3.
S - S - S1,2 1,3 S1,3 - 1,3 S1,4 1 + 2 < 1 2 b1 + b2 > A b3 b3 A b2 + b2 = A 2 2
VS0,2 VS0,3 V0,2 VB0,3 SB
Tab. 3 Theorem 4. If n ≡ 6ω + 3 is a number of twisting, where ω is an arbitrary n integer number and the GML6 body is cut along some of its slit-surfaces, then 7different cases from a geometric forms of the radial cross sections appear and each this case generates four possible twist of the GML bodies which appear after cutting. More precisely following results hold: n • Case A. after an S1,2-zone-slit of the GML6 body appears an object bulk
ω + ( (ω + )) link-2, of GML4(2 1){0}and GML3 2 1 ω + 1 bodies. The first one has 8 3 { 2} the same structure {(0)1} as a initial body before cutting and second {(2ω+1)1}. 44 sandra pinelasi, ilia TavxeliZe
Alsotheir radial cross sections are nine and three angular plane figures, i.e. for each natural ω = 0,1,2,. . .
ω + S ( ω + ) ( ω + ) 1 GML6 3 1,2 →link − 2 of the GML 8 4 {0} and GML 6 6 ω + (32) 6 8 3 2 n • Case B. after an S1,3-zone-slit of the GML6 body appears an object bulk ( ω + ) ( (ω + )) link-2, of GML3 2 1 {0}and GML4 2 1 ω + 1 bodies .The first one has the 6 4 { 2}
same structure {(0)1} as a initial body before cutting and second {(2ω+1)1}. Al- sotheir radial cross sections are six and four angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) ( ω + ) 1 GML6 q 1,3 →link − 2 of the GML 6 3 {0}, and GML 8 8 ω + (33) 6 6 4 2 Case C. Taking into account remark 3 we have two different subcases: n • CaseC.Iafter an S1,4 -zone-slit of the GML6 body appears an object bulk
( (ω + )) link-2, of 2(2ω +1){ } and GML5 2 1 ω + 1 bodies. The first one has GML4 0 5 { 2}
the same structure {(0)1} as a initial body before cutting. Alsotheir radial cross sections correspondingly are six, three, four and five angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + S ( ω + ) ( ω + ) 1 GML6 3 1,4 →link − 2 of the GML 4 2 {0} and GML10 10 ω + (34) 6 4 5 2
n • Case C. II after an SB-zone-slit of the GML6 body, appears an object bulk GML5(2(ω +1)) ω + 1 link-1 (or bulk knot) of 5 { 2} body (Möbius strip phenomenon). Which radial cross section isfife angular plane figure, i.e. for each naturalω= 0,1,2,. . .
ω + SB ( ω + ) 1 GML6 q SB →link −1 of the GML10 10 ω + (35) 6 5 2 n • Case D. I after an VS0,2-zone-slit of the GML6 body, appears an object
( ω + ) 3(2(ω +1)) bulk link-2, of GML3 2 1 {0} and GML ω + 1 bodies. Which radial 6 3 { 2} cross sections are six and three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + VSVS ( ω + ) ( ω + ) 1 GML6 q 0,2 →link − 2 ofof the GML 6 3q {0} and GML 6 6 ω + 6 6 3 2 ω + VS ( ω + ) ( ω + ) 1 GML6 q 0,2 →link − 2 of the GML 6 3q {0} and GML 6 6 ω + (36) 6 6 3 2 45 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
n • Case D.II after an VS0,3-zone-slit of the GML6 body, appears an object ( ω + ) 4(2(ω +1)) bulk link-2, of GML2 2 1 {0} and GML ω + 1 bodies, which radial 4 4 { 2} cross sections are four angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + VSVS ( ω + ) ( ω + ) 1 GML6 q 0,2 →link − 2 ofof the GML 4 2 {0} and GML 8 8 ω + (37) 6 4 4 2
n • Case E. after an V0,2-zone-slit of the GML6 body, appears an object bulk
( ω + ) 3(2(ω +1)) link-2, ofGML2 2 1 {0}and GML ω + 1 bodies. Which radial cross sec- 4 3 { 2} tions are correspondingly three angular plane figures, i.e. for each natural ω= 0,1,2,. . .
ω + V ( ω + ) ( ω + ) 1 GML6 3 0,2 →link − 2 of the GML4 4 2 {0}and GML 6 6 ω + (38) 6 3 3 2 n • Case F. after an VB0,3-zone-slit of the GML6 body, appears an object bulk ( (ω + )) link-1 (or bulk knot) of the GML4 2 1 ω + 1 body. Which radial cross sec- 4 { 2} tion is four angular plane figure, i.e. for each natural ω= 0,1,2,. . .
ω + VBVB ( ω + ) 1 GML6 3 0,3 →link −1 of the GML 8 8 ω + (39) 6 4 2 Sketch of the proof. proof absolutely similar to previous theorem and its n based on the corresponding results for the surfaces GML5 (see. f.e. (Tavkhelid- ze, Ricci, 2006: 191-212; Tavkhelidze, 2011: 177-190; Tavkhelidze, Ricci, 2017: 158-185). All possible cases and corresponding shapes of the radial cross sections after the cutting process are given in the table 4. Acknowledgement. The project has been fulfilled by a financial support of Shota Rustaveli National Science Foundation (Grant SRNSF/FR/358/5-109/14).
S1,2 S1,3 S1,4 SB
46 sandra pinelasi, ilia TavxeliZe
VS0,2 VS0,3 V0,2 VB0,3
Tab. 4
References: 1. Doll H. and Hoste J., A Tabulation of Oriented Links, Math. Comput., 57, (1991), 747-761. 2. Gray A., Albena E. and Salamon S., Modern Differential Geometry of Curves and Surfaces with Mathematica, (Third Edition), J. Capman and Hall / CRC. 3. Gielis J., Caratelli D., Fougerolle Y., Ricci P.E., Tavkhelidze I., Gerats T.,Universal Natural Shapes: From Unifying Shape Description to Simple Methodsfor Shape Analysis and Boundary Value Problems journal PlosONE- D-11- 01115R210.1371/journal.pone.0029324. 27, IX, 2012 pp.1-18. 4. Kupenberg G., Quadrisecants of Knots and Links - J. Knot Theory Ramifica- tions, 3, (1994), 41-50. 5. Sossinsky A., Knots Mathematics with a Twist, Harvard University Press, 2002, 1-147. 6. Tavkhelidze I., Ricci P.E., Rendiconti Accademia Nazionale dell Scienze detta dei XL Memorie di Matematica a Applicazioni, 2006, 1240 vol. XXX, fasc.1, 191-212; 7. Tavkhelidze I., About Connection of the Generalized Möbius-Listing’s sur- faces with Sets of Ribbon Knots and Links, Ukrainskiy matematichesky congress -2009, Sektsiya 2. Tonologiya i Geometriya, Zbirnik prats, In-my matematiki NAN Ukraini, 2011, pp. 177-190; 8. Tavkhelidze I., Cassisa C., Gielis J. and Ricci P.E., About “Bulky” Links, n Generated by Generalized Mëbius-Listing’s bodies GML3 , Rendiconti Lin- cei Mat. Appl. 24 (2013), pp. 11-38; 9. Tavkhelidze I., Ricci P.E. Some Properties of “Bulky” Links, Generated by Generalised Möbius-Listing’s Bodies _ Modeling in Mathematics- Chapter 11- Atlantis Transactions in Geometry 2, DOI 10.2991/978-94-6239-261- 8_11 _ Springer (2017), pp.158-185. 10. Tavkhelidze I., Caratelli D., Gielis J., Ricci P.E., Rogava M. and M. Transirico. On a Geometric Model of Bodies with “Complex” Configuration and Some 47 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Movements _ Modeling in Mathematics - Chapter 10 - Atlantis Transactions in Geometry 2, DOI 10.2991/978-94-6239-261-8_10_ Springer (2017), pp.129-158. 11. Vekua I. Shell theory: general methods of construction. Pitman Advanced Publishing Program, Boston-London-Melbourne, 1985, 287 p. 12. Weisstein E.W., The CRC concise Encyclopedia of Mathematics, (Second edition), Chapman & Hall/CRC, Boca Raton, FL, (2003). sandra pinelasi, ilia TavxeliZe
n SeniSvnebi GML6 _ ganzogadebuli mebius-listingis gaWris Sedegad warmoqmnili moculobiTi xlarTebis Sesaxeb
reziume
bunebaSi arsebuli formebi Zalze STambeWdavia rogorc sila maziT, agreTve mravalferovnebiT. dRemde daudgenelia es forme bi gansazRvaven maTTan dakavSirebul movlenebs Tu piriqiT, isini raRac movlenis `bunebriv~ Sedegs warmoadgenen. erTi `moulodne li~ fenomenis arsi SemdegSi mdgomareobs: Cveulebriv SemTxvevaSi sxeuli erTi sruli gaWris Sedegad or nawilad iSleba da am mxriv cnobili gamonaklisia mebiusis lenti, romelic amgvari gaWris Se degad isev erT (magram sxvanairad daxveul) obieqtad rCeba. winam de ba re naSrom Si ganxi lu lia ganzo ga de bu li mebi us-lis tingis sxeu le bi, da avto re bis (i. Tavxe li Zi sa da s. pine la sis) mier napov ni anali zu ri warmod ge nis saSu a le biT naCve ne bi a, rom maTi erTi sruli gaWris Sede gad warmo iq m ne ba rogorc erTi ge omet ri u li obieq ti (anu e. w. mebi u sis feno me ni Zala Sia rea lu ri sxeu le bi saT vi sac), agreT ve, zogi erT SemTx ve va Si orze meti geo metri u li obieq tic. konkretulad, rodesac sxeulis radialuri kveTi wesieri n eqvskuTxedia, anu GML6 (ganzogadebuli mebius-listingis) sxeu- lisaTvis, nebis mi e ri n ricxvi saT vis Wris zeda pi ris adgil m de ba reo bi dan damo ki de bu le bis gaTva lis wi ne biT daTv li lia warmoq mni li xlarTis kompo nen te bis rao de no ba da dadge ni lia gaWris Sede gad warmoq m nil kompo nen tebs Soris gans x va ve ba rogorc maT radi a lur kveTebs Soris, agreT ve, maT saba zi so wireb sa da Cax larT vis maxa si a Teb lebs Soris. 48 Tinatin Davitashvili, Hamlet Meladze, Iulia Meladze
NONLOCAL CONTACT PROBLEM FOR NONHOMOGENEOUS SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
Abstract In the present work, the non-local contact problem for nonhomogeneous second order ordinary differential equations with constant coefficients is considered. The analytical solution of the stated problem is built. The iteration process is constructed, which allows one to reduce the solution of considered non-local problem to the solution of a sequence of first boundary value problems for the second order ordinary differential equation. 1. Nonlocal problems represent very interesting and important generalization of classical problems for differential equations (see, for example, (Bitsadze, Samarskiy, 1969: 739-774; Ilin, Moiseev, 1990: 130-156; Gushchin, Mikhailov, 1994: 121-160; Gordeziani, Davitashvili, Meladze, 2003: 66-78). In present time, there appeared several research papers, devoted to the non-local contact problems (Gordeziani, Davitashvili, Meladze, 2015: 143-147; Gordeziani, Meladze, 2014: 40-46; Gordeziani, Meladze, Davitashvili, meladze, 2014: 159-161). In the present paper, the boundary value problem with non-local contact conditions for second order ordinary differential equations with constant coefficients is studied. The specific example is considered and solved numerically. 2. Let us consider the following problem: Find the continuous function u(x), defined on [0,1]
− u (x), if if 0 ≤ x ≤ c, u(x) = + (1) u (x), if if c ≤ x ≤ 1, + − where 0 < c < 1, u (c) = u (c) , which satisfies the equations
d 2u − − ω 2u − = f − (x) , 0 < x < c , (2’) dx22 1 2 + d u 2 + + − ω2 u = f (x) , c < x < 1, (2’’) dx22 ω = > − where 1 const 0 , ω2 = const > 0 , f (x) is continues function on + (0,c) and f (x) is continues function on (c,1). u(x) function also satisfies the following boundary conditions u − (0) = 0 , u + (1) = 0 , (3) 49 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
and non-local contact conditions − + − − + + u (c) = u (c) = u(c) = γ1u (x ) + γ 2u (x )+ ϕ0 , − + (4) 0 < x < c < x < 1, γ 1 > 0 , γ 2 > 0 , γ 1 + γ 2 ≤ 1 ,
where ϕ0 is given constant.
3. Let us first construct the general solution of the equation (2') . The respective homogeneous equation can be written in a following way: 2 − d u 2 − − ω1 u = 0 . dx2 The fundamental system of solutions of this equation is the following
− ω1x − −ω1x u1 (x) = e , u2 (x) = e . Find the general solution of the equation (2’) in a following form:
− − ω1x − −ω1x u1 (x) = c1 (x)e − c2 (x)e ,
where c1 (x) and c2 (x) are the functions of independent variable x and they can be defined from the following system of linear algebraic equations [8]:
ω1x −ω1x c1′(x)e + c2′ (x)e = 0, ω1x −ω1x − c1′(x)ω1e − c2′ ω1e = f (x),
from this system, we will receive
1 − −ω1x 1 − ω1x c1′(x) = f (x)e , c′ (x) = − f (x)e . 2ω 2 2ω Thus, 1 − −ω x c (x) = f (x)e 1 dx + σ , 1 2ω ∫ 1 1 − ω c (x) = − f (x)e 1xdx + σ , 2 2ω ∫ 2
where σ 1 and σ 2 are arbitrary constants. The general solution of the equation (2’) can be written in a following way: x − ω −ω 1 − ω ξ −ω ξ = σ 1x + σ 1x − ξ , 1 − , ξ u (x) 1e 2e ∫ f ( )[e e ]d ω 0 or x − ω −ω 2 − u (x) = σ e 1x + σ e 1x − f (ξ )sh(ω ξ )dξ . 1 2 ω ∫ 1 0 50 TinaTin daviTaSvili, hamlet melaZe, iulia melaZe
Let us choose σ 1 and σ 2 constants such that to satisfy the boundary conditions u − (0) = 0 u − (c) = u(c) , (5) where u(c) is still unknown. We will receive the system of equations
σ1 + σ 2 = 0, (6) ω1c −ω1c − σ1e + σ 2e = Φ + u(c),
and c − 2 − Φ = f (ξ )sh (ωξ )dξ . (7) ω ∫ 0 After solving the system of equations (6) we have Φ − + u(c) Φ − + u(c) σ1 = σ 2 = − . eω1c − e−ω1c eω1c − e−ω1c Thus, finally we receive that the solution of the problem (2’), (6) is
− − x − Φ + u(c) ω Φ + u(c) −ω 2 − u (x) = e 1x − e 1x − f (ξ )sh(ωξ )dξ ω1c −ω1c ω1c −ω1c ω ∫ e − e e − e 1 0 or − x − [Φ + u(c)]sh (ω x) 2 − u (x) = − f (ξ )sh (ω1ξ )dξ (8) shsh (ωc) ω ∫ 1 0 4. Analogously, the general solution of the problem (2’’) is x + ω −ω 2 + u (x) = σ e 2x + σ e 2x − f (ξ )sh (ω ξ )dξ . (9) 1 2 ω ∫ 2 2 c − Let us choose σ 1 and σ 2 constants such that the function u (x) could satisfy the boundary conditions u + (c) = u(c) u + (1) = 0 , (10) where u(c) is still unknown, as in previous case. We will receive the following system of equations
ω2c −ω2c σ1e + σ 2e = u(c) , (11) ω2 −ω2 + σ1e + σ 2e = Φ where 1 + 2 − Φ = f (ξ )sh(ω ξ )dξ . (12) ω ∫ 2 2 c 51 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
After solving the system of equations (11) we have
−ω2 + −ω2c + ω2c ω2 u(c)e − Φ e Φ e − u(c)e . σ1 = σ 2 = sh ω − shω − 2sh 2 (c 1) 2sh (c 1) Thus, finally we receive that the solution of the problem (2’’), (11) is x −ω2 − Φ + −ω2c Φ + ω2c − ω2 + u(c)e e ω1x e u(c)e 2 + u (x) = e + − f (ξ )sh(ω2ξ )dξ, 2shω (c −1) 2shω(c −1) ω ∫ 2 c or x + shω2 (x −1) sh ω2 (c − x) − 2 − u (x) = u(c) + Φ − f (ξ )sh (ω2ξ )dξ . (13) sh ω (c −1) shsh ω (c −1) ω ∫ 2 2 c 5. u(c) can be defined using nonlocal contact condition (4):
− − − x sh(ω1x ) sh(ω1x ) 2 − u(c) = γ1 u(c) + γ1 − γ1 f (ξ )sh(ω1ξ )dξ + sh(ω c) sh(ω c) ω ∫ 1 1 1 0 + + + x shsh ω2 (x −1) shω2 (x −1) 2 + + γ 2 u(c) + γ 2 − γ 2 f (ξ )sh(ω2ξ )dξ +ϕ0. shω (c −1) shω (c −1) ω ∫ 2 2 1 0 Then we obtain − + sh (ω1 x ) shsh [ω2 (x −1)] 1− γ 1 + γ 2 u(c) = F + ϕ0 , (14) sh (ω1c) sh[ω2 (c −1)] where x− − x+ + 2 − sh(ω1x ) 2 + sh [ω2 (x −1)] F = γ1 f (ξ )sh (ω1ξ )dξ − + γ 2 f (ξ )sh (ω2ξ )dξ − ω ∫ sh(ω c) ω ∫ sh [ω (c −1)] 1 0 1 2 0 2 x− − x+ + ω sh ω − 2 − sh ( 1x ) 2 + sh [ 2 (x 1)] (15) F = γ1 f (ξ )sh (ω1ξ )dξ − + γ 2 f (ξ )sh(ω2ξ )dξ − ω ∫ sh (ω c) ω ∫ sh[ω (c −1)] 1 0 1 2 0 2 Let us consider − + sh ω x sh ω x −1 − γ ( 1 ) + γ [ 2 ( )] > − γ + γ > . 1 1 − 2 + 1 ( 1 2 ) 0 sh (cx ) sh[c(x −1)] As − + shsh (ω x ) shsh [ω (x −1)] 1 < and 2 < , − 1 + 1 shsh (cx ) shsh [c(x −1)] 52 TinaTin daviTaSvili, hamlet melaZe, iulia melaZe
From the equation (14) we will have −1 + sh (ω1x) sh[ω2 (x −1)] u(c) = 1− γ1 + γ 2 (F + ϕ0 ). (16) sh(ω1c) sh[ω2 (c −1)] Thus, (2)-(4) has unique solution and it can be written in an analytical form:
− x [Φ + u(c)]sh (ω1x) 2 − − f (ξ )sh(ω1ξ )dξ, Tu 0 ≤ x ≤ c shsh (ω c) ω ∫ 1 1 0 u(x) = x− sh[ω2 (x −1)] sh[ω2 (c − x)] 2 − + u(c) + − f (ξ )sh(ω2ξ )dξ, TuTu c ≤ x ≤ 1, sh[ω (c −1)] shsh [ω (c −1)] ω ∫ 2 2 2 c where u(c) is defined from the equality (15), and the values Φ − , Φ + - from the equalities (7) and (12).
6. Let us consider the following iteration process, which allows us to reduce the solution of the problem (2)-(4) to the solution of a sequence of first boundary value problems for the second order ordinary differential equation:
− (k) d 2u (k) − ω 2 u − = f − (x) 2 1 [ ] , 0 < x < c , (17') dxdx + (k) d 2u (k) − ω 2 u + = f − (x) < < 2 2 [ ] , c x 1, (17'') dxdx
(k) (k) [u − (0)] = 0 , [u + (1)] = 0 , (18)
− (k) + (k) (k) − − (k−1) + + (k−1) [u (c)] = [u (c)] = [u(c)] − γ1[u (x )] + γ 2 [u (x )] + ϕ0 , (19)
k = 1,2,3, and
(−1) + + (−1) [u − (x− )] = 0 , [u (x )] = 0 . (20)
We denote (k ) (k ) [z − (x)] = [u − (x)] − u − (x) , 0 ≤ x ≤ c ,
+ (k ) = + (k ) − + [z (x)] [u (x)] u (x) , c ≤ x ≤ 1, 53 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
− + where u (x) and u (x) are the solutions of the problem (2)-(4). Then for − + the functions z (x) and z (x) we obtain the following problem: − (k) d 2 z (k) − ω 2 z − = 0 , if 0 ≤ x ≤ c , (21') 2 1 [ ] dxdx + (k) d 2 z (k) − ω 2 z + = 0 , if c ≤ x ≤ 1, (22'') 2 2 [ ] dxdx
(k) (k) [z − (0)] = 0 , [z + (1)] = 0 , (23)
(k) − (k) + (k) − − (k−1) + + (k−1) [z(c)] = [z (c)] = [z (c)] = γ1[z (x )] + γ 2 [z (x )] . (24) k = 1,2,3, From the equality (24) we obtain
− (k) + (k) − − (k−1) + + (k−1) [z (c)] = [z (c)] ≤ γ1 [z (x )] + γ 2 [z (x )] . (25)
If we use Schwarz’ Lemma, we will get
(k−1) (k−1) [z − (x − )] ≤ q − [z − (c)]
(k−1) (k−1) [z + (x + )] ≤ q + [z + (c)]
+ where q − = const , 0 < q − < 1, q = const , 0 < q + < 1. If we use inequality (25), we will get
− (k) + (k) − − (k−1) + + (k−1) [z (c)] = [z (c)] ≤ γ1q [z (c)] + γ 2q [z (c)]
as (k) (k) [z − (c)] = [z + (c)] = [z(c)](k) ,
Then we obtain
[z(c)](k) ≤ Q [z(c)](k−1) ,
where − + Q = γ 1q + γ 2 q < 1, 54 TinaTin daviTaSvili, hamlet melaZe, iulia melaZe
i.e. lim[z(c)](k) → 0 By the maximum principle [8] we obtain: ck [u − (x)] − u + (x) = 0(Qk ),
[u + (x)]− u + (x) = 0(Qk ).
Thereby we proved the following theorem Theorem. The iteration process (17)-(20) converges to this solution of the problem (2)-(4) at the rate of an infinitely decreasing geometric progression.
7. We consider the following problem as an example: find the function (1) - u(x) , defined on [0,1], which satisfies the equations 2 − d u − 1 1 − 2u = π cos(πx)− π 2 xsin(πx), 0 < x < , dx 2 2 2 2 + d u + 1 πx 2 πx 1 − u = − 6π cos + (9 + π )(x −1)sin , < x < 1, dxdx 2 9 3 3 2
u(x) function also satisfies the following boundary conditions u − (0) = 0 , u + (1) = 0 , and non-local contact conditions 1 1 1 1 1 1 3 1 3 u − = u + = u = u − + u + + − , 2 2 2 2 4 2 4 4 16 2 The exact solution of this problem is
1 xsin(πx), 0 ≤ x ≤ 0.5, u(x,t) = 2 π (1− x)sin x, 0.5 ≤ x ≤ 1. 3
55 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Fig. 1. Exact solution
To solve this problem, we consider the iteration process (17)-(20). Below one can see the figures of approximate solution and respective absolute error for k=1 and k=6.
Fig. 2. Approximate solution, k=1
Fig. 3. Absolute error, k=1
56 TinaTin daviTaSvili, hamlet melaZe, iulia melaZe
Fig. 4. Absolute error, k=18.
It’s enough about 18 iterations to find the approximate solution with absolute error ~ 10-7.
References: 1. Bitsadze A., Samarskiy A. Ob odnom prostom obobshenii lineinikh elliticheskikh kraevikh zadach, Dan ANSSSR А, 185, 1969. 2. Gordeziani D., Meladze H., Avalishvili G. On One Class of Nonlocal in Time Problems for First Order Evolution Equations // Jurn. Vich. I Prikl. Mat. _ 2003, №1 (88), pp.66-78. 3. Gordeziani D., Davitashvili T., Meladze H., Numerical Solution of Nonlo- cal Contact Problems for Elliptic Equations. Proceedings of 10th Interna- tional Conference on Computer Science and Information Technologies (CSIT’2015), September 28 _ October 2, 2015, Yerevan, Armenia, pp.273- 276; IEEE Conference Publications, Pages: 143 _ 147. 4. Gordeziani D., I.Meladze I., On a Nonlocal Contact Problem, Bulletin of the Georgian Academy of Sciences, vol. 8, no. 1, pp. 40-46, 2014. 5. Gordeziani D., Meladze H., Davitashvili T., Meladze I. Ob odnoy nelokalnoy kontaktnoy zadache//PROCEEDINGS Of the Ninth International Scientific- Practical Conference INTERNET-EDUCATION-SCIENCE (IES-2014), 14- 17 October, 2014, Vinnytsia, Ukraine, pp.159-161. 6. Gushchin A.K., Mikhailov V.P., On the Stability of Nonlocal Problems for a Second Order Elliptic Equation // Math. Sb. (1994), №1, pp.121-160. 7. Ilin V., Moiseev E. Dvumernaya nelokalnaya kraevaya zadacha dlya opera- tora puassona v differentsialnoy i raznostnoy traktovkakh. Matematicheskoe modelirovanie, 1990, t. 2, №8, pp.130-156. 8. Stepanov V. Kurs differentsialnykh uravneniy, Fizmat-giz, 1959. 57 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
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moce mul naSrom Si ganxi lu lia aralo ka lu ri sakon taq to amo cana meo re rigis araer T g va ro va ni dife ren ci a lu ri ganto le be bisaT vis mudmi vi koe fi ci en te biT. agebu lia ganxi lu li amoca nis anali zu ri amonax s ni, agebu lia itera ci u li proce si, romel sac dayavs aralo ka lu ri amoca na meo re rigis Cveu leb ri vi dife ren cia lu ri ganto le be bis mimdev ro bis pirve li sasazR v ro amoca ne bis amoxs nis ken.
58 maTematikuri modelireba MATHEMATICAL MODELING
Temur Chilachava
ABOUT SOME FIRST INTEGRALS OF NONLINEAR SYSTEM OF THE DIFFERENTIAL EQUATIONS DESCRIBING PROCESS OF TWO_LEVEL ASSIMILATION
Abstract In the real model it is supposed that the powerful state with a widespread state language carries out assimilation of the population of less powerful state and the third population talking in two languages, different in prevalence. Carries out assimilation of the population of the state formation with the least widespread language to the turn, less powerful state. Not triviality of model assumes negative demographic factor of the powerful state-assimilating and positive demographic factor of the state formation which is under bilateral assimilation. For some ratios between demographic factors of the sides and coefficients of assimilations, for nonlinear system of three differential equations with the corresponding conditions of Cauchy the first integrals are found. In particular, in the first case the first integral in space of required functions represents a hyperbolic paraboloid, and in the second case _ a cone. In these cases, the nonlinear system of three differential equations is reduced to nonlinear system of two differential equations for which the second first integrals are found and in the phase plane of decisions are investigated behavior of integrated curves. In more general case with application of a criteria of Bendixson the possibility of existence of the closed integrated curves is proved that indicates a possibility of a survival of the population finding under double assimilation.
Introduction Mathematical and computer modeling has been widely recognized in such disciplines as sociology, history, political science, and others (Samarski, Mihailov, 2006; Chilachava, Dzidziguri, 2008). There is an interest in creation of a mathematical model, which would give the opportunity to determine the dynamics of changes in the number of voters of political subjects during the election period. Elections can be divided into two parts: the two-party and multi-party elections.
59 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
In (Chilachava, Kereselidze, 2010; Chilachava, Kereselidze, 2009a; Chi- lachava, Kereselidze, 2009b) quantities of information streams by means of new mathematical models of information warfare are studied. By information warfare the authors mean an antagonism by means of mass media (an electronic and print- ing press, the Internet) between the two states or the two associations of states, or the economic structures (consortiums) conducting purposeful misinformation, propagation against each other. It was shown that in case of high aggression of the contradictory countries, not preventive image the operating peacekeeping organi- zations won’t be able to extinguish the expanding information warfare. In works (Chilachava, Kereselidze, 2011a; Chilachava, Kereselidze, 2011b) linear and nonlinear mathematical models of information warfare, and also opti- mizing problems are considered. In (Chilachava, Chakhvadze, 2014) the new nonlinear mathematical and computer model of information warfare with participation of interstate authoritative institutes is offered. The model is described by Cauchy’s problem for nonlinear non-homogeneous system of the differential equations. Confronting sides in extend of provocative statements, the third side (the peacekeeping international organizations) extends of soothing statements, interstate authoritative institutes the peacekeeping statements call the sides for the termination of information warfare. In that specific case, modes of information warfare “aggressor- victim”, for the third peacekeeping side are received exact analytical solutions, and functions defining number of the provocative statements distributed by the antagonistic sides satisfy to Cauchy’s problems for Riccati certain equations which are solved by a numerical method. For the general model computer modeling is carried out and shown that irrespective of high aggression of confronting sides, interstate authoritative institutes will be able to extinguish information warfare and when for this purpose efforts of only the international organizations insufficiently. The article (Kereselidze, 2006) concerns of Chilker task is entered refers to the boundary value problem for a system of ordinary differential equations and optimal control problem. In Chilker tasks right boundary conditions are set in different, uncommitted time points for different coordinates of the unknown vector _ functions. Proposed methods solutions of Chilker tasks. In works (Mihailov, Maslov, Iuhno, 2000; Mihailov, Iuhno, 2001; Mihailov, Petrov, 2011) the mathematical model of political rivalry devoted to the description of fight occurring in imperious elite competing (but not necessarily antagonistic) political forces, for example, power branches is considered. It is supposed that each of the sides has ideas of «number» of the power which this side would like to have itself, and about «number» of the power which she would like to have for the partner. These papers (Chilachava, Dzidziguri,Sulava, Chakaberia, 2009; Chilachava, Dziziguri , Sulava, Chakaberia, 2010a; Chilachava, Dziziguri, Sulava, Chakaberia, 60 Temur CilaCava
2010b; Chilachava, Sulava, Chakaberia, 2010; Chilachava, Sulava, 2013) present the nonlinear mathematical model of the public or the administrative management (or the macro and micro model). The cases of both constant and variable pressure forces on freethinking people were analyzed. Exact analytical decisions which de- termine dynamics of a spirit both free-thinking people, and operated (conformists) of people by time are received. During this analyses various governance systems were considered: a liberal, democratic, semi dictatorial and dictatorial. These works (Chilachava, 2012a; Chilachava, 2012b; Chilachava, 2013a; Chilachava, Chochua, 2013a; Chilachava, 2013b, Chilachava, 2013c; Chilachava, Chochua, 2013b) considered a two or three-party (one pro-government and two opposition parties) nonlinear mathematical model of elections when coefficients are constant. The assumption was made that the number of voters remain the same between two consecutive elections (zero demographic factor of voters). The exact analytical solutions were received. The conditions under which opposition party can win the upcoming elections were established. These works (Chilachava, Sulava, 2015a; Chilachava, Sulava, 2015b; Sulava, 2015; Chilachava, Sulava, 2015c) considered a two-party (pro-government and opposition parties) nonlinear mathematical model of elections with variable coefficients. In work (Chilachava, Sulava, 2016) proposed the nonlinear mathematical model with variable coefficients in the case of three-party elections, that describes the dynamics of the quantitative change of the votes of the pro-government and two opposition parties from election to election. The model takes into account the change in the total number of voters in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. The model considered the cases with variable coefficients. In the particular case obtained exact analytical solutions. The conditions have been identified under which the opposition can win the forthcoming elections, and in some cases, the pro-government party can stay in power. In general Cauchy problem was solved numerically using the MATLAB software package. In work [30] computer research of a trajectory of development of three ethnos living in one territory is conducted. Thus assimilation is supposed as a result of mixed marriages. In (Chilachava, 2014) consider the nonlinear mathematical model of bilateral assimilation without demographic factor. It was shown that the most part of the population talking in the third language is assimilated by that widespread language which speaks bigger number of people (linear assimilation). Also it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological 61 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV and economic capabilities of the assimilating states. In (Chilachava T.I., Chakaberia, 2014) mathematical modeling of nonlinear process of assimilation taking into account demographic factor is offered. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model “predator - the victim”, thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilating side. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model “a predator _ the victim”, with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states. In (Chilachava, Chakaberia, 2015) mathematical modeling of nonlinear process of the assimilation taking into account positive demographic factor which underwent bilateral assimilation of the side and zero demographic factor of the assimilating sides is considered. In model three objects are considered: the population and government institutions with widespread first language, influencing by means of state and administrative resources on the population of the third state formation for the purpose of their assimilation; the population and government institutions with widespread second language, influencing by means of state and administrative resources on the population of the third state formation for the purpose of their assimilation; population of the third state formation which is exposed to bilateral assimilation from two powerful states or the coalitions. 62 Temur CilaCava
For nonlinear system of three differential equations of the first order are received the two first integral. Special cases of two powerful states assimilating the population of small state formation (autonomy), with different initial number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in all cases there is a full assimilation of the population to less widespread language. Thus, proportions in which assimilate the powerful states the population of small state formation are found. In (Chakaberi, 2015) work mathematical and computer modeling of nonlinear process of the assimilation taking into account positive demographic factor which has undergone bilateral assimilation of the party and negative demographic factors of the assimilating parties is considered. Computer modeling of nonlinear system of three differential equations of the first order in case of fixed coefficients of model is carried out. Special cases of two powerful states assimilating the population of small state education with different initial quantities of the population, both with identical and with various economic and technological capabilities are considered. New numerical results which qualitatively differ from results in case of zero demographic factors of the assimilating parties are received. In (Chilachava, 2015) work mathematical modeling of nonlinear process of two-level assimilation taking into account demographic factors of three sides is offered.
I. System of the equations and initial conditions
Using analogies to earlier us of the offered mathematical model (Chilachava, 2012) , and also developing mathematical model of bilateral assimilation (Chilachava, 2014; Chilachava Chakaberia, 2014; Chilachava, Chakaberia, 2015; Chakaberia, 2015) , we will consider the following general nonlinear mathematical model of two-level assimilation [29]
du (t) du = α + β + β 1 (t)u(t) 1 (t)u(t)v(t) 2 (t)u(t)w(t) dtdt dv (t) = α 2 (t)v(t) − β3 (t)u(t)v(t) + β 4 (t)v(t)w(t) (1.1) dtdt dw (t) = α 3 (t)w(t) − β5 (t)u(t)w(t) − β 6 (t)v(t)w(t) dtdt
u(0) = u0 ,v(0) = v0 , w(0) = w0 , (1.2)
u(t), v(t), w(t) ∈ C1[0,T], t ∈ [0,t].
[0,T] _ assimilation process consideration period (as a rule some tens years). 63 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
u(t) _ the population and powerful government institutions with very widespread language, influencing by means of the state and administrative resources the population of two states or theautonomy for the purpose of their assimilation; v(t) _ the population and government institutions with widespread second language which underwent assimilation from the powerful state, but in the turn, influencing by means of the state and administrative resources the third population with some less widespread language for the purpose of their assimilation; w(t) _ the third population (autonomy) which underwent bilateral assimilation from two rather powerful states (look the scenario of process of two- level assimilation, fig. 1).
Fig. 1
The new mathematical model of assimilation offered by us assumes performance of the following natural inequalities β (t) > 0,i = 1− 6, ∈ i t [0,T]. (1.3) For the description of nontrivial process (trivial we will call assimilation process when one strong side completely assimilates two other sides) 64 Temur CilaCava of assimilation it is necessary to make one or the other the following assumptions: Assumption 1:
α1 (t) < 0 α 2(t) ≤ 0 t ∈[0,T ] (1.4) α 3 (t) > 0 Assumption 2:
α1 (t) < 0 α 2(t) ≥ 0 t ∈[0,T ] (1.5) α 3 (t) > 0
II. Some special cases
We will assume that all coefficients of system of the equations (1.1) are constants.
du (t) = α u(t) + β u(t)v(t) + β u(t)w(t) dt 1 1 2 dt dv (t) = α 2v(t) − β 3u(t)v(t) + β 4v(t)w(t) (2.1) dt dw (t) = α 3 w(t) − β5u(t)w(t) − β 6v(t)w(t) dtdt
Assumptions 1, 2 will take a form
α1 < 0 α1 < 0 α 2≤ 0 α 2≥ 0 (2.2) α > α 3 > 0 3 0
We will enter transformation
u = u − u0 , v = v − v0 , w = w − w0 (2.3)
Then from (2.1) - (2.3) it is easy to receive
65 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
du(t) dtdt = α1 + β1v0 + β 2 w0 + β1 v + β 2 w u + u0 dv(t) dtdt = α 2 − β 3u0 + β 4 w0 − β 3 u + β 4 w v + v0 (2.4) d w(t) dtdt = α 3 − β5u0 − β 6v0 − β5 u − β 6 v w + w 0 We will pick up parameters of model so that constants in the right part of system of the equations (2.4) have become equal zero
α1 + β1v0 + β 2 w0 = 0 α 2 − β 3u0 + β 4 w0 = 0 (2.5) α 3 − β 5u0 − β 6v0 = 0 Then
β1v0 + β 2 w0 = −α1 β3u0 − β 4 w0 = α 2 (2.6) β5u0 + β 6v0 = α 3 (2.6) represents linear algebraic system of the non-homogeneous equations for
u0 ,v0 , w0 . Existence of a set of decisions, requires also enough become equal to zero four determinants
0 β β 1 2 det β 3 0 − β 4 = 0, (2.7) β 5 β 6 0
66 Temur CilaCava
−α β β 1 1 2 det α 2 0 − β 4 = 0, (2.8) α 3 β 6 0
0 −α β 1 2 det β 3 α 2 − β 4 = 0, (2.9) β 5 α 3 0
0 β −α 1 1 det β 3 0 α 2 = 0 (2.10) β 5 β 6 α 3 From (2.7) it is easy to receive a condition
β 2 β3 β 6 = β1β 4 β 5 (2.11) From (2.8) _ (2.10) taking into account (2.11), we will receive
β 5 β 6 α 3 = α 2 − α 1 (2.12) β 3 β1 According (2.4),(2.5) we will receive
du(t) dtdt = β1 v + β 2 w u + u0 dv(t) dtdt = −β 3 u + β 4 w (2.13) v + v0 d w(t) dtdt = −β5 u − β 6 v w + w 0
We will multiplay the equations of system (2.13) respectively on
γ 1 ,γ 2 ,γ 3 also we will pick up
67 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
β 2γ 1 + β 4γ 2 = 0 β1γ 1 − β 6γ 3 = 0 (2.14) β 5γ 3 + β 3γ 2 = 0 It is easy to receive
d γ γ γ ln(u 1 v 2 w 3 ) = 0 (2.15) dtdt Then taking into account initial conditions (1.2), from (2.15) we will receive the first integral of system (2.1)
γ γ1 γ 2 γ 3 γ1 γ 2 3 u v w = u0 v0 w0 (2.16)
The determinant of a matrix of system of the equations (2.14), according to (2.7) is equal to zero, γ 1,γ 2 ,γ 3 therefore there is an uncountable set of decisions (2.14). We will consider several classes of decisions and according to the first integrals (2.16)
β 6 γ 1 = β1 β 1. γ = − 5 2 β 3 γ 3 = 1 β 6 β6 β1 β u w u 1 w = 0 0 (2.17) β5 β5 β3 β3 v v0 β 4 γ 1 = − β 2 2. γ 2 = 1 β 3 γ 3 = − β 5
β β3 4 β4 β3 β2 β5 β β u w u 2 w 5 = 0 0 (2.18) v v0 68 Temur CilaCava
3. γ = − 1 1 β 2 γ 2 = − β 4 β1 γ 3 = β 6 β 1 β1 β6 β uw u w 6 uw = 0 0 (2.19) β2 β 2 β4 β4 v v0 We will consider the first case
β1 = β 6 (2.20) β 5 = β 3 Then from (2.11), (2.12) we will receive
β 4 = β 2 (2.21) α 3 = α 2 −α1 And from (2.17) we will receive
uw u w = 0 0 (2.22) v v0 (O,u, v, w) In phase space (2.22) represents a hyperbolic paraboloid. From (2.22) we will receive v = puw v = puw v p = 0 (2.23) uvw p = 0 0 0 Takingu0 intow0 account (2.21), (2.23) task (2.1), (1.2) will take a form
du (t) du = α + β 2 + β 1u(t) 1pupu (t)w(t) 2u(t)w(t) dtdt (2.24) dw (t) 2 = (α 2 −α1 )w(t) − β3u(t)w(t) − β1 pu (t)w (t) dtdt
u(0) = u0 ,w(0) = w0 .
69 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
(2.24) it is easy to rewrite in the following look • u = α + β puw + β w u 1 1 2 • (2.25) w = α − β puw − β u w 3 1 3 We will assume that
α 2 = 0 (2.26) β 2 = β 3
Then from (2.25) we will receive • (uw ) = −β 2uw (u − w) (2.27) u Having multiplyed the first equation of system (2.24) on w and the second equation on the after of some transformations we will receive 2 2 • (u + w ) = 2(u − w)[α1 (u + w) + β 2uw + β1 puw(u + w)] (2.28) Having divided (2.28) on (2.27) we will receive d(u 2 + w2 ) 2[α (u + w) + β uw + β puw(u + w)] = 1 2uw 1 (2.29) d(uw ) − β 2uw We will enter designations u + w ≡ z (2.30) uw ≡ y Then the differential equation (2.29), taking into account (2.30) will correspond in the following look d(z 2 − 2y) 2[α z + β y + β pyz)] = 1 2 1 (2.31) dydy − β 2 y The decision (2.31), taking into account initial conditions (2.24) anddesignations (2.30), has an appearance
α1 y β1 p z − z0 = − ln − (y − y0 ) (2.32) β 2 y0 β 2 Thus taking into account designations (2.30) from (2.32) we will (O, w,u)
70 Temur CilaCava receive an integrated curve in the phase plane
α1 uwuw β1 p u + w − (u0 + w0 ) = − lnln − (uw − u0 w0 ) (2.33) β 2 u0 w0 β 2 We will enter designations 2 F1 (u, w) ≡ α1u(t) + β1 pu (t)w(t) + β2u(t)w(t) 2 (2.34) F2 (u, w) ≡ (α 2 − α1 )w(t) − β3u(t)w(t) − β1 pu (t)w (t) It is easy to receive ∂F 1=α +2β pu(t)w(t)+β w(t) ∂u 1 1 2 (2.35) ∂F 2= α _ α _ β u(t) _ 2β pu(t)w(t) ∂w 2 1 3 1 ∂F1 ∂F div F = + 2 = α +2β pu(t)w(t)+β w(t)+ ∂u ∂w 1 1 2
+ α2 _ α1 _ β3 u(t) _ 2β1 pu(t)w(t) = α2+β2w _ β3u≡G(u,w) (2.36)
G(u,w) = 0
β2 α2 u= w + (2.37) β3 β3
Fig. 2 (α 2 = 0) Theorem 1. A task (2.24) in some one-coherent area D ⊂ (O,u(t), w(t)) the first quadrant has the decision in the form of the closed trajectory which is completely lying in this area. Thus according to (2.37) in the first quadrant of the phase plane /there is such area in which G (u;w) function of a sign change and according to Bendixson’s kriterium in this area existence of the closed integrated curve is possible, i.e. in this case function doesn’t become equal to zero and there is no full assimilation of the third side.
We will consider the second special case
β1 = β 6 (2.38) 2β 3 = β 5 Then from (2.17) respectively we will receive v 2 v 2 = q 2uw , q 2 = 0 (2.39) u0 w0 71 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
(O,u, v, w) In phase space (2.39) represents a cone. Taking into account (2.39) system of the equations (2.1) will assume an air:
dudu (t) = α1u(t) + β1qu (t) wuwu + β 2u(t)w(t) dt (2.40) dt dw (t) = (2α 2 −α1 )w(t) − 2β3u(t)w(t) − β1q wuuw w(t) dtdt We will enter designations u(t) ≡ ϕ 2 (t) w(t) ≡ψ 2 (t) (2.41) Then from (2.40), (2.41) we will the following task
dϕ(t) α1 β1q 2 β2 2 = ϕ(t) + ϕ (t)ψ (t) + ϕ(t)ψ (t) dtdt 2 2 2 (2.42) dψ (t) 2α 2 − α1 2 β1q 2 = ψ (t) − β3ψ (t)ϕ (t) − ϕ(t)ψ (t) dtdt 2 2
ϕ(0) ≡ u 0 ψ (0) ≡ w 0
We will enter designations α β q β F (ϕ,ψ ) ≡ 1 ϕ(t) + 1 ϕ 2 (t)ψ (t) + 2 ϕ(t)ψ 2 (t) 1 2 2 2 (2.43) 2α − α β q F (ϕ,ψ ) ≡ 2 1 ψ (t) − β ψ (t)ϕ 2 (t) − 1 ϕ(t)ψ 2 (t) 2 2 3 2 It is easy to receive ∂F α β 1 = 1 + β qϕ(t)ψ (t) + 2 ψ 2 (t) (2.44) ∂ϕ 2 1 2
∂F 2α − α 2 = 2 1 − β ϕ 2 (t) − β qϕ(t)ψ (t) ∂ψ 2 3 1 → ∂F ∂F β div(F) = 1 + 2 = α + 2 ψ 2 (t) − β ϕ 2 (t) (2.45) ∂ϕ ∂ψ 2 2 3 β G (ϕ(t), ψ (t)) ≡ α + 2 ψ 2 (t) − β ϕ 2 (t) 1 2 2 3
G1 (ϕ(t), ψ (t)) = 0,
72 Temur CilaCava
β α + 2 ψ 2 (t) − β ϕ 2 (t) = 0 (2.46) 2 2 3 Theorem 2. A task (2.42) in some one-coherent area D ⊂ (O,ϕ(t), ψ (t)) the first quadrant has the decision in the form of the closed trajectory which is completely lying in this area. Thus according to (2.46) in the first quadrant of the phase plane (O,ϕ,ψ ) there is such area in G1 (ϕ,ψ ) function of a sign change and according to Bendixson’s kriterium in this area existence of the closed integrated curve is possible, i.e. in this case ψ function (according 2.41 w(t) ) function doesn’t become equal to zero and there is no full assimilation of the third side. We will consider the third special case
2β1 = β 6 β 3 = β 5 (2.47) 2β 2 = β 4 From (2.12), (2.47) we will receive
α 3 = α 2 − 2α 1 (2.48) Then, from (2.18) we will receive v. = 2 = 0 v qu w, q 2 (2.49) u0 w0 Taking into account (2.47) - (2.49) task (2.1), (1.2) will take a form
du (t) du = α + β 3 + β 1u(t) 1qu (t)w(t) 2u(t)w(t) dtdt (2.50) dwdw (t) 2 2 = (α 2 − 2α1 )w(t) − β3u(t)w(t) − 2β1qu (t)w (t) dtdt
u(0) = u0 ,w(0) = w0 . (2.50) it is easy to rewrite in the following look • u = α + β qu 2 w + β w u 1 1 2 (2.51) • w 2 = α 3 − 2β1qu w − β 3u w 73 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
The first equation of system (2.51) multiplay on 2 and added second equation, then we will receive d (ln(u 2 w)) = 2α + α + 2β w − β u (2.52) dtdt 1 3 2 3 We will assume that
α 2 = 0 (2.53) Then from (2.48), (2.52) we will receive
α 3 + 2α1 = 0
d 2 (ln(u w)) = 2β 2 w − β 3u (2.54) dtdt
d 2 2 (u w) = u w(2β 2 w − β 3u) dtdt We will assume that
β3 = 2β 2 (2.55) Then from (2.54), (2.55)
d 2 2 (u w) = 2β 2u w(w − u) (2.56) dtdt The first equation of system (2.50) multiplay on 2 and added second equation, then we will receive
• • 2 2u+ w = (u − w)( 2α1 + 2β1qu w) (2.57)
d 2 (2u+ w) = 2(u − w)( α1 + β1ququ w) (2.58) dtdt Devided (2.58) on (2.56) d(2u + w) α + β ququ 2 w = − 1 1 2 2 (2.59) d(u w) β 2u w Integrated (2.59) α u 2 w β q + − + = − 1 − 1 2 − 2 (2.60) 2u w (2u0 w0 ) ln 2 (u w u0 w0 ) β 2 u0 w0 β 2 Thus, we have received the first integral (2.60) systems of the differential equations (2.51). 74 Temur CilaCava
References: 1. Atnabayeva L.A., Halitova T.B., Malikov R. F. Imitating Modeling of As- similation of Ethnos. http://simulation.su/uploads/files/default/2012-conf- prikl-math-and-mod-33-35.pdf 2. Chilachava T.I.Dzidziguri Ts.D. Mathematical Modeling. Tbilisi, Inovacia, 2008 (Georgian). 3. Chilachava T.I., Kereselidze N. Mathematical Modeling of the Information- warfare. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2010, № 1 (24), pp.78 -105 (Georgian). 4. Chilachava T.I., Kereselidze N.G. Non-preventive Continuous Linear Math- ematical Model of Information Warfare. Sokhumi State University Proceed- ings, Mathematics and Computer Sciences, 2009a, #VII, pp. 91- 112. 5. Chilachava T.I., Kereselidze N.G. Continuous Linear Mathematical Model of Preventiveinformation Warfare. Sokhumi State University Proceedings, Mathematics and Computer Sciences, 2009b, #VII, pp.113- 141. 6. Chilachava T.I., Kereselidze N.G. Optimizing Problem of Mathematical Model of Preventive Information Warfare, Informational and Communication Technologies – Theory and Practice: Proceedings of the International Scien- tific Conference ICTMC-2010 USA, Imprint: Nova, 2011a, pp. 525- 529. 7. Chilachava T.I., Kereselidze N.G. Mathematical Modeling of Information Warfare. Information Warfare, 2011b, #1(17), p. 28- 35 (Russian). 8. Chilachava, T.I. Chakhvadze A. Continuous Nonlinear Mathematical and Computer Model of Information Warfare with Participation of Authoritative Interstate Institutes. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2014, #4(44), pp. 53-74. 9. Chilachava T.I., Dzidziguri Ts.D.,Sulava L.O., Chakaberia M.R. Nonlinear Mathematical Model of Administrative Management. Sokhumi State Uni- versity Proceedings, Mathematics and Computer Sciences, vol. VII, 2009, pp.169 - 180 (Georgian). 10. Chilachava T.I., Dziziguri Ts.D, Sulava L.O., Chakaberia M.R. Nonlinear Mathematical Model of Administrative Pressure. First International Confer- ence, Book of Abstracts, Batumi, 2010a, pp. 74-75. 11. Chilachava T.I., Dziziguri Ts.D., Sulava L.O., Chakaberia M.R.A Nonlinear Mathematical Model of Administration. Abstracts of the International Con- ference “Information and Computer Technology, Simulations” .Dedicated to the 80th Anniversary of Prangishvili I.V., 2010b, pp. 203 - 204. 12. Chilachava T.I.,Sulava L.O., Chakaberia M.R.On Some Nonlinear Math- ematical Model of Administration. Problems of Security Management of Complex Systems. Proceedings of the XVIII International Conference, Mos- cow, 2010, pp. 492- 496 (Russian). 75 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
13. Chilachava T.I.,Sulava L.O.A Nonlinear Mathematical Model of Manage- ment. Georgian Electronic Scientific Journal: Computer Science and Tele- communications, 2013, #1(37) pp. 60 – 64 (Russian). 14. Chilachava T.I. Nonlinear Mathematical Model of the Dynamics of the Vot- ers Pro-Government and Opposition Parties (the Two Election Subjects) Ba- sic Paradigms in Science and Technology. Development for the XXI Cen- tury. TransactionsII. 2012a, pp. 184- 188 (Russian). 15. Chilachava T.I Nonlinear Mathematical Model of the Dynamics of the Voters Pro-Government and Opposition Parties. Problems of Security Management of Complex Systems. Proceedings of the XX International Conference, Mos- cow, 2012b, pp. 322- 324 (Russian). 16. Chilachava T.I. Nonlinear Mathematical Model of Dynamics of Voters Three Electoral Subjects. IV International Conference of the Georgian Mathemati- cal Union, Book of Abstracts, Tbilisi - Batumi,2013a, pg. 161. 17. Chilachava T.I., Chochua Sh.G. Two-Party Nonlinear Mathematical Model of Elections Taking Account Falsification. IV International Conference of the Georgian Mathematical Union, Book of Abstracts, Tbilisi - Batumi, 2013, pg. 162. 18. Chilachava T.I. Nonlinear Mathematical Model of Dynamics of Voters of Two Political Subjects. Seminar of the Institute of Applied Mathematics Named I. Vekua Reports, 2013b, vol.39, pp. 13- 22. 19. Chilachava T.I. Nonlinear Mathematical Model of Three-Party Elections. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013c, pp. 513 - 516. 20. Chilachava T.I., Chochua Sh.G. Nonlinear Mathematical Model of Two- Party Elections in the Presence of Election Fraud. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013b, pp. 349- 352 (Russian). 21. Chilachava T.I., Sulava L.O. Nonlinear Mathematical Model of Elections with Variable Coefficients. VI International Conference of the Georgian Mathematical Union, Book of Abstracts, Tbilisi - Batumi, 2015a, pg.97. 22. Chilachava T.I., Sulava L.O. Mathematical and Computer Modeling of Nonlinear Processes of Elections with Two Selective Subjects. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2015b, # 2(46), pp. 61- 78. 23. Chilachava T.I., Sulava L.O. Mathematical and Computer Simulation of Pro- cesses of Elections with Two Selective Subjects and Float Factors of Model. Problems of Security Management of DifficultS ystems. Works XXIII of the International Conference, Moscow, 2015c, p. 356 - 359 (russian). 24. Chilachava T.I. Nonlinear Mathematical Model of Bilateral Assimilation. 76 Temur CilaCava
Georgian Electronic Scientific Journal: Computer Science and Telecommu- nications, 2014, # 1(41), pp. 61 – 67. 25. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Pro- cess of Assimilation Taking into Account Demographic Factor. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2014, # 4 (44), pg.35-43. 26. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Processes Bilateral Assimilation, Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2015, #2(46), pg. 79- 85. 27. Chakaberia M.R. Mathematical and Computer Modeling of Nonlinear Process- es of Bilateral Assimilation. The International Conference “Information and Computer Technologies, Modelling, Management”, Devoted to the 85 Anni- versary Since the Birth of I.V. Prangishvili, Georgia, Tbilisi, 2015, pp. 524-526. 28. Chilachava T. About New Mathematical Model `Beast – Predator – Victim. III International Conference of the Georgian Mathematical Union. Book of Abstract. Batumi, 2012, pp. 158. 29. Chilachava T. Nonlinear Mathematical Model of the Two-Level Assimila- tion. VI International Conference of the Georgian Mathematical Union, Book of Abstracts, 2015, p. 79-80. 30. Kereselidze N.G. Chilker’s Type Mathematical and Computer Models in the Information Warfare. Information Warfare, 2016, #2(38), pp. 28 – 35 (Russian). 31. Mihailov A.P., Maslov A.I., Iuhno L.F. Dynamic Model of Competition Be- tween Political Forces. Reports of the Academy of Sciences, 2000, v.37, # 4, pp. 469 - 473 (Russian). 32. Mihailov A.P., Iuhno L.F. The Simplest Model of Balance Between the Two Branches of Government. Math modeling., Moskow, 2001, v.13, #1, pp. 65-75 (Russian). 33. Mihailov A.P., Petrov A.P. Behavioral Hypotheses and Mathematical Modeling in the Humanities. Math Modeling, 2011, v.23, #6, pp.18 - 32 (Russian). 34. Samarski A.A., Mihailov A.P. Mathematical Modeling. Moskow,Fizmatlit, 2006(Russian). 35. Sulava L.O. Mathematical and Computer Modelling of Nonlinear Processes of Elections. Works of the International Conference “Information and Com- puter Technologies, Modelling, Management” Devoted to the 85 Anniversary Since the Birth of I. V. Prangishvili, Tbilisi, 2015, by p. 387- 390 (Russian). 36. Sulava L.O. Mathematical and Computer Modeling of Three-Party Elections. GESJ: Computer Sciences and Telecommunications, 2016, # 2 (48), pp. 59-72.
77 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Temur CilaCava
ordoniani asimilaciis procesis aRmweri arawrfivi diferencialuri gantolebaTa sistemis zogierTi pirveli integralebis Sesaxeb
reziume
moce mul model Si nagu lis x me vi a, rom mZlavri saxel m wi fo ax dens nakle bad mZlavri saxel m wi fo s da saxel m wi fo eb ri vi warmo naqm nis (avto no mi a) mosax le o be bis asimi la ci as, xolo, Tavis mxriv, meo re saxel m wi foc axdens saxel m wi fo eb ri vi warmo naq m nis mosax leo bis asimi la ci as . mode lis aratri vi a lu ro bis gamo, gaTva lis wine bu lia mZlavri saxel m wi fos uaryo fi Ti da saxel m wi fo eb ri vi warmo naq m nis dade bi Ti demog ra fi u li faqto re bi. demog ra fi u li faqto re bi sa da asimi la ci is koe fi ci en te bis Soris zogi er Ti Ta nafar do be bi saT vis, napov nia arawr fi vi dife ren ci a lu ri samgan tole bi a ni siste mis koSis amoca nis pirve li integ ra le bi. kerZod, pirvel SemTx ve va Si, pirve li integ ra li saZeb ni fun qci a Ta sivr ce Si warmo ad gens hiper bo lur para bo lo ids, xolo meo re SemTx ve va Si _ konuss. am SemTx ve veb Si, arawr fi vi dife ren cia lu ri samgan to le bi a ni siste ma dayva ni lia arawr fiv dife ren cia lur organ to le bi an siste meb ze, romel TaT vis napov nia meo re pirve li integ ra le bi da amonax s n Ta fazur sibr tye ze Seswav li lia integ ra lu ri wire bis yofaq ce va. ufro zogad SemTx ve va Si, bendiq so nis krite ri u mis gamo ye ne biT, damt ki ce bu lia Sekru li integ ra lu ri wire bis arse bo bis Se saZleb lo ba, rome lic miu Ti Tebs im mosax le o bis gadar Ce na ze, ro melic imyo fe ba orm x ri vi asimi la ci is qveS.
78 Temur Chilachava, Tsira Gvinjilia
ABOUT SOME EXACT SOLUTIONS OF NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS DESCRIBING INTERFERENCE OF FUNDAMENTAL AND APPLIED REASERCHES
Introduction Mathematical and computer modeling has been widely recognized in such disciplines as sociology, history, political science, and others (Samarski, Mi- hailov, 2006; Chilachava, Dzidziguri, 2008). There is an interest in creation of a mathematical model, which would give the opportunity to determine the dynam- ics of changes in the number of voters of political subjects during the election period. Elections can be divided into two parts: the two-party and multi-party elections. In (Chilachava, Kereselidze, 2010; Chilachava, Kereselidze, 2009a; Chi- lachava, Kereselidze, 2009b) quantities of information streams by means of new mathematical models of information warfare are studied. By information warfare the authors mean an antagonism by means of mass media (an electronic and print- ing press, the Internet) between the two states or the two associations of states, or the economic structures (consortiums) conducting purposeful misinformation, propagation against each other. It has been shown that in case of high aggression of the contradictory coun- tries, not preventive image the operating peacekeeping organizations won’t be able to extinguish the expanding information warfare. In works (Chilachava, Kereselidze, 2011a; Chilachava, Kereselidze, 2011b) linear and nonlinear mathematical models of information warfare, and also opti- mizing problems are considered. In (Chilachava, Chakhvadze, 2014) the new nonlinear mathematical and computer model of information warfare with participation of interstate authorita- tive institutes is offered. The model is described by Cauchy’s problem for nonlin- ear non-homogeneous system of the differential equations. Confronting sides in extend of provocative statements, the third side (the peacekeeping international organizations) extends of soothing statements, interstate authoritative institutes the peacekeeping statements call the sides for the termination of information war- fare. In that specific case, modes of information warfare “aggressor- victim”, for the third peacekeeping side are received exact analytical solutions, and functions defining number of the provocative statements distributed by the antagonistic sides satisfy to Cauchy’s problems for Riccati certain equations which are solved by a numerical method. For the general model computer modeling is carried out 79 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV and shown that irrespective of high aggression of confronting sides, interstate au- thoritative institutes will be able to extinguish information warfare and when for this purpose efforts of only the international organizations insufficiently. The article (Kereselodze, 2016a; Kereselidze, 2016b) concerns of Chilker task is entered refers to the boundary value problem for a system of ordinary dif- ferential equations and optimal control problem. In Chilker tasks right boundary conditions are set in different, uncommitted time points for different coordinates of the unknown vector - functions. Proposed methods solutions of Chilker tasks. These papers (Chilachava, Dzidziguri,Sulava, Chakaberia, 2009; Chilacha- va, Sulava, Chakaberia, 2010; Chilachava,Sulava, 2013) present the nonlinear mathematical model of the public or the administrative management (or the mac- ro and micro model). The cases of both constant and variable pressure forces on freethinking people were analyzed. Exact analytical decisions which determine dynamics of a spirit both free-thinking people, and operated (conformists) of peo- ple by time are received. During this analyses various governance systems were considered: a liberal, democratic, semi dictatorial and dictatorial. These works (Chilachava, 2012a; Chilachava, 2012b; Chilachava, 2013; Chilachava, Chochua, 2013) considered a two or three-party (one pro-govern- ment and two opposition parties) nonlinear mathematical model of elections when coefficients are constant. The assumption was made that the number of voters remain the same between two consecutive elections (zero demographic factor of voters). The exact analytical solutions were received. The conditions under which opposition party can win the upcoming elections were established. These works (Chilachava,Sulava, 2015a; Sulava, 2015; Chilachava, Sulava, 2015b) considered a two-party (pro-government and opposition parties) nonlin- ear mathematical model of elections with variable coefficients. In work (Chilachava, Sulava, 2016) proposed the nonlinear mathematical model with variable coefficients in the case of three-party elections, that describes the dynamics of the quantitative change of the votes of the pro-government and two opposition parties from election to election. The model takes into account the change in the total number of voters in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. The model considered the cases with variable coefficients. In the particular case obtained exact analytical solutions. The conditions have been identified under which the opposition can win the forthcoming elections, and in some cases, the pro-government party can stay in power. In general Cauchy problem was solved numerically using the MATLAB software package. In (Chilachava, 2016) consider the nonlinear mathematical model of bilat- eral assimilation without demographic factor. It was shown that the most part of the population talking in the third language is assimilated by that widespread 80 Temur CilaCava, cira Rvinjilia language which speaks bigger number of people (linear assimilation). Also it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimi- lated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In (Chilachava, 2014) mathematical modeling of nonlinear process of as- similation taking into account demographic factor is offered. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coef- ficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are consid- ered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model “predator - the victim”, thus, naturally a role of the victim plays the population which has under- gone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation ofthe population of assimilators in an initial time point) to the population of the first assimilating side. In the second case the problem is actually reduced to nonlin- ear system of two differential equations describing type model “a predator _ the victim”, with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situa- tions, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the popula- tion of the assimilating states. In (Chilachava, Chakaberia, 2015) mathematical modeling of nonlinear pro- cess of the assimilation taking into account positive demographic factor which underwent bilateral assimilation of the side and zero demographic factor of the assimilating sides is considered. In model three objects are considered: the popu- lation and government institutions with widespread first language, influencing by means of state and administrative resources on the population of the third state 81 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV formation for the purpose of their assimilation; the population and government institutions with widespread second language, influencing by means of state and administrative resources on the population of the third state formation for the purpose of their assimilation; population of the third state formation which is exposed to bilateral assimilation from two powerful states or the coalitions. For nonlinear system of three differential equations of the first order are re- ceived the two first integral. Special cases of two powerful states assimilating the population of small state formation (autonomy), with different initial number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in all cases there is a full assimila- tion of the population to less widespread language. Thus, proportions in which assimilate the powerful states the population of small state formation are found. In (Chilachava, Chakaberia, 2016) the model it is supposed that the powerful state with a widespread state language carries out assimilation of the population of less powerful state and the third population talking in two languages, differ- ent in prevalence. Carries out assimilation of the population of the state formation with the least widespread language to the turn, less powerful state. Not triviality of model assumes negative demographic factor of the powerful state-assimilating and positive demographic factor of the state formation which is under bilateral assimila- tion. For some ratios between demographic factors of the sides and coefficients of assimilations, for nonlinear system of three differential equations with the corre- sponding conditions of Cauchy the first integrals are found. In particular, in the first case the first integral in space of required functions represents a hyperbolic parabo- loid, and in the second case _ a cone. In these cases, the nonlinear system of three differential equations is reduced to nonlinear system of two differential equations for which the second first integrals are found and in the phase plane of decisions are investigated behavior of integrated curves. In more general case with application of a criteria of Bendikson the possibility of existence of the closed integrated curves is proved that indicates a possibility of a survival of the population finding under double assimilation. One of the perspective and quickly field of application of mathematical mod- eling is dynamics of innovative processes. Researches in this area show that the crisis phenomena have not the casual, but systematic character defined by the determined mechanisms. Therefore many features of behavior of innovative pro- cesses can be described within the determined systems of the differential equa- tions. The difficult behavior of these systems, including self-organization pro- cesses, gives in to the description thanks to existence of the nonlinear members who are present at mathematical models of dynamic systems. Research of math- ematical models of innovative processes in scientific and educational areas is of a great interest (Chilachava, Dzidziguri, 2008). 82 Temur CilaCava, cira Rvinjilia
In (Chilachava, Gvinjilia, 2016a) work the nonlinear mathematical model of dynamics of processes of cooperation interaction in innovative system: fundamen- tal researches _ applied researches _ developmental works _ innovations is offered. In (Chilachava, Gvinjilia, 2016b) the new nonlinear mathematical model of interaction of fundamental and applied researches is considered.
I. Nonlinear system of differential equations and initial conditions
The nonlinear continuous mathematical model of interference of the funda- mental and applied researches conducted in one scientifically_ research institute has an appearance (micro-model):
du (t) du = α − β 2 + γ + δ − δ 1 (t)u 1 (t)u 12 (t)uv 1 (t) 2 (t) dtdt (1.1) dv (t) 2 = α 2 (t)v − β 2 (t)v + γ 21 (t)uv dtdt
u(0) = u0 , v(0) = v0 , (1.2)
u(t),v(t)- according to the number of fundamental and applied researches in time-point t; a1 (t), a2 (t)- respectively growth rates of number of fundamental and applied researches in time-point t; β1 (t), β2 (t) - respectively coefficients of super- saturation of number of fundamental and applied researches in time-point t;
γ 12 (t),), γγ 211221 (tt)), -γ respectively21 (t) coefficients of interference of fundamental and applied researches in time-point t; δ1 (t), δ2 (t) - according to the speed of inflow and outflow of fundamental researches to time-point t;
a1 (t), a2 (t), β1 (t), β2 (t), γ 12 (t),), γγ211221 ((tt),)), γδ121 (t(),t )δ2 (t) - positive functions on a segment t ∈[[0,0,TT],],u u(t(),t),v v((tt))∈C 1[0,[0,TT].].
II. Some special cases.
Let’s consider a special case
δ1 (t) = δ 2 (t), (2.1) α = α = > α = α = > 1 (t) 1 const 0, 2 (t) 2 const 0
β1 (t) = β1 = const > 0, β 2 (t) = β 2 = const > 0,
γ 12 (t) = γ 12 = const > 0,γ 21 (t) = γ 21 = const > 0. 83 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Then from (1.1), (1.2), (2.1) we will receive the following Cauchy’s problem for nonlinear system of the differential equations
du (t) du = α − β 2 + γ 1u(t) 1u (t) 12 u(t)v(t) dtdt (2.2) dvdv (t) 2 = α 2v(t) − β 2v (t) + γ 21 u(t)v(t) dtdt 21
u(0) = u0 , v(0) = v0 (2.3)
Let’s find the stationary nontrivial solution of system (2.2) which- corre sponds to performance of the following system
dudu (t) = 0 dtdt dvdv (t) = 0 dtdt Then from (2.2) we will receive non-homogeneous system of the linear alge- braic equations for (u,v) functions
− β1u + γ 12 v = −α1 12 (2.4) γ 21 u − β 2v = −α 2
According to Kramer’s formulas we will calculate the corresponding deter- minants
− β1γ 12 ∆ = = β1β 2 − γ 12 γ 21 γ 21 − β 2
−α1 γ 12 ∆1 = = α1β2 +α 2γ 12 > 0 (2.5) −α 2 − β2
− β1 −α1 ∆ 2 = = α 2 β1 + α1γ 21 > 0 γ 21 −α 2 84 Temur CilaCava, cira Rvinjilia
Then the solution of system (2.4) owing to (2.5) exists only when it is executed
− β1γ 12 ∆ = = β1β 2 − γ 12 γ 21 ≠ 0 γ 21 − β 2 and the stationary nontrivial decision of system (2.2) will register in the fol- lowing look
∆ ∆ u = 1 , v = 2 (2.6) stst ∆ st ∆ According to (2.5), (2.6) in order that this stationary solution was found in the first quarter of the phase plane (O,u,v) , performance of the following in- equality is necessary
∆ = β1β 2 − γ 12 γ 21 > 0 (2.7) Thus, when performing inequality on constant models (2.7), the system of the differential equations (2.2) has the nontrivial stationary decision in the first quarter (other quarters don’t make physical sense) the phase plane (O,u,v)
α1β 2 + α 2γ 12 α 2 β1 + α1γ 21 u = ust = , v = vst = (2.8) β1β 2 − γ 12 γ 21 β1β 2 − γ 12 γ 21
For a special case when conditions are satisfied ((2.7) in this case it isn’t satisfied)
α1 = α 2 , β1 = γ 21 , β 2 = γ 12 (2.9) Cauchy’s task (2.2), (2.3) is definitely decided analytically. Really, (2.2), (2.3), taking into account (2.9) will take a form
du (t) du = α − β 2 + β 1u(t) 1u (t) 2u(t)v(t) dtdt (2.10) dv (t) 2 = α1v(t) − β 2v (t) + β1u(t)v(t) dtdt
u(0) = u0 , v(0) = v0 Multiplying the first equation of system (2.10) onv (t), and the second on u(t), and then added the received expressions, we will receive the first integral of system (2.10)
2α1t u(t)v(t) = u0v0e (2.11) 85 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Substituting the first integral (2.11) in the first equation of system (2.10), for unknown function u(t) we will receive Ricatti’s equation
du (t) 2 2α1t = α1u(t) − β1u (t) + β 2u0v0e (2.12) dtdt It is known that generally in quadratures Ricatti’s equation isn’t solved as knowledge of one particular decision is necessary.
It is easily possible to check that the following function u1(t) is the particular decision equations (2.12). β 2u0v0 α1t u1 (t) = e (2.13) β1 Then entering the transformation canceling the non-homogeneous member in the equation (2.12)
u(t) = u1 (t) + z(t) (2.14) from (2.12) - (2.14) for function z(t) we will receive Bernoulli’s equation
dzdz (t) 2 = (α1 − 2β1u1 )z(t) − β1 z (t) (2.15) dtdt Entering transformation 1 y(t) = (2.16) z(t) for y(t) function we will receive the non-homogeneous linear equation of the first order dydy (t) = −(α1 − 2β1u1 )y(t) + β1 dt which common decision has an appearance
t t − (α −2β u (τ )) dτ t ∫ 1 1 1 ∫ (α1 −2β1u1 (τ )) dτ = 0 + β 0 τ y(t) e (c 1 ∫ e d ) (2.17) 0
Considering (2.10), (2.13), (1.16), (2.16) for y(t) function we will receive an initial condition 1 1 β v y(0) = = , u ≠ 2 0 0 β z(0) β 2u0v0 1 u0 − β1 86 Temur CilaCava, cira Rvinjilia
taking into account which we will receive the only decision for y(t) function t t − (α −2β u (τ )) dτ t ∫ 1 1 1 ∫ (α1 −2β1u1 (τ )) dτ = 0 + β 0 τ y(t) e (y(0) 1 ∫ e d ) (2.18) 0 Respectively, it agrees (2.11), (2.14), (2.16) we will define requiredu (t), v(t) functions Cauchy’s tasks (2.10)
t −1 α − β τ τ t t ∫ ( 1 2 1u1 ( )) d ∫ (α −2β u (τ )) dτ 1 1 1 β u v α t u(t) = e 0 y(0) + β e 0 dτ + 2 0 0 e 1 (2.19) 1 ∫ β 0 1
2α1t −1 v(t) = u0v0e u (t) From (2.19) it is possible to find an asymptotics of u(t), v(t) decisions at big times
β u v α t u(t) ≈ 2 0 0 e 1 , t → ∞ β1
β u v α t v(t) ≈ 1 0 0 e 1 , t → ∞ β 2 Let’s rewrite system of the equations (2.2) in a vector form
d w(t) = F, (2.20) dtdt
u(t) F1 w(t) = , F = , v(t) F2
where designations are entered 2 F1 (u,v) ≡ α1u(t) − β1u (t) + γ 12 u(t)v(t) (2.21) 2 F2 (u,v) ≡ α 2v(t) − β 2v (t) + γ 21 u(t)v(t) Theorem. When performing system of inequalities on constant models
γ 12 ≥ 2β 2 12 (2.22) γ 21 ≥ 2β1 in the first quarter of the (O,u,v) phase plane of solutions of a task of Cau- chy (2.2) there is no closed integrated curve entirely lying in this area. 87 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Proof. Let’s consider divergence of the vector field F ∂F ∂F divF = ∇i F = 1 + 2 = α − 2β u(t) + γ v(t) + α − 2β v(t) + γ u(t) i ∂u ∂v 1 1 12 2 2 21
divF = α1 + α 2 + (γ 1221 − 2β1 )u(t) + (γ 1221 − 2β 2 )v(t)
It is clear, that owing to inequalities (2.22), and also a natural assumption
α1 > 0,α 2 > 0 in the first quarter of the (O,u,v) phase plane of decisions
divF = α1 + α 2 + (γ 1221 − 2β1 )u(t) + (γ 1221 − 2β 2 )v(t) > 0 i.e. divergence of the F vector field doesn’t change a sign, and then owing to Bendikson’s criteria there is no closed integrated curve entirely lying in this area.
The theorem is proved. The offered nonlinear mathematical model allows to estimate influence of fundamental and applied researches (works) at each other, to find conditions on constant models in case of which there can be limited decisions, i.e. closed inte- gral curves in the first quadrant of the phase plane of decisions.
References: 1. Chilachava T.I., Dzidziguri Ts.D. Mathematical Modeling. Tbilisi, Inovacia, 2008 (Georgian). 2. Chilachava T.I., Kereselidze N.G. Non-Preventive Continuous Linear Math- ematical Model of Information Warfare. Sokhumi State University Proceed- ings, Mathematics and Computer Sciences, 2009a, #VII, pp. 91-112. 3. Chilachava T.I., Kereselidze N.G. Continuous Linear Mathematical Model of Preventive Information Warfare. Sokhumi State University Proceedings, Mathematics and Computer Sciences, 2009b, # VII, pp. 113-141. 4. Chilachava T. I., Dzidziguri Ts. D., Sulava L.O., Chakaberia M.R. Nonlinear Mathematical Model of Administrative Management. Sokhumi State Uni- versity Proceedings, Mathematics and Computer Sciences, vol. VII, 2009, pp.169-180 (Georgian). 5. Chilachava T.I., Kereselidze N.G. Mathematical Modeling of the Informa- tion Warfare. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2010, # 1 (24), pp.78-105 (Georgian). 6. Chilachava T.I., Sulava L.O., Chakaberia M.R. On Some Nonlinear Mathemat- ical Model of Administration. Problems of Security Management of Complex 88 Temur CilaCava, cira Rvinjilia
Systems. Proceedings of the XVIII International Conference, Moscow, 2010, pp. 492-496 (Russian). 7. Chilachava T.I., Kereselidze N.G. Optimizing Problem of Mathematical Model of Preventive Information Warfare, Informational and Communication Technologies _ Theory and Practice: Proceedings of the International Scien- tific Conference ICTMC- 2010 USA, Imprint: Nova, 2011a, pp. 525-529. 8. ChilachavaT.I., Kereselidze N.G. Mathematical Modeling of Information Warfare. Information warfare, 2011b, #1(17), стр. 28-35 (Russian). 9. Chilachava T.I. Nonlinear Mathematical Model of the Dynamics of the Vot- ers Pro-Government and Opposition Parties (The Two Election Subjects) Basic Paradigms in Science and Technology. Development for the XXI Cen- tury. Transactions II. 2012b, pp. 184-188 (Russian). 10. Chilachava T.I Nonlinear Mathematical Model of the Dynamics of the Voters Pro-Government and Opposition Parties. Problems of Security Management of Complex Systems. Proceedings of the XX International Conference, Mos- cow, 2012, pp. 322-324 (Russian). 11. Chilachava T.I. Nonlinear Mathematical Model of Dynamics of Voters of Two Political Subjects. Seminar of the Institute of Applied Mathematics Named I. Vekua Reports, 2013, vol. 39, pp. 13-22. 12. Chilachava T.I. Nonlinear Mathematical Model of Three-Party Elections. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013, pp. 513-516. 13. Chilachava T. I., Chochua Sh. G. Nonlinear Mathematical Model of Two- Party Elections in the Presence of Election Fraud. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013, pp. 349- 352 (Russian). 14. ChilachavaT.I., Sulava L.O.A Nonlinear Mathematical Model of Manage- ment. Georgian Electronic Scientific Journal: Computer Science and Tele- communications, 2013, #1(37) pp. 60- 64 (Russian). 15. Chilachava T.I., Chakhvadze A. Continuous Nonlinear Mathematical and Computer Model of Information Warfare with Participation of Authoritative Interstate Institutes. Georgian Electronic Scientific Journal: Computer Sci- ence and Telecommunications, 2014, # 4(44), pp. 53-74. 16. Chilachava T.I. Nonlinear Mathematical Model of Bilateral Assimilation Georgian Electronic Scientific Journal: Computer Science and Telecommu- nications, 2014, #1(41), pp. 61-67. 17. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Process of Assimilation Taking into Account Demographic Factor. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2014, # 4 (44), pg.35-43. 89 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
18. Chilachava T.I.,Sulava L.O. Mathematical and Computer Modeling of Nonlinear Processes of Elections with Two Selective Subjects. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2015a, # 2(46), pp. 61-78. 19. Chilachava T.I., Sulava L.O. Mathematical and Computer Simulation of Pro- cesses of Elections with Two Selective Subjects and Float Factors of Model. Problems of Security Management of DifficultS ystems. Works XXIII of the International Conference, Moscow, 2015b, p. 356-359 (Russian). 20. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Pro- cesses Bilateral Assimilation, Georgian Electronic Scientific Journal: Com- puter Science and Telecommunications, 2015, # 2(46), pg. 79-85. 21. Chilachava T.I., Sulava L.O. Mathematical and Computer Modeling of Three-Party Elections.GESJ: Computer Sciences and Telecommunications, 2016, # 2 (48), pp. 59-72. 22. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Pro- cesses of Two-Level Assimilation, Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2016, # 3(49), pg. 34-48. 23. Chilachava T., Gvinjilia Ts. Nonlinear Mathematical Model of Dynamics of Processes of Cooperation Interaction in Innovative System.VII International Conference of the Georgian Mathematical Union, Book of Abstracts, Ba- tumi, 2016a, pp. 104-105. 24. Chilachava T., Gvinjilia Ts. Nonlinear Mathematical Model of Interaction of Fundamental and Applied Researches, Problems of Security Management of DifficultS ystems.Works XXIV of the International Conference, Moscow, 2016b, pp. 289-292 (Russian). 25. Kereselidze N. An Optimal Control Problem in Mathematical and Com- puter Models of the Information Warfare. Differential and Difference Equa- tions with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. Springer Proceedings in Mathematics & Statistics, 164, DOI 10.1007/978-3-319-32857-7-28, Springer International Publishing Switzer- land 2016a, pp. 303 - 311. 26. Kereselidze N.G. Chilker’s Type Mathematical and Computer Models in the Information Warfare. Information Warfare, 2016b, # 2 (38), pp. 28-35 (Russian). 27. Samarski A.A., Mihailov A.P. Mathematical Modeling. Moskow, Fizmatlit, 2006 (Russian). 28. Sulava L.O. Mathematical and Computer Modeling of Nonlinear Processes of Elections.Works of the International Conference “Information and Com- puter Technologies, Modelling, Management” Devoted to the 85 Anniversary Since the Birth of I. V. Prangishvili, Tbilisi, 2015, by p. 387-390 (Russian). 90 Temur CilaCava, cira Rvinjilia
Temur CilaCava, cira Rvinjilia
fundamenturi da gamoyenebiTi kvlevebis urTierTgavlenis aRmweri arawrfivi diferencialuri gantolebaTa sistemis zogierTi zusti amonaxsnis Sesaxeb
reziume
naSrom Si ganxi lu lia axali arawr fi vi uwyve ti maTe ma ti ku ri mode li funda men tu ri da gamo ye ne bi Ti kvleve bis urTi er T gavle ni sa erT, SesaZ lo gare momx ma reb li sa gan daxu ruli samec nie ro- k v le vi Ti ins ti tu tis maga liT ze (mikro mo de li). kerZo Sem Txve va Si, koSis amoca na pirve li rigis arawr fi vi dife ren ci a lu ri ganto le ba Ta siste mi saT vis, amoxs ni lia anali zu rad zustad. ufro zogad SemTx ve va Si, bendiq so nis krite ri u mis safuZ vel ze, damt ki ce bu lia Teo re ma amonax s n Ta fazu ri sibr tyis pirvel me oTxedSi Sekru li integ ra lu ri wire bis ar arse bo bis Sesa xeb. na povnia piro be bi mode lis para met re bi saT vis, romel TaT vis SesaZ lebe lia arawr fi vi dife ren ci a lu ri ganto le ba Ta siste mis Semo sazRv ru li amonax s ne bis arse bo ba.
91 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
maTematikuri da kompiuteruli modelireba MATHEMATICAL AND COMPUTER MODELING nugzar kereseliZe
informaciuli omis gaerTianebuli maTematikuri da kompiuteruli modelebi
Sesavali. informaciuli omis warmoebis mravalferovan saxeo- baTa Soris Cven yuradRebas ipyrobs mowinaaRmdegeTa dapirispire- ba sainformacio velSi: rodesac mxareebi sargebloben magaliTad, informaciis masobrivi gavrcelebis saSualebebiT da maTi meSveo- biT cdiloben mowinaaRmdegis dezinformacias, kompromentirebas Tu sxva. am mimarTulebiT informaciuli omis warmoebis mizne- bi da saSualebebi dawvrilebiT aRwerilia naSromebSi (Chilachava, Kereselidze, 2010; Kereselidze, 2012) informaciuli omis aRniSnul mi- marTulebas SeiZleba vuwodoT informaciuli dapirispireba, ma- gram simartivisTvis momavalSi informaciuli omis am mimarTule- bas movixseniebT ubralod informaciul omad. informaciuli omis Seswavla maTematikuri meTodebiT sakmaod produqtiulia da mas msoflios sxvadasxva qveynebSi warmatebiT axorcieleben. SemuSavebulia araerTi maTematikuri da kompiu- teruli modeli, romelic iTvaliswinebs informaciuli omis mi- mdinareobas sxvadasxva reJimebis pirobebSi: SezRudulobas in- formaciis gavrcelebaze, uwyvetobas, diskretulobas da sxva. modelebSi ZiriTadad gamoyofilia ori Sesaswavli obieqti. pir- veli - Tavad informacia, romelsac nakadis saxiT avrcelebs mxa- re da dapirispirebuli mxaris diskretidaciisTvis aris gamiznuli. meore - adamianTa is raodenoba, romlebmac miiRes, gaecnen mxaris mier gavrcelebul informacias. amasTan aRsaniSnavia, rom am dromde SemuSavebuli modelebi ZiriTadad ganixilavdnen an mxolod infor- maciis nakadebis raodenobas, anac mxolod im adamianebis raodenobas, romelTac aRiqves es informaciebi. warmodgenil naSromSi SemoTava- zebulia mcdeloba am ori midgomis gaerTianebisa, romlis Sedegadac vRebulobT axali tipis maTematikur da kompiuterul modelebs. sanam warmodgenili iqneba informaciuli omis am ori tradi- ciuli modelebis gaerTianebis Sedegebi, gavecnoT maT calcalke. 1. informaciuli omis nakadebis maTematikuri da kompiuteru- li modelebi. informaciul omSi nakadebis maTematikuri modeli- 92 nugzar kereseliZe reba saTaves iTvlis 2009 wlidan, qarTveli mecnieris, profesor Temur CilaCavas originaluri ideis damuSavebidan, da romlis pirveli Sedegebi moxsenebul iqna imave wels, saqarTvelos ma- TematikosTa mexuTe kongresze (Chilachava, Kereselidze, 2009a) da daibeWda soxumis saxelmwifo universitetis SromebSi (Chilachava, Kereselidze, 2009b), (Chilachava, Kereselidze, 2009c). Cven aq moviyvanT zogad wrfiv models, aseve arawrfiv models SezRudvebiT (Kere- selidze, 2017). ganvixiloT informaciuli omis maTematikuri da kompiuteru- li modelebi, romlebSic saZebn sidideebad miCneulia ori anta- gonisturi mxaris mier gavrcelebuli maprovocirebeli informa- ciebis raodenobebi da mesame, mSvidobismyofeli mxaris mier ga- vrcelebuli samSvidobo mowodebebis raodenoba. informaciuli omis procesSi CarTuli samive mxare avrcelebs informacias Ta- visi miznis misaRwevad. drois t ∈[0; +∞) momentSi TiToeuli mxa- ris mier gavrcelebuli informaciis raodenoba aRvniSnoT Sesaba- misad Nt1 ( ), Nt2 ( ), Nt3 ( ) -Ti. informaciis raodenoba drois t mo- mentSi, gamoiTvleba, rogorc jami, Sesabamisi mxaris, nebismieri maprovocirebuli informaciis raodenobisa, romelic gavrcele- bulia masobrivi informaciis yvelanairi saSualebis mier. amas-
Tan, dapirispirebuli mxareebi Sesabamisad avrceleben Nt1 ( ) da Nt2 ( ) raodenobis informacias. mesame - mSvidobismyofeli mxare mouwodebs dapirispirebul mxareebs Sewyviton informaciuli omi, risTvisac avrcelebs Sesabamis, Nt3 ( ) raodenobis informa- cias. radganac dapirispirebuli mxaris mizania moaxdinos mis me- toqeze informaciuli zemoqmedeba, igi cdilobs gaavrcelos rac SeiZleba meti madiskreditirebuli informacia mowinaaRmdegeze. amasTan adre gamoyenebuli informaciis Tavidan gavrceleba da- saSvebia da amasTan mas emateba axali dezinformacia. amdenad, da- pirispirebuli mxaris mier informaciis gavrcelebis siCqare da- mokidebulia ukve gavrcelebuli informaciis raodenobazec: dNdN1 (1 t() t) dNdN2 2( t() t) �~�ααNtNt(()) �~� ββNt22Nt(()) . garda amisa dapirispirebuli dtdt 1111 dtdt 22 mxare reagirebs mowinaaRmdege da mSvidobismyofeli mxareebis mier gavrcelebul informaciebis raodenobaze. amdenad, dapirispire- buli mxaris mier informaciis gavrcelebis siCqare damokidebulia dNdN( t t) dNdN( t() t) aseve: 11( ) ~ 2 2 ~ . ��((αααα22NtNt(( ))−− 33 Nt Nt(( )))),, � �(ββ(11ββNt11Nt( () −) − 33 Nt 33 Nt( ()))) dtdt 22 33 dtdt
93 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV mesame, mSvidobismyofeli mxaris mier gavrcelebuli informaciis intensiuroba damokidebulia ara marto mis mier gavrcelebul in- formaciis raodenobaze, aramed imazec, Tu ramdenad mZafrad mim- dinareobs informaciuli omi, anu, Tu ra raodenobis informacias avrceleben dapirispirebuli mxareebi. am mosazrebebis gaTvaliswi- nebiT SegviZlia ganvixiloT informaciuli omis zogadi wrfivi uwyveti maTematikuri modeli:
dN1 ( t) =+−αα11Nt( ) 2 Nt 2( ) α 33 Nt( ), dt dN2 ( t) =+−ββ11Nt( ) 2 Nt 2( ) β 33 Nt( ), (1.1) dt
dN3 ( t) =++γγ11Nt( ) 2 Nt 2( ) γ 33 Nt( ), dt sawyisi pirobebiT
N1 (0) = N10 , N 2 ( 0) = NN20 ,0 3 ( ) = N30 (1.2)
sadac αα1323,,, β β≥ 0, γ i ≥ 0 i =1, 3 , αβ21, , - mudmivi sididee- bia. am mudmiv sidideebs vuwodoT modelis koeficientebi. zogad wrfiv (1.1) modelSi pirveli da meore mxareebis mier gavrcelebuli informaciis raodenobis cvlilebis siCqare wrfi- vadaa damokidebuli mxareebis da saerTaSoriso - mSvidobismyofe- li organizaciebis mier gavrcelebuli informaciis raodenobaze. mesame - saerTaSoriso organizaciebis mier gavrcelebuli da- mamSvidebeli informaciis raodenobis cvlilebis siCqare wrfi- vad izrdeba anu pirdapirproporciulia samive mxaris mier gavr- celebuli informaciis raodenobisa. sawyis (1.2) pirobebSi N10 ,
N20 , N30 arauaryofiTi mudmivi sididebia. mesame mxare Tavidan ar avrcelebs informacias ( N30 = 0 ) an akeTebs prevenciuli xasiaTis Semrigebel gancxadebebs ( N30 > 0 ) da Semdeg iwyebs reagirebas mxareebis mier gavrcelebul mapro- vocirebel informaciaze. pirvelad informaciuli omis maTematikuri da kompiuteruli modelebi, informaciuli teqnologiebis SesaZleblobebis gaT- valiswinebiT SemoTavazebuli iqna 2012 wels (Kereselidze, 2012a), (Kereselidze, 2012b), da ganzogadda mogvianebiT (Kereselidze, 2017):
94 nugzar kereseliZe
d xt( ) xt( ) =αβ11 xt( )1 −−zt( ) dt I1 d yt() yt( ) =αβ22 yt( )1 −−zt( ) (1.3) dt I2 d zt() zt( ) =+−(γγ xt( ) y( t))1 1 22 dt I3
x(0) = x0 , y(0) = y0 , z(0) = z0 (1.4) sadac, x(t), y(t) dapirispirebuli mxareebis mier Sesabamisad ga- vrcelebuli informaciebis raodenobaa drois t momentSi, ana- logiurad, Z0 mSvidobismyofeli _ mesame mxaris mier gavrcele- buli informacia drois imave t momentSi. αα12, aris Sesabamisad pirveli da meore dapirispirebuli mxareebis agresiulobis koe- ficientebi, ββ12, _ Sesabamisad dapirispirebuli mxareebis sam-
Svidobo mzadyofnis parametrebi, γγ12, _ mesame mxaris samSvido- bo aqtiurobis indeqsi Sesabamis dapirispirebuli mxaris mimarT.
Iii ,= 1,2,3 _ Sesabamisad aris pirveli, meore da mesame mxa- reebis mier teqnologiuri SesaZleblobebiT maqsimaluri raode- nobis informacia. x(t), y(t), z(t) funqciebi gansazRvrulia drois [0,∞) monakveTze. dapi ris pi re bu li mxare infor ma ci is gavr ce le bis siCqa res am cirebs imis da mixed viT, Tu rogor axlos imyo feba mis mier dro is momen t Si gav r ce le bu li infor ma ci is rao de no ba misT vis maqsi malu rad dasaS ve bi gasav r ce le be li infor ma ci is rao de no bas Tan. infor ma ci u li omis naka de bis garda moyva ni li maTe ma ti ku ri mode le bi sa, Semu Sa ve bu lia mowi na aR m de gis igno ri re bis wrfivi uwyve ti da disk re tu li mode le bi; arawr fi vi uwyve ti da wrfi vi disk re tu li mode le bi avto ri te tu li orga ni za ci e bis an ins titu te bis (reli gi u ri, arasam Tav ro bo, samec ni e ro, poli ti ku ri da sxva) gaTva lis wi ne biT (Chilachava, Chakhvadze, 2014a),(Chilachava, Chakhvadze, 2014b). 2. infor ma ci u li naka de bis gavr ce le bis maTe ma ti ku ri mode le bi. informaciis gavrcelebis yuradsaRebi maTematikuri modelia ganxiluli klasikur naSromSi maTematikuri modelirebis ganxriT a.a samarskisa da a.p. mixailovis avtorobiT (Samarskiy, Mihailov, 2005). SemoTavazebulia sareklamo kampaniis organizebis maTematikuri modeli, rac modelis universalobis principis safuZvelze,
95 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
SeiZleba gamoyenebul iqnes informaciuli omis maTematikuri mo- delirebaSi. Tumca am modelSi uSualod ara gakeTebuli aqcenti informaciul nakadebze, arsebiTad ganixileba informaciis mimRe- bebis - informirebuli personebis raodenobis cvalebadoba. ker- Zod, ganxilulia Semdegi modeli: vTqvaT Nt( ) aris nivTis Sesaxeb informirebuli momxmareblebis raodenoba, N0 - potencialuri momxmareblebis saerTo raodenoba, α1 (t) - sareklamo kampaniis in- tensiuroba, α2 (t) - reklamis intensiuroba im momxmareblebis dN( t) mxridan, romlebmac ician nivTis Sesaxeb, aris informire- dt buli momxmareblebis raodenobis cvlilebis siCqare, romelic bunebrivia damokidebulia arainformirebil momxmarebelTa ricx- vze da sareklamo kampaniis intensiurobaze. amitomac miviRebT Se- mdegi saxis samarski-mixailovis maTematikur models: dN( t) =+−[αα(t) ( tNt) ( ) ].( N Nt( )) (2.1) dt 12 0 ganvixiloT (2.1) modelis dasabuTeba ufro dawvrilebiT. re- klama, rogorc informacia vrceldeba ori gziT: erTi uSualod sareklamo kampaniis saSualebiT, magaliTad masmediiT, rodesac am gziT, informirebuli mosaxleobis gazrdis siswrafe propor- ciulia jer kidev arainformirebuli mosaxleobis raodenobisa
- α10(t)( N− Nt( )) da meore, reklamis Sesaxeb informirebuli pi- rovneba amis Sesaxeb uambobs Tavis nacnobebs da ase xdebian re- klamis gamavrcelebelni am gziT, informirebuli mosaxleobis ga- zrdis siswrafe proporciulia jer kidev arainformirebuli mo- saxleobis raodenobisa _ α20(t)( N− Nt( )) , faqtiurad reklamis gavrceleba xdeba pirovnebaTaSorisi urTierTobebiT. rodesac am ori gziT reklamis gavrcelebis siswrafeebs SevkrebT, miviRe- bT reklamis erTiani gavrcelebis siswrafis models. gantoleba (2.1)-Si sawyis pirobad miviRebT, drois dasawyisSi reklamiT in- formirebuli pirovnebebis raodenobis nulTan toloba:
Nt( ) |0t=0 = (2.2) (2.1), (2.2) modelebs maTi erT-erTi avtori _ mixailovi a.p. droTa ganmavlobaSi saxelebs ucvlida. Tavidan akademikos sa- marskisTan TanaavtorobiT 1997 wels gamoqveynebul monografia- Si models erqva sareklamo kampaniis modeli, Semdeg, 2002 wli- dan, mas daerqva informaciuli safrTxis modeli (Marevtseva, 2011), 96 nugzar kereseliZe
2004 wlidan _ informaciis gavrcelebis modeli (Mihailov, 2004), 2009 wlidan informaciuli dapirispirebis modeli (Marevtseva, 2009), 2011 wels _ informaciuli omis modeli (Chilachava, Kereseli- dze, 2009b), 2015 wels _ informaciulis Setevis da orTabrZolis modeli (Mihailov, Petrov, Proncheva, Marevtseva, 2015), (Mikhailov, Petrov, Proncheva, 2015). (2.1), (2.2) modelis variaciiT a.p. mixailovi da misi Tanaavto- rebi qmnian informaciis gavrcelebis sxvadasxva modelebs, ase magaliTad modelebs: informaciis daviwyebiT, informaciuli or- TabrZolis da sxva. 3. informaciuli omis informaciuli nakadebisa da informaciis gavrcelebis integrirebuli maTematikuri da kompiuteruli mode- lebi. informaciuli omis integrirebuli maTematikuri modele- bisTvis SemovitanoT Sesabamisi aRniSvnebi arsebuli tradiciis gaTvaliswinebiT. kerZod, drois t ∈[0; +∞) momentSi TiToeuli mxaris mier gavrcelebuli informaciis raodenoba aRvniSnoT Se- sabamisad Nt10 ( ), Nt20 ( ), Nt3 ( ) -Ti. informaciis raodenoba drois t momentSi, gamoiTvleba, rogorc jami, Sesabamisi mxaris, nebis- mieri maprovocirebuli informaciis raodenobisa, romlebic ga- vrcelebulia masobrivi informaciis yvelanairi saSualebis mier. amasTan, dapirispirebuli mxareebi Sesabamisad avrceleben Nt10 ( ) da Nt20 ( ) raodenobis informacias. mesame _ mSvidobismyofeli mxare mouwodebs dapirispirebul mxareebs Sewyviton informaciu- li omi, risTvisac avrcelebs Sesabamis, Nt3 ( ) raodenobis infor- macias. vuwodoT am SemTxvevaSi Nt10 ( ), Nt20 ( ), Nt3 ( ) -s Sesabamisi mxareebis mier `oficialurad~ gavrcelebuli informaciis rao- denobebi. maSin (1.3), (1.4) modeli miiRebs saxes: d Nt10 ( ) Nt10( ) =αβ 1 Nt 10 ( )1 −−1Nt 3 ( ) dt I1 d Nt20 ( ) Nt20 ( ) =αβ2 Nt 20 ( )1 −−2Nt 3 ( ) (3.1) dt I2 d Nt( ) Nt( ) =+−(γγ N( t) N( t))1 3 3 1 10 2 20 dt I3
sawyisi pirobebiT = Nn10(0) 10 , Nn20 (0) = 20 , Nn3(0) = 30 (3.2) 97 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
vTqvaT pirveli mxare warmoadgens mosaxleobas, romlis maq- simaluri mniSvnelobaa xp . analogiurad, meore mxare warmoadgens mosaxleobas, romlis maqsimaluri mniSvnelobaa . aRvniSnoT xt1 ( ) y p -iT pirveli mxaris mosaxleobis is raodenoba, romlebmac drois t ∈[0; +∞) momentSi `miiRes~ pirveli mxaris mier oficialurad ga- vrcelebuli informacia, gaxdnen misi adeptebi da Tavad pirovne- baTaSoriso urTierTobiT an sxva saSualebiT avrceleben pirveli mxaris sasargeblo informacias raodenobiT - Nt11 ( ) . aseve aRvniS- noT xt2 ( ) -iT pirveli mxaris mosaxleobis is raodenoba, romelmac drois t ∈[0; +∞) momentSi `miiRes~ meore mxaris mier oficialu- rad gavrcelebuli informacia, gaxdnen misi adeptebi da Tavad pirovnebaTaSoriso urTierTobiT an sxva saSualebiT avrceleben meore mxaris sasargeblo informacias raodenobiT - Nt12 ( ) . analo- giurad Semogvaqvs aRvniSnebi meore mxaris mosaxleobisTvis: aR- vniSnoT yt1 ( ) -iT meore mxaris mosaxleobis is raodenoba, romel- mac drois t ∈[0; +∞) momentSi `miiRo~ pirveli mxaris mier ofi- cialurad gavrcelebuli informacia, gaxda misi adepti da Tavad pirovnebaTaSoriso urTierTobiT an sxva saSualebiT avrceleben pirveli mxaris sasargeblo informacias raodenobiT - Nt21 ( ) . aseve aRvniSnoT yt2 ( ) -iT pirveli mxaris mosaxleobis is raodenoba, ro- melmac drois t ∈[0; +∞) momentSi `miiRo~ meore mxaris mier ofi- cialurad gavrcelebuli informacia, gaxda misi adepti da Tavad pirovnebaTaSoriso urTierTobiTan sxva saSualebiT avrceleben meore mxaris sasargeblo informacias raodenobiT - Nt22 ( ) . Nt11 ( ) informaciis gavrcelebis siqCare bunebrivia damokide- bulia xt1 ( ) adeptebisa da am informaciisgan Tavisufali mosaxe- leobis Sexvedraze, kerZod xt11( )( xp − xt( )) -ze. garda amisa, Tu ki adepti avrcelebs informacias pirovnebaTaSorisi urTierTobis gareSe, vTqvaT socialuri qselebiT, an sakuTari veb-saSualebe- biT, maSin damatebiT unda ganvixiloT am adeptis I4 informa- ciuli teqnologiebis maqsimaluri SesaZleblobebi. amasTan bune- brivia, rom im mxaris `oficialuri~ aqtiuroba, romlis adeptsac ganvixilavT, zemoqmedebas axdens Sesabamisad adeptis aqtiuroba- ze. maSasadame gvaqvs Semdegi Tanafardoba:
dN11 ( t) =αα11N 11 ( t)( xp − xt1( )) xt 1( ) +− 12 N 10( I 4 N 11 ( t)) (3.3) dt sawyisi pirobiT:
N11 (00) = (3.4) 98 nugzar kereseliZe
analogiuri msjelobiT SegviZlia SevadginoT Tanafardobebi Nt, 12 ( ) Nt21 ( ), Nt22 ( ) -sTvis. sadac III567,,-iT aRvniSnoT Sesabamisi xtytyt212( ),,( ) ( ) adeptebis informaciuli teqnologiebis maqsima- luri SesaZlebloba.
rac Seexeba adeptebs xtxtytyt1212( ),,,( ) ( ) ( ) , maTTvis Tanafardo- bebi samarski-mixailovis modelidan gamomdinareobs. sadac inten- siuri sareklamo kampania warmodgenilia αijNt0 ( ) -is saxiT sadac ij=3, 5, 7 . = 1, 2 . , xolo adeptis mier informaciis gavrcelebis iten- siuroba Sefasebulia rogorc αkNt ls ( ) , sadac k= 4,6,8,10.ls ,= 1,2. Sedegad vRebulobT informaciuli omis integrirebul maTema- tikur models SezRudvebiT:
d Nt10 ( ) Nt10( ) =αβ 1 Nt 10 ( )1, −−1Nt 3 ( ) dt I1 d Nt( ) Nt( ) =αβ Nt( )1, −−20 Nt( ) dt 20 2 20 I 2 3 2
d Nt3 ( ) Nt3 ( ) =+−(γγ1 N 10( t) 2 N 20 ( t))1 dt I3 dx1 ( t) =+−(αα3N 10( t) 4 N 11( txt) 1 ( ))( xp xt1 ( )), dt dx2 ( t) =+−(αα5N 20( t) 6 N 12( txt) 2 ( ))( xp xt2 ( )), dt dy1 ( t) (3.5). =+−(αα7N 10( t) 8 N 21( tyt) 1 ( ))( yp yt1 ( )), dt
dy2 ( t) = (αα9N 20( t) +− 10 N 22( tyt) 2 ( ))( yp yt2 ( )), dt dN11 ( t) =αα11N 11 ( t)( xp −+ xt1( )) xt 1( ) 12 N 10( t)( I 1 − N 11 ( t)), dt dN12 ( t) =αα13N 12 ( tx)( p −+ xtxt2( )) 2( ) 14 N 20( tI)( 2 − N 12 ( t)), dt dN21 ( t) =αα15N 21 ( t)( yp −+ yt1( )) yt 1( ) 16 N 10( t)( I 1 − N 21 ( t)), dt dN22 ( t) =αα17Ntyytyt 22 ( )( p −+2( )) 2( ) 18 NtINt 20( )( 2 − 22 ( )). dt sawyisi pirobebiT:
99 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
N10(0) = nN 10 , 20 ( 0) = nN20 ,0 3( ) = n 30 , NNNN11(0,) 12( 0,) 21( 0,) 22 ( 0) 0, (3.6). xx1212(0,) ( 0,) yy( 0,) ( 0) 0. amdenad, miviReT informaciuli omis integrirebuli maTema- tikuri modeli SezRudvebiT, romelic aRiwereba Cveulebrivi diferencialur gantolebaTa sistemiT (3.5), romelSic TerTmeti saZiebeli funqciaa da gvaqvs TerTmeti sawyisi piroba mocemu- li (3.6)-Si. SevniSnoT, rom (3.5), (3.6) koSis amocanaSi (3.5) siste- mis marjvena mxaris Tvisebebi gvaZlevs imis safuZvels, rom da- vaskvnad _ mocemul koSis amocanas gaaCnia erTaderTi amonaxsni drois t ∈[0; +∞) monakveTze. amdenad pirveli mxarisTvis sasargeblo informaciis raode- noba Nt1 ( ) warmoadgens jams pirveli mxaris mier `oficialurad~ gavrcelebuli informaciisa, pirveli mxaris mosaxleobaSi pir- veli mxaris adeptebisa da meore mxaris mosaxleobaSi pirveli mxaris sasargeblo, adeptebis mier gavrcelebuli informaciisa -
NtNtNtNt1 ( ) =++10( ) 11( ) 21 ( ), (3.7) xolo meore mxarisTvis sasargeblo informaciis raodenoba -
Nt2 ( ) , warmoadgens Semdeg jams:
NtNt2 ( ) =++20( ) Nt 12( ) Nt 22 ( ), (3.8) mesame mxaris zemoqmedeba cxadi saxiT xorcieldeba mxolod
N10( tN), 20 ( t) informaciul nakadebze da maTi saSualebiT ki es zemoqmedeba xorcieldeba N11( tN),, 21 ( t) N21( tN), 22 ( t) nakadebze. am- denad bunebrivia daisvas sakiTxi, SesaZlebelia, Tu ara, rom me- same mxaris aqtiurobiT moxerxdes informaciuli omis Cacxroba, anu drois romelime, zogadad sxvadasxva momentebSi NtNt12( ), ( ) gaxdnen nulis tolni:
* ** N1(t )=0, N2(t )=0 (3.9) (3.5),(3.6),(3.9) sasazRvro amocanas imis gamo, rom marjvena mxa- risTvis pirobebi specifiuria, kerZod is, rom NtNt12( ), ( ) funq- ciebi nulze gadian zogadad sxvadasxva droSi, Tanac es droebi dafiqsirebulni ar arian, vuwodoT Cilkeris tipis amocana. (3.5),(3.6) modelSi adeptebis gavrcelebul informaciul nakadebSi dapirispirebuli mxareebis `oficialuri~ informaciuli nakadebi 100 nugzar kereseliZe monawileoben, piriqiT ki ar xdeba, Tumca es SesaZlebelia. amitom bunebrivia, rom N10( tN), 20 ( t) informaciuli nakadebis siCqaris Ta- nafardobebSi CarTuli iqnen adeptebis mier gavrcelebuli in- formaciebi: N11( tN),,, 21( tN) 21( tN) 22 ( t) . es SemTxveva ganixileba sxva modelebSi. 4. informaciuli omis mowinaaRmdegis ignorirebis gaerTiane- buli maTematikuri da kompiuteruli modelebi. ganvixiloT in- formaciuli omis integrirebuli maTematikuri da kompiuteruli modelebis modeluri amocana, anu ganvixiloT modelis gamarti- vebuli SemTxveva. amisTvis informaciuli nakadebisTvis aviRoT mowinaaRmdegis ignorirebis modeli d =αβ − Nt10( ) 1 Nt 10( ) 1 Nt 3 ( ), dt d Nt20( ) =αβ 2 Nt 20( ) − 2 Nt 3 ( ), (4.1) dt d Nt3( ) =γγ 1 N 10( t) + 2 N 20 ( t). dt (3.2) sawyisi pirobebiT. xolo samarski-mixailovis modelSi mxareebisa da adeptebis aqtiobis intensioba gamovsaxoT wrfivi saxiT, amasTan CavTva- loT, rom ganvixilavT mxolod xt12( ), yt( ) adeptebs, romlebic Sesabamisad mxolod N10( tN), 20 ( t) -mxareebis mier gavrcelebul informaciis TanafardobebSi monawileoben. CavTvaloT, rom x12( t) = xt( ), y( t) = yt( ) . Sedegad miviRebT informaciuli omis im in- tegrirebul maTematikur models, romelic Camoyalibda soxumis saxelmwifo universitetis maTematikisa da kompiuterul mecnie- rebaTa fakultetze profesor T. CilaCavasTan diskusiis Sedegad 2017 wlis gazafxulze, da romelsac aqvs Semdegi saxe:
d Nt10( ) =αβ 1 Nt 10( ) +− vxt 1 ( ) 1 Nt 3 ( ), dt d Nt20( ) =αβ 2 Ntvyt 20( ) +− 2 ( ) 2 Nt 3 ( ), dt d (4.2) Nt3( ) =γγ 1 N 10( t) + 2 N 20 ( t) dt dx( t) =+−(αγ33xt( ))( xp xt( )), dt dy( t) =+−(αγ44yt( ))( yp yt( )). dt 101 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
sawyisi pirobebiT
N10(0) = nN 10 , 20 ( 0) = nN20 ,0 3( ) = n 30 , (4.3) xy(0) =( 0) = 0. Tu ki davuSvebT, rom αααβββγγ1= 2 =; 12 = = ;; 12 = = γααδγγ 3 = 4 = ;, 34 = = µ αααβββγγ1= 2 =; 12 = = ;; 12 = = γααδγγ 3 = 4 = ;, 34 = = µvvv12= = . maSin (4.2) miiRebs saxes: d Nt10 ( ) =αβ Nt10 ( ) +− vxt( ) Nt3 ( ), dt d Nt20 ( ) =αβ Ntvyt20 ( ) +−( ) Nt3 ( ), dt d Nt( ) =γγ N( t) + N( t) dt 3 10 20 (4.4) dx( t) =+−(δµxt( ))( xp xt( )), dt dy( t) =+−(δµyt( ))( yp yt( )). dt sawyisi pirobebi mocemulia (4.3)-Si. (4.4) sistemaSi xuTi uc- nobi funqciaa, magram am sistemis bolo ori gantoleba, rome- lic samarski-mixailovis modelidan gamomdinareobs, analizurad amoixsneba, roca sruldeba (4.3)-is meore striqonSi mocemuli toloba sawyisi pirobebisTvis, Sedegad gvaqvs:
δ δµ+− xppexp(( xt) ) 1 xt( ) = , (4.5) δexp(( δµ++xtpp) ) µ x δ δµ+− yppexp(( yt) ) 1 yt( ) = , (4.6) δexp(( δµ++ytpp) ) µ y (4.4)-is pirvel or gantolebaSi, (4.5) da (4.6)-is Casmis Sedegad vRebulobT sistemas sami gantolebiT: d =αβ +− Nt10 ( ) Nt10 ( ) vxt( ) Nt3 ( ), dt d Nt20 ( ) =αβ Ntvyt20 ( ) +−( ) Nt3 ( ), (4.7) dt d Nt3 ( ) =γγ N10 ( t) + N20 ( t). dt 102 nugzar kereseliZe
sawyisi pirobebiT
N10(0) = nN 10 , 20 ( 0) = nN20 ,0 3( ) = n 30 , (4.8)
SevniSnoT, rom (4.7),(4.8) koSis amocanis analizuri amonaxsne- bis povna SesaZlebelia, radganac (4.7) sistemidan gardaqmnebiT mi- viRebT Nt3 ( ) -is mimarT meore rigis wrfiv mudmivkoeficientebian araerTgvarovan Cveulebriv diferencialur gantolebas, romlis amonaxsnis (4.7) sistemis pirvel or gantolebaSi moTavsebiT vRe- bulobT Sesabamisad Nt10 ( ) , Nt20 ( ) -is mimarT pirveli rigis wrfiv mudmivkoeficientebian araerTgvarovan Cveulebriv diferencia- lur gantolebebs. magram, Cven davumatebT, ra (4.7), (4.8) koSis amocanas pirobas marjvena bolosaTvis: ∗ ∗∗ N10 ( t) = 0, Nt2 ( ) = 0. (4.9) sadac t∗ , t∗∗ arafiqsirebuli, zogadad sxvadasxva droiTi mo- mentebia [0;T > 0] drois monakveTze, miviRebT Cilkeris tipis amocanas, romlis gamokvlevasac SevudgebiT kompiuteruli mode- lirebiT, da CavatarebT kompiuterul eqsperiments. CavTvaloT rom gvaqvs Semdegi sawyisi pirobebi:
NN10 (0) = 0.1,20 ( 0) = .001, N3 ( 0) = .3, (4.10) xy(0) =( 0) = 0. (4.7)-(4.9) Cilkeris tipis amocanis amoxsnadoba, rogorc kom- piuteruli eqsperimentebidan irkveva damokidebulia mxareebis agresiulobis sidideze, kerZod D =α2 −8 βγ sididis mniSvne- lobaze. ase magaliTad, Tu ki antagonisturi mxareebis agre- siuloba didia, rac iwvevs D sididis arauaryofiTobas: D ≥ 0 , maSin Cilkeris tipis amocanas amoxsna ar gaaCnia, rac imas niS- navs, rom mesame mxares Tavisi qmedebebiT ar SeuZlia Caaqros informaciuli omi. magaliTad, Tu ki α = 1.8; β = .05; ν = .05; γ = 0.5; δ = µ = .3; .2; xp = 155; y p = 150; rac niSnavs, rom D = 3, 04 . rogorc nax. 1_a-ze sCans orive antagonisturi mxare informaciul oms aZlierebs da mesame mxaris zemoqmedeba maTze uSedegoa. SevniS- noT, rom mxareebis mier maRali agresiulobis pirobebSi, Tu ki D = 0 -s, rac magaliTad xdeba parametrebis am mniSvnelobebisT- vis: α=.08; β = .08; ν = .05; γδ = 1; = .3; µ = .2; xp = 155 , y p = 150 , ma- Sin erTi mxaris mier nulze gasvla SesaZlebelia, anu mesame mxa- res SeuZlia moaxdinos zemoqmedeba erT-erT antagonistur mxare- ze, ixileT nax.1-b. rac Seexeba dabali agresiulobis SemTxvevas, 103 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV anu roca D < 0 -ze, kerZod parametrebisTvis: α = .08; β = .5; ν = .05;
γ = .3; δ = .3; µ = .2; xp = 155; y p = 150, maSin mesame mxaris zemoqmedeba antagonistur mxareebze efeqturia, isini gadian nulze, rac imas niSnavs, rom Sesabamis Cilkeris tipis amocanas gaaCnia amonaxsni. kompiuteruli eqsperimentebis Sedegebis analizidan gamomdi- nare, SeiZleba davaskvnaT - mowinaaRmdegis ignorirebis modeluri amocanis integrirebuli maTematikuri modelis amonaxsnTa yofaq- ceva analogiuria Sesabamisi araintegrebuli maTematikuri modelis amonaxsnebisa (Chilachava T., Kereselidze, 2009c). (Mikhailov, Petrov, Pronche- va, Marevtseva, 2015), kerZod amonaxsnTa damokidebuleba D -s mniSvne- lobaze - anu, mxareTa agresiulobis xarisxze. amasTan unda iTqvas, rom modelSi adeptebis raodenobis asaxvam Seitana garkveuli ko- reqtivebi, ase magaliTad dabali agresiulobis pirobebSi, Tu ki D uaryofiTia da moduliT izrdeba, maSin drois mcire mniSvnelobe- bisTvis antagonisturi mxareebi parametrebis am mniSvnelobebisTvis
α = .08; β = 15; ν = .05; γ = 3.5; δ = .3; µ = .2; xp = 155; y p = 150, D = −419,9 ga- dian nulze, ixileT nax. 2_a. magram, ukve didi t -sTvis, erT erTi an- tagonisturi mxare (damokidebulia mxareTa sawyisi mniSvnelobebis TanafardobasTan) aRar gadis nulze, ixileT nax. 2_b. kompiuretuli eqsperimenti Catarda aseve (4.7)-(4.9) Cilkeris tipis amocanis ganzogadoebul SemTxvevaSi. kerZod, roca anta- gonistur mxareebs sxvadasxva agresiulobis (a1,a2) da samSvidobo mzadyofnis ( ββ12, ) maCveneblebi gaaCniaT, aseve sxvadasxvaa sam-
Svidobo aqtiurobis maCveneblebi mxareTa mimarT ( γγγ123,,), xolo adeptebis raodenobis gantolebebSi CarTulia Sesabamis dapiris- pirebul mxareTa informaciuli nakadebis raodenobebi: d Nt10( ) =αβ 1 Nt 10( ) +− vxt 1 ( ) 1 Nt 3 ( ), dt d Nt20( ) =αβ 2 Ntvyt 20( ) +− 2 ( ) 2 Nt 3 ( ), dt d Nt3( ) =++γγ 1 N 10( t) 2 N 20( t) γ 3 Nt 3 ( ), (4.11) dt dx( t) =+−(αγ3N 10( t) 4 xt( ))( xp xt( )), dt dy( t) =+−(αγ4N 20( t) 5 yt( ))( yp yt( )). dt kompiuteruli eqsperimenti Catarda (4.11) sistemisTvis (4.10) sawyisi pirobebisa da parametrebis sxvadasxva mniSvnelobebisTvis. miRebuli Sedegebis analizidan SeiZleba davaskvnaT, rom Sesabamis 104 nugzar kereseliZe
Cilkeris tipis amocanas _ (4.11), (4.6),(4.9) gaaCnia amonaxsni, maRali samSvidobo mzaobisa da aqtiurobis SemTxvevaSi. kerZod, Tu ki gva- qvs parametrebis monacemebi, sadac agresiuloba Warbobs samSvido-
bo mzaobasa da aqtiurobebze: α1 = 4.8; ν1 = 1.5; β1 = .5; α2 = 5.6; ν 2 = 1.3; β = γ= γγ = = = = γ = 2 .7; 1.05; 23 .3; .07; xp 155; y p 150; α3 = 2.3; α4 = 2.2; 4 .2; γ 5 = .3 , maSin antagonisturi mxareebi anviTareben informaciul oms da mesame mxaris zemoqmedeba uSedegoa, ixileT nax. 3_a. romelic
NNN10 (0) = 0.2,20 ( 0) = .01,3 ( 0) = .03, xy(0) =( 0) = 0. sawyisi mniSvnelobebisTvisaa miRebuli. Cilkeris tipis amocanas _ (4.11), (4.6),(4.9) gaaCnia amonaxsni, roca dapirispirebul mxareTa agresiuloba SedarebiT dabalia,
ase magaliTad, parametrebis mniSvnelobebisTvis: α1 = .08; ν1 = .05; γ= γ = γ = = =α = αγ = = γ = β1 = 1.5; α2 = .06; ν 2 = .03; β2 = 1.7; 1.05; 2 .03; 3 .07;xypp 155; 150;3 .3; 44 .2; .2; 5 .3,
γ1=.05; γ 2 = .03; γ 3 = .07;xypp = 155; = 150;α3 = .3; αγ 44 = .2; = .2; γ 5 = .3, ixileT nax. 3_b. kompiuteruli eqsperimenti Catarda MatLab-is garemoSi, Seqm- nili iyo m-failebi, erT-erTi programuli kodi warmodgenilia listing 1-Si. listingi 1. Sawy_gae1. m faili %integrirebuli_ignorir_uSvebs povnas [T,Y]=ode15s(@GAE1,[0,0.15],[0.002 .001 .3 0 0]); plot(T,Y,’linewidth’,2) title(‘inf warfare’) xlabel(‘Time’) ylabel(‘amount of information’) legend (‘n1’,’n2’,’n3’,’x’,’y’) grid on %Integrirebuli MMIW_ode-s marjvena mxareebi function dxdt=GAE1(t,x) dxdt=zeros(5,1); a1=.08; a2=.05; b1=1.5; a21=.06; a22=.03; b2=1.7; p4=155; p5=150; g1=.05; g2=.03; g3=.07; a3=.3; m1=.2; a4=.2; m2=.3; dxdt(1)=a1*x(1)+a2*x(4)-b1*x(3); dxdt(2)=a21*x(2)+a22*x(5)-b2*x(3); dxdt(3)=g1*x(1)+g2*x(2)+g3*x(3); dxdt(4)=(a3*x(1)+m1*x(4))*(p4-x(4)); dxdt(5)=(a4*x(2)+m2*x(5))*(p5-x(5)); end 105 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
37 16 x 10 inf warfare x 10 inf warfare
20 n1 4 n1 n2 n2 3 n3 n3 15 n1 x 2 x y y 10 1 n1 n2 0 5 n3 -1 n3 amount of information amount of information -2 0 y x n2 -3 x y
47.5 48 48.5 49 49.5 20 25 30 35 40 45 50 55 60 65 Time Time a b nax. 1. informaciul omSi mxareebis CarTulobis grafikebi, roca D>0-ze (a) da roca D=0-s (b)
inf warfare inf warfare 200 3 n1 n1 n2 2.5 x,y n2 n3 150 x 2 n3 n3 y x n1 y x 1.5 100 y 1 n1 50 0.5
0 amount of information 0 -0.5 amount of information
-1 -50 n3 n2 -1.5 n2
0 0.5 1 1.5 2 5 10 15 20 25 30 35 40 45 50 Time Time a b nax. 2. informaciul omSi mxareebis CarTulobis grafikebi, roca D <0-ze, drois mcire (a) da didi (b) mniSvnelobebisTvis
inf warfare inf warfare
3 n1 250 n1 n2 n2 n3 2 n3 x x 200 x n3 y 1 y
150 0
n1,n2 y -1 100 amount of information amount of information n1 -2 50 y x n3 n2 -3
0 -4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Time Time a b nax. 3. infor ma ci ul omSi mxare e bis CarTu lo bis grafi ke bi, (4.11),(4.8),(4.9) Cilke ris tipis amoca nis T vis maRa li (a) da daba li (b) agre si u lo bis T vis 106 nugzar kereseliZe
5. daskvna. warmodgenil naSromSi SeTavazebulia informaciu- li omis integrirebuli maTematikuri da kompiuteruli modele- bi, romlebSic asaxulia aqamde damoukideblad asaxuli midgomebi informaciuli omis modelirebaSi. kerZod, gaerTianebulia aka- demikos a.a. samarskisa da misi Tanaavtoris profesor a.p. mixai- lovis sareklamo kampaniisa da profesor T. CilaCavas sami mxaris informaciuli nakadebis modelebi. warmodgenilia informaciuli omis zogadi wrfivi, informaciul teqnologiebze SezRudvebis, mowinaaRmdegis ignorirebis kerZo da gafarToebuli integrire- buli maTematikuri da kompiuteruli modelebi. ukanaskneli ori modelebisTvis Catarebulia kompiuteruli eqsperimentebi, ris safuZvelzec dadginda infirmaciuli omis integrirebuli mode- lebis Cilkeros tipis amocanebis amoxsnadobis pirobebi.
Nugzar Kereselidze
THE UNITED MATEMATICAL AND COMPUTER MODELS OF INFORMATION WARFARE
Summary
In this paper, the first attempt is made to combine existing approaches of mathematical and computer modeling of information warfare. As a result, integration mathematical and computer models of information warfare were created. Until now, in the mathematical modeling of the information warfare, issues of information flows and information dissemination were considered separately. The first direction was initiated by the idea of Professor T. Chilachava, to study the distribution of information flows of the two opposite and third peacekeeping sides by mathematical models. The second direction was laid by Academician A.A. Samarskii and Professor A.P. Mikhailov, who proposed a mathematical model for the dissemination of information among the population. Both these directions have been intensively developed and many scientific studies have been devoted to them. Several dozens of interesting models were created, which reflect the various nuances of the problem. But it is natural that the information and the information for which it is intended should be studied together. During the implementation of this idea, integrated mathematical and computer models of information warfare were created. Integrated common linear and nonlinear mathematical and computer models of information warfare were created. In this paper, integrated general and 107 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV particular mathematical and computer models for ignoring the enemy are presented. With the help of computer research, a numerical experiment, the question of the existence of a solution to the problem of the Chilker range is studied, which is equivalent to the task of completing information warfare. literatura: 1. Chilachava T., Kereselidze N. Sainformacio omis matematikuri modelireba. Georgian Electronic Scientific Journal: Computer Science and Telecommu- nications. 2010, # 1 (24). p. 78-105. 2. Chilachava T., Chakhvadze A. Continuous Nonlinear Mathematical and Computer Model of Information Warfare with Participation of Interstate Authoritative Institutes. Georgian Electronic Scientific Journal: Computer Science and Telecommunications 2014a, #. 4(44), p. 53-74. 3. Chilachava T., Chakhvadze A. Non llinear Mathematical and Computer Mo- dels of Information Warfare with Participation of Autoritative Interstate Ins- titutes. Book of abstracts V Annual International Conference of the Georgian Mathematical Union, Batumi, September 8-12, 2014b. p. 76. 4. Chilachava T., Kereselidze N. About One Mathematical Model of the Infor- mation Warfare. Fifth Congress of Mathematicians of Georgia. Abstracts of Contributed Talks. Batumi/Kutaisi, 9-12 October. 2009a. p. 85. 5. 15. Chilachava T., Kereselidze N. Non-Preventive Continuous Linear Mathematical Model of Information Warfare. Sokhumi State University Pro- ceedings, Mathematics and Computer Sciences vol. 7. 2009b, #7. p. 91- 112. 6. 16. Chilachava T., Kereselidze N. Continuous Linear Mathematical Model of Preventive Information Warfare. Sokhumi State University Proceedings, Mathematics and Computer Sciences vol. 7. 2009c, #7. p. 113-141. 7. Kereselidze N. Informaciuli omis matematikuri modelireba. Monografia. Sa- qartvelos parlamentis erovnuli biblioteka ISBN: 978-9941-0-4892-0. 2012, p. 176 http://kereseli.besaba.com/monografia%20formatizaziiT.pdf 8. Kereselidze N. Informaciuli omis matematikuri da kompiuteruli modelebi. Monografia. ISBN 978-9941-0-9617-4 (PDF). 2017. http://kereseli.besaba. com/Math_and_comp_models_IW_monograph_2017.pdf 9. Kereselidze N. Matematicheskaya model informatsionnoy voyny s uchyotom vozmozhostey informatsionnykh tekhnologiiy protivoborstvuyushchikh sto- ron, Ttransactions II The Internashional Scientific Conference Dedicated to the 90th Anniversary of Georgian Technical University “Basic Paradigms in Science and Technilogy Development for the 21st Century, Tbilisi, Georgia, September 19-21, 2012. Publishing House “Technical University”, Tbilisi, 2012a, p. 188-190. 108 nugzar kereseliZe
10. Kereselidze N. Matematicheskaya model informatsionnogo protivoborstva s uchyotom vozmozhnostey informatsionnykh tekhnologii storon. Trudy XX Mezhdunarodnoy konferentsii problem upravleniya bezoposnosty u slo- zhnykh system. Moskva, dekabr, 2012b, pp. 175-178. 11. Marevtseva N. A. Prosteyshie matematicheskie modeli informatsionnogo protivoborstva. Serya “Matematicheskoe modelirovanie i sovremennie in- formatsionnye tekhnologii”, vip. Prosteyshie matematicheskie modeli in- formatsionnogo protivoborstva. Seriya “Matematicheskoe modelirovanie i sovremennie informatsionnie tekhnologii”. Vip. 8. // Sbornik trudov Vse- rossiyskikh nauchnikh molodezhnikh shkol. Rostov-na-Donu, izdatelstvo Yuzhnogo federalnogo universiteta, 2009. pp. 354-363. 12. Marevtseva N. A., Matematicheskie modeli informatsionnogo napadeniya i informatsionnogo protivoborstva. Zhurnal Sotsiologiya, #3, 2011, pp. 2-35. 13. Mikhailov A. P. Izmodenova K. V. Ob optimalnom upravlenii v matema- ticheskoy modeli rasprostraneniya informatsii. Trudy seminara “Matema- ticheskoe modelirovanie sotsialnykh prtsessov”, sbornik, vip. 6. Moskva, MAKC Press, 2004. 14. Mikhailov A. P. Marevtseva N. A. Modeli informatsionnoy borby. Matema- ticheskoe modelirovanie, 2011, t. 23. # 10. pp. 19-32. 15. Mikhailov A. P., Petrov A. P. Proncheva O. G. Marevtseva N. A. Mate- maticheskoe modelirovanie informatsionnogo protivoborstva v sotsiume. Mezhdunarodniy ekonomicheskiy simpozium - 2015. Materialy Mezhduna- rodnikh nauchnikh konferentsiy, posvyashchonnikh 75-letiyu ekonomiches- kogo fakulteta Sankt-Peterburgskogo universiteta: sbornik statey. Otv. red. S.A. Belozerov, Sankt-Peterburg, 2015. pp. 293–303. URL: http://econ-conf. spbu.ru/files/Symposium_Sbornik_Statey.pdf 16. Mikhailov A.P., Petrov A.P., Proncheva O.G., Marevtseva N.A. Mathemati- cal Modeling of Information Warfare in a Society // Mediterranean Journal of Social Sciences. Vol. 6. No. 5 S2. pp. 27–35. doi: 10.5901/mjss.2015. v6n5s2p27. 17. Samarskiy A. A., Mikhailov A. P. Matematicheskoe modelirovanie: Idei. Metody. Primery. 2-e izd., Moskva, FIZMATLIT, 2005. 320 p.
109 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
Leila Sulava
COMPUTER MODELING OF THREE-PARTY ELECTIONS TAKING INTO ACCOUNT DEMOGRAFIC FACTOR
Introduction In this paperis proposed the nonlinear mathematical model with variable co- efficients in the case of three-party elections, that describes the dynamics of the quantitative change of the votes of the pro-government and two opposition par- ties from election to election. The model considers four objects: state and admin- istrative structures, acting by means of administrative resources for opposition- minded voters with the aim to win their support for the pro-government party; voters who support the first opposition party; voters who support the second op- position party; voters who support the pro-government party. The model takes into account the change in the total number of voters in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. The model considered the cases with variable coefficients. In general Cauchy problem was solved numerically using the MATLAB software package. Synergetics initiated the application of mathematical models in social sci- ences: sociology, history, demographic studies, political science, conflict studies, etc. (Samarski, Mihailov, 2006; Chilachava, Dzidziguri, 2008). In (Chilachava, Kereselidze, 2010; Chilachava, Kereselidze, 2009a, Chi- lachava, Kereselidze, 2009b) quantities of information streams by means of new mathematical models of information warfare are studied. By information warfare the authors mean an antagonism by means of mass media (an electronic and print- ing press, the Internet) between the two states or the two associations of states, or the economic structures (consortiums) conducting purposeful misinformation, propagation against each other. It was shown that in case of high aggression of the contradictory countries, not preventive image the operating peacekeeping organi- zations won’t be able to extinguish the expanding information warfare. In works (Chilachava, Kereselidze, 2011a; Chilachava, Kereselidze, 2011b) linear and nonlinear mathematical models of information warfare, and also opti- mizing problems are considered. In (Chilachava T. I. Chakhvadze, 2014) the new nonlinear mathematical and computer model of information warfare with participation of interstate authorita- tive institutes is offered. The model is described by Cauchy’s problem for nonlin- ear non-homogeneous system of the differential equations. Confronting sides in extend of provocative statements, the third side (the peacekeeping international organizations) extends of soothing statements, interstate authoritative institutes 110 leila sulava the peacekeeping statements call the sides for the termination of information war- fare. In that specific case, modes of information warfare “aggressor- victim”, for the third peacekeeping side are received exact analytical solutions, and functions defining number of the provocative statements distributed by the antagonistic sides satisfy to Cauchy’s problems for Riccati certain equations which are solved by a numerical method. For the general model computer modeling is carried out and shown that irrespective of high aggression of confronting sides, interstate au- thoritative institutes will be able to extinguish information warfare and when for this purpose efforts of only the international organizations insufficiently. In (Chilachava, 2014a) consider the nonlinear mathematical model of bi- lateral assimilation without demographic factor. It was shown that the most part of the population talking in the third language is assimilated by that widespread language which speaks bigger number of people (linear assimilation). Also it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimi- lated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In (Chilachava, Chakaberia, 2014b) mathematical modeling of nonlinear pro- cess of assimilation taking into account demographic factor is offered. In consid- ered model taking into account demographic factor natural decrease in the popula- tion of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model “predator - the victim”, thus, naturally a role of the victim plays the population which has undergone as- similation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of as- similators in an initial time point) to the population of the first assimilating side. In the second case the problem is actually reduced to nonlinear system of two dif- ferential equations describing type model “a predator _ the victim”, with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical 111 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV models which in some approach can model real situations, with the real assimilat- ing countries and the state formations (an autonomy or formation with the unrec- ognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in popu- lation and hope for natural decrease in the population of the assimilating states. In (Chilachava, Chakaberia, 2015) mathematical modeling of nonlinear pro- cess of the assimilation taking into account positive demographic factor which underwent bilateral assimilation of the side and zero demographic factor of the assimilating sides is considered. In model three objects are considered: the popu- lation and government institutions with widespread first language, influencing by means of state and administrative resources on the population of the third state formation for the purpose of their assimilation; the population and government institutions with widespread second language, influencing by means of state and administrative resources on the population of the third state formation for the purpose of their assimilation; population of the third state formation which is exposed to bilateral assimilation from two powerful states or the coalitions. For nonlinear system of three differential equations of the first order are received the two first integral. Special cases of two powerful states assimilating the population of small state formation (autonomy), with different initial number of the popula- tion, both with identical and with various economic and technological capabili- ties are considered. It is shown that in all cases there is a full assimilation of the population to less widespread language. Thus, proportions in which assimilate the powerful states the population of small state formation are found. In works [Mihailov, Maslov, Iuhno, 2000; Mihailov, Iuhno, 2001; Mihailov, Petrov, 2011) the mathematical model of political rivalry devoted to the description of fight occurring in imperious elite competing (but not necessarily antagonistic) political forces, for example, power branches is considered. It is supposed that each of the sides has ideas of “number” of the power which this side would like to have itself, and about “number” of the power which she would like to have for the partner. These papers (Chilachava, Dzidziguri, Sulava, Chakaberia, 2009; Chilachava, Dzidziguri, Sulava, Chakaberia, 2010a; Chilachava, Dzidziguri, Sulava, Chaka- beria, 2010b; Chilachava, Sulava, Chakaberia, 2010; Chilachava, Sulava, 2013) present the nonlinear mathematical model of the public or the administrative man- agement (or the macro and micro model). The cases of both constant and variable pressure forces on freethinking people were analyzed. Exact analytical decisions which determine dynamics of a spirit both free-thinking people, and operated (con- formists) of people by time are received. During this analyses various governance systems were considered: a liberal, democratic, semi dictatorial and dictatorial. In terms of governance of particular interest is the description by mathemat- ics (the creation of a mathematical model) of a social process, how is the process 112 leila sulava of political elections. Many scientists worked on this subject, but in most cases, they were interested in analyzing statistical data of results of carried out elections. Extremely important is the creation of a mathematical model, which would give an opportunity to define the dynamics of change in the number of supporters of different political subjects during the election period and a possible forecast of the election results. These works (Chilachava, 2012a; Chilachava, 2012b; Chilachava, 2013a; Chilachava, 2013b; Chilachava, 2013c; Chilachava, 2013d; Chilachava, Cho- chua, 2013e) considered a two or three-party (one pro-government and two op- position parties) nonlinear mathematical model of elections when coefficients are constant. The assumption was made that the number of voters remain the same between two consecutive elections (zero demographic factor of voters). The ex- act analytical solutions were received. The conditions under which opposition party can win the upcoming elections were established. These works [Chilachava, Sualava 2015; Chilachava, Sulava, 2015a; Sulava, 2015; Chilachava, Sulava, 2015b) considered a two-party (pro-government and op- position parties) nonlinear mathematical model of elections with variable coefficients. In (Chilachava, Sulava, 2015a) the nonlinear mathematical model describ- ing dynamics of voters of pro-government and oppositional parties is offered. The case when coefficients of attraction of votes of pro-government and oppo- sitional parties are exponential increasing functions from elections to elections is considered. Cauchy’s task for nonlinear system of the differential equations with variable coefficients of model is solved by means of the program Matlab environment. Cases as maximum and certain voter turnout on elections, and also the set falsification of voices of opposition party are considered. The following qualitatively various results are received: _ despite superiority of coefficient of attraction of votes of opposition party over pro-governmental, due to administrative impact on voters of opposition party from government institutions, the pro-government party will win the next elections; _ despite superiority of the voters supporting opposition party by the election day due to the best mobilization on elections of the voters, the pro-government party will win the next elections; _ despite superiority of the voters supporting opposition party by the elec- tion day at an identical voter turnout on elections, due to a certain falsification of elections, the pro-government party will win the next elections; _ the opposition party, despite the best appearance on elections of voters of pro-government party and a certain falsification of elections, nevertheless will win the next elections. In (Chilachava T.I.,Sulava, 2016) the development of our previously pro- posed two-party electoral models, is proposed the nonlinear mathematical model 113 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV with variable coefficients in the case of three-party elections, that describes the dynamics of the quantitative change of the votes of the pro-government and two opposition parties from election to election. The model takes into account the change in the total number of voters in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. The model considered the cases with variable coefficients. In particular, we assume that in the period between elections coefficients of “attracting” voters are expo- nentially increasing function of time. In the particular case we obtain exact ana- lytical solutions. The conditions have been identified under which the opposition can win the forthcoming elections, and in some cases, the pro-government party can stay in power. In this publication the nonlinear mathematical model with variable coefficients in case of three-party elections which describes dynamics of quantitative change of votes of pro-government and two oppositional parties is presented. The model takes into account the change in the total number of vot- ers in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. In model four objects are considered: 1. The state and administrative structures that utilize state resources in or- der to have an influence on the pro-oppositions voters with the aim to gain their support for the pro-government party. 2. Voters who support first opposition party. 3. Voters who support second opposition party. 4. Voters who support the pro-government party. In model there are various indicators of a voter turnout in the election day, and also falsification chances in advantage the pro-government party.
1. A System of Equations and Initial Conditions
To describe the dynamics of choosing between three election subjects (pro- government and two opposition parties), we propose the following nonlinear mathematical model:
dN (t) 1 α α α α β γ = ( 1 (t) − 2 (t)) N1 (t)N 2 (t) + ( 1 (t) − 3 (t)) N1 (t)N 3 (t) − 1 (t)N1 (t) + 1 (t)N1 (t) dtdt dN22 (t) = (α 2 (t) −α1 (t)) N1 (t)N 2 (t) + (α 2 (t) −α 3 (t)) N 2 (t)N 3 (t) − β 2 (t)N 2 (t) + γ 2 (t)N 2 (t) (1.1) dtdt dN33 (t) = (α 3 (t) −α1 (t)) N1 (t)N 3 (t) + (α 3 (t) −α 2 (t)) N 2 (t)N 3 (t) + β1 (t)N1 (t) + β 2 (t)N 2 (t) + γ 3 (t)N 3 (t) dtdt The system of the equations (1.1) is considered on an interval t ∈(0,T ], cor- responding initial conditions (Cauchy’s condition) at the moment of t = 0
N10 = N1 (0) , N2020 = N 2 (0) , N30 = N 3 (0) . (1.2) 114 leila sulava
The solution of a task of Cauchy (1.1), (1.2) we look for on a segment t ∈[0,T ]in a class of continuously differentiable functions
1 N1 (t), N 2 (t), N3[t]∈C [0,T ] (1.3) In system of the equations (1.1): 1 N1 (t), N 2 (t), N3([t])∈theC number[0,T ] of voters in support of the first, second opposition and pro-government parties, respectively, at time t,t ∈[0,T]; t = 0 _ moment the last elections, in consequence of which party won the elections and became the pro-government party ( N10 + N20 < N30 ); t = T _ time of the next elections (usually T = 4 years or 1460 days);
α1 (t),α 2 (t),α 3 (t) - coefficients corresponding to the activity to attract the votes of the first, second opposition and the pro-government parties, respectively, at time t, depending on the program of action, financial and information capabili- ties of these parties;
β1 (t),β 2 (t) _ continuous positive functions which characterize the scale of use of the administrative resources directed to oppositional voters for the purpose of their attraction on the party of pro-government partybyvarious, perhaps non- democratic methods; γ 1( t ),γ 2 ( t ),γ 3 ( t ) _ coefficients of the accounting of so-called selective demographic change of the parties.
2. Computer Modelling of Three-Party Elections
We will consider Cauchy’s task (1.1), (1.2) generally when change model parameters, and also change of so-called selective demographic factor is consid- ered. As it has been already noted, the decision of nonlinear system of the dif- ferential equations (1.1), (1.2) gives the chance to show dynamics of possible, estimated votes from elections to elections and to define estimated voices of three selective subjects in case of 100% of a voter turnout (N1 (T), N 2 (T ), N 3 (T )). It is clear that such voter turn out on elections isn’t real. Therefore it is nec- essary to take into account an assessment of the indicator of appearances at elec- tions and in case of the non-democratic countries some falsification of voices of opposition parties. Computer modeling of the offered mathematical model allows to consider these processes and to make the corresponding amendments of the received results. In model the case of variable coefficients is considered, in particular, we assume that from choices to choices coefficients of attraction of votes are expo- nential increasing function of time.
115 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV
t δ i T α i (t) = α i0e ,i = 1,3 , (2.1)
where
α i0 > 0,δ i > 0,i =1,3 .
For β1 (t), β 2 (t) functionsof use of administrative resources and so-called demographic coefficients γ 1 (t),γ 2 (t),γ 3 (t) cases are considered:
t δ j T β j (t) = β j0e , β j > 0,δ j > 0, j = 1,2 . (2.2)
t δ i T γ i ( t ) = γ i0e ,δ i > 0,i =1,3 .
Then the system (1.1) will take a form
t t t t δ δ δ δ t t dN (t) 1 2 1 3 δ δ 11 T T T T 1 T 1 T = N1 (t)((α10 e − α 20 e )N 2 (t) + (α10 e − α3030 e )N 3 (t) − β10 e + γ1010 e ) dt t t t t δ δ δ δ t t dN (t) 2 1 2 3 δ δ 22 T T T T 2 T 2 T = N 2 (t)((α2020 e − α10 e )N1 (t) + (α 20 e − α 30 e )N 3 (t) − β 20 e + γ 2020 e ) (2.3) dtdt t t t t δ δ δ δ t t t dN (t) 3 1 3 2 δ δ δ 33 T T T T 3 T 1 T 2 T = N 3 (t)((α3030 e − α10 e )N1 (t) + (α 30 e − α2020 e )N 2 (t) + γ3030 e ) + β10 e N1 (t) + β20 e N 2 (t) dtdt We will enter designations;
k1 _ relative value of the supporters of first opposition who voted in the elec- tion day from all number of the voters supporting first opposition party;
k2 _ relative value of the supporters of second opposition who voted in the election day from all number of the voters supporting second opposition party;
k3 _ relative value of the supporters of ruling party who voted in the election day from all number of the voters supporting pro-government party;
f1 _ relative value of the forged voices of the first opposition party;
f 2 _ relative value of the forged voices of the second opposition party. We consider two cases: when the elections are held, without falsification, and when in the falsification takes place during the elections(scenario of model, picture 1.). Numerous numerical experiment (1.2), (2.1)-(2.3) is made and the corre- sponding graphics (visualization) are received. For example, in fig. 1 - fig.6cases of various relative turnout of voters of three parties are given, falsification and so-called demographic factor.
116 leila sulava
x 106 k1=0.5 k2=0.45 k3=0.4 3.5 al10=3*10(-10); al20=2*10(-10); 3 al30=0.5*10(-10); b1=6*10(-4); b2=10(-4); 2.5 g1=g2=g3=0
2 N3
1.5 N2 N1
amomrCevelTaraodenoba 1
N1=1400000 N2=1000000 0.5 N3=2600000 N3(T) Fig.1 x 106 k1=0.5 k2=0.45 k3=0.5 3.5 N1=1400000 al10=5*10(-10); N2=1000000 ( N3=2600000 al20=3.5*10 -10); ( 3 N3(T) 2 N3 1.5 amomrCevelTaraodenoba 1 N2 0.5 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 dro Fig.2 117 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV x 106 k1=0.5 k2=0.45 k3=0.37 3.5 al10=4*10(-10); al20=3.5*10(-10); 3 al30=2.5*10(-10); N3 b1=4.5*10(-4); b2=2.5*10(-4); 2.5 g1=g2=g3=0; N1=1400000 N2=1000000 2 N3=2600000 N3(T)>N1(T)+N2(T) k3*N3(T) 1.5 N1 N2 amomrCevelTaraodenoba 1 0.5 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 dro Fig.3 k =0.46 k =0.38 k =0.64 f =0.24 f =0.19 x 106 1 2 3 1 2 10 alfa >alfa >alfa N3(T) 7 6 5 number of votes 4 3 N1(T)f N3(t) 2 N1(t) 1 N2(T)f N2(t) 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 number of days Fig.4 118 leila sulava 6 k =0.6 k =0.45 k =0.45 f =0.15 f =0.05 x 10 1 2 3 1 2 10 N3(T)>N1(T)+N2(T) k *N (T) 8 alfa1>alfa2=alfa3 beta1>beta2 0 6 5 number of voters 4 N1(T)f 3 N1(t) N3(t) 2 N2(t) 1 N2(T)f 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 number of days Fig.5 x 106 k1=0.52 k2=0.45 k3=0.5 f1=0.15 f2=0.1 10 N1=1400000 al10=3.2*10(-10); N2=1000000 9 al20=2.3*10(-10); N3=2600000 ( N3(T) 5 4 N3 amomrCevelTaraodenoba 3 N1F N1 2 N2 1 N2F 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 dro Fig.6 119 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Scenario of model We proposed a mathematical model having both theoretical and practical importance. Political opponents (the power and opposition parties) by means of intellectual (programs of action), financial (sponsors), information (the print and electronic media which is under their department) means can widely use the re- sults received by us and calculate parameters and choose strategy for achieve- ment of the desired purposes. 120 leila sulava References: 1. Chilachava T.I., Dzidziguri Ts. D. Mathematical Modeling. Tbilisi, Inovacia, 2008 (Georgian). 2. Chilachava T.I., Kereselidze N.G. Non-Preventive Continuous Linear Math- ematical Model of Information Warfare. Sokhumi State University Proceed- ings, Mathematics and Computer Sciences, 2009a, #VII, pp. 91 - 112. 3. Chilachava T.I., Kereselidze N.G. Continuous Linear Mathematical Model of Preventive Information Warfare. Sokhumi State University Proceedings, Mathematics and Computer Sciences, 2009b, #VII, pp.113 -141. 4. Chilachava T. I., Kereselidze N. Mathematical Modeling of the Information- warfare. Georgian Electronic Scientific Journal: Computer Science and Tele- communications, 2010, # 1 (24), pp.78 -105 (Georgian). 5. Chilachava T.I., Kereselidze N.G. Optimizing Problem of Mathematical Model of Preventive Information Warfare, Informational and Communica- tion Technologies _ Theory and Practice: Proceedings of the International Scientific Conference ICTMC-2010 USA, Imprint: Nova, 2011a, pp. 525- 529. 6. Chilachava T.I., Kereselidze N.G. Mathematical Modeling of Information Warfare. Information Warfare, 2011b, #1(17), стр. 28 - 35 (Russian). 7. Chilachava T. I. Chakhvadze A. Continuous Nonlinear Mathematical and Computer Model of Information Warfare with Participation of Authoritative Interstate Institutes. Georgian Electronic Scientific Journal: Computer Sci- ence and Telecommunications, 2014a, # 4(44), pp. 53- 74. 8. Chilachava T.I. Nonlinear Mathematical Model of Bilateral Assimilation Georgian Electronic Scientific Journal: Computer Science and Telecommu- nications, 2014a, № 1(41), pp. 61- 67. 9. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Pro- cess of Assimilation Taking into Account Demographic Factor. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2014b, # 4 (44), pp.35-43. 10. Chilachava T.I., Chakaberia M.R. Mathematical Modeling of Nonlinear Pro- cesses Bilateral Assimilation, Georgian Electronic Scientific Journal: Com- puter Science and Telecommunications, 2015,№ 2(46), pp. 79 - 85. 11. Chilachava T.I., Dzidziguri Ts. D., Sulava L.O., Chakaberia M.R. Nonlinear Mathematical Model of Administrative Management. Sokhumi State Uni- versity Proceedings, Mathematics and Computer Sciences, vol. VII, 2009, pp.169- 180 (Georgian). 12. Chilachava T.I., Dziziguri Ts. D, Sulava L.O., Chakaberia M.R. Nonlinear Mathematical Model of Administrative Pressure. First International Confer- ence, Book of Abstracts, Batumi, 2010a, pp. 74 -75. 121 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 13. Chilachava T.I., Dziziguri Ts.D., Sulava L.O., Chakaberia M.R.A Nonlinear Mathematical Model of Administration. Abstracts of the International Con- ference “Information and Computer Technology, Simulations”. Dedicated to the 80th Anniversary of Prangishvili I.V., 2010b, pp. 203 - 204. 14. Chilachava T.I., Sulava L.O., Chakaberia M.R. On Some Nonlinear Math- ematical Model of Administration. Problems of Security Management of Complex Systems. Proceedings of the XVIII International Conference, Mos- cow, 2010, pp. 492- 496 (Russian). 15. Chilachava T.I., Sulava L.O. A Nonlinear Mathematical Model of Manage- ment. Georgian Electronic Scientific Journal: Computer Science and Tele- communications, 2013, №1(37) pp. 60 - 64 (Russian). 16. Chilachava T.I. Nonlinear Mathematical Model of the Dynamics of the Vot- ers Pro-Government and Opposition Parties (the Two Election Subjects) Ba- sic Paradigms in Science and Technology. Development for the XXI Cen- tury. Transactions II. 2012a, pp. 184 - 188 (Russian). 17. Chilachava T.I. Nonlinear Mathematical Model of the Dynamics of the Vot- ers Pro-Government and Opposition Parties. Problems of Security Manage- ment of Complex Systems. Proceedings of the XX International Conference, Moscow, 2012b, pp. 322 - 324 (Russian). 18. Chilachava T.I. Nonlinear mathematical Model of Dynamics of Voters Three Electoral Subjects. IV International Conference of the Georgian Mathemati- cal Union, Book of Abstracts, Tbilisi - Batumi, 2013a, p. 161. 19. Chilachava T.I., Chochua Sh .G. Two-Party Nonlinear Mathematical Model of Elections Taking Account Falsification. IV International Conference of the Geor- gian Mathematical Union, Book of Abstracts, Tbilisi - Batumi, 2013b, p. 162. 20. Chilachava T.I. Nonlinear Mathematical Model of Dynamics of Voters of Two Political Subjects. Seminar of the Institute of Applied Mathematics Named I.Vekua Reports, 2013c, vol. 39, pp. 13- 22. 21. Chilachava T.I. Nonlinear Mathematical Model of Three-Party Elections. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013d, pp. 513 _ 516 (Russian). 22. Chilachava T.I., Chochua Sh. G. Nonlinear Mathematical Model of Two- Party Elections in the Presence of Election Fraud. Problems of Security Management of Complex Systems. Proceedings of the XXI International Conference, Moscow, 2013e, pp. 349 -352 (Russian). 23. Chilachava T.I., Sulava L.O. Nonlinear Mathematical Model of Elections with Variable Coefficients. VI International Conference of the Georgian Mathematical Union, Book of Abstracts, Tbilisi - Batumi, 2015, p.97. 24. Chilachava T.I., Sulava L.O. Mathematical and Computer Modeling of Nonlinear Processes of Elections with Two Selective Subjects.Georgian 122 leila sulava Electronic Scientific Journal: Computer Science and Telecommunications, 2015a, # 2(46), pp. 61-78. 25. Sulava L.O. Mathematical and Computer Modeling of Nonlinear Processes of Elections.Works of the International Conference “Information and Com- puter Technologies, Modelling, Management” Devoted to the 85 Anniversary Since the Birth of I. V. Prangishvili, Tbilisi, 2015, by pp. 387-390 (Russian). 26. Chilachava T.I., Sulava L.O. Mathematical and Computer Simulation of Pro- cesses of Elections with Two Selective Subjects and Float Factors of Model. Problems of Security Management of DifficultS ystems. Works XXIII of the International Conference, Moscow, 2015b, pp. 356-359 (Russian). 27. Chilachava T.I.,Sulava L.O. Mathematical and Computer Modeling of Three- Party Elections. Georgian Electronic Scientific Journal: Computer Science and Telecommunications, 2016, # 2(48), pp. 59-72. 28. Mihailov A.P., Maslov A.I., Iuhno L.F. Dynamic Model of Competition Be- tween Political Forces. Reports of the Academy of Sciences, 2000, V. 37, # 4, pp. 469 - 473 (Russian). 29. Mihailov A.P., Iuhno L.F. The Simplest Model of Balance Between the two Branches of Government. Math Modeling., Moscow, 2001, V.13, # 1, pp. 65-75 (Russian). 30. Mihailov A.P., Petrov A.P. Behavioral Hypotheses and Mathematical Model- ing in the Humanities. Math Modeling, 2011, V. 23, # 6, pp.18 - 32 (Russian). 31. Samarski A.A., Mihailov A.P. Mathematical Modeling. Moskow, Fizmatlit, 2006 (russian). 123 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV leila sulava sampartiuli arCevnebis kompiuteruli modelireba demografiuli faqtoris gaTvaliswinebiT reziume naSrom Si ganxi lu lia sami saar Cev no subi eq tis (mmarT ve li da ori opozi ci u ri parti is, blokis, koa li ci is) arCev ne bis arawr fi vi maTe ma ti kuri da kompi u te ru li mode li, rome lic saSu a le bas gvaZlebs ganv sazR v roT poli ti ku ri subi eq te bis momx re Ta rao de nobis dina mi ka peri od Si arCev ne bi dan arCev ne bam de mode lis yvela koe fi ci en te bis cvale ba do bis gaTva lis wi ne biT. arawr fiv maTe ma ti kur model Si, rome lic aRwers am process, mona wi le obs oTxi obieq ti: 1. saxel m wi fo da admi nis t ra ci u li struqtu re bi, romle bic mmarT ve li resur se bis gamo ye ne biT zegav le nas axde nen opozi ci u ri parti e bis mxardam Wer amomr Cev leb ze mmarT ve li parti is mxare ze gadmoy va nis mizniT (ama ve dros isini, cxadi a, arian mmarT ve li parti is mxardam We ri amomr Cev le bic). 2. mmarT ve li parti is mxardam We ri amomr Cev le bi. 3. pirve li opozi ci u ri parti is mxardam We ri amomr Cev le bi. 4. meo re opozi ci u ri parti is mxardam We ri amomr Cev le bi. model Si gaTva lis wi ne bu lia demog ra fi u li faqto ri, arCev nebze amomr Cev le bis gamocxa de bis sxvadas x va maCve ne be li da opo zici u ri parti is xmebis gark ve u li gayal be ba arCev ne bis dRes. zemoT aRniS nu li faqto re bis gaTva lis wi ne biT miRe bu lia ricxvi Ti amoxs ne bi. gamoT v le bi saT vis gamo ye ne bul iqna progra muli gare mo MATLAB. aRwe ril maTe ma ti kur da kompi u te rul models aqvs rogorc Teo ri u li, aseve praqti ku li mniSv ne lo ba. poli ti kur oponen tebs (xeli suf le bas da opozi ci as) SeuZ li aT farTod gamo i ye non miRe buli Sede ge bi: airCi on strate gi a, gaTva lon Tavi si SesaZ leb lo bebi, anu para met re bi sasur ve li miznis misaR we vad. 124 qimia CHEMISTRY Mineda Chanturia, Antonina Mskhiladze SOME ASPECTS OF PROBLEM-BASED TEACHING IN THE CHEMICAL KINETICS Development of skills of working in independent laboratory-practical train- ings of students in higher educational facilities is connected with a problem-based teaching/learning, having the key essence in the idea that acquiring knowledge occurs on independent, active, cognitive activity process in the condition of prob- lem situation. While examining chemical reaction, the first task is the determina- tion of its rate and those conditions when the process goes on with the rate desired for practical application. Acceleration of chemical reactions under the impact of various factors (catalyzer, high pressure and temperature) as well as deceleration of dissolution of nutritional products, medical agents is important in industry. Hundreds of biochemical reactions take place in a human body in accord with the rate designed for viability with participation of ferments, due to shortage or surplus of which, the change one of the rates from complex of reactions might become reason for many diseases. For practical solution of this problematic issue, students have to acquire the skill to determine the rate of the reaction constantly. Working on the problem solution way makes students realize the importance of knowledge, that knowledge is not only instinctive information but it is a life liver to solve real problems. While working on the problem solution the question “Why do we need to know this?” is transformed in the question “What should we know to solve a problem?” Through such approach, the problem-based teaching methods have been elaborated in curricula of Chemistry Department at the Faculty of Natural Sci- ences and Health Care of Sokhumi State University, which is discussed on the model of chemical kinetics. The research purpose is: 1. Lecturer has to show the students the problem on the essence of the given topic and its practical application, based upon this, a student should develop the research skills, to comply with the safety rules concerning the practical works, skills of individual and team work. 2. Student should be able to search information, media and technological re- sources, analyze interpret them and apply them to solve the vital problems, to study the preparatory stage, conduct experiments, analyze (dividing components, deter- mination of interrelations among them), model the situation, summarize the results. 125 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 3. Intersubject links of a problem shows how the peculiarities of the given topic might be solved in various disciplines of chemistry. 4. Demonstration of applied aspect of the issue during teaching _ in order to give students the possibility to link the acquired knowledge with everyday life. The rate of the process is the fundamental notion of chemistry and physics. In the school physics course the school learns the movement and its rate, finds out that the instant rate is the distance derivative in time: ∆S dS V = lim = ; (∆t→0) ∆t dt The rate as a change notion of a certain physical dimension in time is effec- tive even when determining the rate of chemical reaction, with the difference that the change in the concentration of reagents is the variable dimension instead of the distance and therefore the chemical reaction rate is considered as a concentra- tion derivative of time: ∆C dC V = lim = ; (∆t→0) ∆t dt Both formulas describe different processes - mechanical movement and chemical reaction. The physical essence and mathematical interpretation of both formulas are equivalent. For the effective conducting of the learning process, in mathematics, phys- ics, and different chemical disciplines: in learning process of general and inor- ganic, analytical, physical, medical chemistry, during considering chemical reac- tion rate, it is necessary to collaborate with teachers and develop joint strategies. Problem-based training takes one of the central places among the learning strategies through which the student will obtain knowledge, develop, analyze, critically evaluate, memorize, and in case of need she/he will use it in different situations. Chemical kinematics studies the chemical reaction rate, the influence of dif- ferent factors on it and the mechanism of reaction, i. e. the reaction process and the nature of substances produced from them. The rate of the transformation changes in the course of the process for differ- ent reactions, i.e. The rate concentration is produced by time, the time function is: v = f (t), therefore the concept of instant rate is used instead of average rate: dc V = ± . dt The rate is determined on the dependency curve of time of the concentration at the corresponding point of time in the direction of X axis carried out by the incline tangent angle: 126 mineda Wanturia, antonina msxilaZe C C α α t0 t t ∆C<0 ∆C>0 The key factors for the chemical reaction rate are: concentration of reagents, the nature of the reactor substances, the size of the touch surface (heterogeneous reaction), temperature, catalysts, pressure (during interaction of the gaseous sub- stances) and more. The rate of homogenous reactions depends on the concentration of reagents, the nature of the reactors, and in the case of heterogeneous reaction _ on the phase separation surface area. The Russian chemist N. N. Beketov first emphasized the rate dependence of the chemical reaction on the concentration. In 1867 it was established by the Norwegian scholars P. Guldberg and C. M. Waage, and was called the main law of chemical kinetics - the law of active substances, according to which: the chemical reaction rate in the homogeneous area at constant temperature is the proportion of the molar con- centrations of substances taking as quality indicators of stoichiometric coefficients. For interaction reaction of A and B substances the equation gives the following: aA + bB → cC + dD Thus, the kinetic equation is mathematically modeled: a b v1 = k1∙ [A] ∙ [B] is the rate reaction of constant not dependent on the concentration of reactor substances; it depends on the nature of the substances, the temperature and the catalyst. Physical essence of lies in the fact that it is equal to the reaction rate when the concentrations of interactive substances are equal to 1 mol/l or their product is equal to 1 by the stoichiometric coefficients. c d v2 = k2 ∙ [C] ∙ [D] The reaction rate constant gives chemists the possibility to characterize quantitatively the issues connected with the chemical reaction speed. According to the mechanism, there are simple and complex reactions. A sim- ple reaction is based on a mono- and bi- trimolecular equation and the order of reactions is the first, second or third. Hard reactions can be parallel, sequential, conjugate and chain. The complicated reactions happens by formation of inter- 127 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV mediate compounds and the final product is obtained through a few simple reac- tions. All biochemical reactions are difficult. The number of molecules involved in the elemental element determines molecu- larity of reaction. In complex reactions, molecularity is defined for individual stages. In kinetic equation the figure quality sum of concentrations of substanc- es is called a reaction row. The total number of a + b = n from the equation a b v1 = k1∙ [A] ∙ [B] is called as a common reaction. There are zero (v = k), the first (v = k ∙ C), the second (v = k ∙ C2) the third (v = k ∙ C3) or reactions of fraction row. The reaction order and molecularity coincides with one another for simple (one-step) reactions. The reason for the differentiation of the reaction row and the molecularity: • Is the process of gradual mechanism; • Concentration constancy of one of the substances. For example, in the hydrolysis reaction of the ester: R - COORˈ + H2O RCOOH + RˈOH; 1 [H2O] = const, v=k ∙ C ester = k ˈ ∙ C [ester reaction is bimolecular but it is the first row]. If there is only one compound⇄ in the conversion, the speed of reac- tion is only the proportion of its concentration _ it is the first row reaction V=k(α-x), where a - is the initial concentration of substance at the moment of t = 0; x - is concentration of substance entering in the reaction in time. The k reaction speed constant is determined by the mathematical transformations: 1 α k = ln ; t α-x 2,303 α k = lg ; t α-x 2,303 - the constant transiting to the decimal logarithm from the natural logarithm. After acquiring the theoretical material, students are able to find necessary information, make its analysis and interpretation in order to use the obtained infor- mation in solving the vital problems. Chemical reactions are chemists’ key task. The two approaches are mainly used to solve the issues based on this problem _ thermodynamic and kinetic. Thermodynamic analysis of chemical transforma- tions is not enough to find out the process performing in the reaction system and the study of reaction kinetics shows the actual reaction process, its mechanism, dependence between the reaction rate and the influencing factors over them. On studying chemical disciplines, it is necessary to carry out various priority activities to determine the criteria of specific indicators: observation, description, planning experiment, organizing data (table, diagram, building graphs, represent- ing experiment results by protocol, presentation, developing tasks, control and 128 mineda Wanturia, antonina msxilaZe testing questionnaires etc.), mathematical calculation of experiment results, per- forming logarithms, integrals and other mathematical operations using computer technologies. Students’ work is organized gradually. At the initial stage they are given a small presentation about project approach, which is mainly used to solve the problem. By reasoning student will determine the possible methods and means of solution based on subjective-theoretical knowledge, in particular, based on the methodological knowledge of chemical kinetics which gives the possibility to solve the problem. From this viewpoint, we have chosen laboratory work on the subject: Determining of the rate of reaction constant. Laboratory Work: Determining the reaction rate of constant of iodine hydrogen acid by peroxide oxidation. Table 1 Get The reaction rate constant is of particular importance: acquainted • For biochemical processes; with the • For elucidation of the possible mechanism of proceeding research process by means of experiment; method: • How much can be possible to manage technological pro- cesses of the noted reaction Get The experimental study of the reaction 2HI + H2O2 → H2O + I2 acquainted confirms that it is the first row and is conducted by two levels: with the d[I ] theoretical V= 2 = k[HI] • [H O ] dt 2 2 essence of laboratory HI + H2O2 → HIO + H2O slow level work HIO + HI → I2 + H2O fast level. The speed of bimolecular total reaction is determined by the slow level - the maximizing stage - the rate. Iodine hydrogen acid is obtained by action of concentrating sulfuric acid on solid iodides: KI(sol) + H2SO4(conc.) → KHSO4+HI or 2KI(sol) + H2SO4(conc.) → K2SO4 + 2HI the reaction is instantly performed. The concentration of hy- drogen peroxide enters into the reaction is determined by equivalently isolated the quantity of iodine which is titrat- ed by sodium thiosulfate _ it is used iodometric method: I2 + 2Na2S2O3→2NaI+Na2S4O6 KI, HI concentrations are permanent and reaction speed dur- ing experiment conditions depends only on the concentration of hydrogen peroxide. 129 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Get For the purpose of practical solution of this problematic issue, acquainted it is necessary for students to study the method of determination with the aim of the reaction rate and development of practical skills of the laboratory work Check out The available materials and technological resources are used material resources Preparation Making different concentrations of solutions based on math- of solutions ematical calculation See the Methods for experimentation: experimental 1. 50 ml 0,4% KI and 2 drops of 1M H SO solutions are placed part: 2 4 in the Erlenmeier flask; 2. A solution of 0,05N Na2S2O3 is poured out with a glass funnel into the burette; 3. A solution of 1 ml 0,05N Na2S2O3 and a few drops of solvent of 0.5% starch are added from the burette. 4. A solution of 1 ml 0,05 N H2O2 is added and stir the flask inside with circular motion; 5. By stop-watch take notes during formation of the blue color shade - free iodine is released; 6. A solution of 1 ml 0,05 N H2O2 is added again and stir the flask inside with circular motion anf by stop-watch take notes during formation of the blue color shade; The experiment is made 4-6 times. In the result of interaction of each added ration of sodium thiosulphate with the released iodine the shade disappeares; 7. The catalyst - 0,1N (NH4)2Mo2O7 - ammonium molybdate solution is added to Erlenmeier flask; 8. The released iodine is titrated with a solution of 0,05 N Na2S2O3 till decolorizing by means of which is tested the equivalent point - how many ml of 0,05 N Na2S2O3 solution is equivalent taken to the solution of 10 ml hydrogen peroxide , or how correctly is the concentration of initial solution determined. 130 mineda Wanturia, antonina msxilaZe Get Depending on the law of equivalents of Richter (1793), the acquainted substances interact with each other in proportion to their equi- with the valents. The basic equation of tytimetric analysis - substances results of the are interactively quantified when the normal concentration ratio processing of their solutions is inversely proportional to the volume ratio and of the solution. calculation V N 1 = 2 V2 N1 1 1 or C ( X) ∙ V(X) = C ( R) ∙ V(R) z z Hence for determining the continuity of the reaction rate the following equation can be determined: 2,303 V k = lg ; t Vt where: V _ is initial concentration of hydrogen peroxide: Vt is the concentration of hydrogen peroxide at t moment. If 10 ml 0,05 N Na2S2O3 of solution is spent, during I shading there are 9 ml of hydrogen peroxide in the solution, the following color corresponds to diminution with 1 ml of hydrogen peroxi- de. In case of hydrogen peroxide solution of 10 ml 0,05 N the reaction speed constant is determined by the following equa- tion: where the volume of 9 hydrogen peroxide is at the moment of the formation of blue color; 2,303 k = [lg9 - lg (9 - x)]; t x - reacted volume of hydrogen peroxide is after formimg each subsequent shade. k1 +k2 +k3 + ∙ ∙ ∙ kn k = ; n The difference in meanings of calculated rate constant of the reaction for different intervals of time cannot exceed a thousand part which confirms the con- tinuity of the reaction rate. The average number of tests of the data is calculated and the temperature is measured. Performance of laboratory work will help to develop students’ research skills. Taking into consideration individual peculiarities, every student’s involve- ment will ensure the development of their multilateral intellect. By demonstrat- 131 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ing the applied aspect of the issue, they can connect acquired knowledge with everyday life. Modern technologies and computer programs (EXEL) can be used to ana- lyze the results of the study of the chemical reaction speed. Reaction rate and determination of reaction order For a reversible reaction A+B→C the determination of reaction rate using the table 2 data at 3260 C temperature. The dependence of the substance concentration on the time (t). Table 2. t, second 0 6 12 18 24 30 ¯ CA mmoli∙l ¹ 2.00 1.64 1.34 1.10 0.90 0.735 t, second 36 48 60 90 54 120 ¯ CA mmoli∙l ¹ 0,60 0.405 0.27 0.095 0.045 0.035 The initial concentrations of reacting substances CAo and CBo are similar. On the basis of the conducted experiments, students calculate the half transforma- tion time τ(1⁄2) of the substance and make the schedule according to the following dependency: (y=f(t), where t _ is time of reaction. CAo 1 1 y = CAo - CA; y = ln ; y= - CA CA CAo The equation of the dependence on the reaction rate concentration is called kinetic equation in differential form and can be received experimentally and can- not be written only in accordance with the strictometric equation of the reaction. The differential and integral equations of simple irreversible reactions, as well as formulas for calculating the half transformation time of reagents are pre- sented in the table 3. Table 3. The number Equation of the After integration τ of reactions speed 1⁄2 y=CAo _ CA =k0t dC CAo 0 A _ = k0 CAo _ CA 2k dt k = 0 0 t 132 mineda Wanturia, antonina msxilaZe C y = In Ao = k t dC 1 In2 1 A CA _ = k1CA k dt 1 CAo 1 k1 = ln t CA 1 1 y = _ = k t 2 1 dC CA CAo 2 A 2 _ = k2C A dt CAok2 1 CAo _ C k2 = t CAoC 1 1 y = _ = (n _ 1)k t Cn-1 Cn-1 n n-1 dC A Ao 2 _ 1 A n N n-1 _ = knC A dt kn(n _ 1) C Ao The task must be initiated in graphical and excel programs, which transforms the chemical system fast and straightforward prediction. Diagram (diagram type “Point”, without connecting lines) are being built the y = f (t) dependency graph, so that the order of the reaction is selected correctly. For this approach, the trend line will be developed, and by this means the reaction speed constant has an aver- age statistical significance. In this case, the trend line parameters are required to refer to the “show equation on the diagram” and “Y axis crossing point 0” at the intersection of the curve with the axis at the point. Excel calculation table. Table 4. t. CAo 1 CAo CAo 1 1 C CAo-CA second ln k1= ln τ1⁄2= _ CA t CA 2k0 CA CAo 0 2 6 1.64 0.36 0.198450939 0.033075156 20.95673172 0.109756098 12 1.34 0.66 0.400477567 0.033373131 20.76961823 0.246268657 18 1.1 0.9 0.597837001 0.033213167 20.86965048 0.409090909 24 0.9 1.1 0.798507696 0.033271154 20.83327739 0.611111111 30 0.735 1.265 1.00103196 0.033367732 20.77297853 0.860544218 36 0.6 1.4 1.203972804 0.033443689 20.72579913 1.166666667 133 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 48 0.405 1.595 1.597015392 0.033271154 20.83327739 1.969135802 60 0.27 1.73 2.002480501 0.033374675 20.76865708 3.203703704 90 0.095 1.905 2.353878387 0.026154204 26.50232339 10.02631579 114 0.045 1.955 3.79423997 0.033282807 20.82598339 21.72222222 120 0.035 1.965 4.045554398 0.033712953 20.56026282 28.07142857 Drawing 1 Drawing 2 Drawing 3 Drawing 4 Students mastered analytical and graphical methods for determining the con- tinuity of the chemical reaction rate. They built the schedules depended on the time of concentration of substances using modern technologies (EXEL), made calculations and on the basis of the mentioned calculations proceeding from data of the figure 4 found out that the reviewed reaction is a first order. The result is obvious if a student can: describe a chemical reaction accord- ing to kinetic indicators; List the factors of chemical reaction rate; Establish the physical essence of the reaction rate constant; Explain the order of kinetic equa- tions of chemical reaction and molecularity of chemical reaction; Explain the elemental act of chemical reaction, simple and complex reactions, dependence between the reaction order and molecularity for simple and complex reactions; 134 mineda Wanturia, antonina msxilaZe Indicate the possibility of increasing or decreasing the chemical reaction rate by changing temperature and catalysts (enzymes, inhibitors); Show the change of kinetic equation order in the case of difficult air hydrolysis according to condi- tions of reaction; Conduct an experiment during a chemical reaction to determine the rate changes and to draw the data graphically; to perform the laboratory work on the theme: determining the reaction rate of constant of iodine hydrogen acid by peroxide oxidation determine the rate of the chemical reaction based on mathematical calculation; to make calculations using the law of active masses; use the acquired knowledge during the optimization of technological processes; learn the methods of quantitative analysis. Thus, planning such activities for the learning process will develop students’ interest and motivation to the study topic, the prerequisite of which is the acquisi- tion of effective strategy training methods based on a problem. References: 1. Chanturia M. M., Main Aspects of Complexometric Method in Chemical Analysis used in Higher Educational System of Georgia, Academic Journal of Science, CD-ROM. ISSN: 2165-6282: 06(01): 247-256, 2016. 2. Chanturia M., Tsintsadze M., Mskhiladze A. - Laboratory Practicum Quanti- tative Analysis, Tbilisi, TSU, 2012. 3. Chanturia M., Mskhiladze A., Gogonaia I. _ Project-Based TRaining Issue Photoeleqtric Colorimetry Analysis, Tskhum-Abkhazian Academy of Sci- ences, Publishing “Meridian”, 2015, T. IX-X, 234-244. 4. Dolidze V., Tsitsishvili V. _ Russian-Georgian-English-German, Chemical Glossary, Tbilisi, 2004. 5. Gabrichidze O., Arziani B., Medicinal Chemistry, Tbilisi, “Inteleqt”, 2003. 6. Gogonaia I., Chanturia M., Mskhiladze A. _ Students’ Independent Work Or- ganization Issues Analytical Chemistry Laboratory in Praktikum, Tskhum- Abkhazian Academy of Sciences, Publishing “Meridian”, 2011, T. II, 420- 425. 7. New Approaches to Teaching and Learning, The Ministry of Education and Science, Tbilisi, 2005. 8. Otto M. _ Modern Methods of Analytical Chemistry. T.1-2 , Moscow, Tech- nosphere , 2003 9. Skyg D., West. D. _ Analytical Chemistry Т. 1-2. М., 1979. 10. The National Curriculum, Tbilisi, 2011-2016. 135 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV mineda Wanturia, antonina msxilaZe problemaze dafuZnebuli qimiuri kinetikis swavlebis zogierTi aspeqti reziume umaRles sagan ma naT leb lo sivr ce Si studen t Ta damo u ki de beli labo ra to ri ul - p raq ti ku li meca di ne o be bis muSa o bis unar- Cveve bis Camo ya li be ba dakav Si re bu lia proble ma ze dafuZ ne bul swavle ba/ s wav la ze, romlis Ziri Ta di ideis arsi mdgoma re obs ima Si, rom codnis SeZe na mimdi na re obs damo u ki de be li aqti u ri Se mecne bi Ti saqmi a no bis proces Si proble mu ri situ a ci is piro beb Si. qimi u ri reaq ci is ganxil vis dros upirve le si amoca naa misi siCqa ris gansazR v ra da im piro be bis dadge na, romel Ta dros proce si praqti ku li gamo ye ne bi saT vis sasur ve li siCqa riT mimdi na re obs. mniSv ne lo va nia rogorc mrewve lo ba Si sxvadas x va faqto ris gavle niT (kata li za to ri, maRa li wneva da tempe ra tu ra) qimi u ri reaq ci e bis aCqa re ba, aseve, sakve bi produq te bis, samkur na lo sa Sua le be bis daSlis proce se bis Sene le ba. adami a nis orga niz m Si asobiT bio qi mi u ri reaq cia SeTan x me bu lad, cxovel q me de bi saT vis gansazR v ru li siCqa riT mimdi na re obs ferme nte bis mona wi le o biT, romlis defi ci tis an Warbi rao de no bis gamo reaq ci a Ta komp leq sidan erT -er Tis siCqa ris cvlile ba SesaZ le be lia mrava li daa vade bis mize zi gaxdes. am proble mu ri sakiTxis praqti ku lad ga dawyve tis mizniT, studen te bi saT vis aucile be lia reaq ci is siCqa ris mudmi vas dadge nis unaris SeZe na. soxu mis saxel m wi fo univer si te tis sabu ne bis mety ve lo mecni ere ba Ta da jandac vis fakul te tis qimi is mimar Tu le bis saswav lo kurseb Si Semu Sav da proble ma ze dafuZ ne bu li swavle bis meTo di ka, romel sac ganvi xi lavT qimi u ri kine ti kis maga liT ze. kvlevis miza ni a: 1. peda gog ma students daa na xos proble ma moce mu li Temis arsi sa da misi praqti ka Si gamo ye ne bis Sesa xeb, ris safuZ vel ze mas unda gamo u mu Sav des kvleva- Zi e bi s, praqti kul samu Sa o eb Tan dakav Si re bu li usafr Txo e bis wese bis dacvis, indi vi du a lu ri da jgufu ri muSa o bis unar- C ve ve bi. 2. studen t ma dasa xu li proble mis gada sawy ve tad unda SeZ los infor ma ci is, media da teqno lo gi u ri resur se bis moZi e ba ana lizi -in ter p re ta cia da misi gamo ye ne ba sasi cocx lo proble me bis 136 mineda Wanturia, antonina msxilaZe gadaW ris T vis, mosam za de be li etapis kvleva, eqs pe ri men tis Cata reba, anali zi (kompo nen te bis gamo yo fa, maT Soris urTi er T kav Si rebis dadge na), situ a ci is mode li re ba, Sede ge bis Seja me ba. 3. proble mis sagan Ta So ri so kavSi re bi miu Ti Tebs, Tu rogor aris SesaZ le be li qimi is sxvadas x va discip li neb Si moce mu li Temis Tavi se bu re be bis gadawy ve ta. 4. swavle bi sas sakiTxis gamo ye ne bi Ti aspeq tis demon s t ri re ba, raTa studen teb ma SeZlon miRe bu li codnis yovel dRi ur cxovre basTan dakav Si re ba. saswav lo proce sis T vis aseTi tipis aqti vo be bis dageg m va stu dentebs ganu vi Ta rebs swor damo ki de bu le bas Sesas wav li sakiTxis mimarT, romlis wina pi ro baa proble ma ze dafuZ ne bu li swavle bis meTo dis efeqti a ni strate gi e bis dauf le ba. 137 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Natia Shengelia, Zurab Pachulia, Lali Tabatazde, Ramaz Gakhokidze MODELLING OF THE GLYCOLSYLATION PRINCIPLE BY QUANTUM-CHEMICAL METHOD Sulfanilamide interaction with β-D-glucose molecule diluted in alcohol area by formation of monoglycoside and with two molecules in absolute al- cohol area by formation of streptocide diglycoside have been conducted by means of quantum-chemical method AM1 calculations. The interaction of streptocide with single molecules glucose diluted in alcohol area by forma- tion of streptocide monoglycoside is energetically more favorable. Modification of carbohydrates by various types of organic compounds has recently played a significant role in the synthesis of new of biological and pharmacologically active compounds. Traditional approach to the solution of efficiency of medical preparations problems is the search of new classes of defined biologically active compounds as well as creation of already known structural analogues of pharmacological preparations for the purpose of increasing of the therapeutic effect and reducing of the toxicity action. The glycosylation principle of medicinal remedies presented by the professor, A. Gakhokidze based on the carbohydrate fragments of active transport in cell membranes is considered as a new approach in creation of a problem connected with targeted action of effective medical preparations. The deficiency of the preparations not being soluble in water can be taken only by internal way or external influence. This circumstance limits their usage in medical practice; in case of the possible usage it is necessary to take them in large doses. The transfer of insoluble drugs in water-soluble forms will be extensively used in medical practice, as it will be possible to inject them subcutaneously or intravenously, which in turn, will change not only the speed of assimilation, but nature of validity. The transfer of sylph amid preparations in water-soluble forms (streptocide, sulfidinum, sulfazolum and others) has gained great importance especially in medicine as bacteriostatic agents towards a number of pathogenic microorganisms. By “binding’’ of carbohydrate molecules insoluble drugs are dissolved in water and easily absorbed into the body, their toxicity is significantly reduced, which greatly increases the effectiveness of treatment preparations. Such approach is now widely used for “ennobling” of anti-cancer drugs and other medicines (Goetchius, Lawrence, 1945; Nagaraja, Naik, Shrestha, Shivakumar, 2007; Pamreddy, Hidalgo, Havel, Salvado, 2013). Interaction of streptocide with glucose by the formation of mono- and di- glucosides has been studied experimentally by A.M. Gakhokidze (Gakhokidze, 138 naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe Sidamonidze, Mamulia, Vardiashvili, Tabatadze, 2006). The purpose of our study was the theoretical confirmation of results and the fixation of recommendations for improving experiments. For full characterization of the reaction, the calcu- lations have been carried out by means of semi-empirical quantum-chemical method - AM1 (Gakhokidze, 1960 : 29-33). For all initial, intermediate and fi- nal products there have been were calculated formation heat (∆Ηf), a system of energy transfer (∆Η) on linking distance (RC-N) alteration, as well as meanings of charges on atoms (qi), dipole moments (μ) and linking orders (Pij). For the purpose of preservation of β anomerical structure of D-glucose, some valent and bi _facet angle have been preserved in a constant fixing regime maintained in a series of calculations. For the first time it has been considered interaction of streptocide in the area of one molecule of β-D-glucose diluted with alcohol (Cω% = 95, ε = 24.95) by monoglycoside of streptocide formation. CH2OH H O OH H O2S NH2 + H OH OH NH H 2 H OH CH2OH O H H O2S NH OHH + H2O H OH NH2 OH H The distance between N13 amino group nitrogen atom and C1 glucose carbon atom connected with C14 atom of carbon of streptocide has been taken more than 1.0 A than linked distance in the final product. The alteration of C-NR distance be- tween N13 nitrogen atom and C1 carbon atoms, as well as RN-H N13 nitrogen atom and H37 hydrogen atom, between RC-O -O8 atom oxygen and C1 carbon atom was occurring by 0.05 Å intervals. The dependency of energy system alteration (ΔH) between nitrogen and carbon atoms RC-N distance is given in figure 1. 139 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Figure 1. The dependence of energy system change (ΔH) between nitrogen and carbon atoms RC-N distance during interaction of streptocide glucose with a single molecule As figure 1 shows, the system of energy is increasing at approach of 13N ni- trogen atom to the C1 atom of carbon to the distance of RC-N = 1.84 Å. The row of link between N13 and C1 atoms increases from 0.008 to 0.480. At the same time the row of link is decreasing between nitrogen and H37 atoms (PN-H = 0.890-0.632) and O8 and C1 atoms (PO-C = 0.964-0.333). It is noticeable a new link formation (PO-H = 0.012-0.233) by the possibility of forming a water molecule. The system energy decreases in the 1.44 Å distance between N13 and C1 atoms. The linking row between N13 and C1 atoms reaches to 0.973, between O8 and H37 atoms gets to 0.932, but between N13 and H37 atoms reduces to 0.005. Thus, the hydrogen atom is entirely separating from the nitrogen atom and is joining to the oxygen atom by means of the water molecule formation. Streptocide monoglycoside will be formed by making a single linking between N13 and C1 atoms. The activation energy of the reaction is ΔΔH # = 427.77 kJ/mol, and the reaction heat effect is ΔΔH = 109.02 kJ/mol. Initial, intermediate and final conditions are given in figures 2-4. 140 naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe Figure 2. Initial interaction condition of streptocide glucose with a single molecule Figure 3. Intermediate interaction condition of streptocide glucose with a single molecule 141 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Figure 4. Final interaction condition of streptocide glucose with a single molecule For the second time has been considered streptocide interact with two mol- ecules of the β-D- glucose in the area of absolute alcohol (ε = 26.31) by formation of D glucoside. CH2OH CH2OH H O OH O H O OH H H H OH + NH2 S NH2 + H OH OH H O OH H H OH H OH CH OH 2 CH2OH H O O O H H H OH NH S NH H OHH + 2 H2O OH H O H OH H OH OH H Similar calculations have been carried out in parallel regime by joining N13 and N21 nitrogen atoms to C1 and C24 carbon atoms by forming streptocide diglu- cosid and two molecules of water. (Figure 5) 142 naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe Figure 5. Dependence of energy alteration system between nitrogen and carbon atoms in the RC-N direction during interaction of streptocide glucose with two molecules Initial, intermediate and final conditions are given in figures 6-8 Figure 6. Initial condition of interaction of streptocide glucose with two molecules 143 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Figure 7. Intermediate condition of interaction of streptocide glucose with two molecules Figure 8. Final condition of interaction of streptocide glucose with two molecules 144 naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe In case of connection of activation energy with two molecules ΔΔH # = 781.03 kJ/mol, and the reaction heat effect is equal to ΔΔH = 110.66 kJ/mol. Proceeding from the comparison of activation energies (ΔΔH # = 427.77 kJ/ mol, ΔΔH # = 781.03 kJ/mol) and the reaction of thermal effects (ΔΔH = 109.02 kJ/mol, ΔΔH = 110.66 kJ/mol) the streptocide interaction with single molecule of glucose in dilute alcohol area by the streptocide monoglycoside formation is energetically more favorable. It is possible to provide the formation of diglyco- side by sequential reactions in more favorable conditions which are the subject of further research. Sulfanilamide interaction with β-D-glucose molecule diluted in alcohol area by formation of monoglycoside and with two molecules in absolute al- cohol area by formation of streptocide diglycoside have been conducted by means of quantum-chemical method AM1 calculations. The interaction of streptocide with single molecules glucose diluted in alcohol area by forma- tion of streptocide monoglycoside is energetically more favorable. References: 1. Dewar M.J.S., Zoebisch E.G., Healy E.F. and Stewart J.J.P. AM1:. A New General Purpose Quantum Mechanical Molecular Model. J. Am. Chem.Soc., 1985, 107: p. 3902 2. Gakhokidze R., Sidamonidze N., Mamulia S., Vardiashvili R., Tabatadze L. Carbohydrate Chemistry of Laboratory Practicum. _ Tbilisi, 2006. 3. Gakhokidze A. M. Kondencatsiya streptotsida s glyukozoy. Trudy Tbilissk- ogo gosudarstvennogo pedagogicheskogo institute im. A. Pushkina. T. 15, 1960. 4. Goetchius G. R. and Lawrence C. A. A Series of New Sulfonamides which are Unaffected by P-Aminobenzoic Acid., Research Laboratories, Winthrop Chemical Company, Inc., Rensselaer, New York Received for publication January 25, 1945. 5. Nagaraja P., Naik S. D., Shrestha A. K., Shivakumar A. A Sensitive Spectro- photometric Method for the Determination of Sulfonamides in Pharmaceuti- cal Preparations (2007) Acta Pharm., 57: 333_342 6. Pamreddy A., Hidalgo M., Havel J. and Salvado V. Determination of Antibi- otics (Tetracycline’s and Sulfonamides) in Bio Solids by Pressurized Liquid Extraction and Liquid Chromatography-Tandem Mass Spectrometry., 2013, Journal of Chromatographya A, 1298: 68-75. 145 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe kvantur-qimiuri meTodiT glikozilirebis principis modelireba reziume naxev ra dem pi ri u li kvantur - qi mi u ri meTo diT AM1 Cata re bul iqna strepto ci dis erT da or mole ku la D-gluko zas Tan kon densa ci is gaTv le bi kalci u mis qlori dis Tandas w re biT mono- da diglu kos t rep to ci dis warmoq m niT. urTi er T q me de bis gaTv le bi, sulfa ni la mi dis monog lu ko zi dis warmoq m niT. N13 atomsa da C1 atoms Soris 1,44 Å manZil ze siste mis energia mkveTrad mcirde ba. bmis rigi N13 atomsa da C1 atoms Soris aRwevs 0,973-s, O8 atom sa da H37 atoms Soris 0.932-s, xolo N13 atomsa da H37 atoms So ris mcirde ba 0,005-mde. wyalba dis atomi srulad wydeba azotis atoms da uerT de ba Jang ba dis atoms wylis mole ku lis warmoq m niT. N13 atomsa da C1 atoms Soris erT ma gi bmis damya re biT war moiq m ne ba sulfa ni la mi dis monog lu ko zi di. reaq ci is aqti va ci is energia ΔΔH# = 427,77 kj/moli, xolo reaq ci is siTbu ri efeqti ΔΔH = 109,02 kj/moli. abso li tur spirt Si kalci u mis qlori dis Tandas w re biT wyalba dis atomi srulad wydeba azotis atoms da uerT de ba Jang ba dis atoms wylis ori mole ku lis warmoq m niT. N13 atomsa da C1 atoms Soris erT ma gi bmis damya re biT warmo iq m ne ba sulfa ni la mi dis diglu ko zi di. reaq ci is aqti va ci is energia ΔΔH# = 781.03 kj/moli, xolo reaq ci is siTbu ri efeqti ΔΔH = 110,66 kj/ moli. strepto ci dis urTi er T q me de ba gluko zis erT mole ku las Tan ganza ve bu li spirtis areSi strepto ci dis monog lu ko zi dis warmoq m niT energe ti ku lad ufro xelsay re li a. 146 ekologia ECOLOGY Marat Tsitskishvili, Gulnara Karchava, Mariam Tsitskishvili, Eka Esebua REGIONAL PARAMETERISATION OF ATMOSPHERIC TRANSFER FOR REDUCTION RADIOACTIVE POLLUTION Introduction: The pollution of the radionuclide at identical loads is usually limited by atmospheric thermodynamically stability; for this purpose the Richardson parameter is often used. Results: For practical purposes approximately a determined stability parameter is used to characterize the distribution of pollutants in the atmosphere g ΔT/ΔH Ri= · 2 T0 (ΔU/ΔH) where: ΔT и ΔU are correspondingly the variability of the temperature and wind ve- locity according to the height. ΔH are height differences in the upper surface layer. We worked out climatologically data of Russian, Caucasian and Crimea re- gions. The systems of methodological stations bordering Russia, Georgia, Arme- nia and Azerbaijan have been studied in detail. We estimated the conventional stability coefficient of the atmosphere (M) in the following way: g · ΔH Tmax-Tmin m"= 2 · (γmax-γmin) T Conventional values of M for a number of stations are given in Table 1. While analysing the data in Table 1 it becomes evident that the assumed parameter M expresses quite the objective geoclimatic peculiarities and stable characteristics. Thus in one and the same gradation zone appear such geoclima- tologically similar regions as: I zone - Krasnodar (data are obtained basically from the meteorological sta- tions of the Black Sea coastal region), the Crimea and Odessa regions; II zone - Volgograd, Dagestan, Rostov and Stavropol regions (with a little error Astrakhan region as well); III zone - Armenia and Azerbaijan; IV zone - North Ossetia and Chechen. 147 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Such gradation can be assumed according to the values of conventional sta- bility coefficient of the atmosphere M (this parameter is never negative M < 20) - Characteristic to seaside circulation: 0 < M < 20; - Plains (above the sea level 200-300 m): 20 < M < 30; - Mountainous regions with a comparatively difficult relief: 30 < M < 50; - Highland regions: M < 55. Table 1 The values of conventional stability coefficient dT I Conventional Region M’ M T Vmax2 Gradation Zones Astrakhan 9.102 0.034 0,312 31.2 III Volgograd 11.191 0.026 0.91 29.1 II Dagestan 6.286 0.044 0.275 27.5 II Krasnodar 6.260 0.024 0.152 15.2 I Rostov 9.431 0.025 0.238 23.8 II North Ossetia 8.696 0.111 0.966 96.6 IV Stavropol 8.197 0.028 0.228 22.8 II Chechen 7.327 0.082 0.598 59.8 IV The Crimea 5.767 0.030 0.173 17.3 I Odessa 7.311 0.014 0.107 10.7 I Azerbaijan 4.552 0.075 0.340 34.0 I1I Armenia 8.491 0.040 0.342 34.2 I1I For practical estimations let M=100· M’ Such classification is done with the account of the Georgian necessities _ see Table 2. This allows minimizing the costs of the atmospheric protection by means of using the results for the optimisation of regional approaches. It is absolutely new and original approach. It allows without greater expenses and long-term experi- ments, on climatologically long-term standard climatologically given to spend ecologically proved optimisation of accommodation in concrete regions of the industrial enterprises with greater emissions in an atmosphere. It is considered that it is urgent for a choice of atomic power stations site. All types of industrial activities require to follow the norms of air basin pro- tection, preserve its pollution and degradation. At the same time, the environment 148 marat cicqiSvili, gulnara qarCava, mariam cicqiSvili, eka sebua protection itself constitutes an industrial activity, so the separation of these activi- ties is symbolic. Nevertheless, let follow the tradition; thus the above-mentioned industrial and protective activities will develop and become perfect due to scien- tific progress and the design of programmes aimed at reducing the pollution and improving environmental quality. The occurred political changes and economic development caused by them have altered the ways of enhancement of such pro- grammes. For such country as Georgia it is impossible to carry out the similar programmes by its own sources without transnational economic instruments such as pollution permits tradable at the international level environmental cost - ben- efit analysis, large investments into special programmes Development of com- mon economic area of countries of the Black Sea basin an increase of integration processes makes possible to carry out a number of political and economical mea- sures. Common industries activities connected with joint enterprises require cre- ating unified regulatory mechanisms. Man juridical, technological, economical and political regulatory mechanisms permitting to reduce harmful anthropogenic influence on environment are based on stand arts adopted by the state committee on environment protection. It was conditioned by great climatic and ecological significance. The solid or liquid microscopic particles, suspended in atmosphere differ from atmospheric dust having long “life” time in atmosphere. These particles constitute atmospheric aerosols. Their chemical and dispersive composition has a wide range of changeability. A lot of researches have recently been dedicated to the study of physicochemical qualities of atmospheric aerosols. It was con- ditioned by great climatic and ecological significance. The research results of atmospheric aerosolise component for Transcaucasia have been summarized in our paper where we show the “climatic stability” of atmosphere’s lower layer “self-rectification’s velocity”. The methodology of its experimental definition became possible after the determination of simple gauzed manifold catching ef- fectiveness which is used widely in Georgian Hydromet network i.e. the effective of atmospheric sediment collectors. All types of industrial activities require to follow the norms of air basin pro- tection, preserve its pollution and degradation. At the same time, the environment protection itself constitutes an industrial activity, so the separation of these activi- ties is symbolic. 149 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Table 2 Values of the conventional stability coefficient for various regions of Georgia dT I Region M’ M T Vmax2 Gagra 5.760 0.040 0.150 15.0 Sokhumi 3.690 0.040 0.148 4.8 Poti 3.610 0.038 0.137 13.7 Batumi 3.330 0.040 0.133 13.3 Black Sea coast 3.560 0.040 0.142 14.2 Zugdidi 4.275 0.104 0.449 44.9 Samtredia 4.028 0.038 0.153 15.3 Kutaisi 4.069 0.016 0.064 6.4 Westem Gergia 4.070 0.034 0.140 14.0 Akhalkalaki 14.694 0.022 0.327 32.7 Akhaltsikhe 7.889 0.148 1.167 116.7 Borjomi 7.143 0.104 0.43 74.3 South Georgia 9.013 0.060 0.53 53.6 Gudauri 28.571 0.148 4.228 422.8 Shovi 12.500 0.160 2.000 200.0 Oni 6.500 0.174 1.128 112.8 Mountains 10.914 0.160 1.460 174.6 Gori 5.872 0.049 0.288 28.8 Tbilisi 4.961 0.066 0.327 32.7 Dmanisi 8.077 0.059 0.476 47.6 Gurjaani 4.839 0.059 0.286 28.6 Telavi 5.170 0.069 0.357 35.7 Eastern Georgia 5.491 0.059 0.324 32.4 The geophysical essence of obtained characteristics is: “self-rectification’s velocity”, compared with regions, which are far from the sea (Tbilisi, Yerevan, and Rostov). _ Conventionally, we can say that for the given region there is “three types” (groups) of atmospheres “self-rectification’s velocity” according to the follow- ing gradation: _ Continental (Tbilisi, Yerevan) wit velocities up to ~0,5 transitional up to 2,0 (Rostov): _ And seaside (Volgograd, Astrakhan, Sokhumi, Baku), where velocities ex- ceed 2,4 Km/24 hours. 150 marat cicqiSvili, gulnara qarCava, mariam cicqiSvili, eka sebua Various kinds of admixtures (solid, liquid or gaseous) getting in atmosphere stay there for definite time. It depends on many processes: the turbulent calcu- lation, sedimentation or coagulation with particles of clouds, their washing by atmospheric sediments. During the study of geo-ecological aspects of the atmo- sphere soiling, processes of the admixtures sedimentation from the atmosphere are divided conventionally into two groups: dry “sedimentation” and “washing” by atmospheric sediments (“dry” and “wet” sedimentation). The conventionality of such division is clear, if we go deep into physical and chemical mechanisms of processes, taking place in the atmosphere. The simple analysis shows that gravity and elementary forces as well as the turbulence, moisture and density of gas (in this case different layers of the atmosphere) always participate in each process (in the case of loaded particles). In spite of the conventionality of such division, it gives us the possibility to reveal regional geophysical peculiarities in processes of the same admixture (or pollution’s) sedimentation from the atmosphere. It’s a well-known fact, that during the sedimentation of aerosolise particles from the atmosphere, there are much more “wet” sediments, than “dry” ones, but it’s dif- ficult to make the correct numerical estimation, in spite of huge number of experi- mental and theoretical data. The whole region is characterized by annual washing: Cold season: 9.966 x 10-5 sec-I; Warm season: 4.119 x 10-5 sec-I; Average annual: 7.029 x 10-5 sec-I. References: 1. Erkomaishvili G., Shatberashvili I., Tsitskishvili M., Atmosphere Self-Rec- tification Peculiarities from Aerosols. Bulletin of the Georgian Academy of Sciences, 158, N2, 1998, pp. 240-243. 2. Khutsidze Sh., Tsitskishvili M., Improvement of Air Pollution Protective Technical Measures with Regional Geophysical Parameterization. Bulletin of the Georgian Academy of Sciences, 155, N2, 1997, pp. 77-79. 3. Shatberashvili I., Tsitskishvili M. et all. Integrated Characteristics in Mod- els Aerosol Transfer in Atmosphere. ISTC Russian _ Canadian Workshop “Modelling Atmospheric Dispersion of Weapons Agents. June 19 -21, 2006. Moscow, pp. 102 -104. 4. Tsitskishvili M., Diasamidze R., Shatberashvili I., Ninua T., Regional Peculiari- ties of A ir Basins Ecology on the East Coastal Zone of the Black Sea, “Prob- lems of Ecology”, V. II, Tbilisi, “Technical University”, 2000. pp. 147-158. 151 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV marat cicqiSvili, gulnara qarCava, mariam cicqiSvili, eka esebua atmosferuli gadatanis regionaluri parametrizacia radiaciuli daWuWyianebis Sesamcireblad reziume atmosferuli mdgradobis dasaxasiaTeblad, (romelic ganapi- robebs damaWuWyianebeli nivTierebis, maT Soris radioaqtiulis, gadatanas miwispira fenaSi), miRebulia `riCardsonis~ parametri, romlis gansazRvra moiTxovs ZviradRirebuli gradientuli dak- virvebebi. am winaaRmdegobis gadasalaxavad Cvens mier SemoRebu- lia `pirobiT-klimatologiuri~ parametri, romelsac vangariSobT klimatologiuri cxrilebis meSveobiT. kavkasiisa da volgispireTis punqtebisaTvis Catarebuli ga- moTvlebi Sepirispirebuli iqna saqarTvelos regionebTan, ramac gamoavlina SemoRebuli parametris regionaluri mdgradoba da SesaZlebloba misi efeqturobisa da raionirebisaTvis gamosayene- blad, radionuklidebis atmosferuli gadatanis SemTxvevaSi. naSromSi ganxilulia agreTve savsebiT originaluri axali klimatologiuri parametri `atmosferos qveda fenis TviTganw- mendis siCqare~. moyvanilia gasaSulebeli monacemebi sxva da sxva sezonisaTvis amierkavkasiisaTvis. 152 enaTmecniereba LINGUISTICS manana Selia toponimuri warmoSobis ferTa Seferilobebi Tanamedrove inglisur enaSi samyaros enobrivi suraTi warmoadgens mravalferovan mo- zaikas, romelic asaxavs sxvadasxva eTnosisa da enis istoriul ganviTarebas, maT zogadkulturul monapovars. enis cvlileba da ganviTareba mudam dakavSrebulia istoriul movlenebTan, romlis drosac sakmaod swrafi tempiT mimdinare- obs masStaburi cvlilebebi. aSkaraa, rom am procesis gamomwvevi mizezebi ara Sinagani, aramed garegani faqtorebicaa. kerZod, is socialuri cvlilebebi da teqnikuri miRwevebi, romelsac adgi- li aqvs yoveldRiur cxovrebaSi. sxva enebis msgavsad, inglisuri enac moqceulia mudmiv cvlilebasa da dinamikaSi. sityvebi, romelsac viyenebT yoveldRiur cxovrebaSi, sain- teresoa Tavisi istoriiT da TaviseburebebiT. nebismieri enis leqsikis ganviTarebaSi yvelaze mkafiod gansazRvrul procesad iTvleba enis mudmivi da intensiuri Sevseba axali, adre ucnobi sityvebiT, rac mudmivad xorcieldeba Cvens garemomcvel samya- roSi momxdari cvlilebebisa da enis matarebelTa moTxovnebis Sesabamisad (Crystal, 2003: 47). sityva SeiZleba SevadaroT mozaikis kenWebs. sxvadasxva enaSi am nawilebis ganlageba sxvadasxvanairad xdeba, rac sxvadasxva suraTs iZleva. es suraTebi gamoirCevian Tavisi ferebiT da SeferilobebiT. bunebaSi arsebobs ferTa uTvalavi raodenoba. bunebis sao- cari qmnilebebis ferebi da Seferilobebi warmodgens sxvadasxva sferoSi moRvawe adamianTa interess. mocemuli naSromi eZRvneba Tanamedrove inglisuri toponi- muri warmoSobis ferTa Seferilobebis leqsikur-semantikuri Taviseburebebis ganxilvas da aseve maTi etimologiis detalur aRweras eqstralingvisturi TvalsazrisiT. analizisTvis Sevar- CieT toponimTa, kerZod, oikonimTa erT-erTi saxe _ asteonimebi, romlebic inglisuri leqsikis ferTa jgufSia Sesuli. feris fenomeni warmoadgens mravali fundamentaluri mec- nierebis sagans, romlebic did rols TamaSoben sazogadoebis 153 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV cxovrebaSi. adamianis mier ferebi da Seferilobebi aRiqmeba sxva- dasxvanairad. rogorc cnobilia, feris simbolikas uZvelesi istoria aqvs. mecniereba feris Sesaxeb, anu ferTa Teoria didi xnis win gaCnda. misi daarsebis TariRad SeiZleba CaiTvalos i. niutonis mier XVII saukunis Sua wlebSi gakeTebuli aRmoCena, rom mzis sxivi Seicavs bunebaSi arsebul yvela fers. mzis sxivis uwyvet speqtrSi arCeven 130-mde feris tonalobas. realur cxovrebaSi am ferebis naxva ci- sartyelaze SeiZleba. niutonma speqtris sawyisi feri daukavSira speqtris bolo fers da Seqmna ferTa wre, romelzec feris SerCe- va Zalian advilia da romliTac dRemde sargebloben isini, visac odnavi Sexeba mainc aqvT ferebTan da saRebavebTan. ferTa gamam asaxva pova miTologiaSi, xalxur gadmocemebSi, zRaprebSi, wes-CveulebebSi, sxvadasxva religiur Tu mistikur swavlebebSi. ferTa speqtrSi gamoyofilia 7 ZiriTadi feri: wiTe- li, narinjisferi, yviTeli, mwvane, cisferi, lurji da iisferi. yvelanairi feri swored am 7 feris sxvadasxva raodenobiT Sere- vis gziT miiReba. astrologiaSi cisartyelas 7 fers 7 ZiriTadi planeta Seesa- bameba: wiTeli marsis feria, lurji _ venerasi, yviTeli _ merku- ris, mwvane _ saturnis, alisferi _ iupiteris, narinjisferi _ mzis, iisferi ki mTvaris simboloa. amasTan erTad, ferebi ara mxolod planetebsa da maT gavlenas asaxaven, aramed adamianTa gansxvavebul fsiqologiur mdgomareobazec miuTiTeben. sxva- dasxva ers, droTa ganmavlobaSi, maTTvis damaxasiaTebeli ferTa simbolika Camouyalibda. XIX-XX saukuneebSi ferTa mravali atlasi da skala Seiqmna. pirveli albomebi safrangeTSi gamoqveynda. es iyo racionaluri klasifikaciis pirveli cdebi. erT-erT yvelaze srul atlasad r. polisa da maersis atlasi miiCneva, romelSic 7000-mde ferisa da elferis nimuSia moyvanili (Zaqaraia, 1971: 7). amerikis SeerTebul StatebSi SemuSavda `feradi harmoniis saxelmZRvanelo~ (Iakobsoni, granvili, Forsi, 1948), romlis safuZvel- zec Sedgenil iqna bunebriv ferTa sinaTlis atlasi “Natural Color System”. dasavleTis qveynebis ferTa standartebis nacionaluri biuroebisa da feris dargTaSorisi sabWos monacemTa mixedviT SemuSavda ferTa aRmniSvneli leqsika inglisur enaze. leqsikonSi Sesulia 7000 sityva (Belyavskaya, 2004: 6). amerikeli mecnierebi b. berlini da p. qei miiCneven, rom fer- Ta kategoria enis individualuri Tavisebureba ki ar aris, aramed 154 manana Selia adamianTa rasis saerTo konceptualuri sistemaa. Tumca, aqve saWi- roa davazustoT, ferTa kategoria ara mxolod individualuri Ta- viseburebaa konceptualuri TvalsazrisiT, aramed mas aqvs univer- saluri, kacobriobisaTvis damaxasiaTebeli, tradiciuli niSnebi. am zogad konceptualur sistemaSi sainteresoa, Tu raSi vlindeba ferTa terminologiis specifika da ferTa aRmniSvneli sityvebis ra Tvisebebi warmoCndeba enaSi. inglisuri enis leqsikaSi gansakuTrebul jgufs qmnian ferTa aRniSvnebi. isini ZiriTadad kompoziciuri da derivaciuli mode- lebis mixedviT arian miRebuli da sagrZnoblad amdidreben fer- Ta aRmniSvneli sityvebis marags. b. berlinma da b. qeim daadgines, rom ferebis aRmniSvneli le- qsikis universaluri sistema 11 ZiriTadi kategoriisagan Sedgeba (white, black, red, green, yellow, blue, brown, purple, pink, orange, grey) da isini mkacri maTematikuri rigiT moawesriges (Leech, 1977: 235). speqtrul ferTa sistema samganzomilebiania. maT gaaCniaT sami ZiriTadi Tviseba, esenia: feris toni, anu Tvisebrioba (romeloba), sinaTlis xarisxi (naTeloba) da feris najeroba. toni aris is Tvi- seba ferisa, rasac yoveldRiur metyvelebaSi feri ewodeba. Tvi- sebrioba mxolod qromatulebs gaaCniaT, amasTan, eseni sinaTlis xarisxiTac gansxvavdebian: erTi da imave feris toni met-naklebad muqic SeiZleba iyos da Riac, xolo najeroba feris siwmindesa da ferobis xarisxSi mJRavndeba (Dzadzamia, 2005: 18). ferTa gama brunavs ZiriTadi feris irgvliv, romelic xdeba Ria an muqi. ZiriTadi feri (primary colors) samia. esenia: wiTeli, yviTeli da lurji, romlebic qmnian meorexarisxovan (secondary) ferebs. meorexarisxovani ferebia: mwvane, stafilosferi da isam- nisferi, romlebic miiReba ZiriTadi ferebis erTmaneTSi SereviT. ase, magaliTad, lurjisa da yviTelis erTmaneTSi areviT viRebT mwvanes; wiTlisa da yviTlis areviT _ stafilosfers; lurjisa da wiTlis areviT _ iasamnisfers. rac Seexeba mesame donis (tertiary) ferebs, isini warmoadgenen ZiriTadi da meorexarisxovani ferebis nazavs. amgvarad, ferTa gamas kidev 6 feri emateba: stafilosfer-yviTeli, wiTel-stafi- losferi, iasamnisfer-wiTeli, lurj-iasamnisferi, lurj-mwvane, yviTel-mwvane. inglisur enaSi ferTa aRmniSvnel sityvaTa jgufs miekuTvne- bian umTavresad geografiuli saxelebi, adamianTa saxelebi, Zvir- fasi da naxevrad-Zvirfasi qvebisa da mineralebis, mcenareTa, cxo- velTa, frinvelTa, liTonTa, ciur sxeulTa, Txevad nivTierebaTa 155 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV dasaxelebebi, romlebic zogjer iwveven azrobriv kavSirs konkre- tul ferTa tonalobasTan. rogorc zeviT aRvniSneT, Cveni kvlevis mizans warmoadgens toponimuri warmoSobis ferTa Seferilobebis deskriptiuli ganxilva etimologiur da eqstralingvistur WrilSi. sityva toponimika berZnuli warmoSobisaa (topos _ niSnavs adgils, adgilmdebareobas, xolo onoma _ saxels), onomastikis dargia, romelic geografiul saxelebs (toponimebs), maT funq- cionirebas, mniSvnelobasa da warmoSobas, struqturas, gavrce- lebis, ganviTarebisa da droSi cvlilebis areals ikvlevs. topo- nimika, toponimTa erTobliobaa, romlebic ama Tu im niSnis mixed- viT gamoiyofa: teritoriuli (inglisis, safrangeTis toponimika), enobrivi (inglisuri, qarTuli toponimika), qronologiuri (XVIII saukunis toponimika) niSnebiT (Gurgenidze, 2013: 40). yovel toponims gaaCnia sxvadasxva informacia: istoriuli, geografiuli, lingvisturi, radganac geografiuli saxelebi es epoqaTa istoriuli pirobebis momswreebi arian, roca xdeboda maTi warmoSoba, formireba da gavrceleba ama Tu im qveyanaSi. inglisuri sityva marengo _ Marengo, romelic aris vardis- fris Seferiloba, evropaSi XVIII saukuneSi gamoCnda. igi warmo- adgens muq yavisfer qsovils TeTri laqebiT. qsovili pirvelad daamzades sofel spineta marengoSi _ Spinetta Marengo _ italiis CrdiloeT nawilSi. safrangeTSi am fers uwodebdnen marengo ou brun (marengos an yavisfers). 1800 wlis 14 ivnisis marengos brZolis Semdeg, romelSic na- poleon bonapartis jarebma daamarcxes avstriis armia, marengo cnobili gaxda rogorc nacrisferi, an rogorc Savi qsovili Te- Tri an nacrisferi ZafebiT. es feri asocirdeboda nacrisfer farajasTan, romelic bonapartma Semoitana modaSi. Seferiloba _ Marengo gaxda popularuli ruseTSic. XIX saukunis dasawyisSi gamoCnda kidev erTi, marengo-kleri (Ria nacrisferi), romelic gaxda Ria nacrisferis variacia. Hollywood cerise _ holivud seris _ vardisfris erT-erTi Sefe- rilobaa. sityvis pirveli komponenti Hollywood _ holivudi qalaqis saxewodebaa, romelic, rogorc cnobilia, mdebareobs aSS-is ka- liforniis Statis, los-anjelesis ubanSi. misi saxeli asocirdeba amerikis kino da satelevizio industriasTan, varskvlavebTan. 1853 wels, am qalaqis adgilze, romelic Semdeg gaxda holivu- di, erTi TixiT nalesi qoxi idga. 1870 wlamde am adgilas eweodnen 156 manana Selia soflis meurneobas da moyavdaT xorbali. qalaq “Hollywood”-is saxe- lwodebis warmoSobaze ramdenime versia arsebobs. is rTuli sityvaa, romlis pirveli komponenti “holly” aris maradmwvane mcenare _ baZgi, Wyori (laT. Ilex), romelic ekuTvnis baZgisebrTa ojaxs. aqvs martivi, tyavisebri xeSeSi, kideekliani foTlebi. nayofi kurkiania, wiTeli an Savi, iSviaTad yviTeli. sityva Hollywood niSnavs baZgis tyes. qalaqis saxelwodeba Hollywood-Tan dakavSirebiT arsebobs sxva versiac. `holivudis mamis~ h. j. uiTlis mixedviT, is 1886 wels, Tavis Taflobis TveSi, gorakze idga. swored am drois Cinelma kacma Camoiara SeSiT savse furgoniT. kaci gadmovida furgoni- dan da Tavdaxrili miesalma mas. Cinels hkiTxes Tu ras akeTebda, man umalve upasuxa, rom is SeSas ezideboda _ “I holly-wood”, mea- ning “hauling wood”. h. j. uiTlim gadawyvita axal qalaqs darqmeoda Hollywood. misTvis Holly _ holi iqneboda wamodgenili rogorc in- glisi, xolo wood _ vudi misi Sotlandiuri dedul-mamuli, xolo sityva Hollywood cerise -is meore komponenti _ cerise warmoSobilia frangulidan (XIX saukunis Sua periodi), is saTaves iRebs laTi- nuridan ceresia, romelic aris cherry-s dubleti. sainteresoa vardisfris erT-erTi Seferilobis _ mewamulis inglisuri varianti _ Magenta majentas etimologia, romelic pir- velad gamoiyena 1859 wels eduard Ceimber nikolsonma majentas brZolis. brZolebi mimdinareobda qalaq majentaSi, romelic mde- bareobs italiis CrdiloeTiT, milanis provinciaSi, lombardiaSi. frangebma da sardinielebma daamarcxes avstrielebi 1859 wels, romelmac saTave daudo italiis damoukideblobas. mewamuli, Jolosferi, aWarxalebuli anilinuri saRebavi aRmoaCines male brZolis Semdeg. qalaqis saxeli dakavSirebulia romael general da imperator markus avrelius valerius maqsenciusTan (278-312), romelsac aq savaraudod Stabi hqonda ganlagebuli. maSasadame, qalaqis saxelwodeba momdinareobs laTinuridan _ castrum Maxen- tiae _ “castle of Maxentius”, niSnavs maqsenciusis cixe-simagres. maSa- sadame, majenta aris vardisfris ferTa jgufSi erT-erTi Sefe- riloba. majenta _ Magenta aseve wiTeli feris erT-erTi Seferilobaa (Magenta), romelsac uwodeben fuqsins. is fotokopirebaSi Ziri- Tadi feria, sityva momdinareobs saRebavis saxelwodebidan, ro- melic pirvelad aRmoaCina londonSi Simpson, Nicholson da Maule-is kompaniam. 1859 wels, eduard nikolsonma es saRebavi miiRo ani- linisgan da daiwyo misi gayidva majentas _ Magenta saxelwode- biT CrdiloeT italiaSi garibaldis gamarjvebis pativsacemad. 157 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV am qimiur saRebavs fuqsini _ fuchsine _ uwoda frangma e. verginma (E. Verguin), romelmac aRmoaCina misi miRebis meTodebi. es saxe- lwodeba momdinareobs mewamuli-wiTeli feris mcenaris _ fu- qsisagan, romlic, Tavis mxriv, atarebs XVI saukunis germaneli botanikosis leonard fuqsis saxels. XXI saukuneSi yvelaze cnobili gaxda majentas ori standar- tuli varianti. is rogorc meoradi feri miRebulia, ZiriTadad, wiTlisa da lurji ferebis Tanabari proporciiT, adiciuri Sere- viT. TviT majentas aqvs calke Seferilobebi mag: Amaranth, Ama- ranth pink, Amaranth purle, Blush, Cherise, Crimson, Eggplant, Fandaggo, Folly, Fuchsia, Hollywood cerise, Hot Magenta, Magenta, Magenta (panto- ne), Magenta Dye, Magenta Haze, Mulberry, Orchid, Plum, Purple Pizzazz, Quianacridone Magenta, Raspberry, Razzle Dazzle Rose, Red Violet, Rose, Choking Pink, Sky Magenta, Steel Pink, Telemagenta, Ultra Pink, Violet Red. adelaida _ Adelaide aris SroSanisfris wiTeli Seferilo- ba. sxva wyaroebis mixedviT muqi-lurjia. XIX saukunis 40-50-ian wlebSi gamoiyeneboda presaSi, aseve vxvdebiT i. turgenevisa da T. dostoevskis nawarmoebebSi («цвета аделаида, или, как у нас говорится, оделлоида»), («Так этот галстух аделаидина цвета? _ Аделаидина-с. _ А аграфенина цвета нет?») qalaqi adelaida (ingl. Adelaide) aris samxreT avstraliis Sta- tis administraciuli centri da sididiT me-5 qalaqi, romlis mo- saxleoba Seadgens 1 milionze met adamians. qalaqi daarsda 1836 wlis 28 dekembers, romelic britanuli mosaxleobisTvis war- moadgenda avstraliis erTaderT Tavisufal qalaqs. mas saxeli daerqva britaneTis monarqis, vilhelm IV-is (1830-1836) meuRlis, dedofal adelaidas pativsacemad. saxel adelaidas etimologia Semdegia: franguli varianti _ Adelaide (fr. Adélaïde); Zvelgerma- nikuli saxeli _ adelheidi (Adalheid, Adelheid, Adelheidis) _ Sedge- ba ori Zirisgan: adal (keTilSobili, pativsacemi) da heid (saxeoba, gvari). maSasadame, Adelheid niSnavs `keTilSobils, keTilSobilur warmoSobas an ubralod keTilSobilebas~. Tuscan red _ toskanuri wiTeli, wiTeli feris erT-erTi Sefe- rilobaa, romelic gamoiyeneboda pensilvaniis rkinigzis samgza- vro vagonebisTvis da satvirTo manqanebisTvis. am feris gamoyeneba pirvelad daregistrirda inglisur enaSi 1887 wels, romelic po- pularuli gaxda XIX saukunis bolos, magram iTvleboda arastan- dartul ferad. Tuscan toskanur wiTels gaaCnia variaciebi (inglisur enaSi es feri TariRdeba 1800 wlis dasawyisiT): Tuscan Beige (inglisur 158 manana Selia enaSi pirvelad gamoCnda 1922 wels), Tuscan Tan (color) (inglisur enaSi pirvelad gamoCnda 1926 wels), Tuscan Brown (inglisur enaSi pirvelad gamoCnda 1913 wels). Tuscan _ toskana regionia centralur italiaSi. regionuli dedaqalaqia florencia. toskanuri dialeqti literaturuli italiuris safuZvelia. toskana adre iyo romauli etruria, da- saxlebuli etruskebiT Zv.w. 500 wels. toskanas etimologia Semdegia: 1350-1400; Middle English < Tuscānus Etruscan,equivalent to Tusc(ī) the Etruscans + -ānus a race of ancient Italy “belonging to the Tusc”, from Tuscus, earlier _ Truscus, shortened form of Etruscus (cf. Etruscan). rogorc aRniSnuli qalaqis etimologiidan Cans is warmoSobilia etruski Semoklebuli variantidan _ Truscus. rogorc cnobilia, etruskebi Crdilo-dasavleT italiaSi cxo- vrobdnen. maT SeiTvises elinTa didi civilizacia da damwerlo- bac Zveli berZnulidan aiRes. etruskebma Seqmnes TviTmyofadi kultura da didi gavlena moaxdines mezobel xalxebze, maT Soris romaelebsa da frangebze. frangebs etruskebma aswavles Rvinis dayeneba, romaelebs _ gzebis dageba-mSenebloba, danarCen evro- pas _ weris xelovneba. etruskuli kultura ayvavda Zv.w. 900-500 wlebSi. Charleston green _ Savi feris Seferilobaa _ muqi cianidis feri. misi warmoSoba ukavSirdeba amerikis samoqalaqo oms, daaxloebiT TariRdeba 1865 wliT. am feriT Rebavdnen saxlebs qalaq Carl- tonSi, samxreT karolinaSi (qalaqs saxeli ewoda inglisis mefis Carlz II pativsacemad). Portland Orange _ portland narinjisferi, narinjisferis erT- erTi Seferilobaa. portlendi (ingl. Portland) oregonis Statis qa- laqia, romelic mdebareobs mdinareebis vilametisa da kolumbiis SesarTavTan. is aSS-Si erT-erTi yvelaze gamwvanebuli qalaqia. Portland Orange _ portland narinjisferi aris aSS-sa da kana- daSi gamoyofili sacalfexo gadakveTis signalebis DONT WALK _ fazis Suqi. Naples yellow _ neapoluri yviTeli, romelsac aseve uwodeben antimon yviTels, meryeobs mkrTali an miwisferi mowiTalo yvi- Teli pigmentidan naTel Ria yviTel feramde. es aris qimiuri naerTis _ tyviis (II) antimonati. neapoluri yviTeli eqstensiurad gamoiyeneboda rogorc Zveli ostatebis, aseve XX saukunis mSene- blebis mier. XVIII saukuneSi man didwilad Secvala lead-tin-yellow. inglisSi naples yellow-s feri leqsikonSi pirvelad gamoCnda 1738 wels. antimonuri yviTeli cnobilia jer kidev uZvelesi droidan 159 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV rogorc minanqris feri, romelic napovni iyo babilonur agure- bze daaxloebiT Zv. w. aR. 2500 wels. sparsuli Tixis WurWeli Cv. w. aRr.-iT XIII saukuneSi zogjer antimonialuri yviTeli feriT aris gaformebuli. rogorc cnobilia, neapoli (italiurad apoli) aris samxreT italiaSi erT-erTi istoriuli qalaqi, mdidari istoriuli war- suliT, xelovnebiTa da kulturiT, romelic Zvelma berZnebma da- aarses da Νέα Πόλις _ `nea polis~ (axali qalaqi) uwodes. Naples yellow _ neapoluri yviTeli feris saxelwodeba TariRdeba 1730-40 wlebiT da Tavdapirvelad awarmoebdnen neapolSi. burgundi wiTeli feris erT-erTi Seferilobaa, romelic asocirdeba burgundis RvinosTan. burgundia _ istoriuli olqi aRmosavleT safrangeTSi, romelic saxelganTqmulia saocari meR- vineobiT da dakavSirebulia Zveli germaneli tomebis saxelTan _ burgundielebTan. es Seferiloba wiTeli feris sxva Seferilo- bebis maroon (wablisferi, Ria yavisferi), cordovan (burgundisa da vardisfris muqi Seferiloba), da oxblood (wiTeli feris muqi Seferiloba)-is msgavsia, odnav SeumCneveli sxvaobiT, rogorc feris aRmniSvneli termini burgundi _ burgundy inglisur ena- Si pirvelad gamoCnda 1881 wels. Vivid burgundy aris burgundis ufro naTeli tonaloba da gamoiyeneba kosmetologiaSi, Tmis sa- Rebavis saxiT. Old burgundy _ Zveli Sindisferi aris burgundis muqi tonaloba. am feris saxelwodeba inglisur enis leqsikaSi pirvelad Seitanes 1926 wels. parizuli mwvane _ Paris green mwvane feris mkrTal da cocxal lurjSi gardamavali Seferilobaa, romelic aris spileZis (II) ace- toarsenitis araorganuli naerTi da popularobiT sargeblobda impresionistebis mxatvarobaSi. Sinopia (aseve cnobili, rogorc sinoper) _ sinopis feri _ ya- visfris muqi mowiTalo-yavisferi Seferiloba, Turquli qalaq Sinop _ sinopis saxels atarebs, romlis mowiTalo feri warmo- Sobilia hematitisgan, rkinis oqsidis dehidratirebuli formis- gan. igi farTod gamoiyeneba klasikur antikur da Sua saukuneebis mxatvrobaSi, xolo renesansis dros xSirad iyenebdnen karikatu- raSi an freskul mxatvrobaSi. zogi ferTa Seferiloba atarebs saxelmwifoTa saxelebs maT Sorisaa: Congo pink, India green, Pakistan green (X11 Dark green) da a.S. India green _ indoeTis mwvane, indoeTis erovnuli droSis qve- da jgufis feri, romelic asocirdeba nayofierebasa da keTil- dReobasTan. 160 manana Selia Congo pink (inglisurSi gamoiyeneba 1921 wlidan), vardiferis SemadgenlobaSi Semavali narinjisferis elferi gadahkravs. Pakistan green pakistanis mwvane aris muqi mwvane feris erT- erTi Seferiloba, romelic gamoiyeneba veb-gverdis SemuSavebasa da grafikul dizainSi. is aseve, pakistanis droSis fonis feria. Turkey red _ Turquli wiTeli aris wiTeli feris Seferilo- ba, romelic farTod gamoiyeneboda XVIII da XIX saukuneebSi. igi mzaddeboda endros (Rubia) fesvisgan, rac iyo rTuli procesi da moiTxovda xangrZliv dros. igi warmoiSva indoeTSi an Tur- qeTSi da 1740 wels evropaSi Semoitanes. safrangeTSi cnobili iyo rogorc rouge d’Andrinople. industriuli revoluciis gavrce- lebisTanave, qimikosebi da mwarmoeblebi mTel evropaSi eZebdnen axal wiTel saRebavebs, romelic moxmardeboda qsovilebis far- TomasStabian warmoebas. mravali saswavlebeli: universitetebi, kolejebi, skolebi iyeneben sxvadasxva ferebSi agebul logoebs. arsebobs mravali Tvalsazrisi logotipis SemuSavebisas. logotipi warmoSobilia berZnuli sityvidan da niSnavs sityvas. berZnebi logotipebis sa- SualebiT erTmaneTisgan iRebdnen saidumlo informacias. Zveli romauli da berZnuli monetebis gaformeba xdeboda mefeTa lo- gotipebiT. asiriuli kultura, maias, egvipturi, Cinuri da babi- lonis kulturebi aseve iyenebdnen piqtogramebs, romelic waro- adgenda Zvel logotipebs. XIII da XIV saukuneebSi arsebobda mo- nogramebi, romlebic Tanamedrove periodSi warmodgens savaWro markebs. maT iyenebdnen fermerebi, iuvelirebi da vaWrebi. niSan- doblivia aRiniSnos, rom brendingi ukve mraval saukunes iTvlis. rac Seexeba saswavleblebis logos, narinjisfris Seferilo- bas _ prinston orinjs _ Princeton orange, iyenebs prinstonis uni- versiteti, q. niu jersi, aSS. Castleton green, mwvane feri erT-erTi Seferiloba aris qaslto- nis universitetis (vermontis Stati) erT-erTi oficialuri feri. Carolina blue _ karolina lurji (zogjer moxseniebulia, ro- gorc Tar Heel blue) aris karolinis universitetis erT-erTi sko- lis logos lurji feris Seferiloba. Columbia blue, igive Jordy blue _ kolumbiis universitetis saxe- liTaa cnobili, romelic warmoSobilia universitetis filoso- fiuri sazogadoebis (universitetis uZvelesi studenturi orga- nizaciis) oficiluri feris tonalobisgan. Oxford Blue _ aris oqsfordis universitetis lurji feris Se- feriloba, romelic Tavdapirvelad SeirCa Carlz vordsvortisa 161 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV da Tomas garnies mier, romlebic 1829 wels iyvnen universitetis niCbosnobis klubis wevrebi. Yale Blue _ ielis lurji aris ielis universitetTan asocire- buli muqi laJvardovani feri. Cambridge Blue aris kembrijis universitetis sportuli gun- dis feri. Eton blue aris lurji feris momwvano-lurji Seferiloba, ro- melsac XIX saukuneSi iyenebdnen itonis kolejis sportsmenebi. am fers, agreTve, iyenebs jilongis gramatikuli skola _ Geelong Grammar School (avstralia). Dartmouth green aris darmuTis kolejis oficialuri feri, mwvane feris erT-erTi Seferiloba, romelic miiRes 1866 wels. am fers amJamad iyenebs darmuTis kolejis aTletTa gundi. rogorc cnobilia, ferTa asociaciebi sxvadasxva kulturis xalxSi gansxvavebulad aRiqmeba. ferTa aRniSvnebi toponimebSi gansxvavebuli sityvawarmoebiTi modelebiT realizdeba. toponimuri warmoSobis ferTa Seferilobebis lingvo-des- kriptiuli analizi iZleva informacias rogorc geografiul saxelTa etimologiaze, istoriaze, aseve sxvadasxva ferTa da Se- ferilobaTa warmoSobaze, qimiur Semadgenlobaze da maT gamoye- nebaze. literatura: 1. Belyavskaya E. G. Semanticheskaya sruktura slova v nominativnom kom- munikativnom aspektah (kognitivnie osnovaniya formirovaniya i funktsio- nirovaniya semanticheskoy strukturi slova). Moskva, 1992. 2. Crystal D. The Cambridge Encyclopedia of the English Language, 2nd ed. Cambridge University Press, 2003. 3. Dzadzamia C. Ferta aghmnishvneli leqsikis semantikur-struqturuli analizi megrulshi. Disertacia, Tbilisi, 2006. 4. Gurgenidze N. Oikonimia rogorc toponimiis sakheoba da misi struqturul-se- mantikuri taviseburebani frangul da qartul enebshi. disertacia, Batumi,2013. 5. Leech G. Semantics , Aylesbury, Penguin books, 1977. 6. Zaqaraia M. Feris modelebis klasifikacia akaki Tseretlis sakhelobis sakhel- mtsifo universiteti,VII saertashoriso samecniero-praqtikuli konferencia inso, 2015, Qutaisi, Saqartvelo. 7. https://en.wikipedia.org/wiki 8. https://en.wikipedia.org/wiki/List_of_colors_by_shade 9. https://en.wikipedia.org/wiki/Category:Shades_of_colo 162 manana Selia Manana Shelia COLOUR SHADES OF TOPONYMIC ORIGIN IN MODERN ENGLISH LANGUAGE Summary Colour feelings and perception of people is defined by identity of the person. Features of a human eye and mentality are very important. The nominations with a color component can be found in all areas and spheres of human life. Various English colours and shades also can find reflection and in toponymics. Topon- ymy is the study of place names (toponyms), their origins, meanings, use, and typology and it also involves the study from the various linguistic viewpoints. In English vocabulary colour designations create a special group. They are basically made according to compositional and derivative models and signifi- cantly enrich the vocabulary denoting color concepts. The paper deals with colour shades of toponymic origin in Modern English and makes etymological, lexical-semantic analysis of toponyms _ asteonyms. Problem of color and its shades is an important component in origin of the place names. We analyze the semantics of the colour shades associated with place names. Lexical units are studied with regard to features of the forming and func- tioning of place names including extra-linguistic descriptive analysis. 163 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Nonna Ushveridze SOME ASPECTS OF FORMATION NATIONAL (ENGLISH) LANGUAGE The English language has had a remarkable history. According to historical records, it is a language of none-too-civilized tribes on the continent of Europe along the North Sea. From those murky and undistinguished beginnings, English has become the most widespread language in the world, used by more peoples for more purposes than any language on the Earth. The formation of a national language was greatly fostered by two events of the late 15th century. The most significant event of the period was the Wars of the Roses (1455-1485), which marked the decay of feudalism and the birth of a new social order. Another great event was the introduction of printing. Printing was invented in Mayence (Germany) by Johann Gutenberg in 1438. From Mayence printing spread to Strasburg, then to Italy and to Netherlands. The creation of printing was, undoubtedly, one of the greatest inventions. It eased the writing process as the whole, and had a great influence over the language. Linguists claim that the most important things printing brought was a development of a standard language of symbols and codes that we use today. In the town of Burges, in Flanders, the Englishman William Caxton (1422- 1491) became acquainted with this art. Printing which was introduced into England by William Caxton in 1476, helped to increase the spread of knowledge and literacy level among the British public as more and more people had better access to reading materials. Over the centuries, as more English texts were printed, such as novels, dictionaries, the Bible and other documents, the English language gradually gained popularity and established itself as the national language of England. Apart from the advent of printing, political, social and economic factors also contributed to the development of English as a national language. Through printing Caxton played a very significant role in establishing English as the national language of England. By adopting the dialect of London and the South-East as the English for his books, Caxton took a decisive step forward in establishing that particular variety as the English language. William Caxton as the first printer in England was highly responsible for imposing some form of uniformity to the English language simply by default. His choice of the dialect of the southeast Midlands has given us the present form of Standard English William Caxton was a native of Kent, but he had acquired the London dialect. In spelling, he stuck to the tradition of the scribes. There are hardly any specific Kenticisms in Caxton’s language; thus, the typical Kentish feature of the Old 164 nona uSveriZe English “y” appearing as “e” (for London “i”) is not more frequent in his texts than in those of purely London authors of the time (Ilysh, 1973). In 1445 Caxton moved to Bruges (Belgium) as a mercer to take part in the trade of the ‘Merchant Adventurers.’ There he was successful in business and became governor of the Company of Merchant Adventurers of London. His trade brought him into contact with Burgundy and it was thus that he became a member of the household of Margaret, Duchess of Burgundy, the third wife of Charles the Bold and sister of two Kings of England: Edward IV and Richard III . This led to more continental travel, including travel to Cologne, in the course of which he observed the new printing industry and was significantly influenced by German printing. He wasted no time in setting up a printing press in Bruges, in collaboration with a Fleming named Colard Mansion, and the first book to be printed in English was produced in 1475, Recuyell of the Historyes of Troye, a translation by Caxton himself. His translation had become popular in the Burgundian court, and requests for copies of it were the stimulus for him to set up a press. His first touch with literature was not in printing, but in translating. He knew enough Dutch, Flemish, French and Latin to translate books into English. This was unheard of before; English was not a scholarly language like French or Latin, but one used only by the common folk. The first book to be translated by him was” History of Troy,” that had been translated from French. However, he had such a difficult time in translating that he would almost given up on the notion Many translators of those days stated that they tried to be as close to the original text as possible, but it was not so, their only one wish was to have more books for selling. Caxton made the same claims, probably out of obligation. How would it look if everyone were doing it except him? His number one priority was not accuracy of translation, but ensuring that there was always something on the press. Because he owned it, it was up to him how many books he had available for printing and if nothing was to print, he wasn’t making money. In his closing remarks on the subject of Caxton as a translator, Henry Blake says, that in general he can hardly be distinguished from the host of translators who crowd the 15th century scene, except perhaps in the sheer quantity of his output. Of the 106 works printed by or attributed to Caxton, he translated at least twenty-five. It is hardly surprising that he did not always have time to polish his version for the press. Caxton eventually resigned as the Governor within the Merchant Adventurers, a post he held for several years, so he could travel to Cologne, Germany. He lived there for about eighteen months. It is assumed that his intention in going there was to learn how to be a printer so that he could print his own books. Cologne, with a press dating from about 1465, was the town nearest to Bruges which had a press at that time, and Caxton had little choice where to go. It had become the capital of the Low Countries because of its university, which attracted a lot of 165 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV scholars and students; an important archbishopric; and strong trade, especially with English tradesmen. An interesting aspect to the printing world is the fact that there was an immediate division of labor within the profession. There were the skilled craftsmen who actually did the work on the presses and then there were the tradesmen that already had connections to sell the books who were considered the publishers and entrepreneurs. Paper was the most expensive investment that had to be available upfront, before any books were sold, and it was the tradesmen who had the money readily available for purchasing. Surely Caxton learned how to print, for it was his responsibility to teach his assistants once he returned to Bruges and set up shop as a printer. Blake explains it thus: “Normally he would not have interfered in the actual printing operations, and it is not right to think of Caxton as a printer. He was the publisher and entrepreneur. He provided the capital, chose the books and distributed them, leaving the printing to others” (Blake, 1969). Once returned to Bruges, Caxton used the patronage of Margaret of Burgundy to help him publish his book. The first book he printed, and the first book to appear in English, was his own translation of the History of Troy in 1475. Before returning to England to set up a printing press there, Caxton printed six or seven other volumes while in Bruges. Two were in English, the one already mentioned and Game of Chess, and four were in French. The seventh pamphlet is attributed to him but has not been confirmed to be his work. Caxton finally returned bringing the knowledge back to England, he set up a press at Westminster in 1476, and the first book known to have been produced there was an edition of Chaucer’s ‘The Canterbury Tales’. Since Caxton settled in Westminster instead of his hometown of London, it was supposed that the relations between the scribes and the printers were at odds. It was thought that perhaps the scribes felt threatened by this new device that would ultimately outdate them, stealing all of their work. However, this has never been proved and, in fact, there are several accounts of printers working closely with the scribes. As an example, the first known item to be printed in England is an indulgence which must be dated prior to 13 December 1476, since that date has been entered by hand in the surviving copy. It is printed in Caxton’s type 2 with six letters in his type 3 (Blake, 1969). Obviously he was working with the abbots, who were also scribes, in the production of indulgences. Caxton could not have ever hoped to have the entire publishing market of England in his hands for the rest of his life. And accordingly, rivals began to arrive, setting up their own print shops. The first few were no real threat to the well-known Caxton; however, by 1480 a real competitor entered the stage. John Lettou, a native of Lithuania, moved into London and actually had better books than Caxton. It at once became evident that the new printer had learnt his art under a much better master than Caxton had (Plomer,1925). This became a wake-up call to William 166 nona uSveriZe Caxton, letting him know that he needed to begin fixing some of the problems with his own printing so as not to lose the business entirely and this he did. At the time of Caxton’s translations, English was a language that was still new. It had begun to change from the Old English to a more modern English but different ways of spelling and pronunciation abounded. This was bound to make any printer go insane. It is said the English vernacular was only just beginning to develop a prose form, and Caxton coped with the problem of meager vocabulary and wide variations in the spelling of even the simplest English words. As an example, the word “little” can be spelled in several ways in Caxton’s texts. Two variants are “litil” and “lytel”. At this very period, the English language was still passing from its mediaeval pronunciation into that state with which we are familiar today, and it was precisely then that the press began to crystallize the orthography of a language still in flux. Gradually, the spelling tended to become fixed, while the pronunciation continued to evolve (Blake, 1969). Caxton knew of these difficulties personally and recognized the need for a remedy. Through his efforts as a printer and publisher, things began to slowly change. An interesting side note about this event in English history is the current spellings and pronunciations found in the language today. Because the written word began to take a more permanent form while the spoken word had not, many variants developed on how to pronounce the same word. For this reason, we see many differences in the pronunciation of British English and American English. Even within England there are dialects with differences in word pronunciation. This all developed due to the solidifying of the written and spoken language at different times . The standardization of the English language or any language is an issue which linguists always have to grapple with. Printing had brought into focus problems regarding the variations in the English language, which Caxton had observed, such as: • Should he use foreign words in his translations or replace them with native English words? • Which variety of English should he follow, given the existence of major regional differences? • Which literary style should be used as a model? • How the language should be spelled and punctuated, given the scribal variations of the previous centuries? • In publishing native writers, should he change their language to make it more widely understood? Nevertheless, printing provides a way to reduce these variations in the language. As Caxton himself showed, publishers would set their own system of spelling and somewhat codify the language Hence, the introduction of the printing by William Caxton gave an unprecedented impetus to the formation of a standard language and the study of 167 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV its properties. Apart from its role in fostering norms of spelling and punctuation, the availability of printing provided more opportunities for people to write, and gave their works much wider circulation. As a result, more texts of the period have survived. Within the following 150 years, it is estimated that nearly 20,000 books appeared. The story of English thus becomes more definite in the 16th century, with more evidence available about the way the language was developing, both in the texts themselves, and in a growing number of observations dealing with such areas as grammar, vocabulary, writing system, and style. In that century, scholars seriously got down to talking about their language (Emerson,1996; Morton,1986). The influence of the first printings in spreading the written form of English was significant. The language they used was the London literary English established since the Age of Chaucer and slightly developed in accordance with the linguistic change that had taken place during the intervening hundred years. The introduction of the printing by William Caxton was one of the most significant factors of the Standard English diffusion. This resulted in the spread of a single norm over most of the country, so much that during the 15th century it becomes increasingly difficult to determine on internal linguistic grounds the dialects in which a literal work is written. With cheap printed books becoming available to a greater number of people the London form of speech was carried to other regions and was imitated in the written works produced all over England. References: 1. Baugh A. History of the English Language [Text]. London: Pearson Educa- tion, 1978. 2. Blake N. Caxton and His World [Text]. _ London: Andre Deutsch, 1969. 3. Buhler C. William Caxton and His Critics [Text]. _ Syracuse: Syracuse Uni- versity Press, 1960. 4. Chadwick H. The origin of the English nation [Text]. _ Cambridge: Cam- bridge University Press, 1907. 5. Crystal D. The Cambridg Encyclopedia of Language. _ Cambridge: Cam- bridge University Press, 2010. 6. Emerson O. The History of the English Language [Text]. _ NY: Macmil- lan,1906. 7. Ilysh B. History of the English Language. Leningrad, 1973. 8. William Caxton [Text] _ London: Leonard Parson Ltd.,1925. 9. Rastargueva T. A History of the English Language. Moscow, 2007. 10. Ushveridze N., Shelia M. A History of the English Language. Tbilisi, 2009. 11. Wright L. The Development of Standard Language. 2000. 168 nona uSveriZe nona uSveriZe erovnuli (inglisuri) enis formirebis zogierTi aspeqti reziume literaturul inglisur enas safuZvlad udevs londonis dialeqti, romlis baza literaturuli enis formirebis adreul etapze Seicvala. wignebis beWdvam da j. Coseris nawarmoebTa popularobam ga- moiwvia londonis dialeqtis formebis gamyareba da gavrceleba. inglisuri erovnuli enis ganviTarebaze gadamwyveti mniSvne- loba iqonia XV s. bolos momxdarma movlenebma: pirveli _ wiTeli da TeTri vardebis omi (1455-1485 ww.) da meore mniSvnelovani mo- vlena enis istoriaSi _ inglisSi wignuri beWdvis SemoReba. wignuri beWdva dakavSirebulia ioane gutenbergis (Johanes Gutenberg) saxelTan (q. mainci, germnia, 1438). am xelovnebam SeaRwia strasburgSi, Semdeg italiasa da holandiaSi. qalaq briugeSi, flandriaSi wignur beWdvas daeufla ingliseli uiliam keksto- ni (William Caxton, 1422-1491), warmoSobiT kentidan, romelic moR- vaweobda niderlandebSi da iq eziara am axal gamogonebas. is 1475 wels q. briugeSi beWdavs pirvel wigns inglisur enaze “The Recuyell of the Histories of Troye” (`moTxrobebis krebuli troaze~). 1476 wels is brundeba londonSi da aarsebs pirvel tipografias. 1477 wels am tipografiaSi ibeWdeba pirveli wigni _ “The Dictes and Sayings of the Philosophers” (`aforizmebi da filosofosTa gamonaTqvamebi~). beWduri wignebis gavrcelebam didad Seuwyo xeli enis nor- malizacias, rogorc grafikis da orTografiis, aseve gramatiku- li formis sferoSi. magram wignebis beWdva afiqsirebda zogierT tradiciul damwerlobas da ar asaxavda XV saukunis dasasru- lis gamoTqmis normebs. daiwyo Tanamedrove inglisuri enisaTvis damaxasiaTebeli gansxvaveba gamoTqmasa da damwerlobas Soris. literaturuli enis ganviTarebasTan erTad farTovdeboda da rTuldeboda stilTa funqcionaluri sistema, mimdinareobda ze- pirmetyvelebis da weriTi metyvelebis formaTa gamijvna. lite- raturuli enis ganviTarebaSi didi roli iTamaSa inglisuri enis pirdapirma da arapirdapirma enobrivma kontaqtebma sxva enebTan. 169 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Диана Алания РУССКИЙ ЯЗЫК В ГРУЗИИ В XXI ВЕКЕ (СТАТУС И ПОЛОЖЕНИЕ) Языковая проблема в Грузии всегда была актуальной и сложной. И се- годня она сложна. В Грузии сегодня наряду с государственным грузинским языком сосу- ществуют другие языки. На уровне социума это, безусловно, положитель- ный фактор. Недаром существует пословица: «сколько языков ты знаешь, столько раз ты человек». На социологическом уровне многоязычие воспринимается сложнее, т.к. государственно-политические, национально-этнические, общественные и эмоциональные аспекты переплетаются, и порой функционирование одного из языков происходит за счет ущемления функций другого языка. Русский язык относится к числу распространенных и широко извест- ных в мире богатых и научно разработанных языков. Это _ язык великой культуры, один из ведущих языков мира. Однако язык, как и любая историческая категория, подвластна глобаль- ным процессам, которые корректируют и мотивируют масштабы и формы его распространения в мире. До недавнего времени в Грузии он занимал привилегированное положе- ние среди иностранных языков, а порой и конкурировал с государственным языком Грузии _ грузинским, «являясь» языком межнационального общения. Времена изменились. Сегодня США является ведущей и развитой в эконо- мическом отношении страной, оказывающей политическое и государственное влияние на весь мир. Английский язык преобладает почти во всех сферах: в политике, в промышленности, в общественной жизни и т.д. (Alaniya, 2008: 10). Статус английского языка определила экономическая и военная мощь США. Экспансия английского языка на сегодняшний день очевидна, она объ- ясняется распространением процесса глобализации. Этот процесс не может быть остановлен. Английский язык упорно внедряется во все сферы и регионы Грузии, за исключением Абхазии, Южной Осетии и части компактно проживающего негрузинского населения в Верхнем и Нижнем Картли. Грузинский язык сегодня в полной мере выполняет функции государ- ственного языка на территории распространения фактической юрисдикции Грузии (за исключением сепаратитски настроенных автономий _ Абхазии и Южной Осетии). 170 diana alania Однако язык, как и любая историческая категория, подвластна глобаль- ным процессам, которые корректируют и мотивируют масштабы и формы его распространения в мире. До недавнего времени в Грузии русский язык (Alaniya, 2008: 12) за- нимал привилегированное положение среди иностранных языков, а порой и конкурировал с государственным языком Грузии _ грузинским, являясь языком межнационального общения. Социальные изменения изменили статус русского языка, официально он стал одним из иностранных языков. Следует признать, что статус русского языка в Грузии фактически явля- ется не вполне определенным, так как русский язык все еще является основ- ным языком функционирования для определенной части населения Грузии, которое представлено не только этническими грузинами, но и русскими, армянами, азербайджанцами, украинцами, осетинами, абхазами, греками, евреями и др. Временно и неофициально на данном этапе можно были бы определить статус русского языка как интерязыка (Alaniya, 2008: 13). Русский язык De facto является интерязыком в общении с нашими со- седями по региону / на Южном Кавказе, на Северном Кавказе/. Сегодня на официальном уровне русский язык обслуживает националь- ные меньшинства внутри нашего государства в их контактах с представите- лями стран Ближнего и Дальнего Зарубежья, владеющими русский языком. Многие грузины и представители национальных меньшинств получили об- разование на русском языке; некоторые передачи по радио и телевидению ведутся на русском языке, выходит много газет, журналов, книг. Таким образом, русский язык продолжает, хотя и не в таком объеме, как прежде, функционировать на официальном уровне, функционирует от также и на бытовом уровне. Но, как и почти во всех бывших советских ре- спубликах, русский язык в Грузии занимает все же скромное положение, потому что в какой-то степени, надо признать, на данном этапе в связи с глобализацией он подвергается двойному выдавливанию: со стороны госу- дарственного (грузинского) и английского языков. Известно, что Грузия _ многонациональная страна. Здесь проживают, помимо этнических грузин, русские, абхазы, осетины, армяне, азербай- джанцы, греки, евреи, украинцы и др. Кроме того, в Грузии представлены языки, статус которых юридически не оформлен, это курдский, ассирий- ский, удинский и др. Языковая политика Грузии должна базироваться на многоязычии, вклю- чающем знание нескольких языков: грузинского, английского, русского _ в обязательном порядке, др. иностранных языков и языков национальных 171 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV меньшинств, существующих в Грузии. Следует признать, что владение рус- ским (Alaniya, 2008: 13) языком на сегодняшний день является важной соци- альной задачей. Коммуникация с негрузинским населением, народами Гру- зии, осуществлялась и осуществляется при помощи русского языка. Одновременно повышается значимость национально-культурных осо- бенностей и тенденция к сохранению языков национальных меньшинств. Налицо внутренне противоречивый процесс: с одной стороны _ глобализа- ция, с другой _ тенденция к дифференциации. Многообразие мира является источником его совершенствования. Литература: 1. Tolkovyy slovar russkogo yazika kontsa XX veka yazykovye izmeneniya. Red. Sklyarevskaya G.N. Sankt-Peterburg, 2000. 2. Alaniya D.A. Globalizatsya I yazikovaya situatsia v mire. “Slavistika v Gruzii”, T.9. Tbilisi, 2008. diana alania rusuli ena saqarTveloSi XXI saukuneSi (mdgomareoba da statusi) reziume axalma social-politikurma pirobebma, globalizaciam, aSS-is ekonomiurma, politikurma da samxedro Zlierebam gansazRvra in- glisuri enis saerTaSoriso statusi. dRes inglisuri ena epoqis mTavari donoria da globalizaciis epoqaSi is msoflios Taname- gobrobisaTvis saerTaSoriso enis funqcias asrulebs. Tanamedrove rusuli enis leqsika ivseba neologizmebis, na- sesxebi sityvebis da semantikuri gardaqmnebis xarjze (deaqtua- lizacia, politizacia, metoforizacia da sxv.). Tanamedrove rusul enaSi SeiniSneba axali realiebis nomina- ciaSi pasiuri leqsikis, axali wignieri leqsikis, Jargonebis gamo- yeneba, aTvisebulia adre tabuirebuli konfisionaluri leqsika. Tanamedrove rusuli enis axalma tendenciebma gavlena moax- dina rusuli enis mecnierebis ganviTarebaze: samecniero intere- sebma lingisturidan kulturis sferoSi gadainacvla. 172 diana alania rusuli enis, rogorc ucxo enis, Seswavlisas mecnierebs dRes izidavs eniT aRwerili konkretuli situaciis mniSvneloba, azri da codna. socialurma Zvrebma Secvala rusuli enis statusi saqarTve- loSi: is gaxda erT-erTi ucxo ena. rusuli ena arsebobs da viTardeba Tavisi istoriuli kanone- biT. oficialur doneze rusuli ena emsaxureba nacionalur um- ciresobas saxelmwifoSi. mezoblebTan urTierTobaSi rusuli ena de-faqto aris inter _ ena. Diana Alaniya THE POSITION AND STATUS OF THE RUSSIAN LANGUAGE IN GEORGIA IN THE XXI CENTURY Summary The new socio-political conditions, globalization, as well as the US eco- nomic, political and military strength have determined the international status of the English language. Presently, the English language is the main donor in the era of globalization and acts as an international language for the world community. Modern Russian language vocabulary is filled with neologisms, borrowings and semantic transformations (deactualization, politicization, Metaphorization, etc.). The modern Russian language for the nomination of any new reality uses passive vocabulary, new bookish vocabulary and jargon, as well as the confes- sional vocabulary that was previously tabooed. New trends in the modern Russian language have influenced on the develop- ment of the Russian language science: the scientific interests have moved from linguistic to the cultural sphere. While studying the Russian language as a foreign language, the scientists today are interested in the meaning, sense and knowledge of a particular situation expressed by the language. Social developments have changed the status of the Russian language in Georgia: it has become one of the foreign languages. The Russian language exists and develops according to its historical laws. At the official level the Russian language serves the national minority in the country. In relations with neighbors the Russian language De facto is an inter-language. 173 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV literaturaTmcodneoba LLITERATURE STUDIES tite mosia rusTavelis mijnurobis Teoriis interpretaciebidan sityva `mijnu ri~ TavCe ni lia `vefxistya os nis~ prolo gis meo re strofSi ve (`momec mijnur Ta survi li~...). poe ma Si mogve po ve ba `mijnu ris~ sino ni mu ri cnebe bi: siyva ru li, trfia lo ba, aSiko ba. termi ni `mijnu ri~ `vefxistya o san Si~ naxma ria 39-jer. `mijnu ro ba~ _ 22-jer. `siyva ruli~ _ 38-jer. `aSi koba~ _ 5-jer `saaSiko~ _ orjer. rusTa ve li prolog Si ve gang vi mar tavs `mijnu ris~ arabul warmo mav lo bas (`mijnu ri Smagsa gviqvi an arabu li Ta eniTa~). prolo gi se u li mijnu ro bis Teo ri a ze gamoT q mu lia urTi erT ga mom ricx ve li koncef ci e bi. es exeba gansa kuT re biT 20-22-e strofebs da mis filo so fi ur - m sof l m xed ve lob riv gaaz re bas. vidre sakiTx ze sau bars Sevud ge bo deT, saWi rod vTvliT im bib liur - q ris ti a nul wyaro eb ze miniS ne bas, rome lic rusTa vels uci loblad asazr do eb da siyva ru lis rao bis gaaz re bi sas. es kidev erTi dastu ri iqne ba imis gasaT va lis wi neb lad, Tu ramde nad iyo Semo su li Sua sa u ku ne ob ri vi `vefxistya o san Si~ rene san sul azrov nebas Tan Sesar wy me lad. axali aRT q ma gvaswav lis, rom siyva ru lis mSobe li RmerTi a: `siyva ru li RuTi sa gan ars~ (I kaT.ep. 4,7), ufro metic. siyva ru li ara marto momdi na re obs RmerTi dan, aramed Tavad RvTae bac siyu aru li a: `RmerTi siyva rul ars~ (I kaT. ep. 4,16). pavle moci qu lis pirvel episto le Si korin Tel Ta mimarT erT ma neT Tan Seda re bu lia sarw mu no e ba, saso e ba da siyu a ru li, romel Ta gan es ukanas kne li Seu va li upira te so biT sargeb lobs: `xolo aw esera hgies: sarw mu no e ba, saso e ba da siyu a ru li. sami ese. xolo ufros amaTgan siyu a ru li ars~ (I kor. 13,13). Zvel aRTqmaSi miTiTebulia siyvarulis sworupovrobaze: `ra meTu mtkice ars, viTarca sikudili, siyuaruli, ficxel ars, vi Tarca jojoxeTi, Suri garemois missa klde, garemois missa klde cecxlisai, cecxlisa alTa misTai, wyalsa mravalsa ver Zaluc daS reta siyuarulisa, mdinareni ver warRunian mas, ukeTu misces kac man yoveli cxovrebai Tvisi siyuarulsa~ (qeb. 8,67). an kidev: `siyu aruli sulgrZel ars da tkbil, siyuarulsa ara hSurn. siyuaruli 174 tite mosia ara maRloin, ara ganlaRnis, yovelsa Tavs-idebn, yoveli hrwamn, yovelsa esavn, yovelsa moiTmenn~ (I kor. 13,4-7). usiyvarulod ada mianis arsebobas azri ekargeba. araraoba xdeba: `siyuaruli Tu ara maqun des, arave ra var~ (I kor. 13, 1). sagu lis x moa siyva ru lis dasax va sulis nayo fad: `xolo nayo fi suli sa ars siyu a ru li~ (gal. 5,22). bibliu ri saRv To mijnu robis safuZ vels qmnis uflis siyva ru lad ve aRia re ba, vina i dan xilu li da uxila vi arse ba ni Tu samya ro RmerTi- siy va ru li dan gamom di na re o ben. bibli is mixed viT, RvTae bis Seyva re bis ufle ba aqvs mxolod imas, visac ZaluZs misi mcnebe bis dacva: `rame Tu si yua ru li RuTi sa, raTa mcnene ba Ta misTa vimar x vi deT da mcneba ni misni mZime ar arian~ (I kaT. ep. 5,3). am mcneba Ta Soris pirve li ad gili swored adami an Ta erT ma ne Ti sad mi siyva ruls uWiravs: `rame Tu ese ars mcneba ni Cemni, raTa iyua re bo deT urTi er Tas, viTar ca me Segiy vu a ren Tquen~ (i. 15,12). amg va ri siyva ru lis maga li Ti ki macxovris T vis mamaR merTs miu ci a: `viTar ca Semi yu a ra me mama man. meca Segi yu a ren Tquen, daad ge riT siyu a rul sa Cemsa zeda~ (i. 15,9). qriste ase STaago nebs adami a nebs: `uke Tu mcneba ni Cemni dai marx neT, hgieT siyu a rul sa Cemsa zeda, viTar ca me mcneba ni mami sa Cemi sa ni davi mar xen da vhgie siyu a rul sa zeda missa~ (i. 15,10). am frazis Tanax mad siyva ru li sa da mcnebe bis Senax va- dac vis maga li Ti qristes T vis mamaR merTs miu cia da rogorc Ze baZavs mamas, ise adami a neb mac macxovars unda miba Zon, vina i dan mesi is movli ne biT RvTis siyva ru li gamocxad da adami a nebs Soris maTi ve sacxoneb lad: `amiT gamocxad da siyva ru li RuTi sa Cuen Soris, rame Tu Ze Tvisi mxolod Sobi li moav li na RmerT man soflad, raTa vscxon deT mis mier~ (I kaT. ep. i. 4,9). axal aRT q ma Si mogve po ve ba uaRre sad sayu radRe bo Sego ne ba: `RmerTi ara sada vis uxilavs, ukue Tu viyu a re bo deT urTi er Tas, RmerTi Cuen Soris hgies da siyu a ru li misi Cuen Soris aRs ru lebul ars~ (I kaT. ep. i. 4,12). e. i. uxilav, Seucnobel RmerTTan miax lo e ba da misi Secno ba SesaZ le be lia adami an Ta erT ma ne Tis mi marT siyva ru lis gziT. kidev erT sain te re so nimuSs davi mow mebT: `sayu a rel no! viyu a re bo deT urTi er Tas, rame Tu siyu a ru li Ru Tisgan ars, da yovel sa, romel sa uyuar den, RuTis gan Sobil -ars da icis RmerTi~ (I kaT. ep. 4,7). amdenad, rogorc moci quli gvas wavlis, RmerTis codna, uwina re sad, erT ma ne Ti sad mi adami an Ta siyva rul Si gamo i xa te ba. RmerTis wvdoma da Secno ba mxolod mas SeuZ li a, visac adami an Ta siyva ru li ZaluZs, vina i dan `romel sa ara uyuar des, man ar icis RmerTi, rame Tu RmerTi siyu a ru li ars~ 175 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV (I kaT. ep. i. 4,8). am Sego ne bis dama xin je ba Tu darR ve va zneob ri vi kano nis iavaryo fas moas wa vebs, romlis moqme di macdu rad cxad deba: `uke Tu vinme hsTqua, viTar med miyu ars RmerTi da Zmai Tvisi hsZuldes, mtyuar ars rame Tu romel sa ara uyuar des Zmai Tvisi, rome li ixila, RmerTi, rome li ara uxilavs, viTar ZaluZs Seyu a rebad~ (I kaT. ep. i. 4,20). visac Seswevs Zala RvTaebis trfialisa, mas, upirve le sad, Zmisa da moyva si sad mi siyva ru li unda axsov des: `da ese mcnebai movi ReT misgan, raTa romel sa uyuar des RmerTi, uyuar des Zmai ca Tvisi~ (I kaT. ep. i. 4,21). amri gad, uflis Seyva re bamde adami an ma kacTa Soris, ZmaTa da moyvas Ta Soris unda gamos cados siyva ru li. `viyu a re bo deT urTi er Ta Si~ warma te ba RmerTis siyva rul Sic gamar j ve bis sawin da ri a: `yovli sa wina urTi er Tas si yua ru li ganmar te bu li gaqun din, rame Tu siyu a rul man dahfa ris simravle coduaTa~ (I kaT. ep. p. 4,8). adami an Ta siyva ru li erT ma ne Ti sad mi Tavis Tav Si moi cavs (sa Wiro e bis SemTx ve va Si) kacTaT vis saku Ta ri sicocx lis msxverp lad mita na sac: `ufro si amisi siyu a ru li sa aravis aqus, raTa suli Tvi si dahs du as mego bar Ta TvisTa Tvis~ (i. 15, 13, Sdr. rusTa ve li: `xams moyva re moyv ri saT vis Tavi Wirsa ar damri dad, guli misces guli saT vis, siyva ru li _ gzad da xidad~). zemoT damow me bu li Sego ne be bi dan gamom di na re, sulxan - sa ba orbe li a ni ityvis: `vina iT gan RmerTi ars siyva ru li, raRa- me gnebavsT siyva ru li sa maZi e bel no? romel man moi goT siyva ru li, RmerTi mogi gi es da, romel mac hpooT siyva ru li, RmerTi gipov nies. siyva ru li sxva arRa ra ra ars, garna Zed maRli sad wode bad. netar xarT, romel man moi goT ese... saRm r To siyva ru li Tavi ars yove li sa keTi li sa~ (Orbeliani,1963: 92-93). SeiZ le ba davas k v naT: bibli u ri moZRv re biT, RmerT ma yvela ferTan erTad siyva ru lic gaa Ci na, TviT RmerTic siyva ru lad gamo ecxa da adami a nebs. RmerTis arse ba adami a neb ma rom Seic non, Sina ga nad ixilon, misi trfia li SeZlon, uwina re sad, erT ma ne Ti sadmi siyva rul Si unda gamos ca don saku Ta ri Tavi _ guli, grZno ba, gone ba. amiT dai ax lo e ben RmerTs da Tavi anT Soris amyo fe ben mudam. visac moyvas Ta, ZmaTa, saer Tod, adami an Ta siyva ru li ar SeuZ li a, mas arc RvTaeb ri vi mijnu ro bis Zala Seswevs, Sors dgas RmerTis codnis gan da rwmenis ga nac. davub run deT prolo gi se u li mijnu ro bis Teo ri as. mkvlevar Ta Soris azr Ta sxvadas x va o bis gamom w ve vi mizezi gaxda me-2 0 - 2 2 -e strofe bi: `vTqva mijnu ro ba pirve li da tomi gvarTa zena Ta, 176 tite mosia Znelad saTq me li, saWi ro, gamo sa ge bi enaTa; igia saqme saze o, momce mi aRmaf re na Ta; vinca ecde bis, Tmobam ca hqonda mraval Ta wyena Ta. mas erT sa mijnu ro ba sa Wkvian ni ver mixv de bi an, ena daSv re bis, msmenli sa yurni ca daval de bi an; vTqvne xelo ba ni qvena ni, romel ni xorc Ta xvdebi an, marT masve hbaZven, Tu oden ar siZven, SoriT bndebian. mijnu ri Smagsa gviqvi an arabu li Ta eniTa, miT rome Smagobs misi sa ver mixv do mi sa wyeni Ta; zogTa aqvT saRm r To siax le, daSv re bis aRmaf re ni Ta, kvla zogTa qve uc bune ba kekluc Ta zeda frfeni Ta~ (Rustaveli, 1988: 11). am strofe bis erT ma ne Ti sa gan gans x va ve bul inter p re ta ci ebs vecno biT samec ni e ro lite ra tu ra Si. ufro gavr ce le bu li da po pula ru li Sexe du le biT, ilust ri re bul masa la Si erT ma neTs da piris pi re bu lia RvTaeb ri vi da miwi er - xor ci e li siyva ru li. am ukanas k ne lis keTil So bi le bas, amaRle bu lo bas, zneob riv aRma te bule bas gansazR v ravs misi baZva saRv To siyva ru li sad mi (`marT masve hbaZven, Tu oden ar siZven, SoriT bndebi an~). `rusTa vels Tavi si Semoq me de bis sagnad auRia ara misti ku ri, saRm r To, sazeo mijnu ro ba, aramed saam q vey no, miwi e ri, xorci e li, rea lu ri, mate ria lu ri, buneb ri vi, adami a nu ri grZnoba. rusTa ve li amiT saci lo bels ar xdis sazeo mijnu ro bis mniSv ne lo bas, TviTon saam q vey no siyva ru lic saze os hgavs, Tu man zneo bis gama fa qi ze be li, suli erad amamaR le be li da adami a nis Rirse bis damam S ve ne be li forma mii Ro (Baramidze, 1975: 27). citi re bu li strofe bis `zeci ur~ siyva rul Si k. keke li Ze su fiur trfobas gulis x mob da. analo gi u ri mosaz re bi sa gaxl daT z. avaliS vi li. nawi lob riv ase fiqrob da p. Sari ac: Cveni azriT, aq nagu lis x me viao swored sufi e bis siyva ru li. Tumca mkvleva ri iqve akonk re teb da: sufi e bi mxolod RmerTis mimarT iCend nen `ide a lur siyva ruls~. xolo rea lur cxovre ba Si sxva sasiy va ru lo praqti kas misdev d nen (Sharia, 1976: 95). S. nucu bi Ze rusT ve lur `zena gvarSi~ (`tomi gvarTa zena Ta~) plato nis filo so fi ur termins _ `ide as~ xedavs. plato nis turs, ganye ne buls. arasa am q vey no siyva ru lis Teo ri as rusTa vel ma da upi ris pi ra saam q vey no siyva ru lis Teo ri a, rome lic xorc Ta naa dakav Si re bu li, aSka rad gulis x mobs plato nis Teo ri as, romlis mixed viT mijnu ro ba `gvarTa zena Ta~, e. i. idea Ta `tomi a~ anu mag vari da masTan pirvel idea Ta (Nucubidze, 1958: 166). 177 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV n. naTa Zis mixed viT, rusTa ve lis mier gamo ye ne bu li filo so fiu ri termi ne bi plato nis cnobi li cnebe bi a. `gvari~ plato nur `ide as~ niSnavs, xolo `tomi~ _ zogads, idea Ta gama er Ti a ne bel ideas. plato ni saT vis umaRle si idea anu idea Ta idea, samya ros ierarqi is mwverva li aris sike Tis idea, rome lic misT vis agreT ve WeSma ri te ba caa da mSveni e re bac. rusT vel ma sike Tis adgi las am ierarqi a Si mijnu ro ba anu siyva ru li daa ye na (Natadze, 1966: 134). marTa li a, e. xinTi bi Zem sworad CaTva la `tomi sa~ da `gvaris~ naTa Zi se u li ganmar te ba. magram araswo rad miiC nia mkvlevris mier `pirvel~ mijnu ro ba Si mijnu ro bis ideis danax va. e. xinTi bi Ze `pirvel~ mijnu ro ba Si qristi a nul saRm r To siyva ruls xedavs. misi mtkicq biT, poe mis gmirTa mijnu ro ba aris `sa Sua lo~ saRm r To mijnu ro ba sa da siZvas Soris. aq sau ba ria aris tote les `saSu a los~ Teo ri is anarek l ze rusTa ve lis eTikur Se xedu le beb Si. 2005 wels gamo ce mul wign Si ki e. xinTi bi Ze wers: `rusTa ve li prolog Si ar lapa ra kobs `pirvel mijnu ro ba ze~ rogorc saRv To mijnu ro ba ze da miwi er, amq vey ni ur mijnu ro ba ze. ar miu Ti Tebs mijnu ro bis pirvel saxe o ba ze, rome lic emijne ba Semdeg daxa si a Tebul meo re da mesa me saxe o bebs... prolo gis mijnu ro bis Teo ri aSi is ki ar aris Tqmuli, rom RmerTis siyvaruli pirveli, umaR lesi saxea mijnu ro bis, xolo amq vey ni u ri, xorci e li siyva ru li masze daba li da misi sapi ris pi ro saxe o ba a o, aramed Semde gi: mij nuro bis RvTaeb ri vi gamov li ne ba. RmerTis siyva ru li adami a nu ri eniT ar gamo iT q mis, adami an Ta gone biT ar miix ved re ba~ (Kintibidze, 2005:79-80). rusTa ve lis gamoT q ma Si _ `vTqva mijnu ro ba pirve li da tomi gvarTa zeni Ta~ _ e. xinTi bi Zes `gvari~ esmis rogorc `wesi~. kano ni, mcneba: `gvarTa zena Ta~ _ zeci ur, umaRles wesTa _ RvTa ebriv mcneba Ta~ (Khintibidze, 2005: 79). z. gamsa xur di as Tvalsaz ri siT, `vefxistya o san Si~ asaxu li mijnu ro ba aris `qvena xelo ba~, rome lic baZavs `pirvel~, `zena~ mijnu ro bas. `pirve li~ mijnu ro ba qristi a nu li saRv To siyva ru lia. z. gamsa xur di as dask v niT: `rusTa ve li saT vis adami a nur siyva rulSi gamos W vi vis saRv To siyva ru li, siyva ru li misT vis erTi a noba a~ (Gamsakhurdia, 1984: 98). rusTa ve lis mijnu ro bis Teo ri as vrceli nark ve vi miuZR v na a. abJan da Zem. sai da nac Cans, rom mkvlevar ma uaryo zemoT moxmo bili mosaz re ba ni cnobi li mecni e re bi sa. damow me bul Sexe du le ba Ta gada sin j vis mizniT Semdeg dask v nam de mivi da: `pirvel~ mijnu roba Si~ igulis x me ba poe ma Si asaxu li mijnu ro ba (anu qal- va Ju ri 178 tite mosia siyva ru lis umaRle si saxe), romel sac baZavs siyva ru lis ufro daba li saxe _ `qvena xelo ba~, zogjer siZva Si rom gada dis. a. ab Janda Ze wers: `vefxistya os nis~ prolo gis me-20 da 21-e strofe bis pirvel eqvs taep Si lapa ra kia poe mis idea lur gmirTa mijnu ro ba ze, bolo or taep Si ki dabal siyva rul ze, romel sac rusTa ve li `qvena xelo bas~ uwodebs~ (Abzhandadze, 1994: 168). al. bara mi Zis TqmiT, mijnu ro bis umaRles saxe o bas rusTa ve li uwodebs saRm r Tos, magram TviTon emijne ba mijnu ro bis am sa xeo bas. es Tvalsaz ri si damk vid r da rusT ve lo lo gi a Si. rogorc vTqviT, z. gamsa xur di am cxadyo am Sexe du le bis umarTe bu lo ba. misi mtkice biT, rusTa ve li saT vis adami a nur siyva rul Si gamos W vi vis saRv To siyva ru li. siyva ru li misT vis erTi a no ba a, saRv To da adami a nu ri mijnu ro ba erTi mTlia no ba a. ufro adre p. Saria am bobda: rusTa ve li siyva ruls TviT RvTaeb ri vi arsis gamov le nad miiC nev da adami a nis sulSi (Sharia, 1976: 86-107). vfiqrobT, prolo gis 20-22-e strofe bi rusT ve lo lo gi a Si didxans darCe ba gans jis sagnad. es iTq mis uwina re sad erT -erT ta epze: `vTqva mijnu ro ba pirve li da tomi gvarTa zena Ta~. am stri qonis pirve li naxe var ta e pi (`vTqva mijnu ro ba pirve li~) STago ne buli unda iyos axali aRT q mis wigniT, sadac qriste Tavis Tavs uwodebs `pirvels~: `me var ani da hoe pirveli da ukanas kneli, ityvis ufali, rome li ars, rome li iyo da rome li moma val ars, yovli sa mpyrobe li~ (gamocx. 1,8); `me var pirve li da ukanas k ne li~ (gamocx. 1,17). Sesity ve ba `siyva ru li pirve lic~ aqve figu ri rebs: `ange loz sa efeso is ekle si i sa sa miu we re. aramed maqus Senda mo marT, rame Tu siyu a ru li igi Seni pirve li dau te ve~ (gamocx. 2, 1-4). aqve gvaxsen de ba `RvTaeb ri vi kome di is~ erTi gamo naT q va mi: `Tvali mivapy roT axla ukve siyva ruls pirvels~. `vTqva mijnu ro ba pirve lis~ gamoT q mi sas rusTa ve li ucilob lad bibli i dan amodis; `RmerTi siyu a ru li ars~ (I kaT. ep. 4,16). radga nac qristes nacval sa xe lad Cans `pirve li~ da ufali Tavad aris siyva ruli, gamo dis, rom `mijnu ro ba pirvel Si~ swored macxovris xate ba unda davi na xoT, romli sad mi siyva ruls aRavlens, uwina re sad, rusTa ve li. meo re naxe var ta ep Si dasa xe le bu li `tomi sa~ da `gvarTa zena Ta~ - Si plato nis filo so fi u ri cnebis danax va Tu masTan gai give ba wina aR m de gob ri vi a. amiT safuZ ve li ecle ba rusTa ve lis bib liur - q ris ti a nul msofl m xed ve lo bas samya ro sa da adami a nis Seq mnas Tan dakav Si re biT. didi poe ti poe mas iwyebs swored RmerTis mier samya ros Seqm nis aqtiT `daba de bis~ (Sesaq mis) safuZ vel ze. igi nayo fia bibli u ri epizo dis TiTq mis leqsad gardaT q mi sa: 179 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV `romel man Seqm na samya ro Zali Ta miT Zlie ri Ta, zegar d mo ars ni suli Ta yvna zeciT mona be ri Ta. Cven, kacTa, mogv ca qveya na, gvaqvs uTva la vi feri Ta, misgan ars yovli xelmwife saxiTa mis mieriTa~ (Rustaveli, 1988: 9). plato ni xom samya ros, qveyni e re bis safuZ v lad sike Tis ideas (samya ros ierarqi is mwvervals) aRia rebs. n. naTa Zis mtkice ba, rom rusT vel ma sike Tis adgi las am ierarqi a Si mijnu ro ba anu siyva ru li daa ye na, gada sa sin ji a. erT rame Si unda dave Tan x moT n. naTa Zes _ es aris `mijnu ro ba pirve lis~ da `tomis~ Sina ar sob ri vi gai gi ve ba. oRond aq ar movi az rebT `toms~, rogorc plato nis filo so fiur cnebas _`gvarTa~ idea Ta gama er Ti a ne bel zogad anu idea Ta ideas. rusTa ve lis `mijnu ro ba pirve li~ da `tomi~ moce mu li ti pis mixed viT sino ni mur cnebe bad unda wavi kiTxoT. `gvarTa zenaTa~ Cven migvaCnia petre iberielis (fsevdo-dionise areo pa ge lis) mier sam ierarqi ad (umaR le si ierarqi a: sera fim ni, qero bim ni, saydar ni; saSu a lo ierarqi a: ufle ba ni, Zalni, xelm wi feba ni; daba li ierarqi a: mTavro ba ni, mTava ran ge loz ni, ange loz ni) dayo fil ange loz Ta nacval sa xe lad, iseve rogorc RvTis metyve le ba Si ange lo ze bis saer To saxe lad damk vid re bu li `Zal ni zeci sa ni~. swored mas Caa nac v la rusTa vel ma `gvarni zena ni~. RvTismety vel Ta Tanax mad, RmerT ma samya ros Seqm nam de gaa Ci na ange loz ni. `vefxistya o san Sic~ figu ri rebs ange loz ni, rogorc `cis ZalTa dasi~. RmerTi viT ange lo ze bic `miuw do mel ars da da farul~. am mxriv Cveni yuradRe ba miiq cia viktor noza Zis Tval sazris ma, rasac abso lu tu rad vizi a rebT: `vefxistya os nis~ Sair Si moxse ni e bu li `tomi gvarTa zena Ta~ Semdeg na i rad gani mar te ba: `gvarni zena ni~ arian mudam myofni~, `samu da mo~, `sau ku no zena ni~, anu ange los Ta tomi, `gvarni zena ni~ _ ange los ni. maT SeuZ li aT RmerTis mimarT sruli siyva ru li~ (Nozadze, 1975: 28). saanalizo taepSi `mijnuroba pirveli~ anu RmerTi-siyvaruli gvevlineba aseve `tomad~ rogorc zeciur arsebaTa _ sam ierarqiad dayofil angelozTa _ gamaerTianebel Zalad. aseTi qristianuli RmerTi-siyvarulisadmi adamianis mxridan satrfialo damokide buleba poetis mier monaTlulia `sazeo saqmed~, romelic `aRmaf renaTa momcemia~. rogor gavigoT `mijnuroba pirvelze~ naTqvami sityvebi: `Znelad saTqmeli, saWiro, gamosagebi enaTa~... `vinca ec debis, Tmobamca hqonda mravalTa wyenaTa~. vfiqrobT, rusTave lis mier aq gamoyenebulia RmerTis Secnobis, logikuri codnis apofatikuri gza: `Znelad saTqmeli~ anu gamouTqmeli, eniT ver gamoTqmuli (`gamosagebi enaTa~). poeti am meTods sakuTriv poemis 180 tite mosia teqstSic mimarTavs: `ucnauro da uTqmelo, ufalo uflebaTao~. es fsevdo-dionise areopagelis apofatikuri cnebaa: `gamouTqmel ars yovlisa sityvisagan zeSTasityvasa igi saxierebai~ ... (Iberi e li, 1961: 6). `uin uZlos kacobriviTa sityviTa qebad cxovrebisa mis uTqmelisa da gamouTqmelisa~. miqael modrekilic ityvis: `caTa dautevneli gamouTqmeli RmerTi da gareSeuwereli, mizezi yo velTa mizezTai usxeuloi~ (Modre ki li, 1978: 14). `saWiro~, cxadia, ar gaigeba saWiroebis mniSvnelobiT. igi war moebulia sityvidan `Wiri~. uflis Seucnobloba siZnelis, Wiris winaSe ayenebs rigiT adamians, amitomac man unda iqonios didi moT minebis unari, gauZlos amiT gamowveul wyenas (`Tmobamca hqonda mravalTa wyenaTa~, igive WirTa). swored amitomac `mas, erTsa, mij nurobisa Wkvianni ver mixvdebian, ena daSvrebis, msmenlisa yurnica davaldebian~. gamoTqma `erTsa~ RmerTis saxelia. rusTveli amaze uSualod migvaniSnebs poemis dasawyisis meore strofis pirvel ta epSive: `he, RmerTo, erTo, Sen Sehqmen saxe yovlisa tanisa~. poemis teqstSic vkiTxulobT: erT-arsebisa, erTisa~. didi Semoqmedi uSu alod bibliidan Tu areopagitikidan amodis: `RmerTi Seni ufali erT ars~ (mark. 12,7); `vinaiT gan erTi ars RmerTi~ (rom. 3,30); `yo velTa mogonebaTagan mougonebel ars zeSTagonebisa igi erTs~. `mas, erT sa, mijnu ro ba sa~... aq `mijnu ro ba sa~ `erTis~ anu Rmer Tis sino ni mi a, vina i dan saxa re bis eniT, `RmerTi siyu a ru li ars~. rusT ve lis mixed viT, swored am `erTs~, `mijnu ro bas~ `Wkvian ni ver mixv de bi an, ena daSv re bis, msmenli sa yurni ca daval de bi an~. z. gamsa xur di as umarTe bu lod miaC nia `Wkvia nis~ Sina ar sis gai gi veba `brZenTan~. misi azriT, `Wkvian Si~ igulis x me ba Cveu leb ri vi adami a ni, amsof li u ri Wkuis kaci, rome lic dayr d no bi lia miwi er Wkua- go ne ba ze (Gamsakhurdia, 1984: 103-106) a. abJan da Zes miaC ni a, rom saa na li zo tae pis `Wkvia ni~ arc brZens niSnavs da arc amsof li u ri Wkuis kacs. igi niSnavs gau mij nu re bels, gauS ma ge bels. am taep Si mas `Wkvia ni~ `mSvidis~ sino ni mad esaxe ba (Abzhandaze, 1994: 188). sa kiTxisad mi amg va ri midgo ma yovel g var logi kas mokle bu li a. ga moTq ma Si _ `mas, erT sa, mijnu ro ba sa Wkvian ni ver mixv de bi an~ is az ri gamos W vi vis, rom RmerTis Secno ba Wkua- go ne biT SeuZ le be li a. misi Secno bis sxva gzebi arse bobs, romel Ta Soris gansa kuT re biT gamo ir Ce va e. w. logi ku ri codnis meTo de bi _ kata fa ti kur -a po fati ku ri RvTismety ve le ba. v. noza Zis mixed viT, aseTi misti ku ri siyva ru li Wkui sa gan ar aris damo ki de bu li... Wkvian ni RvTisad mi siyva ruls ver Sesw v de bi an. aseTi misti ku ri siyva ru lis T vis Wkua ar aris saWi ro, radgan RmerTi sad mi siyva ru li aris Wkuis 181 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV gare Se, gone bis gare Se. igi misti cizms ekuTv nis (Nozadze, 1975: 94). miTi Te bu li a, rom apofa ti ku ri codna aris arcod nis codna, misi ukanas k ne li da umaRle si safe xu ri, abso lu tu ri umecre bi sa da adami a nu ri gone bis sruli umwe o bis aRia re ba RvTaeb ri vi bune bis Semec ne ba Si (Shua saukuneebi…, 1987: 53). rogorc SeniS nu li a, rode sac codnis meTo de bi uZlur ni ari an sinam d vi lis pirvel sawyi sis Sesa mec neb lad, swored amis Semdeg iwyeba misti ciz m ze gadas v la. es aris RvTis wvdomis misti ku ri Wvretis gza, rasac areo pa gi tul misti ciz mam de mivya varT. ase ve, areo pa gi ti kis mixed viT, RmerT Tan misv li sa, misi wvdomi sa da xilvis erT -er Ti mTava ri gzaa locva. `mijnu ro ba pirvel ze~, `sazeo saqme ze~ anu saRm r To siyva rul ze mkiTxve lis T vis Tavi si koncef ci is gacno bis Semdeg rusTa ve li sau bars ganag r Zobs miwi er - xor ci el siyva rul ze. amiT ki ar emij neba poe ti saRm r To siyva ruls, aramed mis mimbaZ vel, mas mims gav sebul zneob riv miwi er mijnu ro ba ze gviqm nis srul warmod ge nas: `vTqvne xelo ba ni qvena ni, romel ni xorc Ta hxvdebi an. maT masve hbaZven, Tu oden ar siZven, SoriT bndebi an~, araswo ria `xelo ba nis~ ganmar te ba Smago bad moce mul taep ze msjelo bi sas, rogorc amas mimar Tavs a. abJan da Ze. z. gamsa xur di as Tanax mad, saa na li zo striqon Si da sxvaga nac (`misT vis vxelob, misT vis mkvdari~) `xe loba~ wminda, amamaR le bel siyva ruls gulis x mobs. es mosaz re ba vrcelde ba, cxadi a, miwi er siyva rul ze, rome lic saRm r To mijnu robas baZavs: `marT masve hbaZven, Tu oden ar siZven, SoriT bnde bian~, anu Sori dan idage bi an trfobiT. saa na li zo strofSi rusTa ve li gamo yofs adami an Ta or ka tego ri as: `zogTa aqvT saRm r To siax le, daSv re bis aRmaf re ni Ta, kvla zogTa qve uc bune ba kekluc Ta zeda frfeni Ta~. bunebrivia, pirvel kategorias miekuTvnebian saRmrTo siyva rulis mimbaZvelni Seyvarebulni anu zneobrivi mijnurni, meore kategorias ki siZva-mruSobasTan wilnayarni. 23-e strofSi rusTa velma warmoaCina idealuri moyme-mijnuris zneobrivi Rirsebani: `mijnur sa Tvalad situr fe marTebs, marT viTa mzeo ba, sibr Z ne, siux ve, simdab le, siyme da moca le o ba, ena, gone ba, daTmo ba, mZleTa mebr Zol Ta mZleo ba. visca es srulad ara sWirs, aklia mijnurT zneo ba~ (Rustaveli, 1988: 12). prolo gis momdev no strofeb Sic ganfe ni lia rusTa ve lis mij nuro bis Teo ri a. poe ti erT ma neTs upiris pi rebs WeSma rit, amamaR lebel grZnobas _ mijnu ro bas da mis dama ma xin je bel, Sery v nil 182 tite mosia siZvas, sibil wes da mruSo bas. visac es erT ma neT Si aereva, Sors dgas siyva ru lis grZnobis adami a nu ri uzado gage bi sa gan: `mijnu ro ba aris turfa, sacod ne lad Zneli gvari, mijnu ro ba sxva rame a, ar siZvi sa dasa da ri. igi sxvaa, siZva sxvaa, Sua uzis didi zRvari, nuvin garevT erT ma ner T sa, gesmas Cemi nau ba ri~ (Rusta ve li, 1988: 12). rusTavelis gagebiT, zneobriobas daqvemdebarebuli, saRmrTo siyvarulis matarebeli adamiani unda gamoirCeodes `xanierobiT~ (simtkiciT, erTgulebiT), `guli erTsa daajeros~ unariT, satr fosadmi TavganwirviT (`mas cocxali nu elevis, raca pirvel Seuy vardes~). mijnurisTvis yvelaferi unda daTmos, Tundac `misTvis velTa gamovardes~, uari unda Tqvas amsofliur keTildReobaze Tu siamtkbilobaze (`kargi mijnuri igia, vin iqms soflisa Tmoba sa~); kargi mijnuri garegnulad siyvaruls ar unda imCnevdes (`ars pirveli mijnuroba ar-daCena). SeeZlos `WirTa malva~, ar unda Seu Sindes `SoriT bnedas, SoriT kvdomas, SoriT dagvas, SoriT alvas~ (cecxlis aliT wvas), samijnuro grZnobebs, siyvarulis saidumlo ebas saTuTad unda inaxavdes (`xams Tavissa xvaSiadsa arvisTana am JRavnebdes. ar bediTad `hais~ zmides, moyvaresa ayivnebdes: arsiT aCndes mijnuroba, arasada iferebdes~); arafrad agdebdes gansac dels (`misTvis Wiri lxinad uCndes, misTvis cecxlsa moidebdes~) rusTa ve li gmobs meZa vo bas, sibil wes, mruSo bas, ugulo siy varuls (`mZuls ugulo siyva ru li, xvevna- koc na, mtlaSa- m t lu Si~). misT vis miu Re be lia e. w. Seyva re bu li, rome lsac `dRes erTi undes, xvale sxva, sTmobdes gayri sa Tmoba sa~. poets ukvirs im adami a ni sa, romel ic TiTqos iferebs sayvar lis siyva ruls, mag ram `ayiv nebs misT vis mkvdari misT vis wylulsa~. igi aRS fo Te biT kiTxulobs: `Tu ar uyvars, rad ara sZuls? rad ayivnebs, raca sZulsa?~ Tumca aseTi kacis gan ra unda ukvir des, roca gai Ta vi sebs: `avsa kacsa avi sityva urCev nia sulsa, gulsa~. SeiZ le ba davas k v naT: `vefxistya os nis~ prolog Si rusTa vel ma Sai ro bis (poe zi is) Teo ri is para le lu rad gamiz nu lad warmog vid gina mijnu ro bis Teo ri ac. mkiTxve lis yuradRe ba miapy ro saRv To misti kur siyva ruls, xorci el, kacob riv trfobas. erT ma ne Ti sa gan gamij na saRv To (`mijnu ro ba pirve li~) siyva ruls mims gav se buli miwi e ri, wminda, ubiwo, zneob ri vi mijnu ro ba da eroti ku li siZva- m ru So bas Tan wilna ya ri trfia le ba. poetis mier prologSi mocemuli taepi _ `vTqva mijnuroba pir veli da tomi gvarTa zenaTa~ samecniero literaturaSi gansxvave bulad gansjis sagani gaxda. `mijnuroba pirveli~ swored RvTier 183 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV siyvaruls gulisxmobs. cnebebi `mijnuroba~ da `tomi~ sinonimur sityvebad unda miviCnioT, xolo `gvarTa zenaTa~ _ angelozebad. maTTan platonis filosofiuri cnebebis (tomi, gvari) Sinaarsis gaigiveba winaaRmdegobrivia. amiT safuZveli ecleba rusTavelis bibliur-qristianul msoflmxedvelobas samyarosa da adamianis SeqmnasTan dakavSirebiT. prolog Si saRv To siyva rul ze saub ris dasru le bis Semdeg rusTa ve li mkiTxvels safuZ v li an warmod ge nas uqm nis idea lu ri mijnu ro bis zneob riv da fizi kur Rirse beb ze. gasa zi a re be lia koncef ci a, rom Sua sa u ku ne ob ri vi sa da rene san su lis Serwy ma ro gorc dantes, ise rusTa ve lis Semoq me de ba Si yvela ze metad siyva rulis gage ba Si gamov lin da. literatura: 1. Abzhandadze A. “Vefkhistkaosani” da misi avtori, Tbilisi, 1994. 2. Baramidze A. Shota Rustveli, Tbilisi, 1975. 3. Biblia (mckheturi khelnatseri). Gamosacemad moamzada da gamokvleva daurto Elene Dochanashvilma, Tbilisi, 1981-1986. 4. Iberieli Petre (Fsevdo_Dionise Areopageli), Shromebi (S. Enuqashvilis ga- mocema), Tbilisi, 1961. 5. Gamsakhurdia Z. “Vefkhistkaosnis” inglisuri targmani, Tbilisi, 1984. 6. Khintibidze E. “Vefkhistkaosnis” sikvaruli,Tbilisi, 2005. 7. Miqael Modrekilis himnebi, teqsti gadmotsera dednidan da gamosca Vazha Gvakhariam, Tbilisi, 1978. 8. Natadze N. Rustveluri mijnuroba da renesansi, Tbilisi, 1966. 9. Nozadze V. “Vefkhistkaosanis” mijnurtmetyveleba, Parizi, 1975. 10. Nucubidze Sh. Qartuli filosofiis istoria, II, Tbilisi, 1958. 11. Orbeliani Sulkhan-Saba, Tkhzulebani, III, gamosacemad moamzada, gamokvleva, shenishvnebi da leqsikoni daurto Iv. Lolashvilma, Tbilisi, 1963. 12. Sharia P. Shota Rustavelis msoflmkhedvelobisa da shemoqmedebis zogierti dziritadi sakitkhi, Tbilisi, 1976. 13. Shota Rustaveli. Vefkhistkaosani (poemis akademiuri teqstis damdgeni komisiis gamocema), Tbilisi, 1988. 14. Shua saukuneebis filosofiis istoriis problemebi, I, Tbilisi, 1987. 184 tite mosia Tite Mosia FROM THE INTERPRETATION OF RUSTAVELI’S ROMANCE THEORY Summary This paper considers the romance concept of the Georgian national epic poem The Knight in the Panther’s Skin written by the Georgian classic writer Shota Rustaveli. In the prologue of the Knight in the Panther’s Skin Rustaveli intentionally represented the romance theory in parallel with the poetry theory. He attracted reader’s attention to the holy or mystical love and the earthly, physical lust. He separated from each other the innocent, sacred and moral love equaled to divine love and erotic, immoral lust. The verse in the prologue _ “I speak of the romance the first and the tribe of the highest families” _ has become the subject to diverse discussion in the scientific literature. “The romance first” means the Lord, divine love, while the terms “romance first” and “the tribe” must be considered as synonyms and “the highest families” must be perceived as angels. Identification of the sense of Plato’s philosophical terms (“tribe”, “family”) with them would be contradictory. It takes away the basis from Rustaveli’s Biblical-Christian worldview in relation to the creation of the universe and mankind. After speaking about the divine love in the prologue Rustaveli offers readers the comprehensive vision of the moral and physical values of the ideal lover . The perception of love _ this worldly human feeling has most apparently revealed the mixture of medieval and renaissance epochs both in Dante and Rustaveli’s creative works. 185 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV marine jaiani `vefxistyaosani~ da afxazeTi (`rusTveli msoflio literaturaSi~, mesame tomSi gamoqveynebuli rusTvelologiuri masalis mixedviT) Tbili sis saxel m wi fo univer si te tis Zveli qarTu li lite ra turis isto ri is kaTed ris (rusT ve lis kabi ne tis) mecni er - Ta nam S romel Ta inici a ti viT daiwyo samec ni e ro krebu lis, saxel wo de biT `rusT ve li msoflio lite ra tu ra Si~, damu Sa ve ba, Sedge na da ga moce ma. pirve li tomi dais tam ba 1976 wels (sare daq cio kole gi a: al. bara mi Ze, o. baqa ni Ze, v. gamy re li Ze, l. menab de (mTava ri re daqto ri), a. uruSa Ze, v. Sadu ri). 1980 wels Cveni univer si te tis qarTu li lite ra tu ris isto ri is kaTed ras (kaTed ris gamge, prof. o. WurRu li a) dae va la moem za de bi na da mie wo de bi na sare daq cio kole gi i saT vis bibli og ra fi u li masa le bi, wigne bi, Jurnal - ga ze TebSi gamoq vey ne bu li masa le bi rusT ve li sa da misi poe mis Sesa xeb, foto pi re bi da a.S. Catar da didi mocu lo bis samu Sa o. fur cel- fur cel Semow m da da aRinus xa peri o du li presis mona ce me bi (afxaze Tis avto no mi u ri respub li kis masS ta biT), qarTul, afxa zur da rusul enaze Sesru le bu li samec ni e ro stati e bi, nark ve vebi, leqse bi da a. S. am faqts sagan ge bod aRniS navs sare daq cio kole gia gamo ce mis me-3 tomis wina sity va o ba Si: `gansa kuT re bu li madlo biT unda movix se ni oT a. m. gorkis saxe lo bis afxaze Tis sa xelm wi fo univer si te ti, rome lic mxurva led gamo ex ma u ra Cvens Txovnas erTob li vi muSa o bis Sesa xeb. soxu mel ma kole geb ma (z. an Caba Zem, S. gvara mi am, t. mosi am, o. WurRu li am, m. jai an ma) erTob didi wvlili Sei ta nes krebu lis momza de ba Si~ (Rustveli msoflio lite raturashi, 1988, t. III, 15). gamo ce mis redaq to ri miu Ti Tebs, rom, bib liog ra fi is zedme tad gazr dis Tavi dan acile bis mizniT, ar aris Seta ni li Semow me bu li da dazus te bu li cnoba Ta umrav le so ba. tomSi warmod ge ni li masa le bis nawi li adre ve iyo Targ m ni li da gamoq vey ne bu li (d. guli a, m. delba, b. Sinqu ba, m. lasu ria da sxva), xolo zogi er Ti ki sagan ge bod iTarg m na. qarTu le no va ni rusT ve lolo gi u ri lite ra tu ris dabeW d vac buneb ri vi iqne bo da, magram kole gi am Tavi Sei ka va Semdeg gare mo e ba Ta gamo: es lite ra tu ra ise usazRv ro a, rom ramde ni me tomic ki ar eyofa. sxva masa leb Tan erTad xelmi saw v do mi a, radgan zogi er Ti weri li Tu wigni ramden jermec ki dai beW da. 186 marine jaiani rac See xe ba Cven mier Sekre bil -aR nus xu li bibli og ra fi u li masa la 200 aTeul ze meti iyo da inaxe bo da afxaze Tis univer si te tis qarTu li lite ra tu ris isto ri is kaTed ra ze. cnobi li movle nebis gamo, misT vis xeli ar migviw v de ba. Tsu rusT ve lis kabi ne tisT vis gamog zav ni li masa lis kvalic ar Cans, dai kar ga. Cvens naSrom Si warmo va CenT afxaz mecni er - m k v le var Ta dakvir vebebs, Sexe du le bebs, naaz revs SoTa rusT ve li sa da misi poe mis Sesa xeb, samec ni e ro krebu lis `rusT ve li msoflio lite ra tu ra Si~ (III t.) gamoq vey ne bu li rusT ve lo lo gi u ri masa lis mixed viT. afxazTa Soris `vefxistya o sa ni~ ZvelTa gan popu la ru li iyo. sau ku ne Ta manZil ze qarT ve le bi da afxaze bi erTad cxovrob d nen, mxardam xar ibr Zod nen moZa le bu li mtrebis wina aR m deg, iRv wod nen kultu rul - li te ra tu rul sarbi el ze. buneb ri vi a, afxazebs adre ve SeeZ loT gaec noT rusT ve lis poe ma. maTi umrav le so ba kargad flobda qarTul enas da Tavi suf lad SeeZ loT `vefxistya os nis~ dedan Si wakiTx va. es imas niSnavs, rom poe mis Targ m nam de sau ku ne ebiT adre iyo afxazTaT vis rusT ve lis poe ma cnobi li da, Sesa ba misad, gacno bi e re bu li, gaaz re bu li. XIX s-is meo re naxev ri dan da gansa kuT re biT XX s-is damde gi dan afxaz inte li gen ci a Si Sei niS ne ba `vefxistya os ni sad mi~ inte re sis gaZli e re ba. XIX sau ku nis afxaze Tis ganaT le bul ma warmo mad gen leb ma po ema zepi rad icodnen. gior gi Sarva Si Zem da daviT Cqotu am, rad gan aRz r dil ni iyv nen Zveli qarTu li kultu ris nia dag ze. afxazi poe ti da sazo ga do moRva we g. Sarva Si Ze, qarT vel Tana mo kal me ebTan erTad, aqti u rad mona wi le ob da `vefxistya os nis~ teqs tis dadge ni sa da ilust ri re bis saqme Si. ung re li mxatv ris m. ziCis `vefxistya os nis~ ilust ra ci e bis gamo fe na- war mod ge na quTa is Si Sedga, iuwyeba `droe ba~ (5. VI. 1882, #115), `g. Sarva Si Ze tari e lis sura Tad imisTa na iyo, rom mgonia TviT safla vi dan amd ga ri SoTac ar dai wu neb da iers da saxis mety ve le ba so~ (Rustveli msoflio literaturashi, 1988: 572). sayu radRe bo a, rom bibli u ri iobiviT wame buli daviT Cqotu a, rome lic bavS vo bi dan ve ezia ra rusT ve lis sibr Z nes, sibe rem de ar Sele via mas: `bavS vo bi dan ve dakav Si re bu li var am did nawarmoebTan: jer iyo da mis kiTxvas vismendi mSobli ur ojaxSi. ufro gvian daviwye misi kiTxva, gada kiTx va, zepi rad daswav la, kvlav gada i kiTx va a. S. ase grZelde ba dRemde, TiTq mis samo ci wlis manZil ze~ (Rustveli msoflio lite raturashi, 1988: 572). Semd gomSi igi Cine bu li rusT ve lo lo gi dadga da vrceli gamok v le vac dawe ra _ `rusT ve lis poe mis gmire bi da maTi msofl m xed ve lo ba~. 187 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV am naSrom ma, samwu xa rod, Tavi si avto ris, udana Sa u lo damna Sa vis tragi ku li bedi gai zi a ra. amave peri od Si rusT ve lis poe mis afxazu rad Targ m nis pirve li mcdelo ba ekuTv nis dimit ri Tlafsis Ze maans (marRa ni as). _ `ambo ben, rom d. maans gansa kuT re biT uyvar da `vefxistya o sa ni~. poe mis naxe var ze meti zepi rad scodni a, saub ri sas mudam imow mebda rusT ve lis aforiz mebs, surda rusT ve lis mSveni e ri poe zia gae zi a re bi na mSobe li xalxis T vis afxazur enaze. swored amitom mohki da xeli poe mis Targ m nas. SesaZ lo a, d. maa nis Targ ma ni rusT velis geni is Sesa fe ri si iyo, magram, misi sikv di lis Semdeg, xelna were bi ugzo -uk v lod dai kar ga~ (Rustveli msoflio lite raturashi, 1988: 586). aRsa niS na via is faqtic, rom XIX sau ku ne Si qarTul kultu rasTan axlos myofi afxaze bi poe mis xmamaR la kiTxvis tradi ci as amk vid re ben. `vefxistya os nis~ zepi rad Seswav la ki sapa tio saqmed iTv le bo da. `vefxistya os ni sa~ da rusT ve li sad mi inte re si afxazeT Si yo velT vis igr Z no bo da, magram am inte res ma gansa kuT re biT Sesam C ne vi saxe mii Ro me-20 sau ku nis 30-ian wlebSi _ poe mis 750 wlisTa vis sai u bi leo zei mis win da dResas wa u lis dReeb Si. mTel afxazeT Si gaCaR da samza di si. Jurnal - ga ze Teb Si afxazur, qarTul da rusul enebze dai beW da didZa li masa la rusT vel sa da mis poe ma ze. ker Zod, weri le bi, infor ma ci e bi, qroni ka, Txzule bis mokle Sina ar si da a. S. mraval Ta gan ramde ni mes dava sa xe lebT: m. haSbas _ `SoTa rusT ve lis poe ma `vefxistya o sa ni~ afxazur folk lor Si~. poe mis nawyve te bi Targ m nes d. guli am, a. arZin bam, m. goCu am, l. kviwi ni am, b. Sinqu bam, s. Wanbam. Seiq m na rusT ve li sad mi miZRv ni li leqse bi: d. guli a, s. adle i ba, l. kviwi ni a, b. Sinqu ba, r. Wama gua da sxva. dais tam ba `vefxistya os nis~ poe tu ri Targ ma ne bi sa da weri le bis ori krebu li. ssr kavSi ris mweral Ta kavSi ris gamge o bis plenum ze (28.XII. 1937 weli) sityva warmoT q va x. bRaJbam, romel mac isaub ra poe mis popu la ro ba ze afxazeT Si, qarTu li Txzule bis afxazu rad ametyve le bis cdebze. XX sau ku nis ormoc -or moc da a Ti a ni wlebis mTavar movle nad iqca d. guli as mier `vefxistya os nis~ afxazur enaze Sesru le bu li teqs tis gamoq vey ne ba. poe mis pirve li afxazu ri Targ ma ni (`abu as cia zSiu~), zemoT dasa xe le bu li mZlavri kultu rul - yo fi Ti wa namZR v re bis logi kur Sedegs warmo ad gen da. d. guli am `Cine bu lad daag vir g vi na afxazur - qar Tu li lite ra tu rul - kul tu ru li ur Tier To bis erTi etapi da am sfero Si sama ga li To pers peq ti va ga daSa la im gage biT, rom, rogorc maSin de li presa iuwyebo da, misi 188 marine jaiani mniSv ne lo ba gasc da `lite ra tu ris viwro~ farg lebs da ori xal xis megob ro bis ganm t ki ce bas dae do safuZ v lad~ (gaz. ,`lite ra tu ruli saqar T ve lo~, 1941, #19). amito mac afxazma xalx ma mSobli ur enaze rusT ve lis poe mis ametyve le ba erovnu li dResas wa u lis done ze aiyva na. 1941 wlis 26 aprils soxu mis saxel m wi fo Teat r Si Targ ma nis gamo ce mi sad mi miZRv ni li lite ra tu ru li saRa mo gai marTa. Semd gom Si d. guli as Targ ma ni ganme o re biT samjer dai beW da _ 1953, 1959, 1984 wlebSi. 1978 wels gamoq vey n da `vefxistya os nis axali, sruli poe tu ri Targ ma ni, Sesru le bu li m. lasu ri as mier. afxazur enaze axali Targ ma nis gamos v la poe zi is namd vi li dResas wa u li iyo. m. lasu rias S. rusT ve lis saxe lo bis premia mie ni Wa. samec ni e ro krebu lis _ `rusT ve li msoflio lite ra tu ra Si~ (III t), sare daq cio kole gi a, m. lasu ri a se u li Targ ma nis rao bi sa da mniSv ne lo bis gaTva lis wi nebiT, beWdavs ramde ni me mkvlevris Sefa se ba- ga mox ma u re bas (Rust veli msoflio lite raturashi, 1988: 578-592). aRsa niS na vi a, rom afxazeT Si farTod gai Sa la muSa o ba 60-ia ni wlebi dan, rode sac daiwyo mzade ba rusT ve lis 800 wlisTa vis aR saniS na vad. peri o dul presa Si gamoq vey n da qarT ve li, afxazi da rusi avto re bis weri le bi, leqse bi, poe me bi `vefxistya o san ze da mis Semoq med ze. Catar da leqci a- mox se ne be bi, moewyo gamo fe ne bi, lite ra tu ru li saRa mo e bi. calke wignad gamo vi da S. inal-i fas monog ra fia `SoTa rusTa ve li~ (1966 w.) faqti a, rom es iyo afxa zur enaze gamoq vey ne bu li pirve li samec ni e ro xasi a Tis gamok - vle va rusTa vel ze. aq Seja me bu lia avto ris mraval w li a ni rus- Tve lo lo gi u ri kvleva- Zi e ba. poet ma b. Sinqu bam gamo aq vey na rus Tve lis aforiz me bi afxazur enaze. man, 1966 wlis 26 seqtem bers, sityva warmoT q va ssr kavSi ri sa da saqar T ve los mweral Ta kav Sire bis gamge o ba Ta rusT ve li sad mi miZRv nil plenu meb ze. b. Sin qubam vrclad isaub ra qarT vel -afxaz Ta isto ri ul - kul tu rul urTi er To ba sa da `vefxistya os nis~ Targ m na- Ses wav lis isto ri a ze afxazeT Si. samar T li a na daa miCne u li 1966 weli afxazu ri rusTa ve li a nas Seja me bis Tari Rad. am wels dai beW da weri le bi, romleb Sic ganxi luli iyo afxazeT Si rusT ve lis popu la ro bis, poe mis Targ m nis isto ri i sa da afxaz swavlul Ta Ziri Ta di rusT ve lo lo gi u ri sa mecni e ro xasi a Tis naSro me bi. maga li Tad, m. dedba sa da m. mirne lis `vefxistya o sa ni~ afxazur folk lor sa da lite ra tu raT m cod ne o baSi, S. sala ya i as `rusT ve lis poe ma afxazur poe zi a Si, n. Soni a sa da g. zuxbas `vefxistya o sa ni da afxaze Ti~. 189 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV afxazTa Soris `vefxistya os nis~ popu la ro ba ze miu Ti Tebs xalxur sityvi e re ba Si Semo na xu li masa le bi poe ma sa da mis av torze. afxaz mecni er - m k v le var Ta dakvir ve biT, uZve les afxazur folk lor sa da eTnog ra fi ul yofa Si `vefxistya os nis~ keTil m yofe li gavle na naTlad sacna ur de ba. eri rusT ve lis dide bu le bas Tavis folk lor Si, xalxur poe zi a Si gamo xa tav da. Zveli drois afxazi xSirad rusT ve lis poe tu ri saxe e biT azrov neb da. misT vis poe mis perso naJ Ta Zleva mo si li saxe e bi gaxda sila ma zis, adami a nis fizi ku ri da suli e ri mSveni e re bis, gmiro bis, sima ma cis, sike Ti sa da huma nu ro bis idea lu ri simbo lo. poe mis mTava ri gmiris tari e lis saxe afxazTaT vis iqca si lama zis, fizi ku ri da suli e ri sijan sa Ris, gmiro bis, mama co bis simbo lod. roca afxazebs surT aRniS non, rom mama ka ci Sesa xe da vad mSveni e ri da tana di a, ambo ben: `ata ri al defef Sup~ (tari e lis msgavsi). `unan sikux San das atari al dSpeif Sut~ (o, rogor veTay vane bi tari els), `ata ri al epS dSvrZa~ (tari e li viT tanke na ri) da a. S. (Rustveli msoflio lite raturashi, 1988: 567). afxazu ri onomas ti ka Seiv so da gamdid r da `vefxistya os nis~ perso naJ Ta saxe le biT: SoTa, tari e li, Tandel (avTan di li), rus tan, arustan, astan, darja na, darja (kacis saxe la dac yofi la cnobi li), TinaT... sagu lis x mo a, rom afxazi patar Z le bi Tavi anT mazleb sa da naTe sav mama ka cebs metsa xe lad sayva rel da sapa tio saxels _ tari els uwodeb d nen. am Cvevas, rome lic xalxur tradi ciad iyo qceu li, `axiZ Sa ra~ _ saxe lis Serq me va ewode bo da. rus Tve lis poe mis gmirTa saxe leb ma afxaz xalx Si gani ca da erT g va ri fone ti ku ri cvlile ba da maTi trans k rif ci ac zogjer odnav gan sx vav de ba qarTu li sa gan, rac saqmis viTa re bas ar cvlis. saintereso faqtia, rom `vefxistyaosnis~ erT-erTi personaJis saxels _ dularduxts win uswrebs afxazi dedoflis saxeli _ gu randuxti (bagrat mesamis deda) da dedofalT dedofali sagduxti (RmuriSis warwerebidan), romelTa etimologiuri msgavseba uda vod miaCniaT (Rustve li msoflio lite ra tu ras hi, 1988: 570). afxazi mkvlevre bis azriT, poe mis gmirTa ukv da vi saxe e bi, rom lebic gvanc vif re ben Tavi an Ti monu men tu ro biT, Rrmad Casw v d nen eris sulsa da gone bas. aki rusT ve lis perso na Je bi ase Zlier mogva go ne ben afxazu ri narTe bis eposis gmirebs, romel TaT vi sac niSan dob li via maRa li zneob ri vi Tvise be bi: samar T li a no ba, pati os ne ba, saku Ta ri Rirse bis Segne ba, Tavi suf le bis siyva ru li, ltolva sagmi ro saqme e bi sa ken, sikv dil Tan Seu ri geb lo ba~ (Rustveli msoflio lite raturashi, 1988: 567). 190 marine jaiani isto ri ko se bi n. Sonia da g. zuxba sagan ge bod amaxvi le ben yu radRebas `qaje Tis~ etimo lo gi a ze (Rustveli msoflio literaturashi, 1988: 569). sofel reCxocxirSi, rusT ve lis epoqis sain te re so mate ri alu ri Zegle bis gverdiT, mdeba re obs gamoq va bu li `oqa je~ (qaje Ti), rome lic Zali an grZelia da mrava lo Ta xi a ni. `oqa je ze~ le genda arse bobs sofel Si, rome lic mTlia nad See saty vi se ba m. del bas ganmar te bas: `qaje bi, romle bic rusT vels uaryo fi Tad hyavs daxa tu li, afxaze bis mxriTac uaryo fiT damo ki de bu le bas iwve ven. am saxels uwode ben gesli an da mavne adami a nebs maga li Tad, afxa zebi ambo ben, _ `urt aqajku a~, `aqa jaa urw So up~, `aqa jaa jrxuxa it~, rac niSnavs, _ es qaje bi, qajeb ma SegWa mon, qajeb ma dagw van~ da sxva. (Rustveli msoflio lite raturashi, 1988: 568). rogorc irk ve va, rus Tve lis poe ma Si daxa tul miTo lo gi ur saxe Ta identu ris daZeb na afxazur folk lor Si Zneli ar aris. niSan dob li vi a, rom rusT ve li da misi poe ma mraval g zis gamx dara afxaz poet Ta STago ne bis wyaro. SoTa rusT ve li sad mi miZR nili maRal m xat v ru li leqse bi Seqm nes a. lasu ri am, l. kviwi ni am, l. laba xu am, b. Sinqu bam, b. gurgu li am da sxvebma. 1937 wels, roca mTeli qveya na zei mob da `vefxistya os nis~ Seq mnidan 750-e wlisTavs, soxumis erT-erT umniSvnelovanes quCas rusTvelis sanapiro _ prospeqti ewoda. aqve gaSenda rusTvelis saxelobis ulamazesi baRi, sadac daidga poetis STamagonebeli Zegli (avtori-moqandake k. merabiSvili). afxazeTis saxalxo poet ma d. guliam am Zeglis gaxsnas leqsi miuZRvna (Rustve li msoflio lite ra tu rashi, 1988: 575). masSi poetis, moazrovnisa da didi humanistis cxov reba, adamianuri Tvisebebi moxdeniladaa erTmaneTs Serwymuli: `zRvis piras Zegli damd ga ra mzis sxive bis gan naTa li, Tavs adgas Sara van de dad dide bis Suqi marTa li, Zegli ki ara _ leqsi a, SoTas simRe ra qebu li, amayi mTebis grexi liT arSia Semov le bu li!~ (T. jangulaSvilis Targmani, Rustve li msoflio lite ra tu ras hi, 1988: 654). afxazi poe ti l. kviwi nia didi poe tis Semoq me de bis kargi mcodne da damfa se be lic iyo. mas Seswav li li hqonda rusT ve lis Sesa xeb arse bu li Tqmule be be bi, sadac gadmo ce mu lia poe tis bi ogra fi u li mona ce me bi: SoTas warmo mav lo ba, cxovre bis gza, Ta marTan urTi er To ba, uiRb lo siyva ru lis isto ria da a. S. leqsi `rusT ve lis wyaro~ mesxe Tis mimzid ve li bune bis aRwe riT iwyeba. mesxeT - ja va xe Tis simS ve ni e ris xilviT STago ne bul poets Tvalwin warmo ud ge ba rusT ve lis d ro in de li saqar T ve los isto ri is dide buli sura Te bi. SoTa am Tvalwar m ta ci bune bis Svili iyo: 191 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV `o, Sori ax lo is aq cxovrob da, es mxare mas ekuTv no da, mis Seum C nev lad, faru lad nadi ric ver gaiv li da. sanTe li viT idga sofel rusTav Si saxe lo va ni, mudam aboboq re bul did zRvasa viT uSiSa ri~. (pwkare di ekuTv nis S. gvara mi as. Rustveli msoflio lite raturashi, 1988: 575). cnobi li afxazi mkvleva ri S. sala yaia yuradRe bas miaq cevs im gare mo e bas, rom afxazu ri poe zi is forma sa da teqni ka ze didi gavle na moax di na rusT ve lis leqs T wyo bam, ritmi kam, musi ka lo bam. igi aRniS navs, rom es movle na gansa kuT re biT rusT ve li sad mi miZRv nil leqseb Si Seim C ne va da maga li Tad mohyavs b. Sinqu bas leq si `SoTa rusT ve li~. `sark mel Si Suqi Semo dis, mzis RimiT naxa ver de bi, gadmoh yu re ben freske bi, xmalab j ri a ni mxedre bi, mgoni a, ai, sacaa unda dato von kedle bi, Sevc qe ri Cafiq re bu li, SoTa ze vkiTxav vedre biT~. (Rustveli msoflio lite raturashi, 1988: 577). rusT ve lis poe zi is siyva ru li Taa gamT ba ri s. adle i bas, r. Wa magu as, b. gurgu li a sa da sxvaTa leqse bi. Cveni azriT, naSrom Si warmod ge ni li, ganxi lul - Se fa se bu li vrceli samec ni e ro masa la (`rusT ve li msoflio lite ra tu ra Si~, III tomSi gamoq vey ne bu li), misi mraval fe rov ne bis, mniSv ne lo bi sa da rao bis gaTva lis wi ne biT, yovel T vis iqne ba xelis Sem S le li faq tori qarTul -afxa zu ri urTi er To be bis rRvevis mosur ne TaT vis. literatura: 1. Delba M., Shota rustaveli da misi “Vefkhistkaosani” (Shenishvnebi poemis afkhazuri gamocemisatvis), “Mnatobi”, 1941, #4. 2. Delba M., Dimitri Gulia, Tbilisi, 1949. 3. Gulia G., Dimitri Gulia, Tbilisi, 1974. 4. Janashia S., D. Chqotua da misi narkvevebi “Vefkhistkaosnis” shesakheb, Tbilisis sakhelmtsifo universitetis shromebi. T. I. Tbilisi, 1937. 5. Rustveli msoflio literaturashi. Tbilisis sakhelmtsifo universitetis rustvelis kabineti. T. III, 1988. 192 marine jaiani Marine Jaiani THE KNIGHT IN THE PANTHER’S SKIN AND ABKHAZIA (ACCORDING TO RUSTVELOLOGICAL MATERIAL PUBLISHED IN VOLUME III, RUSTAVELI IN WORLD LITERATURE) Summary Abkhazia has always been a part of the Georgian cultural and historical world. It should be noted that for ages the Georgians and the Abkhazians have lived side by side, have always been shoulder to shoulder in grief and joy. His- torically, Georgian_Abkhaz interaction has alternated between close cooperation. The Georgians stood on guard of national interests of the Abkhaz people, facili- tated the development of their spiritual culture. The paper presents the Abkhazian scholars and researchers’ observations, views and opinions about Shota Rustaveli’s poem and according to publishecollec- tion “Rustaveli in World Literature”, volume III, based on rustvelological material. Naturally, Abkhazians could read Rustaveli’s poem earlier. Most of them were fluent in Georgian and could read freely in the original. This means that the poem for Abkhazians has been popular and well interpreted for centuries before its translation. From the second half of the XIX century and the beginning of the XX century the great interest to the poem was noticed by the Abkhaz intelligentsia. The educated representatives of the XIX century knew the poem by heart and therefore Giorgi Sharvashidze and Davit Chkotua were brought up by the Georgian traditions and cul- ture. The Abkhazian poet and public figure G. Sharvashidze was actively involved with the Georgian scholars in establishing and illustrating the text of the poem. The main event of the 40-50s of the XX century was the publication of the text made in Abkhazian language by D. Gulia. The first Abkhazian translation of the poem was a logical outcome creating new epoch in Georgian - Abkhazian cultural relationship. According to Abkhazian scholars’ observations and opinions in the ancient Abkhaz folklore and lifestyle, the heartfelt influence of the poem is clearly re- flected. The powerful characters of the poem’s characters were the ideal symbol of humanism, kindness, physical and spiritual beauty, heroism, bravery and humility. In 1978, the poem was translated for the second time by the famous Abkha- zian poet A. Lasuria. It should be noted that Rustaveli and his poem have been the source of inspira- tion for Abkhaz poets. Highly artistic poems dedicated to Shota Rustaveli were cre- ated by A. Lasuria, L. Kvitsinia B. Shinquba, L. Labakhua, B. Gurgulia and others. 193 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV joni marRania vladimer misabiSvilis moTxrobebis mxatvruli samyaro vladi mer misa biS vi li Jurna lis tur moRva we o bas Tan erTad warma te biT iRvwo da qarTul mwerlo ba Sic, man Seqm na metad sa yuradRe bo moTxro be bi sa da pie se bis cikli, romleb mac savse biT samar T li a nad daim sa xu res mkiTxve lis mowo ne ba da aRia re ba. am etapze Cvens mizans ar warmo ad gens mwerlis mTeli lite ratu ru li memk vid re o bis Rrma da mraval m x ri vi anali zi, rame Tu es metad Sroma te va di da xang r Z li vi proce si a, amito mac Semo vi farg le biT misi ramde ni me moTxro bis mimo xil viT, rome lic mkiTx vel sazo ga do e bas Seuq m nis warmod ge nas imaze, rogorc profe so ri n. lemon ja va SeniS navs _ `Tu ra marTa li TvalTa xed viT aRiqvams da afasebs avto ri sagnebs, movle nebs da situ a ci ebs~ (Lemonjava, 2001:120), Tu ramde nad sarw mu no da dama je re be lia mwerlis mier Seqm ni li mxatv ru li samya ro, romlis masaz r do e bel wyaro sac war moad ge nen cxovre bi se u li faqte bi da movle ne bi, swore dac rom rea lu ri faqte bi sa da movle ne bis gansa xi e re ba xdeba mis lite ratu rul memk vid re o ba Si, romel sac avto ri zedmi wev niT kargad arT mevs Tavs. mwerals Sesa niS na vad esmis rea liz mis upirve le si moTxovna, rom mkiTxve li, rome lic aRiqvams mxatv rul nawar mo ebs _ darw mu ne bu li unda iyos asaxu lis simar T le Si, rom swored mxat vru li simar T lis arse bo ba aniWebs xelov ne bis nawar mo ebs damo u ki debel esTe ti kur Rire bu le bas. mwera li ara marto qmnis calke ul, erT ma ne Ti sa gan izoli re bul, anda cota Ti erT ma ne Ti sa gan gancal kave biT arse bul saxe ebs, aramed aCve nebs maT kavSirs, xsnis erTi saxis T vis dama xa si a Te bel Tvise bebs meo ris meSve o biT, mis Ziri Tad amoca nas Sead gens is, rom mkiTxvels sain te re so- cxov re bi se ul mdgoma re o ba Si uCve nos adami a ne bi, romel Ta Sesa xe bac is saub robs. vl. misa biS vi lis moTxro be bis didi nawi li eZRv ne ba meo re msoflio omis Temas da es arc aris moulodneli, vinaidan is Ta vad iyo aqti u ri mona wi le faSiz mis wina aR m deg brZoli sa, is iyo TviTm xil ve li im saSi ne le be bi sa da ubedu re be bi sa, rac Tavs da atyda aTeul Tu aseul mili o no biT adami ans. mweral ma umetes wi lad swored omSi miRe bu li STabeW di le be bis qaRal dis furc leb ze gadmo ta na dai sa xa miznad, rom eCve ne bi na mkiTxvel TaT vis misi Ta named ro ve gmire bi Tu rogo ri spetak ni, gulw r fe li siyva ru li sa 194 joni marRania da mtkice megob ro bis, maRa li grZnobe bis mata re bel ni arian. Tavis moTxro beb Si avtor ma gviCve na maTi xasi a Te bi, Seqm na araer Ti amaR lebu li da sain te re so situ a ci a. mkiTxve li, rome lic ecno ba am moTxro bebs, erT ba Sad iviwyebs gare samya ros, Sedis mwerli se ul mxatv rul samya ro Si da SeiZ le ba iTq vas, xdeba mona wi le, mWvrete li avto ris mier asaxu li viTa re bisa. yove li ve amas Semoq me di aRwevs imis safuZ vel ze, rom nawar moe beb Si asaxu li movle ne bi, moqmed pirTa qceve bi TvalnaT liv da dama je reb lad aris axs ni li da dasa bu Te bu li, ise rom mkiTxvels moqme de bis an pirso naJ Ta qcevis sxvagva rad axs na warmo ud gen lad miaC ni a. vl. misa biS vi lis moTxro be bis erT -er Ti krebu lia `qanda ke ba~, sadac mwera li misT vis sain te re so Tema ze _ meo re msoflio omze, am omSi sxvadas x va erovne bis adami a ne bis mier gamo Ce nil Tavda de bebsa da gmiro beb ze mogviTx robs. `qanda ke ba~ avtors uwode bia moTxro ba Ta krebu li saT vis, ase ve is konk re tu li moTxro bis saxel wo de ba ca a, sadac avto ri mis pirad cxovre bas Tan dakav Si re bul erT -erT epizod Tan erTad acocxlebs im gmirebs, romleb mac didi wvlili Sei ta nes faSiz m ze gamar j ve ba Si. moTxro bis mTava ri gmiria axalgaz r da, niWi e ri, didi momav lis mqone xelo va ni qali, romel mac RvTisgan boZe bu li niWis bolom de rea li ze ba ver SeZlo kacob ri o bis mimarT Cade ni li im sisas tikis gamo, rome lic hitle ru li germa ni is mier iqna warmo e bu li gasu li sau ku nis 40-ian wlebSi. avto ri moTxro bis Sesa val Si gviyve ba mis moxved ra ze hospi talSi, im Zmur da keTil gan wyo bil urTi er To ba ze, rac iq su fevda. swored daWril Ta laza reT Si yofnis, iq mkurnal Ta Soris urTi er To bis aRwe ra emsa xu re ba mTavar mizans _ moqme de ba Si mTa vari gmiris Semoy va nas. avto ri mkiTxvels Tanda Ta no biT amza debs mTavar gmirTan Sesax ved rad. mkiTxve li mouT men lad elis pasuxs kiTxva ze ras unda gulis x mob des usafr Txo e bis gvirab Si aRmo Ce nili qanda ke bis avto ri, ra iyo misi miza ni da yove li ve amis Sem deg irk ve va xelov ne bis am nimu Sis arsi da daniS nu le ba _ qanda kebis avto ria _ axalgaz r da, niWi e ri, lamaz cxovre ba ze uzomod Seyva re bu li vio le ta Cerni a e va _ cnobi li moqan da kis Svili, ro melic avto ris TqmiT, `amq vey nad mxolod naTels, keTils, maRals Wvretda, radgan lite ra tu ra da xelov ne ba rea lur sinam d vi les iseTad miiC nevs, rogorc unda iyos sau ke Te so gage biT, mis pir vel ferwe rul sa Tu skulp tu rul nawar mo eb Si naTe li gone bi sa 195 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV da gake Til So bi le bu li sulis mqone adami an Ta Cvene bis udide si survi li gamos W vi vis~ (Misabishvili, 1981: 7). yove li ve zemoT q mu lis aRwe ris Semdeg ixs ne ba kvanZi _ qanda kebis (mindor ze wamo wo lil gojs inda u ri CabRau We bia klanWe biT) avto ris azri gasa ge bi xdeba, mwera li mas skulp to ris sityve biT gadmos cems: `gadam Ti e le bo, gavi ge mowo ne biT Sexved ri xarT Cems qanda ke bas, igi marT lac rom Cine bu li a! gavi ge isic, rom, rogorc mosa lod ne li iyo. ver Cawv diT avto ris Cana fiq ris siRr mes, vaJba tono krei cer, miwa ze ganr Tx mu li goWi Roro bis simbo lo a, Tqven xom namd vi li Rori xarT! sxva Sefa se bas ver mogcemT. inda u ri ki Tqveni gazu lu qe bu li colis simbo lo a... (Misabishvili, 1981: 11). yove li ve es Zali an efeqtu ria da mkiTxvel ze Zlie ri STabeW dile bis momx de ni. avto ri aq ar svams wertils, is nawar mo e bis da sasruls gadmos cems im Sedegs rac buneb ri vad unda mohyo lo da mtrisgan yove li ve amas: `polkov ni ki dau da raj da Turme vio las. quCa Si wauq ce via da Ceqme biT didxans ucemi a. am saRmer Te bel qals RviZli da naRv lis buSti aqvs sasik v di lod dazi a ne bu li... eqimeb ma Tqves, vio le ta Cerni a e va ganwi ru li a, ar gadar Ce ba o~ (Misabish vili, 1981: 11). omis Tema zea Seqm ni li kidev erTi moTxro ba `saCe mo tyvia~, sadac avto ri mkiTxvels sao ca ri naTe li sura Te biT uCve nebs, samSob lo saT vis gulan Te bu li mebr Zo le bis gancdebs, im wina aR mdegobebs, rac maT win eRobe baT, maT Semar Tebas _ rac ar unda dauj deT, Tundac sicocx lis fasad, Seas ru lon dava le ba, raTa ixs nan alya Si moqce u li Tana meb r Zo le bi. am moTxro bas Tan dakav Si re biT unda aRiniS nos, rom avto ri wi naswar amza debs mkiTxvels mosa lod ne li ubedu re bis aRsaq me lad. amis dastu ria erT -er Ti mebr Zo lis, aleqsis sizm ris gadmo ce ma (TiTqos misi avto ma tis lula dafS v ni li ZvlebiT iyo amoxer gi li). `Zvlis naxva sizmarSi cudad maqvs dacdilio~ _ ambobs igi. am sityve biT xdeba mkiTxve lis gone bis daZab va, igi grZnobs, rom raRac sabe dis we ro unda moxdes. misi ganwyo ba marT l de ba, aleqsi mego bars gada ar Cens, Tavad ki mtris tyvias ems x ver p la. am pata ra moTxro ba Si avto ris mier asaxu li faqte bi da mov lene bi imde nad dama je reb lad da logi ku rad aris gadmo ce mu li, rom mkiTxve li TviTm xil ve lis rolSi gamo dis yove li ve si, igi ab solu tu rad darw mu ne bu li a, rom yvela fe ri ise unda momx da ri yo, rogorc amas avto ri gvixa tavs da ara sxvana i rad. moTxrobaSi `msaxiobebi~ avtori agrZelebs misTvis yvelaze sa intereso Temaze _ meore msoflio omTan dakavSirebul movlenebsa 196 joni marRania da faqtebze mxatvrul xorcSesxmas. nawarmoebSi martivad, magram sainteresod da marTebulad aris motivirebuli yvela niuansi _ movlenebi, personaJTa qcevebi da rac mTavaria da yvelaze sain teresoa _ avtoris mier moTxrobaSi moulodnelobis mxatvruli xerxis gamoyeneba metad efeqturia da mkiTxvelze saocari zemoq medebis momxdeni. SesaZ le be lia nawar mo e bis aRm q mels nakle bad dama je reb lad moeC ve nos mwerlis mier naCve ne bi germa ne li oficris gulub r y vilo ba, araSor s m W v re te lo ba, magram aq unda gaviT va lis wi noT is momen ti, rom avto ris mizans ar warmo ad gens germa ne li oficri sa da saer Tod faSiz mis mesve ur Ta avkar gi a no bis Cvene ba, misi miza nia _ warmo a Ci nos qveya na ze uzomod Seyva re bul adami an Ta saxe e bi. avto ri mizans aRwevs, mkiTxve lis Tvalwin cocxl de ba gmiri qali ludmi la, profe si iT msaxi o bi, rome lic mzadaa samSob los Tavi sufle bas saku Ta ri sicocx le anacva los. mweral vl. misa biS vi lis moTxro be bis didi nawi lis saTa u ri, rogorc es zoga dad xdeba xolme, Zalzed metyve li a, igi imTa viT ve ganawyobs mkiTxvels asaxu lis aRsaq me lad, ase xdeba es nawar mo eb Sic `dava le bis miRe bam de~, rome lic aseve omis Tema zea Seqm ni li. aq moTxro bi lia imis Sesa xeb Tu ra gamoc da mouwyo parti zan Ta razmis meTa ur ma erT -erT mebr Zols, erovne biT qarT vels da ro gor darw munda igi, imaSi, rom swored mas da ara sxvas xele wifeba im saxi fa To dava le bis Sesru le ba, rome lic did risk Tan aris da kavSir be u li, magram aucile be li da saWi roa qveyni saT vis. moTxro ba Si didi siTbo Ti, mowi we bi Ta da siyva ru liT aris sa uba ri saqar T ve lo sa da qarT ve leb ze. razmis meTa u ri ver malavs Tavis keTil gan wyo bas parti za nis mSobli ur kuTxeze, saku Ta ri azris WeSma ri te bis gasam ya reb lad mohyavs cnobi li kompo zi to ris Cai kov s kis sityve bi: `borjo mi deda mi wa ze erT -er Ti umS ve ni e re si adgi li a, Cemi azriT, igi yvela ze RvTaeb ri vi da saucxoo adgi lia mTels msofli o Si~. avto ris azri savse biT naTe li a, igi xazs usvams imas, rom am lamaz da umS ve ni e res kuTxeSi yovel T vis ibade bod nen da dai ba de bian qveynis erT gu li gmire bi, romel Ta mTava ri sazru na via qveya na, misi dacva da misT vis Tavgan wir va. vl. misa biS vi lis ramde ni me moTxro bis analiz ma cxadyo, rom misi Semoq me de bis wyaro rea lu ri cxovre ba, yofi Ti faqte bi da movle ne bi a. moqme di gmire bi xalxis wia Ri dan Sobi li ubra lo ada mia ne bi arian, romel Ta mTava ri miza nia qveyni sad mi erT gu le ba da misT vis Tavda de ba. 197 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV lite ra tu ra: 1. Misabishvili V., Qandakeba, Sokhumi, 1981. 2. Lemonjava N., Qartuli enisa da mtserlobis sakitkhebi, Tbilisi, 2001. Joni Marghania ARTISTIC WORLD OF VLADIMER MISABISHVILI’S STORIES Summary Vladimir Misabishvili, a famous journalist successfully worked in Georgian writings. He has created a series of notable stories and poems, which have been popular among the readers and received their approval and recognition. The paper aims to review V. Misabishvili’s some stories where the author perceives the truth and evaluates things, events, and situations. The artistic world created by the writer is full of life facts and events. His main task is to show read- ers the most interesting situations of his heroes’ life. Majority of V. Misabishvili’s stories is dedicated to World War II. He was an active participant in the fight against fascism. He witnessed horrors of war where millions of people have given lives on protection of the homeland. In most part of his stories the writer expresses his feelings and emotions, the impressions of the war. He shows the readers his contemporary heroes, their heroic character full of a sincere love and friendship as well as creating a number of impressive situations and fighting episodes. The analysis of V. Misabishvili’s several stories made it clear that the source of his creations is a real life and true facts as well. Acting heroes are simple people whose main purpose is self-sacrifice and devotion to the country. 198 eka vardoSvili qarTveli qalis saxe germanul dramatul xelovnebaSi andreas grifiusi germaneli Semoqmedia, romelmac 1647 dawera, xolo 1657 wels gamosca xuTmoqmedebiani tragedia `qeTevan qarT veli anu gautexeli simtkice~ (“Catharina Von Georgien Oder Bewehrete Beständigkeit”). poema asaxavs iranis winaaRmdeg saqarTvelos mraval saukunovani brZolis erT epizods. miuxedavad imisa, rom andreas grifiusi barokos xanis udidesi Semoqmedia da misi poezia da dra maturgia miCneulia germanuli barokos mwvervalad, misi tragedia `qeTevan qarTveli anu gautexeli simtkice~ sakmaod Warbad Seicavs realistur tendenciebs, eyrdnoba realur istoriul faqtebs da amavdroulad gamoxatavs qarTveli da germaneli xalxis intere sebs. Tavis komediebsa da tragediebSi a. grifiusi xatavda germa niis yofis amsaxvel suraTebs. Temis damuSavebiT a. grifiusi exeba politikur da patriotul sakiTxebs, romlis aqtualobas karna xobda Tavisi qveynis sinamdvile. nawarmoebs aqvs moraluri da eTi kuri mxareebic. andreas grifiusis tragedia qarTveli sazogado ebisaTvis cnobili gaxda 1904 wels, rodesac `cnobis furcelSi~ daibeWda iv. ramiSvilis korespondencia `qarTveli qali germanul dramatul xelovnebaSi~. statiaSi avtori msjelobda aRniSnul pi esaze da SeniSvnebSi ganmartavda misi avtoris vinaobas. germa ne li avto ri mTeli sicxadiT asaxavs Sah-a ba sis karze Seqm nil poli ti kur viTa re bas. qmnis qeTe va nis, rogorc qveynis inte re se bi sa da sarw mu no e bis damc ve li, gau te xe li sulis mqone dedof lis srulyo fil saxes, rome lic 1624 wels Sahis brZane biT sasti kad awames da sikv di liT dasa jes. a. grifi u sis trage dia mniSv ne lo va nia im mxrivac, rom masSi Cans evro pel Ta dain te re se ba saqar T ve los sakiTxiT, radgan sa qarT ve lo wina aR m de go bas uwevda mahma di a nur samya ros, rome lic evro pis T vi sac safr Txes warmo ad gen da. pie sa Si aseve naCve ne bia osma le Ti sa da sparse Tis poli ti ku ri gaaq ti u re ba da ruse Tis da moki de bule ba aRniS nu li qveyne bi sad mi. saqar T ve lo Si fexis mo ki de bis SemTx ve va Si osma le Ti preten zias ganacxa deb da Crdilo- kav ka si a sa da samx reT ruse Tis miweb ze. Turqe Tis sawi na aR m de god Sah-a ba sis karze Cadis ruse Tis elCi da raki sasax le Si igi gaxda qeTe van dedof lis Seviw ro e bi sa da dev nis mowme, ruse Tis mefis saxe liT moiTxo va misi ganTa vi suf le ba. 199 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV samec ni e ro lite ra tu ra Si grifi u si saT vis xelmi saw v do mi ram deni me wyaro saxel de ba, romel Ta safuZ vel zec man dawe ra Tavi si trage di a. pirve li a, domi nikeli be ris grigo ri orsi nos mier 1626 wels romSi ward ge ni li moxse ne ba saqar T ve lo Si qristi a nu li sarw mu no e bis mdgoma re o bis Sesa xeb. aRsa niS na via isic, rom 1624 wels, rode sac qeTe van dedo fa li sikv di liT dasa jes, igi spar seTSi imyo fe bo da. meo re a, avgus ti ne li moZRv ris amb ro zi os mox sene ba imis Tao ba ze, Tu 1628 wels misi meTa u ro biT ispa ha ni dan avgus ti nel mona zon Ta monas t ri dan saqar T ve lo Si q. gorSi ro gor gadmo as ve nes dedof lis neSti. mesa me wyarod saxel de ba ita lie li aRmo sav leT m cod nis patri cis piet ro dela vales Srome bi: `infor ma cia saqar T ve los Sesa xeb~ (`Information della Georgia~) da `rela ci o ne bi sparse Tis mefis abasis saxel m wi fos mdgoma re o bis Sesa xeb~ (`Relatione della condizione di Abbas, Re de Persia~). meoTxe wyarod miCne u lia grifi u sis nacno bo ba im adami a neb Tan, romle bic sxvadas x va dros dakav Si re bul ni iyv nen qeTe van Tan. eseni arian Tina Tin di ciba piet ro dela vales meuR le, sparseT Si ZaliT Camoy va ni li erT -er Ti qarT ve li Tava dis umS ve ni e re si asu li, romel sac urTi er To ba hqonda qeTe van dedo fal Tan da iezu iti beri aTana si us kirxe ri. mexu Te wyaro `rome lic SeiZ le bo da gamo e ye ne bi na grifi uss, esaa cnobi li holS ta i ne li gener li sa da diplo ma tis adam olea ri u sis mogza u ro bis aRwe ri lo ba ni. olea riu sis Sromi dan grifi uss auTvi se bia Sah-a ba sis karis wese bi, ag reTve zogi zne-C ve u le ba. olea ri u sis Sromi dan yofi la aRebu li grifi u sis trage di a Si zai nel xa nis isto ri u li saxe, rome lic vales Tan saer Tod araa moxse ni e bu li. olea ri u si da naa aRebu li agreT ve mou ra vis mier yizil baS Ta Tavka ce bis daxoc vis amba vi, kerZod, yarCi xa- xa nis mkvlelo ba~ (Revishvili, 1977:111). mniSv ne lo va nia is faqti, rom garda isto ri u li wyaro e bi sa sa isto rio poe ma Ta rigi qarTul lite ra tu ra Si iwyeba qeTe van de doflis wame biT. pirve li mwera li, romel sac gau leq savs Cveni is tori is es epizo di aris TviT Rvawl mo si li dedof lis Svili, mefe Tei mu raz pirve li. mis Sromas ewode ba: `wigni da wame ba qeTe van dedof li sa~. wina sity va o ba Si avto ri mimar Tavs RmerTs, RvTis mSo bels, wminda nebs da sTxovs maT, miscen Zala, raTa Rirse u lad aRwe ros dedis Rvawli da mowa me ob ri vi sikv di li. Txzule ba Si isto ri ul sinam d vi les Tan erTad moxde ni la daa gadmo ce mu li suli e ri ganc da, rogorc tanju li dedof li sa, ise TviT avto ris, Tei mu ra zi sa. Tei mu ra zis msgavsad qeTe va nis wame ba aRuwe ri aT mRvdelmo na zon kozmans, rome lic lekeb ma mokles 1735 wels, 200 eka vardoSvili aseve dimit ri bagra ti ons, rome lic cxovrob da da moRva we ob da meTv ra me te sau ku nis miwu rul sa da mecxra me te sau ku nis pirvel meoTxed Si. aRsa niS na via isic, rom al. yazbe gis kalams ekuTv nis pirve li qarTu li isto ri u li drama, `wame ba qeTe van dedof li sa~, rome lic 1883 wels Jurnal `ive ri a Si~ dai beW da. rode sac qeTe van dedof lis mowa me ob ri vi sikv di lis Sesa xeb vsaub robT, CvenT vis sayu radRe bo unda iyos aseve ucxoe li mec nie ris r. gelbe ki a nis naSro mi, `namd vi li cnobe bi saqar T ve los dedof lis qeTe va nis mowa me ob ri vi sikv di lis Sesa xeb~, sadac av tori aRniS navs: `sxvadas x va mizez Ta Soris, romel sac unda ga nepi ro be bi na Sah-a ba sis gadawy ve ti le ba _ ewame bi na udana Sa u lo dedo fa li, or Ziri Tad mizezs miu Ti Te ben. pirve li isaa, rom Tu rome li me qristi a ni tyve qristes sjuls mia to vebs da mahma di an Ta kanons mii Rebs, mahma di a ne bi (sparse le bi iqne bi an Tu Turqe bi) samSob lo Si dabru ne bis nebas aRar aZle ven: aRar aZle ven ufle bas daub run d nen mSobleb sa da axlob lebs, aseTi nebar T vis mice ma di di codvaa da maTi kano niT akr Za lu li a. meo re mize zi is gaxlavT, rom am dedof lis vaJi, Tei mu raz mefe, mas Semdeg rac same fo wa arT ves da iqidan gandev nes, Turqeb Tan wavi da da ramde ni me weli maTTan dayo; Semdeg mosko vis mTavar dimit ris mia Su ra~ (Gulbeki ani, 1987:35). rogorc vnaxeT, saqar T ve los hero i ku li warsu lis gacocx le ba dama xa si a Te be lia qarT vel da evro pel mweral Ta da mecni er TaTvis. a. grifi u sis trage dia iTarg m na da gamo i ca qarTul enaze 1975 wels. isto ri u li wyaro e bis Tanax mad, qeTe van dedo fa li iyo mefe aleqsan d re II Svilis mefe davi Tis meuR le da deda Tei mu raz pirve li sa. dais mis kiTxva: ra Tvise be bis safuZ vel ze gaxda qeTe van dedo fali esoden mniSv ne lo va ni msoflio lite ra tu ri saT vis? esaa is suli e ri fase u lo be bi, rac mas axasi a Teb da da ris sa fuZvel zec qarTul ma ekle si am igi wminda nad Seracxa. trage di is Sesa val Si a. grifi u si mimar Tavs Tavis mkiTxvels: `didad mowya leo mkiTxve lo! Cemi marad da mudam sasur ve li qeTe va ni amie ri dan Cveni samSob los scena ze gamo dis da Tavi si sxeu li Ta Tu tanj viT TvalnaT liv gvaZlevs gamo uT q me li simt ki cis am droi saT vis gau go nar maga liTs. sparse Tis gvirg vi ni, Zleva mo si li da saxel ganT q mu li mefis pativ - di de ba, siymaw vi lis sia me ni, eniT uTq me li Sveba- l xe na, Tavi suf le bis dafa se ba sicocx le ze metad, saSi ne li wame ba, parTel Ta Zala do ba, TviTon sikv dil ze ufro zardam ce mi saxe sikv di li sa, dedo fal Tan erTad tyveqm nil qalTa cremle bi, 201 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Tavi si dakar gu li taxtis, Svili sa da same fos dardi, - yvela es gansac de li erTad Sebmia am naz mandi lo sans, da bolos mis ferx TiT dace mu lan Zleul ni. mokled: Rirse ba, sikv di li da siyva ru li ibr Z vi an mis sulSi da gulSi im saun ji saT vis, rasac Sei cavs siyva ru li, oRond ara miwi e ri da warma va li, aramed wminda- ma ra diu li. sikv di li ki mxsnelad da nuge Sad evli ne ba. ase Zlie ria am usustes arse ba Si is Zala, romlis dide bi saT vis es dedo fa li sakuTar sisxlsa Rvris. me ki mxolod imas vwuxvar, rom Cemi ka lami uZlu ria Rirse u lad asaxos aseTi didi moTmi ne ba, aseTi sa gulda gu lo simt ki ce, aseTi mza gadawy ve ti le ba, rom warma vals mara di u li amjo bi nos~. and re as grifi u si 1647 weli~ (Grifiusi, 1975:58). trage dia iwyeba mzis amosv li sas da srulde ba dRis miwu ruls. moqme de bis adgi lia Sira zi. pie sa asaxavs dedof lis sicocx lis ukanas k nel dRes. Sah-a ba si qeTe va nis gan iTxovda or rai mes: sarw muno e bis Secv las da sTxovda mas colo bas. trage di a Si dedo fa li warmo Ce ni lia rogorc utexi suli sa da mtkice nebis yo fis pirov neba. urye vi rwmena, samSob los siyva ru li da ojaxis erT gu le ba mateb da mas Zalas, gaeZ lo yovel g va ri gasa Wi ri saT vis. igia saxe idea, romlis saxis mety ve le ba dama xa si a Te be lia ro gorc qarTuli, ise evro pu li lite ra tu ri saT vis. trage dia eZRv neba qeTe va nis suli er fase u lo bebs. qeTe va nis saxe, rogorc sar wmu no e bi saT vis Tavda de bu li dedof lis para dig mad iqca qarTul lite ra tu ra Si. igi `wminda mxedar~ qalTa tria dis mesa me wevria wminda nino sa da Tamar dedof lis gverdiT. mniSv ne lo va nia qeTe va nis pirve li gamos v la, sadac igi ambobs soflis samdu ravs, yveba Tavi si ojaxis trage di as, rome lic ga dajaW vu lia qveynis isto ri as Tan da SesTxovs uzena ess, rome lic samya ros alagebs da icavs, awesri gebs casa da miwas, tanj viT dam Zime bu li da gvemiT damci re bu li misi sxeu li male gana So ros suls. mivmar ToT grifiuss: `uze na e so, vinc samya ros alagebs, icavs, Tvlis yofnis dReebs, awesri gebs casa da miwas, rodem de vevno? ros meRir sos simS vi de sruli? rodis inebeb, am Cems sxeuls ganSor des suli? vai, sawuT rov! Tavo, tanj viT damZi me bu lo! aTasi vnebiT, xang r Z liv gvemiT damci re bu lo! raRa mina xavs bavS vo bi dan vara mis meti? 202 eka vardoSvili axal-a xal Ta wylulTa garda ras maZlevs bedi? ...... Tqven, visac kidev gwamT dide ba TqvenTa mefe Ta, naxeT, ra miyo mrude bedma! laxv rad mekve Ta~ (Grifiusi, 1975: 73). mniSv ne lo va ni a, aseve Sah-a ba si sa da qeTe va nis sau ba ri, miu xe davad Sahis didi mcdelo bi sa igi mainc qristi a nu li rwmeni sa da adaT- we se bis erT gu li rCeba. Sah-a bas ma warmo ud ge ne li sisas ti kiT awama aTi weli tyveo ba Si myofi dedo fa li da 1624 wels sikv di liT dasa ja igi. qeTe va nis wame bas esw re bod nen Sahis karze myofi sxvadas x va qveynis elCe bi da ucxoe li misi o ne re bi. Ziri Ta dad maTi saSu a le biT gavr cel da cnoba evro pis qveyneb Si qeTe va nis mowa me ob ri vi sikv di lis Sesa xeb. aRsa niS na vi a, rom Sah-a ba si qeTe va nis wina Se Tavs yovel T vis damar cxe bu lad Tvlida. trage dia srulde ba misi sina nu liT savse sityve biT: `ase a, ase, dedo fa lo! amg li je dafna! dalax v re spars Ta dide ba da daam xe dabla! mZle muStiT mospe zviad Sahis uxeSi Zala, ramac miqcia saqar T ve lo gode bis Walad. sakur Txe vel ze, sadac TviTon gaqci es ferf lad, mec amiyva ne, Seni wyromis gamxa de msxverp lad! magram sasjels ki ufro mwares gaveq ce versad: marad miyvar de, Tayvans gcemde wame bul mtersa~ (Grifiusi, 1975 :214). and re as grifi us ma Tavis traged i a Si Seqm na srulyo fi li saxe qveyni sa da sarw mu no e bi saT vis Tavda de bu li qarT ve li dedof lis, romel mac gauZ lo sau ku ne e bis gamoc das da Tavi si adgi li daim k vidra msoflio lite ra tu ra Si. literatura: 1. Grifiusi A., Qetevan qartveli anu gautekheli simtkice, Tbilisi, 1975. 2. Gulbekiani R., Namdvili cnobebi saqartvelos dedoflis Qetevanis motsameo- brivi sikvdilis shesakheb, Tbilisi, 1987. 3. Revishvili S., Germanul-qartuli etiudebi, Tbilisi, 1976. 203 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Eka Vardoshvili GEORGIAN WOMAN’S FACE IN GERMAN DRAMATIC ART Summary Andreas Gryphiusis a German dramatist who in 1647 wrote a five act play “Katharina von Georgien” and published it in 1657. The play described one episode of many-centuries’ struggle of Georgia against Iran. While revising the topic Gryphius touched political and patriotic issues the actuality of which dictated him the reality of his country. The play has moral and ethic sides as well. Andreas Gryphius’s play became known to Georgian society in 1904 when Iv. Ramishvili’s correspondence “Georgian woman in German dramatic art” was printed in “Tsnobis Purtseli” (News Letter). In the article the author discussed about the mentioned play and in his notes he explained the author’s identity. Andreas Gryphius clearly described political situation at Shah-Abbas’s court, created Katharina’s perfect face, the Queen with unbroken spirit, as of a defender of the country’s interests and religion, who in 1624 was severely tortured by order of Shah Abbas. In the play Gryphius’s deep interest towards Georgia is shown.A. Gryphius’s play was published in Georgian in 1975. Animation of Georgia’s heroic past is characteristic for many Georgian as well as European writers. 204 medea kvaracxe lia `sabav S vo lite ra tu ra yvela ze sarw mu no eb ri vi dargi a~ es sityve bi poet mari am wikla urs ekuTv nis da ucilob lad mi viCni eT, srulad Semog Ta va zoT misi mosaz re ba am sakiTx ze: `erTi fantas ti ku ri rame aRmo va Ci ne: sabav S vo lite ra tu ra sae ro lite ratu ris yvela ze sarw mu no eb ri vi dargi a, radgan igi dau eW ve be li rwmenis mata re be lia sike Ti sa da boro te bis mara di ul brZola Si sike Tis ucilo be li gamar j ve bi sa. sadi do lite ra tu ra ki sul eW vebs ebr Z vis da verc amarcxebs, ase pirw min dad, rogorc sabav S vo, anu adami a ni sabav S vo wiaR Si sul gamar j ve bu lia fsiqo lo gi u ra dac, suli e ra dac fantas ti ku rad grZnobs Tavs~ (Tsiklauri, 2011). marT lac Sesa niS na vi gansazR v re ba a, risi dastu ri caa mTeli qarTu li (da ara marto qarTu li) sabav S vo lite ra tu ra, sabav S vo folk lo ri, romlis fesve bi sau ku ne e bis wiaR Si ikarge ba, misi mdida ri tradi ci e bi ki myari safuZ ve li gaxda Semde gi Tao be bis Semoq med TaT vis, rome li Tac axali saxe e biT, axali fere biT, axali Strixe biT gaam did res wina par Ta memk vid re o ba (Kiladze, 2007). Cvens qveya nas yvela droSi mravlad hyavda sabav S vo lite ra turis ubadlo osta te bi. cnobi li faqti a, rom qarTu li sityvis klasi ko se bic uyuradRe bod ar toveb d nen am sferos da qmnidnen saymaw vi lo nawar mo e bebs, radgan mozar di Tao bis swori aRz r da, ganaT le ba da formi re ba umTav res saqvey no saqmed miaC n daT. maTze sau ba ri am pata ra stati a Si Sors wagviy van da. Tana med ro ve qarT vel sabav S vo avtor Ta Soris ki erT -er Ti gamor Ce u lia po eti mari am wikla u ri. igi mraval m x ri vi Semoq me di a: poe ti, mTar gm ne li, publi cis ti, redaq to ri, saav to ro gada ce me bis wamy va ni (radio `ive ri a~) sabav S vo lite ra tu ris ganvi Ta re bis fondis _ `libos~ erT -er Ti dama ar se be li, ast rid lind g re nis saer Ta So riso premi is nomi nan ti. misi umS ve ni e re si sabav S vo Tu sadi do leqse bis krebu le bi dajil do e bu lia sxvadas x va lite ra tu ru li konkur sis premi e biT. misi nawar mo e be bi Targ m ni lia msofli os mraval enaze. rogorc Tavad poe ti aRniS navs, misi pirve li gamo ce ma sabav S vo leqse bis krebu li iyo: `ise moxda, rom pirve li TviTga mo ce ma sabav S vo krebu li gava ke Te. mere uceb davbeW de yvela fe ri, gamo vida sadi do da sabav S vo krebu le bi: es yvela fe ri ise uceb da qa riSxa li viT damaty da Tavs~ (Ramdenime kitkhva Mariam Tsiklaurs). 205 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV sabav S vo lite ra tu riT dain te re se bas igi bedis we rad miCnevs `bedis we riT Zali an aqti u ri urTi er To ba Camo mi ya lib da lite ra turis am darg Tan~. am mosaz re ba Si mxolod nawi lob riv SeiZ le ba dave Tan x moT mis avtors, radgan, Cveni azriT, Rire bu li sabav S vo nawar mo e be bis Se saqm ne lad aucile be lia niWi da unari, Rrmad Casw v des mozar dis fsiqi kas, mis sufTa, faqiz suli er samya ros, hqondes grZnobeb Si gark ve vis gansa kuT re bu li alRo, rac poet mac Sesa niS na vad uwyis: `bavS ve bis T vis weram erT rame Si damar w mu na. mas marT lac sWirde ba buneb ri vi da gansa kuT re bu li unaris floba, rome lic an gaqvs, an ara. da Tuki gaqvs es unari, unda CaeWido mas da arafer Si gac valo~ (Kiladze, 2007:12). diax _ `ara fer Si gacva lo!~ es mowo de baa, aseTi unariT da jildo e bul Ta mimarT, Tavad ki mtkiced mihy ve ba am gzas da axal- axal umS ve ni e res krebu lebs uZRv nis pata rebs. rogorc weri lis dasawyis Si aRv niS neT, mari am wikla u ri mra valm x ri vi Semoq me di a. sabav S vo nawar mo e be bis para le lu rad, igi poe zi is moyva ru lT sadi do krebu le bi Tac anebiv rebs, romleb mac karga xania moi po ves kriti kos Ta da sazo ga do e bis aRia re ba. amave dros aqti u rad CarTu lia sazo ga do eb riv saqmi a no ba Si. erTi adami a nis inte res Ta aseTi farTo speqt ri mavans SeiZ le ba tvirTad moeC ve nos, oRond ara mari am wikla urs, radgan: `Cems dRe-Ra me Si rom 31 saa Ti a, es yvelam icis, weli wad Si rom xuTi droa _ esec, da sul rom dama tebiT or xels vnatrob, egec ara feri, zogjer imas vfiqrob, ratom erTi sami ar var, ramden saqmes movas w reb di- meT qi~. rea lu ri drois CarCo e bi ecota ve ba uamrav saqmes SeWi de bul Semoq meds. winam de ba re weril Si Seve xe biT mari am wikla u ris sabav S vo leqsebs. gamo ce mu lia ramde ni me krebu li: `dedis namRe ri leqsi~ (1997), `wiko- miko~ (2000), `brandi- b ren di~ (2011), `WiWi ta~ (2011), `zRapar iyo~ (2011), `qarTu li anba ni~ (2013), `saa li lo~ (2005). SevCer de biT nani ne bis cikl ze, romel Sic Torme ti iavna na Se dis. maTSi ikve Te ba uZve le si xalxu ri iavna ne bis moti ve bi _ mra val keTi li survil Tan erTad, umTav re si moti ve bia modg mis gam ravle ba, samSob los msaxu re ba da dacva. amona ri di erT -er Ti xalxu ri iavna na dan: `... mama mixv da, roca Tqvao, nani- na ni na Sengan gmiri gamo va o, nani- na ni na... ... ar Sela xo gmiris fasi, nani- na ni na, da mters zurgi araso des, nani- na ni na, 206 medea kvaracxe lia ar uCve no, es gaxsov des, nani- na ni na~. mari am wikla u ri: `cxra vaJas gaCu qebs ufali, puriT agivsebs saxl sa o, marj ve nas gagi la ma zebs, mters dau ye neb Tvalsa o, sul siyva ru liT gadix di, mSoblis uwonel valso~. mraval omga dax dil saqar T ve lo Si, romel sac mteri, momx du ri ar eleo da, akvan Si mwoli a re yrmas mamu lis siyva rul ze, gmiro ba ze umRe rod nen dede bi da ufals mis Rirse ul vaJka cad gazr das sTxovd nen: `nana, nana, nana sa, gazr da, gaxa re ba sa... ... Semo gak rav qamar sa, zed dagki deb xanjal sa~. swored am sulis k ve Te bis gamo Za xi li a, mari am wikla u ri stri qone bi: `Zils ki ara, daim S ve nebs male fars da xmalsao dai bo xebs devka cu rad moRu Ru ne xmasa o... ... yvela avs da borots erTad dascems SiSis zarsa o~. (Tsiklauri, 2009) warmar Tul saqar T ve lo Si mze umTav re si RvTae ba iyo, romel sac saga lob lebs uZRv nid nen. saqme isaa, rom Zis daba de bac RvTa ebriv rang Si iyo ayva ni li da TiTqos mzes utolde bo da: `mzev, Sina da, mzev, gareTa, mzev, Sin Semo di o, Cven vaJi dagv ba de bi a, mzev Sin Semo di o~. mari am wikla u ri: `nana, Cemo pawa wi nav, Cemo mzev da naTe lo, dedis gulSi uflis xeliT anTe bu lo sanTe lo~. (Tsiklauri, 2009) erTob mdidari da mravalferovania mariam wiklauris sabavSvo krebulebis personaJTa samyaro. vis ar SexvdebiT aq _ zRaprebis gmirebi, devebi, cxovelebi, frinvelebi, mwerebi, mcenareebi, mTebi, zRva, mdinareebi da nakadulebi, onavari gogo-biWebi, keTili bebi ebi da kidev vin moTvlis... aq aris rogorc Zalian patarebisTvis, 207 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV aseve mozrdilTaTvis Sesaferisi leqsebi da, rac yvelaze mTavaria, bavSvis cnobierebaze morgebuli, mxatvrulad galeqsili am patar -patara saxaliso ambebidan isini Zaladautaneblad swavloben sam Soblosa da moyvasis siyvaruls, Sromisa da garjis fass, sikeTes da yvela im sulier faseulobas, rac adamians pirovnebad ayalibebs. erT -erT leqs Si, romel sac `RvTis sagz lo ba~ hqvia, bavS vi Za los vaSls sTxovs, sanacvlod ki jer zaqs da taxs hpirdeba, Zalo ki gai Za xis, ar kmara o. mere Tanda Tan umatebs mamals, yveliT savse xalams, fardags, xalaTs, sarkes, CiT-at lass. Zalo mainc uarze a. pa tara mkiTxve li, albaT, ifiqrebs, es ra gau maZR ro ba sWirs Zalo so, magram ara, leqsis final Si vaSlis mTxovne li swor pasuxs miag nebs da am gziT misi kbila mkiTxve lic xvdeba, rom sixar be arafer Sua Si a. `_ madls mogiZRvni _ RvTis sagzals, dila o biT _ tkbil salams! _ maS, Sebr Zan di baRSi, ar darCe bi valSi~, _ miugebs Zalo, misi pasuxidan ki Cans, rom madls, keTil salams, saerTod, sikeTes veraviTari simdidre ver gadawonis. ager patara Rele, romelic did tirifebs fesvebs da xelebs hbans, boColebs da kravebs ki peSviT asmevs wyals; lokokinas kakali daubertyavs, Cur Cxelebis amosavlebad emzadeba, mere yvelas uwilados: erTma yoCaR ma Citma-Cioram ki saarako gmiroba Caidina, roca ugunurma Tevzma zRva gadaylapa. man niskartiT moaTria wyliT gavsebuli Rrubeli, mere TqeSad Camowura, zRvas daclili peSvi amouvso da lifsitebi gadaarCina; mrecxavi ki yvelas exmareba da recxvaSi aTen-aRamebs. mravla daa iseTi leqse bic, sadac gaki lu lia zarma ci, uqna ra Rormu ce la. uvici, Tavker Za, crupen te la, traba xa perso na Je bi. maTi kiTx visas bavS vis cnobi e re ba Si ileqe ba kargi sa da avis garCe vis unari, sxvadas x va aucile be li Cveva, maga li Tad, radgan kanfe ti uyvars, Zilis win kbilebs Tu ar gai xe xavs, kiWi ast kiv de ba da mere vai- vi Si ver uSve lis. sibin Zu ris mteri gamr je cocxi ki sul Sroma Si a, magram Cveni marj ve nis gare Se, aba, ras gaxde bo da: `es qveya na saxli viT unda davak ri a loT, rom lamaz ma bavS veb ma nagav Si ar iaroT! cocxi ase mReris, movaS ve loT xeli!~ calke gamosayofia weliwadis droze, mnaTobebze dawerili leq 208 medea kvaracxe lia sebi, aseve, krebuli `qarTuli anbani~, saidanac bavSvi codnasac iZens, swavlobs da Tan es bunebrivad, Zaldautaneblad xdeba. reli giur Temebze (saalilo, saSobao), sagmiro da patriotuli leqsebi ufro mozrdili asakis bavSvebisTvisaa: `Seiyvare moyvasi~, `vedre ba~, `deduli da mamuli~, `maswavlebeli~, `rixiT saTqmeli~ da a. S. `gasaferadebeli leqsebi~ (2010) erTgvari saxaliso savarjiSoa patarebisTvis, romelTac gamotovebuli sityvebi unda Seavson: `TeTria gviri la, ... a ca, ... yaya Co, pepe las frTa. ...a bala xi, ... mze Citu na ugalobs sicocx lis fers. mariam wiklauris rogor Tematurad, aseve personaJTa mxriv metad mdidari da mravalferovani sabavSvo nawarmoebebis gacnobis Semdeg marTebulad SegviZlia davaskvnaT, maTi mizani, arsi erTia: `Tama Sob Tu Sromob, daix so me, kargo didze didi saqmea _ kacad gai zar da o!~ amde nad, poe ti agr Ze lebs qarTu li sabav S vo poe zi is umdid res tradi ci ebs da axali, fere biT amdid rebs mas. misi fraze bi moq nili a; leqsi ka mdida ri; ritmi _ cocxali, melo di u ri; poe tu ri saxe e bi _ maRal m xat v ru li. sabavSvo wignebisTvis leqsebze ara sanakleb Rirebulia maTi ilustraciebi, radgan maTi meSveobiT erTiorad izrdeba bavSvis aRqmis unari. mariam wiklauris sabavSvo krebulebi am kuTxiTac ga moirCeva. magaliTad, krebuli `brandi-brundi~ gaformebulia mxat var dali muxaZis umSvenieresi feradi ilustraciebiT, romlebSic iSviaTi sizustiTaa naCvenebi personaJTa xasiaTi Tu ganwyoba. dabolos, minda davasrulo erT-erT krebulze wamZRvarebuli (Tavad avtoris) sityvebiT: `ramdeni kibe unda gadaaba erTmaneTze, rom cas miswvde da varskvlavebi dakrifo? bevri, Zalian bevri... albaT, imdeni, ramdeni yvavilic xarobs, ramdeni Citic stvens, ram deni wyaroc moCuxCuxebs da ramdeni bavSvic cxovrobs qveynad. am leqsebs vuZRv ni maT, vinc camde ver miaR wi a, magram kibe ze jiu tad adis da adis... kala Ta sac xels ar uSvebs, rom vars k v la vebiT aavsos da Tavis usayvar les adami a nebs Camo u ta nos deda mi waze~ (Tsiklauri, 2009). 209 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV mari am wikla u ris sabav S vo leqse bi marT lac rom caze dak refi li vars k v la ve bi a, romel Tac pirTam de gavse bu li kala Ti dan uSurve lad uZRv nis usayvar les pata rebs. lite ra tu ra: 1. Jalashvili m., “Poezia _ samyaros sizmris axsna” _ Dedis namgheri leqsi (sabavshvo tsigni) 1997. 2. Kiladze G., Interviuebi Jurnalistebtan. Mariam Tsiklauri blitfo bechdviti gamomcemloba “Taobebi”, 2007 . 3. Tsiklauri M., Gasaferadebeli leqsebi, Tbilisi, 1997. 4. Tsiklauri M.., Brandi_brundi, Tbilisi, 2005. 5. Tsiklauri M., Tsiko_miko, Tbilisi, 2000. 6. Tsiklauri M., Naninebi, 2009. 7. Tsiklauri M., Zghapar iyo, Tbilisi, 2011. 8. Tsiklauri M., Chichita, Tbilisi, 2011. 9. Tsiklauri M., Qartuli anbani, Tbilisi, 2011. 10. Tsiklauri Mariam, “Sabavshvo literaturis bedi” http://mastsavlebeli.ge/in- dex1.php?action=news&npid=2932 11. http://libofund.blogspot.com/2010/01/blog-post_2072.html 12. lib.ge./books/2587 Medea Kvaratskhelia “CHILDREN’S LITERATURE IS THE MOST RELIABLE SOURCE” Summary Georgia belongs to a small group of countries having rich folklore and the oldest poetry tradition. Children’s literature contains multiple genres and passes from generation to generation. It is the most reliable source of secular literature, because it is the unreliable belief in the eternal battle of good and evil. The paper describes Mariam Tsiklauri’s poetry, who is one of the most im- portant representatives of modern Georgian poetry for children. Her literary heri- tage is very interesting _ she uses samples of Georgian folklore, phrases from Georgian literature. The children’s poems of Mariam Tsiklauri are shimmering stars picked up lovingly in the sky and sent to lovely children. We have studied Mariam Tsiklauri’s poems and compared them with the verses of other Georgian authors. 210 Зоя Адамия ПЕРЕВОДЫ ПРОИЗВЕДЕНИЙ ПУШКИНА НА ГРУЗИНСКИЙ ЯЗЫК Из истории литературы знаем немало примеров, когда признание и сла- ва приходили к гениям в самом начале творческого пути. Пушкин тоже не мог пожаловаться на невнимательность к нему Сла- вы. Его называли «солнцем русской поэзии», его сочинения были названы «Энциклопедией русской жизни», его имя было отожествлено с понятия- ми Свободы, Гения, Славы; его боялись те, кто никого не боялся, а цари и всесильные жандармские были вынуждены считаться с ним и говорить обходительно. Почитателей таланта поэта его бессмертная поэзия пленяла своим гуманным содержанием и изяществом формы, ненавистников и за- вистников же страшило его всенародное признание, что тоже способствова- ло, правда, очень своеобразно популярности поэта «по всей Руси великой» задолго до появления переводов его произведений на другие языки. Грузинская общественность стала интересоваться русским поэтом и его творчеством и переводить его стихи на грузинский язык. Пушкина встречала и чествовала Тифлисская элитарная интеллигенция и аристократия. Прием в Ортачальских садах был подчеркнуто радостен, и вызывающе приветлив, что доставило немало хлопот секретным сыщикам и жандармам. Многие из участников приема о русском поэте знали только понаслышке. Однако общий настрой встречи ясно отражал антиимперские настроения всех слоев и сословий общества. Так неотвратимо входил Пуш- кин в дух и душу Грузии. Поэтому трагическая гибель великого русского поэта в Грузии была воспринята как утрата очень близкого человека, чьи добрые мысли и художественные образы помогали жить и сохранять свое человеческое достоинство. Такие нравственные и психологические предпосылки подготовили и предопределили непрерывающийся до сих пор плодотворный процесс пе- ревода на грузинский язык мелких и крупных произведений великого рус- ского писателя. Александра Пушкина стали переводить на грузинский язык в конце 20-х годов XIX века. Первые переводы читались в литературных салонах и распространялись в рукописях. Переводили многие и, естественно, одни переводы были сильнее, другие _ слабее. Но важно было то, что грузин, посвятивших всего себя служению своей обездоленной Отчизне, тянуло к русскому поэту, который давал «инородцам» нечто такое, что противоречи- ло официальной имперской политике. 211 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Пушкина переводили гранды грузинского поэтического слова _ Алек- сандр Чавчавадзе, Григол Орбелиани, Николоз Бараташвили, Илья Чавча- вадзе и др. Они, воспитанные на великих традициях пятнадцативековой грузинской поэзии, безошибочным чутьем и вкусом увидели в молодом Пушкине дар, достойный почитания, прославления и подражания. Переводы нередко повторяют судьбы оригиналов, т.е. создаются, одна- ко их обнародование задерживается по совсем не литературным причинам. Так случилось, например, со стихотворением «Анчар». Оно 4 года пролежа- ло в столе цензуры и увидело свет только после того, как слово «царь» было заменено словом «князь». И именно стихотворение привлекло внимание А. Чавчавадзе. Рассказ о смелом, беспощадном разоблачении преступлений сильных мира сего был понят как резкий протест против деспотизма, и цен- зуры, естественно, наложили лапу. Что-то в этом же духе произошло и с грузинским переводом «Анчара», выполненного Александром Чавчавадзе. В чем дело? Анчар источник зла и им распоряжается всесильный злодей. Стихотворение написано вскоре поле жестокой расправы над декабриста- ми и, естественно, эмоции были еще очень свежи как в обществе, так и в цензуре. Ко времени же перевода этого стихотворения на грузинский язык в Грузии до предела были накалены отношения в связи с провалом анти- русского заговора 1832 года. Символика зла и злодеяний одинаково была воспринята как из подлинника, так и в переводе, тем более что переводчик был одним из участников заговора. Другой участник заговора Григол Ор- белиани, впоследствии достигший чина генерала от инфантерии русской армии и должности второго лица в наместничестве царя на Кавказе, даже перевел отрывки из старого, запрещенного в России произведение Рылеева «Исповедь Наливайко», что сочли за отягчающее обстоятельство его уча- стия в заговоре и выслали из Грузии. Так что переводчики знали, что дела- ли, а не просто заигрывали с музой. Протестантский дух Пушкина всегда сопутствовал переводчикам того времени. Пушкин фактически весь переведен на грузинский язык и теперь идет качественное обновление переводов. Многие произведения переведены по нескольку раз, _ даже такие крупные и сложные, как «Евгений Онегин», «Маленькие трагедии», «Повести Белкина», «Борис Годунов» и др. При этом переводили все известные писатели XIX и XX веков, с любовью при- общая грузинского читателя к бессмертным идеям и образам Пушкина. При анализе повторных переводов в глаза бросается стремление устра- нить ранее допущенные неточности, которые могли появиться по разным причинам. Учитываются возросшие требования и вкусы читателя, и новые достижения переводческого мастерства. Чтобы достичь совершенства в переводе пушкинского стиха, надо быть не только ювелиром слова, но и 212 zoia adamia поэтом по душе, иметь достаточную эрудицию и хорошо разбираться в вер- сификации. К счастью, таких переводчиков становится все больше. Методисты нашли еще один эффектный прием _ привлечение перево- дов к процессу изучения русских писателей в грузинской школе. И при ква- лифицированной презентации оригинала и перевода результат получается весьма положительный. А для будущих переводчиков прекрасным приме- ром служит великолепный, почти эталонный перевод самого Пушкина бал- лады Мицкевича «Будрыс и его сыновья». Хорошей традицией стало в Грузии издание двуязычных сборников оригиналов и переводов, которые удовлетворяют интерес квалифицирован- ных читателей. Подобные сборники повышают и ответственность перевод- чиков. Грузинского читателя переводами не удивишь. И это так вот уже 15 ве- ков. Но переводы произведений Пушкина занимают особое место. Это что- то очень близкое, очень понятное и свое. В основе такой близости лежит не- показной, светлый, добрый гуманизм, уважение к человеку независимо от национальности и социального положения без амбиции на превосходство и старшинство. Так думали наши абсолютные авторитеты И. Чавчавадзе, А. Церетели, Якоб Гогебашвили, Важа-Пшавела, позже М. Джавахишвили, К. Гамсахурдия, Г. Табидзе, Г. Леонидзе. Литература: 1. Buachidze T. Russkiy literaturnyy kriticheskiy ocherk [Tekst], Tbilisi, izd. Tbilisskogo gosudarstvennogo universiteta, 1980. 2. Burjanadze K. Me-19 saukunis kartuli mkhatvruli targmanis istoriis sakitkhebi. Tbilisi, 1992. 3. Shaduri V. Pushkin I gruzinskoe obshchestvo [Tekst], izd. “Literatura da khelovneba”, Tbilisi, 1966. 4. Shaduri V. Shumit Aragva redomnoyu…[Tekst]. Tbilisi, izd. “Merediani”, 1974. 5. Shaduri V. Zakhrebtom Kavkaza [Tekst] .Tbilisi, izd. “Merediani”, 1977. 6. Shaduri V. Poeti cheskiykray [Tekst]. Tbilisi, izd. “Merediani”, 1978. 7. Taliashvili G. Istoriyarusskoy literatury (nagruzinskomyazyke) [Tekst], 2-oe izd., Tbilisi, izd. Tbilisskogo gosudarstvennogo universiteta, 1960. 8. V tsarstve gor. Gruziya v zhizni i tvorchestve dekabristov-literatorov [Tekst], Tbilisi, izd. “Merediani”, 1988. 213 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV zoia adamia aleqsan d re puSki nis nawar mo e be bis Targ ma ni qarTul enaze rezi u me qarTul enaze TiTq mis srula daa Targ m ni li aleqsan d re puS kinis Semoq me de ba, amJa mad mimdi na re obs aRniS nu lis xaris xi a ni ga naxle ba. iseTi msxvilta ni a ni da rTuli nawar mo e be bi, rogo ri caa `evge ni onegi ni~, `pata ra trage di a~, `belki nis moTxro be bi~, `bo ris godu no vi~ da sxv. Targ m ni lia ramden jer me. aRsa niS na vi a, rom XIX da XX sau ku neebis yvela gamo Ce ni li mwera li Targ ma niT cdi lobda qarT ve li mkiTxve lis T vis Seey va re bi na rusi mwerlis ukv davi idee bi da perso naJ Ta saxe e bi. unda iTq vas, rom puSki nis nawar mo e be bi gansa kuT re bul yu radRebas imsa xu re ben, isini Zali an axlos midi an mkiTxelis sul Tan, ufro advi lad gasa ge bi da Rrma Sina ar sis mata re bel ni ari an; amis safuZ ve li ki naTe li, keTil So bi li huma niz mi a, erovne bis, soci a lu ri mdgoma re o bis miu xe da vad, ambi ci i sa da upira te so bis gare Se. amasve aRniS nav d nen aRia re bu li sazo ga do moRva we ni (av tori te te bi) i. WavWa va Ze, ak. were Te li, i. goge baS vi li, vaJa- f Sa vela da mogvi a ne biT, mix. java xiS vi li, k. gamsa xur di a, g. tabi Ze, g. leo ni Ze. 214 zoia adamia Zoia Adamia THE TRANSLATIONS OF PUSHKIN’S WORKS INTO GEORGIAN Summary Pushkin’s works actually have been translated into Georgian and now there is a high-quality updating of the translations. His works have been translated several times, _ even such large and difficult works as “Eugene Onegin”, “Small tragedies”, “Belkin’s Stories”, “Boris Godunov”, etc. It should be noted all XIX and XX centuries famous writers translated the great author’s works with love introducing the Georgian reader to his immortal ideas and images. Georgian readers cannot be surprised with translations and this process has been going on for 15 years. Pushkin’s works have a special place that is so close to the readers of all generations. Such closeness is based on the bright, kind hu- manism, respect for man regardless of nationality and social status without am- bition for supremacy and seniority. Our prominent figures of the Georgian Lit- erature, great poets and writers thought so among which were I. Chavchavadze, A. Tsereteli, Jacob Gogebashvili, Vazha-Pshavela, later M. Dzhavakhishvili, K. Gamsakhurdia, G. Tabidze and G. Leonidze. 215 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV religiaTmcodneoba RELIGION STUDIES qeTe van pavli aS vi li saqar T ve los samo ci qu lo ekle si is avto ke fa li is aRd ge nis erovnul - sa xel m wi fo eb ri vi mniSv ne lo ba (1917 weli) saqar T ve los samo ci qu lo ekle si is mier ganv lil ma rTulma aTasw lo van ma isto ri ul ma gzam, is mebr Zol ekle si ad Camo a ya li ba; mTeli Tavi si arse bo bis manZil ze, erovnu li saxel m wi fos ganu yo feli nawi li iyo da isto ri u li katak liz me bis para le lu rad, sa qarT ve los ekle si ac, rogorc saxel m wi fos ideo lo gi u ri berke ti, mZime proce sebs ganic di da. aRniS nul ma funq ci am saqar T ve los ekle sia eris TviTm yo fa do bis Senar Cu ne bis sada ra jo ze daa ye na. civi li za ci a Ta gzasa yar ze saqar T ve los mdeba re o bam gana pi roba misi isto ri u li miwa- wy liT msofli os saxel m wi fo Ta da inte re se ba, ramac qveya nas mraval sike Tes Tan erTad auracxeli proble mac Seuq m na. sxvadasxva epoqis dampyrobelisaTvis, qarTuli saxelmwifos ganadgurebisaTvis dartymis obieqti saqarTvelos eklesia da mi si TviTmoweseobis moSla iyo. ucxo elementisaTvis cnobili iyo erovnuli eklesiis adgili da mniSvneloba qarTul saxelmwifoeb riobaSi. rogorc saxelmwifos ideologiuri sayrdeni, saqarTvelos eklesia saukuneebis manZilze erovnuli TviTSemecnebis TeoriiT kvebavda qarTvel ers da misi kulturuli aRorZinebis garanti iyo. aRniSnuli ganapirobebda dampyrobelTa misdami agresias. es agre sia atarebda rogorc praqtikul, ise Teoriul xasiaTs, razec ers swrafi da Seuqcevadi reaqcia hqonda. agresorTa Teoriuli zewola ukiduresi veragobiT gamoirCeoda da qarTvelTa gabrueba-miZinebi saken iyo mimarTuli. amgvari politikis xelsayreli saSualeba ki, saqarTvelos eklesiis avtokefaliis iuridiuli kanonierebis mi zanSewonilobis problemis dayeneba iyo. epoqaTa interesebis Sesa bamisad, saqarTvelos eklesia xan avtokefaluri uflebis arakano nier mflobelad gamocxadda, xan mwvaleblobamoZalebulad, xanac politikuri interesebiT gajerebul eklesiad (Pavliashvili, 2008: 11). politikuri interesebiT Seqmnil ucxo saxelmwifoTa progra mebSi mudmivad idga saqarTvelos eklesiis avtokefaluri uflebis 216 qeTe van pavli aS vi li kanonierebis sakiTxi, romelic mimarTuli iyo misi TviTmoweseobis gauqmebis, momijnave eklesiasTan SeerTebis da qarTuli saxelmwi foebriobis gauqmebisaken. epoqaTa Sesabamisad, gare ZalTa interesebs erovnuli eklesia da sazogadoeba erTiani ZalebiT ebrZoda; saerTo interesebi aer Tianebda sasuliero dass, sazogadoebis yvela socialur fenas, rac yovelTvis iZleoda dadebiT Sedegs rogorc saxelmwifosaT vis, ise eklesiisaTvisac. saqarTvelos eklesia uwyvet reJimSi ebr Zoda istoriuli ZnelbedobiT gamowveul kataklizmebs da qarTu li saxelmwifoebriobis sadarajoze idga (Pavliashvili, 1995: 30). nebis mi e ri qristi a nu li saxel m wi fo saT vis saek le sio damo uki deb lo ba uSua lo kavSir Sia qveynis saxel m wi fo eb ri o bi sa da erovnu li cnobi e re bis simt ki cis sakiTx Tan; aRniS nu li, Sesa ba mi si movle naa qarT ve li erisT vi sac, romel sac sau ku ne e bis manZil ze uwevda brZola erovnu li ekle si is saer Ta So ri so masS ta biT aRia re bi saT vis, saek le sio ufle bis dacvi sa, Tu gare Zalis ag resi is Sede gad warT me u li TviTmo we se o bis aRd ge ni saT vis. amg var brZolebs adgi li hqonda adreq ris ti a nul, Sua sa u ku ne e bis, axal da uaxles isto ri ul epoqeb Si. qarT ve li sazo ga do e bi sa da sa xelm wi fo eb ri vi azrov ne bis isto ri u li siZli e re mdgoma re ob da epoqa lur gamow ve veb ze zust orien ta ci a sa da Sesa ba mi si pasu xis mige be ba Si. zemox se ne bul epoqebs Soris, saek le sio avto ke fa li is aRd ge ni saT vis eris erT su lo va ni brZolis gansa kuT re bu li maga liTi XIX-XX sau ku ne e bi a, romel Sic mTeli simw va viT warmo Cin da erovnu li ekle si is TviTmo we se o bis sasi cocx lo mniSv ne lo ba qar Tuli saxel m wi fo eb ri o bis aRd ge nis, ganvi Ta re bi sa da misi Tana medro ve o bas Tan Sesa ba mi so ba Si moyva nis saqme Si. XIX-XX sau ku ne e bi saqar T ve los isto ri is erT -er Ti umZi me si peri o di a. saer Ta So ri so masS ta biT ganvi Ta re bu li poli ti ku ri katak liz me bis fonze da mezo be li rusu li impe ri a liz mis saqar T velo sad mi mwvave agre si is Sede gad gauq m da qarTu li saxel m wi fo ebri o ba da erovnu li ekle si is avto ke fa li a. qarT ve li eri ar See gua erovnu li fase u lo be bis _ saxel m wi fo eb ri o bi sa da avto ke fa liis gauq me bis faqts da Rirse ba ay ri li eri, mTeli am sau ku ne e bis manZil ze dakar gu li ufle be bis dabru ne bi saT vis Tavda u zo ga vad meca di ne ob da. saxel m wi fo eb ri vi Tavi suf le bi saT vis brZola qarT vel ma xalx ma imTa viT ve dau kav Si ra avto ke fa li is aRd ge ni saT vis brZo las. saqar T ve los samo ci qu lo ekle si am da qarT vel ma sazo ga doe bam avto ke fa li is aRd ge ni saT vis brZolis ramde ni me etapi 217 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ganv lo, rome lic gamov lin da saqar T ve los ekle si is mona wi le obiT erovnul - gan man Ta vi suf le bel moZra o ba Si, avto ke fa li is daka no ne bi saT vis brZola Si, saek le sio qone bis dabru ne bi saT vis Zalis x me va Si da aTeiz mis xana Si avto ke fa li is aRia re bi saT vis me cadi ne o ba Si. XIX-XX sau ku ne eb Si sirTu le e biT aRsav se avto ke fa lii saT vis brZola xang r Z li vi aRmoC n da da 1990 wels dasrul da (Pavliashvili, 2000: 101-102). XIX saukunis pirvel aTwleulSi qarTuli saxelmwifoebriobisa da eklesiis avtokefaliis xelyofas qarTvelma xalxma imTaviTve protestiT upasuxa. aRmosavleT saqarTvelos 1802, 1804, 1812 wle bisa da dasavleT saqarTvelos 1819-1820 wlebis amboxebebSi erov nuli saxelmwifos aRdgenis moTxovnis gverdiT pirvelad dadga sakiTxi avtokefaliis aRdgenaze. e. w. `imereTis bunti~ (1819-1820) pirdapir kavSirSi aRmoCnda ruseTis saeklesio reformis sawinaaR mdego da avtokefaliis aRdgenis sakiTxTan. es amboxebebi TandaTa nobiT gadaizarda saeklesio saprotesto gamosvlebSi, romelSic sazogadoebis yvela fena iyo CarTuli. qarTvelma xalxma erovnu li saxelmwifos aRdgenis moTxovnas gauTanabra saqarTvelos ek lesiis avtokefaliis aRdgenis sakiTxi (Khutsishvili, 1987: 89-72). XIX sau ku nis ambo xe be bis marcx ma qarT ve li sazo ga do e bi sa gan moiTxo va brZolis meTo deb Si arse bi Ti cvlile be bis Seta na. 30-ia ni wlebis sazo ga do e bam Sei mu Sa va erovnul nia dag ze mdgo mi sazo ga do eb riv - po li ti ku ri Sexe du le be bi, romel Ta Soris iyo avto ke fa li is aRd ge nis sakiTxic. SemTx ve vi Ti ar iyo, rom saqar Tve los anti ru sul sai dum lo wreeb Si aqti u rad iyv nen CarTul ni qarT ve li sasu li e ro pire bic (Gorgiladze,1967: 68-74). Tu XIX saukunis pirveli naxevris TavisuflebisaTvis brZoleb Si marcxma daadamblava mowinave inteligenciisa da samRvdeloebis sazogadoebriv-politikuri moRvaweoba; 30-iani wlebis miwuruli dan, isev amoZravda erovnuli energia da axalma Taobam inteleq tiT, Tu praqtikuli qmedebebiT daiwyo niadagis Semzadeba qveynisa da eklesiis gamoxsnisaTvis. qarTvelma erma brZola mimarTa erov nuli kulturis ganviTarebisaken, erovnuli cnobierebis gaRvive bisaken, saqarTvelos istoriisa da mwerlobis Sedegebis Sejamebi saken da a. S. am periodis avtokefalistebs saqarTvelos istoriaSi `mwignobarTa fenis~ saxeliT icnoben. wina TaobasTan SedarebiT, es Taoba energiuli, aqtiuri da iniciativiania. avtokefalistebma, avtokefaliisaTvis brZola erovnuli kulturisa da cnobierebis dacvaSi gadaitanes; kulturuli moRvaweobiT daupirispirdnen im periul interesebs da am gziT cdilobdnen eklesiis Tavisufle 218 qeTe van pavli aS vi li bis moTxovna STaenergaT qarTvel sazogadoebaSi. isini, ideiT Tu praqtikuli qmedebebiT niadags amzadebdnen avtokefaliis aRdge nisaTvis (Khutsishvili,1972: 129). XIX sau ku nis meo re naxe var Si msofli o Si mimdi na re sazo ga do ebriv - po li ti kur ma Zvrebma Secva la saqar T ve los ganvi Ta re bis gza _ qarT ve leb Si gaZli er da erovnu li Tavi suf le bi sa ken misw rafe ba. ekle sia ruse Tis poli ti ku ri wnexis qveS moeq ca, romlis miza nic iyo qarT vel sazo ga do e ba Si avto ke fa li is moTxovnis er Txel da samu da mod likvi da ci a. aseTi viTa re ba, safr Txes uqm ni da avto ke fa li i saT vis brZolis miznebs, amitom aucile bel piro bad iqca erovnu li Tavi suf le bi saT vis brZolis Sekav Si re ba avto ke fali is aRd ge ni saT vis brZolas Tan (Pavliashvili,1995: 192). avto ke fa li is aRd ge ni saT vis brZolis wina pi ro bad qarT vel ma samR v de lo e bam ori amoca na dasa xa: 1. ruseTis xelisuflebisaTvis saqarTvelos eklesiis avtoke faluri uflebis damadasturebeli istoriuli wyaroebis gacnoba; 2. saqar T ve los ekle si a ze codnis axalgaz r da Tao ba Si daner g va. avto ke fa lis teb ma isargeb les ruse Tis pirve li burJu a zi uli revo lu ci iT (1905-1907) erovnu li ekle si is avto ke fa li is aRsad ge nad . avto ke fa li is sakiTxi gamocxad da erovnul - gan man Tavi suf le be li moZra o bis Semad ge nel nawi lad . sam R v de lo e ba av toke fa li is moTxovna Si xedav da saqar T ve los gare Zali sa gan gan Tavi suf le bi sa ken gadad g mul nabijs; impe ri is xeli suf le ba ki mis wina aR m deg mimar Tul brZolas, ris gamoc mTavro ba avto ke fa lis tebs dau pi ris pir da. miu xe da vad samTav ro bo repre si e bi sa, samR vde lo e ba rCebo da impe ri is Zlier opozi ci ad da cdilob da qar Tuli ideis ganxor ci e le bas sazo ga do e bis yvela fenas Tan mWidro Tanam S rom lo biT . avto ke fa lur moZra o ba Si didi roli Seas ru la avto ke fa lis te bis mier daar se bul ma orga ni za ci a- sa zo ga do e beb ma: `saqar T ve los ekle si is damo u ki deb lo bis aRm d ge nel ma Zmobam~, peri o dul ma orga no eb ma da sxv., romle bic avto ke fa li is moTxov nis propa gan das eweod nen sazo ga do e ba Si . avto ke fa li is brZolis orga ni ze bi saT vis 1906 wels daar s da gaze Ti `sityva~, romlis furc leb ze gamoq vey ne bu li weri le biT mimdi na re ob da avto ke fa liis ideis, sazo ga do eb riv - po li ti ku ri movle ne bis gaSu qe ba da maTi xalx Si propa gan da (Nikoladze, 1918: 49-51). avto ke fa li i saT vis moZra o bis gaaq ti u re bam, uwmin de si sino di aiZula saqar T ve los ekle si is sakiTx ze ems je la. 1906 wlis sino dis wina saTaT bi ro sxdomeb Si mona wi le ob d nen qarT ve li da rusi ar qie le bi. qarT vel ma samR v de lo e bam sino dis sxdomeb ze warmo ad gi na 219 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV saqar T ve los ekle si is avto ke fa lu ri ufle bis dama das tu re be li is tori u li doku men ta ci a. sino dis wevre bis mtkice bu le biT, avto ke fali is moTxovna saqar T ve los avto no mi is aRia re bas ukavSir de bo da, rac impe ri is erTi a no bas safr Txes uqm ni da (Tonk me lis, 1905: 40-51). ruse Tis impe ra tor ma avto ke fa li is sakiTxi gansa xil ve lad gadas ca sruli ad ruse Tis saek le sio krebas. am gadawy ve ti le bam qarT vel sazo ga do e ba Si urTi er T gan s x va ve bu li azri warmoS va: erT ni miiC nev d nen, rom avto ke fa li is sakiTxis ganxil va unda ga dade bu li yo im dromde, sanam ruse Ti ar Camo ya lib de bo da saxel mwi fo sa da ekle si is urTi er To bis sakiTx Si; meo re ni emx ro bod nen avto ke fa li is aRd ge nis etapob riv princips; nawi lic, saqar T velos ekle si is avto ke fa li is gada u de bel ganxil vas emx ro bo da (Durnovo,1907: 17). 1906 wlis saek le sio krebis meo re ganyo fi le ba ze ixile bo da avto ke fa li is sakiTxi, sadac miRe bul iqna dadge ni le ba saqar T ve los ekle si is farTo refor ma ci a ze, saeg zar qo sos sae pis ko po sod gada ke Te ba ze da mis ruse Tis ekle si a ze daqvem de ba re ba ze. dadge nile ba ver ganxor ci el da qveynis SigniT mimdi na re mwvave poli tiku ri proce se bis gamo da misi rea li ze ba `mSvidi~ gare mo e bis piro be bi saT vis gada i do. sinod ma droe biT Sea Ce ra avto ke fa li is sakiTxis Semd go mi ganxil va da saqar T ve los ekle sia darCa sino dis iurisdiq ci a Si kvlavin de bu rad saeg zar qo sos statu siT (Ep. Kirion,1901: 152). avto ke fa li is moZra o ba Si, saqar T ve los ekle si is isto ri is obieq tu rad gaSu qe bas didi mniSv ne lo ba hqonda maSin, rode sac rusi swavlu le bi cdilob d nen avto ke fa li is uufle bo bis mec nie ru lad dasa bu Te bas da avto ke fa li is gauq me bis gamar T le bas. qarT vel ma mecni e reb ma: al. caga rel ma, n. marma, al. xaxa naS vil ma, iv. java xiS vil ma, s. gior ga Zem, T. Jorda ni am da sxvebma didi wvli li Sei ta nes avto ke fa li is sakiTxis ganmar te ba Si da saqar T ve los ekle si is avto ke fa lu ri ufle bis mraval sa u ku no va ni tradi cia mecni e ru lad daa sa bu Tes da argu men te biT gaam ya res. qarT vel ma swavlu leb ma Tavi an Ti gamok v le ve biT saqar T ve los ekle si is av toke fa lur ufle bas Seuq m nes isto ri ul - sa mar T leb ri vi da mec nie ru li safuZ v le bi (Tsagareli, 1912: 64-66). avtokefaliis sakiTxi interesis miRma ver darCeboda saqar TveloSi moqmedi politikuri partiebisTvisac; da, miuxedavad urTierTgansxvavebuli politikuri platformisa, avtokefali is sakiTxis gadawyvetaSi partiebi erTsulovanni iyvnen da er Tad eZiebdnen misi gadaWris gzas. politikuri partiebi partiuli 220 qeTe van pavli aS vi li principebis da ideologiis gaTvaliswinebiT kategoriulad iTxov dnen saqarTvelos eklesiis uflebis aRdgenas (Pavli as h vi li, 1995: 37). saqar T ve los ekle si is avto ke fa li is moTxovni sad mi damo ki de bule ba Si ruse Tis sazo ga do e ba araer T g va ro va ni iyo. sazo ga do e bis erTi nawi li avto ke fa li as ar Tana ug r Z nob da da mis gadawy ve tas ruse Tis poli ti kis sawi na aR m de go movle nad miiC nev da, radgan masSi saqar T ve los poli ti ku ri avto no mi is pers peq ti vas xedav da. rusul poli ti ka Si avto ke fa lis te bi poli ti kur meam bo xe e bad mo iaz re bod nen da maT wina aR m deg repre si ebs atareb d nen. reaq ci o ne ri rusi samR v de lo e ba cdilob da dae sa bu Te bi na av toke fa li is usafuZ v lo ba. maTi aseTi damo ki de bu le ba naTlad warmo Cin da 1906 wlis ruse Tis saek le sio krebis wina sa TaT bi ro sxdomeb ze, sadac avto ke fa li is wina aR m deg gamo di od nen mecni e rebi: glubo lov s ki, berd ni ko vi, alma zo vi; mitro po li te bi: vla dime ri, maka ri; episko po se bi: sera fi me, inoken ti; deka no ze bi: vos torgo vi, butke vi Ci da sxv. avtokefaliis sakiTxs ruseTSi Tanamoazre-gulSematkivrebic hyavda. isini aSkarad gamoxatavdnen ukmayofilebas ruseTis saekle sio politikisadmi saqarTvelos eklesiis mimarT. qarTveli avto kefalistebis brZola samagaliTod miaCndaT ruseTSi patriarqo bis aRdgenisaTvis brZolaSi. avtokefaliis ideas TanaugrZnobdnen cnobili rusi mecnierebi: n. sokolovi, n. zaozerski da n. palmovi. qarT ve li avto ke fa lis te bi gansa kuT re bul mxarda We ras sla via no fi le bi sa gan grZnobd nen, romle bic iTxovd nen ruseT Si pat riar qo bis ins ti tu tis aRd ge nas. xarko vis univer si te tis docen ti n. durno vo publi cis tu ri weri le biT amxel da ruse Tis saek le sio inte re sebs saqar T ve los ekle si i sad mi. marTa li a, is avto ke fali is moTxovnis aqti u ri mxardam We ri iyo, Tumc gans x va ve bu li Sexe du le ba hqonda saqar T ve los ekle si is samo mav lo status ze. n. durno vo saqar T ve los ekle si as avto no mi as sTava zob da. misi am Sexe du le bis Sede gi iyo mogvi a ne biT, Tbilis Si rusu li samit ropo li tos _ kavka si is saeg zar qo sos daar se ba rusul ekle si a ze daqvem de ba re biT (Pavliashvili, 2000: 147). qarT ve li avto ke fa lis te bis brZolis Tanx ved ri iyo ruseT Si patri ar qo bis aRd ge ni saT vis brZola. patri ar qo bis ins ti tu tis ruseT Si aRd ge na, saqar T ve los ekle si is avto ke fa li is aRd ge nis Se saZleb lo bebs zrdida; e. i. maTi inte re se bi erT ma ne Tis Tanx ved ri iyo, ris gamoc progre su li rusi sazo ga do e ba saqar T ve los ekle si is avto ke fa li is mxardam We ri iyo da aqti ur propa gan da sac eweo da ruse Tis sazo ga do e ba Si. amis maga li Tia qarT ve li avto ke fa lis te bis 221 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Tanam S rom lo ba ruse Tis `32 mRvdlis kavSir Tan~ da ruse bis Tanag r Zno bis peti ci e bi avto ke fa lis te bis repre si eb ze. 1916 wlidan avto ke fa li is sakiTxi gardam tex faza Si Sevi da, rasac xels uwyobda impe ri a Si Seqm ni li mZime poli ti ku ri gare mo eba. qarT ve li avto ke fa lis te bi cdilob d nen Seqm ni li viTa re bis gamo ye ne bas da kidev ufro gaa aq ti u res avto ke fa li is aRd ge nis moTxovnis mimar Tu le biT muSa o ba. ganax le bul moZra o bas xeli sufle bam mkacri Ronis Zi e be biT upasu xa; sinod Si daiwyo saek le sio refor mis progra mis Semu Sa ve ba, romel sac unda gae uq me bi na saqar T ve los saeg zar qo so da mis nacv lad dae ar se bi na kavka si is sa mitro po li to. am droi dan avto ke fa lis teb Si daiwyo avto ke fa li is ideis garSe mo konso li da ci is proce si; mTavro ba Si igzav ne bo da sae par qio krebeb ze miRe bu li avto ke fa li is aRd ge nis moTxovnis peti ci e bi (Durnovo, 1910: 111). qarT vel Ta brZola avto ke fa li is aRd ge ni saT vis xasi aT de bo da radi ka lu ro biT da princi pu lo biT, lega lu ri da iatakq ve Sa saqmi a no biT. qarT vel sazo ga do e bas swam da, rom erovnu li ekle si is damo u ki deb lo bis aRd ge na sawin da ri iqne bo da qarTu li saxel m wi fo eb ri o bis aRd ge ni sa, swored amito mac avto ke fa li is aRd ge nis moTxovnas erovnul - gan man Ta vi suf le beli moZra o bis nawi lad moi az reb d nen da am saqme Si aucile bel faqto rad miiC nev d nen sruli ad qarT ve li eris konso li da ci as, brZolis medro Sed ki Tavad qarT ve li samR v de lo e ba gamo di o da. isini saer To erovnu li inte re se bis sada ra jo ze dadg nen. ruseT Si 1917 wlis gadat ri a le bam saqar T ve los mosax le o bas erovnu li ekle si is TviTmo we se o bis aRd ge nis gadawy ve ti le bi sa ken ubiZga; es maSin, rode sac rusu li TviTm yo fa do bis damxo ba da `axa li ruse Tis~ formi re ba sruli ad ar moas wa veb da saqar T velo sad mi rusu li impe ri a lis tu ri mizne bis likvi da ci as. `axa li ruse Ti~ saqar T ve los poli ti kur - sa ek le sio Senar Cu ne bis axle bur meTo do lo gi as amuSa veb da, romel sac unda gaeT va lis wi ne bi na uwmin de si sino dis kompe ten cia saqar T ve los ekle si a ze da ar daeS va qarTu li saxel m wi fo eb ri o bis aRd ge na, romlis wina pi ro ba iyo saqar T ve los ekle si is gauq me bu li avto ke fa li is Senar Cu neba. zemo aR niS nul ma gana pi ro ba 1917 wlis erovnu li ekle si is TviTmo we se o bis aRd ge nis faqti, ramac avto ke fa li i saT vis brZo la axal faza Si gada iy va na; ganvi Ta re bu li poli ti ku ri proce se bis Sesa ba mi sad, avto ke fa li is aRia re bi saT vis meca di ne o ba sae ro xeli suf le bas Tan lavi re bis poli ti kiT gani sazR v ra, kerZod, ek lesi as erT d ro u lad uwevda muSa o ba saqar T ve los demok ra ti ul mTavro bas Tan, ruse Tis droe biT mTavro bas Tan da mogvi a ne biT, 222 qeTe van pavli aS vi li sabWo ur -im pe ri a lis tu ri ruse Tis xeli suf le bas Tan (Pavliashviki, 2008: 432). ruse Tis xeli suf le bis mier saqar T ve los ekle si is avto ke fa liis aRia re ba TviTne bur aqtad kvali fi cir da. ruseT ma saqar T velos ekle si is damo u ki deb lo ba mxolod eTni ku ri niSniT aRia ra, rac imis momas wa ve be li iyo, rom `axa li ruse Ti~ saqar T ve los sa momav lo dac Tavis teri to ri a lur sazRv reb Si moi az reb da. saqar Tve los ekle si is iurisdiq ci is teri to ri a lu ri niSniT aRia re ba, qarTu li saxel m wi fo eb ri o bis aRia re bas niSnav da, rame Tu saek le sio kanon m deb lo biT qveynis saek le sio sazRv re bi, misi poli ti ku ri sazRv re bis Sesa ba mi si unda yofi li yo; aRniS nu li ki buneb ri vad, arc moma va li ruse Tis poli ti kur inte re seb Si ar Sedi o da. swo red am poli ti ku ri inte re se bis gata re bas emsa xu re bo da ruse Tis axali saek le sio ujre di _ kavka si is saeg zar qo so. es ukanas k ne li 1917-1920 wlebis manZil ze ruse Tis ekle si a ze daqvem de ba re biT aqti u rad funq ci o ni reb da kavka si a Si. saeg zar qo sos iurisdiq cia vrcelde bo da kavka si is araqar T vel mrevl ze. amri gad, saqar T ve los maga liT ze, uxeSad dair R va saek le sio kanon m deb lo ba, rac gamov lin da erT saxel m wi fo Si ori ekle si is erT d ro ul funq ci o nire ba Si, romel Ta gan erTi ucxo saxel m wi fos _ ruse Tis ekle sia iyo (Pavliashvili, 2000: 89-94). saqar T ve lo sa da ruse Tis ekle si ebs Soris saek le sio qone bis gayo fis sakiTx ma ori ekle si is urTi er To ba Si gordi is kvanZis mniSv ne lo ba Sei Zi na. saek le sio qone bis dabru ne ba saqar T ve los ekle si is ekono mi ku ri berke tis gamya re bis momas wa ve be li iyo; Se saba mi sad, misi avto ke fa li is aRia re bis garan ti; ruse Tis ekle si isaT vis ki aRniS nu li qone ba saqar T ve los ekle si a ze ufle ba mo si lebis myari garan ti iqne bo da. qone bis irg v liv davam 3 weli wads gasta na da demok ra ti u li saqar T ve los arse bo bis wlebSi das rulda saqar T ve los ekle si is nawi lob ri vi gamar j ve biT. proble mis mogva re ba gamo i xa ta saek le sio qone bis naci o na li za ci a Si da kavka si is saeg zar qo sos gauq me ba Si. amri gad, saqar T ve los teri to ria ze Sewyda rusu li saek le sio ujre dis funq ci o ni re ba; saqar T velos demok ra ti u li xeli suf le bis gadawy ve ti le biT saqar T ve loSi momq me di araqar Tu li samrev lo e bi saqar T ve los ekle si is daqvem de ba re ba Si gada vi da da amiT saqar T ve los mTels teri to ria ze erovnu li ekle si is iurisdiq cia aRd ga. es iyo xeli suf le bis mier erovnu li ekle si is sasar geb lod miRe bu li erTader Ti gadawy ve ti le ba, rac erovnul - sa xel m wi fo eb riv inte re sebs emsa xure bo da (Pavliashvili, 2008: 177). 223 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV saqar T ve los ekle si is avto ke fa li is aRia re bis sakiTxi ruse Tis ekle si am XX sau ku nis 20-ia ni wlebis dasawyis Si xelme o red daa ye na, amJa mad, misi teri to ri u li niSniT cnobis kuTxiT. aSka ra iyo, rom ruse Tis `ganax le bul ma~ ekle si am daiwyo respub li ke bis poli ti ku ri mowyobis msgavsad sabWo Ta ekle si is mowyobi sa da sabWo Ta saxel m wi fo Si Sema va li ekle si e bis masze daqvem de ba re bis proce si. saa mi sod ki, mas regi o na lu ri ekle si e bis neba esaWi ro ebo da; dasa xu li miznis Sesa ba mi sad, ruse Ti moqni lad speku li rebda saqar T ve los ekle si is avto ke fa li is aRia re bis piro biT. sabWo Ta xeli suf le bis am proeq t ma rea li ze ba ver moas w ro 1937 wels `ganax le bu li~ rusu li ekle si is TviTlik vi da ci is mize ziT. miu xe da vad aRniS nu li sa, saqar T ve los ekle sia ganag r Zob da brZo las avto ke fa li is aRia re bis misaR we vad, rome lic 1943 wlis 31 oqtom b ris aqtiT dasrul da. XX sau ku nis 80-ia ni wlebis Sua xane bi sabWo Ta impe ri is `gar dama va li~ epoqis saxe liT aris cnobi li. TviTga mocxa de bu li res publi ke bis demok ra ti u li ganvi Ta re bis proces ma, calke ul sa xelm wi fo ebs uamra vi Sida cvlile bis SesaZ leb lo ba misca. saqar Tve los ekle si am qristi a nul samya ro Si farTo muSa o ba gaSa la avto ke fa lu ri ufle bis saer Ta So ri so aRia re bi saT vis, rac 1990 wlis saek le sio aqtiT dasrul da. lite ra tu ra: 1. Durnovo N., Istoricheskiy ocherk avtokefalii tserkvi: Iverskoy i Imeretins- koy, Moskva,1910. 2. Durnovo N., Sudbi Gruzinskoy Tserkvi, Moskva,1907. 3. Ep. Kirion, Kratkiy ocherk istorii Gruzinskoy Tserkvi i Ekzarkhata za XIX stoletie,Tiflis,1901. 4. Gorgiladze L., Kartuli sazogadoebrivi azris istoriidan,Tbilisi,1967. 5. Grekulov E.,Tserkov, samoderjavie, narod, Moskva,1969. 6. Kandidov B., Tserkov v 1905 godu, Moskva,1926. 7. Khutsishvili M., Sakartvelos eklesiis sotsial-politikuri pozitsia XIX-XX saukuneebshi,Tbilisi,1987. 8. Khutsishvili M., Sakartvelos saegzarkosos reaqtsiuli gonizdiebebi revolutsi- uri mozraobis ganvitarebis periodshi,Tbilisi,1972. 9. Lominadze B., Eklesiis reaktsiuli roli 1905-1907 tslebis revolutsiashi, Tbili- si, 1959. 10. Lukin N., Revolutsiya i tserkov, Moskva,1925. 11. Nikoladze Ev., Sakartvelos eklesiis istoria, Kutaisi, 1918. 224 qeTe van pavli aS vi li 12. Pavliashvili K., Sakartvelos samotcikulo martlmadidebeli eklesiis istoria (1800-1945), Tbilisi, 2008. 13. Pavliashvili K., Sakartvelos saegzarkoso 1900-1917 tslebshi,Tbilisi, 1995. 14. Pavliashvili L., Sakartvelos martlmadidebeli eklesia 1917-1921 tslebshi, Tbilisi, 2000. 15. Tonkmelis, Pravda ob avtokefalii Gruzinskoi tserkvi, Kutaisi,1905. 16. Tsereteli A., Statii i zametki po gruzinskom tserkovnomu voprosi , S.-Peter- burg, 1912. 17. Zirianov P., Pravoslavnaia Tserkov i samoderjavie, Moskva, 1984. Ketevan Pavliashvili THE NATIONAL-STATE MEANING OF THE GEORGIAN ORTHODOX CHURCH AUTOCEPHALY RE-ESTABLISHMENT Summary The Georgian Church has played a key role in the country’s history and be- come a vital component of Georgian national consciousness and identity. The paper considers the problem of the national-state meaning of the Geor- gian Orthodox Church and autocephaly reestablishment process. The Georgian Christian Orthodox Church regained its independence on March 12, 1917. This was the most important and difficult step which consolidated the position of the Georgian Church as an autocephalous structure. The struggle for independence of Georgian Church was a cornerstone to the reestablishment of Georgian state and national sense. The history of XIX-XX centuries represented the unity struggles of Georgian people by long, legal or illegal way and they assuring that the rees- tablishment of autocephaly of Georgian Orthodox Church would be the decisive precondition of the national state restoration. The struggle for autocephaly was streaming in several stages and ended in 1990. 225 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV medea bendeliani saqarTvelos samociqulo eklesiisTvis teritoriuli avtokefaliis miniWebis sakiTxi sabWoTa sistemaSi (1943 weli) ruse Tis xeli suf le bis `gaTi Se da ibato nes~ poli ti kam sava lalo Sede gi mou ta na sabWoTa saxel m wi fo eb ri o bas. sabWo Ta kav Siris vrcel teri to ri a ze, saer To poli ti kis ganxor ci e le bis T vis mTavro bas meo re msoflio omis win yvela sferos cent ra li zacia esaWi ro e bo da, buneb ri vi a, es sakiTxi ekle si a sac exebo da: saxel m wi fo poli ti kur kurss daqvem de ba re bu li rusu li ekle sia saek le sio mmarT ve lo bis cent ri unda yofi li yo yvela respub li kis marT l ma di de be li ekle si e bis T vis. meo re msoflio omis msvle lobi sas, dadga xelsay re li peri o di rusul ekle si a Si patri ar qo bis ins ti tu tis aRd ge nis T vis. umaRles ma xeli suf le bam daa fa sa ekle si i sa da misi xelm ZR va ne lis roli did sama mu lo omSi da neba darTo ekle si as 1943 wlis 8 seqtem bers moew via saeklesio kreba marT l ma di de be li ekle si is patri ar qis asarCe vad da patri ar q Tan arse bu li wminda sino dis Sesaq m ne lad. episkoposTa krebam mitro poli ti sergi erT su lov nad airCia mosko vi sa da sruli ad ruse Tis patri ar qad. krebam erTx mad mii Ro mitro po lit sergis mimar T va ssr kav Siris mTavro bi sad mi, romel Sic gamo xa tu li iyo madlo ba ruse Tis marT l ma di de be li ekle si i sad mi gamo Ce ni li yuradRe bi saT vis. swored, am peri o di dan iwyeba sabWo Ta xeli suf le bi sa da rusu li ekle si is inte re se bi regi o na lu ri ekle si e bis mimarT, maT Soris, upirve les yovli sa, aRsa niS na via saqar T ve los marT l ma di de be li ekle si isadmi. sabWo Ta mTavro ba Tavi si poli ti kis gamta re bel er Tgul rusul ekle si as Tan erTad eZebs gzebsa da xerxebs saqar Tve los ekle si a ze sruli ufle bis mopo ve bi saT vis da am saqme Si iZule bu lia gaiT va lis wi nos qarTu li ekle si is didi xnis moTxov na _ teri to ri u li avto ke fa li is aRia re ba. sruli ad ruse Tis part ri ar qis arCe vas kmayo fi le biT Sexv da saqar T ve los ekle si a. qveynis poli ti kur ma viTa re bam xelsay re li piro be bi Seqm na, saqar T ve los ekle si is ufle ba Ta aRia re bi saT vis. kaTa li kos-pat ri ar q ma kalis t ra te cinca Zem iseTi pozi cia Sei muSa va, rome lic adgi li dan daZrav da qarTu li ekle si i saT vis me tad saSur saqmes _ aRedgi na Zmuri urTi er To ba or erT mor w mu ne 226 medea bendeliani ekle si a Ta Soris, romlis Sede gic iqne bo da ruse Tis mxridan qar Tuli ekle si is avto ke fa li is aRia re ba. rasak vir ve li a, am SemTx veva Si gasaTva lis wi ne bu li iyo is saSi nao da saer Ta So ri so viTa reba nic, romel sac adgi li hqonda XX sau ku nis ormo ci a ni wlebis mRelva re cxovre ba Si. erT -erT aseT mniSv ne lo van piro bad meo re msoflio omi unda miviC ni oT. sama mu lo omSi qarTu li ekle si is didi damsa xu re ba, saqar T ve los kaTa li kos - pat ri arqs ufle bas aZ levda, rom erTxel kidev aReZra rusu li ekle si is mier erovnu li ekle si is damo u ki deb lo bis aRia re bis sakiTxi. am mimar Tu le biT saqar T ve los kaTa li kos - pat ri ar qi, kalis t ra te iwyebs diplo ma tiur muSa o bas da saba bad iyenebs rusul ekle si a Si patri ar qo bis ins ti tu tis aRd ge nas. 1943 wlis 14 seqtem bers kaTa li kos - pat ri ar q ma kalis t ra tem depe Sa gaug zav na sruli ad ruse Tis patri arqs sergis da miu lo ca am umaRles ierarqi a ze arCe va, gamoT q va imedi, rom ekle si e bi (ru suli da qarTu li _ m.b.) icxovreb d nen erT ma neT Tan mSvido biT da Tana zi a rad, RvTis sadi deb lad da SeTan x me biT. sapa su xo depe Sa, rome lic patri ar q ma sergim gamog zav na Tbi lisSi, gamo xa tav da qarTu li ekle si is gamox ma u re biT gamow ve ul udides sixa ruls. man gamoT q va survi li, rom ekle si e bis Ta nacxovre ba xels Seuwyob da am or xalxs Soris urTi er To be bis ufro gaRr ma ve bas. aRniS nu li viTa re ba ssrk-s poli ti ku ri kursis sisx l xor ce uli nawi li iyo. xeli suf le bis T vis aSka ra gaxda, rom qarTu li ekle si is morCi le ba Si moyva nis T vis ukve momwi fe bu li viTa re ba Seiq m na da aqti ur qmede beb ze gada vi da. omis wlebSi sabWo Ta mTav robas gansa kuT re biT esaWi ro e bo da erTi a ni, daraz mu li armia so cia liz mis dacvi sa da Senar Cu ne bis T vis. mxolod aseTi meTo diT iyo im etapze SesaZ le be li qveyni sa da misi poli ti ku ri kursis gadar Ce na. saxel m wi fo xeli suf le bas moux da seri o zul komp ro misze wasv la da es komp ro mi si qarTu li ekle si is ufle ba- mo si le bis aRia re ba iyo ruse Tis marT l ma di de be li ekle si is mxridan. XX sau ku nis 40-ia ni wlebi swored aseTi didm niS v ne lo va ni movle nis Semam za de be li etapi a, rome lic qarTu li ekle si is T vis warma te biT dagvir g vin da. ori saek le sio ierarqis urTi er To bis ken ltolvam is nayo fi gamoiRo, rom 1943 w. 28 oqtombers daiwyo mTel rig sakiTxebze Semam za de be li mola pa ra ke be bi. am misi iT ruse Tis patri ar q ma ser gim saqar T ve los saka Ta li ko so Si warmog zav na misi warmo mad ge ne li, stavro po li sa da pia ti gor s kis arqi e pis ko po si meu fe anto ni. 227 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV saqar T ve los sasu li e ro xeli suf le bas Tan Sexved ri sas arqi e pis kopos ma anton ma aRniS na, rom is ruse Tis patri ar qis gan movli ne buli iyo saqar T ve los ekle si is xeli suf le bas Tan, raTa adgil ze gamo er k via ruse Ti sa da saqar T ve los ekle si ebs Soris locvi Ti da kano ni ku ri ganxeT qi le bis likvi da ci is saSu a le ba ni. man saek le sio kanon m deb lo bi dan gamom di na re, aRniS na, rom saek le sio sazRv re bi unda damTx ve o da samo qa la qos, rom ruse Tis sapat ri ar qo Tanax ma iyo eRia re bi na saqar T ve los ekle si is teri to ri u li avto ke fa lia saqar T ve los sabWo Ta soci a lis tu ri respub li kis sazRv reb Si. bu nebri via aq igulis x me ba afxaze Tis avto no mi u ri respub li kis saek lesio sazRv re bic. para le lu rad man qarTu li ekle si is xeli suf lebis gan kate go ri u lad moiTxo va saxel m wi fo poli ti ku ri kur sis aRia re ba, misda mi erT gu le ba, rac unda gamo xa tu li yo rusu li ekle si is anti ka no ni ku ri dajgu fe bis uaryo fa Si, maTTan yovel g vari kavSi ris aRk ve Ta Si. imisT vis, rom ekle si a Ta Soris locvi Ti gaer Ti a ne ba wminda kano ne bis dacvis safuZ vel ze momx da ri yo, misi uwmin de so bis saqar T ve lo Si warmo mad gen lo bi Ti mova le o ba iyo: amomwu ra vad da SeZle bis dag va rad, weri lo bi Ti formiT, qarTu li ekle si is mesve urT epasu xaT rig kiTxveb ze, romelTa pasux sac un da gada ewy vi ta qarTu li ekle si is bedi. aseT kiTxva Ta Soris iyo: ra urTi er To ba Si imyo fe bo da saqar T ve los ekle sia anti ru sul saek le sio dajgu fe beb Tan? saqar T ve los kaTa li kos - pat ri arqs kiTxva ze vrceli pasu xis gace ma moux da. man mokle isto ri u li eqs kur siT mimo i xi la qarTu li ekle si is erT gu le ba marT l ma di de be li orTo doq sa lu ri rwme nisad mi: dai mow ma gior gi mTawmin de lis sityva warmoT q mu li 1053 wels anti o qi is patri ar q petre mesa mis wina Se, aseve, XVII sau ku nis pirvel naxe var Si qarT lis mefe Tei mu raz pirve li sa da odiSis mTavris levan meo re dadi a nis warg zav nil qarT vel samR v de lo e baTa Sexved ra ruse Tis sasu li e ri pireb Tan, sadac qarT ve lebs mo uwi aT damt ki ce ba, rom kaTo li kur aRm sa reb lo bas ar izia reb d nen da marT l ma di deb lu ri mrwamsis erT gu li damc vel ni iyv nen; pat riar q ma aseve dai mow ma mosko vis mitro po lit fila re tis sityve bi (1867 w.), romel mac saqar T ve los ekle sia moix se nia _ `uZve le si marT l ma di deb lo bis erT gul mcvelad da rusu li ekle si is marT lma di deb lo bis mowmed~. kaTa li kos-pat ri ar qis SeniS v niT, qarTu l ekle si as ar gaaC n da anti ka no ni ku ri gadax ra, rome lic xels SeuS li da ruseT sa da saqar T ve los ekle si ebs Soris locviT, kano ni kur urTi er To ba Ta aRd ge nas. 228 medea bendeliani yove li ve amis Semdeg arqi e pis ko pos ma anton ma misi uwmin de so bis mosko vis patri ar qis mier boZe bu li ufle ba mo si le biT, kano ni kurad SesaZ leb lad CaTva la eTxova nebar T va erTob liv msaxu re baze, rome lic Sedga 1943 wlis 31 oqtom bers uZve les saka Ted ro taZar Si _ sion Si, ris safuZ vel zec faqtob ri vad aRd ga locviT Tana zi a re ba or ekle si as Soris. locviT-kanonikuri urTierTobis aRdgena ruseTsa da saqarT velos eklesiebs Soris iyo udidesi mniSvnelobis istoriuli mov lena saqarTvelos istoriaSi. es ukanaskneli ki, Tavis mxriv, saek lesio-politikuri kursis is nawili iyo, romelic didi brZoliT, politikuri sifrTxiliTa da araCveulebrivi sibrZniT gadawyvita saqarTvelos eklesiis imdroindelma xelmZRvanelobam. kaTalikos -patriarqis k. cincaZis saeklesio politikuri sibrZne TviT ar qiepiskoposma antonmac aRniSna: `pativi da dideba Tqven, radgan Tqven pirveli iyaviT siyvarulisa da mSvidobis iniciatori or ek lesias Soris, pativi da dideba Tqven, rom pirvelma moisurveT da SeicaniT or wminda RvTiur eklesiebs Soris locviT da kanonikur urierTobaTa aRdgenis mniSvneloba da aucilebloba!~ sino da lu ri ganCi ne bis Semdeg ruse Tis uwmin des ma patri ar q ma sergim weri li gamo ug zav na saqar T ve los kaTa li kos - pat ri arqs ka list ra tes, romel Sic miu Ti Teb da, rom ar unda mieq ces yuradRe ba imas, rac iwere bo da da iTq mo da qarTu li ekle si is wina aR m deg Tu mxarda sa We rad. aseve ar unda daiwyos urTi er Tan ga ri Sis wo re bani, romle bic xels uSlid nen moce mu li sakiTxi sad mi miu ker Zo e bel midgo mas. saqar T ve los ekle si is avto ke fa lia ukve aRar aris am or ekle si as Soris cilo bis saga ni. saqar T ve los sabWo Ta soci a lis tu ri respub li kis sazRv reb Si ruse Tis ekle sia cnobda saqar T ve los marT l ma di de bel ekle si as mis ganCi ne ba Si: aRavlen da locviT da evqa ris tul kavSirs marT l madi de be li sarw mu no e bi sa da saek le sio wese bis dogma te bis dac vis piro biT, kerZod, ganSo re bas locviT urTi er To bis gan pireb Tan da sazo ga do e beb Tan, romle bic ganye ne bu li iyv nen zia re bi dan rusu li marT l ma di deb lu ri ekle si is sams jav ros mier. qarTu li ekle si is am mimar Tu le biT gamov le ni li pozi cia me tad origi na lu ri a. is aSka rad ar gamo dis sabWo Ta saxel m wi fos inte re se bis wina aR m deg, piri qiT, aqti u rad ebmis saxel m wi fos po liti kur kurs Si da gvevli ne ba mis damc ve lad da gamamar T leb lis erT -erT inici a to rad. qarTu li ekle si is inte re se bi am metad rTul poli ti kur vi Tare ba Si iuridi u li ufle be bis mopo ve biT Semo i far g le bo da. 229 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV sabWo Ta wyobi le bis dasawyi si dan ve, qarTu li ekle si is saqmi a no bac am mimar Tu le biT warmo eb da da misi mcdelo ba iyo yove li xelsay re li mdgoma re o bis Tavis sasar geb lod gamo ye ne ba. gaer k va ra aRniS nul poli ti kur katak liz meb Si, qarTu li ekle si is xelm ZRva ne lo ba yovel na i rad cdilob da Seqm ni li viTa re bis Tavis sa sargeb lod gamo ye ne bas da sae ro xeli suf le bis gan komp ro mi sul nabijs iTxovda. qarTu li ekle si is sasu li e ro krebu lis did dam saxu re bad unda miviC ni oT yvela drois mZime poli ti kur viTa re baSi gark ve vis goniv ru li meTo di da qmede ba ni. niSan dob li vi a, rom swored saqar T ve los ekle si is T vis yvela ze mZime peri od Si _ komu nis tu ri mmarT ve lo bis xana Si, qarTu li ekle sia aRwevs udi des gamar j ve bas _ nayo fi e rad iyenebs mis did Rvawls sama mu lo omSi da moipovebs erovnu li ekle si is iuridi u li ufle bis aRia rebas rusu li marT l ma di deb lu ri ekle si is gan. qarTul ekle si as SesaZ leb lo ba mie ca gamo su li yo msofli os marT l ma di de bel ekle si a Ta samoR va weo arena ze, Seiqm na aSka ra pi roba misi samo mav lo aRia re bi saT vis msoflio ekle si e bis gan, ris ganxor ci e le bac mxolod XX sau ku nis 90-ia ni wlebis dasawyis Si gaxda SesaZlebeli. lite ra tu ra da wyaro e bi: 1. SUISSA (Sakartvelos uakhlesi istoriis sakhelmtsifo saistorio arqivi), fondi 1879, aghtsera 1, saqme 2. 2. Zhurnal Moskovskoiy patriarkhii, Moskva, #3, 1944. 230 medea bendeliani Medea Bendeliani THE ISSUE OF TERRITORIAL AUTOCEPALY RECOGNITION FOR THE APOSTOLIC CHURCH OF GEORGIAN IN THE SOVIET SYSTEM Summary The paper discusses the issue of the independence of the Georgian Orthodox Church. During the World War II the Catholicos Patriarch of Georgia was once again allowed to raise the issue of recognition of the independence of the National Church by the Russian Church. On October 28, 1943, the Russian Patriarch Sergi sent his representative Archbishop of Stavropol and Pyatigorsk Archbishop Anthon to the Catholicos of Georgia. Archbishop of Stavropol and Pyatigorsk Archbishop Anthon. According to the ecclesiastical legislation, he stated that the Russian Patriarchate agreed to recognize the territorial autocephaly of the Georgian Church within the borders of the Soviet Socialist Republic of Georgia. The independence of the Georgian Orthodox Church was finally recognized by the Russian Orthodox Church on October 31, 1943. It was a great event in the history of Georgia. 231 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV arqimandriti Sio (kvaracxelia) asketizmis warmarTuli da ZvelaRTqmiseuli elementebi sityva `asketizms~ mravali mniSvneloba aqvs da niSnavs: moR- vaweobas, varjiSs, wvrTnas, mecadineobas, meomars, aTlets. eli- nizmis epoqisa da gvianantikuri xanis literaturaSi `asketizmma~ sami ZiriTadi mniSvneloba SeiZina: 1. `fizikuri~ mniSvneloba, anu sxeulis varjiSi; 2. zneobrivi mniSvneloba, anu gonebisa da nebelobis wvrTna; 3. religiuri mniSvneloba. sxeulis varjiSis mniSvnelobiT `asketizmi~ gamoiyeneboda Zvel berZnul sityvierebaSi, kerZod, herodotesTan, TukididesTan da sxv. xolo meore, anu zneobrivi mniSvnelobiT, romelic gonebisa da nebelobis wvrTnas gulisxmobs, is gvxvdeba qsenofontesTan da gansakuTrebiT ki sofistebTan.* rac Seexeba mesame, anu reli- giur mniSvnelobas, am kuTxiT asketizms iyenebdnen piTagorelebi,** Tumc am niSniT ufro mkafiod iyenebdnen gviani antikuri epoqis dasawyisSi. magaliTad, filon aleqsandrielTan vxvdebiT gamoTq- mas: `wminda RvTismosaobaSi moRvaweni~. niSandoblivia isic, rom aRniSnul sityvaTa jgufi Zvel aRTqmaSi spontanurad gamoiyeneba mxolod `makabelTa wignSi~,*** xolo axal aRTqmaSi zmna `λιτότητα~ gvxvdeba vrceli mniSvnelobiT mxolod `mociqulTa saqmeSi~: `amas zeda viRuwi, daubrkolebeli gonebai maqus RmrTisa mimarT da kacTa maradis~ (Sakme 24, 16). klimenti aleqsandrielisa da ori- genes Semoqmedebidan moyolebuli sityva `asketizmma~ qristianul mwerlobaSi SeiZina `moRvaweobis~ is Cveuli mniSvneloba, romli- Tac is gamoiyeneba dRevandel qristianul sivrceSi. Tu aske- tizmSi moviazrebT RmerTTan SeerTebisa da religiur-zneobrivi srulyofilebisaken mimaval gzas, romelic adamianis sulisa da sxeulis garkveul Sinagan da garegan mdgomareobas gulisxmobs (qalwuloba, TavSekaveba, marxva, locva da a. S.), aseT SemTxvevaSi, dasaSvebia, rom asketizmi saTanadod gavrcelebuli movlena unda * sofistebi _ Zvel saberZneTSi, Cv. w. aR. V-IV ss. filosofiisa da oratoruli xelovnebis fasiani maswavlebelebi. ** piTagorelebi _ piTagorizmis mimdevrebi. piTagorizmi iyo religiur-filoso- fiuri swavleba Zvel saberZneTSi Cv. w. aR.-mde V-IV ss., romelic Camoayaliba piTagoram. *** makabelTa wigni _ Zveli aRTqmis arakanonikuri wigni, romelic oTxi nawilisgan Sedgeba. 232 arqimandriti Sio (kvaracxelia) yofiliyo berZnul-romaul samyaroSi da ZvelaRTqmiseul reli- giaSi qristes Sobamde, radgan zeciuri srulyofilebisaken swra- fva yvela epoqis adamianis midrekileba da saxasiaTo Tviseba iyo. am mxriv, arc berZnul-romauli da ZvelaRTqmiseuli epoqebi iyo gamonaklisi. saukuneebis manZilze da Tanamedrove etapzec saki- Txis irgvliv Catarebuli kvlevebi naTlad adasturebs, rom qris- tianul asketizmSi asketizmis dRemde moqmedi calkeuli elementi swored antikuri epoqis warmarTobidan da Zveli aRTqmidan aris nasesxebi. asketizms SedarebiT iSviaTad vxvdebiT berZnul-ro- maul religiebSi (kerpTayvanismcemloba _ S. k.), sadac asketizmis daniSnuleba ritualuri sisufTavis dacvaa, amitomac mas mxolod garegnuli, formaluri xasiaTi gaaCnia. magaliTad, flaminebis,* wesebi da akrZalvebi, romelTa Tanaxmad maT ar SeeZloT Tavs- aburavis gareSe gareT gasvla, cxenze amxedreba, TxasTan Sexeba, iaraRTan Sexeba da a.S. vestalebs** hqondaT qalwulobis aRTqma, riTac msaxurobdnen samsxverplos. maTi mTavari daniSnuleba iyo samsaxverploze cecxlis dacva da misi mudmivi SenarCuneba. gansakuTrebuli Sinaarsobrivi datvirTva hqonda `asketizms~ berZnul filosofiaSi. piTagorelebTan filosofia moiazreboda, rogorc adamianis sulisa da gonebis gansawmendi `instrumenti~. filosofos piTagoras mixedviT, asketi iyo adamiani, romelic cdilobda, mieRo sibrZne samyaros Semecnebisa da saTnoebebSi moRvaweobis gziT, sadac uvnebobas Zalze didi mniSvneloba eniWe- boda, radgan vnebebi ganixileboda, rogorc adamianSi borotebis arsebobis mTavari mizezi (Trubetski, 1997: 123). asketizmis analogiur tradicias adgili hqonda berZnuli fi- losofiis ganviTarebis Semdgom etapzec, magaliTad, kinikosebsa*** da stoikosebTan.**** magaliTad, kinikosTagan yvelaze cnobili dio- gene kasrSi cxovrobda. erTxel, rodesac kasris gverdiT ijda da mzes eficxeboda, masTan aleqsandre makedoneli mivida. imperator- ma diogenes hkiTxa: `ra SemiZlia gavakeTo SenTvis, nuTu araferi gsurs? ho, _ uTxra diogenem, _ iqiT gaiwie, mzes nu miCrdilav~ * flaminebi _ Zvel romSi calkeuli RvTaebebis _ iupiteris, cereras, kvirinisa da sxvaTa _ qurumebi. ** vestalebi _ qalRmerT vestas qurumebi Zvel romSi. gadataniTi mniSvnelobiT `vestali~ niSnavda qalwul qals. *** kinikosebi _ filosofiuri skolis mimdevrebi, romlebic sokrates mowafe antisTenem daaarsa (daaxloebiT Cv. w. aR.-mde 450-360 ww.). kinikosebi sruliad uaryofdnen sazogadoebriv institutebs, adaTebsa da kulturis dadgenilebebs. **** stoikosebi _ filosofiuri skolis mimdevrebi. stoicizmis fuZemdeblad iT- vleba zenoni (Cv. w. aR.-mde IV-III ss). is mouwodebda vnebebisagan gaTavisuflebisa da bedis morCilebisaken. 233 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV (Gorderi, 2005: 129). amgvari pasuxiT diogenem aCvena, rom mis win mdgom imperatorze nakleb bednieri ar iyo, romelsac yvelaferi hqonda, rasac ki moisurvebda. kanikosebis mixedviT ki bedniereba aris ara materialur keTildReobaSi, Zalauflebasa da janmrTelobaSi, ara- med sulis vnebebisagan ganwmendaSi. aRsaniSnavia is faqtic, rom war- marTul, elinistur asketizmSi arsebobda dapirispireba, erTgvari gaoreba, ganwyobasa da am ganwyobis gamoxatvis formas Soris. erT vnebasTan brZolas Tan sdevda meore vnebis mimarT monoba, upirate- sad siamayisa da ampartavnebis mimarT monuri damokidebuleba. war- marTuli asketizmisaTvis simdablis saTnoeba sruliad ucxo md- gomareobaa. gansxvavebuli viTarebaa qristianul asketizmSi, sadac simdable aris yovelgvari moRvaweobis fundamenti, romlis gare- Sec asketizmis WeSmariti gageba martivad aris dayvanili fizikur wvrTnamde. kidev ufro Tvisobriv maxasiaTeblebs vxvdebiT Zve- laRTqmiseul religiaSi, sadac asketur elementebs gansazRvravda RmerTi da Tavis rCeul xalxs ucxadebda: `wminda iyaviT, radganac wminda var me, ufali, RmerTi Tqveni~ (Lev. 19, 2). iudaizmSi asketizmi SeiniSneba nazorevelobaSi* (Rits. 6, 1-21), karvis msaxurebasa da mRv- delmsaxurebaSi, aRTqmis dadebaSi (1Mep. 1-2, 12), winaswarmetyvelTa cxovrebasa (3Mep.18, 4; 22, 6) da gandegilobaSi. zemoCamoTvlilTa- gan, gandegilebis garda yvela colosani iyo, radgan qalwuloba ebraeli xalxisaTvis ucxo elementi iyo im mizeziT, rom maTSi Rr- mad iyo damkvidrebuli Svilierebis azri, rogorc amqveynad mesiis mosvlis saSualeba. ebrauli asketizmis arsi iudauri religiis mo- Txovnidan gamomdinare RvTis umwikvlo msaxurebaSi mdgomareobs (Rits.19, 2; 20, 7), Tumca, aRniSnuli ar miuTiTebs imaze, rom Zvel aRTqmaSi araferia Tqmuli qalwulobaze. ase magaliTad, solomon brZeni iuwyeba, rom `umjobesia uSviloba saTnoebiT~ (Sibrdz.4,1); ase- ve `TviT saWurissac, visac ar Caudenia usjuloeba da ar ganuzra- xavs boroteba uflis mimarT, miecema gamorCeuli madli rwmenisa da sasurveli wili uflis taZarSi~ (Sibrdz. 3,14). esaias wignSi vki- TxulobT: `nu ityvis saWurisi: < * nazorevelebi _ iudaizmSi ewodebaT adamianebs, romlebic sakuTar Tavs RmerTs uZRvnidnen da amis gamo met religiur akrZalvas icavdnen, vidre sxva morwmuneni. isini ar iRebdnen yurZnis nayofs (pirvel rigSi, Rvinos), ar ikvecdnen Tmas da ar exebodnen micvalebuls. nazorevelTa aRTqma SeiZleboda yofiliyo rogorc droebiTi, aseve mudmivi. 234 arqimandriti Sio (kvaracxelia) asulebze ukeTess, saukuno saxels mivcem maT, romelic ar waiS- leba~ (es. 56,3-5). ieremias wignSi aRniSnulia: `da iyo sityva ufli- sa: < * eseebi _ mimarTuleba (eresi) iudaizmSi Cv. w. aR.-mde II saukunis II naxevari _ I saukune. eseebi qadagebdnen sazogadoebriv sakuTrebas, asketizms, miiltvodnen sulis ganwmendisken. ** Terapevtebi _ iuduri seqta. misi warmoSoba da istoria ucnobia. erTaderTi wyaro, sadac Terapevtebis Temis aRweraa SemorCenili aris filon aleqsandri- elis traqtati `mWvretelobiTi cxovrebis Sesaxeb~. 235 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV `Terapiis~ gzas adgebodnen, anu RvTismsaxurebasa da sulis gankurnebas misdevdnen, rasac, vinmes magaliTis mixedviT, an mowodebisa da rCevis safuZvelze ki ar akeTebdnen, aramed gansa- kuTrebuli zegardamo STagonebiT (Smirnovi, 1909: 3-4). Tera pev te bi saxl de bod nen udabur adgi leb Si. `isi ni marto obi sa ken isw raf vod nen ara dana Sa u leb ri vi kacT mo Zu le o bis ga mo, aramed im mizniT, rom gasc lod nen adami an Ta iseT sazo ga do ebas, romlis cxovre bis wesi gans x va ve bu li iyo. maT ician, rom msgavsi sazo ga do e ba saxi fa Toa da damam Zi me be li maTT vis... maTi sacxovre be li ubra loa da iTva lis wi nebs or rames: sici ve sa da mzis mcxunva re bas. sacxovreb le bi erT ma ne Ti sa gan moSo re biT aris ganla ge bu li, radgan mWidro dasax le ba damam Zi me be li iqne bo da ganmar to e bis meZi e be li kacis T vis. qale bi da kace bi Tera pev teb Tan gancal ke ve biT cxovrob d nen da ikri be bod nen mxolod saer To RvTism sa xu re bis dros. amasTa na ve, kace bi da qale bi msaxu re ba ze gancal ke ve biT idg nen da maT erT ma ne Ti sa gan maRa li zRude hyof da. da saer Tod, maTi cxovre bis T vis dama xa si a Te be li iyo mkacri TavSe ka ve ba. isini dReSi orjer locu lob d nen, dili Ta da saRa mos. Sua led Si ki wminda weri lis Semec ne bi Ta da ganmar te biT iyv nen daka ve bu le bi~ (Smirnovi, 1909: 8-11). Tera pev te bis cxovre bis es wese bi imde nad msgavse ba Sia qristi anu li monaz v no bis cxovre bis wesTan, rom IV sau ku ne Si `ekle si is isto ri is mamam~ _ evse vi kesa ri el ma _ dama je reb lad ganacxa da: `vfiqrobT, rom filo nis es cxadi da ukama Tod misa Re bi sityve bi Cveni aske te bis Sesa xeb aris naTq va mi~ (Evsebi, 2007: 70). filon aleqsan d ri e lis aRniS nul naSroms akri ti ke ben Tana medro ve mkvlevre bi. maT miaC ni aT, rom is obieq tu rad ar asaxavs Tera pev t Ta cxovre bas, radgan Tera pev t Ta cxovre bis wesi da Se xedu le be bi nawi lob riv axlos idga Tavad filo nis idea leb Tan, amitom misi miker Zo e ba Tera pev te bi sad mi maTi cxovre bis aRwe ra Sic aisaxe ba (Ivanitski, 1911: 451); sxva sityve biT rom iTq vas, Tavis traqtat Si _ `mWvrete lo bi Ti cxovre bis Sesa xeb~, filon aleqsan dri e li Tera pev t Ta cxovre bi sa da swavle bis aRwe ra ze ufro me tad saku Tar aske tur Sexe du le bebs gadmog v cems. amri gad, sityva `aske tizms~ sxvadas x va epoqa sa da civi li za ci aSi gans x va ve bu li mniSv ne lo be bi gaaC n da. maT Soris, is gamo i ye ne boda, rogorc `fizi ku ri~, anu sxeu lis varji Sis mniSv ne lo biT. aske tiz mi sakma od gavr ce le bu li movle na iyo rogorc warmar Tul da ZvelaR T q mi se ul, aseve qristi a nul samya ro Sic. TiTo e ul maTgan Si aske tiz mi sxvadas x va formiT, Sina ar si Ta da `doziT~ 236 arqimandriti Sio (kvaracxelia) vlinde ba. zogan is ufro mkacrad da xSir SemTx ve va Si gamo i ye ne boda, zogan ki _ Seda re biT nakle bad da msubu qad. berZnul-romaul religiebSi asketizmis SedarebiT msubuqi da martivi formebi SeiniSneba, rac mxolod kerpebis garegnul msa xurebaSi aisaxeba. ZvelaRTqmiseul religiaSi asketizmi ganisazR vreboda RvTis gancxadebiT da is sxvadasxva formiT vlindeboda, kerZod, karvis msaxurebiT, winaswarmetyvelebiT, nazorevelobiT da a.S. Zvel aRTqmaSi arsebuli moRvaweobis es gansxvavebuli for mebi gamowveuli iyo ebraeli xalxis saWiroebiT da RmerTic Ta vis ers moRvaweobis iseT formebs udgenda, romelic mis sulier saWiroebas Seesabameboda. rac Seexeba berZnul filosofias, masSi arsebuli gansxvavebuli da xSir SemTxvevaSi urTierTsapirispiro mimarTulebebidan gamomdinare, asketizmis elementebic gansxvave buli iyo. zogi filosofiuri mimdinareoba SedarebiT aqtiurad mimarTavda asketizms, zoganac misi niSnebi naklebad SeimCneoda. arsa niS na via is gare mo e ba, rom qalwu lo bis aRT q ma, rome lic qristi a nu li monaz v no bis erT -er Ti mTava ri da upiro bo arT q ma a, Sei niS ne ba Zvel romSi quru mi vesta li qale bis saxiT. aseve, Zvel aRT q ma Si moce mu lia qalwu lo bis ramde ni me maga li Ti, kerZod, miri a mis (moses da), ilia winas war mety ve li sa da ioane naTlis m cemlis saxiT. iudaiz m Si warmo So bi li esee bis seqta Sic gavr ce lebu li iyo qalwu lo bis dacva, rome lic sava ra u dod vesta le bis msgavsad mudmi vi ar iyo. da bolos, miu xe da vad imisa, rom sxvadas x va epoqa sa da kultu raSi arse bul aske tizms mrava li saer To da ganmas x va ve be li niSa ni aqvs, aman mainc didi zegav le na moax di na qristi a nu li aske tiz mis Camo ya li be ba sa da ganvi Ta re ba ze. qristi a nul ma aske tiz m ma ki, Ta vis mxriv, sruli ad gans x va ve bu li Sina ar si da srulyof li forma Sei Zi na qristi a nul monaz v no ba Si. lite ra tu ra da wyaro e bi: 1. Evsebi k., Saeklesio istoria, Tbilisi, 2007. 2. Ivanitski V., Filon Aleksandriskiy.Zhizn i obzor literaturnoy deyatelnosti, Kiev, 1911. 3. Gorderi I., Romani pilosopiis istoriis shesakheb, Tbilisi, 2005. 4. Sidorov A., Sviatootecheskoe nasledie i tserkovnie drevnosti, Moskva, 1967. 5. Smirnov N. P., Terapevty i sochinenie Filona Iudeya, "A zhizni sozertsatel- noy", Kiev, 1909. 6. Trubetskiy S., Kurs istorii drevnei filosofii, Moskva, 1997. 237 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Archimandrite Shio (Kvaratskhelia) PAGAN AND THE OLD TESTAMENT ELEMENTS OF ASCETICISM Summary The paper touches upon diverse and different meanings of the word “Asceticism” used in different epochs and civilizations, namely, in the pagan, the Old Testament and the Christian cultures. The term comes from the Greek word askḗsis, which means training or exercise. The original usage did not refer to self-denial, but to the physical training required for athletic events. Its usage later extended to rigorous practices that are used in all major religious traditions, in varying degrees to attain redemption and higher spirituality. Asceticism is seen in the ancient theologies as a journey towards spiritual transformation, where the simple is sufficient, the bliss is within, the frugal is plenty. The phenomenon of asceticism was spread historically significant only within the religious realm particularly in the pagan, the Old Testament and the Christian worlds. Asceticism has been adopted by worshipers of various faiths. The paper considers pattern, content and quantity of this phenomenon revealed in each religious environment. The similarities and distinctions of asceticism have also been discussed in parallels. It has been emphasized that in the Christian asceticism, currently acting certain element of asceticism is borrowed from the paganism and the Old Testament of antique epoch, in particular it has acquired entirely different content and perfect pattern in Christianity in which the highest level of activities and ascetics, precisely represent the monastic life. 238 avTan dil were Te li romis ekle si is saek le sio damo ki de bu le bis sakiTxi da msoflio avtoritetulobis Taviseburebebi I-V saukuneebis dasavleTSi (pati vi sa da Zala uf le bis sakiTxi) imperiis sxvadasxva regionSi qristianuli Temebis arsebobam ganapiroba adgilobrivi eklesiebis warmoSoba-dadgineba. adgi lobrivi eklesiebi gaerTianebulni iyvnen episkoposebis garSemo, romlebic, Tavis mxriv, mociqulebis memkvidreebi da maTgan uwy vetad xeldasxmis madlis matareblebi iyvnen. zogadad, samociqu lo memkvidreobis matarebeli aris mTliani adgilobrivi eklesiis sxeuli episkoposTan erTad, romelic warmoadgens amave dros am adgilobrivi eklesiis Tavs. episkoposisa da adgilobrivi eklesi is erToba ar iyo mxolod mmarTvelobiTi, an martivad urTierTo ba ori gancalkevebuli jgufis _ sasulierosa da saerosi, aramed, rogorc organuli erToba mTliani eklesiis sxeulisa. sisavse da kaTolikuroba (sayovelTaooba) TiToeuli adgilobrivi eklesiis ar gaiazreba damoukideblad da calke sxva adgilobriv kaToli kuri eklesiebisgan, radganac yvelas aqvs RvTis eklesiis igive si savse da msgavseba. amgvarad, yvela msoflio adgilobrivi eklesia Seadgens organulad qristes sxeuls. maT axasiaTebdaT sinodalu ri sistema, romelic misi bunebidan momdinareobda. amis pirveli magaliTi Tavad mociqulebis krebaa. aRniSnuli gamoixateboda Zi riTadad evqaristul saidumloSi, episkoposis xeldasxmaSi, Tvi Ton adgilobrivi eklesiebis urTierTobaSi (Phei das, 2002: 183-191). sawyisi etapi dan ve, ekle sia ar ugulve bel yof da ukve arse bu li romis impe ri is admi nis t ra ci ul struqtu ras. am admi nis t ra ciul struqtu reb Si buneb ri vad ganvi Tar da pirve li qristi a nu li Teme bi. II-III sau ku ne eb Si qristi a no bis gavr ce le ba Ziri Ta dad Tavis Tavze aiRes am poli ti ku rad mniSv ne lo van ma cent reb ma, romle bic Tavis mxriv Camo ya lib d nen rogorc deda -ek le si e bi. maTi avto ri teti ufro didi iyo vidre sxva poli ti ku rad umniS v ne lo qala qis ekle si e bi sa da eparqi e bis cent rebs warmo ad gen d nen. II sau ku ni dan ukve aucile be li xdeba TiTo e ul eparqi as hqono da erTi cent ri, sadac gani xi le bo da adgi lob ri vi ekle si is Sida sakiTxe bi Tu proble me bi. aseT cent rebs warmo ad gen d nen kesa ri a -i e ru sa li mi, korin To -a Te ni da sxv. (Pheidas, 2002: 195-196). 239 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV II saukunis Sua wlebidan wamyvani avtoritetia episkoposi; igi xdeba mTavari maswavlebeli da Temis xelmZRvaneli. am droidan iwyeba eklesiis centralizaciis axali etapi _ urTierTobebi cal keul adgilobriv eklesiebs Soris. amrigad, yalibdeba saepisko poso instituti da masTan erTad eklesiis mmarTvelobiTi struq tura. eklesia inarCunebda erTianobas dogmatur da struqturul sakiTxebSi. romis eklesia mniSvnelovani, amave dros avtorite tuli centri gaxda dasavleTSi, rogorc imperiis dedaqalaqi da wvlilis Semtani devnasa da eresebTan brZolaSi. romic, ierusa limis msgavsad iwyebs zrunvas msoflio Tu sxva adgilobriv ekle siebze. klimenti romaelis (102 w.) epistole korinTelTa mimarT gamsWvalulia siyvaruliT, zrunviT, mokrZalebiT, romelsac uZR vnis erTi eklesia meores gaWirvebis Jams. romis eklesia Txovnis gareSe (rogorc Cans) iZleoda rCevebs umaRlesi administraciu li sibrZniT, aRmosavleTis eklesiebisaTvis; mouwodebda wesri gisken da erTianobisken mSvidad da Rirseulad, rogorc RvTisa da suliwmindis iaraRi. ierarqiuli suli gaCnda romis eklesiis dominirebuli sulisgan, vidre romis episkoposisgan, an presvite rebisgan (Schaff, 1914: 157-159). klimenti romaelis epistoleebis av toritetis Sesaxeb saubrobs wminda dionise korinTeli, romelic mis Tanamedrove romis episkoposs soteris wers: `radgan Tqven Tavidanve gaqvT aseTi Cveuleba, rom yvela Zmas sxvadasxvagvarad uwevT qvelmoqmedebas da mraval eklesias yvela qalaqSi ugzavniT Sewirulobas... dRes uflis wminda dRes vatarebT, da vkiTxulobT Tqvens epistoles, romlis wakiTxvas gavagrZelebT mudam, Jamidan Jamamde Segonebis misaRebad, rogorc adre Cvens mimarT klimen tis mier mowerils~ (Euse bi us, 2007: 170-171). egnate RmerTSemosili wers romis eklesias da avedrebs raTa izrunos antioqiis eklesi aze. `moixseneT Tqvens locvebSi eklesia siriisa, romelsac Cems sanacvlod RmerTi hyavs mwyemsad. episkoposobs masze martooden iesu qriste da Tqvenmieri siyvaruli~ (Chelid ze, 2011: 44). aseve, is faqti, rom sxva eklesiisamebr ki ar arigebs romis eklesias ara med _ `arasodes gSurdaT vinmesi; sxvebs aswavlidiT. msurs mtki ced egos yovelive, rac Tqven aswavleT da ganaCineT~ (Chelid ze, 2011: 42). mogvianebiT ki, ukve II saukuneSi, episkoposi viqtori I (189-199 ww.) Tavs amJRavnebda, rogorc damoukidebeli mmarTve li. am drois romis eklesia Zlier gamdidrda moqceuli mdidari da maRali fenis mrevlis xarjze. dasavleTi jvarcmas aRniSnavda nisanis (aprilis) 14 ricxvis momdevno paraskevs, xolo mesame dRes -aRdgomas. aRmosavleTi ki jvarcmas aRniSnavda, romel dResac 240 avTan dil were Te li mouwevda nisanis 14 ricxvi da aRdgomas mesame dRes am dRidan. aseTi iyo aRmosavleTis tradicia. viqtori moiTxovda, rom paseqi aRniSnuliyo dasavleTis tradiciiT, anu nisanis 14-is momdevno kvira dRes, raTa ar yofiliyo kavSiri ebraelebis dResaswaulTan. winaaRmdeg SemTxvevaSi, imuqreboda, rom mcire aziis qristianul Temebs garicxavda qristianuli samyarodan. man 196 wels moiwvia romSi kreba, sadac italiis 14 episkoposi monawileobda, aRiara mxolod dasavleTis tradicia da ganavrco mTels msoflio ekle siaze. mcire aziis eklesiebma ar miiRes efesos krebaze es gadawy vetileba da aRmosavleTis tradiciis erTgulni darCnen. es Sem Txveva ukve mowmobs romis episkoposis miswrafebas Tavisi gavlena gaavrcelos dogmatur sakiTxebzec. romis episkoposis stefane I-is (254-257) karTagenis episkoposis mimarT epistoleebSi naTlad Cans romis episkoposis upiratesoba rwmenis principul sakiTxebSi (Gergey, 1996: 23). am dros, afrika moicva sakiTxma imis Sesaxeb Tu, rogor daebrunebinaT eklesiaSi isini, romlebmac uaryves rwmena. am SemTxvevaSic, romis episkoposi iTxovda erTi dasavluri tra diciis miRebas yvela eklesiis mier (Zadvorny, 1995: 105-106). aseve misi cnobili konfliqti kiprianesTan masTan paeqrobisas xazs us vams petre mociqulis gamorCeulobas. aqedan gamomdinare ki naT lad Cans misi ambiciebi romis kaTedris upiratesobaze, romelsac kipriane ar eTanxmeba (Wace, 1911: 916-917). am periodidan, dasav leTis RvTismetyvelebaSi ikveTeba kavSirebi petre mociqulsa da romis episkoposs Soris. III sau ku ne romis ekle si is T vis ayva ve bis xana a. misi Zala uf le ba ufro da ufro izr de ba. romis ekle si is episko po seb ma ukve III sa uku nis meo re naxe var Si moa xer xes qristi a ne bis devnis gamo ye ne ba Tavi si Zala uf le bis gaZli e re bis T vis. gamo acxa des ra, rom papi siqs tus II (257-258 ww.), misi wina mor bed ni da memk vid re ni mowa me ob rivad aResrul nen, romis episko po se bi saTa ve Si Caud g nen mTeli apeni nis naxe var kun Zu li sa da mimde ba re kunZu le bis sae pis ko po so ebs. papma mii sa kuT ra ufle ba ara mxolod episko po se bis gada ye ne bis, aramed, maTi ganwe se bi sac. male misi Zala uf le ba gavr cel da gali i sa da espa ne Tis mniSv ne lo van nawil ze, aseve, samx reT afri kazec. am droi saT vis, mxolod itali a Si iricxebo da 160 sae pis ko poso (Lozinsky, 1986: 20). IV saukuneSi icvleba qristianobis mdgomareoba da is devni lobidan imperiis saxelmwifo religiad gvevlineba. konstantine didis (306-337 ww.) reformebiT qristianobis devna Sewyda, qris tianoba saxelmwifo religia gaxda. amave dros, icvleba imperiis 241 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV dedaqalaqic; romis magivrad centri konstantinepolSi inacvlebs. konkurencia da mwvave paeqroba iwyeba romsa da konstantinepols Soris; pap silvester I-is (314-335 ww.) dros xdeba romis eklesi is mier didi avtoritetis, simdidrisa da Zalauflebis moxveWa, radganac igi konstantine didis mzrunvelobis qveS iyo da gulux vad eZleoda yvela saxis privilegiebi (Lozinsky, 1986: 26). romis pap iulius I-is (337-352 ww.) dros, dasavleTis episkoposebma, romle bic iyvnen damokidebulni romis saepiskoposoze, sardikiis krebaze (343 w.), romi aRiares gasaCivrebis umaRles instanciad saepiskopo soebs Soris. es faqti romis pirvelobisken erT-erTi nabiji iyo (Kowalski, 1991:16). am saukuneSi yalibdeba pentarqia, romlis pirve li wevri romia, meore konstantinepoli, mesame aleqsandria, anti oqia da ierusalimis sapatriarqoebi. am SemTxvevaSi, roms pativis mixedviT mieniWa pirveli adgili, Tumc is agrZelebda ara marto pativisTvis, aramed ZalauflebisTvis brZolasac. aRniSnulis faq tia is, rom pap inoken ti I-is (401-417 ww.) azriT, adgilobrivi kre bebi mxolod TaTbiris xasiaTisaa da maTi gadawyvetilebebi maSin iZenen Zalas, rodesac maT romis papi daamtkicebs (Gergey, 1996:42). V sau ku ne Si ukve gaCn da idea petre moci qu lis mier romis ek lesi is daar se ba ze da, rogorc petre moci qu li iyo pirve li mo ciqul Ta Soris, aseve, romis kaTed rac moi az re bo da msoflio ek lesi ebs Soris upira te sad. papma leo I didma (440-461 ww.), rogorc brwyinva le diplo mat ma barba ros Ta Semo te ve bis gan daic va romi 452 wels hune bis mTavar sar dal atilas gan; 455 wels ki vanda le bisgan. man miaR wia imdens, rom valen ti ni a ne III gamos ca dekre ti pa pebis sasa mar T los T vis episko po se bis daqvem de ba re ba ze da pape bis gadawy ve ti le bis samar T leb riv Zala ze. yove li vem, impe ri a Si papis avto ri te ti aamaRla (Lozinsky,1986: 31). igi romis ekle si is pirve lobis sakiTxs siste ma tu ro bas Zenda da qada ge beb Si gadmos cem da _ petre moci qu li upira te sia sxva moci qu leb ze Zala uf leb ri vad. petres dace ma (romis ekle si is dakni ne ba) safr Txes uqm ni da sxva moci qu leb sac, amitom, qriste masze gamor Ce u lad locu lobs. `perte moci qu li aris safuZ ve li mTeli ekle si is. TviTon eyr d noba uZle vel cixe simag res erTi an safuZ vels, qristes, magram es simt ki ce bune bi Tia qristes T vis, xolo petres gada e ce ma Tana zi a rebiT. petre miCne u lia uaxlo es kavSi riT daur R ve ve li erTo bis qristes Tan da warmo ad gens Sua ma vals qriste sa da mTel ekle si as Soris. dakav Si re bu li masTan (ekle si as Tan), rogorc Tavi sxeul Tan, igi Tavis TavSi Tavs uyris madli an niWebs, romle bic misi meSve o biT garda mo di an moci qu leb ze~ (Bolotov, 1913: 281-283). 242 avTan dil were Te li romis pap gela si I dros (492-496), pape bi ukve Tavs moi az reb d nen WeSma ri ti swavle bis, rogorc nebis mi e ri kano nis da sayr de nis wyarod. man, ise aRamaR la papo ba, rom paps SeeZ lo yvela ekle si is gasa mar T le ba. mogvi a ne biT ukve pap sima xis (498-514 ww.) sasa mar T lo proces ze vxvdebiT sabo loo formu las: «papa a nemine iudicatur» _ aravis aqvs ufle ba papis gasa mar T le bis. gela sis dros dasrul da papis prima tis Teo ri u li princi pi, jeri mis rea li ze ba ze mid ga (Gergey, 1996: 49). papo bis ins ti tu tis, rogorc saxel m wi fos damc ve lis amaR leba, romis impe ra to re bis avto ri te tis dace mis para le lu rad mimdi na re ob da. es dro, msxvili miwaT m f lo be le bis romi dan bi zanti a Si didi migra ci is peri o di a. mito ve bu li mamu le bi Ziri Ta dad romis papis mflobe lo ba Si gada di o da. ase izr de bo da papis poli ti kur prestiJ Tan erTad misi mate ri a lu ri bazac (Lozinsky, 1986: 31). 476 wels dae ca dasav leT romis impe ria da mTeli Zala uf le ba rogorc saxe li suf lo, ise sasu li e ro, romis paps daeq vem de ba ra. ekle sia dasav leT Si mas Semdeg kidev ufro gamyar da, rode sac frankTa mefem xlodvig I (481-511 ww.) im mizniT, rom gali is qristi a nu li mosax le o ba gada e bi re bi na frank Ta didi same fos Se saqm ne lad mii Ro qristi a no ba romis ekle si is tradi ci iT da Tavi gamo acxa da qristi a no bis damc ve lad. igi ekle si is maRal ierarqi as uxvad asaCuq reb da miwe biT (Lozinsky,1986: 31). miuxedavad imisa, rom msoflio krebebis dros aRmosavleTma eretikosebTn xangrZlivi brZolis mTeli sirTule gadaitana da mTeli Zalisxmeva dogmaturi azrovnebisaken warmarTa, dasavleT Si piriqiT, papma amiT sargebelic ki miiRo barbarosebisgan da aR mosavleT saqristianodanac; ar iRebda ra is cocxal monawileo bas dogmatur kamaTebSi, papi yuradRebiT adevnebda Tvalyurs da, arasodes uSvebda xelidan SesaZleblobas gamoexata Tavisi damo kidebuleba mimdinare procesebisadmi. papebi TiTqmis yovelTvis warmatebiT dgebodnen marTlmadideblebis mxares, Sediodnen maT mdgomareobaSi da aRmouCendnen kidec qmediT daxmarebas, uTanx moeba jer dasavleTSi, xolo Semdeg dasavleTsa da aRmosavleTs Soris urTierTobebSi gamoiwvia konstantinepolis saepiskoposos daarsebam; Semdeg ki misma amaRlebam dedaqalaqis rangSi. konstan tinepolis krebamde (381 w.), aRmosavleTSi, pirvel kaTedrad iT vleboda aleqsandriis saepiskoposo. Svidi msoflio saeklesio krebebis dros dasavleTis da aRmosavleTis eklesiebis rwmena erTmaneTisgan ar gansxvavdeboda. aRmosavleTi aRiarebda romis 243 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV pirvelobas mxolod pativiT; aseve, misgan gamogzavnil legatebs msoflio krebebze xvdeboda Sesabamisi pativiscemiT. romis papebma araTu SeinarCunes I-III saukuneebSi mopovebuli uflebebi, aramed V saukunis miwurulSi dasavleT imperiis dacemis Semdeg kidev ufro gaafarToves da gaaZlieres TavianTi gavlena msoflio saqristi ano samyaroze. msoflio krebebis periodSi, romis papebi aqtiu robdnen aRmosavleTis saeklesio movlenebSic. marTalia, papebi piradad ar monawileobdnen msoflio saeklesio krebebis proce durebSi, magram iq TavianT warmomadgenlebs (legatebi) gzavnidnen (Pavli as h vi li, 2010: 237). isto ri u li da Teo lo gi u ri mize ze bi dan gamom di na re, dasav leTis saqris ti a no Si ganvi Tar da sakiTxi romis ekle si is pirve loba ze. dasav leT ma romis pirve lo ba dau kav Si ra erTis mxriv petre moci quls, xolo meo res mxriv, TviTon romis impe ri is Zvel centrs da moci qu le bis _ petre si da pavles aRs ru le bis adgils. samec ni e ro wreeb Si arse bobs mosaz re ba, rom romis episko po si sadmi aseTi damo ki de bu le ba imTa viT ve efuZne bo da saxa re bis cno bebs _ `miu go iesu da hrqua mas: netar xar Sen, simon, bari ona, ra me Tu xorc Ta da sisx l Ta ara gamo gix ca des, aramed mama man Cemman zecaTa man. da me getyv Sen, rame Tu Sen xar klde, da amas kldesa zeda aRva Se no ekle si a Cemi, da bWeni jojo xe Ti sa ni ver ereo di an mas~ (Mate, 16: 17-19); `xolo meve ved re mama sa Cemsa SenT¢s, ra¡Ta ara mogak l des sarw mu no e ba Seni, da Seno des me mii qec da ganam t ki cen Zmani Senni~ (Luka, 22: 32); `da odes isadil nes, hrqua simon - pet res iesu: simon iona so, giyu ar mea ufro samaTsa? hrqua mas petre: he, ufalo, Sen uwyi, rame Tu miyu ar Sen. rqua mas iesu: aZoen krav ni Cemni~ (Ioane, 21: 15); pavle moci qu li roma el Ta mimarT Tavis episto le Si aRniS navs roma e li qristi a ne bis rwmenas _ `pirve lad vhmadlob RmerT sa Cemsa qriste iesus mier Tquen yovel TaT ¢s, rame Tu sarw mu no e ba ege Tque ni ganiT qu mis yovel sa sofel sa~ (Ro maelta, 1: 8). amri gad, rogorc gamoC n da, romis ekle si is avto ri te ti sayo velTa od iyo aRia re bu li, radgan romis qristi a nu li Temi imTa viTve gamo ir Ce o da mxurva le rwmeniT. TiTq mis yovel mxriv, yvela mimar Tu le biT gvevli ne bi an mowi na ve, an ukeT, rom vTqvaT brZo lis wina xazze, rogorc qristi a no bis devnis dros, ise qristi anu li azrov ne bis siste mu rad Camo ya li be ba- for mi re bi sas. isini gamo ir Ce od nen qristi a nu li gadmo ce mis dacva Si simt ki ciT, er Tsu lov ne bi Ta da saek le sio morCi le biT. amaze metyve lebs e. w. pape bis kata lo ge bi `Liber Pontificalis~, `pape bis wigni~. am kata lo gis 244 avTan dil were Te li Tanax mad, petre dan pap milti a dem de (314) iyo 32 romis episko po si. ori maTga ni aResru la gada sax le ba Si, xolo danar Cen ma 30-ma mii Ro mowa me ob ri vi aRsas ru li (Gergey, 1996: 20-21). amaze dayr d nobiT SegviZ lia vTqvaT, rom romis episko po so ba faqtob ri vad sikv dils niSna da, rac, ra sakvir ve li a, did mowo ne ba sa da pativs aRZ rav da morw mu ne eb Si. aseve, mzrunve lo biT damo ki de bu le ba Si sxva adgi lob ri vi qristi a nu li Teme bis mimarT. qristi a nu li swav lebis yvela Ziri Ta di sakiTxi, rome lic II-III sau ku ne eb Si zoga dad ekle si i saT vis warmo iS va; romSi gadawy da: pase qis aRniS v na, ereti kose bis gada naT v la da a. S. impe ra to ris gadas v lam impe ri is axal dedaq laq Si gamo iw via pape bis xelSi rogorc sasu li e ro, ise sae ro Zala uf le bis Tavmoy ra. maT moa xer xes mTeli dasav le Tis ekle sie bis daqvem de ba re ba. amas xeli Seuwyo aseve sae pis ko po so e bis, samit ro po li to e bi sa da sapat ri ar qo e bis warmoq m nam, ramac gamo iwvia ekle si e bis mmarT ve lo biT daqvem de ba re ba -aR ma te bu lo ba. Tu aRmo sav leT Si ramde ni me sapat ri ar qo a, dasav leT Si mxolod romis sapat ri ar qo iyo. romi mxolod pati viT pirve lo bas ar jerde bo da da Zala uf leb riv upira te so ba ze acxadeb da preten zi as. amri gad, Tu romis sapat ri ar qo iyo aRia re bu li saek le si o- sa su li e ro pa tiviT, mogvi a ne biT moxda misi saxel m wi fo- Za la uf leb ri vi pati viT aRia re ba. lite ra tu ra da wyaro e bi: 1. Bolotov B. Lektscii Po Istorii Drevney tserkvi, T. III, S-Peterburg, 1913. 2. Chelidze E. Guli Gonieri, #1, Tbilisi, 2011. 3. Gergey E. Istoria Papstva, Moskva, 1996. 4. Lozinsky C. Istoria Papstva, Moskva, 1986. 5. Mtatsmindeli Giorgi, Akhali Aghtkma, Tbilisi, 2000. 6. Pavliashvili K. Qristianobis Istoria, Tbilisi, 2010. 7. Pheidas B. Ekklisiastiki Istoria A, Athinai, 2002. 8. Schaff P. History of the Christian Church, Vol. II, New York, 1914. 9. Wace, 1911-Wace H. A Dictionary of Christian Biography and Literature, Boston, 1911. 10. Zadvorny B. Istoria Rimskikh Pap, T. I, Moskva, 1995. 245 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Avtandil Tsereteli THE ISSUE OF ECCLESIASTICAL DEPENDENCE OF ROMAN CHURCH AND THE PECULIARITIES OF WORLDLY AUTHORITY IN THE WEST IN THE I-V CENTURIES (ISSUE OF HONOR AND POWER) Summary The article deals with the issues of Roman Church’s attitude toward world authority in I-V centuries. In the early period all the local Christian churches were independent and totally responsible for making their own decisions. By the end of the 2nd century Christian communities had evolved a more structured hierarchy, with a central bishop having authority over the clergy in his city. The organization of the Church began to mimic that of the Empire; bishops in politically important cities exerted greater authority over bishops in nearby cities. During the Early Church, the bishops of Rome had a great authority in the Christian world. They were in a position to assist other churches financially and defence the faith and resolve doctrinal disputes. By the 3rd century the Roman bishops were representing themselves as having succeeded to the primacy that Peter had enjoyed among the apostles and as wielding within the universal church a primacy of authority in doctrinal matters. Gradually increasing the wealth of the Roman Church grows his power as well, which increasingly advanced and confirmed its pre-eminence in the West and even attempted to assert itself further abroad. He also had attempts to recognize himself supreme authority over all the churches not only with honor but with power. Especially after Christianity was legalized under Emperor Constantine, also after shifting the political centre to the East and falling the Western empire bishops of Rome were given great authority and power and the seat of the old Roman Empire. 246 istoria HISTORY qeTevan mania daviT yolbaia da polonuri qarTvelologia qarTuli kulturis ganviTareba-popularizaciis saqmeSi gan- sakuTrebul rols asruleben sazRvargareTuli kulturis cen- trebi. maTi saqmianobis asaxva erT-erTi mniSvnelovani sakiTxia qarTul istoriografiaSi. aRniSnuli TvalsazrisiT friad sain- tereso naSromi _ `masalebi sazRvargareTuli qarTvelologiis istoriisaTvis~, gamoqveynda 2012 wels J. feiqriSvili, i. vaSakiZis avtorobiT (Feiqrishvili, Vashakidze 2012: 214-226), romelSic Tvalsa- Cinod aris warmodgenili ucxoeTis ramdenime qveynis _ italia, germania, safrangeTi, inglisi, ungreTi, poloneTi, Cexoslova- kia, belgia, amerikis SeerTebuli Statebi, Sveicaria, norvegia _ qarTvelologiuri centrebis roli qarTuli kulturisa da is- toriis Seswavla-popularizaciis saqmeSi, maT Soris warmoCeni- lia polonuri qarTvelologiis wvlili. TavisTavad Sromatevadi samuSaoa Sesrulebuli da dainteresebul mkiTxvels aZlevs sayu- radRebo informacias sazRvargareT qarTvelologiis ganviTare- bis Sesaxeb. qronologiuri TvalsazrisiT monacemebi modis 2007 wlamde. Tumca raoden gasakviric ar unda iyos, iseTi sagulisx- mo cnobebi aris yuradRebis miRma darCenili, rogoricaa varS- avis universitetis qarTvelologiuri krebuli da misi damaar- seblis, amave universitetis qarTveli profesoris d. yolbaias mier gaweuli metad dauRalavi da nayofieri saqmianoba. rogorc Cans, avtorTaTvis cnobili ar iyo prof. d. yolbaias damsaxure- ba. amgvar STabeWdilebas qmnis is garemoeba, rom zemoxsenebul publikaciaSi mocemulia profesoris mier Targmnili qarTuli saistorio wyaros `moqceva¡ qarTlisa¡s~ Sesaxeb informacia. Sevecdebi Sevavso aRniSnul publikaciaSi arsebuli xarvezi. am TvalsazrisiT naSromi pirvelad gamovaqveyne krebul `qarTul wyaroTmcodneobaSi~, sadac warmodgenilia polonuri qarTvelo- logiis ganviTarebis reprezentacia ukanasknel ocwleulSi (Mania, 2013-2014: 273-278). aRniSnuli naSromis gamoqveynebis Semdeg, pro- fesori d. yolbaia araerTi sayuradRebo gamocemiT Tu kvleviT warsdga saerTaSoriso samecniero sazogadoebis winaSe. amitomac 247 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV gadavwyvite kidev erTxel mivawodo qarTvel mkiTxvels misi saq- mianobis Sesaxeb cnobebi. sakiTxis analizs daviwyeb 1991 wlidan, rodesac prof. d. yol- baia iwyebs moRvaweobas varSavis universitetis aRmosavleTmcod- neobis fakultetze (1990 w. Tbilisis i. javaxiSvilis saxelobis universitetis damTavrebis Semdeg). swored, am periodidan aqtiur fazaSi Sedis qarTvelologiuri kvleva-Zieba, romelsac saTaveSi Caudga qarTveli profesori. igi, amave wels, aarsebs qarTelolo- giur Jurnals `pro georgia~*. aqedan moyolebuli dRemde Jurnal- Si qveyndeba qarTvelologiuri sakiTxebis istoriuli, wyaroT- mcodneobiTi, eTnologiuri, literaturaTmcodneobiTi, lingvis- turi, folkloruli analizi. Tavidan polonur enaze, SemdgomSi daemata inglisur-germanul-frangulenovani gamokvlevebi. daviT yolbaias mondomebiT, sistematuri xasiaTi miiRo varSavis univer- sitetSi qarTuli Tematikis Seswavlam polonel mematianeTa da Ja- mTaaRmwerelTa, diplomatTa da mogzaurTa, kaTolike-misionerTa da mweralTa naSromebSi. JurnalSi intensiurad ibeWdeboda aRniS- nuli sakiTxebis kvlevisadmi miZRvnili statiebi. amdenad, didia Jurnalis roli qarTuli kulturis popularizaciis saqmeSi. 2002 wlidan qarTvelologiuri kvleva-Ziebis gaaqtiurebas uwyobda xels varSavis universitetSi Seqmnili kavkasiuri kvle- vebis mudmivi seminari da wm. grigol feraZis** xsovnisadmi miZR- vnili yovelwliuri saerTaSoriso samecniero konferencia, ro- melic dRemde prof. d. yolbaias xelmZRvanelobiT imarTeba wm. grigol feraZis xsenebis dRes, 6 dekembers***. * Jurnali gamodis 1991 wlidan varSavis universitetis orientalistikis fakul tetis aRmosavleT evropis institutis egidiT. ** varSavis universitetis qarTvelologiur Jurnal `pro georgiis~ mier 2010 wels daarsebul iqna wm. grigol feraZis saxelobis premia. premia gaicema or weli- wadSi erTxel im humanizmisa da faseulobebisaTvis, romlebsac misi laureate- bi mTeli cxovrebis ganmavlobaSi amkvidrebdnen. premia warmoadgens X saukunis uZvelesi qarTuli xelovnebis nimuSis martvilis panageas asls (oqro, vercxlisa da margalitis TvlebiT mooWvili (zoma 8 sm X 5,5 sm), sadac tixruli minanqriT wminda grigolis xati aris gamosaxuli, qarTuli warweriT wmida grigoli. mart- vilis oqros panageas aslis proeqti Seasrula saqarTveloSi cnobilma xelovanma nino burkaZem. wm. grigol feraZis saxelobis premiis laureatebi 2010-2016 wlebSi iyvnen: poloneli Teologi henrik paprocki, Jurnal `pro georgiis~ damaarsebeli, istorikosi daviT yolbaia, medievisti ian malicki, frangi qarTvelologi bernar utie, Zveli saberZneTis istoriis mkvlevari vloJimeJ lengaueri, qarTvelologi da baskologi ian brauni, poeti da filosofosi qarTveli sasuliero moRvawe ad- ami (vaxtang axalaZe), arqeologi vaxtang liCeli, germaneli kavkasiologi iost giperti, istorikosi vaxtang feraZe (grigol feraZis universitetis damaarsebeli). *** konferencia tardeba varSavis universitetis orientalistikis fakultetis aR mosavleT evropis institutis egidiT. 248 qeTevan mania rogorc wm. grigol feraZis TxzulebaTa krebulis pir- vel wigns wamZRvarebuli varSavis wm. grigol feraZis saxelobis marTlmadidebluri eklesiis* winamZRvris, henrik paprockis wina- sityvaobidan vgebulobT, swored pirvel konferenciaze dasmula wm. grigol feraZis Sromebis krebulis gamocemis sakiTxi. prof. d. yolbaias mravalwliani muSaobis Sedegad, dReisaTvis ukve mki- TxvelTa farTo wrisaTvis xelmisawvdomia wm. grigol feraZis Sromebis oTxtomeuli pirveli da meore wigni (Kolbaia, 2012, 2014). pirveli tomi gamoqveynda misi yovlad usamRvdeloesobis samTavi- sis da goris mitropolitis andria (gvazavas) locva-kurTxeviT. am mravalmxriv saintereso naSromis gamocemamde mkvlevars ukve ga- moqveynebuli hqonda sayuradRebo gamokvleva `wm. grigol feraZe da ber-monazvnobis dasawyisi saqarTveloSi~ (Kolbaia 2009: 202-211)**. aRsaniSnavia, rom ukanasknel xans gansakuTrebuli interesi SeiniSneba wm. grigol feraZis cxovreba-moRvaweobis Seswavlis TvalsazrisiT rogorc saqarTveloSi, aseve ucxoeTSi (polonel da germanel mkvlevrebs Soris). wmindanis cxovreba-moRvaweobis SeswavlaSi didi wvlili miuZRvis istorikossa da sasuliero pirs henrik paprockis, agreTve qarTvel mkvlevrebs: T. WumburiZes, g. jafariZes, n. papuaSvils, aseve germanel mkvlevrebs: S. xotiva- ri-iungers, i. raisners, h. kaufholds, l. fiSers da sxvebs. sru- liad gamorCeulia prof. d. yolbaias TaosnobiT gamocemuli Sro- mebis krebuli. igi warmoadgens erTgvar Semajamebel gamocemas. Sromebis krebuls win uZRvis wm. grigol feraZis cxovreba- moRvaweobis amsaxveli vrceli werili (gamokvleva ekuTvnis d. yolbaias), romelic samecniero literaturaSi cnobili monaceme- bis garda, efuZneba varSavis mitropoliis arqivSi dacul aqamde ucnob dokumentur masalas. naSromis mniSvnelovan siaxles war- moadgens wm. grigol feraZis gardacvalebis TariRTan dakavSire- biT mecnieris mier londonis poloneTis biblioTekaSi gamovle- nili axali masalebis publikacia. es garemoeba axali detalebiT avsebs da amdidrebs wm. grigol feraZis mravalmxrivi saqmianobis amsaxvel biografiul monacemebs. * aRniSnuli eklesia, romelic ganTavsebulia varSavis mitropoliis xatweris muze- umSi, 2005 wlidan arsebobs varSavaSi, lelexovskas q. # 5. igi varSavaSi mcxovreb qarTvelTa sulieri TavSeyris adgilad iqca. eklesiis mamaoebi arian h. paprocki da a. aleqseiuki. wirva sruldeba yovel kviras polonur enaze da saxareba ikiTxeba qar- Tulad d. yolbaias mier. arsebobs wm. grigol feraZis saxelobis saeklesio sazoga- doeba, romlis Tavmjdomareebi arian mama henrik paprocki da daviT yolbaia. ** es aris leqcia, romelic wakiTxul iqna d. yolbaias mier hale-vitenbergis (ger- mania) universitetis qristianobisa da bizantologiis institutSi. 249 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV krebuli iwyeba wm. grigol feraZis avtobiografiuli werile- biT. pirveli werili `bediswera~ gadmogvcems feraZeebis gvaris STamomavlobiTi xvedris _ sulTa mwyemsobis saswaulebriv isto- rias. aqve Jurnal `Der Orient~-Si gamoqveynebuli biografiuli xa- siaTis werili `qarTuli kulturis samsaxurSi~, romelic Seexeba germaniaSi swavlis periods. werili warmoadgens sakuTari saqmia- nobis erTgvar Sejamebas da sainteresoa im TvalsazrisiTac, rom mkvlevari istoriografiis, rogorc samecniero dargis aucile- blobaze akeTebs xazgasmas. igi miiCnevs, rom momavlis gegmebSi saWiroa ganvlil periodSi momxdari movlenebis gaTvaliswineba. avtobiografiul werilebs mosdevs wm. grigol feraZis sa- mecniero naSromebi. maT Soris sayuradReboa misi pirveli naS- romi _ `bermonazvnobis istoriisaTvis saqarTveloSi~, romelSic gaanalizebulia qarTuli bermonazvnobis istoria misi dasawyi- sidan 1065 wlamde. wm. grigol feraZis bermonazvnobis istoriiT daintereseba, rogorc misive biografiuli werilebidan Cans, gan- pirobebuli yofila berobis gansakuTrebuli roliT da misiiT saqarTveloSi. es misia iyo qristianobis ganmtkiceba-gaZliereba. pirvel nawilSi exeba siriel mamebs, wm. serapion zarzmels, wm. ila- rions da wm. grigol xanZTels, vinaidan isini arian qarTuli ber- monazvnobis mTavari warmomadgenlebi. kvlevas iwyebs `cxovreba- nis~ mokled gadmocemiT da TiToeulTan dakavSirebiT svams maTi Seqmnis TariRis, tendenciis, avtorTa vinaobis sakiTxs. Semdgom nawilSi ikvlevs bermonazvnobis dasawyiss aTonis mTis ivironis monasterSi da qarTveli berebis literaturul saqmianobas. exe- ba wmindanebs: ioanes, eqvTimes da giorgi mesvetes. gamokvlevaSi qarTuli wyaroebis mixedviT warmodgenilia qarTveli beris tipi. mesame nawilSi iZleva kvlevis Sedegebis Sejamebas. krebulSi Sesulia wm. grigol feraZis sxva kvlevebic, ro- melTa Soris gansxvavebuli midgoma (istoriul-religiur WrilSi ganxilva) SeiniSneba wminda giorgis rolis gansazRvraSi qarTveli eris cxovrebasa da sarwmunoebaSi. gamokvlevaSi yuradReba gamax- vilebulia qristianobis gavrcelebis Sedegad warmarTuli pan- Teonis qristianuli modificirebis sakiTxze. am TvalsazrisiT ganxilulia wminda giorgis roli qarTvelTa cxovrebaSi. mkvle- vari varauds gamoTqvams, rom mTvaris warmarTuli RvTaebis wmin- da giorgis saxeSi qristianuli modificirebis i. javaxiSviliseu- li Tvalsazrisi myar argumentebs moklebulia. Semdegi sakiTxi, romelic mkvlevris yuradRebis centrSi eqceva aris ucxoel pi- ligrimTa cnobebi palestinis qarTveli berebisa da qarTuli mo- 250 qeTevan mania nastrebis Sesaxeb. im droisaTvis aRniSnul sakiTxTan dakavSire- biT mxolod a. cagarelis naSromi arsebobda, romelic qarTuli wyaroebis monacemebs eyrdnoboda. sakiTxis srulyofili Seswa- vlisaTvis gansakuTrebuli mniSvneloba hqonda piligrimuli li- teraturis monacemebis gaTvaliswinebas. gamokvlevaSi, swored pi- ligrimuli literaturis monacemebis safuZvelze warmodgenilia qarTuli monastrebis mokle istoria, rasac erTvis mis mierve pa- lestinaSi aRmoCenili axali warwerebi. aqve qveyndeba oqsfordis bodleanis wignTsacavSi aRmoCenili XVIII s-is ioane naTlismcemlis monastris qronikis Sesaxeb naSromi; rogorc Cans, xelnawerma wm. grigol feraZis yuradReba masSi gadmocemuli bermonazvnobis is- toriiT miiqcia. xelnaweri Seicavda cnobebs ioane naTlismcemlis monastris garda, daviT garejis monastris cxovrebidanac, magram radgan xelnaweris avtori naTlismcemlis monastris wevri yofi- la, amitomac uwodebs ioane naTlismcemlis qronikas. aseve Sesu- lia gamokvleva saqarTvelos eklesiis uZvelesi istoriis pro- blemebis (saqarTvelos moqceva) Sesaxeb, sadac ganxilulia iseTi kardinaluri sakiTxebi, rogoricaa saqarTvelos ganmanaTleblis da pirveli qristiani mefis sakiTxi, qarTlis moqcevis TariRi, Txzulebis (wm. ninos cxovrebis) wyaro. gamocemaSi Sesuli Sromebi wm. grigol feraZes umTavresad sxvadasxva enaze _ inglisurad, germanulad, frangulad, polo- nurad hqonia gamoqveynebuli. aRniSnuli publikaciebi sxvadasxva dros sxvadasxva avtorTa mier ucxouridan qarTulad iqna Tar- gmnili, romlebic d. yolbaiam erTad moaqcia, waumZRvara wm. gri- gol feraZis cxovreba-moRvaweobis amsaxveli vrceli werili, daurTo mis mier varSavis mitropoliis arqivSi londonis polo- neTis biblioTekaSi gamovlenili mkvlevarTaTvis aqamde ucnobi dokumentebi, komentarebi, pirTa saZiebeli da ase erT mTlianobad qceulma uZvirfasesma gamocemam sakuTar samSobloSi daido savane. d. yolbaias mier 2014 wels gamoica wm. grigol feraZis Sro- mebis krebulis meore tomi (Kolbaia, 2014), romelSic Sesulia li- turgiuli, patrologiuri da literaturuli kvlevebi, aseve dRiurebi da qadagebebi, werilebi da poezia. gamocema saintereso naSromebis publikaciasTan erTad gamorCeulia imiTac, rom pir- velad qveyndeba wm. grigol feraZis poeturi nimuSebi. wm. grigol feraZis Sromebis d. yolbaiaseuli gamocema mniS- vnelovani SenaZenia ara marto qarTuli eklesiis istoriiT dain- teresebuli mkiTxvelisaTvis, aramed zogadad, qarTvelologiu- ri sakiTxebis mkvlevarTaTvisac. 251 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV didia d. yolbaias damsaxureba qarTuli kulturis popu- larizaciis saqmeSi. am TvalsazrisiT aRsaniSnavia misi rogorc mTargmnelobiTi saqmianoba, aseve gamokvlevebi saqarTvelos is- toriis sakiTxebze Tu qarTul-polonur urTierTobebze. mkvlevarma qarTuli mwerlobis nimuSebis polonur enaze TargmaniT farTo samecniero wreebisaTvis gaxada misawvdomi qar- Tuli sulieri kulturis mniSvnelovani monapovrebi. 1995 wels d. yolbaias mondomebiT polonurad gamoqveynda `moqceva¡ qarT- lisa¡~ (Kolbaia, 1995), romlis wyarod gamoyenebulia uZvelesad miCneuli `Zveli qarTuli agiografiuli Zeglebis~ pirvel tomSi gamoqveynebuli Satberduli redaqcia. Targmans uZRvis m. lor- TqifaniZis winasityvaoba, erTvis d. yolbaiaseuli komentarebi da Txzulebis problematikasTan dakavSirebuli bibliografia. 2011 w. mkvlevarma varSavaSi oficina olSinkas gamomcemlo- baSi gamoaqveyna qarTuli himnografiuli mwerlobis erT-erTi gamorCeuli nimuSi _ daviT aRmaSeneblis `galobani sinanulisa- nis~ polonuri Targmani (Kolbaia, 2011). Targmans safuZvlad udevs z. WavWavaZiseuli kritikuli gamocema. Targmans darTul bolo- TqmaSi ki TvalsaCinod aris warmodgenili avtoris msoflmxedve- loba, religiuri ganaTleba, saxelmwifoebrivi da sazogadoebri- vi damsaxureba. mocemulia istoriuli epoqis daxasiaTeba, romlis drosac Seiqmna qarTuli himnografiuli nimuSi, raTa sakiTxiT dainteresebuli ucxoeli specialistisaTvis naTeli gaxdes, gan- viTarebis ra safexurze idga qveyana, romlis mefem Seqmna mso- flio mwerlobis nimuSi. 2016 wels ki `galobani sinanulisani~ gamoica albrext diureriseuli graviuirebiT (Kolbaia, 2016). daviT yolbaias naSromebi imiTac aris gamorCeuli sxva did- mniSvnelovnebasTan erTad, rom mkvlevari mkiTxvels axal wya- roebs sTavazobs. amgvar siaxles warmoadgens mis mier oqsfordis universitetis bodleanis biblioTekaSi gamovlenili apokrifuli saxarebis qarTuli xelnaweris publikacia. d. yolbaia aqveynebs samecniero sazogadoebisTvis ucnobi (arasodes yofila qarTu- lad gamoqveynebuli) apokrifuli saxarebis qarTul xelnawers (Kolbaia, 2013: 43-47). d. yolbaia qarTuli sasuliero mwerlobis ZeglebTan erTad, polonur samecniero sazogadoebas acnobs saero mwerlobis nimu- Sebs. qarTuli saistorio Txzulebebis krebul `qarTlis cxovre- bidan~ dReisaTvis gamoqveynebuli aqvs sumbat daviTis Zis `cxo- vreba da uwyeba bagratonianTas~ polonuri Targmani (Kolbaia, 2012: 9-47). mkvlevars gamosacemad momzadebuli aqvs krebulSi Sesuli 252 qeTevan mania sxva Txzulebebic (`mefeTa cxovreba~, juanSeris `vaxtang gor- gaslis cxovreba~, `arCilis wameba~, `matiane qarTlisa~, `daviT aRmaSeneblis cxovreba~), romlebsac uaxloes momavalSi ixilavs dainteresebuli mkiTxveli. imisaTvis, rom polonel mkiTxvels sruli warmodgena Seeqnas qarTuli saero literaturis Sesaxeb, iseve rogorc zemoT aRniSnuli sxva gamocemebi, `qarTlis cxo- vrebis~ krebulSi Sesuli Zeglebis Targmanic aRWurvili iqneba sruli samecniero aparatiT _ winasityvaobiT, komentarebiTa da bibliografiiT. mkvlevars aseve gamosacemad momzadebuli aqvs qarTuli ha- giografiuli mwerlobis gamorCeuli Zeglis `grigol xanZTelis cxovrebis~ polonuri Targmani samecniero aparatiT _ winasi- tyvaobiT, boloTqmiT, komentariT, saZieblebiT, romelsac aseve uaxloes momavalSi ixilavs dainteresebuli mkiTxveli. d. yolbaia kidev erTi sayuradRebo gamocemis iniciatorad gvevlineba. amjerad polonuri mwerlobis saintereso nimuSs ac- nobs qarTvel specialistebs. misi TaosnobiT varSavaSi 2011 wels gamoqveynda adam mickeviCis `pan Tadeozi anu ukanaskneli Tavdasx- ma litvaSi~ qarTuli Targmani polonuridan Sesrulebuli vita- li ugrexeliZis mier. Targmani xelnaweris saxiT daculi yofila londonis poloneTis biblioTekaSi. daviT yolbaiam biblioTekis direqciis nebarTviT da xelnaweri Targmanis saavtoro uflebe- bis dacviT gamosacemad moamzada, dedanTan Sedarebuli teqsti boloTqmiT (Kolbaia, 2011). teqsts erTvis, agreTve, avtoriseuli (vitali ugrexeliZiseuli) komentarebi. mniSvnelovania daviT yolbaias damsaxureba qarTul-polo- nuri istoriuli urTierTobebis Seswavlis TvalsazrisiT. misi iniciativiT 1991 wels Camoyalibda poloneT-saqarTvelos mego- brobis sazogadoeba. 1995 wels cnobil polonel sazogado moR- vawesTan sergo yuruliSvilTan erTad daaarsa `varSavis qarTuli klubi 1920 weli~. Jurnal `pro georgiis~ specialuri gamocema miuZRvna qarTveli iunkrebis istorias poloneTis armiis sam- saxurSi 1922-1944 wlebSi (Kolbaia, 2008), romelsac uZRvis polone- Tis respublikis prezidentis lex kaCinskis winasityvaoba. SemdgomSic agrZelebs muSaobas mkvlevari qarTul-polonuri urTierTobis TvalsazrisiT. dReisaTvis specialistTa farTo wrisaTvis aris xelmisawvdomi daviT yolbaias gamokvleva 1921- 1939 ww. poloneTis qarTuli emigraciis cxovrebis Sesaxeb. naS- roms uZRvis istoriuli eqskursi qarTuli damwerlobis, Rirs- SesaniSnaobebis, saSinao da sagareo politikis Sesaxeb; mimoixi- 253 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV lavs imdroindeli saqarTvelos saSinao da sagareo urTierTobis ucnob detalebs; unikaluri fotomasaliT mkiTxvels acnobs im qarTvel emigrantebs, romlebmac saqarTveloSi wiTeli armiis Se- mosvlis Semdeg, samSoblo datoves da cxovreba poloneTs dauka- vSires. wigni `reCpospolitas frTebqveS. qarTuli emigracia po- loneTSi 1921-1939 wlebSi~, pirvelad polonur enaze 2015 wels gamoica (Kolbaia, 2015), xolo misi inglisuri da qarTuli Targmani saTauriT “Under Polish Wings.The Georgian Emigration in Poland 1921- 1939~ varSavis universitetSi poloneTis sagareo saqmeTa saminis- tros finansuri mxardaWeriT gamovida (Kolbaia, 2016) da misi pre- zentacia varSavis samitze 2016 wlis 8-9 ivliss Sedga. qarTuli kulturis popularizacias isaxavda miznad 2014 wels daviT yolbaias iniciativiT udidesi qarTveli poetis SoTa rusTavelis saiubileo TariRis aRniSvna. misi organizebiT varSa- vis universitetSi `vefxistyaosnis~ Seqmnis 825 wlisTavi aRiniSna. SoTa rusTavelis Semoqmedebas mieZRvna Jurnal `pro georgias~ specialuri nomeri (Pro Georgia, 25/2015: 299). JurnalSi gamoqveynda qarTveli da ucxoeli aRiarebuli mkvlevarebis naSromebi SoTa rusTavelis cxovrebasa da Semoqmedebaze. aRsaniSnavia, rom varS- avis universitetSi 2016 wlis 6-8 dekembers Sedga wm. grigol fe- raZis saxelobis kavkasiologTa saerTaSoriso konferencia, sadac warmodgenili iyo polonel da qarTvel mkvlevarTa gamokvlevebi qarTuli civilizaciis Sesaxeb. konferencia mieZRvna SoTa rus- Tvelis dabadebidan 850 wlisTavs. daviT yolbaia paralelurad muSaobas agrZelebs polonur- qarTul leqsikonze fonetikuri da gramatikuli TvalsazrisiT. garda samecniero moRvaweobisa, aRsaniSnavia daviT yolbaias sazogadoebrivi saqmianoba. 2016 wels man daaarsa sakuTari qarTve- lologiuri biblioTeka wm. grigol feraZis saxelobis eklesiaSi. qarTuli wignTsacavis daarseba varSavaSi did sargeblobas mou- tans iqaur qarTvelobas da qarTvelTa sulieri TavSeyris kidev erT kerad iqceva momavalSi. daviT yolbaia qarTvelologiaSi miRweuli warmatebebisa da saqarTvelo-poloneTs Soris samecniero urTierTobebis damyare- baSi Setanili wvlilisaTvis dajildoebulia sxvadasxva jildoTi: 2008, 2007 wlebSi dajildovda varSavis universitetis reqtoris jildoTi; 2009 wlis seqtemberSi airCies wm. grigol feraZis uni- versitetis sapatio doqtorad. 2010 wels dajildovda wm. grigol feraZis premiiT da erTdroulad arCeul iqna „wm. grigol feraZis saxelobis premiis~ mimniWebeli sabWos Tavmjdomared; 2013 wels 254 qeTevan mania saqarTvelos prezidentis 2 ivlisis gankargulebiT Rirsebis or- deniT; 2004 da 2014 wlebSi iv. javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis medliT. 2015 wels arCeul iqna goris saxelmwifo universitetis sapatio doqtorad. amdenad, gamorCeulia d. yolbaias damsaxureba polonuri qarTvelologiis ganviTarebasa da qarTuli kulturis populari- zaciis saqmeSi. misi uangaro samsaxuri qveynisa da qarTuli fes- vebisadmi namdvilad samagaliToa da saamayo TiToeuli qarTve- lisaTvis. literatura: 1. Feiqrishvili J., Vashakidze L., Masalebi sazgvargaretuli qartvelologiis istori- isatvis. Tsigni pirveli. Tbilisi: Universali, 2012. 2. Hymnografia Gruzińska, Kanon pokutny galobani sinanulisani króla Dawida IVBudowniczego Z języka starogruzińskiego przełożył Dawid Kol- baia.Ilustracja drzeworyty Albrechta Dürera, Warszawa, 2016. 3. Kolbaia D. Mokcewaj Kartlisaj. Nawrócenie kartlii. Ze starogruzinnskiego prezetozyti prezypisami opatrzyt Dawid Kolbaja. Wstep Mariam Lortkipan- idze. Warszawa, 1995. 4. Kolbaia D. (red.): Pro Georgia. Journal of Kartvelological Studies. Centre for EastEuropean Studies, Faculty of Oriental Studies. Warsaw: University of Warsaw, 2008 #18. 5. Kolbaia D. St. Grigol Peradze and the Beginings of Monasticism in Georgia. ProGeorgia.Journal of Kartvelological Studies. Centre for East European Studies, Faculty of Oriental Studies. Warsaw: University of Warsaw, 2009, #19. 6. Kolbaia D. Kanon pokutny.Z języka starogruzińskiego przełożył Dawid Kolbaia. Warszawa, 2011a. 7. Kolbaia D. Adam Mickevichis pan tadeozi anu ukanaskneli tavdaskhma lit- vashi. Polonuridan targmna Vitali Ugrekhelidzem. teqsti dedantan sheadara, bolotqma daurto da gamosacemad moamzada David Kolbaiam. Warshawis Universiteti: Ossolnikebis sakhelobis erovnuli instituti, 2011b. 8. Kolbaia D. Żywot i opowieści o Bagrationach, O królach Kartwelów, skąd przybyli dotegokraju, od jakiego czasu władają królestwem Kartlii, opisał Sumbat Dawitis-dze, ckhovreba da uwyeba bagratonianta, z języka starogruzińskiego przełożył i komentarzem opatrzył Dawid Kolbaia. Pro Georgia. Journal of Kartvelological Studies. Centre for East European Stud- ies, Faculty of Oriental Studies. Warsaw: University of Warsaw, 2012a, # 22. 9. Kolbaia D..Tsm. Grigol Feradze.Tkhzulebata krebuli. Tsigni pirveli. Ber- monazvnobis istoriisatvis saqartveloshi. Qartuli eklesiis udzvelesi istoria. 255 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Gamosacemad moamzada, shesavali tserili da damatebiti shenishvnebi dau- rto David Kolbaiam. Warshawa: Warshavis universiteti, 2012b. 10. Kolbaia D. Nieznana Ewangelia apokryficzna z biblioteki bodlejanskiey w Oksfordzie (ucnobi apokrifuli sakharebis qartuli khelnaweri).Pro Georgia. Journal of Kartvelological Studies. Centre for East European Studies, Fac- ulty of Oriental Studies. Warsaw: University of Warsaw., 2013, # 23. 11. Kolbaia D. Tsm. Grigol Feradze.Tkhzulebata krebuli.Tsigni meore.Tsinare bizantiuri qartuli liturgikis shesakheb.Patrologia, poezia, qadagebani.Gamo- sacemad moamzada, shesavali tserili da damatebiti shenishvnebi daurto Da- vid Kolbaiam. Warshawa: Warshavis universiteti, 2014. 12. Kolbaia D. Pod skrzydłami Rzeczypospolitej. Emigracja gruzińska w Polsce 1921-1939.Uniwersytet Warszawski, Warszawa, 2015. 13. Kolbaia D. Under Polish Wings. The Georgian Emigration in Poland 1921- 1939.University ofWarsaw; Rechpospolitas frtebqvesh.Qartuli emigracia polonetshi 1921-1939.Warshavis universiteti (inglisur da qartul enebze). Warszawa, 2016. 14. Mania K. David Kolbaia da polonuri qartvelologia. Qartuli tskarotmcodneo- ba. XV-XVI. Tbilisi: universali, 2013-2014. 15. Pro Georgia. Journal of Kartvelological Studies. Centre for East European Studies, Faculty of Oriental Studies. Warsaw: University of Warsaw, 2015, #25. 256 qeTevan mania Ketevan Mania DAVID KOLBAIA AND GEORGIAN STUDIES IN POLAND Summary The paper is about Warsaw University Professor David Kolbaia and his permanent efforts for developing of Georgian Studies outside of Georgia, namely, in Poland. Kolbaia has begun his activities since 1991. Every year Professor Kolbaia holds the scientific international conferences dedicated to the memory of St George Peradze. Georgian as well as non-Georgian experts in field of Georgian Studies (Kartvelian studies or Kartvelology) are par- ticipants of these conferences. Professor Kolbaia is an editor of the journal ProGeorgia which is the only jounal targeted on Georgian Studies issuing abroad Georgia. Professor Kolbaia has translated from Georgian into Polish and published with relevant commentaries and investigations several monuments of medieval Georgian literature and historiography. He has also translated the Polish monu- ments into Georgian promoting by this way to strengthening of Georgian-Polish cultural interrelations. Professor Kolbaia is an author of many scientific works in Polish in field of Georgian Studies published in Poland. He is one of the main initiators of establishing center for Georgian studies in Poland and also the Society of Georgian-Polish Friendship. Several times for his outstanding contribution Professor Kolbaia was awarded by the orders of honor of the Warsaw University and Ivane Javakhishvili Tbilis State University. These and aslo many other facts are displayed in present paper about Kartvelology in Poland. 257 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV socialuri da politikuri mecnierebani SOCIAL AND POLITICAL SCIENCES xaTuna amaRlobeli religiis analizi marqsis, veberisa da diurkemis SexedulebaTa SedarebiT iTvleba, rom sociologiis Camoyalibebaze didi gavlena iqo- nia me-19 saukuneSi dawyebulma industrializaciis procesma, ro- melmac evropuli sazogadoebis Zireuli gardaqmna gamoiwvia. am epoqis moazrovneebi cdilobdnen maT garSemo mimdinare cvli- lebebi aReweraT, aexsnaT da maTi meSveobiT momavalSi ganviTa- rebuli tendenciebis winaswarmetyveleba gaekeTebinaT. axsna-gan- martebebisa da Teoriebis formirebis procesSi didi mniSvneloba mieniWa religias, rogorc sazogadoebis simtkicisa da erTiano- bis erT-erT wamyvan faqtors. swored ase Caeyara safuZveli re- ligiis sociologias, romlis, rogorc mecnieruli mimdinareobis ganviTarebaSi didi roli iTamaSa sociologiis samma klasikosma _ karl marqsma, maqs veberma da emili diurkemma. karl marqsis (1818-1883) Teoriebis Camoyalibebaze mniSvnelo- vani gavlena iqonia germanelma filosofosma ludvig foierbaxma. Tavis wignSi „qristianobis arsi~, foierbaxi gaucxoebis fenomenze saubrobs. is aRniSnavs, rom religia im RirebulebaTa erTobliobas warmoadgens, romlebsac adamianebi TavianTi kulturuli ganviTare- bis konkretul etapze qmnian, magram radgan maT ar SeuZliaT sru- lad gaacnobieron istoriuli ganviTarebis es procesebi, am Rire- bulebebisa da normebis damkvidrebas RvTaebriv Zalebs miaweren. am gziT, adamianebi maT mierve Seqmnili Rirebulebebisgan gaucxovde- bian da swored es gaucxoeba aniWebs RmerTebs Zalauflebas. ase ma- galiTad, aTi mcneba Tavisi bunebiT socialuria, Tvlis foierbaxi, radgan masSi is Rirebulebebi devs, romlebic iudevelTa kultu- ruli ganviTarebisTvisaa damaxasiaTebeli (sicocxlis, sakuTrebis, kacTmoyvareobis, simarTlisa da samarTlis principebi), Tumca maTi damkvidreba RmerTTan asocirdeba da ara adamianis kulturuli gan- viTarebis gansazRvrul etapTan (religiis sociologia, 2009). marqsi iziarebs gaucxoebis foirbaxiseul fenomens da amodis ra klasobrivi uTanasworobis principebidan, aRniSnavs, rom „reli- gia xalxis opiumia~, iluziaa, radgan igi xalxs sanatreli saiqio 258 xaTuna amaRlobeli cxovrebis imeds usaxavs da mouwodebs ufro momTmeni iyvnen arse- buli socialuri uTanasworobisa da usamarTlobebisadmi (religiis sociologia, 2009). Sesabamisad, religia mTlianad ekonomikaze, ka- pitalistsa da muSas Soris arsebul urTierTobazea damokidebu- li da radgan igi kapitalisturi wyobis eqspluataciuri xasiaTis SeniRbvas cdilobs, aucilebelia misgan gavTavisufldeT. Tumca marqsis azriT, uklaso sazogadoebis damyarebasTan erTad religia TavisiT, bunebrivad gaqreba da ar iqneba misi xelovnurad moSore- bis saWiroeba, rogorc es realurad sabWoTa kavSiris dros moxda (Davie, 2006). marqsisgan gansxvavebiT, emil diurkemi (1858-1917) miiCnevs, rom religia sazogadoebis wevrebis SekavSirebas uwyobs xels. man re- ligiisa da misi funqciebis Seswavla avstraliel aborigen tomebze dakvirvebiT daiwyo, raTa religiis SedarebiT primitiuli forme- bis Semecnebis safuZvelze naTeli moefina Tanamedrove religie- bisTvisac (Berdzenishvili, 2013). Tavis wignSi „religiuri cxovrebis elementaruli formebi~ (1912), diurkemi amtkicebs, rom religiis aucilebeli atributi ara RmerTis arsebobis idea, aramed samya- roSi arsebul movlenaTa da saganTa wmindad da saerod, profanu- lad dayofaa. is iyo pirveli sociologiis klasikosebs Soris, vinc religiis ganmarteba mogvca: „religia rwmenebisa da Cveulebebis gaerTianebuli sistemaa, romelic wminda sagnebTanaa dakavSirebu- li _ sagnebTan, romlebic gancalkevebuli da akrZalulia. es rw- menebi da Cveulebebi, iseve rogorc adamianebi, vinc maT misdeven erTi moraluri Temis _ eklesiis qveS erTiandebian~ (Davie, 2006). diurkemis mixedviT, sasulieros/wmindas sazogadoebrivi xasia- Ti aqvs, radgan is, erTi mxriv, amqveyniuri movlenebisgan ganyene- bulia da akrZalviTobis Tviseba gaaCnia, xolo, meore mxriv, sayo- velTao siyvarulisa da ridis obieqtia, iseve rogorc sazogadoeba, romelic erTdroulad kontrolisa da pativiscemis wyaroa. amis sa- pirispirod, profanuli sagnebi adamianis yoveldRiur cxovrebas- Tan, kerZo interesebsa da vnebebTan asocirdeba. Sesabamisad, diur- kemisTvis wmindisa da saeros dixotomia sazogadoebrivsa da indivi- dualurs Soris arsebuli Widilisgan gamomdinareobs. eklesia ki is institutia, romelic adamianebis religiur cxovrebas awesrigebs da yoveldRiuri mZime SromiTi saqmianobis Semdeg religiuri cere- moniebisa da ritualebis meSveobiT maT gantvirTvis, mxiarulebisa da sulieri amaRlebis saSualebas aZlevs. aqedan gamomdinare, sa- kulto praqtikebs disciplinaruli, kvlavwarmoebiTi da eiforiu- li xasiaTis socialuri funqciebi gaaCnia (Berdzenishvili, 2013). 259 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV foierbaxis msgavsad, diurkemic miiCnevs, rom swored sazo- gadoeba „qmnis religias da iwvevs religiur Tayvaniscemas, igi erTdroulad RmerTicaa da morwmunec~ (Berdzenishvili, 2013: 178). saboloo jamSi, religiisgan RmerTis, rogorc wamyvani faqto- ris gamoricxviT da yvela amqveyniur saganTa sasuliero-saero dixotomiaze dayvaniT, diurkemma religia abstraqtul ideolo- giasTan gaaigiva, romelic maradiulia da yvela sazogadoebaSi erTnairi formiT vlindeba (Berdzenishvili, 2013). maqs veberi (1864-1920) religiis rolze saubrisas emijneba mar- qsis mosazrebas religiis mTlianad ekonomikaze damokidebulebis Sesaxeb da, nacvlad amisa, xazs usvams maT Soris arsebul kavSirsa da urTierTgavlenas. Tavis erT-erT yvelaze popularul naSromSi „protestantuli eTika da kapitalizmis suli~ (1904-05/1920), veberi cdilobs axsnas Tu ra gavlena iqonia protestantizmma dasavluri kapitalizmis Camoyalibebasa da ganviTarebaze da askvnis, rom pro- testantulma eTikam, romelic xazs usvamda Sromis, rogorc Rmer- Tisadmi pativiscemis gamoxatvis umTavres saSualebas da ewinaaRm- degeboda sizarmacesa da mflangvelobas iseTi cxovrebis stilis danergvas Seuwyo xeli, romelic Semdgom dasavluri, racionaluri, mogebaze orientirebuli kapitalizmis saTave gaxda. momdevno wle- bSi, veberi Tavisi kvlevis sferos mniSvnelovnad afarToebs da mso- flio religiebs Seiswavlis. Tu religia gavlenas axdens adamianis yoveldRiur cxovrebaze, fiqrobs is, maSin yovelgvari cvlileba religiur eTikaSi iwvevs cvlilebebs adamianTa cxovrebaSi, rac, Ta- vis mxriv, sociumSi arsebul sxva sferoebzec aisaxeba (Davie, 2006). Tu diurkemi miiCnevs, rom msoflio religiebi erTmaneTs wmin- disa da profanulis gamijvnis safuZvelze gvanan, veberi msgavsebis sruliad sxva moments usvams xazs _ misi azriT, nebismier sakulto praqtikas amqveyniuri miznebi aqvs (magaliTad, wvimis gamowveva, miwisZvrisgan Tavis dacva, avadmyofobis gankurneba da sxv.), rac, saboloo jamSi, religias „SefardebiT racionalurs~ xdis. veberi miiCnevs, rom dasavleTSi religiam racionalizacia ganicada, ris magaliTadac samRvdeloeba moyavs, romelic profesionalurad ganswavlulia da karieruli winsvlis SesaZlebloba eZleva. aqedan gamomdinare, mRvdlebi racionalizaciis procesis produqtebi da misi ganmaviTareblebi arian. Tumca veberi aRniSnavs, rom racio- nalizaciis sawyis etapze didi mniSvneloba winaswarmetyvelebsa da eriskacebsac eniWebaT, radgan swored maTi meSveobiT xdeba adamianebis Semokreba da erTmorwmune jgufad gaerTianeba. Semd- gom etapebze, winaswarmetyvelTa iracionaluri bunebis gamo, maTi 260 xaTuna amaRlobeli Canacvleba racionaluri, ganaTlebuli mRvdlebiT xdeba, romle- bic sazogadoebis wevrebs problemaTa gadaWris konkretul gzebs Tavazoben. veberi aRniSnavs, rom dasavleTSi religiam warmatebu- lad SeZlo Tavisi iracionaluri da racionaluri aspeqtebis erT- maneTTan SeTavseba, ris Sedegadac motivirebuli, Sromismoyvare saSualo klasi warmoSva da xeli Seuwyo kapitalizmis racionalu- ri formebiT ganviTarebas (Berdzenishvili, 2013). bolos, veberi msoflio religiebis sxvadasxva niSnis mixedviT klasifikacias axdens. pirveli, maTi samyarosadmi arsebuli damoki- debulebaa: konfucianelobisTvis damaxasiaTebelia samyaros miRe- ba, budizmisTvis _ misi uaryofa, xolo qristianoba da islami mas gamosworebis pirobiT iRebs. meore, imis gagebaa, Tu xsnis rogor gzebs gvTavazobs sxvadasxva religia. magaliTad, budizmi aRiarebs xsnas sakuTari moqmedebis safuZvelze, islami da qristianoba ki Suamavali mxsnelis meSveobiT. veberi aqac xazs usvams xsnis misaRwe- vad aqtiur qmnadobas, Sromas, rac protestantuli eTikisTvisaa damaxasiaTebeli da ramac, sabolood, dasavluri samyaros ekono- mikur winsvlas mniSvnelovnad Seuwyo xeli (Berdzenishvili, 2013). sociologiis am sami didi klasikosis naazrevis gacnobis Sem- deg naTeli xdeba, rom maTTvis religias sazogadoebis ganviTarebis procesebSi mniSvnelovani adgili uWiravs. samive maTgani aRiarebs religiis gavlenas adamianTa yoveldRiuri cxovrebis sxvadasxva as- peqtze, Tumca klasikosTa mosazrebebs Soris sayuradsaRebo gansx- vavebebic arsebobs, rac maTi zogadi Teoriuli mimarTulebebiTaa ganpirobebuli. marqsi did mniSvnelobas aniWebs bazisis _ sawarmoo Zalebisa da urTierTobebis gavlenas zednaSenze, romelic sazoga- doebrivi cxovrebis yvela sxva danarCen sferos (kultura, poli- tika, ganaTleba, sxv.) moicavs. misi azriT, warmoebiTi urTierTobebi da sawarmoo Zalebi gansazRvravs zednaSens da ara piriqiT. Sesaba- misad, ar aris gasakviri marqsis mosazreba religiis ekonomikiT gan- pirobebulobis Sesaxeb. metic, igi miiCnevs, rom klasTa Soris arse- buli konfliqtis fonze religia iluziaa, romelic kapitalistTa mier muSebze ganxorcielebuli eqspluataciisa da usamarTlobis SeniRbvas cdilobs. marqss ar eTanxmeba veberi, romelic racionali- zaciis principebidan amodis da xazs usvams religiuri eTikis wamyvan rols ekonomikuri saqmianobis ganviTarebis saqmeSi. veberis azriT, racionalurma, disciplinasa da mogebaze orientirebulma protes- tantizmma dasavluri kapitalizmis Casaxvas Seuwyo xeli. Sesabamisad, religia ar aris sazogadoebis pasiuri elementi, rogorc amas marqsi miiCnevs, aramed mas konkretuli ekonomikuri wyobis Camoyalibebaze 261 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV didi gavlena gaaCnia. diurkemi religiaze saubrisas Tavisi „socio- logizmis~ principebs eyrdnoba, romlis mixedviTac sazogadoeba in- dividze primati, masze upiratesia (Berdzenishvili, 2013). xolo religia konkretuli sociumis rogorc qmnileba, aseve misi gansaxiarebacaa _ is erTdroulad siyvarulisa da krZalvis obieqtia. marqsis, veberisa da diurkemis Teoriebs Soris arsebuli gan- sxvavebebis miuxedavad, maT Srobebma religiis mniSvnelobisa da gavlenis Sesaxeb Sedgom kvlevebs daudo saTave. Sedegad, dRei- saTvis, religiis sociologia mecnierebis damoukidebeli dargia, romlis Seswavlis saganic religiasa da sazogadoebas Soris arse- buli kavSir-urTierTobebia. literatura: 1. Berdzenishvili A. Emil diurkemis sociologia. Klasikuri sociologiuri teoriebi (p. 129-189), Tbilisi, 2013. 2. Berdzenishvili A. Maqs veberis sociologiis dziritadi principebi. Klasikuri so- ciologiuri teoriebi (p.190-266), Tbilisi, 2013. 3. Davie, G. (2006). Sociology of Religion (Edited by Segal R. A.). The Black- well Companion to the Study of Religion (pp. 171-192). Blackwell Publish- ing Ltd., 2006. 4. Religiis sociologia (2009). Modziebulia 22.10.2017: https://goo.gl/TQnd97 Khatuna Amaghlobeli ANALYSIS OF RELIGION BASED ON THOUGHTS OF MARX, WEBER AND DUKHEIM Summary The development of sociology was greatly influenced by the 19th century Industrialization, which led to fundamental transformation of European society. Thinkers of this epoch tried to describe and explain changes taking place around them and, based on these explanations, predict future tendencies. During process- es of theory formation, a significant role was given to religion as one of the lead- ing factors of society’s solidity and unity. This is how sociology of religion as a scientific field of study was emerged, the development of which is strongly linked to three classical sociologists _ Karl Marx, Max Weber and Emily Durkheim. 262 Meri Gabedava THE CHALLENGE OF CONFIDENCE-BUILDING AND RECONCILIATION PROCESS IN THE POST-CONFLICT GEORGIA One of the most significant challenges for the government of Georgia is to promote the process of reconciliation and trust building in the occupied territories of Abkhazia and South Ossetia, among the population residing beyond the lines dividing the conflict zones. Despite the fact that Georgian jurisdiction does not include those territories, Georgian government bears the responsibility to main- tain security along its administrative borders. It is actively involved in COBERM, Confidence Building Early Response Mechanism, a joint program by European Union and UNDP which supports immediate and concrete initiatives seeking to influence confidence building within and across conflict divided communities. The objective of COBERM is to strengthen an enabling environment involving conflict affected communities by addressing local needs and supporting initia- tives that foster social cohesion, peace and stability. COBERM was set up in May 2010, and implemented in two phases during 2010-2015. The third phase of COBERM was launched in January 2016 and lasted three years. In 2010 the Georgian Government developed a special “Action Plan Engagement Strategy” for confidence-building and reconciliation with Abkhazians and South Ossetians, which is fully consistent with the main principles of COBERM. The paper aims firstly to specify the definition of reconciliation and confi- dence building and then to address the achievements made in the field for the last five years. The meaning of confidence building and reconciliation remains controversial among the experts. Daniel Bar-Tal, professor of psychology at Tel Aviv University, defines reconciliation as “a psychological process for the forma- tion of lasting peace”. In this process, past rivals come to mutual recognition and acceptance, have invested interests and goals in developing peaceful relations, feel mutual trust, positive attitudes as well as sensitivity and consideration of the other party’s needs and interests. According to Bar-Tal, reconciliation is not essential in all societies but only in those that have been subjected to protracted, intractable conflict; that is, conflicts “…in which the societies involved evolve a widely shared psychological repertoire that supports the adherence to the conflic- tive goals, maintain the conflict, delegitimize the opponent and thus negate the possibility of a peaceful resolution of the conflict and prevent the development of peaceful relations” (Brouneus, 2003: 15). A leading scholar and practitioner of conflict resolution, John Paul Lederach defines reconciliation as being constituted by both “a focus and a locus”. The 263 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV focus of reconciliation is upon building new and better relationships between former enemies. Thus, relationships must be the core focus. As a locus, Lederach argues, “reconciliation represents a space, a place or location of encounter, where parties to a conflict meet.” In this place, the traumas of the past and the hopes for the future must be formulated and brought together by discussing the issues of truth, forgiveness, justice, and peace (Brouneus, 2003: 15). Some researchers argue that it is simultaneously unrealistic and impolitic to talk about the restoration of mutual trust in the aftermath of severe, brutal con- flict, when memories of the violence perpetuated by the warring groups are still fresh and the social vestiges of destruction quite visible. Under these conditions, the reconciliation process can at best promote intergroup tolerance, an attitude of live-and-let-live and the process cannot go beyond this. Second, intergroup har- mony did not always exist before the conflict; to presume so would be incorrect (Kumar, 1999). Reconciliation is never a theoretical matter, but always happens in a specific context. As every conflict and democratic settlement are different, so a process of reconciliation differs from all others in important respects, even if it shares many similarities with them. The only aspect which applies to every post-violence tran- sition is the need to address the issue of reconciliation itself (Reconciliation after Violent Conflict, 2003). To achieve the objective of confidence building and reconciliation, conflict theorists and practitioners have proposed several basic strategies around which a wide array of social reconciliation interventions can be devised and implemented. Some of them include uncovering the past, promoting dialog, broadening the understanding through media, developing grass-roots structures for Peace and designing collaborative activities (Kumar, 1999); Despite the importance of the issue, Georgian scientific literature has yet to address challenges of reconciliation. Moreover, for the last 25 years, there has been a huge amount of material that requires adequate scientific analysis. The problem of post-conflict reconciliation requires special attention in the future. The international community in the wider sense could contribute to the pro- cess of reconciliation in several ways. Firstly, it is a potential source of infor- mation, expertise and training on the issue; Secondly, the slow but inexorable development of international humanitarian and human rights law has a growing effect by setting and supporting standards in the shape of an international legal order which forms a supportive external consensus on issues such as impunity for serious human rights violations, the right to truth, the unacceptability of certain crimes and the need to bring perpetrators to justice irrespective of where their crimes were committed. However, reconciliation in post-conflict societies cannot be imported from 264 meri gabedava the outside. Foreign actors should perceive their role as one of a support and fa- cilitation of domestic policies. International experience attests that occasionally the neighboring or other countries or regions which are involved in the conflict or demand involvement in the reconciliation process greatly complicate the design of the process, or on the contrary, might contribute resources to it. According to the experts in the field, the third-party states’ long-term engagement in a conflict usually has a negative effect (Reconciliation After Violent Conflict, 2003). How to evaluate the impact of neighboring countries on the process of rec- onciliation and confidence building in Georgia? As mentioned above, on the initiative of European Union and UNDP Con- fidence Building Early Response Mechanism operates in Georgia and is mainly founded by EU itself. From 2010 to 2015 COBERM has enabled the implementa- tion of 137 initiatives that addressed all key sectors relevant for confidence build- ing: Youth education, People diplomacy, dialogue & policy research, Cultural cooperation, Women’s empowerment, Humanitarian assistance and health care, Community Mobilization, Capacity Building and others. The total amount of in- vestment in the field has reached 5.5 million euro. The attitude of the Russian Federation towards the process of reconciliation and confidence building significantly differs from that of EU and creates seri- ous impediments for it. Russia has been contributing to increased tensions and polarization between Georgia, Abkhazia and South Ossetia over the years. Rus- sian government promotes its political interests in the region with the help of the partly recognized republics of Abkhazia and South Ossetia. The territories of the conflict zones in Abkhazia and South Ossetia are not large, but quite important for Russia since it processes three military bases such as Bombora Air Base, Java and Gyumri in those areas of South Caucasus and maintains control over the Middle East. It also created the so-called state borders which physically separate the parties of a frozen conflict from one another. In addition, Georgia, Abkhazia and South Ossetia contemplate different development Strategies: the Abkhazians partially require independence, while Ossetians move towards Russia and Geor- gia seek to join the EU and NATO. After the annexation of the Crimea in the end of 2014, Russia signed an agreement on alliance and strategic partnership with Abkhazia and an agreement on “Alliance and Integration” with the de facto government of South Ossetia in March 2015. In fact, these documents enabled the Kremlin to carry out the an- nexation of Abkhazia and South Ossetia and establish a complete military control over the territories. The construction of a military town in Gali, at the Georgian-Abkhazian administrative border began in 2016. This town will be base for the Russian troops, as well as a residence complex for the officers and their families. It will be governed 265 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV by military administration with the special regulations and a special permit will be required to enter the town which means further restrictions for internally displaced people crossing the administrative border. During the Soviet Union times there were similar cities in Georgia near the Georgian-Turkish border, Akhaltsikhe and Akhalkalaki that marked the border between two rival blocks: NATO and Warsaw Pact. The strict Russian policy in Abkhazia makes virtually impossible the process of confidence-building and reconciliation between Abkhazians and Georgians. As mentioned above, Georgian government implements the policy of re- conciliation and confidence building according to the “Action Plan Engagement Strategy”. The action plan includes four dimensions, humanitarian, human, so- cial, and economic and aims at improving the welfare of the population of Abkha- zia and the Tskhinvali Region and bringing them closer to the rest of the popula- tion of Georgia. The Humanitarian Dimension implies humanitarian assistance in case of the need, for example, during natural disasters. The Human Dimension includes: intercommunity relations, preservation of cultural heritage and identity, unhindered access to information, human rights and youth activities. The Social Dimension targets education, health and environment, while the Economic Di- mension covers trade, joint production, communication and infrastructure devel- opment. As one might notice, this document is based entirely on trust building and reconciliation theory and practice. The Humanitarian Dimension means meeting the primary requirements for food, shelter, medical supplies, transportation, and so on. Since Russia does not allow Georgia to render humanitarian assistance to the population of Abkhazia, this dimension is enabled to meet its objectives. The only exception is free power supply for the population of Gali District. The Enguri Hydroelectric Power Sta- tion, which remains one of the biggest in the South Caucasus, was built in the 1960-70es in Georgia. The Georgian Government has been providing the Abkhaz with hydroelectric power from the Enguri Statition free of charge since 2014, while Abkhazia buys the rest of the power from Russia. The Georgian Authori- ties are strongly criticized by the opposition, which believes that the government acts against the Georgian interests as the electric power is continuously used for Russia’s military bases. The Human Dimension refers to the following activities and initiatives: par- ticipation in the weddings, birthday parties, funerals, religious ceremonies, visits to cemeteries; promotion of visits of mixed families; support of pilgrimages and visits of cultural and historical nature; professional exchange of journalists and other professions; promotion of joint cultural and sporting activities; search for missing persons, transfer of mortal remains and exchange of prisoners. Only few activities work effectively in this dimension: participation in funerals, search for 266 meri gabedava missing persons, transfer of mortal remains and exchange of prisoners. De facto authorities temporarily close Abkhaz and South Ossetian adminis- trative borders during religious holidays and the Georgians living on the opposite sides are not allowed to visit graves of their relatives. About Thousand and Eight Hundred people went missing during war in Abkhazia including eight hundred soldiers and about one thousand civilians. During last 25 years over 260 mortal remains, mainly of the soldiers, were transferred from Abkhazia under the aus- pices of the Committee of the International Red Cross. Especially noteworthy in human dimension is the promotion of youth activi- ties. Abkhaz young people actively participate with their Georgian counterparts in international events, workshops, exhibitions, conferences, but they can only meet on neutral territory. There is only one professional program for journalists under which the Georgian and Abkhazian journalists come together on neutral territory once a year. Georgian side holds important events in order to preserve cultural heritage and identity of the Abkhaz. Georgian Constitution declares the Abkhazian as an official language and IDP schools and universities are enabled to teach Abkhazian language. Our government promotes the development of the archives in Abkhazia. Many copies of historical documents have been generated and transferred to the Abkhaz side. However, enthusiasm of the government of Georgia is not shared by that of Abkhazia. The young generation of Abkhazians is raised in a way that promotes an enemy image of Georgians. Russian propaganda, including the mass media, does its best not to give opportunity to Georgian and Abkhaz sides to develop their own attitudes to each other independently with- out Russian interference which succeeded in creating enemy image of Georgians “The occupier”, “The Conqueror” and so on. At the same time the mistakes made at different times, starting from the Soviet period, also greatly contributed to the strengthening of hostile attitudes. Ethnic Georgians live in extremely harsh conditions in Abkhazia. Approxi- mately fifty thousand people voluntarily returned to Abkhazia after the war. Vol- untary repatriation was caused by the difficult social and economic conditions in which they found themselves during internal displacement. Ethnic Georgians are devoid of political rights, their right to vote and their freedom of movement are also restricted. Georgian language is banned from public use and from schools and universities. Although ethnic Georgians’ rights are violated, due to Russia’s decision there are no international organizations (the UN and OSCE) operating on the occupied territories that could provide protection of human rights for eth- nic Georgians. Russia facilitates the deliberate destruction of Georgian cultural monuments including the Georgian inscriptions which are erased and Georgian libraries which are frequently destroyed, etc. These actions can be described briefly as 267 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV cultural genocide. All attempts of the Georgian Government at Geneva peace talks aimed at engaging foreign experts in preservation of Georgian cultural heritage in Abkhazia have failed. Such a hostile approach greatly complicates the process of reconciliation and confidence-building. The Social Dimension: education, health and environment. A joint EU-UNDP (United Nations Development Program) initiative is an important breakthrough in the educational dimension. It aims to build confidence between Georgian and Abkhaz academics by establishing contacts and collabo- ration in the field of peace studies and promoting peace education in the Abkhaz State University (ASU). Specific objectives of the project are to build contacts and collaboration between academics of CU, ASU and European universities; develop the resource base for peace education in ASU and design four new under- graduate curriculum, including the topics of peace education at ASU. The Abkhaz enjoy Georgian medical services completely free of charge. ID card issued by the Abkhaz authorities is enough to get free treatment. Number of Abkhaz patients admitted and treated in Georgian medical establishments is on rise. Also, there is a special referral program for Ethnic Abkhaz. Hepatitis C Elimination Program, TB Management as well as HIV program finance Abkha- zians’ as well as Ossetians’ expenses on the occupied territories. The Abkhaz and South Ossetians receive medical assistance anonymously. According to the official statistics, approximately 43 thousand residents of Ab- khazia obtained medical treatment from the year 2012 to 2015. Georgian govern- ment allocated more than 3 million Georgian Lari to this program in 2014. Medi- cal assistance for the population of Ossetia and Abkhazia is also implemented under the “National project on referral treatment”. Official statistics indicate that in total about 4,3 million Lari has been spent on the treatment in 2012-2015 (http://netgazeti.ge/news/41297/). Russian government is actively working towards replacing Georgian health program. In August 2017 during the visit of the president of Russia, the parties signed the agreement on a mandatory involvement of Russian citizens perma- nently residing in Abkhazia in the medical insurance program. Citizens of Russia living in Abkhazia will receive full specialized and high quality medical assis- tance in any Russian medical institution, primarily in Krasnodar. The project aims firstly to foster and accelerate Abkhazians’ declaration of Russian citizenship, while on the other hand, to alienate Abkhazians from Geor- gian health program by offering the alternative medical assistance. The cooperation on the protection of environment has proved to be success- ful. Buxuscolchica (an endangered bush) saving measures implemented jointly in 2016 with the support of UNDP yielded significant results. However, there has been no progress in the field of education so far. The Georgian children are not 268 meri gabedava allowed to receive education in their mother language. Nonetheless, the social dimension is an area which is the most effective in restoration of trust between Abkhaz and Georgians. The Economic Dimension covers trade, joint production, communication, infrastructure development. In 2008, few months before the August War, former President M. Saakash- vili offered Abkhaz side to create a huge free international economic zone under the control of Georgian Government and de facto Abkhaz Government, but the proposal was rejected by the Abkhaz. Today de facto government has its own pro- posal regarding free economic zone, but the proposal is not supported by Russia. Abkhazia’s budget is financed by Russia, and the region is completely economi- cally dependent on Russia. The only functioning segment of the Economic Dimension is trade, which remains weak, involves only small businesses and has no significant impact on development of the Georgian-Abkhaz economic ties. To summarize, one might argue that Russia continues to create serious ob- stacles to the process of confidence building and reconciliation between the Geor- gian and Abkhaz. As for an occupant, the restoration of trust between the former enemies is politically disadvantageous for Russia. After the approval of visa liberalization for Georgia by The European Parlia- ment, occupation regime authorities have further tightened measures to restrict people’s freedom of movement across the administrative border. Russian policy in Abkhazia and South Ossetia once again points to the Kremlin’s desire to im- pede Abkhazians and Ossestians’ reconciliation with Georgia and simultaneously secure Russia’s positions in the South Caucasus. Literature: 1. Brouneus Karen, Reconciliation – Theory and Practice for Development Cooperation, September, 2003. 2. Kumar Krishna, Promoting Social Reconciliation In Postconflict Societies. Selected Lessons From USAID’s Experience, USAID Program and Opera- tions Assessment Report No. 24, Center for Development Information and Evaluation U.S. Agency for International Development, January 1999. 3. Reconciliation After Violent Conflict. A Handbook. Editors: David Bloom- field, Teresa Barnes, and Luc Huyse, International Institute for Democracy and Electoral Assistance, 2003. 4. Samedicino dakhmareba gaukhmaureblobis dacvit afkhazi pacientebistvis, (http://netgazeti.ge/news/41297/). 269 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV meri gabedava ndobis aRdgenisa da Serigebis procesis gamowvevebi postkonfliqtur saqarTveloSi reziume upirve le sad unda aRv niS no evro kav Si ris roli afxaze Ti sa da e.w. samx reT oseTis konf liq tis mowes ri ge ba Si. evro kav Si ri war moad gens mniSv ne lo van donor sa da poli ti kur moTa ma Ses, rome lic dain te re se bu lia mis sazRv reb ze stabi lu ro bi Ta da keTil dReo biT. saqar T ve los xeli suf le bis mier Semu Sa ve bu lia axle bu ri midgo ma saqar T ve los iurisdiq ci is qveS myofi, saqar T ve los ga nuyo fe li nawi le bis _ afxaze Ti sa da cxinva lis regi o nis mimarT, romlis miza nia okupi re bu li regi o ne bis mosax le o bas Tan daax loe ba, maTi keTil dRe o bis gaum jo be se bis, izola ci is Semci re bis, pirov ne bis da regi o nu li usafr Txo e bis dacvis mizniT. samwu xa rod, qarT ve leb sa da afxazebs, qarT ve leb sa da osebs Soris ndo bis aRd ge na sa da Seri ge bas mniSv ne lov nad uSlis xels ruse Tis faqto ri, rome lic 25 welze metia xels uwyobs xalxebs Soris pola ri za ci as da daZa bu lo bis zrdas. amis gamo efeqtu rad ver xorci el de ba `CarTu lo bis strate gi is samoq me do gegmis~ prog ramu li ganzo mi le be bi. 270 jandri zarandia, irma maxaraSvili ekonomika ECONOMICS jandri zarandia, irma maxaraSvili kidev erTxel klasteruli menejmentis Sesaxeb ganviTarebis Tanamedrove etapze TvalsaCino gaxda qveynebis ekonomikebis radikaluri transformacia. globalizaciis Sedegad warmoebis faqtorebi ufro mobilurebi gaxdnen, gaZlierda konku- rencia, gaqra bevri tradiciuli dargi da gaCnda axali dargTaSori- si struqturebi. ramac dasabami misca axal qselur struqturebs- klasterebs. TerTmet qveyanaSi moqmedi klasteruli sistemebis gamocdilebis Seswavlam saSualeba misca „gaeros samrewvelo gan- viTarebis organizaciis~ (UNIDO-s) specialistebs, SeemuSavebinaT instituciuri politikis ganzogadebuli koncefcia,* romelic mi- marTuli iqneboda qseluri samewarmeo kavSirebis mxardasaWerad. sawarmoTa klasterebi, rogorc wesi, yalibdeba programebis farglebSi Semdegi sami subieqtidan erT-erTis iniciativiT, esenia: _ sakuTriv mcire sawarmoebi; _ xelisuflebis adgilobrivi organoebi; _ msxvili korporaciebi; termini klasteri inglisuridan iTargmneba, rogorc: 1) mte- vani; 2) jgufi; 3)koncentracia; 4) Tavmoyra. klasteri - es mxolod terminia klasteruli analizis ins- trumentariumidan, romlis ganviTarebas Tvals adevnebdnen XX saukunis Suaxanebidan. mas iyeneben im sferoebSi, sadac Tavmo- yrilia pirveladi monacemebis uzarmazari masivi. meTodi Tavda- pirvelad, 1939 wels, aRwera r. trionma. manve uwoda am meTods klasteruli analizi. sawarmoTa klasterebi cariel adgilze ar warmoqmnila. biz- nesis organizaciis aratradiciuli formebis upiratesobebis Sesaxeb ideebi warmoiSva sakmaod didi xnis win. am sferoSi erT- erTi yvelaze adreuli gamokvleva iyo alfred marSalis naSromi `ekonomikis principebi~, romelSic man Seiswavla didi britane- Tis samrewvelo raionebi. Tavis kvlevaSi mas ar Semoaqvs specia- luri terminebi `lokalizebuli warmoebisTvis~ an `samrewvelo zonebisTvis~, Tumca aRweridan gamomdinareobs, rom igulisxmeba klasteri, sakmaod Rrma firmaTaSorisi Sromis ganawilebiT. * `gaeros samrewvelo ganviTarebis organizacia~ (UNIDO)http://www.unido.ru/ 271 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV qveynis an regi o nis konku ren tu na ri a no bis da sawar mo Ta klas tere bis ganvi Ta re bis xaris xis urTi er T kav Si ris dawv ri le bi Ti anali zi mogv ca m. porter ma. porte ri gansazR v ravs klasters, rogorc `geog ra fi u lad mezob lad myof urTi er T da kav Si re bul kompa ni a Ta jgufs da masTan dakav Si re bul orga ni za ci ebs, romle bic moqme de ben gark ve ul sfero Si da xasi aT de bi an saqmi a no bis er Tia no biT, amasTa na ve avse ben erT ma neTs~. am gansazR v ra Si aqcen ti keTde ba sawar mos klaste re bis sam Ziri Tad Tvise ba ze: 1. geog ra fi u li loka li za ci a. porte ris mixed viT, klaste ris masS ta bi SeiZ le ba vari reb des erTi qala qi dan an regi o ni dan qvey namde an ramde ni me qveynam dec ki. 2. urTi er T kav Si ri sawar mo ebs Soris. porte ri aRniS nav da rom klaste ri aris urTi er T da kav Si re bu li sawar mo e bis qselis forma da kavSi ris ufro Rrma ganvi Ta re ba mowmobs Tavad klaste ris gan viTa re bis xaris x ze. 3. darge bis teqno lo gi u ri urTi er T kav Si ri. klaster Si arse bobs teqno lo gi u rad urTi er T da kav Si re bu li sxvadas x va dargis sawar mo e bi. Cveu leb riv, es mza produq tis kompa ni e bi a; warmo e bis speci a li ze bu li faqto re bis, kompo nen te bis, manqa ne bis mimwo deb lebi, agreT ve servi su li momsa xu re bis; finan su ri ins ti tu te bi; Tanm x le bi produq te bis mwarmo eb le bi da sxv. regi o nu li soci a lu ri sivr ce _ regi o nu li soci a lu ri da eko nomi ku ri strati fi ka ci a. rusu li warmo So bis ameri kel ma soci o log ma piter soro kin ma gaa na li za ekono mi ku ri strati fi ka ci a, romlis cvlile ba dro Si, aRwe ra termin `fluqtu a ci is~ daxma re biT. mdgoma re o ba da Se mosa va li icv le ba droSi. fluqtu a cia xorci el de ba ciklu rad, gamdid re bas mosdevs gaRa ri be ba. pata ra cikle bia 3-5, 7-8 weli, saSu a lo _ 10-12 weli, didi _ 40-60 weli. misi Teo ria uaryof da kacob ri o bis progre sis ideas, ekono mi ku ri mdgoma re o bis mudmiv gaum jo be se bas. gaanalizebulia biznes Sre, romelic iyofa sam Semosavli an kategoriad: 1) mewarmeebi, binznes menejerebi da TviTdar wmunebulebi; 2) naxevrad mewarmeebi da menejer-Tanamflobe lebi; 3) klasikuri menejerebi. msoflioSi yvelaze cnobili mkvlevari qveynebis da regionebis konkurentunarianobis dar gSi aris m. porteri. Tavis koncefciaSi man scada erTmaneTis Tvis Seexamebina a. marSalis neoklasikuri ekonomikuri Te oria firmaTa saqmianobis sagareo ekonomikur TeoriasTan. porterma amocanad daisaxa im siRrmiseuli Zalebis gamovlena, romlebic gavlenas axdendnen qveynis konkurentunarianobaze. misi 272 jandri zarandia, irma maxaraSvili Teoriis mTavari postulatebi iyo mtkicebebi: `erovnuli ayvave ba memkvidreobiT ar gadadis _ igi iqmneba~ da `erovnul doneze konkurentunarianobis erTaderTi gonivruli koncefcia _ es Sro mis mwarmoeblurobaa~. amgvarad, porterma qveyanaSi Sromis maRali mwarmoebluroba gautola mis maRalkonkurentunarianobas. Sromis mwarmoeblurobis donis mudmivi zrdisTvis aucilebelia inovaci aTa gamogonebis mudmivi procesi da maTi danergva warmoebaSi. ma Rali inovaciuri potenciali _ es mniSvnelovani wanamZRvaria qvey nis mosaxleobis keTildReobis misaRwevad. amasTan, porteri gamo yofs or cnebas: inovaciasa da samecniero aRmoCenas (gamogoneba). porteris kvlevaTa mTavari Sedegi gaxda konkurentuli upira tesobebis rombis Seqmna; igi Sedgeba 4 determinantisgan, romlebic gansazRvravs qveynis konkurentunarianobas msoflio meurneobaSi: I _ piro be bi warmo e bis faqto re bis T vis; II _ moTxovnis mdgoma re o ba; III _ mona Te sa ve da mxardam We ri darge bi; IV _ mdgradi strate gi a, struqtu ra da meto qe o ba. konku ren tu li upira te so be bis 4 deter mi nan t ze gavle nas ax dens 2 damo u ki de be li Zala: `mTavro ba~ da `SemTx ve va~ . mTavro bas, porte ris mixed viT, wamy va ni roli ekisre ba qveynis konku ren tu li upira te so be bis Seqm na Si. `mTavro bis adekva tu ri roli niSnavs, rom igi gamo di o des kata li za to ris da axlis maZi eblis rolSi~. SemTx ve va agreT ve aranak leb mniSv ne lo van rols asru lebs qveynis konku ren tu na ri a no bis gansazR v ra Si, amasTan am faqto ris marT va praqti ku lad SeuZ le be li a. maT mie kuT v ne ba omebi, xanZ re bi, stiqi u ri ubedu re be bi da a.S. maga li Tad, imis wyalo biT, rom aSS-s meo re msoflio omis dros Tavs ar daes xnen, am qveya nam mi iRo konku ren tu li upira te so ba sxva qveyneb Tan Seda re biT. igi ve SeiZ le ba iTq vas Sei ca ri a sa da SvedeT ze, romleb mac 1939-1945 wlebSi Sei nar Cu nes neit ra li te ti. `klaste ri - esaa `geog ra fi u lad mosazR v re urTi er T da kav Si rebu li kompa ni e bis jgufi da masTan dakav Si re bu li orga ni za ci e bi, romle bic moqme de ben gark ve ul sfero Si da xasi aT de bi an saqmi a no bis erTi a no biT amasTan avse ben erT ma neTs~. eris ganvi Ta re bis oTxi stadi is koncef cia porters ekuTv nis, romlis Tanax ma dac, saxel m wi fo gadis konku ren tu na ri a no bis ganvi Ta re bis oTx stadi as: 1. konku ren cia warmo e bis faqto re bis safuZ vel ze (qveyne bi mosax le o bis erT sulze daba li Semo savliT); 2. konku ren cia inves ti ci e bis safuZ vel ze (qveyne bi erT sul mosax le ze saSu a lo Semo sav liT); 3. konku ren cia inova ci e bis 273 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV safuZ vel ze (qveyne bi cxovre bis maRa li doniT); 4. konku ren cia simdid ris safuZ vel ze. m. enra i ti m. porte ris uaxlo e si mimde va ri a. m. enra i tis naSro mebi gamo ir Ce va kvlevis ufro didi geog ra fi u lo biT, vidre por teris. m. enra i tis mTava ri amoca naa konku ren tu li upira te so bis geog ra fi u li maSta bis gamok v le va. igi vara u dob da, rom konku ren tuli upira te so ba iqm ne ba ara zena ci o na lur an naci o na lur done ze, aramed regi o nul done ze, sadac mTavar rols asru lebs regi o ne bis ganvi Ta re bis isto ri u li wanam ZR v re bi, bizne sis warmo e bis kultu ra Ta mraval fe rov ne ba, warmo e bis orga ni za cia da ganaT le bis miRe ba. amg va rad, enra i ti mivi da dask v nam de, rom arse bobs regi o nu li klaste re bi. regi o nu li klaste ri _ es samrew ve lo klaste ri a, romel Sic klaste ris firma wevre bi imyo fe bi an erT ma neT Tan ge ogra fi ul siax lo ve Si. an regi o nu li klaste ri _ es im firma Ta geog ra fi u li aglo me ra ci a a, romle bic muSa o ben meur ne o bis erT an ramde ni me mona Te sa ve darg Si. mcire qveyneb Si klaste ri za ci is proble me bis kvleva Ta mimo xil vi sas, SeiZ le ba gamov yoT 4 tipis klaste ri Tavi si geog ra fi u li daxa si a Te biT: 1. erovnu li klaste re bi _ sivrcis gareSe momijnave konkuren tunariani dargebi, romlebic ZiriTadad gamoyofilia lokaliza ciis koeficientisa da sauwyebaTaSoriso balansis meTodikiT; 2. regi o nu li klaste re bi, romle bic mdeba re obs regi o nis farg leb Si da gamo yo fi lia gamo kiTx ve bis an saeq s per to Sefa se bebis daxma re biT; 3. trans sa sazR v ro klaste re bi viTar de ba ori da meti qveynis regi o neb Si; 4. loka lu ri klaste re bi mdeba re obs erT qalaq Si; maT agreT ve mie kuT v ne ba norve gi a Si gamo yo fi li `samrew ve lo rai o ne bi~. klaste re bis gamo yo fis Semdeg SeiZ le ba daviwyoT klaste ru li poli ti kis gata re ba qveynis konku ren tu na ri a no bis asamaR leb lad. dResdRe o biT gamo yo fen ori Tao bis klaste rul poli ti kas: pirve li Tao bis klaste ru li poli ti ka Tavis Ta vad zome bis komp leq si a, romel sac axorci e lebs saxel m wi fo klaste ris inden tifi ka ci is T vis; meo re Tao bis klaste ru li poli ti ka efuZne ba ukve karg cod nas qveyna Si arse bul klaste reb ze. igi gulis x mobs indi vi du a lur midgo mas TiTo e u li klaste ris ganvi Ta re bis proble mis mimarT. enra i ti gamo yofs klaste ru li poli ti kis 4 sxvadas x va tips, romle bic gans x vav de ba erT ma ne Tis gan saxel m wi fos roliT misi gata re bi sas: 1. kata li za to ru li klaste ru li poli ti ka, 274 jandri zarandia, irma maxaraSvili 2. mxardam We ri klaste ru li poli ti ka, 3. direq ti u li klaste ru li poli ti ka, 4. inter ven ci o na lis tu ri klaste ru li poli ti ka klaste ru li poli ti kis gata re bis inici a to re bad SeiZ le ba ga movid nen ara marto marT vis cent ra lu ri orga no e bi, romle bic atare ben klaste rul poli ti kas `zemo dan~, aramed regi o nu li xe lisuf le bac an mewar me Ta adgi lob ri vi gaer Ti a ne be bi, romle bic `qvemo dan~ warmo g vid gens klaste re bis ganvi Ta re bis stimu li re bis progra ma Ta rea li za ci as. aseT progra mebs ewode ba klaste ru li inici a ti va. klaste rul inici a ti va Ta ganvi Ta re bas Tan dakav Si rebiT ganvi Ta re ba daiwyo: klaste rul ma konsal tin g ma (momsa xu re bis gawe va regi o nis teri to ri a ze rome li me klaste ris gamo yo fis proeq t Tan dakav Sire biT, agreT ve klaste ru li inici a ti ve bis marT vis Teo ri u li safuZ v le bis swavle ba warma te bu li klaste ru li proeq te bis gasa RebTa meTo dis gamo ye ne biT). klaste ru li menej men t ma (klaste re bis marT vis conda Ta siste ma). anali ti kos ma, axalze lan di el ma a. fuksk. uiliam s ma, warmo ad gina klaste ru li inici a ti vis mene je ris moqme de bis sqema, rome lic Sedge ba 12 etapis gan: 1. regi on Si klaste ris arse bo bis marTe bu lo bis axs na; 2. klaste ris inden ti fi ka ci a; 3. sawyisi anali zi; 4. gundis formi re ba; 5. sasur ve li Sede gis gansazR v ra; 6. sasur ve li Sede gis misaR we vad gegmis Sedge na; 7. gada u de be li moqme de be bis T vis gegmis Sedge na; 8. klaste ru li inici a ti vis dawyeba; klasteri drosa da sivrceSi paralelurad viTardeba, gansa kuTrebiT mniSvnelovania misi sivrciTi Sefaseba da is Tu, rogo ria sivrciTi mocemuloba. swored, amis safuZvelze SesaZlebelia moxdes klasterebis seleqcia _ regi o nul da rai o nul klaste re bad . 1. imere Ti _ regi o nu li turis tul - rek re a ci u li klaste ri: 2. mcxeTa- m Ti a ne Ti _ turis tul - rek re a ci u li da niSan dob li vad guda u ris samTo- saTxi la mu ro klaste ri. 3. kaxe Tis regi o nu li samrew ve lo klaste ri (Rvinis warmo e ba); 4. kaxe Tis regi on Si SesaZ le be lia TuSe Tis tradi ci u li dar gis klaste ri za ci a, aseve samrew ve lo da turis tul - rek re a ci u li klaste ris gamo yo fa; 5. Sida qarT lis regi o nu li soflis meur ne o bis da kvebis mrewve lo bis klaste ri; 275 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 6. Wia Tu ra- zes ta fo nis rai nu li samrew ve lo klaste ri (manga numis mopo ve a- war mo e ba); 7. quTa i sis rai o nu li sagan ma naT leb lo klaste ri, rome lic poten ci u rad uzrun vel yofs dasav leT saqar T ve los inte leq tu a luri da Sromi Ti resur se biT; 8. samcxe- ja va xe Tis regi on Si, borjo mi- waR ve ri- ce mi- ba ku ri a nis samTo- k li ma tu ri klaste ri; 9. Tbili sis saga re ub no zolis: wyneTi -oq ro ya na- Sin di si- wav kisi da sxva rekre a ci u li klaste ri; 10. bolni sis samrew ve lo rai o nu li klaste ri; 11. Savi zRvis sana pi ro regi o nu li turis tul - rek re a ci u li klaste ri; 12. maRal m Ti a ni regi o ne bis T vis samTo- saTxi la mu ro turiz mis regi o nu li klaste ri, ase maga li Tad aWaris maRal m Ti a ni regi o nis samTo- saTxi la mu ri klaste ri; 13. saqarTvelos dacul teritoriebSi erovnuli parkebis klas terizacia. q. Tbili sis Sarde nis quCa misi mimde ba re teri to ri iT gada iq ca adgi lad, sadac firme bis T vis sarfi a ni gaxda kultu ru li da ga sarTo bi dawe re bu le bis gaxs na. aq Tavmoy ri lia kafe e bi, disko Te ke bi, restor ne bi, saga mo fe no darba ze bi muze u mi (qarvas la) mxatv re bi sa da diza i ne re bis salo ne bi da sxvadas x va konfe ren ci is reli gi u ri da wese bu le bi. yvela am obieqts saer To proble ma aqvs ekolo gi as Tan, produq ci is, momsa xu re bis miwo de bas Tan da axasi a Tebs xelsay re li satran s por to mdeba re o ba Tu gamoC n de ba inici a to ri, rome lic Ses Tava zebs mepat ro nebs am adgi lis gadaq ce vas kultu ru li dasve ne bis yvela ze sau ke Te so adgi lad q. Tbilis Si da mepat ro ne e bi SeTan x m debi an koo pe ra ci a ze, maSin ukve SeiZ le ba lapa ra ki rea lur mikrok laster ze. kulturaTa klasterizacia. kultu re bis gans x va ve ba Ta mraval fe rov ne bam mkvleva re bi miiy va na klaste re bis - q vey ne bis (kul ture bis) erTob lo bis _ agebis ideam de. klaste reb Si gaer Ti a ne bu lia im qveyne bis kultu re bi romel Tac msgavsi Tvise be bi aqvs. erT -er Ti amg va ri klasi fi ka cia wamo a ye nes ioenma da Senkar ma, maT gamoy ves: 1. skandi na vi u ri klaste ri 2. germa nu li klaste ri 3. ing li su re no va ni klaste ri 4. roma nu li klaste ri 5. laTi no a me ri ku li klaste ri 6. Sore u li aRmo sav le Tis klaste ri 7. arabu li klaste ri 8. axlo -aR mo sav le Ti Turqe Ti, sabeZ ne Ti, irani. 276 jandri zarandia, irma maxaraSvili klaste ri za ci i saT vis gamo ye ne bu liq na xuTi ganzo mi le ba: in divi du a liz mi, speci a luri urTi er To be bi, univer sa liz mi, neit ralu ri kultu re bi, miRwe vi Ti kultu re bi. holan di el ma mecni er ma f. trompe na ar s ma agreT ve klaste re bad dayo is qveyne bi, romleb Sic tarde bo da gamok v le ve bi. g. hofs te des mona ce me bis mixed viT evro pis kultu ru li mra valfe rov ne ba vlinde ba ind q se bis mniSv ne lo ba Ta mimob ne va Si. es indeq se bia 1) Zala uf le bis distan ci a, 2) indi vi du a liz mis da ko leqti viz mis Tana far do ba, 3) mama ka cu ro bis da qalu ro bis Tana fardo ba 4) gaur k vev lo bis Tavi dan acile ba. man 1 da 4 indeq se bis meSve o biT gamo yo saor ga ni za cio kultu ris oTxi mode li: 1. soflis baza ri _ Zala uf le bis daba li distan cia da gaur k vevlo bis Tavi dan acile bis daba li xaris xi. 2. Seze Ti li manqa na _ Zala uf le bis daba li distan cia da gaur kvev lo bis Tavi dan acile bis maRa li xaris xi. 3. ojaxi _ Zala uf le bis maRa li distan cia da gaur k vev lo bis Tavi dan acile bis daba li xaris xi. 4. adami an Ta pira mi da _ Zala uf le bis maRa li distan cia da ga urk vev lo bis Tavi dan acile bis maRa li xaris xi. mecni e ri, romel sac miiC ne ven eTno met ri is mimar Tu le bis fu Zemdeb lad, aris holan di e li mecni e ri girt hofs te de; romel mac gasu li sau ku nis 70-ian wlebSi Caa ta ra kros- kul tu ru li proeq ti. mis mier Sedge ni li anke tis meSve o biT testi re ba Cau tar da LBM kompa ni is 100 aTasa ze met Tanam S ro mels, is muSa ob da aRniS nu li firmis fsiqo lo gi u ri samsa xu ris ufro sad. ilias univer si tet ma kargi saqme gaa ke Ta da qarTu lad Targ m na g. hofs te des naSro mi, rome lic gamo vi da 2007 wels `kultu re bi da orga ni za ci e bi~. ga suli sau ku nis bolos sxvadas x va qveyneb Si mecni e reb ma yuradRe ba gaa max vi les menej men tis princi pe bis siste mur da Seda re biT anal zze. Seda re bi Ti menej men ti (kroskul tu ru li) gulis x mobs biz nesis erovnu li Tavi se bu re be bis Seswav las. Sesa ba mi sad saqmi a ni kultu ra warmo ad gens bizne sis proces Si princi pe bis, tradi ci e bis da qcevi Ti stere o ti pe bis erTob lo bas. lite ra tu ra: 1. Baratashvili E., Faresashvili N., Abralava T., Biznesis martvis klasteruli politika. Tbilisi, 2012. 2. Baratashvili E., Nadareishvili N., Dzidzikashvili N. Kklasterizaciis teoriuli safudzvlebi da mati danergvis tsinapirobebi. Jurnali Saqartvelos Ekonomika, #9, №10, 2007. 277 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 3. Gagnidze I. Klasterebis roli saqartvelos ekonomikis ganvitarebashi, Jurnali Ekonomika da Biznesi, №3, Tbilisi, 2008. 4. Klastery konkurentnosposobnosni (http //subcontract.ru) Jandri Zarandia, Irma Makharashvili ONCE MORE ABOUT CLUSTER MANAGEMENT Summary At current stage of development the new inter-sector structures have emerged inducing formation of the new network structures _ clusters. Porter defines clus- ter as “geographical proximate group of interconnected companies and associ- ated institutions in a particular field, linked by commonalities and externalities”. In this definition the emphasis is made on three key characteristics of a cluster: geographical localization, mutual connection of the companies and technological links between the sectors. M. Enright distinguishes regional clusters _ this is geographical agglom- eration of the firms working in the same or related economic sectors. Based on overview of the clustering problems in small countries 4 types of clusters can be distinguished: national clusters, regional clusters, trans-border clusters and local clusters. There are 4 different types of cluster policies depending on the role of the state in their implementation. Cluster develops simultaneously in time and space and on this bases selection of clustering into regional and district clusters. Based on the mentioned principle the authors specify 13 regional and district clusters in the territory of Georgia. In their opinion, Chardin Street in Tbilisi, together with adjacent territory could be regarded as real micro-cluster. Based on the cultural differences the researchers came to the idea of the set of clusters _ countries (cultures) with similar characteristics. The clusters unify the cultures of the countries with similar qualities. Dutch scientist F. Trompenaars divided into clusters the countries where the studies were conducted. In 70s of the past century Geert Hofstede implement the cross-cultural project. Cross-cultural management implies studying of the national characteristics of business. Hence, business culture is the set of principles, traditions and behavior stereotypes in the process of conducting of business. 278 pedagogika da meTodika PEDAGOGY AND METHODOLOGY jemal jinjixaZe maTematikis gakveTilebze esTetikuri aRzrdis sakiTxisaTvis esTetika (< berZ. aisthētigos grZnoba, grZnobiTi aRqma, SegrZneba) filosofiis dargia, romelic arkvevs xelovnebisa da mSvenierebis bunebas, Rirebulebasa da sazriss. esTetikuri aRzrda ki sinamd vilisadmi adamianis esTetikuri mimarTebis formirebis mizanmi marTuli procesia; es is procesia, romelic emsaxureba moswavlis esTetikuri emocionalur-grZnobiTi da faseulobiTi Segnebis Ca moyalibebasa da ganviTarebas; igi pirovnebis kulturis erT-erTi universaluri aspeqtia, romelic xelovnebisa da realobis mraval saxovani esTetikuri obieqtebisa da movlenebis gavleniT uzrun velyofs mis socialur da fsiqikur zrdasa da ganviTarebas. rogorc Cans, moswav le Ta aRz r di saT vis esTe ti ku ri wyaro e bi unda veZe boT yvelgan, sadac ki es iqne ba SesaZ le be li. moswav lis esTe ti ku ri aRz r da saer Tod, da kerZod _ maTe ma tikis gakve Ti leb ze, Cveni RvTaeb ri vi peda go gi u ri miza ni a. Cvens sinam d vi le Si ki, maTe ma ti kis swavle bis meTo di kis mTeli isto ri is manZil ze, Zali an didi xnis ganmav lo ba Si, maTe ma ti kis gakve Ti lebze esTe ti ku ri aRz r dis Sesa xeb fiqric ki warmo ud ge ne li iyo. peda go gi ka Si gamo yo fi li hqondaT esTe ti ku ri ciklis sagne bi, rogo ri ca a: simRe ra, xatva, Zerw va, cekva da sxv., maTTan mier Te buli iyo huma ni ta ru li saswav lo sagne bi, da maT rigSi, ra Tqma unda, ar Sedi o da mecni e re ba, miT umetes _ maTe ma ti ka, es zusti da mkacrad abs t raq tu li feno me ni. rusul, da, Sesa ba mi sad, qar Tul meTo di ka Si gaba to ne bu li iyo azri, rom maTe ma ti kas esTe ti kur aRz r das Tan arafe ri esaqme bo da. sinam d vi le Si saqme sruli ad sawi na aR m de go daa (Jinjikhadze, 2011). maTe ma ti kis swavle bis meSve o biT moswav le Ta esTe ti kur aRz rda ze fiqris win, maswav leb lis ganwyo bis Sesaq m ne lad, gvinda ga vixse noT geni a lur adami an Ta zena ar sam de aRze ve bu li azre bi imis Sesa xeb, Tu ra aris maTe ma ti ka, rogo ria am madli a ni mecni e re bis amamaR le be li da aRma ze ve be li mara di u li fasda u de be li fase u lobe bi (Jinjikhadze, 2009) ... 279 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV jer erTi, rao den aRmaf r To va ne be lia sime on deni pua so nis sityve bi: cxovre bas alama zebs ori ram: pirve li is, rom SegiZ lia maTe ma ti ka iswav lo; meo re is, rom SegiZ lia maTe ma ti ka aswav lo! meo re, _ ras warmo ad gens maTe ma ti ka? leon brilu e ni _ `maTe ma ti kur saxe eb Si aris poe tu ri Tvise bebi~. kons tan ti ne gamsa xur dia _ `maTe ma ti ka namd vi li, didi rangis poe zi a a~. karl vai er S t ra si _ `ar SeiZ le ba iyo maTe ma ti ko si, Tu ara xar sulSi poe ti~. leo pold krone ke ri _ `maTe ma ti ko si ver iqne ba is, vinc poe ti ar aris~. norbert vine ri _ `rogorc mxatv ri sa da kompo zi to ris, ise maTe ma ti ko sis Semoq me de bi Ti aqtis saer To maxa si a Te bel Ta Ziri Tadi para met ria swrafva sila ma zis idea le bi sa ken~. ernst eduar kume ri _ `uCve u lo sila ma ze sufevs maTe ma ti kis sauf lo Si~. ivan lepe xi ni _ `maTe ma ti ka dia di da mSveni e ri a, da ar SeiZ le ba ar dava fa soT misi namd vi li sila ma ze, misi poe zi a~. avgust ferdi nand mebi u si _ `maTe ma ti ka Si iseve a, rogorc ferwe ra Si an poe zi a Si~. plato ni _ `maTe ma ti kis Seswav la gvaax lo ebs ukv dav RmerTeb Tan~. alf red prins ha i mi _ `namd vi li maTe ma ti ko si yovel T vis didi mxatva ri a, arqi teq to ri an poe tic ki~. lazar imanu el fuksi _ `maTe ma ti ka saswa u leb ri vi pei za Ji a, gadaS li li yvelas Tvalwin, visT vi sac azrov ne ba warmo ad gens namd vil sixa ruls~. Jozef Jan batist furie _ `maTe ma ti ka warmog vid ge ba adami a nuri sulis Zlie re bad~. gotf ri harold hardi _ `maTe ma ti ko si, rogorc mxatva ri an poe ti, qmnis uzorebs, da es uzore bi Tu ufro dRegr Ze li a, es mxolod imitom, rom isini moqso vi lia idee bi sa gan~. gior gi niko la Ze _ `yove li axali kano ni an Teo re ma jer usa Tuod intu i ci u rad unda gavi goT, geo met ri u lad unda vigr Z noT misi aucileb lo ba~. flori ka kimpa ni _ `roca maTe ma ti ku ri amoca nis amoxs na miRe buli a, misi struqtu ra araiS vi a Tad sunT qavs sila ma ziT, rome lic zemoq me debs gone ba sa da sulze, msgavsad klasi ku ri simfo niis bgere bi sa~. 280 jemal jinjixaZe blez paska li _ `WeSma ri te ba efuZne ba `gulis logi kas~. aleqsandr puSki ni _ `STago ne ba isevea saWi ro poe zi a Si, ro gorc geo met ri a Si~. maqs eive _ `maTe ma ti ka Si aranak le bi logi ka da sila ma ze a, vid re Wadrak Si~. niko lai Jukov s ki _ `maTe ma ti kas, msgavsad ferwe ri sa da musi kisa, Tavi si sila ma ze gaaC ni a~. jeims jozef silves t ri _ `musi ka _ grZnoba Ta maTe ma ti ka a, xo lo maTe ma ti ka _ gone bis musi ka~. oleg gucu li a ki _ `musi ka maTe ma ti kis intu i ci a a~. albert ainS ta i ni _ `maTe ma ti ka da musi ka moiTxovs erT g va ro van azrov ne biT process~. albert ainS ta i ni _ `maTe ma ti ka idee bis logi kis poe zi a a~. iohan keple ri _ `maTe ma ti ka samya ros sila ma zis wina sa xe a~. bert ran rase li _ `kargad gage bu li maTe ma ti ka flobs ara marto WeSma ri te bas, aramed umaRles sila ma ze sac, sila ma zes civ sa da mkacrs, msgavsad qanda ke bi sa..., sila ma zes umaRle si siwmin di sa, daxve wi li srulyo fi le bi sa, rome lic mxolod zeaR ze ve bu li xelov ne bis T vi saa misaw v do mi~. pol lokxar di _ `qveya na ze arafe ria iseTi saoc ne bo da poe turi, iseTi radi ka lu ri, feTqe ba di da fsiqoq me di Ti, rogo ric maTe ma ti ka~. ilia vekua _ `maTe ma ti ka samec ni e ro Semoq me de bi sa da bune bis sai dum lo e beb Si SeRwe vis umZ lav re si iaraRi a~. aseTi gamo naT q va me bi uamra via kidev. maSa sa da me, Cvens wina Se dgeba marad axalgaz r da da marad uk vda vi peda go gi u ri proble ma: jer Cven TviTon davi na xoT da aR viqvaT maTe ma ti ka Si es RvTaeb ri vi sila ma ze, Sevig r Z noT misi sur nele ba da Semdeg vaswav loT maTe ma ti ka, aRv zar doT moswav lis pirov ne ba esTe ti ku rad, mis sulSi sinaT lis, siTbo sa da siyva ru lis Seta niT. esTe ti ku ri aRq mis fsiqo lo gi u ri Tavi se bu re ba ni cnobi li a, rom obieq tis esTe ti kur aRq ma Si mona wi le obs pi rovne bis yvela fsiqi ku ri proce si: Segr Z ne ba, aRq ma, warmod ge na, warmo sax va, azrov ne ba, nebis yo fa, emoci e bi da sxv. 6-12 wlis asa kis moswav le Ta fsiqi ka Si ukve uxvad arse bobs iseTi poli fo ni uri mimar Te be bi, buneb ri vi (gene ti ku ri da sxv.) unari, rome lic vlinde ba pirov ne bi sa da xelov ne bis Tu sxva esTe ti kur sagan Ta 281 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV urTi er T q me de bis aqt Si da srulad gviSlis win pirov ne bis cno bie re ba Si msofl m xed ve lo bis, mora lur - z ne ob ri vi Tvise be bis, Se moqme de bi Ti unare bis formi re bis umdid res SesaZ leb lo bebs. esTe ti ku ri obieq tis aRq mis fsiqo lo gi u ri meqa niz mi warmo adgens gansa kuT re bul siste mas, romel Sic Sedis, erTis mxriv, pirov ne bis afeqtur - moTxov ni le bi Ti struqtu re bi, romle bic gamo xa tu lia moTxovni le beb Si, midre ki le beb Si, inte re seb Si, ide aleb Si da sxv., rac siste mis sakuT riv dina mi kur nawils warmo ad gens, meo res mxriv, _ pirov ne bis opera ci o na lu ri struqtu re bi, iseTi fsiqi ku ri proce se bi, rogo ri ca a: Segr Z ne ba, aRq ma, warmod gena, warmo sax va, azrov ne ba da sxv. am fsiqo lo gi u ri maqa niz mis Siga sis te mu ri mimar Te be bi damo kide bu lia moswav lis asakze, mis indi vi du a lur - ti po lo gi ur pa ramet reb ze, misi mxatv ru li ganvi Ta re bu lo bis done ze, mis cno bie re ba Si ukve formi re bul warmod ge na Ta samya ros simdid re ze da sxva Tavi se bu re beb ze. pirov ne bis fase u lo bi Ti orien ta ci e bi ganpi ro be bu lia adrin de li soci a lu ri gamoc di le biT, ojaxu ri aRz r diT, skolam de li da sasko lo ganaT le biT, yvela saSu a le biT miRe bu li infor ma ci iT. aseTi orien ta ci e bi daiy va ne ba gansazR v rul fase u lo biT -es Te ti kur norma ti ve bam de, esTe ti ku ri gemov nebis krite ri u me bam de. esTe ti kur aRq mas Tan dakav Si re bu li opera ci o na lu ri struq ture bis ganvi Ta re ba neit ra lu ri ar rCeba esTe ti kur moTxovni leba Ta doni sa da xasi a Tis mimarT. ferTa danax vis, musi ka lu ri smenis, da sxva misTa na Ta sfero Si gaZli e re bu li unare bi, rac qm- nis Semoq me de biT warmo sax vas, esTe ti kur fase u lo ba Ta sfero Si unda daetyos pirov ne bis moTxovna Ta da inte res Ta kultu ras. Tavis mxriv, Semoq me de bi Ti warmo sax va da azrov ne ba damo ki de bu lia indi vi dis senso ru li orga ni za ci is ganvi Ta re ba ze. orga niz mis senso ru li apara ti _ es `Sesas v le li~ WiSka ri a, romlis gavli Tac adami a ni aRiqvams gare sam ya ros saRe ba ve bi sa da forme bis, bgere bi sa da surne le ba Ta mTel simdid re sa da saxes x vao bebs. xelov ne bis samya ros Tan srulyo fi li urTi er To ba adami anur aRq ma zea damo ki de bu li. feris, formis, obieq te bis kompo zi ciu ri urTi er T m de ba re o bis dasru le bu lo bi sa da wonas wo ro bis, propor ci is grZnoba da mrava li sxva _ orga niz mis senso rul Se saZleb lo ba Ta mTeli es poten ci a li esTe ti kur obieq t Tan srul faso va ni Sexved ris aucile be li piro ba a. senso rul araam T vi seb lo bas, sinam d vi li sa da mxatv ru li na warmo e be bis grZnobad -es Te ti ku ri aRq mis teqni ki sa da kultu ris 282 jemal jinjixaZe arqo nas sabo loo jamSi mivya varT esTe ti ku ri efeqtis ngrevam de. ai, rato maa ase mniSv ne lo va ni moswav le Ta senso ru li grZnobe bis ganvi Ta re ba jer kidev umc ro si sasko lo asaki dan, SesaZ lo a, uf ro adri da nac. amaSi dagvex ma re ba sasko lo sagne bi, pirvel rigSi _ esTe ti ku ri mimar Tu le bi sa ni. magram grZnobi Ti aRq mis momen ti mxolod pirve li aucile be li biZgia ufro rTuli saqmi a no bis ga moRvi Ze bi saT vis. rogorc viciT, Semec ne bis gza Segr Z ne be bi dan da aRq me bi dan abs t raq tu li azrov ne bi sa ken midis da mTavr de ba praqti kiT. ase, rom, grZnobi Ti Semec ne ba aerTi a nebs yvela fsiqi kur process, romle bic warmo i So ba sagan Ta uSua lo zemoq me de biT da gavle nas axde nen moswav le Ta grZnobe bis orga no eb ze. aRq mis formebs Soris arse bobs forma, rome lic friad mniS vne lo va nia swored xelov ne bis qmnile ba Ta grZnobi Ti Semec ne bis proce si saT vis. igi xasi aT de ba ufro meti aqti vo biT, orga ni ze bu lobiT, gaaz re bu lo bi Ta da Semoq me de bi Ti xasi a TiT, vidre aRq mis sxva forme bi. es aris dakvir ve ba. dakvir ve bis saxes x va o be bi konk re tul amoca neb zea damo ki de buli: dakvir ve ba SeiZ le ba orien ti re bu li iyos sagnis zogad da winas war gacno ba ze, im mizniT, rom amocno bil iqnas es saga ni da gamo yo fil iqnas misi arse bi Ti niSne bi. dakvir ve ba SeiZ le ba orien ti re bu li iyos sagnis arse bi Ti data le bi sa da zogi er Ti mxare e bis gamo yo fa ze. dakvir ve ba SeiZ le ba orien ti re bu li iyos sagne bis an mov lena Ta sxvadas x va etapebs Soris msgavse ba Ta da gans x va ve ba Ta dadge na ze. dakvir ve bam SeiZ le ba moiTxo vos nebis yo fis mniSv ne lo va ni Zalva, daJi ne ba da didi moTmi ne ba. es Tvise be bi moswav le eb Si aR zr das saWi ro ebs, miT umetes _ umc ros k la se leb Si. moswav le eb Si dakvir ve bis kultu ris aRz r dis mizniT aucile be lia goniv ru lad siste mu ri da siste ma tu ri muSa o ba (Jinjikhadze, 2012b). umc ros k la sel Ta zogi er Ti Tavi se bu re ba bavS vis esTe ti kur mimar Te ba Ta sfero Zalze farToa da praqti kulad igi mTel mis msofl Seg r Z no bas afera debs. am asakis bavS vebs, Ziri Ta dad, sjeraT, rom cxovre ba Seqm ni lia sixa ru lis T vis. bavS vis mimar Te ba sinam d vi li sad mi gameS ve o bi Te bu li a. es ki, Tavis mxriv, iw vevs mis esTe ti kur mimar Te ba Ta zeda pi ru lo bas. marTa lia, bavS vi 283 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV advi lad aRmo a Cens samya ros rogorc xali si ans, mSveni ers, moZravs, fere bi Ta da bgere biT savses, rogorc erT m T li ans, rome lic Seqm nilia misi survi le bis Sesas ru leb lad, magram igi jer kidev Rrmad ver aRwevs mSveni e re bis ars Si. samya ros konk re tul - zRap ru li da fera do va ni aRq mis miu xeda vad, umc ros sasko lo asakSi axali valde bu le be bi da axali pasu xis m geb lo ba amza debs xaris xob riv naxtoms bavS vis cnobi e reba Si: mkveTrad icv le ba skolam de lis Cveu li samya ros viwro CarCo e bi, xdeba adrin del fase u lo ba Ta gada fa se ba: Zveli forma ivse ba axali Sina ar siT. da es garda ma va li proce se bi mimdi na re obs esTe ti kur mimar Te ba Ta sfero Sic. dadebiTi gardaqmnebis mTeli rigis miuxedavad, am asakSi bav Svis pirovnul ganviTarebaSi xelisSemSlelia mravali uaryofiTi mxarec. umcrosklaselis aRqmisa da azrovnebis metismeti Tvalsa Cinoeba ara marto gansazRvravs saxeTa agebis fotografiulobasa da difuziurobas, mis fragmentarulobas, aramed ukargavs mos wavles imas, rasac uwodeben sagnisadmi an movlenisadmi pirovnul mimarTebas. magram, Tu gaviTvaliswinebT asakobriv-fsiqologiur TaviseburebaTa kanonzomierebebs da vizrunebT moswavlis esTeti kuri aRzrdilobis donis amaRlebaze, maSin bavSvis, rogorc pirov nebis, ganviTarebis sistemurobaSi warmatebas advilad mivaRwevT. uaRre sad mniSv ne lo va nia Semde gi gare mo e bac: meo ce sau ku nis 60-ia ni wlebis bolos ameri kel ma nei rof si qo logma profe sor ma rojer uolkot sperim (1913-1954) speci a lu ri kvleve bis Sede gad Seqm na Tavis tvinis naxe var s fe ro e bis funq ci ona lu ri asimet ri is Teo ri a, romlis Tanax ma dac irk ve va, rom es naxe var s fe ro e bi Tavi anT erTi a no ba Si damo u ki deb lo ba sac flo ben. es Teo ria medi ci nis sfero Si Seiq m na, magram misi gamo ye ne ba swavle bis meTo di ka Si uaRre sad mniSv ne lo va ni a, miT umetes _ ma Tema ti kis. speris Teo ri is Tanax mad arse bobs ori naxe var s fe ros funq ci ona lu ri orga ni za ci is ramde ni me tipi: domi ni rebs marcxe na naxe var s fe ro _ Semec ne bi Ti proce se bis sityvi er - lo gi ku ri xasi a Ti (marcxe na na xe var s fe ru li adami a nebi). domi ni rebs marj ve na naxe var s fe ro _ konk re tul - xa to va ni azrov ne ba, ganvi Ta re bu li warmo sax va (marj ve na na xe var s fe ru li adami a ne bi). arc erTis domi ni re ba mkveTrad gamo xa tu li ar aris _ (tolna xe var s fe ru li adami a ne bi). 284 jemal jinjixaZe speris kvleve bis Tanax mad: 3-7 wlis bavS vebs rogorc arane bis mi e ri, ise nebis mi e ri yu radRebis situ a ci a Si uaqti ur de ba upira te sad marj ve na naxe var sfe ro, 8-9 wlis moswav le eb Si marj ve na naxe var s fe ro friad aqti u ri a, 10-dan 14 wlamde izr de ba marcxe na naxe var s fe ros aqti u ro ba. ufro konk re tu lad: 3 wlis asaki dan gaaq ti u re bas iwyebs marj ve na naxe var s fe ro, wina planze iwevs Tvalsa Ci no- xa to va ni azrov ne ba. 6-10 wlebis asaki saT vis Tvalsa Ci no- xa to va ni azrov ne ba ma xasi a Te be li xdeba, 10-12 wlebis asaki saT vis Tvalsa Ci no- xa to va ni azrov ne ba wamy va ni xdeba. 10-dan 14 wlamde izr de ba marcxe na naxe var s fe ros aqti u ro ba. 12 wlis asaki dan marcxe na naxe var s fe ro domi nan ti xdeba. es grafi ku lad ase gamo i yu re ba: amasTan, Tu speris kvlevebs gaviT va lis wi nebT, aRsa niS na vi a, rom V-VI klaseb Si maTe ma ti kis swavle bis Tvalsaz ri siT marj ve na- da marcxe na na xe var s fe ro el moswav le Ta zoga di daxa si a Te ba aseTi a: 1. moswav le eb Tan muSa o bis piro be bi marj ve ni saT vis: saxe e bi; konteq s ti; infor ma ci is kavSi ri praq tikas Tan, rea lo bas Tan; Semoq me de bi Ti dava le be bi; eqs pe ri men te bi; musi ka lu ri foni; metyve le bi Ti da musi ka lu ri ritmi. 285 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV marcxe ni saT vis: teqno lo gi e bi; deta le bi; infor ma ci is mowo debis abs t raq tu li, wrfivi stili; saswav lo masa lis mraval je radi game o re ba; siCu me gakve Til ze. 2. moti va ci is formi re ba marj ve ni saT vis: avto ri te tis mopo ve ba; koleq tiv Si mdgoma reo bis presti Ju lo ba; axali kontaq te bis damya re ba; saqmi a no bis soci a lu ri mniSv ne lov ne ba. marcxe ni saT vis: swrafva damo u ki deb lo bis ken; codnis siRr me; goneb ri vi saqmi a no bis maRa li moTxovni le ba; moTxovni le ba ga naTle ba Si. 3. masa lis aRq ma marj ve ni saT vis: erT m T li a ni, Cqari, myisi e ri; gamok ve Ti lia mety vele bis into na ci u ri mxare; bavS ve bi vizu a lis te bia (mxedve lo bi Ti). marcxe ni saT vis: disk re tu li (nawil -nawil), neli, Tana mim dev ruli; gamok ve Ti lia metyve le bis azrob ri vi mxare; bavS ve bi audi alis te bia (smeni Ti). 4. dife ren ci re bu li midgo mis meTo de bi marj ve ni saT vis: sinTe zi; droi Ti dava le be bi; muSa o ba jgufSi; Teo re me bis formu li re ba; sivr ci Ti kavSi re biT operi re ba; dava lebe bi naxa teb Si; muSa obs geo met ria (sivr ci Ti azrov ne ba); sqeme bi, cxrile bi; sura Te bi. marcxe ni saT vis: anali zi; drois ga re Se dava le be bi; muSa o ba calke u lad; Teo re me bis damt ki ce ba; niSne biT operi re ba sibr tyeze; dava le be bi simbo lo eb Si; muSa obs algeb ra (Tana mim dev ru li logi ku ri azrov ne ba sibr tye ze); mraval je ra di game o re ba. Tvalsa Ci no- xa to van azrov ne ba ze pasu xis m ge be lia Tavis tvinis marj ve na naxe var s fe ro, xolo abs t raq tul - lo gi kur azrov ne ba ze pasuxs agebs Tavis tvinis marcxe na naxe var s fe ro. amasTan, Tvalsa Cino- xa to va ni mexsi e re bis siCqa rea 60 ± 5 biti wamSi. Seda re bi saT vis _ abs t raq tu li mexsi e re bis siCqa rea 7 ± 2 biti wamSi. isic sa inte re so a, rom maTe ma ti ku ri wese bi sa da teqs tu ri maTe ma ti ku ri amoca ne bis amoxs nis damax sov re bi saT vis IV-VI klase bis moswav le Ta 30 % sargeb lobs upira te sad xato va ni azrov ne biT, 25 % _ upi rate sad Tana mim dev rul - lo gi ku riT, xolo 45 % _ iyenebs orive naxe var s fe ros (Jinjikhadze, 2011). maSasadame, maTematikis silamazisa da xelovnebasTan maTemati kis kavSiris Cveneba iwyeba sami wlis asakidan, magram saamisod yve laze noyieri niadagi 11-12 wlis asakia. aq mimdinareobs xatovani azrovnebis intensiuri ganviTareba. Tu es niadagi sworadaa gamo yenebuli, maSin zeda klasebSi yvelaferi Tavis adgilze dadgeba. 286 jemal jinjixaZe ziareba saxviT xelovnebas moswav le Ta mxatv ru li aRq mis ganvi Ta re ba yvela maswav leb lis keTil So bi lu ri mova le o ba a, radga nac swored maszea damo ki de bu li moswav le Ta xato va ni azrov ne bis ganvi Ta re ba, romlis gare Sec logi kur abs t raq tul azrov ne ba ze gadas v la yovlad SeuZ le be lia. xato va ni azrov ne bis dros iqm ne ba konk re tu li saxe e bi, rom lebic Tanda Ta no biT abs t raq tul xato van saxe eb Si izr de bi an da bade ben abs t raq tul logi kur saxe ebs. es erTi a ni proce si a, ro melic erTi a ni cnobi e re bis aRze ve bul ganvi Ta re bas gana pi ro bebs. da azrov ne bis saxe Ta am ierarqi a Si Tavi si gansa kuT re bu li adgi li uWiravs farwe ras, qanda ke bas, musi kas, poe zi as, maTe ma ti kas. galak ti o nis sworu po va ri striqo ne bi `me Zlier miyvars iisfer Tovlis qalwu le bi viT xidi dan fena~ abs t raq tu li xato va ni saxe e bis mTeli samya roa da es samya ro Zali an axlos enaTe sa ve ba rogorc musi ka lur, ise maTe ma ti kur abs t raq tul saxe ebs. swored amitom, didi mniSv ne lo ba aqvs Cvens sapa tio mizans: va zia roT moswav le e bi xelov ne bas, mis ukv dav qmnile bebs. mxatv ru li aRq mis ganvi Ta re ba moi cavs Semde gi Ziri Ta di sas wavlo amoca ne bis amoxs nas: xelov ne bis qmnile bis mimarT gulis x mi e re bis gamo Ce nis unaris ganvi Ta re ba. xelov ne bis qmnile bis mimarT saku Ta ri mimar Te bis gamo xat vis unaris ganvi Ta re ba. xelov ne bis Sesa xeb codni sa da warmod ge na Ta mocu lo bis gafar To e ba. dawyebi Ti skolis moswav le ebs gaaC ni aT xelov ne bis qmnile beb ze emoci o na lu ri gamox ma u re bis SesaZ leb lo be bi, magram es SesaZ leblo be bi unare bad jer kidev araa formi re bu li. amito ma a, rom daba li klase bis moswav le e bis STabeW di le be bi daiy va ne ba sityveb ze: `momwons~, `ar momwons~, `lama zi a~, `ar aris lama zi~. aucile be li a, mivdi oT xelov ne bas Tan Sexved ri sa da misi gac nobis gansa kuT re bul meTo di kas, rome lic orien ti re bu lia mos wavle Ta mier mxatv ru li aRq mis Sede gad miRe bu li STabeW di le be bis Sesa xeb saku Ta ri azre bi sa da ganc de bis gamo xat vis xerxe bis ganvi Ta re ba ze. am meTo di kis amoca ne bi a: ganva vi Ta roT moswav le eb Si xelov ne bis qmnile ba Ta Sesa xeb gamom xat ve lo bi Ti saSu a le be bis gamo ye ne biT Txrobis unari. 287 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ganva vi Ta roT xelov ne bis sfero Si moswav le Ta azrov ne bis unari, rom urTi er To beb Si SeZlon gamo xa ton saku Ta ri azre bi xelov ne bis qmnile ba Ta Sesa xeb. amisaT vis saWi roa moswav lis mier mxatv ru li aRq mis proce sis orga ni ze ba. vaswav loT moswav le ebs, xelov ne bis qmnile ba Ta Sesa xeb sa ubri sas gamo i ye non saku Ta ri adrin de li mxatv ru li gamoc di le ba, rome lic miRe bu lia dakvir ve bis Sede gad. ganva vi Ta roT moswav le eb Si xelov ne bis sxvadas x va saxe e bi dan analo gi ur qmnile ba Ta Seda re ba- Se pi ris pi re bis unare bi. rom elemen ta ru lad grZnobd nen maT zogad kavSi rebs. mxatv ru li aRq mis proces Si vaswav loT moswav le ebs `gra fiku li metyve le ba~, e. i. vaswav loT xelov ne bis qmnile ba Ta Sesa xeb STabeW di le ba Ta gadmo ce ma gamo sax ve bis gamo ye ne biT (swrafi mona xa ze bi mexsi e re bis mixed viT). am meTods pirda pi ri mimar Te ba aqvs xato va ni azrov ne bis, xato va ni mxedve lo bi Ti mexsi e re bis, aR qme bis reaq ci e bis simar dis ganvi Ta re bas Tan. es amoca ne bi gadawy ve tas pou lobs xelov ne bis gakve Ti leb ze, sadac moswav le ferwe ris, qanda ke bis, musi kis, poe zi is sila ma ze Si pou lobs saer To abs t raq tul xato van saxe ebs. amis Semdeg, Zneli ar aris aseTi saxe e bis SemC ne va maTe ma ti kis sila ma ze Si. imisaTvis, rom efeqturi iyos aseTi gakveTili, aucilebelia saCvenebel nawarmoebTa raodenobisa da moswavleTa mier maTi aR qmis SesaZleblobebis swori gaTvaliswineba. saCvenebel nawarmoeb Ta raodenoba gakveTilze ar SeiZleba iyos zustad saWiroze me ti. es moswavleTa mxedvelobiT STabeWdilebebs gadatvirTavs; arc naklebi SeiZleba iyos, radganac mosalodneli efeqti Semcirdeba. maSasadame, saWiroa optimaluri raodenobis SerCeva, rom optima luri iyos xelovnebis emocionaluri zemoqmedebis Zala. es opti maluroba damokidebulia moswavleTa momzadebis doneze, maT gan wyobaze da sxv. e. i. aq maswavleblis SemoqmedebiToba friad mniSv nelovania. gamocdilebidan cnobilia, rom aseTi raodenoba saSua lod aris 3-4. uaRresad mniSvnelovania am mxriv maswavleblis mier kiTxvaTa sistemis swori SerCeva. maszea damokidebuli gakveTilis mTeli efeqturoba. kiTxvaTa sistema ise unda iyos SerCeuli, rom faqtobrivad man marTos moswavleTa cnobierebaSi mxatvruli sa xeebis Seqmnis procesi, uzrunvelyos am mxatvrul saxeebSi sagan TaSorisi kavSirebi. maswavlebelma unda gaiTvaliswinos, rom um crosklaselis azrovnebis yovelgvari Tavisebureba mdgomareobs imaSi, rom xelovnebis qmnilebebze moswavleTa sruli metyvele biTi reaqciebi SeiZleba warmoiSvas mxolod maswavleblis kiTxvis 288 jemal jinjixaZe gavleniT, Torem xelovnebis qmnilebaTa damoukidebeli gacnobisas es reaqciebi uRimRamoa an metwilad arc ki warmoiSoba. kiTxvebis, maTi xasiaTisa da Tanamimdevrobis SerCeva damokidebulia moswav leTa asakze, gakveTilis amocanebze da im ganwyobaze, romelic sas wavlo garemoSia Seqmnili. maSasadame, xelovnebis qmnilebaTa aRqma moswavleTa mier unda warmoadgendes inteleqtualur da emoci onalur-SemoqmedebiT saqmianobas, am procesSi unda mimdinareob des azrovnebis xatovani komponentebis rTuli urTierTqmedeba. albert ainStainis sityvebiT _ xelovneba yvelaze rTuli azrebis gamoxatvaa yvelaze martivi xerxiT. maTematikis silamaze maTematika yvela mecnierebis mefea, sibrZnis simbolo. maTema tikis silamaze ki mecnierebisa da xelovnebis urTierTdakavSire bisa da silamazis Semecnebis unikaluri saSualebaa. silamaze mra valwaxnagovani da mravalsaxovania. igi gamoxatavs samyaros agebu lebis uzenaes mizanSewonilobas, adasturebs universalurobas im maTematikuri kanonzomierebebisa, romlebic erTnairad efeqturad moqmedeben kristalebSic, cocxal organizmebSic, atomebSic, sam yaroSic, xelovnebis qmnilebebSica da mecnierul aRmoCenebSic. bert ran rase li ambob da: `maTe ma ti ka ze swor Sexe du le bas miv yavarT ara ubra lod WeSma ri te bam de, aramed mivya varT srulyo fil sila ma zem de, rome lic civia da mkacri, rogorc qanda ke ba; rome lic acile bu lia adami a nur sisus te ebs; rome lic mokle bu lia ferwe ri sa da musi kis RvlarW nil fandebs; _ mivya varT dia di krista lu ro bis sila ma zem de, rome lic xelov ne baT gan umaRle sis srulyo fi le bas warmo ad gens. masTan Sexe ba aRuwe re li aRf r To va neba a, eqs ta zi a, rome lic gvaTa vi suf lebs miwi e ri, warma va li ada mia nu ri garsi sa gan da Seda re ba dia mxolod poe zi as Tan~. maTematikis esTetikuri silamazis maxasiaTeblebad gamoyofen: erT m T li a no bas mraval sa xe o ba Si, mecni e rul WeSma ri te ba Ta sazo ga do o bas, aracxadi WeSma ri te bis mopo ve bas, romlis Sesa xeb vara u di damt ki ce bas saWi ro ebs, garda amisa, maTe ma ti ku ri sila ma zis gamov li ne bad Tvlian: ricxve bis harmo ni u lo bas, geo met ri ul formebs, algeb rul struqtu rebs, geo met ri ul gamom xat ve lo bas, 289 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV maTe ma ti ku ri formu le bis simwyob re sa da gamar Tu lo bas, maTe ma ti ku ri amoca nis amoxs nis SesaZ leb lo bas sxvadas x va, erTis Sexed viT, sruli ad mou lod ne li, xerxiT, maTe ma ti kur mtkice ba Ta elegan tu ro ba sa da moxde ni lo bas, maTe ma ti kur gamo ye ne ba Ta simdid res, maTe ma ti ku ri meTo de bis univer sa lu ro bas. ra Tqma unda, SeiZleba maTematika CavTvaloT (da zogi Tvlis kidec) arasaintereso, rTul, mosawyen, mSral sagnad, magram, Tu masSi aris silamazis elementebi, maSin am silamazes yuradRebis miqveva unda. maSasadame, maTematikis aRqmaSi yuradRebis roli udidesia, sxvanairad rogor SeiZleba maTematikiT gatacebaze sa ubari. gamodis, rom Zalze didia maswavleblis roli maTematiki sadmi moswavlis swori mimarTebis aRzrdis saqmeSi. maswavlebelma maTematika unda aswavlos ara rogorc mxolod mecniereba an mec nierebis safuZvlebi, aramed, agreTve, rogorc romeliRac xelov neba, romelic lamazia, esTetikuria, mSvenieria, yovlismomcvelia, radganac saskolo kursis yvela saganTan aqvs gansakuTrebuli kav Siri. amitom maTematikis esTetikis Tema da misi umdidresi sagan TaSorisi kavSirebi yovelTvis, swavlebis yvela safexurze, fri ad aqtualuria. magram, samwuxarod, Cvens skolebSi gakveTileb ze maTematikis esTetikuri aRqmis ganviTarebaze ar mimdinareobs sistematuri muSaoba, xolo klasgareSe muSaoba an saerTod ar aris, an aqcentirebulia programis calkeuli Temebis siRrmiseul Seswavlaze. friad aqtualuri unda iyos maTematikis gakveTilis esTetika, maTematikis silamazis demonstraciis Tema. Tavisi mniS vneloba aqvs am mxriv maTematikosTa biografiebis Seswavlasac; amasTan, xazi unda gaesvas imas, rom isini iyvnen ara marto udidesi mecnierebi, aramed diadi pirovnebebi, romelTac hqondaT amaR lebuli pirovnuli Tvisebebi. erT-erTi maTgani, gotf ri harold hardi, ambobda: `maTematikosis Semoqmedeba isevea mSvenieris Seq mna, rogorc fermweris an poetis Semoqmedeba, _ es aris ideebis erToblioba, saRebavTa da sityvaTa erTobliobis msgavsad. igi flobs Sinagan harmonias. silamaze aris maTematikuri Teoriis sa jildao qva; samyaroSi ar aris ulamazo maTematikis adgili~. maTematikis istoria _ esTetikuri potenciali maTe ma ti kis isto ri as aranak le bi esTe ti ku ri poten ci a li ga aCni a, vidre TviT maTe ma ti kas rogorc mecni e re bas. vuTi TebT mi si rea li za ci is mxolod zogi erT gzas (Jinjikhadze,20 1 2a)]. 290 jemal jinjixaZe moswav le eb ze Zlier STabeW di le bas axdens isto ri u li amo cane bi, maTi origi na lu ri formu li re be bi, damt ki ce be bi. aseTi amoca ne bi uxva daa gabne u li isto ri ul - ma Te ma ti kur Tu meTo di kur lite ra tu ra Si. Zalze efeqtu ria algeb ru li formu le bis geo met ri u li damt ki ce ba. aseTi maga li Te bis ganxil vis win saWi roa isto ri u li eqs kur si. esTe ti kur zemoq me de bas axdens cnobe bi zogi erT maTe ma ti kur termin Ta da simbo lo Ta Seqm nis isto ri i dan. masa le bi uamra via maTe ma ti kis isto ri a Si. XIV-XVI sau ku ne eb Si ariTme ti kul moqme de ba Ta Sesru le ba gansa kuT re bul xelov ne bad iTv le bo da. isini Tvlis osta te bad iyv nen cnobi li. yovel maTgans saku Ta ri xerxi hqonda gamrav le bisa Tu gayo fis. maTe ma ti kis isto ri a Si cnobi lia mrava li aseTi xerxi. isini roman ti ku li Sefe ri lo bi sa ni arian. esTe ti ku ri aRz r di saT vis didi mniSv ne lo ba aqvs cnobebs maTe ma ti kos Ta biog ra fi e bi dan, maTi mraval m x ri vi inte re se bi sa da niWis Sesa xeb. esTetikur aRzrdaSi friad popularulia saganTaSorisi xa siaTis mqone istoriuli cnobebis gamoyeneba. magaliTad, cnobebi imis Sesaxeb, Tu ra gavlenas axdenda maTematika xelovnebis iseTi saxeebis ganviTarebaze, rogoricaa: ferwera, musika, arqiteqtura. mogv yavs zogi er Ti isto ri u li cnoba, romel Tac, Cvenis az riT, didi esTe ti ku ri zemoq me de bis Zala gaaC ni a. • geometriis ganviTarebaSi didi da mniSvnelovani roli iTa maSa aRorZinebis epoqaSi perspeqtivis Sesaxeb moZRvrebis ganviTa rebam. Tumca, jer kidev berZnebma da romaelebma miaRwies garkve ul warmatebebs perspeqtivaSi, magram misi namdvili ayvaveba mie kuTvneba renesansis epoqas da emTxveva ferweris brwyinvale peri ods italiaSi, niderlandebsa da germaniaSi. gamoCenilma albrext diurerma (1471-1528) dawera Sroma, romelic mieZRvna perspeqtivis kanonebis kvlevas, gamoica 1525 wels niurnbergSi. Semdeg mravali germaneli fermweri muSaobda perspeqtivis kanonebis gamokvlevaze. meTxuTmete saukunis pirvel naxevarSi italiaSi mravali mxatvari da arqiteqtori iyenebda Tavis xelovnebaSi perspeqtivis wesebs. arqi teq tor ma da swavlul ma alber tim (1402-1472) pirvel ma dawe ra wigni pers peq ti vis Sesa xeb daax lo e biT 1446 wels, magram gamo i ca igi mogvi a ne biT, 1511 wels laTi nur enaze. am wign Si man aRwe ra pers peq ti vis agebis wese bi, romel Tac didi praqti ku li mniSv ne lo ba hqonda. 291 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV mraval m x ri vi geni o si leo nar do da vinCi (1452-1518) siste ma turad iyeneb da pers peq ti vis kano nebs. man dawe ra metad mniSv ne lova ni Sroma pers peq ti vis Sesa xeb. itali u ri ferwe ris udide si osta te bi rafa e li, miqe lan je lo, tici a ni, vero ne ze da sxvebi mimar Tav d nen pers peq ti vis wesebs, amasTan, rafa e li da miqe lan je lo am wesebs icavd nen mkacrad, ma Sin, roca, maga li Tad, vero ne ze uSveb da mniSv ne lo van gadax rebs. mecni e ru li Tvalsaz ri siT didi mniSv ne lo ba hqonda 1600 wels gvido ubaldis mier gamo ce mul Sromas pers peq ti vis Sesa xeb. amri gad, rene san sis epoqa Si ferwe ri sa da arqi teq tu ris brwyinva le ganvi Ta re bam pers peq ti vis mimarT udide si yuradRe ba gamo iw via da misma Teo ri ul ma damu Sa ve bam ar daa yov na, gavle na moex di na geo met ri is ganvi Ta re ba ze. pers peq ti vis amoca ne bi amosa va li werti li gaxda frangi ma Tema ti ko se bi saT vis da maT safuZ ve li Cau ya res gegmi lur geo met rias. am mxriv gansa kuT re biT unda aRiniS nos dezar gi (1593-1661), paska li (1623-1662), Jergo ni (1771-1859), brian So ni (1783-1864), ponse le (1788-1867). gansa kuT re bu li adgi li uWiravs gaspar monJs (1746-1818), romel mac Seqm na mxazve lo bi Ti geo met ri a. aRsa niS na via itali e li bona ven tu ra kava li e ris (1598-1647) Rvawli, man pirve li nabi ji gadad ga anali zu ri geo met ri is Seqm na Si. anali zu ri geo met ri is Semq m ne le bi pier ferma da rene dekar ti arian (Jinjikhadze, 2012a: 730-732). • Tavis tita nur Sroma Si `sawyise bi~ evk li dem geo met ri is kursi aqsi o ma ti ku rad aago (im droi saT vis mkacrad). pirvel wigns igi gansazR v re biT iwyebs, Semdeg mohyavs postu la te bi da aqsi o mebi, e. i. iseTi wina da de be bi, romle bic mii Re ba daum t ki ceb lad. erTis garda yvela postu la ti da aqsi o ma marti va daa formu li rebu li da arc erTi maTe ma ti ko sis TvalSi eWvi ar gamo uw ve vi a. mxolod mexu Te postu la ti yvela drois maTe ma ti koss eCve ne bo da rTulad. igi asea Camo ya li be bu li: `Tu wrfe gadak veTs or wrfes da Seqm nis maTTan Siga cal m x riv kuTxeebs, romle bic erTad nakle bia or marT ze, maSin es ori wrfe sakma ri sad gagr Ze le bi sas gadak veTs erT ma neTs im mxriT, sadac kuTxee bi erTad or marT ze nakle bi a~. es mexu Te postu la ti, romel sac para le lo bis aqsi o mas uwo deben, mrava li mize ziT acbu neb da maTe ma ti ko sebs. igi sxva aq sio meb ze ufro rTulia rogorc masSi aRwe ri li faqtiT, ise formu li re biT, amitom cdilob d nen mis damt ki ce bas, e. i. sur daT logi ku rad gamo ey va naT igi sxva aqsi o me bi dan. aseTi cdebi 292 jemal jinjixaZe grZelde bo da ori aTas weli wad ze mets. TiTq mis yvela gamo Ce nil ma maTe ma ti kos ma mii Ro mona wi le o ba, magram amaod, damt ki ce ba ar xerx de bo da. maT Soris aRsa niS na vi a; Zvel droSi _ pose i do ni o si (pirve li sau ku ne Cvens eramde), ptole me klavdi o si (meo re sau ku ne Cveni eriT), prokle dia do qo si; Sua sau ku ne eb Si _ nasi re di ni, klavi, ka taldi, bore li, vali si, jorda ni, vita le da sxv. miu xe da vad imisa, rom mexu Te postu la tis damt ki ce bis cdebi marcxiT mTavr de bo da, es cdebi mainc ar Sewyve ti la. maT ufro inten si u ri saxe mii Res meTv ra me te sau ku ne Si. es imiT aixs ne ba, rom meTeq v s me te sau ku ni dan yalib de ba algeb ra, mis nia dag ze warmo iS va anali zu ri geo met ri a, mas mohy va dife ren ci a luri da integ ra lu ri aRricx vis aRmo Ce na. yove li ve aman gamo iw via maTe ma ti kis da, kerZod, geo met ri is swrafi ganvi Ta re ba. amitom mexu Te postu la tis damt ki ce bis sur vilic gamZaf r da. es iyo ganvi Ta re biT gamow ve u li aucileb lo ba. am sakiTxis Seswav lis saqme axal simaR le ze avida da male miaR wia kidec Tavis sabo loo gadawy ve tas. aRmoCnda, rom mexuTe postulatis damtkiceba SeuZlebelia. aRmoCnda, rom arsebobs geometria mexuTe postulatis gareSe da arsebobs geometria mexuTe postulatis sawinaaRmdego debulebiT. am diad aRmo Ce neb Si Tavi an Ti wvlili Sei ta nes itali el ma swav lulma sake rim, Svei ca ri el ma maTe ma ti kos ma da filo so fos ma lam bert im, frang ma geo met r ma leJan d r ma, ung rel ma maTe ma ti ko seb ma farka Si boi am, fridrix vaxter ma. eseni araek v li du ri geo met ri is wina mor bed ni arian. xolo araev k li du ri geo met ri is erT ma ne Ti sagan damo u ki deb lad aRmom Ce ne bi arian germa ne li karl fridrix gau si, ung re li ianoS boi a, rusi niko loz ivanes Ze loba Cev s ki. axa li geo met ri is aRmo Ce nam de Zali an axlos mivid nen Svai kar ti da tau ri nu si (Jinjikhadze, 2012: 733). dRes geo met ria Zalze mraval dargs Sei cavs. • geo met ri is isto ri a Si gansa kuT re bu li adgi li uWiravs ge omet ri ul ageba Ta isto ri as. aq aRze ve bu lia iseTi saxe le bi, ro gori caa maske ro ni, Stei ne ri da mravali sxva. ageba ze klasi kur amoca neb Tan ki mWidro daa dakav Si re bu li π ricxvis cneba. maTe ma ti kis isto ri a Si arc erT maTe ma ti kur cnebas ar rge bia wilad imde ni Tayva ni da yuradRe ba, iseTi aRze ve ba, rogo ric ergo im mudmi vas, rome lic wrewi ris Sefar de bas warmo ad gens mis dia met r Tan. es aris ulama ze si da umS ve ni e re si ricxvi. 293 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV sao ca ria π ricxv ze warmod ge nis ganvi Ta re bis isto ri a. am ricxvis idumal bune bas adami a ni jer kidev maSin See ja xa, roca natu ra lu ris garda sxva ricxvs ar icnob da. adami ans sWirde bo da es ricxvi da ipova kidec igi, roca Seam C ni a, rom wrewi ris sigr Ze samjer metia mis dia met r ze. am Tana far do ba Si aTasw le u le bis manZil ze aravis Sehpar via eWvi. Semdeg ki adami a ni mixv da, rom wre wiris sigr Ze meti a, vidre misi sami dia met ri, magram, `ramde niT?~ es kvlav sruli iduma le ba iyo. am iduma le bas adami a nis gone ba odnav miu ax lov da maSin, roca mis cxovre ba Si wila de bi gaCn da. π ricxvis gamo an ga ri Se bis cdebi Zveli welTaR ricx vis meoTxe sau ku nes ekuTv nis. bibli a Si moxse ni e bu li a, rom wrewi ris sigr Zis 25 mis dia met r Tan Sefar de ba samis toli a. babi lo ne leb Tan π = . eg 8 25 2 vipte leb Tan π = . indo e leb Tan π =√10 . arqi me de Tvlida, rom 10 ( 8 ) 3 10 < π < 3 . 71 70 dro movi da da dais va amoca na wris kvadra tu ris Sesa xeb. aman kidev ufro gaam Zaf ra ltolv a π-s iduma le bi sa ken. π-s bune ba mis mkvleva reb Si iwvev da qariS x li sebr grZnobebs, ukidu re sad emoci ur ganc debs, Tavda viwye bam de misul kama Tebs. am ricxvis bune bis Zie bam moic va ara marto mecni e re bis, aramed filo so fo se bis, mxatv re bi sa da sxvaTa gone ba. es Zie be bi, romle bic cal- cal ke mimdi na re ob d nen, sivr ce sa da droSi eZebd nen erT ma neTs, pou lob d nen erT ma neTs, er wymod nen erT ma neTs da erT vod nen erT did mdina res, rome lic Tvi Tonve Seqm nes da, rome lic cocxali viT feTqav da, sunT qav da jados nuri sila ma ziT da Zali an hgavda iduma le biT moce mu li klasi ku ri simfo ni is sao ca ri bgere bis jadoq m nil qariS xals, es ukve mdina re iyo, π-s bune bis iduma le bi sa ken mimar Tul azr Ta mCqefa re mdina re. π ricxvis bune bas mrava li maTe ma ti ko si swavlob da. aRmo sav leTe li mecni e re bi π-s Semec ne ba Si xSirad evro pe leb ze winac mi diod nen. ariab xa tas Tan , mexu Te sau ku ne Si, π udri da 3,1416-s, Zu Cun jisTan π-s mniSvneloba 3,141526-sa da 3,141527-s Soris iyo moTav se bu li. 22 mecxre, mea Te, meTer T me te sau ku ne eb Si π = , magram aravin 7 icoda, rogor dadgin da es tolo ba. 4 4 4 4 1400 wels madha vam aRmo a Ci na: π = _ + _ + ··· 1 3 5 7 39 2 meTeq v s me te sau ku ne Si simon van der eikesTan π = , adri an (22) 355 2 anto nis Tan π = . (113) uamra vi maTe ma ti ko si cdilob da π-saTvis Seer Cia raci o na lu ri ricxvi da es Zie ba grZelde bo da daus ru leb lad, magram amaod, 294 jemal jinjixaZe sabo loo Sedegs vera vin aRwev da. ludolf van cei len ma 1610 wels gamo i an ga ri Sa π-s mniSv ne lo ba 34 niSniT. 1706 wels jons ma Tavis wign Si moa Tav sa meCi nis mier π-s gamo an ga ri Se bis Sede gi 100 niSnad cifram de, Senk s ma ipova π-s mniSv ne lo ba 707 niSniT, magram Semd gom Si aRmoC n da, rom 528-e niSni dan dawyebu li yvela cifri araswo ri iyo. eileramde wrewiris sigrZis SefardebisaTvis mis diametrTan, arc erTi simbolo ar iyo SerCeuli. amas mravali mecnieri Seecada, SemoiRes sxvadasxva simbolo, magram arc erTi maTgani ar damkvid rebula. simbolo π-s SemoReba eilers ekuTvnis. dRes orTografi uli `π~ _ da orToepiuli `pi~ arc simboloa da arc aRniSvna, igi sakuTari saxelia, erTi gansakuTrebuli mudmivas sakuTari saxeli. maTe ma ti kos Ta kvleva- Zi e ba Tanda Ta no biT ufro da ufro Sors midi o da da es Zie ba JamTa srbola Si marT lac rom, fantas tikur xasi aTs Rebu lob da. vie tam aRmo a Ci na tolo ba: 2 π π π = cos cos cos ··· π 4 8 16 Tu rkalis kosi nuss Sevc v liT misi mniSv ne lo biT, mivi RebT: 2 1 1 1 1 1 1 1 1 1 = · + · + + ··· π 2 2 2 2 2 2 2 2 2 es ukve brwyinva le ba a. Tanda Ta no biT Sevdi varT π-s sai dum lo labi rin Teb Si. eilerma aRmo a Ci na: π 22 · 42 · 62 · 82 · ... = 2 12 · 32 · 52 · 72 · ... es tolo ba SeiZ le ba aseTi saxi Tac warmo vad gi noT: π 2 2 4 4 6 6 = · · · · · ... 2 1 3 3 5 5 7 imave eilerma aRmoaCina: π2 22 32 52 = · · ... 6 22 _ 1 32 _ 1 52 _ 1 agreTve, π4 24 34 54 = · · ... 90 24 _ 1 34 _ 1 54 _ 1 ai, gamosaxuleba 1665 wels gamoqveynebuli wignidan, romlis avtoria valisi: 295 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 4 1 = 1 + π 32 2 + 52 2 + 72 2 + 92 2 + 2 + ... jaWvuri wiladebiT eilermac isargebla: π 2 4 2 = 1 + = 1 + 2 1 · 3 π 1 · 3 3 + 7 + 3 · 5 3 · 5 4 + 8 + 5 · 7 5 · 7 4 + 8 + 7 · 9 7 · 9 4 + 8 + 4 + ... 8 + ... uamravma maTematikosma Seadgina ricxvisaTvis toloba, da am tolobaTa genialuri arsi ganfenilia brwyinvale usasrulo la- birinTebSi, magram jadoqruli silamazisa da RvTaebrivi harmo- niulobis piks aRwevs maTematikis paganinad wodebuli genialuri indoeli algebraisti srinivaza ramanujani. maTematikosTaTvis kargadaa cnobili π ricxvis gamosaTvleli formula, romelic miRebulia srinivaza ramanujanis mier 1910 wels, teiloris mwkrivSi arktangensis ganfenis gziT: 9801 π = (4k!) [1103+26390k] 2√2 ∑∞ · k=2 (k!)4 (4 · 99)4k ai, kidev ramanujanis ubrwyinvalesi da ueleganturesi for- mulebi: 1+2 1+3 1+4 1+5 ... = 3. 2 1 _ 5 1 3 + 9 1 · 3 3 _ 13 1 · 3 · 5 3 + ... = 2 2 · 4 2 · 4 · 6 π es ki, zesilamazisa da zemSvenierebis yovelgvar zRvars scildeba: Tu 296 jemal jinjixaZe a = 1 + 1 + 1 + 1 + ... 1 · 3 1 · 3 · 5 1 · 3 · 5 · 7 da 1 b = 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 1 + ... maSin π · e a + b = 2 es formula ramanujanis genialuri gonebis zeaRzevebuli ltolvaa mSvenierebis usasrulobisken. roca aseT maTematikur formulebs xedav, da guliTa da go- nebiT iZirebi maTSi, maSin... gana marTali ar aris, rom es maTema- tikuri formulebi zogjer beThovenis mecxre simfoniis bgera- Ta qariSxalSi gagdeben, zogjer baxis saocar musikas gaziareben, zogjer zediadi tatos Tavganwiruli `gaswi, merano!..~ dagimor- Cilebs, zogjer rafaelis ferTa samyaros sidiade gimonebs, zo- gjer ki Saravandmosili mocartis RvTaebrivi brolis bgerebi ga- tyveveben da wargitaceben... 1739 wels, roca leonard eilers gasarCevad misces erTi pa- tara broSura, sadac mtkicdeboda, rom 3844 . π = 1225 eileri werda: `ufro martivi iqneboda, gvemtkicebina, rom wrewiris sigrZis amas win uZRoda is faqti, rom jeims gregorim 1667 wels scada π-s transcendentulobis damtkiceba, magram araferi gamouvida da 1873 wels ermitma daamtkica e ricxvis transcendentuloba. lindemanma srulyo ermitis meTodi da 1882 wels daamtkica, rom π ricxvi aris transcendentuli. amiT dasrulda Ziebis oTxiaTaswlovani istoria da gaixsna π ricxvis WeSmariti maTematikuri buneba (Jinjikhadze, 2012: 734-739). amaod ar damSvrala kacobriobis genialuri gonebebi! Cven aq e vaxseneT. esec maTematikuri cnebaa. e maTematikuri mudmivaa (konstanta), naturaluri logariTmis fuZe, iraciona- luri da transcendentuli ricxvi. zogjer mas eileris ricxvs eZaxian, zogjer neperis ricxvsac. mniSvnelovan rols TamaSobs diferencialur da integralur aRricxvebSi, maTematikis mraval sxva dargSic. e ≈ 2,718 281 828 459 045 235 360 287 471 352 662 497 ... sainteresoa vicodeT, rom iaponiaSi mcxovrebma akira hara- guCim 2006 wels axali msoflio rekordi daamyara, zepirad dai- maxsovra pi ricxvis asi aTasi niSani mZimis Semdeg. imisaTvis, rom xmamaRla warmoeTqva es mniSvneloba, mas dasWirda daaxloebiT 16 saaTi. wina rekordic masve ekuTvnis, maSin man daimaxsovra mZimis Semdeg 83431 niSani. es iyo 1995 wels (Jinjikhadze, 2012a: 739). aqve aRsaniSnavia erTi umniSvnelovanesi garemoeba. yvelam icis, ra aris simetria, magram SeiZleba yvelas ar axs- ovdes, ra aris oqros kveTa da fibonaCis ricxvebi. fibonaCis saxe- liTaa cnobili Suasaukuneebis evropis pirveli gamoCenili maTe- matikosi leonardo pizeli (1170-1250). oqros kveTa _ es aris monakveTis iseTi proporciuli dayo- fa araTanabar (did da mcire) nawilebad, sadac mcire nawili ise Seefardeba did nawils, rogorc didi nawili Seefardeba mTel monakveTs. anu, rac igivea: mTeli monakveTi ise Seefardeba did nawils, rogorc didi nawili Seefardeba mcire nawils. aseTi Ta- nafardoba optimaluri mSvenierebis bunebriv gancdas badebs. fibonaCis ricxvebi aseTia: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, ... aq yoveli ricx- vi, dawyebuli mesamidan, udris wina oris jams. sadac es ricxvebi iCenen Tavs, iq ritmulobis mSvenierebis bunebrivi gancda ibadeba. es cnebebi erTmaneTTan mWidrodaa dakavSirebuli da es kavSiri TavisTavad ganapirobebs harmoniulobas yvelgan da yvelaferSi. uZvelesi droidan dRemde adamiani amCnevs simetrias, oqros kveTas, fibonaCis ricxvebs cxovelTa da mcenareTa samyaroSic, 298 jemal jinjixaZe musikaSic, xuroTmoZRvrebaSic, poeziaSic, ferweraSic, maTema- tikaSic. isini gvxvdeba yvelgan, yvelaze moulodnel da idumal adgilebSi. magaliTad, es mimarTebebi SeimCneva gizaSi piramidis geometriul proporciebSi, meqsikis piramidebSi, parTenonis ar- qiteqturis antikur qmnilebaSi. goeTem Seiswavla bunebaSi spiralismagvari gamovlinebebi. spiralebi SeiZleba davinaxoT mzesumzirebSi, fiWvis girCebSi, kaqtusebSi, ananasebSi da mravalgan kidev. yvela am SemTxvevaSi vlindeba fibonaCis ricxvebi. spiralismagvarad abams oboba Tavis qsels. spiraluradaa Caxveuli qariSxali, asevea Caxveuli gala- qtikebic. iohan goeTe spirals `cxovrebis mruds~ uwodebda. fibonaCis ricxvebi vlindeba cocxali organizmebis biolo- giaSic. oqros simetria SeiniSneba elementarul nawilakebSi, calkeu- li qimiuri SenaerTebis struqturaSi, kosmosur sistemebSi, gene- tikur struqturebSi, adamianis sxeulis zogierTi organos agebu- lebaSi, bioritmebSi, tvinis muSaobaSi da aRqmis TaviseburebebSi. nawilSi SeiZleba meordebodes mTelis struqtura, rac bu- nebaSi fraqtalurobis gamovlinebaa. fraqtalurobaSi ki oqros mimarTebebia. es imas niSnavs, rom Cvens irgvliv da CvenSi yvelgan harmonia sufevs. da swored es harmoniaa, rom adamians mSvenierebasa da RvTaebriv silamazes apovninebs maTematikaSic, poeziaSic, musika- Sic da sxvagan. oqros kveTasa da fibonaCis ricxvebTan dakavSirebulia mTeli dargebi kulturaSi, mecnierebaSi da adamianis praqtikul saqmia- nobaSi. msoflios uamrav mecnierTa mier Catarebulia gamokvle- vebi, romlebic adastureben amas. musikaSi, ferwerasa da poeziaSi oqros kveTis gamoyenebis Taobaze saintereso kvlevebi Caatares g. v. wereTelma, e. k. rozeno- vma, m. a. murataevma da sxvebma. s. m. eizenSteinma gamoikvlia oqros kveTis gamoyeneba kinoxelovnebaSi. oqros kveTis gamoyenebis klasikuri magaliTia wesieri mrava- lwaxnagebis ageba. wesieri mravalwaxnaga mxolod xuTi arsebobs: oTxwaxnaga (tetraedri), eqvswaxnaga (haqsaedri), rvawaxnaga (oqtae- dri), Tormetwaxnaga (dodekaedri), da ocwaxnaga (ikosaedri). yvela es mravalwaxnaga cnobili iyo Zveli berZnebisaTvis da maT miiRes saxelwodebi `platonuri sxeulebi~ anu `platonuri tanebi~, pla- tonis saxelis mixedviT. platonma pirvelma aRwera isini sistema- turad. yoveli maTgani simbolurad aRniSnavda xuTi `sawyisidan~ 299 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV anu `stiqiidan~ erT-erTs: tetraedri _ tani cecxlisa, oqtaedri _ tani haerisa, heqsaedri (kubi) _ tani miwisa, ikosaedri _ tani wylisa, dodekaedri _ tani samyarosi (samyarosi sulisa, eTeri- sa anu gonebisa). Sua saukuneebSi keplerma mzis sistemis mode- li warmoadgina erTmaneTSi Calagebuli politonebis (platonuri tanebis) Tanamimdevrobis formiT. evklidem aago yvela wesieri mravalwaxnaga oqros kveTis safuZvelze. Tvlian, rom termini `oqros kveTa~ ptolemeosidan modis, igi ganmtkicda da popularuli gaxda leonardo da vinCis wyalobiT. maTematika da poezia poeziis qmnilebaTa struqturaSi Zalian bevri ram xelovnebis am saxes aaxloebs musikalurTan. ritmis gamokveTiloba, marcval- Ta kanonzomieri monacvleoba, dalagebuli ganzomiloba da maTi emocionaluri gajerebuloba leqss aaxloebs da saxeebSi utolebs musikalur nawarmoebebs. yoveli leqsi flobs musikalur for- mas Tavisi ritmikiTa da melodiiT. leqsis agebulebaSi mJRavndeba musikalur kompoziciaTa Tvisebebi, musikaluri harmoniis kanon- zomierebebi. es imas niSnavs, rom leqsebis agebulebaSi, mis ele- ganturobaSi da formebis mravalferovnebaSi dominirebs oqros proporcia da fibonaCis ricxvebi. fibonaCis ricxvebi ara marto dominirebs poeziaSi, aramed isini Zalian xSirad gansazRvraven le- qsis kompozicias. am ricxvebis arseboba leqsSi gamoxatavs poetis SemoqmedebiTi meTodis erT-erT fundamentalur kanonzomierebas, mis esTetikur moTxovnilebas, harmoniis gancdas. amiT mxatvruli forma xdeba axali, uCveulo, originaluri da pasuxobs harmoniis kriteriumebs. swored amaSi vlindeba poetis individualuroba. xazi unda gaesvas im garemoebas, rom yovelive es poetis une- bliv xdeba. poeti maTematikaSi ar eZebs misTvis leqsSi gamosaye- nebel Tanafardobebs. muziT Sepyrobili da STagonebuli poeti qmnis poetur nawarmoebs da am nawarmoebSi TavisTavad, avtorisa- gan damoukideblad, Cndeba maTematikuri kanonzomierebebi, poeti intuiciiT xelmZRvanelobs `Sinagani~ maTematikiT. es imitom xde- ba, rom abstraqtul poetur saxeebsa da maTematikur abstraqtul xatovan saxeebs Soris arsebobs garkveuli bunebrivi identuroba. oriveSi daculia xatovan saxeTa logikuri Tanamimdevroba. uamravi poeti eTayvaneboda maTematikas: aleqsandr puSki- ni, mixail lermontovi, aleqsandr bloki, valeri briusovi, lev tolstoi da sxv. Tumca, puSkini bavSvobaSi gaurboda maTematikas. 300 jemal jinjixaZe lermontovi maTematikisa da mxatvrobis (ferwera, fanqari, gra- fika...) mSvenierebaSi Zalze xSirad iZireboda. omar xaiami xom am mxriv unikalurad legandaruli pirovnebaa, poeziaSic da maTema- tikaSic ubrwyinvalesi msoflio aRiareba moipova. luis kerolma da andrei voznesenskim, zusti mecnierebis adamianebma, saxeli gai- Tqves literaturuli SemoqmedebiT. mSvenier leqsebs werdnen ma- Tematikosebi: rene dekarti, nikolai lobaCevski, karl vaierStra- si, sofia kovalevskaia, vladimir arnoldi (mas maTematikis puSkins eZaxdnen), mixail lomonosovi, ibn ruSdi (averoesi), mitag lefle- ri da uamravi sxva. frangi mari Jan antuan kondorse (1743-1794) mweralic gamoCenili iyo da maTematikosic. poeti iyo Sua saukuneebis mravali aRmosavleli brwyinvale maTematikosi. mecnier-enciklopedisti, ai, mxolod zogierTi maTgani: ibn sina (avicena, X-XI sk.), al-xaiami (XI sk.), al-beruni (XII sk.), ibn al-iasmini (XII sk.), ibn al-xaimi (XV sk.), ibn hazi al- fasi (XV sk.), ibn ezra (XII sk.) _ Suasaukuneebis filosofosi, poeti, lingvisti, mTargmneli, astrologi, maTematikosi da eqimi. zusti sityvebis, saxeebisa da riTmebis ritmis harmoniis meS- veobiT leqsebi iZenen emocionalurobas, JReradobas, silamazes. amasTan, ritmi, harmonia, nawarmoebis stilic ki, xeleqveiTeba ma- Tematikas. maTematikisa da poeziis enebs Soris arsebuli Sinagani kavSirebis bunebas maTematikosebi ikvleven, xolo mravali poeti- saTvis es kavSirebi Semoqmedebis intuiciuri sayrdenia. poetis leqsebis metrikasa da kompoziciaSi arsebobs ori sawyisi, romlebic ganapirobeben maT harmoniulobas. es aris si- metria da asimetria. simetria gamoixateba gariTmul striqonebSi, mravali TvalsazrisiT maT ostatur dawyvilebaSi. zogierTi le- qsi simetriulia Sinaarsobrivi gaazrebiT. simetria leqss aniWe- bs mowesrigebulobis silamazes, aRqmis simsubuqes, simkacresa da monumentalurobas. xolo asimetriis formebi leqsSi mJRavndeba maSin, roca es leqsi formis Tavisufal silaRes iZens, roca misi kulminaciuri momentebi arasimetriulia. asimetria leqss aniWebs sicocxles, amaRlebs mis emocionalur zemoqmedebas. leqsis me- trikasa da kompoziciaSi asimetriis gamoxatulebas warmoadgens oqros proporcia da metrikis daqvemdebareba fibonaCis ricxvebs. harmoniis am ori sawyisis Sexameba badebs mxatvruli formebis saocar nairsaxeobebs. magram, sinamdvileSi, Tu SemoqmedebiTad CavuRrmavdebiT saki- Txs, aSkarad SevamCnevT, rom oqros kveTa ar aris simetriis raRaca sawinaaRmdego, igi simetriis erT-erTi Taviseburi gamovlinebaa. 301 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV diax! es asimetriuli simetriaa, geometriis legendaruli fenome- ni, romelic saocar xatovan abstraqtul saxeebs badebs poeziaSic, ferweraSic, musikaSic, skulpturaSic, arqiteqturaSic, grafika- Sic. maTematikaSi xom aris da aris, _ ulamazesi da ueleganturesi. rogorc amboben, forma _ es aris wesrigi, xolo wesrigi _ es aris maTematika, es aris logika... bunebrivia, literatura rac ufro metad misdevs formis kanonebs, masSi, rogorc yvela sxva xelovnebaSi, miT ufro matad mJRavndeba maTematikis kanonebi. poeziaSi oqros kveTisa da fibonaCis ricxvebis gamoyenebis TvalsazrisiT, rac igivea _ maTematikis TvalsazrisiT, yvelaze ufro aleqsandr puSkinis Semoqmedebaa gamokvleuli. aRmoCnda, rom mraval mis nawarmoebs msWvalavs fibonaCis ricxvebis mimar- Tebebi. puSkinis leqsebis metrikis analizisaTvis mkvlevarTa mier ganxiluli iyo 1829-1836 wlebis nawarmoebebi. es is perio- dia, roca poeti qmnida yvelaze srulyofil leqsebs. akademikosma giorgi wereTelma am TvalsazrisiT gamoikvlia SoTa rusTavelis `vefxistyaosani~ da daadgina, rom SoTa rusTa- velis es genialuri qmnileba oqros kveTasa da simetriazea age- buli. igi aRniSnavs: `poeziaSi rusTaveli pirvelia msoflioSi da SeiZleba erTaderTi, romelmac oqros kveTaze aago esoden didi moculobis poeturi nawarmoebi. misi poemis 1587 strofidan 863 oqros kveTazea agebuli~ (Tsereteli, 1972). magram, sadac oqros kve- Ta da simetriaa, iq fibonaCis ricxvebicaa, radganac isini mWidro urTierTkavSirSi imyofebian da erTmaneTidan gamomdinareoben. qarTul maTematikur-meTodikur literaturaSi, (Tsereteli, 1972)-Tan dakavSirebiT, oqros kveTa da fibonaCis ricxvebi kar- gad daaxasiaTa avTandil benduqiZem (Bendukidze, 2005). maTematika da musika sagulisxmoa, rom musikis Teoriis pirveli aRmomCenia Zve- li berZeni maTematikosi piTagora. am aRmoCeniT daiwyo musi- kis Teoriis Camoyalibeba. da am procesSi mraval maTematikoss aqvs monawileoba miRebuli. musikis SesaniSnavi Teoretikosi iyo frangi maTematikosi, fizikosi, filosofosi da RvTismetyveli maren merseni (1588-1648). magram leonard eileris Sroma `musi- kis Teoria~ ukve Semoqmedebis umaRlesi rangia. am wignis Sesaxeb musikosebi da maTematikosebi erTnairad xumrobdnen. musikosebi ambobdnen, rom maTTvis es wigni gaugebaria, radganac masSi metis- meti maTematikaa, xolo maTematikosebi ambobdnen, rom es wigni 302 jemal jinjixaZe maTTvis gaugebaria, radganac masSi metismeti musikaa. amas TviT eileric aRiarebda: `igi maTematikosTaTvis metismetad musika- luria da musikosTaTvis _ metismetad maTematikuri~. maTematika aris musikaluri `bgeris safuZveli~, xolo bgera, mis musikalur aspeqtebSi, warmoadgens ricxvebis SesaniSnav masive- bs. ricxviTi mimarTebebis TvalsazrisiT musikaluri gamis eqspre- siis pirveli mkvlevarebi piTagorelebia. maTi mTavari postulati aseTi iyo: `mTeli buneba Sedgeba ricxvebze damyarebuli harmonie- bisgan~. mravali sakiTxi, romelic dakavSirebulia musikis bunebas- Tan, mis zemoqmedebasTan adamianze, SeiZleba aRiweros maTematikis eniT. amavdroulad, musikalur instrumentebSi bgeris warmoqmna SeiZleba aRiweros maTematikuri amocanebiT. musika aris sulis idumali ariTmetika. is angariSobs da arc ki acnobierebs amas. platonis droidan moyolebuli, harmonia fundamentalur dargad iTvleboda da SemdgomSi amitom iqna igi gamoyofili fi- zikisagan. es aris dRevandeli musikaluri akustika. Zveli in- doeli da Cineli Teoretikosebi swavlobdnen akustikur proce- sebs da harmoniisa da ritmis maTematikur kanonzomierebs funda- mentalurad Tvlidnen. maTematika ufro metadaa dakavSirebuli musikalur akustikasTan, vidre notebTan. musikis struqturebis, agreTve, Seqmnisa da mosmenis axali xerxebis kvleva-Ziebam ga- moiwvia simravleTa Teoriis gamoyenebis aucilebloba am dargSi. zogierTi kompozitori Tavis qmnilebebSi oqros kveTasa da fi- bonaCis ricxvebs uZebnida saTanado adgils. zogierTma Teore- tikosma, aviTarebda ra simravleTa musikalur Teorias, musikis analizisaTvis gamoiyena abstraqtuli algebra. SemTxveviTi araa, rom sityva `riTma~ warmomdgaria sityvisa- gan `ritmi~ da orive erTad iwvevs ricxvis cnebis asociacias. sagulisxmoa, rom ruseTSi moRvawe gamoCenili germaneli pia- nisti henrix neihauzi (1888-1964) ambobda: `xelovnebasa da mecnie- rebaze, maT urTierTkavSirebsa da winaaRmdegobebze dafiqrebisas me mivedi im daskvnamde, rom maTematika da musika imyofebian ada- mianuri sulis sruliad sxvadasxva polusebze, rom am ori antipo- diT Semoifargleba da ganisazRvreba adamianis mTeli Semoqmede- biTi sulieri moRvaweoba da, rom maT Soris Tavsdeba yvelaferi, rac ki kacobriobas Seuqmnia mecnierebisa da xelovnebis dargSi~. am bolo wlebSi damuSavebulia musikalur nawarmoebTa Seswa- vlisadmi `geometriuli~ midgoma. axla ukve musikis ganviTarebis istoria SeiZleba warmovidginoT, rogorc simetriisa da geome- triul formaTa sxvadasxva tipebis Seswavlis procesi. musikis 303 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Teoriis specialistebma: klifton kalenderma (floridis uni- versiteti), ian kuinma (ielis universiteti) da dmitri timoJkom (prinstonis universiteti) daamuSaves musikis analizisa da kla- sifikaciis axali meTodi. am meTods ewoda `musikis geometriuli Teoria~. misi meSveobiT ZiriTadi musikaluri struqturebi da gardaqmnebi iTargmneba Tanamedrove geometriis enaze. axali Teoriis CarCoebSi yoveli noti warmodgenilia rogorc Sesabamisi bgeris sixSiris logariTmi (pirveli oqtavis noti `do~, magaliTad, Seesabameba ricxvs 60, oqtava _ ricxvs 12). amgvarad, akordi warmoidgineba rogorc wertili, mocemuli koordinate- biT geometriul sivrceSi. akordebi dajgufebulia sxvadasxva `ojaxebSi~, romlebic Seesabameba geometriuli sivrceebis sxva- dasxva tipebs (Geometriya muziki). maTematika da arqiteqtura arqiteqtura adamianuri saqmianobisa da moRvaweobis saoca- ri sferoa. masSi erTmaneTSia gadaxlarTuli da mkacradaa gawo- nasworebuli mecniereba, teqnika da xelovneba. Silingi ambobda arqiteqtura gacivebuli musika ariso, goe- Te ki arqiteqturas mimwydar melodias uwodebda. maTematikisa da arqiteqturis mWidro kavSiris Sesaxeb didi xania cnobilia. Zvel saberZneTSi geometria arqiteqturis nawilad iyo miCneu- li. arqiteqturul nagebobaTa samyaros amSvenebs `oqros kveTa~. es _ maTematikuri formulaa, romelsac ufrTxildeba nebismieri arqiteqtori. magram oqros kveTiT ar amoiwureba maTematikis ga- moyeneba arqiteqturaSi. Tanamedrove arqiteqtori kargad icnobs ritmikuli mwkrivebis sxvadasxva urTierTmimarTebebs, romelTa gamoyeneba arqiteqturul qmnilebas xdis ufro harmoniulsa da gamomxatvelobiTs. garda amisa, man icis analizuri geometria da maTematikuri analizi, umaRlesi algebris safuZvlebi da matric- Ta Teoria, igi flobs maTematikur modelirebasa da optimiza- cias. qarTuli xuroTmoZRvrebac swored am aRzevebuli mSvenie- rebiTaa gamsWvaluli. maTematika da skulptura Zveli egviptis mxatvrul qmnilebebSi gvxvdeba oqros kveTis gamoyenebis mravali SemTxveva. am Tanafardobis safuZvelze Seqm- nili iyo Zvelegvipturi kanonis proporciebi _ rva proporciuli 304 jemal jinjixaZe sidide. isini miRebulia kvadratis gverdebis dayofiT oqros kve- Tis proporciiT. miRebul sidideebs Soris Tanafardobebi gamo- yenebuli iyo qandakebaTa agebisas. Zveli berZeni mxatvrebi aRfrTovanebulebi iyvnen egviptele- bis miRwevebiT. isini bevrs mogzaurobdnen egvipteSi, raTa Seeswa- vlaT maTi gamocdileba. berZnebma ganaviTares xelovnebaSi egvip- telTa tradiciebi. isini amtkicebdnen, rom samyaroSi sufevs sa- yovelTao kanonzomiereba, mSvenieris arsi ki mdgomareobs mkacr wesrigSi, simetriaSi, mTelisa da misi nawilebis harmoniaSi, swor maTematikur TanafardobebSi. berZnuli (da saerTod _ msoflio) xelovnebis erT-erTi umaRlesi miRwevaa aTeneli moqandakis fidiusis (V sk Zv.w.) Semoq- medeba. is iyo aTenSi akropolis rekonstruqciis dros perikles mTavari TanaSemwe. fidiusis Semoqmedebam gavlena moaxdina mTeli elinizmis samoqandako xelovnebaze. misi saxeebis Seqmna realuri samyaros Rrma Seswavlazea damyarebuli. yvelaze harmoniul Tanafardobad fidiusi Tvlida oqros kve- Tas. es cneba dResac inaxavs fidiusis saxelis xsovnas, radganac oqros kveTis ricxviTi mniSvneloba aRiniSneba fidiusis saxelis pirveli asoTi . da es mniSvneloba Tavisi aRnagobiT mSvenierebas warmoadgens: 1 φ = 1 + φ = 1+ 1+ 1+ 1+ ... 1 1 + 1 1 + 1 1 + 1 + ... maTematika da ferwera oqros kveTas wamyvani adgili ukavia gansakuTrebiT leonardo da vinCisa da diureris mxatvrul kanonebSi. Sedevrebi `mona liza~ da `saidumlo seroba~ Seqmnilia oqros proporciis safuZvelze. leonardo roca gaecno elementarul geometrias, Tavis naxatSi gamosaxa, Tu rogor SeiZleba adamiani gaSlili xelebiT Caixazos wrewirSi da kvadratSi. ferweraSi imTaviTve, Zveli berZnebidan dawyebuli, gamoi- yeneboda maTematikuri proporciebi. leonardo da vinCim mec- nierulad Seiswavla adamianis sxeulis nawilebi da isini mkacrad 305 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV dauqvemdebara maTematikur proporciebs. ferweraSi oqros kveTa umaRles doneze mniSvnelovani gaxda. ferweraSi sapatio adgili daikava, agreTve, geometriuli si- metriis yvela saxem: centralurma, RerZiTma, sarkulma, brunviT- ma, mosrialem. mxatvarTa yuradReba gamosaxulebaTa ucnaurma Tvisebebma miipyro da maT xSirad SeiZleba SevxvdeT ferwerul tiloebSi. es ucnauri Tvisebebi oTxi saxisaa: aracalsaxa, roca sagani SeiZleba davinaxoT xan Siga, xan gare mxridan. paradoqsaluri, roca suraTze sagani mocemulia rogorc brtyeli, sinamdvileSi igi samganzomilebiania. ganusazRvreli, magaliTad, roca vuyurebT xes, ar Cans, rogoraa ganlagebuli misi totebi. iluzoruli, roca suraTis mxilveli tyuvdeba mxatvris xelovnebiT. am bolo saxis magaliTia es ori rkali (nax. 2). meore rkali TiTqosda ufro grZelia. nax. 2 mxedvelobis mcdarobiT mravali mxatvari iyo gatacebuli. uamravi mxatvari eTayvaneboda maTematikas. italieli juzepe veroneze (1854-1917) mxatvaric brwyinvale iyo da maTematikosic. geometriuli formebi mecxramete saukunis Suawlebidan ferweram, grafikam, skulp- turam gadauxvia naturalistur tradiciebs da wavida im gziT, romelSic suraTis pirdapiri aRqma miuwvdomeli iyo. warmoiSva uamravi mimarTuleba, romelTa Soris avangarduli gaxda kubizmi. misi erT-erTi mTavari fuZemdebeli pablo pikaso iyo da aq mTavar rols figuraTa geometriuli silamaze TamaSobda. kubizmma pir- vel planze wamoswia sibrtyeze moculobiTi formis konstruireba, martivi mdgradi geometriuli formebis gamovlena (kubi, konusi, cilindri, sfero), rTuli formebis daSla sibrtyeze. aseT sura- TebSi geometrizirebulia yvelaferi, maT Soris adamianis sxeulis nawilebi: Tavi, xelebi, fexebi da sxv. isini geometriul figuraTa 306 jemal jinjixaZe abstraqtuli formebiTaa gamosaxuli. kubizmma safuZveli daudo meoce saukunis mraval modernistul mimarTulebas. cnobili holandieli mxatvari mauric kornelis eSeri (1898- 1972) iTvleba maTematikuri xelovnebis mamad. mis suraTebSi, adrindeli namuSevrebis gamoklebiT, centralur rols maTema- tikuri ideebi TamaSobs. maTematikur xlovnebaSi erT-erT aqtiur gamoyenebas poulo- bs mravalwaxnagebi. platonma (Zv.w. 427-348) aago da aRwera xuTi wesieri mravalwaxnaga, Tumca, es mravalwaxnagebi cnobili iyo ma- namdec. arqimedem (Zv.w. 290/280-212/211) aRwera cameti naxevrad- wesieri mravalwaxnaga. rogorc wesier mravalwaxnagebs ewodeba platonuri tanebi, ise naxevradwesier mravalwaxnagebs ewode- ba arqimeduli tanebi. arqimedes es Sroma daikarga da es tanebi kvlav iqna aRmoCenili iohan kepleris mier 1619 wels, arqimedes gardacvalebidan TiTqmis 2000 wlis Semdeg. leonardo da vinCi (1452-1519) didi gamomgonebeli da mxatva- ria. man pirvelma mimarTa anamorful xelovnebas, sadac gamoyene- bulia perspeqtivis damaxinjebuli badeebi. misi daxrili anamor- fuli gamosaxulebebi mxolod garkveuli kuTxiT xedvisas Canan daumaxinjeblad. iohan kepleri (1580-1630) ufro cnobilia rogorc astronomi, magram mas geometriuli mravalwaxnagebisa da sxvaTa gamoyenebis didi interesi hqonda. mis SromebSi sapatio adgili ukavia sibr- tyis Sevsebas wesieri da varskvlaviseburi mravalkuTxedebiT. kolomen mozeri (1868-1918) _ avstrieli mxatvari da grafiko- si, romelic moRvaweobda venaSi da muSaobda modernizmis stilSi. man 1899-1900 wlebis periodSi gamoiyena garkveuli geometriuli mimarTebebi. holandieli mxatvari pit mondriani (1872-1944) cnobilia Ta- vis tiloebSi geometriuli abstraqciebis gamoyenebiT. salvador dali (1904-1989) aris gamoCenili espaneli fermweri, grafikosi, moqandake, reJisori da mwerali. man zogierTi Tavisi qmnileba maTematikur ideebze aago. suraTSi `jvarcma~ gamosaxu- lia hiperkubi, xolo suraTze `La Visage de la Guerre~ gamosaxulia milevad groteskul pirTa fraqtaluri Tanamimdevroba. maqs bili (1904-1989) _ mxatvari, grafikosi da moqandake, ro- melmac Seqmna mebiusis zedapirze damyarebuli qandakebebi. viqtor vasareli (1908-1997) _ ungreli mxatvari, romelic cnobi- lia rogorc optikuri xelovnebis op-art (Op-Art) mimarTulebis pio- neri da praqtikosi. man brtyel naxatze moZraobis, amozneqilobisa 307 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV da Cazneqilobis efeqtis Seqmnis mizniT gamoiyena SeRebili martivi geometriuli formebi, romlebic xSirad masivebSia gaerTianebuli. benua mandelbroti (1924-2010) _ frangi da amerikeli maTe- matikosi, fraqtaluri geometriis Semqmneli, volfis premiis laureati fizikaSi. man aRmoaCina mendelbrotis simravle da misi sityvebia: `SeiZleba Tu ara `adamianma quCidan~ SeamCnios wminda geometriis mSveniereba? ufro zustad, SeiZleba Tu ara adamianma, romelsac geometriasTan kavSiri ara aqvs, aRiqvas figura, ro- melic aRiwereba martivi gantolebiT an agebis wesiT, rogorc esTetikuri mniSvnelobis mqone figura, saxeldobr, iyos dekora- ciuli an, SesaZloa, xelovnebis saxe? Tu es geometriuli figura fraqtalia, maSin pasuxia _ diax!~. fraqtali _ (< laT. fractu- s damsxvreuli, gatexili) _ TviTm- sgavsebis Tvisebis mqone maTematikuri simravle. termini `fraqta- li~ 1975 wels SemoiRo benua mandelbrotma. es sityva gamoiyeneba aramarto maTematikuri azriT. bunebaSi mravali sagani xasiaTde- ba fraqtalis TvisebiT: Tovlis fifqi, Rrublebi, sisxlZarRvTa sistema da sxv. fraqtalis magaliTia Semdegi suraTi: kombostos Tavis fraqtaluri forma (romaneskos jiSi). perspeqtiva _ ferweris geometria perspeqtivis Sesaxeb detalurad gvqonda saubari zemoT. leo- nardo da vinCis sityvebia: `perspeqtivis yvela problema SeiZleba aixsnas maTematikis xuTi terminis saSualebiT: wertili, wrfe, kuTxe, zedapiri da sxeuli~. mas ekuTvnis, agreTve, Semdegic: `perspeqtiva aris ferweris saWe~. mas Semdeg Seiqmna perspeqtiuli agebis mravali meTodi da xerxi, romelTa meSveobiTac zustad SeiZleba sibrtyeze gamoisaxos 308 jemal jinjixaZe nebismieri sagani nebismieri mobrunebiT, suraTis siRrmeSi nebis- mieri CaZirviT, da es yovelive _ nebismieri xedvis wertilidan. dRes arsebobs perspeqtivis mravali sxva saxec. maT Soris aR- saniSnavia perspeqtivis is saxe, romelSic ixateba SeuZlebeli fi- gurebi. es figurebi perspeqtivaSi isea gamosaxuli, rom pirveli SexedviT Cveulebriv figurebad Canan, magram dakvirvebuli Tva- li uceb SeamCnevs, rom aseTi figurebi samganzomilebian sivrceSi ar SeiZleba arsebobdes. SeuZlebeli figurebis mamad iTvleba Svedi mxatvari oskar re- utersvardi (1915-2002). magram aseTma figurebma gansakuTrebuli popularoba moipoves, roca isini Tavis litografiebSi gamosaxa cnobilma holandielma mxatvarma mauric kornelis eSerma. eSeri Tavis namuSevrebSi xSirad mimarTavda or- da samganzomilebiani sivrceebis Sexamebas. SeuZlebeli figurebis magaliTia Tanamedrove ungreli mxatvris _ iStvan orosis (d. 1951 w.) suraTi: suraTze gamosaxulia xidebi, romlebic samganzomilebian si- vrceSi ar SeiZleba arsebobdes. iqve gamosaxulia SeuZlebeli sa- mkuTxedi, romelic Seqmna ingliselma maTematikosma rojer pen- rouzma (d. 1931 w.). maswavleblis roli moswavleTa mier maTematikuri silamazis aRqmaSi maTematikuri silamazis aRqma mxolod maTematikis meSveobiT _ SesaniSnavi da mSvenieria, magram es aRqma ufro efeqturi, ga- momxatvelobiT-zemoqmedebiTi Zalis mqone da aRzevebuli iqneba, 309 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Tu igi organulad daukavSirdeba xelovnebis qmnilebaTa silamazis aRqmas. aq saubaria maTematikisa da xelovnebis Sinagani, siRrmiseu- li urTierTkavSiris esTetikuri idealebis Ziebis Sesaxeb. aseTi Zieba moswavlisaTvis miuwvdomelia, Tu mTeli Sesabamisi pedago- giuri saqmianoba zustad da gonivrulad ar iqneba dagegmili maswa- vleblis mier. am saqmeSi maswavleblis roli udidesia. maswavlebe- li aris Suamavali moswavlesa da xelovnebis ukidegano da mSvenier samyaros Soris. misi pedagogiuri amocana mdgomareobs xelovnebis Semecnebis iseT organizebaSi, romelic xels Seuwyobs moswavles sakuTari sulieri Zalebis bunebriv da organul gamovlenaSi. maswavleblis movaleobaa ara marto xelovnebis Sesaxeb moswa- vleTa gancalkevebuli, daqsaqsuli codnis sistematizireba, ara- med, agreTve, _ muSaobis ise warmarTvac, rom uzrunvelyofili iyos moswavleTa mier axali codnis SeTviseba, grZnobiTi gamoc- dilebis miReba da esTetikuri gancda. es muSaoba unda iyos sis- temuri, Tanamimdevruli, amitom aucilebelia misi pedagogiuri dagagmareba. umcrosklaselis esTetikuri aRzrdis dagegmarebisas saWi- roa, gaTvaliswinebul iqnas Semdegi etapebi: upirveles yovlisa, pedagogiuri garemo unda Sefasdes es- Tetikuri aRzrdis miznebis TvalsazrisiT: aRvzardoT humanu- ri, yovelmxriv ganviTarebuli pirovneba. zogadi mizani reali- zebuli unda iqnes kerZo miznebSi. miznebis formulireba axdens saqmianobis prognozirebas, xels uwyobs Sromis msvlelobisa da misi Sedegebis danaxvas. kerZo miznebis gansazRvra aadvilebs mo- qmedebaTa sistemis formirebis SesaZleblobas, mizanSewonili me- Todebisa da saSualebebis SerCevas. Tu zogadi mizani ar iqneba danawevrebuli kerZo miznebad, maSin es gaaZnelebs gonebriv da praqtikul saqmianobas, gawiravs mas stiqiurobisaTvis. dagegmarebis sapasuxismgeblo nabijia sivrcesa da droSi muSaobis gaTvla-gaangariSeba. erTi saqmea mecadineobis Catareba saklaso oTaxSi, magram sul sxvaa misi Catareba muzeumSi an sxvagan. mniSvnelovani sakiTxia gancalkevebuli nawilebisgan (amo- canebisgan) erTmTliani sistemis Seqmna, magram, amasTan, es sistema SemosazRvruli unda iyos garkveuli CarCoebiT, muSaoba gaTvli- li unda iyos drosa da sivrceSi, gaTvaliswinebuli unda iyos yvela SesaZlo faqti, unda aiwon-daiwonos moswavleTa Zalebi da SesaZleblobebi, sakuTari (maswavleblis) codna, meTodikuri da organizaciuli SesaZleblobebi, moswavleTa momzadebis xarisxi da mravali sxva. 310 jemal jinjixaZe unda iqnes gaTvaliswinebuli moswavleTa individualuri da asakobrivi SesaZleblobebi, maTi potenciali. umcrosklase- lebi advilad iTviseben masalas praqtikidan Teoriisaken svli- sas. magram ar SeiZleba Teoriuli safuZvlis sruli ignorirebac. SemecnebiTi saubrebisa da diskusiebis dros moswavleebma unda gaigon sakiTxis istoria, unda miiRon sawyisi cnobebi xelovnebis im saxeTa Sesaxeb, romlebic Seiswavleba maT mier. praqtika da Teoria erTmaneTTan unda iqnes dakavSirebuli, rom moswavleTa mier miRebuli codna da uSualo STabeWdilebebi erTmaneTs amt- kicebdes da aZlierebdes. dagegmarebis garda, maswavlebelma ar unda daiviwyos, rom warmateba piradad mis SemoqmedebiTobaze bevradaa damokidebuli. amasTan, aucileblad gasaTvaliswinebelia rom, xelovneba flobs sugestiur Zalas. magaliTad, roca vuyurebT saintere- so films, viciT, rom es aris winaswar gadaRebuli msaxiobebis TamaSi, magram mainc gveufleba emociebi: sixaruli, sicili, zo- gjer gvereva cremlebic. swored es aris xelovnebis sugestiu- ri zemoqmedeba. Cvens qvecnobier sferoze moqmedebs ferweruli Tu musikaluri Sedevrebi da Cven xSirad monawileebi vxdebiT im movlenebisa, romlebic gardasul droSi darCa. ai, aseTi saxis sugestiur zemoqmedebebzea agebuli informaciuli barierebis daZlevis meTodika, sugestiur-TamaSobiT formebSi. gavixsenoT xelovnebis sugestiuri zemoqmedebis erTi saoca- ri SemTxveva, romelic Tavis droze msoflioSi elvis siswrafiT gaxmaurda. es moxda 1913 wlis 16 ianvars. tretiakovskis galereaSi gamo- fenili iyo genialuri rusi fermweris _ ilia repinis sworupo- vari tilo `ivane mrisxane da Svili misi ivane 1581 wlis 16 noem- bers~. suraTma sazogadoebis yvela wreSi udidesi gamoxmaureba hpova da ai: mis win aRmoCnda axalgazrda kaci, specialobiT xa- tismwereli, staroobriadceveli abram balaSovi. abramma erTxans ucqira suraTs, da male iseTma risxvam Seipyro, mivarda suraTs da daniT sami Wriloba miayena Svilis mkvlel mefes. es _ saukunis sensacia gaxldaT. abramma SesaniSnavad icoda, rom daxatul suraTs uyurebda. maS, ra moxda? _ moxda is, rom xelovnebis sugestiuri Tvisebis wyalobiT qvecnobierma uzarmazari Zala SeiZina, amotivtivda cnobierebis zedapirze, gaaqtiurda da mTlianad gadafara cno- bieri, TviTon darCa iluzorulad, magram ikisra cnobieris roli da abramic aqtiur moqmedebaSi CaiTria... (Jinjikhadze,2012b: 269-270). 311 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV maSasadame, mSvenierebis sferoSi abstraqtul-xatovani saxee- bis Seqmnisas aqtiuria moswavlis qvecnobiereba. da swored aq aris maswavleblis SemoqmedebiToba uebari pedagogiuri saSualeba. maswavlebelma unda icodes, rom maTematikis gakveTilebze moswavleTa esTetikur aRzrdaSi ganuzomlad didi mniSvneloba eniWeba geometriul cnebaTa da sivrciT-xatovan warmodgenaTa formirebis procesis xarisxobriv aRzevebulobas; abstrahire- bisa da ganzogadebis process moswavle unda grZnobdes, unda ga- nicdides; es procesebi masSi unda iwvevdes amaRlebul grZnobebs. amasTan, Zalze mniSvnelovania xatovani Sedarebebis gamoyeneba. magaliTisaTvis moviyvanoT is SemTxveva, roca abstraqtul msje- lobas axlavs xatovani Sedarebebi da amiT am msjelobas WeSmariti mxatvruloba eniWeba. niSandoblivia akademikos n. n. luzinis mier ricxviTi wrfis swori aRqmis mizniT Seqmnili xatovani saxe: `war- movidginoT, rom yvela racionalur wertilSi anTebulia naTura, maSin mTel wrfeze arc erTi bneli wertili ar rCeba, da, amasTan, gvaqvs usasrulod mravali bneli iracionaluri wertili~. pro- fesorma v. v. nemickim aseTi damateba gaukeTa: `vTqvaT, raciona- lur wertilebSi avanTeT lurji naTurebi, xolo iracionalur wertilebSi _ yviTeli naTurebi, maSin Cvens TvalSi es ferebi erTmaneTs Seereva da Cven davinaxavT mTlian wrfes, ganaTebuls Tanabari mwvane sinaTliT~ (Minkovskiy, 1963: 30). nu vifiqrebT, rom maTematikuri Txrobis stilis mxatvrul doneze ayvaniT maTematika, rogorc mecniereba, an saswavlo sa- gani, simkacrisa da sizustis mxriv raimes dakargavs, piriqiT, igi mSvenierebasa da eleganturobas SeiZens. gaxdeba ufro saintere- so, advilmisawvdomi da saocneboc ki. literatura: 1. Jinjikhadze J., Matematikis datskebiti kursis stsavlebis metodika da teqno- logia. Tbilisi, 2011. 2. Jinjikhadze J., Matematikis datskebiti kursis mecnieruli safudzvlebi. Tbilisi, 2012a. 3. Jinjikhadze J., Tanamedrove pedagogiuri teqnologiebi. Tbilisi, 2012, 343 p. 4. Jinjikhadze J., Mmatematika skhartulebshi. Tbilisi, 2009, 132 p. 5. Tsereteli G., Metri da ritmi Vefkhistkaosanshi, “Sabchota khelovneba”, №2, Tbilisi, 1972. 6. Benduqidze A., Matematika seriozuli da sakhaliso. Tbilisi, 2005. 7. Tsvetkov V. D. Serdtse, zolotoe sechenie i simmetriya. Moskva, 1997. 312 jemal jinjixaZe 8. Arnina N. L. Uroki prekrasnogo. Moskva, 1983. 9. Esteticheskoe vospitanie shkolnikov. Pod. red. A. I. Burova, B. T. Likhache- va. Moskva, 1974. 10. Zenkevich I. Estetika uroka matematiki. Moskva, 1981. 11. Minkovskiy V. L. Ob elementakh esteticheskogo vospitaniya na urokakh matematiki. Matematika v shkole, #4 Мoskva, 1963. 12. Geometriya muzyki http://znanij.blogspot.com Jemal Jinjikhadze AESTHETIC EDUCATION ON THE LESSONS OF MATHEMATICS Summary Aesthetic education of pupils in common, and on the lessons of Mathematics is our Divine pedagogical goal. During the whole history of Mathematics teaching method, during for a long time, it was unimaginable even to think about aesthetic education on the lessons of Mathematics. In Pedagogics, there were the subjects of special aesthetic cycle, such as: singing, drawing, sculpting, dancing and oth- ers, the subjects of humanities were joined to them, and certainly, the science of Mathematics _ this exact and severely abstract phenomena, was not included in that list of subjects. In Russian and Georgian methods of teaching the opinion was prevailed, that aesthetic education has nothing to do with Mathematics. In this paper the basic and fundamental issues of the methods of Aesthetic education of pupils at the lessons of Mathematics are worked out. 313 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV giorgi jinjixaZe agebaze amocanebis amoxsna _ nabiji logikuri azrovnebis ganviTarebisken dawyebi Ti ganaT le bis speci a lo bis baka lav re bis progra ma mo icavs saswav lo kurss: `maTe ma ti kis dawyebi Ti kursis mecni e ru li safuZ v le bi~, romel Sic ageba ze geo met ri ul amoca nebs Tvalsa Ci no adgi li uWiravs. aseTi amoca ne bis amoxs nis unari studen tis maTe ma ti ku ri ganvi Ta re bis erT -er Ti Ziri Ta di maCve ne be li a. amo cane bis samya ro ki Zalze mraval fe ro va ni a. Tavi si unika lu ri mniSv ne lo bis gamo yuradRe ba gava max vi loT erT meTo di kur sakiTx ze: ageba ze geo met ri u li amoca ne bis amox snis etape bi. aseT amoca neb ze muSa o ba students aswav lis amoca ni sad mi iseT midgo mas, romlis drosac amoca na gamo dis rogorc gulmod gi ne Seswav lis obieq ti, misi amoxs na ki _ rogorc kons t ru i re bi sa da gamo go ne bis obieq ti. geo met ri is kurs Si agebis amoca ne bi tradi ci u li amoca ne bi a. am amoca ne bis amoxs nis meTo de bis damu Sa ve ba maTe ma ti ko seb ma jer kidev Zvel saber Z neT Si daiwyes. maga li Tad, piTa go ras skolis warmo mad gen le bi xsnidnen wesi e ri mraval kuTxe de bis agebis sak maod rTul amoca nebs. aseTi amoca ne bi sad mi inte re si ganpi ro be bulia ara marto maTi amoxs nis xerxe bis sila ma zi Ta da origo na luro biT, aramed didi praqti ku li fase u lo bi Tac. mSeneb lo bis dageg ma re ba, arqi teq tu ra, sxvadas x va teqni kis kons t ru i re ba da fuZne bu lia geo met ri ul agebeb ze. ageba ze amoca ne bis amoxs na, mraval sxva sike Tes Tan erTad, avi Tarebs pirov ne bis iseT Tvise bebs, rogo ri ca a: yuradRe ba, gul modgi ne o ba, inici a ti va, gamom go neb lo ba, discip li ni re bu lo ba, Sromis moy va re o ba da sxva. magram ageba ze amoca ne bi marti vi ar aris. ar arse bobs aseTi amoca ne bis amoxs nis erTi a ni algo riT mi. yove li maTga ni Tavi se bu rad unika lu ria da amoxs ni saT vis mo iTxovs indi vi du a lur midgo mas. swored amitom ageba ze amoca nebis amoxs nis swavla Zalze Zneli a. magram es amoca ne bi iZle va unika lur masa las moswav le Ta indi vi du lu ri Semoq me de bi Ti Sro misaT vis. amasTan, amoxs nis gzebis Zie ba moswav le Ta intu i ci i sa da qvecno bi e ris daxma re biT xdeba. amis gamo, mizan Se wo ni lad migvaC nia, gava max vi loT yuradRe ba amoca nis logi ki sa da misi amoxs nis 314 giorgi jinjixaZe Zie bis logi kis analiz ze gacno bi e re bul done ze, amoca nis amoxs namde da mas Semdeg, rac amoca na amoxs ni li a. anali zi da damt ki ce ba amoxs nis proces Si. rogorc cnobi li a, ageba ze amoca nis amoxs na Si gamo i yo fa Sem degi oTxi etapi: • anali zi, • ageba, • damt ki ce ba, • gamok v le va. anali zis proces Si, swored rom vTqvaT, mimdi na re obs amoxs nis Zie ba. imisi daSve bi dan, rom amoca na amoxs ni lia da saZi e be li figu ra agebu li, cdilo ben gamo iy va non iseTi Sede ge bi, romle bic sakma ri si iqnes imisaT vis, rom saZi e be li figu ra iqnes agebu li. ageba mimdi na re obs anali zis mier gakva lu li gziT, etapob ri vad, nabij - na bij, mxolod saxa za vi sa da farg lis meSve o biT, e. i. vrclad da Tana mim dev ru lad aRiwe re ba ageba ze umarti ve si amo cane bis amoxs na, romel Ta erTob li o ba gana pi ro bebs saZi e be li fi guris agebas. damt ki ce ba Si unda dasa buT des, rom agebu li figu ra namd vi lad akma yo fi lebs amoca nis yvela moTxovnas. bolos, gamok v le va Si unda dadgin des: sawyisi mona ce me bis ro meli SerCe vis dros aqvs amoca nas amoxs na da ramde ni amoxs na aqvs amoca nas sawyisi mona ce me bis yove li dasaS ve bi SerCe vi sas. logi kis Tvalsaz ri siT, ageba ze amoca nis amoxs nis sakvan Zo etapia ori: anali zi da damt ki c eba. ageba ze amoca nis amoxs ni sas anali zis Sede ge bi damt ki ce bis pi robe bi xdeba, xolo anali zis piro be bi _ damt ki ce bis Sede ge bi. es imas niSnavs, rom anali zis dros Cven vadgenT pirda pir Teo re mebs, damt ki ce bis proces Si ki viye nebT maT Sebru ne bul Teo re mebs. aqedan gamom di na re obs anali zis amoca na: mis msvlelo ba Si ga movle nil iqnas iseTi Teo re me bi, romel Ta Sebru ne bu li debu le bebi TviTon iqne bi an Teo re me bi. ganvi xi loT agebis erTi maga li Ti, klasi ku ri ins t ru men te bis _ saxa za vi sa da farg lis gamo ye ne biT. elemen ta rul geo met ri ul agebebs, Cveu leb riv, mia kuT v ne ben Semdegs: 1. gavyoT monak ve Ti or tol monak ve Tad. 2. gavav loT kuTxis biseq t ri sa. 3. moce mul wrfeze moce mu li werti li dan moce mu li mimar Tule biT avagoT moce mu li monak ve Tis toli monak ve Ti. 315 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 4. avagoT mocemuli kuTxis toli kuTxe wveroTi mocemul wertilSi, mocemuli kuTxis gverdiT misgan naCveneb mxares. 5. avagoT wrfe, romelic gadis mocemul wertilze mocemuli wrfis paralelurad. 6. avagoT wrfe, romelic gadis mocemul wertilze mocemuli wrfis perpendikularulad. 7. avagoT samkuTxedi mocemuli sami gverdiT. 8. avagoT samkuTxedi mocemuli ori gverdiTa da maT Soris mdebare kuTxiT. 9. avagoT samkuTxedi mocemuli erTi gverdiTa da masTan mdebare ori kuTxiT. 10. avagoT wrfe, romelic exeba mocemul wrewirs da gadis am wrewiris gareT mocemul wertilze. 11. avagoT marTkuTxa samkuTxedi ori kaTetiT, an kaTetiTa da hipotenuziT, an kaTetiTa da maxvili kuTxiT, an hipotenuziTa da maxvili kuTxiT. amocana: avagoT samkuTxedi misi simaRlis, erT-erTi ferdisa da fuZesTan mdebare kuTxeebis sxvaobis mixedviT. mocemulia h _ simaRle a _ erT-erTi ferdi a _ fuZesTan mdebare kuTxeebis sxvaoba 𝐶𝐶 მოცემულია 𝐾𝐾 ℎ _ სიმაღლე _ ერთ-ერთი ფერდი 𝑎𝑎 ℎ 𝑎𝑎 _ ფუძესთან მდებარე𝛼𝛼 𝑎𝑎 კუთხეების სხვაობა ℎ 𝛼𝛼 𝛼𝛼 analizi: 𝐴𝐴 𝐷𝐷ნახ. 1 𝐵𝐵 vTqvaT, ∆ABC saZiebeli (asagebi) samkuTxedia (nax. 1), amasTan: AB misi fuZea CD aris simaRle h BC aris ferdi a axla SeiZleba naxazze aRvniSnoT mocemuli kuTxe a. 316 giorgi jinjixaZe amisaTvis saWiroa, rom fuZesTan mdebare met kuTxes gamo- vakloT masTanve mdebare naklebi kuTxe (nax. 1). CavTvaloT, rom A > B. maSin, Tu BAK = B BAC _ BAK = KAC = α. SeiZleba axlave davadginoT zogierTi piroba, romelTac⇒ unda akmayofilebdes es elementebi. radganac h da α Sesabamisad warmoadgenen ∆CDB-s kaTetsa da hipotenuzas, amitom h < a (1). rac Seexeba kuTxe a-s, SeiZleba iTqvas, rom, rogoric ar unda iyos A da B, maTi sxvaoba, cxadia, iqneba maxvili kuTxe, e. i. α < 900 (2). gadavideT mocemuli amocanis amoxsnis xerxis Ziebaze. davs- vaT kiTxva: SeiZleba Tu ara mocemuli elementebiT uSualod ava- goT saZiebeli samkuTxedi? _ cxadia, ara! magram, iqneb saZiebeli samkuTxedis romelime nawilis ageba SeiZleba? Tu davakvirdebiT pirvel naxazs, SevamCnevT, rom BCD marTkuTxa samkuTxedSi kaTe- ti CD da hipotenuza BC mocemulobaSi Sedis. amitom am samkuTxe- dis ageba SeiZleba. amiT ganisazRvreba B, da, raki viciT a, ma- Sasadame, SevZlebT, rom ∆BCD-s mivuSenoT ∆ACD da amiT srulad avagoT saZiebeli figura. agebis gegma vipoveT! gadavideT agebaze. CaviweroT agebis calkeuli nabijebi ele- mentaruli agebis nomrebis miTiTebiT (nax. 2). 𝐶𝐶 𝐸𝐸 𝑎𝑎 𝑀𝑀 𝛼𝛼 𝛼𝛼 ℎ 𝑁𝑁 2 1 𝐴𝐴 𝐴𝐴 ნახ𝐷𝐷. 2 𝐵𝐵 ageba: 1. ag. 11. vagebT BCD marTkuTxa samkuTxeds BC=a hipote- nuziTa da CD=h kaTetiT. 1. ag. 4. vagebT CBM= CBN=α. 2. ag. 6. vavlebT DB-s perpendikularul BE-s. 317 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 3. ag. 4. vagebT DCA1= MBE. 4. ag. 4. vagebT DCA2= NBE. miRebuli A1BC da A2BC samkuTxedebi saZiebelia. damtkiceba (nax. 2). am ori samkuTxedidan yovel maTganSi simaRle CD, romelic daSvebulia A1B an A2B fuZeze, agebis Tanaxmad tolia mocemuli h monakveTis. am ori samkuTxedidan yovel maTganSi ferdi BC agebis Tanax- mad tolia mocemuli a monakveTis. axla ganvixiloT A1B da A2B fuZeebTan mdebare kuTxeebis sx- 0 vaoba. samkuTxedSi A1BC meti kuTxea A1. maSin: A1 _ B=(90 _ 0 A1CD) _ B=(90 _ MBE)= _ B= MBA1 _ B= CBM=α; samkuTxedSi A2BC meti kuTxea B, amitom vpoulobT sxvaobas B _ A2 da ana- logiurad vamtkicebT, rom isic udris α-s. gamokvleva: davadginoT, romel pirobebSia SesaZlebeli agebis naCvenebi xuTi nabijis Sesruleba. cxadia, rom (1) da (2) pirobebSi pirveli sami nabiji yovelTvis Sesrulebadia. bolo ori nabiji ki damate- biT gamokvlevas saWiroebs. saqme imaSia, rom yoveli maTgani Sed- geba ori agebisgan: 1. mocemuli kuTxis toli kuTxis ageba (Sesa- bamisad MBE da NBE) da 2. miRebuli sxivis DB wrfesTan kveTis wertilis ageba. mocemuli kuTxis toli kuTxis ageba yovelTvisaa SesaZlebeli, magram miRebuli sxivis wrfesTan kveTis wertilis agebis sakiTxi gamosakvlevia. Tu BM sxivi gadis CBE kuTxis SigniT, maSin me-4 nabiji yo- velTvis Sesrulebadia. Tuki BM sxivi gadis xsenebuli kuTxis gareT (me-2 naxazze BE- dan marjvniv), maSin aq SesaZlebelia sami SemTxveva: 1. sxivi BM gadis marjvniv ise, rom BEM ≥ DCB, e. i. , α _ (900 0 0 _ B) ≥ 90 _ B, anu α+2 B ≥ 180 . am SemTxvevaSi CA1 sxivi gaivlis DCB-s gareT, amitom samkuTxed A1BC-s ageba SeuZlebelia. 2. Tu BM gadis BE-s marjvniv ise, rom BEM < DCB, maSin CA1 gaivlis DCB-s SigniT, da aseT SemTxvevaSi samkuTxedi A1BC iqneba blagvkuTxa. 3. Tuki BM emTxveva BE-s, maSin samkuTxedi A1BC emTxveva DCB samkuTxeds. aseT SemTxvevaSi amoxsnaSi miiReba marTkuTxa samku- Txedi. aseTive wesiT gamovikvlevT me-5 nabijsac: • Tu sxivi BN gadis DBC-s SigniT, maSin A2BC samkuTxedis ageba SeiZleba. Tuki BN emTxveva BD-s an gadis DBC-s gareT, 318 giorgi jinjixaZe maSin NBE ≥ 900, amitom ar gadakveTs DB-s D-sagan marcxniv, maSa- sadame, A2BC samkuTxedis ageba SeuZlebelia. amgvarad, vxedavT, rom α da b kuTxeebis sxvadasxva urTierT- mimarTebebis dros amocanas SeiZleba: 1. ar hqondes amonaxsni, 2. hqondes erTi amonaxsni, 3. hqondes ori amonaxsni. amocana amoxsnilia. Giorgi Jinjikhadze SOLVING TASKS BY DRAWING _ A STEP TOWARDS DEVELOPMENT OF LOGICAL THINKING Summary In this article, due to its unique significance, attention is focused on one issue: the stages of solving Geometric tasks by drawing. Working on such tasks teaches students usage of such approach towards the tasks, when the task is represented as the subject of diligent study, and its solution as an object of construction and invention. It is shown that while solving a task by drawing the results of analysis became the conditions of proving and the conditions of the analysis the results of the approval. On the concrete example has been considered the question why we state the straight theorems at the process of analyzing and in the process of approval we use their eversible theorems. 319 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV gulnaz xuxua moraluri devianturoba da maTi sakoreqcio pedagogiur RonisZiebaTa sistema `bavSvis gulis xmas Tu gaigeb, amova mze, wvima gadaiRebs~ meri popinsi morali anu zneoba adamianuri Rirsebis erT-erTi unikaluri parametria, romelic RvTiT boZebuli bunebrivi unarebis, zneo- brivi aRzrdisa da socialuri garemos faqtorTa gavleniT ya- libdeba. zneoba gamoarCevs adamians Tavisi msgavsi arsebebisagan. am gansxvavebas qmnis eTikuri normebisa da wesebis codna, am co- dnis mixedviT cxovrebis survili, (moTxovnileba) da praqtikuli unar-Cvevebi. zneoba sikeTis, siyvarulis, mSvidobis, bednierebisa da aRmSeneblobis safuZvelia. siZulvili, ngreva, Zaladoba, ome- bi, terorizmi, TviTmpyrobeloba, egocentrizmi, materializmi, karierizmi, flobisa da gamdidrebis mania, garyvnileba, loToba, narkomania da sxva msgavsi sisaZagleebi, riTac gansakuTrebiT ga- moirCeva XXI saukune, amoralurobis Sedegebia, romelic arRvevs samyarosa da sazogadoebis harmonias, wonasworobas, silamazesa da mSvenierebas, diadsa da amaRlebuls. zneoba sikeTisa da mSve- nierebis dedaa; uzneoba ki _ simaxinjis, borotebisa da ubedure- bis mSobeli. moraluri gadaxra (devianturoba) raime organuli daavadeba ar aris, magram ufro meti zianis miyeneba SeuZlia pirovnebisa da sazogadoebisaTvis, vidre nebismier avadmyofobas. marTalia, daa- vadeba safrTxes uqmnis sicocxles, rom es yofna-aryofnis sakiTxia da, swored, janmrTelobas amitom ukavia didi adgili adamianisa da sazogadoebis cxovrebaSi. da, amaze namdvilad aravin davobs. problema sxva rameSia. moralis `seni~ exeba adamianis Rirsebas, mis pirovnul srulfasovnebas, damokidebulebas adamianur, sazo- gadoebriv, erovnul da zogadkacobriuli Rirebulebebs; imas, Tu ramdenad aqvs mas gacnobierebuli Tavisi pirovnuli daniSnuleba, movaleoba da pasuxismgebloba. Tu pirovnebis azrebi da fiqre- bi, qcevebi da moqmedebebi fuWia, zianisa da ubedurebis momtani, maSin arafrad Rirs misi arc janmrTeloba da arc sicocxle. ge- nialurad Tqva didma iakob gogebaSvilma adamianis RirsebasTan 320 gulnaz xuxua dakavSirebiT, roca maradiul sulier Rirebulebebze miuTiTeb- da: `adamianis Rirseba ganizomeba gonebrivi simaRliT, zneobrivi sispetakiT da sikeTiT, romelsac Tesavs igi Tavisi moRvaweobiT~ (Gogebashvili 1946). bevrad ufro adre msgavsi azri gamoTqva ian amos komenskim Tavis gauxunar sqeltanian `did didaqtikaSi~: `adamiani Seqmnilia saganTa SecnobisaTvis, zneobrivi harmoniisaTvis da RvTis usa- zRvro siyvarulisaTvis . . . ~ (Komenski, 1949: 46). jer kidev 3500 wlis win bibliaSi Caiwera zusti monacemebi adamianis Seqmnisa da misi daniSnulebis Sesaxeb, saidanac vigebT, rom RmerTma adamiani Seqmna siyvarulis, gamravlebis, Semecnebis, keTebisa da Segnebuli cxovrebis unarebiT, aRWurva moqmedebisaT- vis saWiro mowyobilobebiT, SegrZnebebisa da fsiqikur-intele- qtualuri organoebiT. yovlisSemoqmedma am unikalur qmnilebas imTaviTve gamoucxada Tavisi daniSnuleba da miuCina sacxovrebeli adgili: `gaaSena iehova RmerTma baRi edemSi aRmosavleTiT da iq daasaxla adamiani, romelic Seqmna~ (dabadeba 2:8) da uTxra: `aha, inayofiereT, gamravldiT, aavseT dedamiwa, daepatroneT mas da Tqven gemorCilebodnen zRvis Tevzebi, cis frinvelebi da yvela cocxali arseba dedamiwaze~ (dabadeba 1:28). am bibliur muxlebSi, specialuri kvlevis gareSec, naTlad Cans Semoqmedis mier dadgeni- li kanonebi, uflebebi da movaleobebi, cxovrebis azri da adamianis daniSnuleba. adami da eva unda miyolodnen RvTis xelmZRvanelo- bas, eSromaT, gamravlebuliyvnen da mTeli dedamiwa baRnarad eq- ciaT, aseve unda epatronaT da maT gankargulebaSi unda yofiliyo mTeli ekosistema, yoveli cocxali arseba: zRvaSi Tevzi, frTosne- bi Tu cxovelebi rom bednierad ecxovraT mSvidobian, usafrTxo, lamaz da mdidar garemoSi. mogvianebiT misca werilobiTi instru- qcia jer aTi mcnebis saxiT, Semdeg misca biblia, unikaluri wigni warsulis, awmyosa da momavlis Sesaxeb da mTeli xiluli samyaro uxilavis Sesacnobad. adamianebma ki, romelsac aranairi wvlili ar Seutania samyarosa da sicocxlis SeqmnaSi ise, sruliad daumsaxu- reblad miiRo amxela saCuqari, sicocxle, arsebobisa da Segnebuli cxovrebisaTvis saWiro yvelanairi pirobebi, madlierebis nacvlad, maT kidev ufro meti moindomes. ugulebelyves RvTis mier dadge- nili kanonebi da principebi da uyoymanod, `didi drakonis, Zveli gvelis, romelsac eSmaki da satana hqvia da romelsac SecdomaSi Sehyavs mTeli msoflio~ (gamocxadeba 12: 9), imis mxareze dadgnen. Cadenili codvebis gamo dakarges RvTis kurTxevebi da srulyo- fileba. dRes adamianis inteleqtualuri SesaZleblobebi 2%-s ar 321 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV aRemateba. kacobriobis absoluturi umravlesoba am minimalur SesaZleblobasac ki sworad ver iyenebs. statiis specifika ar gva- Zlevs saSualebas am sakiTxis ufro Rrmad da vrclad ganxilvisa, magram vfiqrobT, esec sakmarisia, im pirveli da mTavri mizezis gasagebad, ramac gamoiwvia adamianis, am unikaluri, srulyofili qmnilebis am doneze daknineba, kerZod, moraluri degradacia. Sei- Zleba, swored adamianis dacemam did mecniers, Carlz darvins afi- qrebina, rom adamiani maimunisgan iyo. kacobriobis istoria dRemde sikeTisa da borotebis Widilia. miuxedavad gonebrivi ganviTarebis mcire procentuli maCvene- blisa, adamianma bevri kargi saqmis gakeTebac SeZlo. amaze metyve- lebs xelTqmnili materialuri saganZuri, mecnierul-teqnikuri miRwevebi, rac swavla-ganaTlebisa da aRzrdis damsaxurebaa. pa- ralelurad, istoriuli da Tanamedrove statistikuri monaceme- bi im borotqmedebebisa, rac dRemde Caudenia adamians, magaliTad: Zaladobebi, dampyrobluri da samoqalaqo omebi, xocva-Jletvebi da sxva araadamianuri qcevebi: egocentrizmi, materializmi, te- rorizmi, sadizmi, nihilizmi, usamarTloba, upatiosnoba, Suri, sixarbe, gaumaZRroba, qurdoba, garyvniloba, loToba, narkomania da a. S., rasac Sedegad mohyva siZulvili, siRatake, ganukurnebe- li daavadebebi, emociuri moSla, fsiqozi, nevrozi ganurCevlad asakisa, naTlad amtkicebs imas, rom adamianurma mmarTvelobis sistemam, RvTis kanonebisa da principebis ugulebelyofam qvey- niereba miiyvana am sazarel mdgomareobamde. dasabamidan dRemde kacobriobis ideals warmoadgens mSvido- ba da usafrTxoeba, siyvaruli da bedniereba. veravin ipovis ada- mians, romelsac es ar undodes. sazogadoebrivi cxovrebis arc erT sferoSi ar dawerila imdeni mecnieruli Sroma, ramdenic zneobasa da zneobriv aRzrdaze. magram Sedegi?! - minimaluri! mizezi? _ uRmerToba da cudi aRzrda. veravin daasaxelebs sxva faqtorebsa da mizezebs, Tu maT niuansebs, romelic mizezTa am or kategoriaSi ar Tavsdebodes. yvelafers, dawyebuli umciresi sagnidan planetebis CaTvliT galaqtikebamde arsebobis Tavisi wesi aqvs; moZraobas, ganviTare- bas, cvlilebas mkacrad gansazRvruli da dadgenili sazRvrebi _ wesebis, kanonebis, principebis, Sesabamisi konkretuli Sinaarsi- sa da sistemebis saxiT. mTel samyaros da rac masSia, yvelafers azri da fasi aqvs, funqcia da daniSnuleba mxolod da mxolod adamianTan mimarTebaSi. adamians Tu es ar esmis da saTanadod ar afasebs, ufro metic, Tu mas zians ayenebs, ngrevis, ganadgurebis 322 gulnaz xuxua da yovelgvari ubedurebis mizezi xdeba, maSinaTve qreba Rirebu- li, faseuli, cxovrebis azri da adamianis daniSnuleba. adamianis srulfasovneba misi potenciuri Sesaleblobebis pi- rovnuli da socialuri unarebis, yovelmxriv harmoniul ganviTa- rebaSi mdgomareobs. magram es procesi avtomaturad ar mimdina- reobs, rogorc es xdeba magaliTad, mis biologiuri da fizikuri determinantis wiaRSi, sadac fiziologiuri procesebi sxeulis nawilebis SeTanxmebul, koordinrebul, sinqronuli wesiT funq- cionirebs zrdis Sesabamis garemoSi. adamianis pirovnuli srulfasovnebis, misi unikalurobis kri- teriumi gansazRvrulia da dagenili aTaswleulTa codna-gamoc- dilebis safuZvelze. pirveli, es aris Semecnebis, gageba-gansjis inteleqtualuri unari, romlis ganviTareba swavlebis gareSe ar arsebobs. ratom?! imitom, rom swavleba iseT funqciebs asrule- bs, romelic uzrunvelyofs srulfasovani pirovnebis formire- bas. es is funqciebia: saganmanaTleblo, ganmaviTarebeli, aRmzr- delobiTi da SromiTi. es sakiTxebi pedagogikis Teoriidan kargad aris cnobili, romelsac eyrdnoba yvela pedagogikur mecniere- baTa sistemaSi Semavali dargi da maTi Seswavlis winapirobas war- moadgens. amitom maT aq detalebSi ar SevexebiT. mxolod imas Se- vixsenebT, Tu ra moiazreba konkretulad swavlebis dasaxelebul funqciebSi, romelTa gareSe ar Sedgeba saswavlo-aRzrdelobiTi procesi, es saklaso-sagakveTilo sistemaSi iqneba, Tu klasgare- Se muSaobis procesSi. saganmanaTleblo funqciaSi moiazreba in- formaciuloba, codna-gamocdilebisa da unar-Cvevebis maragi anu baza, romlis repertuarSi Sedis cnobierebis yvela sfero, es iq- neba sabunebismetyvelo, sazogadoebivi, teqnikuri codnis ciklis sagnebi Tu xelovnebis dargebi. swavlebis ganmaviTarebeli funqcia emsaxureba fsiqikur-in- teleqtualuri anu saswavlo unarebisa da saazrovno operaciebis ganviTarebas. rogoricaa: SegrZneba, aRqma, warmosaxva, gaazreba, yuradReba, nebisyofa, mexsiereba da a. S. rac Seexeba saazrovno operaciebs, aq moiazreba analizis, sinTezis, Sedarebis, klasi- fikaciis, asociaciuri moqmedebebis, daskvnebis, ganzogadoebisa da sistematizaciis da sxva msgavsi moqmedebebis ganviTareba, romelTa sawyis etaps warmoadgens SegrZnebebi sensoruli orga- noebis meSveobiT. SegrZnebebi ki emyareba sagnebsa da movlenebze empiriul dakvirvebs. amaSi mdgomareobs TvalsaCinoebis dida- qtikuri principis daniSnuleba anu swavlebis `oqros wesi~, ro- gorc pedagogikis klasikosebma uwodes mas. 323 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV swavlebis aRmzrdelobiTi funqcia maswavlebels avaldebu- lebs aRsazrdelebs ganuviTaros miRebuli ganaTlebis Sesatyvisi mrwamsi, msoflmxedveloba, damokidebulebebi, Sefasebebi, mid- gomebi, pozicia, urTierTobebis kultura da a.S. romelic ka- tegoriebis mixedviT ganTavsdeba Semdeg cnobil, ucvlel, uni- versalur da Sesabamisad maradiul parametrebSi da gardaiqmneba aRzrdis komponentebad, rogoricaa: gonebrivi aRzrda, zneobri- vi aRzrda, sulieri aRzrda, esTetikuri aRzrda, fizikuri aR- zrda, ekologiuri da SromiTi aRzrda. ekologiuri aRzrda da Sroma zneobrivi kategoriebia da zneobriv aRzrdaSi moiazreba, magram Tanamedrove realuri sinamdvilidan gamomdinare, maTze specialuri muSaobaa saWiro, rom aRsazrdelma miiRos ekologiu- ri ganaTleba da Sromis arsi gaigos, rogorc umaRlesi adamia- nuri funqcia, gamoumuSavdes Sromismoyvareoba, Sromis iaraRisa da Sromis produqtisadmi gafrTxileba da mSromelisadmi pati- viscemis grZnoba, Sromis SedegebiT moraluri kmayofilebisa da esTetikuri siamovnebis gancdis unari, rac amSvenebs da zneobis yalibSi svams adamians, sidiades aniWebs mis moralur saxes. moraluri gadaxra anu uzneoba araa Tandayolili anu endo- genuri warmomavlobis da rogorc ukve vTqviT, arc organuli daavadeba. is aris egzogenuri faqtorebiT gamowveuli cudi aR- zrdis logikuri Sedegi. moraluri devianturoba (gadaxra) sxva- dasxva saxiT vlindeba da Tavsdeba minimum-maqsimum zRurblTa Soris, iwyeba pedagogiuri CamorCenilobiT da TandaTanobiT ga- dadis jer akademiur mouwesrigeblobaSi, Semdeg asocialurobaSi da, bolos, yalibdeba antisocialur kategoriad. adamiani, rogorc biologiur-socialuri arseba, dabadebis- Tanave avlens biologiur moTxovnilebebs: moZraobis, kvebis, Sim- Silis, wyurvilis, siTbos, sicivis, Zilis, dasvenebis, komunkaciis, TamaSis, garTobis, Sromisa da a. S. am biologiuri moTxovnile- bebis dakmayofilebis aucilebloba aiZulebs bavSvs paralelur urTierTobas gare samyarosTan, rac vlindeba iseT sociogenur moTxovnebSi, rogorica: Semecneba, cnobismoyvareoba, mimbaZvelo- ba, yuradReba, mzrunveloba, swrafva didobisaken, Tavisuflebisa- ken, damoukideblobisaken, survili imisa, rom endobodnen, anga- riSs uwevdnen, pativs scemdnen, azrs ekiTxebodnen, masSi pirovne- bas xedavdnen da afasebdnen. moTxovnaTa masStabebi izrdeba asa- kobriv zrdasTan erTad. asakobriv cvlilebebs yofen periodebad da mis mixedviT gansazRvraven damaxsiaTebel rogorc asakobriv, ise individualur Taviseburebebs, fsiqikur-inteleqtualur da 324 gulnaz xuxua fizikur SesaZleblobebs. pedagogiuri kanonebisa da principebis sruli gaTvaliswinebiT adgenen saswavlo gegmebsa da programebs. ganaTlebis Sinaarss, saswavlo-aRmzrdelobiT RonisZiebaTa peda- gogiur sistemebs ojaxSi, sabavSvo baRSi da skolaSi. zemoTqmulidan gamomdinare, ibadeba legitimuri kiTxva: ra- mdenad aris gaTvaliswinebuli bavSvis aRzrdaSi misi moTxovnebi da moTxovnilebebi, aRzrdisa da ganviTarebis pedagogiuri kano- nebi, kanonzomierebebi da principebi? am kiTxvaze pasuxs iZleva skolebsa da umaRles saswavleble- bis pedagogiur fakultetebSi bolo wlebSi Catarebuli pedago- giuri gamokvlevebis Sedegebi, romelmac aCvena, rom maswavlebel- Ta 95%-ze meti pedagogiur kanonebsa da principebis Sesaxeb cod- nis minimumsac ki ver akmayoflebs. miuxedavad imisa, rom aRzrdas garda pedagogiurisa, sxva faqtorebic ganapirobebs, gadamwyveti sityva mainc pedagogikas ekuTvnis, radgan pedagogika warmoad- gens aRzrdis ZiriTad da Seucvlel mecnierebas. bavSvis moraluri gadaxrebis dasadgen kriteriumad iReben prosocialuri kategoriis Tanatolebis qcevebsa da moqmedebe- bs. prosocialur jgufs miekuTvnebian aRsazrdelebi, romlebic sanimuSo yofaqceviTa da maRali akademiuri moswrebiT gamoirCe- vian. aTvisebuli da gacnobierebuli aqvT moswavlis qcevis wesebi da icaven mas. advilad emorCilebian skolis, ojaxisa da sazoga- doebis kanonier moTxovnebs, pativs scemen ufrosebs, mSoblebs, maswavleblebs, Tbili da megobruli damokidebuleba aqvT Tana- tolebis mimarT, aravis Cagraven da amcireben, uyvarT buneba da rac masSia, flora, fauna; afaseben dedamiwas, haers, wyals; Tava- zianebi da Tavmdablebi arian, zomierebi da gawonasworebulebi, damjerebi da momsmenebi, pasuxismgeblobis grZnobiTa da zneke- TilobiT gamorCeulebi. magram, samwuxarod, am kategoriis bavS- vebi yovelTvis umciresobas warmoadgenen. amitom Tanatolebze/ Tanaklaselebze maTi keTilmyofeli gavlenac naklebia. prosocialurobis sapirispiro mdgomarebaa antisocialuroba, zneobrivi ganviTarebis qveda da zeda zRrubli, romelTa Soris xdeba gradacia pedagogiuri CamorCenilobis, akademiuri mouswre- blobisa da asocialurobis saxiT. antisocialurobis maCvenebeli niSnebia sazogadoebrivad miuRebeli, kriminaluri qcevebi. sko- lis, ojaxisa da sazogadoebis moTxovnebisadmi daumorCileblo- ba, yvelasa da yvelafrisadmi upativcemloba, dabali akademiuri moswreba, konfliqturoba, moweva, alkoholisa da narkotikebis moxmareba, qurdoba, seqsualuri TavSeukavlebloba, bilwsityvaoba 325 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV da a. S. magram am kategoriis moswavleebi aseTebad ar dabadebulan. isic sagulisxmoa, rom maT sruliad jansaR mdgomareobaSi aqvT Se- mecnebis unarebi, fsiqikuri da inteleqtualuri da, saerTod, go- nebrivi SesaZleblobebi. gadaxriloba imaSi mdgomareobs, rom isini am bunebriv SesaZleblobebis ganviTarebis nacvlad, mas araswori mimarTulebebiT iyeneben. drosa da energias usargeblo, saziano saqmeebSi xarjaven, mTavari ki gverdze rCebaT. rogorc cnobilia, gonebrivi SesaZleblobebis sworad ganviTarebis erT-erTi ZiriTa- di, mTavari da wamyvani faqtoria swori aRzrda, romelic organul kavSirSia swavlebasTan. antisocialuroba erTbaSad ar yalibdeba. mas safuZvlad ude- vs sxvadasxva mizezebi, magram gonebajansaR bavSvebSi faqtori er- TaderTia. es aris garemo faqtorebi, magaliTad: socialuri gare- mo, ojaxuri mdgomareoba, ekonomiuri siduxWire, usamarTlobisa da araobieqturobis SegrZneba, arasrulfasovnebis kompleqsi, gaumarTavi urTierTobebi, imedebis gacrueba, mware simarTlis gageba, uyuradReboba, upativcemloba, undobloba, zedmeti kon- troli, bunebrivi Tavisuflebisa da damoukideblobis SezRudva, Tundac saukeTeso motivebiT, gonieri winamZRolis, `cxovrebis lamazi megzuris,~ erTguli da mosiyvarule mesaidumlis, mrCe- vlisa da damrigeblis, momsmenisa da gamgebis aryola, romelTa- nac Tavs pirovnebad igrZnobda, guls gauxsnida, miendoboda da gahyveboda. da, rac yvelaze mTavaria, ganicdian wrfeli siyvaru- lis deficits, usamarTlod dasja da yovelive is, rac xels uS- lis TviTdamkvidrebasa da TviTrealizaciis process, sociogenu- ri moTxovnebis dakmayofilebas TavianTi ZalebiT ver umklavde- bian da umweobis dasafaravad, yuradRebis misaqcevad yvelaferze midian. mcdar gzas adgebian. antisocialurobis sawyisi etapi dgeba pedagogiuri CamorCeni- lobis siptomebis gamovlinebisTanave, romelic aisaxeba moswavlis inteleqtualuri aqtivobis SenelebaSi, maswavleblis moTxovne- bisadmi daumorCilebasa da upasuxismgeblobaSi. qcevis araadekva- turobaSi, gonebrivi SesaZleblobebis arasaTanadod gamoyenebaSi. aSkara xdeba SemecnebiTi pasiuroba, ezareba Sroma, mecadineoba, gakveTilze mosmeniliT kmayofildeba, Tumca damakmayofilebel da ufro metad karg Sefasebebs iRebs zogjer. ar mihyveba dRis reJims, naklebad icavs moswavlis qcevis wesebs, agvianebs, acdens gakveTilebs, Tavis gasamarTleblad ityueba, droisa da energiis umetes nawils axmars TamaSs, garTobas missave ganwyobis Tanato- lebTan ezoSi, quCaSi, ubanSi da ase TandaTanobiT farTovdeba 326 gulnaz xuxua e. w. `Tavisuflebis~ areali. Tu am cdomilebebs droulad ar mohyva saTanado reagireba skolisa da ojaxis mxridan, TavaSvebuloba aRsazrdels Cvevad eqceva da ufro met masStabebs iZens, rasac mosdevs akademiuri CamorCeniloba. akademiurad CamorCenilTa ka- tegoriebs miakuTvneben moswavleebs, romlebic dabal Sefasebebs Rebuloben erT an ramdenime saganSi, ar iCenen SemecnebiT aqtivo- bas, daqveiTebuli aqvT inteleqtualuri interesi da motivacia. mimzidvelobas kargavs maTTvis pedagogiuri procesi. ufro izi- davT garToba, TamaSi, eZeben ufro advil gzas TviTdamkvidrebisa da Tavis warmosaCenad da mas axmaren mTel dros, energias da ganze rCebaT mTavari _ ganaTlebis miReba. am kategoriis bavSvebi pirvel aradamakmayofilebeli Sefasebis miRebas mwvaved ganic- dian, meore msgavsi Sefaseba usiamovnebas hgvriT, mesame jerzec ar siamovnebT, magram aman Tu sistemuri xasiaTi miiRo, SeCvevis faqtori gamodis wina planze da masze ukve arc ki reagireben. samagierod erTgvar kompensaciad aRiqvamen maTnair mdgomareo- baSi myof TanatolebTan `grials~ da e. w. `Zveli biWis,~ `magari gogos~ statuss irgeben da TandaTanobiT asocialur kategoriaSi inacvleben. asocialurobis maxasiaTebeli niSnebia: xasiaTis meryeoba, susti nebisyofa, impulsuroba, infantilizmi, sazogadoebrivi azrisadmi uptivcemulo damokidebuleba, mocemul sazogadoebaSi dadgenili qcevisa da moqmedebis normebisa da wesebis ignorireba, skolisa da ojaxis kanonieri moTxovnebisadmi daumorCileblo- ba, socialuri motivebis uqonloba, gavlenebis mopoveba, egocen- truloba, didobisaken swrafva, TviTdamkvidrebisaTvis brZola. amitom advilad eqcevian antisocialuri bavSvebis gavlenis qveS da iwyeba moweva, Zalebis mosinjva e.w. `ZvelbiWobaSi~, akeTeben yvelafers maTTan dasaaxloeblad da a. S. rasac mihyavs antiso- cialurobamde. hgoniaT, rom aseTi qcevebiT kompensacias ikeTe- ben imisa, rac daakldaT skolisa da ojaxis pirobebSi. antisocialuroba warmoadgens kriminalur, sazogadoebri- vad saSiS mdgomareobas, moralur defeqts, romelic SeCvevis gamo tvinis bio-qimiuri struqturis nawilad aris gadaqceuli. am kategoriaSi igulisxmeba moweva, alkoholizmi, narkomania, mkvleloba, qurdoba, yaCaRoba, Zaladoba, garyvniloba, sruli gaunaTlebloba, sulieri da zneobrivi daknineba, gulisTqmebi- Ta da xorcisTqmebiT gataceba da a.S. xSirad Cadian imas, rac sisxlis samarTlis danaSaulad iTvleba da xvdebian kidec gan- sasjelis skamze. 327 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV amasobaSi ferxdeba gonebriv-inteleqtualuri ganviTareba, Raribdeba leqsikuri maragi, metyvelebis kultura, zneobrivi Segneba, esTetikuri gemovneba, graciozuloba da adamiani kargavs moralur saxes, rac aisaxeba mis qcevasa da moqmedebaSi, urTier- TobebSi, kulturuli da materialuri Rirebulebebisa da zneo- brivi faseulobebisadmi damokidebulebaSi, udardelobaSi, ga- regnul iersaxeSi, JestikulaciaSi, JargonebiT metyvelebaSi, Cac- mulobasa da varcxnilobaSi; irCeven eqstravaganturobas, mkveTr gansxvavebulobas; daxeuli Sarvlebi, ukiduresad viwro da mokle kabebi, mkerdis, Wipis moSiSvleba, flirti, JargonebiT metyvele- ba da a. S. maTTvis erTgvar savizito baraTad aris qceuli. aRniSnul problemebs, rogorc zemoT aRvniSneT, uamravi fa- qtori da mizezi iwvevs, magram maT Soris umTavresia aRzrda, romelzedac pasuxismgebelia aRzrdis ori ZiriTadi institucia: skola da ojaxi. skola eyrdnoba aRzrdis mecnierul codnas, ojaxi ki _ mSobliur siyvaruls, pasuxismgeblobasa da gamocdi- lebas. roca orive instituti erTi mizniT arian gaerTianebuli da TavianT aRmzrdelobiT funqciebs uzadod da maRali pasuxis- mgeblobiT asruleben, Sedegic adekvaturia, garda umciresi ga- monaklisisa. cxadia, rom garda skolisa da ojaxisa, Cveni gare- momcveli sinamdvile mravalferovania da aTasi gaTvaliswinebu- li da gauTvaliswinebeli sferoebi Tu situaciebi axdens bavSvze zemoqmedebas da aravinaa am gavlenebisgan dazRveuli. moralur devianturobas zemoaRniSnul faqtorebTan (aRzrda, skola, ojaxi, socialuri garemo) erTad gaaCnia Tavisi mizezebic: skolisTvis moumwifebloba, akademiuri CamorCena, droebiTi avadm- yofoba, ojaxuri mdgomareoba, saswavlo nivTebisa da saskolo tan- sacmlis uqonloba, TanatolebTan SeuTavsebloba, sizarmace, Tama- SiT an raime hobiT, kompiuteriT, mobiluriT zedmetad gataceba, zedmeti simorcxve da gaubedavoba, arakomunikabeluroba an kidev piriqiT, zedmeti siTamame, siamaye, qedmaRloba, ampartavnoba, an maswavleblis araprofesionalizmi, araobieqturi Sefaseba, damcire- ba, upativcemloba da a.S. umizezod bunebaSi araferi xdeba. mizezs yovelTvis mosdevs Sedegi siptomebis saxiT. mizez-Sedegobriobis kanonzomierebis codna iZleva problemis gaxsnis saSualebas. moraluri devianturobis faqtorebisa da mizezebis swori gamokvleva, analizi da obeqturi daskvnebi iZleva aseve swori diagnostikisa da adekvaturi pedagogiuri koreqciis saSualebas. Tanamedrove mecnierul-teqnikurma progresma zenits miaR- wia, magram amas ver vityviT moralis sferoSi. moralis gareSe ki 328 gulnaz xuxua samarTlianobaze, bednier da mSvidobian cxovrebaze ocnebac ki warmoudgenelia. amitom daisva legitimuri kiTxva: `teqnika kur- Txevaa Tu wyevla.~ ra Tqma unda, orivea. saqme misi gamoyenebis kulturaSia. televizias, romelmac 1931 wlidan mTeli msoflio moicva da dRes misma ricxvma 15 miliards gadaaWarba, mas, garkveu- li mosazrebiT, `maswavlebelsac~ uwodeben. misi meSveobiT vecno- biT mTel msoflioSi Tu kosmiur sivrceSi mimdinare movlenebs, qveynebsa da xalxebs, vmogzaurobT tropikul junglebSi da po- lusebze, mTaTa mwvervalebsa da okeanebis siRrmeebSi, viWrebiT kosmosSi, vigebT ra xdeba dedamiwis sxvadasxva kuTxeSi, vecno- biT miRwevebs mecnierebaSi, kulturasa da xelovnebaSi, sportis sferoSi da a. S. erTi sityviT, asrulebs SemecnebiT, eTikur da esTetikur funqciebs. igive iTqmis kompiuterze, internetze, mobilurze, planSet- ze, maTi unikalur dadebiT SesaZleblobebze. Rilakis an mausis erTi dawkapunebiT rom Sens Tvalwin gadaiSleba mTeli samyaro. interneti-msoflios udidesi biblioTeka, droisa da sivrcis dimensionebSi SeuzRudavi. mis sakacobrio _ sazogadoebriv Rire- bulebas ganapirobebs misi gamoyenebis kultura. mobiluri tele- foni _ XXI saukunis saocreba. am miniaturuli aparatis saocrebas dedamiwa ver itevs. es saocreba sul Sens samsaxurSia, Sin xar Tu gareT. divanze wamowolili vis ginda rom ar daukavSirde de- damiwis kidiT-kidemde vizualurad, werilobiT Tu verbalurad. namdvilad kurTxevaa gonivrulad, eTikur da esTetikur sazR- vrebSi gamoyenebuli teqnika. magram Tu ar gaviTvaliswinebT mis uaryofiT mxareebs da borotad gamoviyenebT, namdvil wyevlas- Tan gveqneba saqme. cduneba `stiqiur ubedurebad~ gveqceva. saqme imaSia, rom satelevizio gadacemebisa da internetSi ganTavsebul informaciaTa didi nawili Zaladobasa da pornografias exeba. teleekranebze Tu kompiuteris monitorze farTod da daufa- ravad warmodegenili uxamsi scenebis yureba cnobismoyvareobis, SeCvevisa da mimbaZvelobis Tandayolili unaris wyalobiT, droTa ganmavlobaSi axalgazrdebis mier aRiqmeba rogorc Cveulebrivi movlena, rogorc norma, damangrevel zegavlenas axdens mozarde- bisa da axalgazrdebis (da aramarto maTze!) cnobierebaze, zneo- briv sispetakeze, sulier da materialuri Rirebulebebisadmi da- mokidebulebaze, rac maT qcevebSi, CacmulobaSi, varcxnilobasa da metyvelebaSi aisaxeba. axalgazrdebze pornografiuli suraTebis gamxrwnel gavle- nasTan dakavSirebiT teqnikur-eleqtronuli mediis mimomxilvelma 329 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ton personzma dawera: pornografia `ukuRmarT survilebs badebs adamianSi, is aRvivebs avxorcul vnebebs, romlis dakmayofileba SeuZlebelia~ (Jurn. gamoiRviZeT, 2003). zogjer specialurad, zogjer kidev SemTxveviT, axalgazrda awydeba Tvalis macdunebel pornografiul veb-saitebs, intimur veb-CeTebs, romlis gavlena imdenad didia, rom is mTeli arsebiT ebmeba virtualur intimur urTierTobebSi. amerikel da evropel mecnierTa gamokvlevebSi Tavmoyrilia uamravi statistikuri mona- cemebi pornografiiT gatacebulTa dangreuli ojaxebis, mozard- Ta gonebrivi da zneobrivi degradaciis, seqsualuri Zaladobis, akrZaluli sqesobrivi kavSiris, ukanono fexmZimobis, moralur- emociuri zianis, akademiuri CamorCenilobis, Sidsis gavrcelebis da sxva sisaZagleebis Sesaxeb. masmediis analitikosis denis kalpe- nis azriT, pornografiuli programebis advilad naxvis SesaZle- bloba erT-erTi faqtoria, ramac ganapiroba is, rom adamianTa didi nawili mas miiCnevs bunebrivobisa da Tavisuflebis gamoxat- vis normalur movlenad. publicisti braien makneari pornogra- fiis daubrkoleblad gavrcelebis faqts Tavisufali da jansaRi sazogadoebis ganmasxvavebel niSnad miiCnevs. is wers: `sazogadoe- ba, romelic imdenad ganviTarebulia, rom auRelveblad xvdeba ori srulwlovani adamianis intimuri urTierTobebis daufaravad asaxavas, ufro Semwynareblurad moekideba gansxvavebuli seqsua- luri orientaciis adamianebs da ufro advilad aRiarebs qalebis Tanasworuflebianobasac.~ aseTi mxardamWerTa wyalobiT, `dRes is (umsgavsoebebi _ g.x.) gacilebiT did gavlenas axdens kultu- raze, vidre opera, baleti, Teatri, musika da saxviTi xelovneba erTad aRebuli~, _ wers publicist jermein griri (Jurn. gamoiR- viZeT, 2003). Zaladobisa da seqsualuri Sinaarsis Semcvleli informaciebi uwyvet nakadad moedineba televiziis, kinofilmebis, musikalu- ri video-klipebisa da internetis meSveobiT, romelsac nebayo- flobiTa da didi siamovnebiT ewafebian gauTviTcnobierebeli axalgazrdebi. amas emateba is, rom bavSvTa didi procenti `tele- maniakebisa~ da `kiber-xulignebis~ maxeSi ebmebian da problemebi eqmnebaT Tavad bavSvebs, maT ojaxebsa da skolebs. aranaklebi zianis motana SeuZlia zedmetad Tamam modas. po- pularuli `varskvlavebi,~ romlebic meZaveebisTvis damaxasiaTe- bel Cacmulobas irCeven, mozardebisa da axalgazrdebis moumwi- febeli Tvali iwonebs da baZavs maT (Jurn. gamoiRviZeT, 2003). ufro gamaognebeli is aris, rom prestiJul maRaziebSi iyideba 330 gulnaz xuxua sabavSvo kosmetikuri saSualebebi nair-nairi brWyviala ferebi- Ta da Tvalwarmtaci dizainiT gaformebuli, romlebsac mSoblebi da axloblebi didi siamovnebiT yiduloben da Cuqnian bavSvebs. ufrosebisgan nebadarTuli patarebi iTiTxnebian, ipranWebian, xa- lisoben da kmayofilebi arian. Sedegi: uxamsoba, gemovnebis mda- biuroba, uzneo siTamame da gambedaoba, zneobrivi da sulieri si- Ratake. mere gvikvirs is, rac Cven vaswavleT da risi nebac davr- TeT: urCoba, TavaSvebuloba, moraluri Seusabamoba, akademiuri CamorCeniloba, `ZvelbiWoba,~ e. w. `svetoba~ da a. S. `sazogadoeba imas isisxlxorcebs, riTac mis gonebas kvebaven~. aRzrda, rogorc unikaluri sazogadoebrivi, sayovelTao da permanentuli movlena, mravalmxrivi, kompleqsuri procesia da Sedgeba sxvadasxva komponentebisagan, rogoricaa: gonebrivi aR- zrda, zneobrivi aRzrda, sulieri aRzrda, esTetikuri aRzrda, fizikuri aRzrda, romelTa gareSe SeuZlebelia adamiani srul- fasovan pirovnebad Sedges. amaze fiqric ki danaSaulia. aRzrdis am komponentebs Soris iseTi organuli, harmoniuli da sinqronu- li kavSiria, rogoric Cveni sxeulis nawilebs Soris. yovlisSe- moqmedma RmerTma adamiani daajildova yovelmxriv harmoniulad ganviTarebis, srulfasovan pirovnebad formirebis potenciuri unariT zemoxsenebuli aRzrdis komponentebis saxiT. pedagogiu- ri misia, swored, am SesaZleblobebis gamovlinebasa da ganviTare- baSi mdgomareobs. Tumca, es kapitalisturi sistemis interesebSi ar Sedis. aRzrdis praqtikaSi cnobilia piradi magaliTis udidesi ga- vlena aRsazrdelebze, magram amas ver vityviT, rom zneobriobis idealur nimuSs warmoadgenen qveynis mmarTvelebi, kanonmdeble- bi, aRmasruleblebi da sxvani da sxvani. samwuxarod, es Zalian cudi magaliTia aRsazrdelebisaTvis. zneoba anu morali aTaswleulobiT dagrovili codna-gamoc- dilebis Sedegad sazogadoebaSi dadgenili qcevisa da moqmedebis normebisa da wesebis erTobliobas warmoadgens, romelic pirov- nebis srulfasovnebas gansazRvravs. mas swavlobs eTikuri mec- niereba. xolo pedagogika iRebs am mza eTikur monacemebs da iye- nebs zneobrivi aRzrdis mizniT. aq aris pedagogikasa da eTikas Soris kavSiri, Sexebis wertili. zneobis cnebis yvelaze marti- vi da srulyofili ganmarteba mocemulia g. banZelaZis eTikis saxelmZRvaneloSi, sadac vkiTxulobT: `zneoba sxva araferia, Tu ara adamianis xasiaTis arsebiTi niSani~ (Bandzeladze, 1962: 318), ro- melic gare samyarosTan urTierTobebSi gamoixateba. magaliTad, 331 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV adamianebTan, sazogadoebasTan, saxelmwifosTan, bunebasTan, saer- Tod, nebismier saqmianobasTan, mikro Tu makro garemosTan. ur- TierTobebi, damokidebulebebi ki ZiriTadad ganpirobebulia bu- nebriv-biologiuri moTxovnilebebisa da socialuri moTxovnebis dakmayofileba-daukmayofilebiT. zneobrivi aRzrdis mizani, swo- red, am moTxovnebisa da moxovnilebebis gakeTilSobilebaSi, misi Rirebulebis, saWiroebisa da kanonierebis maRal xarisxSi ayvanasa da daxvewaSi mdgomareobs, rac warmoadgens uSualod maswavle- blis kompetencias, radgan mxolod mas aqvs am sakiTxze specialu- ri akademiuri codna da pasuxismgebelia swavla-ganaTlebisa da aRzrdis Sedegebze. moraluri devianturoba, rogorc wesi, yovelTvis ganpirobe- bulia zneobrivi Segnebis, zneobrivi grZnobebis, zneobrivi moti- vebisa da zneobrivi moqmedebis unar-Cvevebis ganviTarebis defi- citiT. RvTisa da moyvasis siyvarulis naklebobiT, movaleobisa da pasuxismgeblobis, pirovnuli Rirebulebebis grZnobis daqvei- TebiT. amitom zneobrivi da sulieri aRzrdis gareSe patiosnebis SenarCuneba, adamianuri funqciebis Sesruleba praqtikulad Seu- Zlebelia. antonimuri kategoriebis: sikeTe da boroteba, samarT- lianoba da usamarTloba, patiosneba da upatiosnoba _ mudmivi Widilis istoriaa kacobriobis cxovrebaSi dasabamidan dRemde. boroteba saTaves iRebs edemis baRSi Cveni winapari wyvilis adami- sa da evas mier Cadenili codvidan. kacobriobam Tavisi arsebobis manZilze imdeni boroteba da ubedureba Caidina, rom codvebma zenits miaRwia da amas dausjels ar datovebs yovlisSemoqmedi RmerTi. Cven is mainc SegviZlia gavakeToT, rom mosananieblad mocemuli drois darCenili mcire monakveTi maqsimalurad gamo- viyenoT Cveni adamianuri, sulieri, profesiuli da moqalaqeobri- vi movaleobebis Sesasruleblad, rom karze momdgari gankiTxvis dRes sufTa da ganswavluli sindisiT SevxvdeT. vinicobaa, iqneb gadavrCeT da borotmoqmedebTan erTad ar daviRupoT, rogorc es moxda warRvnis dros. zneobrivi da sulieri aRzrda, upirveles yovlisa, saxelmwi- fo politikis erT-erT mTavar prioritetad unda iqces, rom mis saTanado qveda stuqturebSi, kerZod, ganaTlebis sistemaSi Ta- visi adgili daikavos da banalurobad qceuli debuleba: skolis, ojaxisa da sazogadoebis mekavSireoba da erToblivi aqtiuroba aRzrdaSi gamojansaRdes, daixvewos da Tavis uflebebSi aRdges. Sewydes maswavleblebis diskriminacia da yovlad damabneveli ter- minologomania. nebismieri maswavlebeli unda iyos srulfasovani, 332 gulnaz xuxua maRalkvalificiuri, Tavisi qveynis Rirseuli moqalaqe. praqtiko- si maswavlebeli, mentori maswavlebeli, `aseTi maswavlebeli,~ `iseTi maswavlebeli;~ `sruli profesori, (rogoria netav usruli, anu arasruli profesori?!), asocirebuli profesori, asistent profesori da a. S. mawavleblisa da profesoris cnebebi erTmniS- vnelovania da ucvleli. maswavlebels nebismier saskolo Tanam- debobaze unda SeeZlos muSaoba. skolaSi ra saqme unda hqondes arasrufasovan maswavlebels?! Tu am principiT mivudgebiT saqmes, maSin gamodis, rom amave principiT unda moxdes moswavleTa da studentTa jgufuri diferenciacia: susti, saSualo, kargi, war- Cinebuli, an prosocialuri, asocialuri, antisocialuri da a.S. rac Seexeba silabuss, amis winaaRmdegi aravin aris, magram riT ver unda dadgindes 15 wlis ganmavlobaSi misi saboloo varianti, romelic 5 weli mainc ivargebs, rom yovel semestrsa Tu trimes- trebSi ar icvlebodes. maswavleblis Sroma unda Semowmdes misi Sromis SedegiT. mTeli saqarTvelo rom daiaroT, erT maswavle- bels ver naxavT Tavisi samsaxuriT bedniers. amdeni gaugebari re- formebis reformaTa reformebma daRala, moSala maswavlebeli, Taobebis ganmanaTlebeli da aRmzrdeli. vis SeuZlia daasaxelos erTi studenti mainc, repetitor-maswavlebelebTan momzadebis gareSe, skolaSi miRebuli codniT umaRles saswavlebelSi Cari- cxuli?! ratom ar aris sakmarisi repetitoris gareSe 12 wlia- ni saswavleblis damTavreba universitetSi swavlis gasagrZele- blad? pasuxi martivia. maswavlebeli kargad muSaobs iq, sadac Tavisufalia da damoukidebeli, sadac realurad afaseben mis Sromas da adekvaturia anazRaureba. aseTi adgili, samwuxarod, mxolod repetitoroba aRmoCnda. aRniSnulidan gamomdinare, aRsazrdeli dabadebisTanave unda moxvdes adamianur, samarTlian da keTilganwyobil garemoSi, sadac gaTvaliswinebuli da dakmayofilebuli iqneba bavSvis kanonieri biogenuri da sociogenuri moTxovnebi. bavSvi RrubeliviT isru- tavs mxolodi mas, rac SegrZnebaSi eZleva: rac naxa, rac moismina, rac Seiynosa, rac daagemovna da rasac Seexo. e. i. rac SegrZnebaSi ar hqonia, is ara aqvs cnobierebaSi. maSasadame, is arafers uke- Turs ar igonebs, mxolod imeorebs imas, rac mis irgvliv aris da xdeba. amitom dedamiwaze upirvelesi da umTavresi saqmea aRzrda, rom ukeTesi momavali gvqondes. rogorc xis simagre mis fesvebzea damokidebuli, aseve bavSvis srulfasovan pirovnebad Camoyalibe- ba mis aRzrdasTan aris dakavSirebuli. rogorc kvintilianem Tqva, mSoblebis mSobliuri da moqalaqeobrivi, xolo maswavleblis 333 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV profesiuli movaleobaa TavianTi aRsazrdelebi xelCaWidebuli da fexawyobili gaiyvanon damoukidebeli cxovrebis asparezze. CvenTvis bavSvs xom ar uTxovia gaCena, is Cveni siyvarulis nayofia da masze pasuxismgeblobac Cven gvakisria. vinc bavSvis aRzrdaze, swavlebaze da ganaTlebaze pasuxismgebelia, mas uflebebic aqvs masze, rac gonivrulad unda gamoiyenos. esec rom ar iyos, kargad aRzrdili axali Taoba xom Cveni bednieri momavalia. inkluziur klasSi problema isedac didia, magram swavlis unarSeuzRudav moswavleTa moraluri devianturoba, advili war- mosadgenia, rogor arTulebs pedagogur process. amitom sanam mo- raluri koreqciis saWiroeba dadgeba, skolam maqsimalurad unda aamuSaos saprevencio da profilaqtikuri meTodebi. zneobrioba unda gamocxaddes skolisa da klasis, saklaso-sagakveTilo sis- temis, klasgareSe pedagogiuri muSaobisa da ojaxis priorite- tul aqtivobebad, zneobrivi Segnebis, zneobrivi grZnobebisa da zneobrivi qcevisa da moqmedebis unar-Cvevebis gamosamuSaveblad eTikuri normebisa da wesebis Teoriuli aTvisebisa da saxelovani adamianebis cxovrebis, piradi magaliTebisa da praqtikuli gamoc- dilebis safuZvelze. moraluri koreqciis efeqtur saSualebas warmoadgens qceveb- sa da Sedegebs Soris logikuri kavSirisa da Sedarebis meTodebis danaxva da marjved, situaciasTan morgebulad gamoyeneba, rac moswavles daanaxvebs mizez-Sedegobriobis kanonis arss. rom ... `kaci rasac, Tesavs, imas moimkis~ (galatelebis 6:7). magaliTad, Tu gazafxulze gasakeTebeli ar gavakeTeT, Semodgomaze mosavals ver miviRebT da sarCos gareSe davrCebiT mTeli weli. Tu swavlis periodi ganaTlebis miRebas ar movaxmareT, gaunaTleblebi da- vrCebiT. rogorc daviT guramiSvilma Tqva: `Tu kacsa codna ara aqvs, gastanjavs wuTisofeli~. moralur srulfasovnebas moraluri aRzrda sWirdeba. es ki dakavSirebulia, upirveles yovlisa, zneobriv aRzrdasTan, es ki moiTxovs Semdegi ZiriTadi amocanebis gadawyvetas, rogoricaa: • zneobrivi Segnebis amaRleba; • zneobrivi grZnobebisa da emociuri inteleqtis ganviTareba; • zneobrivi qcevisa da moqmedebebis praqtikuli unar-Cveve- bis gamomuSaveba. Segnebis cneba samecniero literaturaSi ganmartebulia ro- gorc yofierebis cnobierebaSi asaxva. zneobrivi Segneba niSnavs eTikuri normebisa da wesebis gaazrebul codnasa da mis Sesa- bamisad cxovrebis aucileblobis gacnobierebas. zneobis arsis, 334 gulnaz xuxua misi Teoriul-praqtikuli da pirovnul-sazogadoebrivi roli- sa da mniSvnelobis Sesaxeb WeSmariti informaciebiT cnobiere- bis gamdidreba iwvevs zneobrivi Segnebis amaRlebas, rac Tavis gamoxatulebas poulobs eTikur msoflmxedvelobasa da qcevisa da moqmedebis kulturaSi. ramdenadac zneobrivi Segneba zneo- briv grZnobebsa da qcevebs udevs safuZvlad, amdenad, aucilebe- lia zneobrivi kategoriebis Sesaxeb sruli informaciebis miReba, rasac emsaxureba eTikuri mecniereba. amasTan dakavSirebiT ko- menskim dawera: moswavleebma `unda SeiTvison moZRvreba zneobis Sesaxeb, romelic gamoxatulia wesebSi da ganmartebulia magali- TebiT asakis Sesabamisad; maT unda esmodeT igi da cdilobdnen saqmeSi gamoyenebas.~ (komenski, 1949: 175). aq mokled SevixsenebT im eTikur kategoriebs anu sazogadoebaSi dadgenil qcevisa da moqmedebis normebsa da wesebs, romelic gansazRvravs zneobrivi Segnebis srulfasovnebas. esenia: • humanizmi • patriotizmi • internacionalizmi • samarTlianoba • sindisiereba • patiosneba • pasuxismgeblobisa da movaleobis Segneba • gulwrfeloba • Tavmdabloba • sisadave da ubraloeba • Tavazianoba • moTmineba da TavSekavebuloba • sulgrZeloba da mimtevebloba • siyvaruli • megobroba • Sromismoyvareoba • stumar-maspinZloba da yovelive is, rasac moaqvs sikeTe, sixaruli, mSvidoba da bedniereba (Khukhua, 2009: 140-153). marTalia, zneobrivi Segnebis amaRlebas uzrunvelyofs eTikuri codna-gamocdileba, informaciuloba, magram mxolod imis codna Tu ra aris kargi da ra cudi, socialurad miRebuli da miuRebeli, es ar aris sakmarisi pirovnebis moraluri srul- fasovnebisaTvis. amasTanave, aucilebelia emociur-nebelobiTi sferos ganviTareba, rom moswavles gauCndes zneobrivi Segne- bis Sesabamisi zneobrivi grZnobebi, survili, Sinagani motivacia 335 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV sikeTis keTebisa. zneobriv grZnobebze keTilmyofel gavlenas axdens dadebiTi TvalsaCino magaliTebi, rogoricaa: zneobiT, gonierebiTa da sibrZniT gamorCeuli bibliuri da literaturu- li personaJebis, saqmiTa da RirsebiT cnobili saxelovani adamia- nebis da a. S. maTi cxovrebisa da moRvaweobis istoriebis gacnoba. magaliTad: mose, romelsac mieca realuri SesaZlebloba egvipte- Si meore oficialuri piri yofiliyo, man RvTis nebis Sesruleba, Tavisi xalxis egviptis monobidan daxsna arCia; noem, dedamiwaze sicocxlisa da kacobriobis gadasarCenad RvTis neba daayena qvey- nierebaze maRla da mTeli guliT Seudga uzenaesis davalebis, cnobili kidobnis (uzarmazari xomaldis) aSenebas Tavis vaJebTan: qami, semi da iafeTTan erTad, ris gamoc adamianebis gaugonari dacinvisa da Seuracxyofis atana mouwia, magram miuxedavad yve- lafrisa, zustad Seasrula RvTis neba, ris Sedegad gadarCa kaco- brioba; israelebze ganrisxebulma egviptis faraonma bebia qalebs mosTxova israeli axalSobili vaJebi dabadebisTanave daexocaT, magram fuas eyo zneobrivi gambedavoba da faraonis es usastikesi brZaneba ar Seasrula; korinToSi stumrad Camosul miletel swa- vlulebs periandrem mdidruli darbazoba mouwyo. Semdeg molxe- nili stumrebi bunebis wiaRSi saTevzaod gaiyvana. ankess amoyva oqros samfexa, romelmac mTeli saberZneTi Semoiara. `am oqros samfexas, _ wers plutarqe, swavlulni mowiwebiTa da pativiscemiT erTmaneTs uTmobdnen da erTimeores ugzavnidneno~ (Plutarqe, 1975: 140). pirvelad es Zvirfasi nadavli saCuqrad uboZes did poets Taless. man masze ufro brZenad biasi CaTvala da mas gaugzavna. biasma ki masze ubrZeness gadaugzavna, magram yvelaze brZenad arc man CaTvala Tavisi Tavi. bolos es samfexi isev Talesis xelSi moxvda, magram man arc amjerad daitova es saganZuri da ukan da- abruna. bolosdabolos `es samfexi miletidan TebeSi gadaitanes da iq ismenios apolonioss Seswires~ (Gogebashvili, 1946: 176). am da msgavsi magaliTebis Sesabamis drosa da situaciaSi mos- mena saswaul pozitiur Zvrebs axdens moswavleTa fsiqikasa da grZnobebze, aRuZravs SemecnebiT interess, saswavlo Siga da gare motivaciebs, rac kargad Cans maT aqtiurobaSi, saTanado lite- raturiT dainteresebaSi, survilebSi diskusiebsa da sxvadasxva pedagogiur aqtivobebSi monawileobisas. zneobrivi aRzrdis wre eTikuri ganaTlebis, zneobrivi grZ- nobebis, qcevisa da moqmedebis praqtikuli unar-Cvevebis gamomu- SavebiT ikvreba. zneobrivi moqmedebis unar-Cvevebi gulisxmobs Teoriuli codnis praqtikuli gamoyenebis, sxvadasxva pedagogiur 336 gulnaz xuxua da cxovrebiseul situaciebSi transferizaciis, saswavlo, pro- fesiuli, moqalaqeobrivi, SromiTi, ojaxuri da sxva movaleobe- bis keTilsindisierad Sesrulebis SesaZleblobas. zneobrivi Segnebis, zneobrivi grZnobebis, zneobrivi qcevisa da moqmedebis unar-Cvevebis gamomuSaveba rTuli, xangrZlivi da Sromatevadi procesia. am amocanebis gadaWra moiTxovs konkre- tul, kompleqsur, koordinirebul, mecnierul safuZvelze age- bul pedagogiur process, rogorc saklaso-sagakveTilo, klasga- reSe Tu skolisgareSe saswavlo-aRmzrdelobiTi muSaobis siste- mebSi, aseve ojaxuri aRzrdis sferoSi. zneobrivi Segnebis amaRleba, ramdenadac is eTikur-Teoriul codnas gulisxmobs, amdenad am procesSi prioritetulia saklaso- sagakveTilo sistema. xolo rac Seexeba zneobriv emociur-nebelo- biT sferosa da praqtikul zneobriv unar-Cvevebs, am problemis gadaWras emsaxureba zemoT dasaxelebuli bolo ori pedagogiuri sistema da ojaxuri institucia. literatura: 1. Bandzeladze G., Etika. Tbilisi, 1962. 2. Komenski Ianamos, Rcheuli pedagogiuri tkhzulebani, Tbilisi, 1949. 3. Khukhua G., Pedadagogika, Tbilisi, 2009. 4. Plutarke, Rcheuli biografiebi, Tbilisi, 1975. 337 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Gulnaz Khukhua MORAL DEVIATION AND SYSTEM OF THEIR CORRECTIONAL PEDAGOGICAL MEASUREMENTS Summary The paper deals with the essence of moral deviance of secondary school stu- dents, their iradequate behavior, academic performance and antisociality, symp- toms, factors, causes of antisociality. Based on the theoretical and practical analy- sis of the problem, its negative impact on the student’s cognitive processes, on relationships, behavior and actions is determined. It contains the principles of in- dividual, group or collective training of students with moral deviations, methods and technologies that correct as well as feelings of moral consciousness, practical strategies and activities to enhance internal and external learning motivations and practical skills. The paper reflects the positive results of cooperation between the family and schools in the field of educational culture. 338 fsiqologia PSYCHOLOGY lia svaniZe adamianis nervul-fsiqikuri Taviseburebebis TviTregulireba, rogorc Tandayolili da SeZenili unarebis daxvewis saSualeba adami a nis fsiqi kis memk vid re o bi Ti da Tanda yo li li Tvise be bis funq ci o na lu ri gamov le na mis unareb Si a. aseve arse bobs Se Zeni li, aRz r dis Sede gad miRe bu li Tvise be bic, romle bic Tavis Tavs mog vi a ne biT, adami a nis cxovre bis gark ve ul etapze warmo aCe nen. amave dros, msgavs gare mo piro beb Si adami a nu ri unare bi gans x va ve bu li doniT da gans x va ve bul dros vlinde bi an. xSirad maTi gamov le na mra val w li a ni zemoq me de bi sa da TviTre gu li re bis gav le niT xdeba. `gone ba- g r Z no bis srul soli da rul - Tan x mo van, erTi an moqme de bas umt kiv ne u lod da mZafri koli zi is gare Se awesri gebs, gone biT miRe bu li aq grZnobi Tac gamT ba ria da nebis yofi Tac gaaq ti ve bu li. d. uzna Zis qceva imde na daa mowes ri ge bu li da wonas wo ro bada cu li, rom Sina ga ni konf liq ti gau Ci na re bu lia, misi qceva Tavi su fa lia da yovel T vis `kacu ri- ka cis~ sawyi sida naa momdi na re~ (Parulava, 1967: 64). qcevis aseT Tavi suf le bas geni a lur ma moaz rov nem miaR wia Tavi si Sina ga ni samya ros sruli mowes ri ge biT. a. Cexo vi Tavis meuR les werda, `Sen mwer, rom gSurs Cemi xasi aTis. unda giTxra, rom bune biT me me tad ukme xi, Wirve u li xasi a Ti maqvs, me var advi lad feTqe ba di da a.S., magram miveC vie Tavis Seka vebas, rame Tu Tavis aSve ba wesi er adami ans ar Sehfe ris~. warma te bu li TviTaR z r dis araer Ti maga li Ti a cno bi li. mori debu li da enablu demos Ten ma Tavi si metyve le bis mraval w li a ni varji Sis gziT sau ke Te so metyve le bas, gamoT q mas miaR wi a, saja ro gamos v lis d ros morcx vo bas sZlia da Semd gom igi brwyinva le orato ri gaxda. bevr ma saqvey nod cnobil ma mecni er ma, mweral ma, kompo zi tor ma udides warma te bas miaR wia mraval w li a ni, muxl mo udre ke li Sromis, Semoq me de bi Ti unare bis gaxs ni sa da mobi li za ciis meSve o biT, romle bic maTSi daba de bi dan iyo Cade bu li. cno bili maTe ma ti ko si gau si, fizi o lo gi helm hol ci, fizi ko si niu toni, mwerle bi svifti da skoti, kompo zi to ri vagne ri da bevri 339 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV sxva cnobi li adami a ni bavS vo ba Si Tavi an Ti swavliT ar gamo ir Ce oda, maT didi dro dasWir daT, rom momwi fe bu li yo maTi Semoq mede bi Ti unare bi, daxve wi li yo maTi niWi e re ba, ramac maT uSre ti energia uboZa miznis misaR we vad _ daxve wi li yo da srulyo fi li gamx da ri yo maTi pirov nu li da nervul - f si qi ku ri Tavi se bu re ba ni. anga riS ga sa we via is gare mo e ba, rom nervul - f si qi ku ri aRz r dis proces Si (ise ve rogorc fizi kur srulyo fa Si), gadam wy ve ti mniSv ne lo ba eniWe ba varjiSs. i. pavlo vi araer T g zis miu Ti Teb da Tavis tvinis naxe var s fe ro e bis varji Sis ganu zo mel SesaZ leb lo baze. rogor c Cans, sruli ad SesaZ le be lia pirov ne bis gark ve u li Tvise be bis aRz r da, raTa ufro srulyo fi lad gamo vav li noT ada mia nis unare bi ama Tu im profe si u li mimar Tu le biT. cnobi lia pirov ne bis xela xa li aRz r dis SesaZ leb lo bac. jer kidev Cv. w. aRricx vam de V sau ku ne Si hipok ra te mivi da im dask v nam de, rom arse bobs oTxi ti pis tempe ra men ti (sang vi ni ki, qole ri ki, flegma ti ki da melan qo li ki), romle bic gana pi ro be ben fsiqo e mo ciu ri sferos indi vi du a lur Tavi se bu re bebs. mraval g zis gamok v leveb ma daam t ki ca, rom pirov ne bis emoci u ri naklo va ne be bis daZ leva da koreq cia xels uwyobs rogorc qceve bis mowes ri ge bas, iseve mrava li avadm yo fo bis (wneve bis, gulsis x l Zar R v Ta daa va de bebis, kuW- naw lav Ta da sxv.) Tavi dan acile bas. fsiqo hi gi e nu ri TviTre gu la cia gamo i ye ne ba rogorc umniS v ne lova ne si saSu a le ba adami a nis qmedu na ri a no bis, Sromis nayo fi e re bis asamaR leb lad. TiTo e ul ma adami an ma saku Ta ri gamoc di le bi dan icis, rom uaryo fi Ti emoci e bi _ SiSi, ganga Si, sibra ze, dardi, sevda da sxv. _ aqve i Tebs da anadgu rebs Cvens Semoq me de biT aqti uro bas, zogjer mTlia nad gvakar g vi nebs Sromis unars. saSiS ro e bis, avari u li an eqs t re ma lu ri mdgoma re o bis sapa su xod, xSirad gveuf le ba dafan tu lo ba, saaz rov no proce se bis Se nele ba, swori, adekva tu ri qceve bis uunaro ba, SfoTva, maSin, ro desac analo gi ur situ a ci eb Si aucile be li da gada u de be lia gam Zle o ba, TavSe ka ve bu lo ba, momen ta lu ri reaq ci e bi, simS vi de, civi gone ba, nebis yo fa. magram gana nakle bi gamZ le o ba, TavSe ka ve ba da nebis yo fa sWirde ba qirurgs opera ci is dros, an fizi kos -eq s pe ri menta tors atomur reaq ci eb ze muSa o bi sas, an sport s mens sapa xu xism geb lo gamos v la ze? mcdari ar iqne ba gveTq va, rom TiTo e u li adami a nis cxovre ba yovel dRi u rad aris datvir Tu li emoci u ri daZa bu lo biT da aravin aris dazRve u li mZafri situ a ci e bi sa gan, romlis drosac aucile be lia swrafi, momen ta lu ri da swori moq mede ba, Tavda We ri lo ba da Tavda je re bu lo ba. 340 lia svaniZe mZafri situaciebis garda, Cvens nervul sistemaze yoveldRi urad zemoq me debs sxva gama Ri zi a neb le bic, romle bic CvenSi iwve ven Sesabamis emociebs da Cveni xasiaTis mdgomareobas ganapirobeben. aris Tu ara saWiro Cveni xasiaTis marTva? xasiaTi! rogor aisaxe ba igi Cvens saqmianobaze, pirovnebaTaSoris urTierTobebze? gvaqvs Tu ara ufleba viyoT `xasiaTze~ an `ar viyoT xasiaTze?~. rodesac vinmeze amboben, rom igi `xasiaTis adamiania~, maSin am SefasebaSi ra Rac eWvi gamosWvivis mis saqmian TvisebebTan dakavSirebiT. gamodis, rom mis xasiaTzea damokidebuli moigebs Tu piriqiT, waagebs saq mes. kargi xasiaTi! Tqven xedavT rogor icvleba samyaro, garSemo- myofni keTilganwyobilni arian, surT dagexmaron sityviT an saq miT. saqme ki kargad midis. adamiani energiiT ivseba, urTierTobebi sasiamovnoa. es kargi guneba-ganwyobileba sxvebsac gadaedeba xol me. magram, samwuxarod, yovelTvis ase rodia. aris iseTi SemTxveve bic samsaxurSi, ojaxSi an sxvagan, rodesac adamiani ar aris xasiaT ze. es yvelasaTvis xdeba SesamCnevi. pirvel rigSi qveiTdeba qmedu narianoba, fuWdeba urTierTobebi. iqneb es adamiani nevroziT aris daavadebuli? ara! ubralod igi cud xasiaTzea da sakuTari Tavis xelSi ayvana ar SeuZlia! aris SemTxvevebi, rodesac gadian dReebi, kvireebi, Tveebi, daZabuloba ki ar klebulobs, ar neldeba. adamiani iZulebulia mimarTos eqims, romelic mas uniSnavs damamSvideblebs, saZile saSualebebs da axla modaSi Semosul trankvilizatorebs. am wamlebis meSveobiT igi icilebs arasasiamovno emociebs, Rrmad iZi nebs, Tumca xelovnuri ZiliT. ukve saxezea `medikamentozuri ada miani~, magram igi avadmyofi xom ar aris? samwuxarod, es adamiani umciresi winaaRmdegobis xaziT wavida. mas dro ara aqvs _ saqmiania. amitom abebis ylapva ufro mosaxerxebelia, vidre sakuTari ner vuli sistemis varjiSi, nervul-fsiqikuri mdgomareobis Segnebuli TviTregulireba, rac savsebiT SesaZlebelia! Tana med ro ve piro beb Si mecni e re bi sa da teqni kis ganvi Ta re bam adami a ni sa gan moiTxo va fsiqi ku ri Zale bis ukidu re si daZab va, didi nervu li dana xar je bi, codnis mara gis ganuwy ve te li Sevse ba. cxovre bis tempi bevrad gai zar da da adami a nis nervul siste mas wamo u ye na moqni lo bis, dreka do bis, simya ris, gamZ le o bis moTxovni le ba. siCqa re, romel sac miaR wia Tana med ro ve mecni e re bam da teqni kam, gaci lebiT aRema te ba saSu a lo donis adami a nis nervul - f si qi ku ri pro cese bis siCqa res. adami a nis orga niz mi, Tavi si ganvi Ta re bis mTeli isto ri iT, adapti re bu lia misT vis norma lu ri siCqa ris samya ro ze. SemTx ve vi Ti ar aris, rom fsiqo lo ge bi SiSs gamo xa ta ven imis Tao baze, rom Cveni fsiqi ka ver SeZlebs daus je lad gauZ los cxovre bis 341 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV giJur temps, rome lic Tana med ro ve civi li za ci is T vis aris dama xa sia Te be li. dRes saqmi a no bis mrava li saxe o ba adami a ni sa gan moiTxovs siste ma tur daZab vas, inte leq tu a lur damo u ki deb lo bas, yuradRe bis gamax vi le bas, rac nervu li energi is uzarma zar xarj vas Tan aris dakav Si re bu li. amas emate ba infor ma ci u li qariS xa li pre si dan, te levi zi i dan da sxva wyaro e bi dan, romlis gada mu Sa ve ba did siCqa res moiTxovs. nervu li siste mis gada Zab va bevr SemTx ve va Si dakav Si re bulia gazr dil profe si ul gadat vir T vas Tan. amasTan dakav Si re biT aucile be lia nevro ge nu ri aSli lo bis profi laq ti kis da tvinis mar gi qmede bis koe fi ci en ti s amaR le bis gzebis Zie ba. dRei saT vis sau ke Tesod iTv le ba autoge nu ri varji Sis meTo dis daufleba.* aRniS nu li meTo di gamo i ye ne ba medi ci na Si, sport Si, peda go gika Si, warmo e ba Si, TviTaR z r da Si da sxva ne bis mi er saqmi a no ba Si. adamianuri cxovreba dinamiuria, misi pirobebi ganuwyvetliv icvleba. amasTan, yofiereba gansazRvravs cnobierebas, xolo es ukanaskneli SesamCnevad CamorCeba cxovrebis pirobebis cvaleba dobas. uCveulo situaciebi, siaxleebi xSirad stresis mizezebic xdeba, magram adamiani yovelTvis egueba cxovrebis cvalebad pi robebs. adamianuri fsiqikis adaptaciuri SesaZleblobebi ganuzo melia. es cxadia, magram cxovrebaSi aris uamravi SemTxveva, rode sac mxolod adaptaciaze dayrdnoba ver Svelis saqmes. adamians eC qareba, dro ar iTmens. mas unda iyos sazogadoebis srulfasovani wevri, iyos jansaRi, qmedunariani, rac individis ekonomikuri da sulieri arsebobis aucilebel pirobas warmoadgens. mas, pirvel rigSi, sakuTari Tavi abaria, romlis marTvac sakmaod rTulia, magram ara SeuZ le be li. siZne le e bi sa da gaWir ve bis miu xe da vad Wkvia ni, moaz rov ne adami a ne bi kacob ri o bi saT vis muSa ob d nen. sai dan hqondaT maT amde ni Zala, rogor miaR wi es fsiqi kis opti mi za cias? rig SemTx ve veb Si maTi energi is wyaros Semoq me de bi Ti Sro miT miRe bu li emoci u ri kmayo fi le ba warmo ad gen da. TviT S ro mis proce sic aniWeb da maT sixa ruls, kurnav da yovel g va ri dardi sa da avadm yo fo bi sa gan. maga li Tad, hai ne mtanj ve li tkivi le bi sa gan Tavs leqse bis weriT aRwev da, kanti da paska li tkivils tvinis da Zabu li muSa o biT jobnid nen. bevr maTgans Wirde bo da aseve yovel dRiu ri, gaaz re bu li TviTgam x ne ve ba. cnobi li a, rom sen- si mon ma msaxurs ubr Za na, igi gaeR vi Ze bi na sityve biT: `ade qiT graf, Tqven * autogenuri varjiSis meTodi varaudobs kunTuri relaqsaciis (simSvidis, mo- dunebis) TviTSTagonebis, yuradRebis koncentraciis swavlebas. warmosaxvis Zalis ganviTarebas, uneblie gonebrivi aqtiurobis kontrolirebis unars subieqtisTvis mniSvnelovani saqmianobis efeqturobis amaRlebis mizniT. 342 lia svaniZe didi saqmeebi gelodebaT~. sakuTari grZnobebisa da nebisyofis da uflebas imTaviTve udides yuradRebas aqcevdnen moazrovne ada mianebi. leonardo da vinCi amtkicebda, rom Cveni Semecneba iwyeba SegrZnebiT da Segnebulad, didi gulisyuriT avarjiSebda grZno bis organoebs: mexsierebas, warmosaxvas, yuradRebas. aRsaniSnavia, rom sen-simonma da leonardo da vinCim aRmoaCines yvelaze Sesa ferisi dro TviTgamxnevebisaTvis, TviTSTagonebisaTvis, nervuli sistemis varjiSisaTvis _ es aris gaRviZebis periodi. amavdrou lad, Tavis tvinis qerqSi warmoiqmneba fizikuri mdgomareoba, ro melic Sualeduria Zilsa da sifxizles Soris da romlis wyalo biTac warmodgenili TviTbrZanebebi gansakuTrebul Zalas iZenen. am momentSi adgili aqvs kunTebis modunebas, risi mniSvnelobac metad didia fsiqo-nervuli moqmedebis regulirebaSi. adamianis fsiqo-fizikuri teqnikis SemuSavebisas gansakuTre buli yuradReba eqceva yuradRebis koncentraciis, emociuri mex sierebisa da moZraobebis marTvasTan dakaSirebuli Cvevebis tre ningsa da gamowafvas. am dros adgili ar unda hqondes kunTebis daZabvas da mTeli fizikuri aparati srulad unda emorCilebodes nebisyofis brZanebebs. aRsaniSnavia, rom kunTebis Tavisufleba vi Tardeba varjiSis gziT, kunTebis daZabvisa da moSvebis varjiSiT, rac ayalibebs ostatobas. nervuli sistema, iseve rogorc kunTe bis sistema, trenings eqvemdebareba. maSasadame, fsiqikuri moqme debis optimizacia SeiZleba miRweuli iqnes nervuli procesebis Segnebuli da Seupovari varjiSis Sedegad an gaazrebuli yovel dRiuri TviTgamxnevebiTa da gaucnobierebeli TviTSTagonebiT. yoveldRiur cxovrebaSi am elementebs aqvs garkveuli mniSvnelo ba, magaliTad, Cven xSirad mivmarTavT TviTSTagonebas ise, rom arc vacnobierebT mas. vidre sakuTar ufrosTan SevalT, Tavs vi wesrigebT. am garegnuli gamovlinebebis ukan Tavdajerebis faru li TviTSTagoneba imaleba. sityvebiT SeiZleba ase gamovTqvaT: `me mowesrigebulad gamoviyurebi da nebismieri davalebis Sesrule ba SemiZlia~. aseT fsiqologiur movlenebs miekuTvneba zogierTi sxva moqmedebebic. magaliTad, saguldagulo dilis makiaJi, axali sagareo tansacmlis Cacma gansakuTrebuli SemTxvevisaTvis da sxva. inte ress iwvevs is faqti, rom nebis yo fis Segne bu li marT vis zegav le niT SeiZ le ba nervu li moqme de bis iseTi arse bi Ti gardaq mna, rogo ric pirve li Se xed viT SeuZ leb lad gveCve ne bo da. cno bilma mkvlevar ma bombar ma saku Tar Tavze daam t ki ca, rom adami ani, romel sac Zlie ri nebis yo fa aqvs, yvela ze mZime piro beb Sic ki gadar Ce ba. man dawv ri le biT aRwe ra eqs t re ma lur situ a ci a Si 343 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV saku Ta ri ganc de bi, maT Sori s apa Ti is, mRelva re bi sa da SiSis gan sakuT re bu li md go ma re o ba. is gadar Ca imitom, rom am nega ti ur grZnobebs Zlie ri nebis yo fis Zale bi dau pi ris pi ra. Tana med ro ve o bis yvela ze didi ubedu re ba _ narko ma ni a, rome lic qmedu na ri a no bas spobs da ususur, mZime avadm yo fad aqcevs adami ans, mxolod nebis yo fis meSve o biT ikurne ba! narko ma ni as Tan brZolis erTa der Ti fsiqo lo gi u ri meqa niz mi nebis yo fa a. rogorc vxedavT, swored adami a nis aqti u ri moq me de ba, mi si nebis yo fa, rig SemTx ve veb Si ki nervul - f si qi ku ri proce se bis Segne bu li TviTre gu li re ba (nebis yo fis daxma re biT), saSu a le bas iZle va aramxo lod gadar Ces pirov ne ba misi cxovre bis mZime gan sacdel Si, aramed safr Txis dros, rome lic mis janm r Te lo bas an sicocx les emuqre ba, goniv ru lad imoqme dos. zemoTqmulidan gamomdinare, ibadeba kiTxva: SeuZlia ki yovel Cvengans Tavisuflad, Segnebulad, nebisyofis ZalisxmeviT gavle na moaxdinos nervuli procesebis regulirebaze? SesaZloa Tu ara damoukideblad, survilisamebr ganvdevnoT SiSis, mRelvarebis, daZabulobis grZnoba, nebismieri gavlena movaxdinoT vegetatiur funqciebze (sisxlZarRvTa da gulis muSaobaze da sxv.), tkivilis SegrZnebaze, gamovimuSaoT garkveul dros daZinebisa da gaRviZe bis unari, anu avamoqmedoT organizmSi arsebuli Sinagani biolo giuri saaTi, avamaRloT aRqmis siCqare, yuradReba, gavaumjobesoT mexsiereba? erTi sityviT, SeiZleba mivaRwioT imas, rom Segnebu lad, nebisyofis meSveobiT vmarToT fsiqo-fiziologiuri proce sebic ki? diax, SeiZleba! `Cven gvaqvs auracxeli Sinagani resursi da imas unda daveyrdnoT. Tu TiToeuli Cvengani ndobas ar gamo vucxadebT CvenSi arsebul Sinagan resursebs da mxolod movle naTa talRebs daveyrdnobiT, araferi gamova~ (Sarjveladze, 1995: 45). qmedu na ri a no bis amaRle bi sa da Senar Cu ne bis fsiqo- fi zi o lo giu ri piro be bi, gark ve ul wi lad, akumu lir de bi an nebis yo fa Si. adami a nis, rogorc pirov ne bis, Sefa se ba Si upirve le si mniSv nelo ba aqvs mis qcevas, qmede bas. adami a nis qmede ba Si igulis x me ba misi cxovre bis is mxare, romel Sic igi aqti u rad axorci e lebs mis wina Se md gar amoca nebs. fsiqo lo gi a Si aqti u ro bis, Segne bu li qme debis proble ma gani xi le ba, rogorc nebis yo fis, nebe lo bi Ti qme debis proble ma. maRali qmedunarianobis mqone pirovnebaTa Soris, rogorc sa magaliTo, SeiZleba davasaxeloT Cveni eris sasiqadulo Svili di mitri uznaZe. `principuli da mtkice nebisyofis kaci iyo d. uznaZe. mas SeiZleba Zlieri nebisyofis pirovneba ewodos. dimitri saqmis 344 lia svaniZe kacia... is yovelTvis Zalian bevrs muSaobs. universitetSi erTd roulad oTx-xuT disciplinaSi kiTxulobs leqciebs, yvela kursis seminars xelmZRvanelobs, Tavmjdomarea fsiqologiuri sazogado ebisa da warmarTavs mis regularul muSaobas, araerT sxva dawe sebulebaSi ganagebs ganyofilebebs da, amave dros, wers Sromebs, beWdavs maT qarTul, rusul da ucxour presaSi, wers recenziebs, redaqtorobs fsiqologiuri Sinaarsis wignebsa da krebulebs, es wreba sxvis leqciebs da arasodes uCivis datvirTvas, daqancvas, drois uqonlobas; yovelTvis didi sixaruliT epatiJeba saxlSi Ta vis mowa fe ebs da didxans esaub re ba maT. cnobi lia isic, rom mas Ta visi piradi megobrebic hyavda da maTTan drois gatarebac uyvarda. aqti u ro ba, saqmi a no ba _ es iyo misi sicocx lis de vi zi~ (Beru- lava, 1967: 68). nebisyofa Segnebuli, mizanmimarTuli fsiqikuri aqtiurobaa, romelic dakavSirebulia winaaRmdegobebis gadalaxvasTan. igi erTi ani fsiqikuri procesia. swored nebisyofa qmnis pirovnebis birTvs. misi aRmocenebis Semdeg qcevisa da gancdis umetesi nawili misi kontrolis safuZvelze mimdinareobs. nebisyofisaTvis specifiku ri funqcia pirovnebaSi gamovlindeba. `pirovneba warmoadgens iseT adamians, visac uWiravs garkveuli adgili sazogadoebaSi da aqvs Tavisi ufleba-movaleobebi da urTierTobani~ (Lomsadze, 1977: 181). rTul nebe lo biT proces Si, rogorc zemo T iyo aRniS nu li, SeiZ le ba ramde ni me etapis gamo yo fa: pirve li etapi iwyeba survi lis aRZ v riT , gansazR v ru li miznis miRwe vi sa ken swrafviT. meo re etapze Tavs iCens am miznis miRwe vis SesaZ leb lo ba Ta Secno ba, amas maSin ve mohy ve ba me sa me e ta pi _ moti ve bi, romle bic amt ki ce ben an uaryo fen am SesaZ leb lo beb s . meoTxe etapze iwyeba moti ve bis brZola. adami a ni awon - da wo nis dade biT sa da uaryo fiTs, sxva dasx va motivs, gaiT va lis wi nebs konk re tul gare mo e bas da mexu Te etapze mii Rebs gadawy ve ti le bas. rTuli nebe lo bi Ti proce sis kulmi na ci ur etaps warmo ad gens meeq v se etapi, rode sac pirov ne ba gana xor ci e lebs miRe bul gadawy ve ti le bas. TiTo e u li CamoT v li li etapis xang r Z li vo ba sx va das x va a. igi damo ki de bu lia pirov ne bis Tavi se bu re beb sa da miRe bu li gadawy veti le bis Sesru le bis obieq tur piro beb ze. miRe bu li gadawy ve ti lebis sisru le Si moyva nas aucileb lad sWirde ba gambe da o ba, sim tki ce, intu i ci a, damo u ki deb lo ba, gamZ le o ba, Tavda We ri lo ba da TviTk ri ti ku lo ba. nebis yo fis, nebe lo bi Ti qmede bis unaris ganvi Ta re ba xang r Z li vi proce si a. adre u li bavS vo bi dan ve mSob le bi Svilebs unerga ven 345 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV dasawyis Si sruli ad martiv da indi vi du mis ganvi Ta re bis mixed viT Tanda Tan garTu le bul Cvevebs. magram Tu raRac obieq tu ri an subi eq tu ri mize ze bis gamo bavS vo ba Si ver moxer x da nebis yo fis ganvi Ta re ba, es ar warmo ad gens trage di as. cnobi li a, rom adami ans nebis mi er asakSi Se uZ lia hqondes TviTaR z r dis, TviTs rul yo fi sa da TviTgan xor ci e le bis momen ti, nebis yo fis Sesa ba mi si Cveve bis Semu Sa ve bis unari. Cveve bi Segne bu li qmede bis avto ma ti ze bu li kompo nen te bi a, ga momu Sa ve bu li rai me moqme de bis xSiri ganme o re biT. SeZe ni li Cveve bis fonze moqme de ba sul ufro Segne bu li xdeba. es ukve nebe lo biTi moqme de ba a. yove li nebe lo bi Ti proce sis dask v ni Ti etapia kunTo va ni moZra o ba. nebis mi e ri moZra o be bi sul axala xa li saxiT mimdi na re o ben da imis mixed vi T icvlebi an Tu ra miza ni aqvs su bieqts dasa xu li. am moZra o be bis momwes ri ge bel cent rad marcxe na hemis fe ros zona iTv le ba. kunTu ri daZa bu lo ba da Zalis x me va, pirvel rigSi, moZra o ba Ta Sesru le bas Ta naa dakav Si re bu li, rom lebic qcevis moto rul Sina arss Sead ge nen da nebe lo bis aqtis zegav le niT xorci el de bi an. Cven vsaub robT ganwyo bis ganu zo mel gavle na ze, qceva sa da moqme de ba ze. `...magram is udide si miRwe ve bi, romle bic adami ans aqvs mopo ve bu li, ganwyo bis uSua lo gavle niT mainc ar aixs ne ba; adami a ni rom am uSua lo gavle ni s ama ra darCe ni li yo, igi piruty vis cxovre bis dones, albaT, vera so des ver asc de bo da. adami a nis speci fi ku ri Tavi se bu re ba da, amave dros, misi udide si mona po vari swored isaa, rom mas Zala Seswevs, Tavi si qce va ganwyo bis uSua lo bato no bas xeli dan gamog li jos, raTa igi cnobi e re bis aqtiT gaSu a le bul ganwyo bas dau mor Ci los~, _ aRniS nav da geni a luri qarT ve li moaz rov ne dimit ri uzna Ze (Uznadze, 1998: 117). ganwyo bas arc marto moTxovni le bis mdgoma re o ba qmnis Tavis Tavad da arc marto obieq tu ri situ a ci a. imisaT vis, rom ganwyo ba gaCn des, moTxovni le ba Tavi si dakma yo fi le bis piro be bis Semc vel obieq tur situ a ci as unda Sexv des. udavo a, rom is ganwyo ba, rome lic nebe lo bis aqt Si isaxe ba da nebis mi e ri moqme de bis process warmar Tavs, subi eq tis damo u ki de beli aqti vo bis nayo fi a. `amri gad, nebis yo fa Tavi su fa li a, ramde na dac aqtu a lu ri si tua ci is gavle nas ar emorCi le ba, ramde na dac aqedan momdi na re iZule bas ar ganic dis. igi Tavi su fa li a, ramde na dac masze moqme di situ a cia warmo sax vi Ti a, maSa sa da me subi eq tis mie raa gacno bi e re buli~ (Uznadze, 1998: 220). 346 lia svaniZe pirovnebas SeuZlia Tavisi nebisyofis meSveobiT moaxdinos sa kuTari Sinagani potencialis gaSla, individualuri qcevis koreq cia, sakuTari Zalebisadmi rwmenis gaZliereba. rogorc cnobilia, TviT adamianis organizmsa da fsiqikaSi aris gamouyenebeli Sinagani resursebi, romelTa aqtualizacia fsiqikuri da fizikuri gajan saRebis sawindaria, yovelive es xels uwyobs qmedunarianobis amaR lebas. literatura: 1. Berulava N., Dimitri Uznadze, ckhovreba da shemoqmedeba,Tbilisi,1967. 2. Lomsadze C. Zogadi fsiqologia, Tbilisi, 1997. 3. Sarjveladze N., fsiqologiuri saubrebi,Tbilisi, 1995. 4. Uznadze D., Zogadi fsiqologia, Tbilisi, 1998. Lia Svanidze SELF- ADJUSTMENT OF NEUROPSYCHIC AND PHYSIOLOGICAL PECULIARITIES AS THE MEANS OF IMPROVEMENT AND PERFECTION OF NATURAL AND ACQUIRED SKILLS Summary The paper deeply considers and represents how occurs functional manifesta- tion of heritable, natural and acquired features of human mentality (psyche) in personal skills. Study results and experience gives us an opportunity to prove a hypothesis that perfection of mental-physiological and neuropsychic features is a key to promotion and preservation of capability. In the paper are formed those essential factors (psychical processes, features, mental conditions etc.), with the help of which the self-adjustment (regulation) of neural andmental-physiological peculiarities is attained. Author credibly substanti- ates that conscious management of mentioned peculiarities is quite possible. She clearly shows that under modern conditions the advance of science and engineering forces humans to heavily strain psychic forces, to exert big nervous energy, to con- tinuously fill fund of knowledge etc., that has to be necessarily taken into account! This work offers us the ways and means, which enable us to reach highest level of success under any circumstances. 347 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV masalebi biobibliografiuli leqsikonisaTvis MATERIALS FOR BIOBIBLIOGRAPHICAL DICTIONARY Отар Жордания КАВКАЗСКАЯ АРМИЯ В БИОГРАФИЯХ ЕЕ ОФИЦЕРОВ ПОЛКОВНИКИ (1901-1914 гг.) ТАЛЫШХАНОВ АСАД-БЕК (род. 16.11.1857), полковник. Воспиты- вался в Бакинской реальной гимназии, 2 военном Константиновском учи- лище, окончил Офицерскую артиллерийскую школу с оценкой «Успеш- но». Службу начал 1.09.1876, произведен в прапорщики _ 16.04.1878, под- поручик _ 20.12.1879, участник военных экспедиций 1880-81, поручик _ 29.11.1882, награжден орденами Св. Станислава 3 ст. с мечами и бантом (1882), Св. Анны 3 ст. с мечами и бантом (1888), чинами штабс-капитана _ 30.08.1888 и капитана _ 5.10.1892, подполковник _ 27.07.1899, за отличие по службе полковник _ 9.06.1910 (в чине по 23.11.1915) (www.rusgeneral.ru). В 1900-10 служил старшим адъютантом окружного артиллерийского управления Кавказского военного округа, командовал батареями в 20 и 21 артиллерийских бригадах, 2 дивизионом 20 артиллерийской бригады и 1 дивизионом 52 артиллерийской бригады. _ с 19.08.1910. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1896), Св. Анны 2 ст. (1899), Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1902). Spisok, 1904: 164; Spisok, 1909, SPb.: 93; Spisok, 1910: 96; Spisok, 1911: 85; Spisok, 1911, SPb.: 1153; Spisok, 1912, SPb.: 1051; Spisok, 1914, SPb.: 615. ТАЛЫШХАНОВ МИРЗА-КАЗЫМ-БЕК (род. 17.07.1855), полковник. Воспитывался в Бакинском реальном и 2 военном Константиновском учи- лищах. Службу начал 1.09.1876, произведен в прапорщики _ 16.04.1878, подпоручик _ 26.06.1882, за отличие поручик _ 8.03.1883, штабс-капитан _ 15.03.1886, награжден чином капитана _ 15.03.1891, за отличия подполков- ник _ 26.02.1899 и полковник _ 21.03.1908. В 1904-09 командовал батальоном 82 пехотного Дагестанского Е.И.В. Великого кн. Николая Михайловича полка, командир 250 пехотного Ахуль- гинского резервного батальона _ 29.01.1909 _ 12.09.1910. С сентября 1910 службу проходил вне Кавказского военного округа. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1888) и 2 ст. (1904), Св. Анны 3 ст. (1896). 348 oTar Jordania Spisok, 1904: 113; Spisok, 1908: 90; Spisok, 1910: 75; Spisok, 1909, SPb.: 1003; Spisok, 1910, SPb.: 940; Spisok, 1912, SPb.: 644; Spisok, 1913, SPb.: 417. ТАМАМШЕВ ВАСИЛИЙ МИХЙЛОВИЧ (род. 26.07.1859), пол- ковник. Воспитывался дома. Выдержал экзамены на получение офицер- ского чина при Тифлисском пехотном юнкерском училище. Службу начал 21.04.1877, участник Русско-Турецкой войны 1877-78, за отличие про- изведен в прапорщики _ 5.04.1878, подпоручик _ 26.06.1882, поручик _ 26.06.1866, штабс-капитан _ 15.06.1893, награжден чинами капитана _ 14.05.1896, подполковника _ 19.12.1902 и полковника _ 6.12.1907(в чине по 1913) (www.rusgeneral.ru). В 1882-1890 служил ординарцем при командующем войсками Кавказ- ского военного округа, с 1890 занимал обер- и штаб-офицерские должности при командующем войсками Кавказского военного округа и наместника на Кавказе, 1901 _ 1903 находился в запасе, назначен и. д. генерала для пору- чений при наместнике на Кавказе _ 23.02.1913. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1888) и 2 ст. (1910), Св. Анны 3 ст. (1892) и 2 ст. (19120. Кавалер иностранных орденов: итальянского _ Итальянской короны (Кавалерийский крест, 1891), бухарского _ серебряного Благородной Буха- ры 2 ст. (1893). Spisok, 1901: 174; Spisok, 1908: 101; Spisok, 1910: 72; Spisok, 1911: 65; Spisok, 1911, SPb.: 688; Spisok, 1912, ch. 3, SPb.: 56; Spisok, 1913, ch. 3, SPb.: 33. ТАНУТРОВ ФЕРДИНАНД ЕГОРОВИЧ (род. 6.09.1847), полковник. Воспитывался в Ставропольской губернской гимназии и Елисаветпольском кавалерийском юнкерском училище, произведен в прапорщики _ 26.07.1871, поручик _ 27.03.1875, штабс-капитан _ 1.01.1879, капитан _ 10.07.1882, подполковник _ 26.02.1895, за отличие полковник _ 6.12.1903. В 1894-1902 служил помощником командира Дагестанского конного полка, начальник Кайтаго-Табасаранского округа Дагестанской обл. _ c 8 декабря 1902. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1886) и 2 ст. (1900), Св. Анны 3 ст. (1894). Кавалер вюртембергского ордена Фридриха (1886). Spisok, 1895: 187; Spisok, 1903: 106; Spisok, 1904: 80; Spisok, 1904, SPb.: 918; Spisok, 1906, SPb.: 622; Spisok, 1907: 52. ТАРАНОВСКИЙ ВИКТОР ПЕТРОВИЧ (род. 12.10.1864), полковник. Воспитывался в Владимировском Киевском кадетском корпусе и 3 военном 349 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Александровском училище. Службу начал 30.08.1882, произведен в подпо- ручики _ 14.08.1884, поручик _ 30.08.1888, штабс-капитан _ 6.12.1895, ка- питан, подполковник _ 6.05.1900, за отличие полковник _ 27.05.1905 (в чине по 3.04.1915) (www.rusgeneral.ru). С 1902 служил штаб-офицером для особых поручений при командую- щем войсками Кавказского военного округа, назначен вице-губернатором Эриванской губ. _ 6.09.1904, состоял при войсках Кавказского военного округа сверх штата _ 1905-06. С июня 1906 службу проходил вне Кавказ- ского военного округа. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1898) и 2 ст. (1909), Св. Анны 3 ст. (1902). Кавалер иностранных орденов: греческого _ Спасителя (Офицерский крест) (1896), датского _ Данеброга (Командорский крест, 1896), сиамско- го _ Белого Слона 4 ст. (1897), нидерландского _ Орано-Нассауского Дома (1897), японского _ Восходящего Солнца 6 ст. (1899). Spisok, 1903: 148; Spisok, 1904: 130; Spisok, 1906, SPb.: 1095; Spisok, 1907, SPb.: 890; Spisok, 1909, SPb.: 613; Spisok, 1912, SPb.:324; Spisok, 1914, SPb.: 107. ТАРАСОВ МИХАИЛ ЯКОВЛЕВИЧ (род. 27.09.1860), полковник. Воспитывался в 1 Московской военной прогимназии, Рижском пехотном юнкерском училище, окончил Офицерскую стрелковую школу с оцен- кой «Успешно». Службу начал 31.03.1879, произведен в прапорщики _ 28.09.1882, подпоручик _ 30.08.1884, поручик _ 30.08.1888, штабс-капитан _ 15.03.1896, капитан _ 6.05.1900, за отличие подполковник _ 19.10.1906, полковник _ 6.12.1912 (в чине по 1.07.1917) (www.rusgeneral.ru). В 1907-14 служил в Карсском крепостном пехотном полку, 81 Апше- ронском и 83 Самурском пехотных полках. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1893) и 2 ст. (1907), Св. Анны 3 ст. (1904). Spisok, 1907: 172; Spisok, 1910: 147; Spisok, 1911: 139; Spisok podp.,1913, SPb.: 335; Spisok, 1914, SPb.: 1229. ТАРХАНОВ ГЕННАДИЙ НИКОЛАЕВИЧ (род. 8.09.1854), полков- ник. Военный инженер. Воспитывался в инженерном училище, окончил Николаевскую инженерную Академию по 1 разряду. Произведен в подпо- ручики _ 7.08.1874, участник Русско-Турецкой войны 1877-78, поручик _ 13.06.1877, награжден чином штабс-капитана _ 1883 (старшинство с 21.02.1881), капитан _ 17.04.1883, подполковник _ 6.12.1895, полковник _ 9.04.1900 (в чине по 6.12.1916) (www.rusgeneral.ru). 350 oTar Jordania В 1900-04 находился в распоряжении Главного инженерного управле- ния, исправлял должность помощника начальника Тифлисской инженерной дистанции, с февраля 1904 начальник этой же дистанции. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. с мечами и бантом (1881) и 2 ст. (1893), Св. Анны 2 ст. (1899), Св. Владими- ра 3 ст. (1907). Кавалер персидского ордена Льва и Солнца 2 ст. (1903). Spisok, 1900: 100; Spisok, 1900, SPb.: 886; Spisok, 1901: 27; Spisok, 1903: 76: Spisok, 1903, sen., SPb.: 552; Spisok, 1906: 214; Spisok, 1909: 59. ТЕМНИКОВ ВИКТОР ЛЕОНТЬЕВИЧ (род. 1856), полковник. Вос- питывался в Екатеринодарской классической гимназии и Казанском пе- хотном юнкерском училище, которое окончил по 2 разряду. Произведен в прапорщики - 28.02.1877, участник Русско-Турецкой войны 1877-78, за боевое отличие награжден чином подпоручика _ 28.11.1877, орденом Св. Станислава 3 ст. с мечами и бантом (1878), ранен и контужен в бою, поручик _ 9.07.1880, за служебное отличие штабс-капитан _ 30.08.1887, капитан _ 30.08.1890, подполковник _ 26.02.1898, полковник _ 23.09.1903 (в чине по 6.12.1911) (www.rusgeneral.ru). В 1880 служил плац-адъютантом Карсского комендантского управле- ния, с 1885 адъютант, а с 1898 штаб-офицер Тифлисского комендантского управления с 1898. С августа 1906 служил вне Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1896) и 2 ст. (1906), Св. Станислава 2 ст. и Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1903). Кавалер иностранных орденов: персидского _ Льва и Солнца 3 ст. (1888) и 2 ст. (1901), бухарского - золотых Благородной Бухары 3 ст. (1896) и 2 ст. (1899). Spisok, 1899: 167; Spisok, 1903: 119; Spisok, 1904: 79; Spisok, 1904, SPb.: 907; Spisok, 1905: 69; Spisok, 1907, SPb.: 420; Spisok, 1910, SPb.: 120. ТЕР-НИКОГОСОВ АРТЕМИЙ ИСАЕВИЧ (род. 12.12.1859), полков- ник. Воспитывался в Тифлисской армянской духовной семинарии и Тифлис- ском пехотном юнкерском училище. Службу начал 10.11.1878, произведен в прапорщики _ 13.03.1883, подпоручик _ 30.08.1884, поручик _ 30.08.1888, штабс-капитан _ 15.03.1898, капитан _ 6.05.1900, за отличие награжден чи- ном подполковника _ 1.01.1906, полковник _ 6.12.1912. В 1907-14 службу проходил в 78 пехотном Навагинском ген. Котлярев- ского полку. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1909), Св. Станислава 2 ст. (1912). 351 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Spisok, 1907: 165; Spisok, 1910: 139; Spisok, 1911: 132; Spisok podp., 1913, SPb.: 286; Spisok, 1914, SPb.: 1222. ТИТОВ ГАВРИИЛ ЯКОВЛЕВИЧ (род. 25.03.1850), полковник. Воспи- тывался в частном учебном заведении и Ставропольском казачьем юнкер- ском училище. Службу начал 1.01.1865, произведен в хорунжие _ 25.02.1875, участник Русско-Турецкой войны 1877-78, за отличие сотник _ 16.10.1877, награжден орденами Св. Станислава 3 ст. с мечами и бантом (1878), Св. Анны 3 ст. с мечами и бантом (1880), подъесаул _ 6.05.1887, есаул _ 6.05.1892, во- йсковой старшина _ 26.02.1900, за отличие полковник _ 6.12.1905. Занимал должности старшего помощника атамана Моздокского (1889- 1906, вторично с марта 1912) и Пятигорского ( 1906 - по март 1912) отделов Терской обл. Награжден орденом Св. Владимира 4 ст. (1900). Spisok, 1907: 74; Spisok, 1907, SPb.: 922; Spook, 1910: 54; Spisok, 1910, SPb.: 591; Spisok, 1912, SPb.: 339. ТИХОБРАЗОВ АЛЕКСАНДР НИКОЛАЕВИЧ (род. 10.10.1859), пол- ковник. Воспитывался в С.-Петербургской 3 военной гимназии и 1 воен- ном Павловском училище. Службу начал 20.08.1879, произведен в подпо- ручики _ 8.08.1881, подпоручик гвардии _ 30.08.1884, поручик гвардии _ штабс-ротмистр армии _ 8.08.1885, ротмистр _ 30.08.1893, подполковник _ 26.02.1904, за отличие полковник _ 30.07.1909. Назначен начальником Кубанского областного жандармского управле- ния _ 24.06.1909. Затем службу проходил в Отдельном корпусе жандармов. За служебные заслуги награжден орденами Св. Станислава 3 ст. (1897), Св. Анны 3 ст. (1907). Spisok, 1910: 88; Spisok, 1910, ch. 3, SPb.: 112; Spisok, 1912, ch. 3: SPb.: 94; Spisok, 1914, SPb.: 477. ТИХОМИРОВ АЛЕКСАНДР КЛАВДИЕВИЧ (род. 6.08.1857), пол- ковник. Воспитывался в прогимназии и пехотном юнкерском училище. Участник Русско-Турецкой войны 1877-78, произведен в прапорщики _ 17.07.1877, подпоручик _ 14.11.1879, поручик _ 8.03.1883, штабс-капитан _ 15.03.1891, капитан _ 15.03.1898, участник Русско-Японской войны 1904- 05, за боевое отличие награжден чином подполковника - 28.09.1904, орде- нами Св. Владимира 4 ст. с мечами и бантом, Св. Станислава 2 ст. с мечами (1905), полковник _ 6.12.1910. В 1907-13 служил в 81 пехотном Апшеронском Имп. Екатерины Вели- кой (позднее Е. И. В. Вел. кн. Георгия Михайловича) полку. 352 oTar Jordania В 1911 награжден орденом Св. Анны 2 ст. Spisok, 1907: 124; Spisok, 1909, SPb.: 571; Spisok, 1910, SPb.: 112; Spisok, 1911: 93; Spisok, 1912, SPb.: 1218; Spisok, 1913: 850. ТКАЧЕНКО ГРИГОРИЙ ГРИГОРЬЕВИЧ (род. 8.11.1845), полковник. За отличие поручик _ 6.04.1874, штабс-капитан _ 10.04.1876, участник Рус- ско-Турецкой войны 1877-78, награжден чином капитана _ 30.08.1877, ор- денами Св. Анны 3 ст. с мечами и бантом, Св. Станислава 2 ст. с мечами (1878), Св. Анны 2 ст. с мечами (1879), чинами подполковника _ 1.01.1887 и полковника _ 21.01.1898. В конце ХIХ в. службу проходил в 45 драгунском Северском Е.В. Коро- ля Датского полку, назначен командиром Осетинского конного дивизиона _ 16.02.1900. За другие военно-служебные заслуги награжден орденом Св. Владими- ра 4 ст. (1884) и 3 ст. (1902). Кавалер иностранных орденов: датского _ Данеброга (Кавалерийский крест, 1879), Данеброга (Командорский крест 2 ст., 1898), бухарского _ Бла- городной Бухары 3 ст. (1895), персидского _ Льва и Солнца 2 ст. (1901). Spisok, 1899: 96; Spisok, 1900: 84; Spisok, 1903: 65; Spisok, 1903, sen., SPb.: 340. ТОВАРИЩЕВ СЕРГЕЙ ПАВЛОВИЧ (род. 6.10.1870), полковник. Вос- питывался в Оренбургском Неплюева кадетском корпусе, Михайловском артиллерийском училище, окончил Николаевскую Академию Генерального штаба по 1 разряду. Службу начал 30.08.1889, произведен в подпоручики _ 4.08.1892, поручик _ 4.08.1893, штабс-капитан _ 17.05.1898, капитан _ 9.04.1900, участник Русско-Японской войны 1904-05, награжден орденами Св. Станислава 2 ст. с мечами, Св. Владимира 4 ст. с мечами и бантом, Св. Анны 2 ст. с мечами (1905), за отличие полковник_ 13.04.1908 (в чине по 16.05.1915) (www.rusgeneral.ru). С 1909 на Кавказе, занимал должность начальник штаба Кавказской ка- валерийской дивизии _ 25.09.1909 _ 2.11.1911. Затем службу проходил вне Кавказского военного округа. В 1911 награжден орденом Св. Владимира 3 ст. Spisok, 1910: 77; Spisok, 1910, SPb.: 971; Spisok, 1911: 69; Spisok, 1912, SPb.: 670; Spisok, 1914, SPb.: 314. ТОВАРОВ ЯКОВ ФЕДОРОВИЧ (род. 14.03.1853), полковник. Вос- питывался во 2 С.-Петербургской военной гимназии и Павловском военном училище. Произведен в подпоручики _ 26.11.1874, поручик _ 9.12.1876, 353 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV участник Русско-Турецкой войны 1877-78, штабс-капитан _ 18.12.1878, на- гражден орденом Св. Станислава 3 ст. с мечами и бантом (1879), за отличие капитан _ 26.11.1884, подполковник _ 25.07.1895, за отлличие полковник _ 6.12.1901. С 1905 службу проходил на Кавказе, назначен командиром Терско-Да- гестанской крепостной артиллерии _ 10.12.1905. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1892), Св. Анны 2 ст. (1896), Св. Владимира 4 ст. с бантом (1900). Spisok, 1904, SPb.: 655; Spisok, 1907: 45; Spisok, 1907, SPb.: 212; Spisok, 1908: 40. ТОЛМАЧЕВ ИЛЬЯ ТИМОФЕЕВИЧ (род. 15.07.1861), полковник. Вос- питывался дома и Ставропольском казачьем юнкерском училище. Службу начал 15.11.1878, произведен в хорунжие _ 13.12.1881, за отличие сотник _ 6.05.1884, подъесаул _ 15.10.1889, награжден чином есаула _ 14.05.1896, войсковой старшина _ 26.02.1904, за отличие полковник _ 23.11.1908. В 1905-1909 заведовал 3 Кубанским полком (с апреля 1905), командовал 2 Таманским полком (с октября 1906), командующий кадром 2 Таманского полка (с августа 1909), назначен командиром 1 Сунженско _ Владикавказ- ского ген. Слепцова полка Терского казачьего войска _ 27.071910. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1901), Св. Анны 2 ст. (1909). Spisok, 1910: 79; Spisok, 1910, SPb.: 1016; Spisok, 1911: 193; Spisok, 1912, SPb.: 708; Spisok, 1913, SPb.: 462. ТОЛСТОПЯТ АЛЕКСАНДР АВКСЕНТЬЕВИЧ (род. 22.07.1860), пол- ковник. Воспитывался в Кубанской войсковой классической гимназии, 1 военном Павловском училище, которое окончил по 1 разряду, с оценкой «Успешно» завершил курс Офицерской кавалерийской школы. Службу на- чал 5.09.1881, произведен в хорунжие _ 12.08.1883, сотник _ 1.01.1885, подъесаул _ 14.10.1890, есаул _ 1.06.1898, войсковой старшина _ 26.02.1903, за отличие полковник _ 6.12.1907. В 1903-1907 занимал должность помощника начальника войскового штаба Кубанского казачьего войска, командующий 2 Полтавским полком того же войска _ с 3.05.1907, командующий кадром названного полка _ с 29.08.1909, командир 1 Кавказского наместника Екатеринославского ген.- фельдм. кн. Потемкина-Таврического полка Кубанского казачьего войска _ с 28.07.1910. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (_) и 2 ст. (1901), Св. Анны 2 ст. (1905), Св. Владимира 4 ст. (1907) и 3 ст. (1909). 354 oTar Jordania Spisok, 1908: 83; Spisok, 1909, SPb.: 955; Spisok, 1911: 66; Spisok, 1911, SPb.: 690. ТОМАШЕВСКИЙ КОНСТАНТИН НИКОЛАЕВИЧ (род. 1847), пол- ковник. В офицерских чинах с 1867, подпоручик _ 27.03.1868, поручик _ 26.05.1870, штабс-капитан _ 16.06.1874, капитан _ 17.06.1878, за отличие по службе награжден чином майора _ 10.11.1881, переименован в подпол- ковники _ 6.05.1884, полковник _ 20.03.1897. Эриванский уездный воинский начальник _ с 20.03.1897. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1878) и 2 ст. (1894), Св. Анны 3 ст. (1886). Spisok, 1897: 116; Spisok, 1899: 93; Spisok, 1900: 81; Spisok, 1900, SPb.: 589; Spisok, 1901: 81; Spisok, 1901, SPb.: 504; ТОМКЕЕВ ВЛАДИМИР ИЛЬИЧ (род. 9.02.1857), полковник. Воспи- тывался в Нижегородской графа Аракчеева военной гимназии, 1 Павловском училище, окончил Николаевскую Академию Генерального штаба по 2 раз- ряду. Службу начал 15.08.1874, произведен в прапорщики _ 10.08.1876, под- поручик _ 26.12.1877, поручик _ 18.12.1878, штабс-капитан _ 12.11.1884, капитан _ 30.08.1891, подполковник _ 26.02.1898, за отличие по службе полковник _ 26.05.1907 (в чине по 1913) (www.rusgenеral.ru). Более 6 лет и. д. редактора Военно-исторического отдела Кавказского военного округа, редактор _ с 26.02.1898, позднее начальник того же отдела _ с 7.01.1912. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1905), Св. Анны 3 ст. (1895) и 2 ст. (1907), Св. Владимира 4 ст. (1910). Spisok, 1901: 151; Spisok, 1906: 99; Spisok, 1907, SPb.: 1225; Spisok, 1908: 83; Spisok, 1910: 71; Spisok, 1910, SPb.: 845; Spisok, 1911: 64; Spisok, 1912, SPb.: 548; Spisok, 1913, SPb.: 348. ТОМКЕЕВ ИВАН ПЕТРОВИЧ (род. 2.02.1859), полковник. Окончил Николаевскую Академию Генерального штаба по 1 разряду. Участник Рус- ско-Турецкой войны 1877-78, военных экспедиций 1880-81, произведен в подпоручики _ 20.12.1879, поручик _ 18.12.1880, награжден орденами Св. Станислава 3 ст. с мечами и бантом и Св. Анны 4 ст. (1882), штабс- капитан _ 23.11. 1888, капитан Генерального штаба _ 10.04.1889, подпол- ковник _ 17.04.1894, за отличие по службе полковник _ 5.04.18989( в чине по 2.04.1906) (www.rusgeneral.ru). В 1896-99 служил начальником штаба Карсской крепости, начальник: 355 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV штаба 1 Кавказской казачьей дивизии _ с 4.12.1899, Тифлисского пехотного юнкерского училища _ с 14.03.1901, директор Тифлисского кадетского кор- пуса _ с 1.03.1905. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1893), Св. Владимира 3 ст. (1903). Spisok, 1899: 97; Spisok, 1900: 85; Spisok, 1901: 85; Spisok, 1903, sen., SPb.: 355; Spisok, 1905: 44; Spisok, 1905, SPb.: 238. ТРЕТЬЯКОВ АЛЕКСАНДР ЛЬВОВИЧ (род. 10.11.1851), полковник. Воспитывался в Оренбургской военной начальной школе, Тифлисском пехотном юнкерском училище, которое окончил по 1 разряду, с оценкой «Успешно» завершил курс Офицерской стрелковой школы. Службу начал 28.07.1867, произведен в прапорщики _ 28.11.1875, участник Русско-Ту- рецкой войны 1877-78, военной экспедиции 1879, награжден орденами Св. Станислава 3 ст. с мечами и бантом, Св. Анны 4 ст. и Св. Владимира 4 ст. с мечами и бантом (1878), награжден чинами поручика _ 13.06.1879, штабс- капитана _ 13.04.1883 и капитана _ 6.05.1889, подполковник _ 26.02.1900, за отличие полковник _ 5.10.1904. В разные годы служил в 156 пехотном Елисаветпольском полку, 260 Ардаганском и 257 Потийском пехотных резервных полках, командир 250 Ахульгинского резервного батальона _ с 6.04.1906. В 1908 командовал 14 гренадерским Грузинским полком. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1895), Св. Анны 2 ст. (1900). Кавалер персидского ордена Льва и Солнца 2 ст. (1901). Spisok, 1900: 167; Spisok, 1904: 119; Spisok, 1905: 82; Spisok, 1906, SPb: 894; Spisok, 1907: 64; Spisok, 1907, SPb.: 696; Spisok, 1908: 57. ТРИДЕНСКИЙ АВТОНОМ ОНУФРИЕВИЧ (род. 21.09.1857), пол- ковник. Воспитывался в Псковской военной прогимназии, Виленском пе- хотном юнкерском училище, окончил Офицерскую стрелковую школу с оценкой «Успешно». Службу начал 31.10.1873, участник Русско-Турецкой войны 1877-78, произведен в прапорщики _ 28.04.1877, награжден орде- нами Св. Анны 4 ст. (1878), Св. Владимира 4 ст. с мечами и бантом, Св. Станислава 3 ст. с мечами и бантом (1879), подпоручик _ 21.06.1879, штабс- капитан _ 31.03.1891, капитан _ 15.03.1898, за отличия по службе награж- ден чинами подполковника _ 18.06.1902 и полковника _ 23.01.1906 (в чине по 8.01.1916) (www.rusgeneral.ru). Командовал 6 Кавказским стрелковым батальоном _ 07.1909 _ 07.1910, командир 6 Кавказского стрелкового полка - с 15.07. 1910. 356 oTar Jordania За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1881), Св Анны 2 ст. (1899), Св. Владимира 3 ст. (1910). Spisok, 1908: 72; Spisok, 1910: 63; Spisok, 1910, SPb.: 680; Spisok, 1912, SPb.: 400; Spisok, 1914, SPb.: 144. ТРИПОЛЬСКИЙ АЛЕКСЕЙ ИВАНОВИЧ (род. 23.02.1849), полков- ник. Воспитывался в Воронцовской духовной семинарии и Московском пехотном юнкерском училище. Службу начал 3.02.1873, произведен в пра- порщики _ 7.09.1875, участник Русско-Турецкой войны 1877-78, подпо- ручик _ 9.03.1877, поручик _ 28.12.1878, участвовал в экспедиции 1879, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1880), штабс- капитан _ 15.05.1893, за отличия по службе награжден чинами подполков- ника _ 26.02.1902 и полковника _ 19.08.1904 (в чине по 18.11.1913) (www. rusgeneral.ru). С ноября 1906 по июнь 1907 служил на Кавказе в должности главного смотрителя Тифлисского вещевого склада. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1898), Св. Владимира 3 ст. с мечами и Св. Анны 2 ст. (1906). Spisok, 1907: 68; Spisok, 1907, SPb.: 807; Spisok, 1910, SPb.: 493; Spisok, 1912, ch. 2, SPb.: 10; Spisok, 1913, ch. 2, SPb.: 6. ТРОИЦКИЙ ДМИТРИЙ МАТВЕЕВИЧ (род. 6.02.1868), полковник. Воспитывался в Сибирском кадетском корпусе, Павловском военном и Ни- колаевском инженерном училищах. Службу начал 1.09.1887, произведен в подпоручики _ 9.08.1888, поручик _ 9.08.1892, участник Китайского по- хода 1900-01, штабс-капитан _ 6.05.1900, капитан _ 6.05.1901, награжден орденом Св. Анны 4 ст. с надписью «За храбрость» (1901), участвовал в Русско-Японской войне 1904-05, подполковник _ 26.02.1908, полковник _ 6.12.1912. В 1910-14 служил в 1 Кавказском железнодорожном батальоне. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1905) и 2 ст. (1911), Св. Станислава 2 ст. (1907). Spisok, 1910: 169; Spisok, 1911: 158; Spisok, 1914, SPb.: 1252. ТРОИЦКИЙ МИХАИЛ ИВАНОВИЧ (род. 1.10.1856), полковник. Воспитывался в Владикавказском реальном училище, Тифлисском пехотном юнкерском училище, которое окончил по 1 разряду, с оценкой «Успешно» завершил учебу в Офицерской стрелковой школе. Службу начал 27.04.1872, произведен в прапорщики _ 16.04.1878, участник военной экспедиции 1879, за боевое отличие награжден чином подпоручика _ 28.08.1879, за отличия 357 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV удостоен чинов поручика _ 15.05.1883, штабс-капитана _ 6.10.1888 и капи- тана _ 15.03.1892, подполковник _ 26.02.1899, участник Русско-Японской войны 1904-05, за отличие полковник _ 5.10.1904 (в чине по 11.04.1916) (www.rusgeneral.ru), награжден орденом Св. Анны 2 ст. с мечами (1905). В 1907 _ 1914 командовал 154 пехотным Дербентским полком. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1896) и 2 ст. (1902), Св. Анны 3 ст. (1897), Св. Владимира 3 ст. (1909). Spisok, 1900: 162; Spisok, 1904: 115; Spisok, 1908: 57; Spisok, 1910: 50; Spisok, 1911: 46; Spisok, 1912, SPb.: 206; Spisok, 1914, SPb.: 54. ТРОФИМОВ ВЛАДИМИР ОНУФРИЕВИЧ (род. 5.08.1860), полков- ник. Окончил Николаевскую Академию Генерального штаба по 1 разря- ду. Произведен в подпоручики _ 24.10.1881, поручик _ 8.08.1885, штабс- капитан _ 21.03.1886, капитан Генерального штаба _ 24.1888, подполковник _ 28.03.1893, за отличие полковник _ 13.04.1897(в чине по 6.04.1903) (www. rusgeneral.ru). В 1893 _ 99 занимал должность старшего адъютанта штаба Кавказского военного округа, вице-директор канцелярии главноначальствующего граж- данской частью на Кавказе _ 31.05.1899 _ 5.05.1902, назначен и. д. директо- ра той же канцелярии _ 5.05.1902. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1890) и 2 ст. (1896), Св. Анны 3 ст. (1894), Св. Станислава 2 ст. (1896), Св. Владимира 4 ст. (1901). Кавалер бухарского золотого ордена Благородной Бухары 2 ст. (1898). Spisok, 1899: 94; Spisok, 1900: 82; Spisok, 1900, SPb.: 593; Spisok, 1903, yan., SPb.: 339. ТРОФИМОВ КОНСТАНТИН ПАВЛОВИЧ (род. 13.03.1851), полков- ник. Воспитывался в Орловском кадетском корпусе и 2 Константиновском военном училище. Произведен в прапорщики _ 10.08.1871, подпоручик _ 6.11.1872, поручик _ 29.12.1873, штабс-капитан _ 9.12.1876, участник Русско-Турецкой войны 1877-78, капитан _ 20.12.1879, подполковник _ 26.10.1894, за отличия награжден орденом Св. Владимира 4 ст. с мечами и бантом и чином полковника _ 6.12.1900. С 1904 службу проходил на Кавказе. Командир Кавказского стрелкового летучего артиллерийского парка _ с 21.06.1904. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1875) и 2 ст. (1883), Св. Анны 3 ст. (1879) и 2 ст. (1896). Spisok, 1903, sen., SPb.: 627; Spisok, 1905: 56; Spisok, 1905, SPb.; 498; Spisok, 1906, SPb.: 269. 358 oTar Jordania ТРОЦКИЙ-СЕНЮТОВИЧ ВИКТОР ВИКТОРОВИЧ (род. 12.06.1868), полковник. Воспитывался в Владимирском Киевском кадетском корпусе, 1 военном Павловском училище, окончил Николаевскую Академию Гене- рального штаба по 1 разряду. Службу начал 1.09.1885, произведен в под- поручики _ 11.08.1886, поручик _ 11.08.1890, штабс-капитан _ 15.03.1896, капитан _ 6.05.1900, участник Русско-Японской войны 1904-05, подполков- ник _ 6.12.1904, награжден орденами Св. Анны 3 ст. с мечами и бантом (1904), Св. Станислава 2 ст. с мечами и Св. Анны 2 ст. (1905), за служебное отличие полковник _ 6.12.1908 (в чине по 6.12.1915) (www.rusgeneral.ru). С 1908 службу проходил на Кавказе. Штаб-офицер при управлении 2 Кавказской стрелковой бригады - 1908-1910, начальник штаба 21 пехотной дивизии _ с 24.07.1910. В 1912 награжден орденом Св. Владимира 3 ст. Spisok, 1910: 82; Spisok, 1910, SPb.: 1078; Spisok, 1911: 74; Spisok, 1912, SPb.: 766; Spisok, 1914, SPb.: 390. ТУМАНОВ КОНСТАНТИН АЛЕКСАНДРОВИЧ (род. 19.05.1862), полковник. Окончил Николаевское кавалерийское училище по 1 разря- ду. Службу начал 1.10.1881, произведен в корнеты 12.08.1883, поручик _ 12.088.1887, штабс-ротмистр _ 15.03.1896, участник Русско-Японской во- йны 1904-05, подполковник _ 26.03.1904, награжден орденами Св. Анны 2 ст. с мечами (1904), Св. Владимира 4 ст. с мечами и бантом (1905), зо- лотым оружием и чином полковника _ 29.03.1906 (в чине по 1912) (www. rusgeneral.ru). С 80-х гг. службу проходил в 44 драгунском Нижегородском Е. В. полку. C 1908 служил вне пределов Кавказского военного округа. Spisok, 1907: 80; Spisok, 1907, SPb.: 1050; Spisok, 1908: 73; Spisok, 1909, SPb.: 742; Spisok, 1910, SPb.: 691; Spisok, 1911, SPb.: 502; Spisok, 1912, SPb.: 406. ТУМАНСКИЙ АЛЕКСАНДР ГРИГОРЬЕВИЧ (род. 23.09.1861), пол- ковник. Воспитывался в Варшавской 1 гимназии, при учебном отделении Азиатского Департамента Министерства иностранных дел успешно завер- шил полный курс восточных языков и сдал зкзамен на получение офицер- ского чина. Службу начал 23.07. 1879, произведен в прапорщики гвардии _ 2.12.1880, подпоручик _ 29.11.1882, поручик _ 8.08.1885, штабс-капитан _ 13.12.1892, капитан _ 6.12.1895, переименован в коллежские советники _ 10.04.1900, полковник _ 1.04.1901 (в чине по 3.04.1917) ( www.rusgeneral.ru). В 1900 _ 05 служил вице-консулом в Вене, находился в распоряжении наместника Е. И. В. на Кавказе _ с 20.05.1905. В 1906 награжден орденом Св. Анны 3 ст. (1906). 359 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Spisok, 1905: 58; Spisok, 1907: 43; Spisok, 1907, ch. 3, SPb.: 17; Spisok, 1910, ch. 3, SPb.: 7; Spisok, 1912, ch. 3, SPb.: 6. ТУМАНСКИЙ МИХАИЛ НИКОЛАЕВИЧ (род. 28.10.1859), полков- ник. Воспитывался в Орловской Бахтина военной гимназии и Николаевском кавалерийском училище. Службу начал 31.08.1878, произведен в корнеты _ 8.08.1880, поручик _ 10.03.1881, штабс-ротмистр _ 26.02.1887, ротмистр _ 30.08.1888, подполковник _ 26.02.1898, награжден чином полковника _ 6.12.1906. С 1908 службу проходил на Кавказе, прикомандирован к Терскому об- ластному жандармскому управлению _ 1.09.1908. Spisok, 1910: 67; Spisok, 1910, ch. 3, SPb.: 54; Spisok, 1911: 60; Spisok, 1912, ch. 3, SPb.: 39; Spisok, 1914, SPb.: 176. ТУНЕБЕРГ МИХАИЛ ФАБИАНОВИЧ (род. 1854), полковник. В офицерских чинах с 17.07.1877. Участник Русско-Турецкой войны 1877-78. Подполковник _ 26.02.1898. Полковник _ 17.03.1904 (старшинство с 5.10.1904). В 1899-1905 служил в 262 Сальянском пехотном резервном полку. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1883) и 2 ст. (1904), Св. Анны 3 ст. (1898), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1903). Spisok, 1899: 158; Spisok, 1901: 155; Spisok, 1903: 124; Spisok, 1904: 110; Spisok, 1905: 81. ТУНЕБЕРГ НИКОЛАЙ ФАБИАНОВИЧ (род. 11.11.1849), полковник. Произведен в прапорщики _ 26.12.1871, подпоручик _ 23.07.1873, поручик _ 12.06.1876, участник Русско-Турецкой войны 1877-78, ранен в бою, на- гражден орденом Св. Анны 4 ст. с надписью «За храбрость» (1878), штабс- капитан _ 18.05.1880, награжден чином капитана _ 6.05.1884, подполковник _ 1.01.1890, за отличие полковник _ 14.04.1902. Командир 256 Гунибского резервного батальона _ 25.06.1902 _ 1.06.1904. С июня 1904 служил вне Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1880) и 2 ст. (1890), Св. Анны 3 ст. (1881) и 2 ст. (1894), Св. Вла- димира 4 ст. (1896) и Св. Владимира 3 ст. (1906). Spisok, 1903: 86; Spisok, 1903, sen., SPb.: 802; Spisok, 1905, SPb.: 661; Spisok, 1907, SPb.: 246. ТУРГИЕВ БЕЙ-БУЛАТ АБИСАЛОВИЧ (род. 29.01.1854, по другим данным:1852), полковник. Воспитывался дома и в Ставропольском казачьем 360 oTar Jordania юнкерском училище. Службу начал 4.10.1872, участник Русско-Турецкой войны 1877-78, произведен в прапорщики _ 17.02.1877, награжден чинами поручика _ 30.06.1878 и штабс-ротмистра _ 15.05.1883, орденами Св. Анны 4 ст. и 3 ст. с мечами и бантом (1877), Св. Станислава 2 ст. с мечами (1879), ротмистр _ 15.03.1894, подполковник _ 26.02.1902, полковник _ 6.05.1913. В 1903-08 - управляющий Терской заводской конюшней, штаб-офицер для поручений VI класса сверх штата при Главном управлении Государ- ственного коннозаводства _ с 4.03.1913. За другие военно-служебные заслуги награжден орденами Св. Анны 2 ст. (1895), Св. Владимира 4 ст. с бантом (1903). Spisok, 1903: 151; Spisok, 1904: 135; Spisok, 1905: 113; Spisok, 1907: 106; Spisok, 1908: 97; Spisok, 1914, SPb.: 1316. ТУРГИЕВ ЗАУРБЕК ДЗАМБУЛАТОВИЧ (ДЖАМБУЛАТОВИЧ) (род. 24.07.1859), полковник. Воспитывался в Ставропольской гимназии, 2 воен- ном Константиновском училище, с оценкой успешно окончил Офицерскую кавалерийскую школу. Службу начал _ 1.09.1880, произведен в хорунжие _ 7.08.1882, сотник _ 30.09.1883, подъесаул _ 31.12.1885, есаул _ 6.05.1888, награжден орденом Св. Станислава 3 ст. (1903), войсковой старшина _ 26.02.1904, участник Русско-Японской войны 1904-05, награжден орденами Св. Анны 3 ст. с мечами и бантом, Св. Владимира 4 ст. с мечами и бантом (1905), за боевое отличие полковник _ 21.10.1907 (в чине по 1912) (www. rusgeneral.ru). Командир 1 Ейского полка Кубанскоо казачьего войска _ 5.01.1908- 13.05.1911, командующий 1 бригады 1 Кавказской казачьей дивизии того же войска _ с 13.05.1911. В 1911 награжден орденом Св. Владимира 3 ст. Spisok, 1908: 84; Spisok, 1910: 72; Spisok, 1910, SPb.: 860; Spisok, 1912, SPb.: 560. ТУРОБОЙСКИЙ ЭДУАРД-КИПРИАН ИОСИФОВИЧ (род. 13.10.1853), полковник. Воспитывался в военной гимназии, 1 военном Павловском учи- лище, которое окончил по 1 разряду, с отличием завершил учебу в Офицер- ской стрелковой школе. Службу начал 12.08.1871, участник Русско-Турец- кой войны 1877-78 (ранен в бою) и военной экспедиции 1879, произведен в поручики _ 13.05.1877, награжден орденами Св. Анны 4 ст. (1877), Св. Ста- нислава 3 ст. с мечами и бантом (1879), за боевое отличие штабс-капитан _ 15.03.1888, за отличие по службе капитан _ 15.03.1888, подполковник _ 26.02.1898, за отличие полковник _ 1.01.1906 (в чине по 1911) (www. rusgeneral.ru). 361 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV В 1899- 1907 службу проходил в 14 гренадерском Грузинском ген. Котля- ревского полку, командир 255 Аварского резервного батальона _ с 4.10.1907. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1884) и 2 ст. (1896), Св. Станислава 2 ст. (1891), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1899). Spisok, 1899: 170; Spisok, 1901: 153; Spisok, 1903: 121; Spisok, 1904: 108; Spisok, 1905: 100; Spisok, 1907: 76; Spisok, 1907, SPb.: 1172; Spisok, 1908: 69; Spisok, 1910: 61; Spisok, 1910, SPb.: 643. УЛЬЯНОВ АФАНАСИЙ ИВАНОВИЧ (род. 5.07.1846), полковник. Воспитывался в классической гимназии и юнкерском училище. Произве- ден в подпоручики _ 22.09.1871, поручик _ 23.03.1874, штабс-капитан _ 30.08.1879, капитан _ 2.11.1884, подполковник _ 1.01.1890, за отличие пол- ковник _ 6.12.1898 (в чине по 6.12.1906) (www.rusgeneral.ru). Начальник Тифлисской военно-фельдшерской школы _ с 16.07.1896, назначен начальником Тифлисского военного госпиталя _ 4.09.1905.. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1895), Св. Анны 3 ст. (1901) и 2 cт. (1904). Spisok, 1899: 101; Spisok, 1900: 89; Spisok, 1903: 69; Spisok, 1903, sen., SPb.: 403; Spisok, 1905: 47; Spisok, 1905, SPb.: 281; Spisok, 1906, SPb.: 125. УЛЬЯНОВ ВИКТОР ВАСИЛЬЕВИЧ (род. 17.12.1863), полковник. Воспитывался в прогимназии и Тифлисском пехотном юнкерском училище. Службу начал 26.03.1881, произведен в подпоручики _ 15.05.1887, поручик _ 15.05.1891, штабс-капитан _ 6.05.1900, капитан _ 6.05.1901, награжден орденом Св. Станислава 3 ст. (1903), за служебные отличия подполковник _ 26.02.1909 и полковник _ 31.12.1912. Назначен и. д. начальника 2 участка Хасан-Юртовского округа Терской обл. _ 23.08.1899, старший помощник начальника Грозненского уезда _ c 26.02.1909, начальник Назрановского округа Терской обл. _ с 22.01.1911. Spisok, 1910: 184; Spisok, 1911: 173; Spisok, 1914, SPb.: 1282. УМАНЕЦ-ДМИТРОВСКИЙ ПЕТР АНДРЕЕВИЧ (род. 18.06.1867), полковник. Воспитывался в реальном и Московском военном училищах. Службу начал 20.06.1887, произведен в подпоручики _ 9.08.1888, поручик _ 9.08.182, штабс-капитан _ 6.05.1900, капитан _ 6.05.1901, участник Русско- Японской войны 1904-05, за отличия подполковник _ 6.02.1909 и полковник _ 6.05.1913 (в чине по 1917) (www.rusgeneral.ru). Казначей окружного интендантского управления Кавказского военно- го округа _ с 29.09.1907, затем в должности главного смотрителя вещевого 362 oTar Jordania склада службу проходил в Казани _ с 21.10.1910, назначен начальником Тиф- лисского интендантского вещевого склада _ 7.03.1913. За военно-служебные заслуги награжден орденами Св. Анны 3 ст., Св. Станислава 2 ст. (1907). Spisok, 1910: 185; Spisok, 1914, SPb.: 1334. УНГЕРН-ШТЕРНБЕРГ МИХАИЛ ЛЕОНАРДОВИЧ (род. 12.09.1870), барон, полковник. Воспитывался в Пажеском Е. В. корпусе. Службу начал 1.09.1889, произведен в хорунжие _ 10.08.1890, сотник _ 10.08.1894, сотник гвардии _ 24.01.1898, подъесаул _ 24.01.1902, есаул _ 24.01.1906, полковник _ 25.03.1912. В 1914 службу проходил во 2 лейб-гвардейской Кубанской казачьей сот- не Собственно Е.В. конвое. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1904), Св. Анны 2 ст. (1907), Св. Владимира 4 ст. (1912). Spisok, 1913, SPb.: 1177; Spisok, 1914, SPb.: 1110. УНГЕРН-ШТЕРНБЕРГ, ФРЕЙГЕР-ФОН ПИРКЕЛЬ ВЛАДИМИР. См.: УНГЕРН-ШТЕРНБЕРГ, ФРЕЙГЕР-ФОН ПИРКЕЛЬ ВЛАДИМИР-ЯКОВ- ФЕЛИКС-АДАМ. УНГЕРН-ШТЕРНБЕРГ, ФРЕЙГЕР-ФОН ПИРКЕЛЬ ВЛАДИМИР- ЯКОВ-ФЕЛИКС-АДАМ (род. 1849), барон, полковник. Воспитывался в Елисаветградском юнкерском кавалерийском училище. Прапорщик _ 31.10.1879, за отличие по службе поручик _ 8.04.1874, корнет гвардии _ 7.09.1876, участник Русско-Турецкой войны 1877-78, поручик гвардии _ 16.04.1878, награжден орденами Св. Анны 4 ст. с надписью «За храбрость», Св. Станислава 3 ст. с мечами и бантом (1878). За служебные отличия на- гражден чинами ротмистра _ 1883 ( старшинство с 27.07.1883), подполков- ника _ 1892 (старшинство с 26.02.1892) и полковника _ 1900 (старшинство с 6 05.1900). Начальник: Шавшет-Имерхевского участка Артвинского округа Батум- ской обл. _ 27.06. _ 1.09.1883, Артвинского участка Артвинского округа _ 1.09.1883 _ 23.10.1886, Самурского участка _ 23.10.1886 _ 1.08.1888. Вла- дикавказский полицмейстер _ 1.08.1888 _ 10.03.1896. Назначен начальни- ком Хасав-Юртовского округа Терской обл. _ 10.03.1896. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1883), Св. Станислава 2 ст. (1896), Св. Владимира 4 ст.с бантом _ за 25 лет безупречной службы в офицерских чинах (1897). 363 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Кавалер иностранных орденов: саксен-альтенбургского - Эрнестинско- го герцегского Дома _ Герцогского Орла 3 ст. с мечами (1877), Румынского креста (1878), персидского _ Льва и Солнца 3 ст. (1890), бухарского _ золо- того ордена Благородной Бухары 2 ст. (1896). Spisok, 1900, SPb.: 905; Spisok, 1901: 99; Spisok, 1902, SPb.: 738; Spisok, 1903, sen., SPb.: 583. УСОВ АНДРИАН ВЛАДИМИРОВИЧ (род. 27.05.1868), полковник. Воспитывался в 3 С.-Петербургской гимназии, Михайловском артилле- рийском училище, окончил Николаевскую Академию Генерального штаба. Cлужбу начал 31.08.1886, подпоручик-подпоручик гвардии _ 10.08.1889, поручик _ 30.08.1893, штабс-капитан гвардии-капитан Генерального штаба _ 20.05.1895, подполковник _ 9.04.1900, участник Русско-Японской войны 1904-05, за отличие полковник _ 6.12.1904 (в чине по 24.09.1913) (www. rusgeneral.ru), награжден орденами Св. Станислава 2 ст. с мечами, Св. Анны 2 ст. с мечами (1906). Штаб-офицер для особых поручений при штабе 2 Кавказского армей- ского корпуса _ с 19.05.1900, штаб-офицер для особых поручений при ко- мандующем Кавказским военным округом _ с 24.11.1901, начальник штаба сводной Кавказской казачьей дивизии _ с 20.11.1904. С мая 1906 службу проходил вне Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1898), Св. Анны 3 ст. (1902). Spisok, 1901: 169; Spisok, 1904: 121; Spisok, 1905: 85; Spisok, 1905, SPb.: 1128; Spisok, 1907, SPb.: 752; Spisok, 1909, SPb.: 483; Spisok, 1909, SPb.: 483; Spisok, 1910, SPb.: 439; Spisok, 1913, SPb.: 138. УСТИНОВ ВЛАДИМИР СЕМЕНОВИЧ (род. 12.07.1855), полковник. Воспитывался в Ставропольской гимназии и Николаевском кавалерийском училище. Службу начал 2.09.1875, участник Русско-Турецкой войны 1877- 78, произведен в прапорщики _ 22.05.1877, поручик _ 1.08.1877, награжден орденами Св. Анны 4 ст., Св. Станислава 3 ст. с мечами и бантом (1878), Св. Анны 3 ст. с мечами и бантом (1879), штабс-ротмистр _ 6.05.1884, ротмистр _ 30.08.1887, подполковник _ 26.02.1896, полковник _ 26.02.1905 (в чине по 1912) (www.rusgeneral.ru). В 1910 занимал должность начальника Терского областного жандарм- ского управления. Награжден орденами Св. Станислава 2 ст. (1893), Св. Анны 2 ст. (1889) Св. Владимира 3 ст. (1906). Spisok, 1910: 56; Spisok, 1912, ch. 3, SPb.: 16. 364 oTar Jordania ФАДЕЕВ ЕВГЕНИЙ ЯКОВЛЕВИЧ (род. 21.03.1846), полковник. Вос- питывался дома и в Тифлисском пехотном юнкерском училище. Произведен в хорунжие _ 27.05.1874, участник Русскo-Турецкой войны 1877-78, сотник _ 30.03.1877, награжден чином есаула _ 30.08.1879, войсковой старшина _ 26.02.1892, за отличие по службе полковник _ 13.01.1900. Командир 6 Кубанского пластунского батальона _ с 18.02.1900. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1880) и 2 ст. (1895), Св. Анны 3 ст. (1883) и 2 ст. (1903), Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1900). Spisok, 1901: 95; Spisok, 1901, SPb.: 765; Spisok, 1902, SPb.: 688; Spisok, 1903, sen., SPb.: 530. ФЕДОРЕНКО БОРИС ИОСИФОВИЧ (род. 4.07.1870), полковник. Воспитывался в Тифлисском кадетском корпусе, 2 военном Константи- новском училище, окончил Николаевскую Академию Генерального штаба с дополнительным курсом по 1 разряду. Службу начал 31.08.1888, произ- веден в подпоручики _ 10.08.1890, поручик _ 10.08.1894, штабс-капитан _ 6.05.1900, капитан _ 23.05.1901, участник Русско-Японской войны 1904-05, подполковник _ 6.12.1904, награжден орденами Св. Анны 3 ст. с мечами и бантом, Св. Станислава 2 ст. с мечами (1904), Св. Владимира 4 ст. с мечами и бантом, Св. Анны 2 ст. с мечами (1905), за отличие по службе полковник _ 6.12.1908. С 1908 службу проходил на Кавказе. Начальник штабов 39 пехотной дивизии _ с 5.12.1908 и Кавказской гренадерской дивизии _ c 24.04.1913. В 1912 награжден орденом Св. Владимира 3 ст. Spisok, 1910: 83; Spisok, 1910, SPb.: 1108; Spisok, 1911: 75; Spisok, 1912, SPb.: 798; Spisok, 1914, SPb.: 419. ФЕДОРОВ ИВАН ИВАНОВИЧ (род. 11.11.1857), полковник. Служ- бу начал 11.10.1875, произведен в прапорщики _ 16.04.1878, подпоручик _ 4.11.1879, поручик _ 23.03.1881, штабс-капитан _ 13.11.1884, капитан _ 2.02.1894, награжден орденами Св. Станислава 2 ст. с мечами (1904), Св. Анны 2 ст. с мечами (1905), подполковник _ 26.02.1905, полковник _ 6.12.1910. В 1910 - 11 служил в 261 пехотном Шемахинском полку. Spisok, 1909, SPb.: 850; Spisok, 1910: 125; Spisok, 1911: 92. ФЕДОТОВ НИКОЛАЙ АЛЕКСАНДРОВИЧ (АЛЕКСЕЕВИЧ) (род. 17.04.1856), полковник. Воспитывался в Ярославской военной прогимназии, Павловском военном училище, окончил Офицерскую стрелковую школу с оценкой «Успешно». Службу начал 16.06.1873, участник Русско-Турецкой 365 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV войны 1877-78, произведен в прапорщики _ 20.07.1877, награжден орденом Св. Анны 4 ст. (1878), подпоручик _ 13.07.1879, поручик _ 18.04.1883, штабс- капитан _ 21.04.1888, капитан _ 15.03.1896, подполковник_ 26.02.1902, пол- ковник _ 6.12.1910. В 1903-13 служил в 79 пехотном Куринском и 80 пехотном Кабардин- ском ген.-фельдм. кн. Барятинского полках. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1887) и 2 ст. (1901), Св. Владимира 4 ст. с бантом (1903), Св. Анны 2 ст. (1905). Spisok, 1903: 151; Spisok, 1905: 112; Spisok, 1908: 98; Spisok, 1910: 99; Spisok, 1911: 91; Spisok, 1912, SPb.: 1133; Spisok, 1913, SPb.: 783. ФЕДЮШКИН ВАСИЛИЙ КОСЬМИЧ (род. 20.03.1860), полковник. Воспитывался в Ставропольском казачьем юнкерском училище, которое окончил по 2 разряду. Службу начал 18.06.1878, произведен в хорунжие _ 11.05.1883, сотник _ 11.05.1887, корнет гвардии _ 6 12.1888, сотник _ 11.05.1891, подъесаул _ 6.05.1900, есаул _ 6.05.104, полковник _ 6.12.1906. В 1906-09 командовал лейб-гвардейской 3 Тверской казачьей сотней, назначен командиром 1 Кизляро-Гребенского ген. Ермолова полка Терского казачьего войска _ 30.05.1909. За военно - служебные заслуги награжден орденами Св. Станислава 2 ст. (1903), Св. Анны 2 ст. (1905), Св. Владимира 4 ст. (1908). Spisok, 1909, SPb.: 847; Spisok,1910: 69; Spisok, 1910, SPb.: 792; Spisok, 1913, SPb.: 1215. ФЕДЮШКИН НИКОЛАЙ КОСЬМИЧ (род. 26.07.1867), полковник. Воспитывался в Ставропольской гимназии и Михайловском артиллерийском училище .Службу начал 5.09.1885, произведен в хорунжие _ 11.08.1886, сотник _ 11.08.1890, подъесаул _ 1.06.1898, есаул _ 6.05.1900, войсковой старшина _ 6.10.1907, за служебные заслуги награжден чином полковника _ 6.05.1912. В 1910 _ 12 командовал 2 Кавказской конно-артиллерийской дивизией, командир 1 Кубанского ген.-фельдм. Вел. кн. Михаила Николаевича полка Кубанского казачьего войска _ c 7.08.1912. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1905), Св. Владимира 4 ст. (1908). Spisok, 1913, SPb.: 1215. ФЕДЯЙ ИВАН ИВАНОВИЧ (род. 14.09.1848), полковник. Воспиты- вался в Петроковской классической гимназии и Варшавском пехотном юн- керском училище. Произведен в подпоручики _ 3.04.1875, участник Рус- ско-Турецкой войны 1877-78, поручик _ 16.04.1878, награжден орденами 366 oTar Jordania Св. Анны 4 ст., Св. Станислава 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бантом (1878), штабс-капитан _ 30.08.1884, капитан _ 1.04.1890, капитан гвардии _ 6.12.1894, полковник _ 9.04.1900. В 1906 командовал 131 пехотным Тираспольским полком. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1893), Св. Владимира 4 ст. с бантом (1899) и 3 ст. (1906), Св. Анны 2 ст. (1901), Св. Владимира 3 ст. (1906). Кавалер австрийского ордена Железной короны 3 ст. (1889). Spisok,, 1903, sen., SPb.: 572; Spisok, 1905, SPb.: 443; Spisok, 1907, SPb.: 136; Spisok, 1908: 36; Spisok, 1909, SPb.: 65; Spisok, 1910, SPb.: 53. ФЕДЯЙ ЛЕОНИД ВАСИЛЬЕВИЧ (род. 15.08.1859), полковник. Окон- чил Пажеский Е. И. В. корпус, Николаевскую Академию Генерального штаба по 1 разряду. Произведен в подпоручики _ 20.12.1879, поручик _ 18.12.1880, награжден чином штабс-капитана _ 21.03.1886, капитан Гене- рального штаба _ 24.1888, подполковник _ 17.04.1891, за служебное отли- чие полковник _ 5.04.1898 (в чине по 15.06.1907) (www.rusgeneral.ru ) С 1900 службу проходил на Кавказе, начальник штаба 21 пехотной ди- визии _ 5.04.1900 _ 16.03.1904. Затем служил в другом военном округе. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1890) и 2 ст. (1901), Св. Анны 3 ст. (1895). Spisok, 1900: 85; Spisok, 1901: 84; Spisok, 1903: 66; Spisok, 1903, sen., SPb.: 349; Spisok, 1906: 100. ФЕРГИС МЕЧЕСЛАВ ИОСИФОВИЧ (ОСИПОВИЧ) (род. 22.06.1848), полковник. Воспитывался в роте топографов №3 и Военно-топографическом училище. Службу начал 24.07.1864, произведен в прапорщики _ 27.11.1873, подпоручик _ 30.08.1875, участник Русско-Турецкой войны 1877-78, пору- чик _ 30.08.1877, штабс-капитан _ 30.09.1880, награжден орденом Св. Ста- нислава 3 ст. с мечами и бантом (1880), капитан _ 30.08.1887, подполковник _ 30.08.1893, за отличие по служебе полковник _ 6.12.1908. С 20.04.1893 служил производителем картографических работ штаба Кавказского военного округа, помощник начальника Военно-топографиче- ского отдела штаба Кавказского военного округа _ с 26.10.1910. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1881), Св. Анны 2 ст. (1893), Св. Владимира 4 ст. _ за 25 лет без- упречной службы в офицерских чинах (1898) и 3 ст. (1912). Spisok, 1894: 217; Spisok, 1908: 85; Spisok, 1910: 80; Spisok, 1910, SPb.: 1024; Spisok, 1911: 72; Spisok, 1911, SPb.: 808; Spisok, 1913, SPb.: 466; Spisok, 1914, SPb.: 345. 367 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ФИДАРОВ АФАКО ПАЦИЕВИЧ (род. 29.08.1859, полковник. Воспи- тывался в Владикавказском реальном училище, 2 Константиновском учи- лище, которое окончил по 1 разряду, с оценкой «Успешно» завершил учебу в Офицерской кавалерийской школе. Службу начал 1.09.1880, хорунжий _ 7.08.1882, сотник _ 30.09.1883, подъесаул _ 31.12.1885, награжден чином есаула _ 6.05.1893, войсковой старшина _ 26.02.1901, получил орден Св. Станислава 2 ст. (1901), участник Русско-Японской войны 1904-05, за от- личие полковник _ 6.12.1904 (в чине по 22.07.1910) (www.rusgeneral.ru), на- гражден орденами Св. Анны 2 ст. с мечами и Св. Владимира 4 ст. с мечами и бантом (1905) и 3 ст. с мечами (1906), золотым оружием (1906). Занимал военно-административные должности в Владикавказском конном, Горско-Моздокском, I Сунженско-Владикавказском и др. полках, около 5 лет ра- ботал военным инструктором в Иране. Командир 1 Хоперского Е. И. В. Вел. кн. Анастасии Михайловны полка Кубанского казачьего войска _ с 12.02.1907. Spisok, 1905: 85; Spisok, 1905, SPb.: 1153; Spisok, 1907: 68; Spisok,1907, SPb.; 784; Spisok, 1910: 55; Spisok, 1910, SPb.: 472. ФИЛИМОНОВ ФЕДОР ПЕТРОВИЧ (род. 7.06.1862), полковник. Вос- питывался в Воронежской военной гимназии, 2 военном Константиновском училище, окончил Офицерскую артиллерийскую школу с оценкой «Успеш- но». Службу начал 1.09.1879, произведен в хорунжие _ 8.08.1881, награж- ден чином сотника _ 6.05.1884, подъесаул _ 1.07. 1894, есаул _ 1. 06.1899, за служебные отличия награжден чинами войскового старшины _ 7.01.1905 и полковника _ 6.06.1909 (в чине по 6.04.1914) (www.rusgeneral.ru). В 1887-88 был личным адъютантом при наказном атамане Кубанского казачьего войска, командовал 2 Кубанской казачьей батареей _ c 7.01.1905, атаман Баталпашинского отдела Кубанской обл. _ 21.01.1909 _ 31.03.1911, командир 1 Таманского ген. Безкровного полка Кубанского казачьего войска _ 31.03.1911 _ 27.08.1913, назначен командующим 2 бригады 3 Кавказской казачьей дивизии _ 27.08.1913. За другие военно-служебные заслуги награжден орденом Св. Станисла- ва 2 ст. (1907), Св. Анны 2 ст. (1913). Spisok, 1910: 87; Spisok, 1910, SPb.: 1172: Spisok, 1911: 79; Spisok, 1912, SPb.: 860; Spisok, 1914, SPb.: 469. ФИЛИППОВ ИВАН ИВАНОВИЧ (род. 7.07.1849), полковник. Вос- питывался в 1 С.-Петербургской военной гимназии и С.-Петербургском пе- хотном юнкерском училище. Произведен в прапорщики _ 7.08.1870, подпо- ручик _ 13.06.1872, поручик _ 11.04.1873, в отставке _ 28.02. _ 20.12.1876, участник Русско-Турецкой войны 1877-78, штабс-капитан _ 20.06.1877, 368 oTar Jordania капитан _ 24.10.1877, награжден орденами Св. Анны 3 ст. с мечами и бан- том, Св. Станислава 2 ст. с мечами (1878), подполковник _ 1.01.1885, за от- личие по службе полковник _ 6.11.1900. Владикавказский уездный воинский начальник _ с 6.11.1900. За другие военно-служебные заслуги награжден орденами Св. Станисла- ва 3 ст. (1874), Св. Анны 2 ст. (1886), Св. Владимира 4 ст. (1894) и 3 ст. (1905). Spisok, 1901: 100; Spisok, 1903:79; Spisok, 1903, sen., SPb.: 610; Spisok, 1905: 55; Spisok, 1905, SPb.: 483; Spisok, 1907: 41; Spisok, 1907, SPb.: 151; Spisok, 1909, SPb.: 69; Spisok, 1910: 35; Spisok, 1911, SPb.: 32. ФИСЕНКО НИКОЛАЙ ИВАНОВИЧ (род. 6.02.1861), полковник. Вос- питывался в реальном училище, 3 военном Александровском военном училище, которое окончил по 1 разряду, завершил учебный курс Офицер- ской кавалерийской школы с оценкой «Успешно». Произведен в хорунжие _12.08.1883, награжден орденом Св. Станислава 3 ст. с мечами и бантом _ 1885, сотник _ 31.12.1885, подъесаул _ 4.10.1890, награжден чином есау- ла _ 18.03.1896, войсковой старшина _ 26.02.1902, за отличие полковник _ 6.12.1905 (в чине по 22.07.1910) (www.rusgeneral.ru). Назначен командиром 1 Сунженско-Владикавказского ген. Слепцова полка _ 25.07.1907. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1892) и 2 ст. (1909), Св. Станислава 2 ст. (1901), Св. Владимира 4 ст. (1909). Spisok, 1907: 74; Spisok, 1907, SPb.: 950; Spisok, 1910: 61; Spisok, 1910, SPb.: 615. ФИСЕНКОВ ВЛАДИМИР ИВАНОВИЧ (род. 31.05.1859), полковник. Воспитывался в Владикавказской военной прогимназии и Ставропольском казачьем юнкерском училище. Службу начал 1.01.1876, произведен в хо- рунжие _ 30.03.1880, сотник _ 5.03.1886, награжден чином подъесаула _ 6.05.1895, войсковой старшина _ 26.02.1907, за служебное отличие полков- ник _ 20.02.1912. Командир 4 Кубанского пластунского батальона _ с 20.02.1912. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1891) и 2 ст. (1912), Св. Анны 3 ст. (1909). Spisok, 1912, SPb.: 1648; Spisok, 1914, SPb.: 1102. ФИЯЛКОВСКИЙ РАФАИЛ РАФАИЛОВИЧ (род. 5.05.1854), полковник. Воспитывался в Темир-Хан-Шуринской прогимназии, Казанском пехотном юнкерском училище, которое окончил по 2 разряду, с оценкой «Успешно» завершил учебу в Офицерской стрелковой школе. Службу начал 9.06.1871, 369 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV произведен в прапорщики _ 20.11.1871, участник Русско-Турецкой войны 1877-78, подпоручик _ 14.05.1877, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1877), поручик _ 12.05.1881, за отличие штабс-капитан _ 6.05.1884, капитан _ 15.03.1890, подполковник _ 26.02.1901, участник Русско-Японской войны 1904-05 (контужен), награжден орденом Св. Ста- нислава 2 ст. (1904) и чином полковника - 25.01.1908. Службу проходил в 16 гренадерском Мингрельском Е. И. В. Вел. кн. Дмитрия Константиновича полку _ с 6.02.1906. За другие военно - служебные заслуги награжден орденами Св. Влади- мира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1902), Св. Анны 2 ст. (1911). Spisok, 1908: 84; Spisok, 1909, SPb.: 995; Spisok, 1910: 74; Spisok, 1911: 67; Spisok, 1911, SPb.: 730; Spisok,, 1912, SPb.: 637. ФЛЕЙШЕР БОРИС ВЛАДИМИРОВИЧ (род. 3.02.1870), полковник. Окончил физико-математический факультет Московского университета с дипломом 1 ст. и военно-учебные курсы Московского пехотного юнкерского училища. Службу начал 22.08.1892, подпоручик гвардии _ 7.08.1897, пору- чик гвардии _ 7.08.1897, штабс-капитан _ 30.11.1900, капитан _ 6.12.1900, подполковник _ 6.12.1903, за отличие по службе полковник _ 6.12.1908. Ротный командир Владикавказского кадетского корпуса _ 16.08.1908 _ 20.08.1910. С августа 1910 службу проходил вне Кавказского военного округа. За военно-служебные заслуги награжден орденом Cв. Станислава 3 ст. (1902), Св. Анны 3 ст. (1905). Spisok, 1910: 81; Spisok, 1910, SPb.: 1054; Spisok, 1912, ch. 2, SPb.: 52; Spisok, 1914, SPb.: 369. ФЛЕЙШЕР СЕРГЕЙ НИКОЛАЕВИЧ (род. 4.02.1856), полковник. Участник Русско-Турецкой войны 1877-78, произведен в прапорщики гвардии _ 5.08.1877, подпоручик _ 30.08.1877, награжден орденами Св. Анны 4 ст. с надписью «За храбрость», Св. Станислава 3 ст. с мечами и бантом (1879), переименован в есаулы _ 23.02.1882, войсковой старшина _ 1.01.1891, за отличие по службе полковник _ 6.12.1894 (в чине по 6.04.1903) (www.rusgeneral.ru). В 1891-97 служил в 1 Уманском полку Кубанского казачьего войска, штаб-офицер, заведовавший офицерским казачьим отделом Офицерской кавалерийской школы, назначен командиром 1 Полтавского полка Кубан- ского казачьего войска _ 14.03.1897, командующий 2 бригады 2 Кавказской казачьей дивизии _ 16.02.1901. 370 oTar Jordania За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1885) и 2 ст. (1899), Св. Станислава 2 ст. (1889). Кавалер персидского ордена Льва и Солнца 3 ст. (1892). Spisok, 1895: 115; Spisok, 1897: 102; Spisok, 1900: 70; Spisok, 1900, SPb.: 391; Spisok, 1901: 70. ФОЛЬБАУМ (с 1916: СОКОЛОВ-СОКОЛИНСКИЙ) МИХАИЛ АЛЕК- САНДРОВИЧ (род. 22.10.1866), полковник. Воспитывался в Александров- ском кадетском корпусе, 1 военном Павловском училище, окончил Никола- евскую Академию Генерального штаба по 1 разряду. Произведен в подпору- чики гвардии _ 11.08.1886, поручик _ 30.08.1890, штабс-капитан, капитан Генерального штаба _ 6.05.1892, подполковник _ 6.12.1896, за служебное отличие полковник _ 6.12.1901 (в чине по 18.10.1907) (www.rusgeneral.ru). В 1907 командовал 82 пехотным Дагестанским полком. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1894) и 2 ст. (1899), Св. Анны 3 ст. (1896) и 2 ст. (1905), Св. Владимира 4 ст. (1906). Кавалер иностранных орденов: бухарского _ Благородной Бухары 3 ст. (1896), персидского _ Льва и Солнца 2 ст. _ (1901). Spisok, 1907: 45; Spisok, 1904, SPb.: 664; Spisok, 1906, SPb.: 371. ФОН-БАДЕР ЛЮДОЛЬФ ОТТОВИЧ. См: ФОН-БАДЕР ЛЮДОЛЬФ- ПАУЛЬ ОТТОВИЧ. ФОН-ДЕР НОННЕ МИХАИЛ АВГУСТОВИЧ. См.:НОННЕ, ФОН-ДЕР МИХАИЛ АВГУСТОВИЧ. ФОН-ДЕР НОННЕ НИКОЛАЙ НИКОЛАЕВИЧ. См.: НОННЕ, ФОН- ДЕР НИКОЛАЙ НИКОЛАЕВИЧ. ФОН-ДЕР ОСТЕН-САКЕН АЛЕКСЕЙ АЛЕКСЕЕВИЧ. См.: ОСТЕН- САКЕН, ФОН-ДЕР АЛЕКСЕЙ АЛЕКСЕЕВИЧ. ФОН-БАДЕР ЛЮДОЛЬФ-ПАУЛЬ ОТТОВИЧ. (род. 2.04.1853), пол- ковник. Воспитывался в С.-Петербургской военной гимназии и 2 военном Константиновском училище, которое окончил по 2 разряду, с отличием за- вершил учебу в Кавказской учебной роте, с оценкой «Успешно» окончил курс Офицерской стрелковой школы. Службу начал 5.08.1870, произведен в прапорщики - 17.07.1872, подпоручик _ 29.08.1873, поручик _ 8.06.1875, участник Русско-Турецкой войны 1877-78, награжден орденом Св. Станис- лава 3 ст. с мечами и бантом (1878), штабс-капитан _ 1.06.1884, подполков- ник _ 26.02.1895, полковник _ 20.10.1904. 371 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV В 1904-05 (апрель) служил в 15 гренадерском Тифлисском Е. И. В. Вел. кн. Константина Константиновича полку, назначен командиром 258 пехот- ного резервного Сухумского полка _ 10.04.1905. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1881), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицер- ских чинах (1898) и 3 ст. (1907), Св. Станислава 2 ст. (1901). Кавалер бухарского золотого ордена Благородной Бухары 3 ст.(1896). Spisok, 1899: 142; Spisok, 1904: 96; Spisok, 1905: 79; Spisok, 1905, SPb.: 1082; Spisok, 1907: 62; Spisok, 1907, SPb.: 710; Spisok, 1908: 58; Spisok, 1910: 52; Spisok, 1910, SPb.: 409. ФОН-ГИЛЛЕНШМИДТ АЛЕКСАНДР ФЕДОРОВИЧ (род. 10.10.1863, по другим данным: 1.10.1867), полковник. В офицерских чинах с 1887. Ге- оргиевский кавалер. Капитан гвардии _ 5.04.1899. Полковник _ 14.04.1902. Участник Русско-Японской войны 1904-05, за выдающееся боевое отличие награжден орденом Св. Георгия 4 ст. (1905) и другими боевыми знаками от- личия: Св. Станислава 2 ст. с мечами (1905), Св. Владимира 4 ст. с мечами и бантом, Св. Владимира 3 ст. с мечами (1905), Св. Анны 2 ст. с мечами (1906), золотым оружием (1906). Известно, что в 1905 службу проходил в Терско-Кубанском конном пол- ку, в 1907 командовал 44 драгунским Нижегородским полком. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1896), Св. Анны 3 ст. (1899). Кавалер иностранных орденов: персидского _ Льва и Солнца 3 ст. (1897), французского _ Почетного Легиона (Кавалерийский крест, 1897). Spisok, 1905: 62; Spisok, 1907: 46. ФОН-ГИЛЛЕНШМИДТ ЯКОВ ФЕДОРОВИЧ (род. 21.10.1870), пол- ковник. Георгиевский кавалер. Воспитывался в Пажеском Е. В. корпу- се, который окончил по 1 разряду. Произведен в подпоручики гвардии _ 10.08.1890, поручик _ 10.08.1894, штабс-капитан _ 5.04.1898, капитан гвар- дии _ 5.04.1902, полковник _ 6.04.1903, участник Русско-Японской войны 1904-05, награжден орденами Св. Станислава 2 ст. с мечами, Св. Анны 2 ст. с мечами, Св. Владимира 4 ст. с мечами и бантом (1904) и 3 ст. с мечами (1905), за выдающееся боевое отличие удостоен ордена Св. Георгия 4 ст., мечами и бантом к ордену Св. Анны 3 ст. и золотым оружием (1906). Разновременно командовал 1 Е. В. батареей гвардии Конно-артиллерий- ской бригады _ 6.04.1903-26.03.1904, Кавказским запасным кавалерийским дивизионом - с 14.01.1906, 17 драгунским Нижегородским Е. В. полком _ с 7.07.1906. 372 oTar Jordania За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1896), Св. Анны 3 ст. (1899). Кавалер французского ордена Почетного Легиона (Кавалерийский крест, 1902). Spisok, 1905, SPb.: 841; Spisok, 1907, SPb.: 395; Spisok, 1910: 40; Spisok, 1910, SPb.: 178; Spisok, 1911: 38; Spisok, 1912, SPb.: 81. ФОН-КЛИМАН ФЕДОР ЛЮДВИГОВИЧ (род. 28.08.1848), полковник. Воспитывался в Михайловском Воронежском кадетском корпусе, 3 воен- ном Александровском училище, которое окончил по 1 разяду. Службу начал 22.08.1886, прапорщик _ 12.06.1868, подпоручик _ прапорщик артиллерии _ 7.05.1871, подпоручик _ 6.11.1872, поручик _ 29.12.1873, штабс-капитан _ 9.12.1876, участник Русско-Турецкой войны 1877-78, награжден орденом Св. Владимира 4 ст. с мечами и бантом (1877), капитан _ 18.12.1878, за отли- чия по службе награжден чинами подполковника _ 30.08.1890 и полковника _ 14.05.1896. С 3.08.1888-11.05.1892 занимал должность редактора Военно- исторического отдела Кавказского военного округа, помощник начальника того же отдела _ 11.05.1892 _ 28.05.1899, состоял при войсках Кавказском военного округа _ с 28.05.1899. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1874) и 2 ст. (1886), Св. Анны 2 ст. (1899). Spisok, 1897: 114; Spisok, 1900: 79; Spisok, 1900, SPb.: 556; Spisok, 1903: 62; Spisok, 1903, sen., SPb.: 266; Spisok, 1905: 159; Spisok, 1905, SPb.: 159; Spisok, 1907: 36; Spisok, 1907, SPb.: 44; Spisok, 1909, SPb.: 26; Spisok, 1910: 33. ФОН-МЕЕРШЕЙДТ-ГИЛЛЕССЕН ИВАН ВЛАДИМИРОВИЧ (род. 26.09.1861), барон, полковник. Воспитывался в Петровской Полтавской во- енной гимназии, Михайловском артиллерийском училище, которое окончил по 1 разряду, питомец Михайловской артиллерийской Академии. Произве- ден в подпоручики _ 12.08.1883, поручик _ 8.08.1885, за отличие по служ- бе награжден чином штабс-капитана _ 4.06.1888, капитан, штабс-капитан гвардии _ 25.07. 1895, капитан _ 6.12.1898, подполковник по полевой артил- лерии _ 3.02.1902, полковник _ 14.04.1902. Начальник Тифлисской окружной артиллерийской мастерской _ c 16.09.1899. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1896) и 2 ст. (1906), Св. Станислава 2 ст. (1901). Spisok, 1903: 148; Spisok, 1904: 130; Spisok, 1905: 62; Spisok, 1906, SP.: 455; Spisok, 1907: 47; Spisok, 1907, SPb.: 294; Spisok, 1908: 41; Spisok, 1910: 38; Spisok, 1911: 36. 373 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ФОН-ОГЛИО ВЛАДИМИР МИХАЙЛОВИЧ (род. 20.12.1862), пол- ковник Отдельного корпуса жандармов. Воспитывался в Владимирской Ки- евской военной гимназии и Николаевском кавалерийском училище. Службу начал 13.09.1881, произведен в корнеты _ 12.08.1883, поручик _ 1.01.1885, штабс-ротмистр _ 30.08.1890, ротмистр _ 30.08.1892, подполковник _ 26.02.1901, за служебное отличие полковник _ 24.11.1906. В 1907-08 занимал должность начальника Терского областного жан- дармского управления. Награжден орденами Св. Станислава 3 cт. (1898) и 2 ст. (1906), Св. Анны 3 ст. (1903) и 2 ст. (1911). Spisok, 1907: 83; Spisok, 1907, ch. 3, SPb.: 99; Spisok, 1908: 77; Spisok, 1910, ch. 3, SPb.: 54; Spisok, 1912, SPb.: 451; Spisok, 1914, SPb.: 173. ФОН-РЕННЕ НИКОЛАЙ АЛЕКСАНДРОВИЧ (род. 25.07.1845), пол- ковник. Произведен в поручики _ 7.03.1869, штабс-капитан _ 2.04.1872, ка- питан _ 11.051877, награжден чином майора _ 16.04.1879, переименован в подполковники _ 6.05.1884, за отличие по службе полковник _ 12.07.1897. Темир-Хан-Шуринский уездный воинский начальник _ с 12.06.1897. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1874) и 2 ст. (1889), Св. Анны 3 ст. (1883) и 2 ст. (1895). Spisok, 1899: 95; Spisok, 1900: 83; Spisok, 1900, SPb.: 620; Spisok, 1901, SPb.; 83; Spisok, 1901, SPb.: 534; Spisok, 1902, SPb.: 456. ФОН-ТИЗЕНГАУЗЕН ОТТОКАР-ГЕНРИХ РЕЙНГОЛЬФ-КОНСТАН- ТИН-ЭДУАРД КОНСТАНТИНОВИЧ (род. 10.03.1848), барон, полковник. Произведен в поручики _ 26.02.1871, штабс-ротмистр _ 6.04.1879, майор _ 21.02.1881, переименован в подполковники _ 6.05.1884, за отличие по служ- бе полковник _ 14.05.1896. В 1899 _ 1901 занимал должность начальника кадра №12 кавалерий- ского запаса, назначен командиром Кавказского запасного кавалерийского дивизиона _ 19.12.1901. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1893), Св. Анны 3 ст. (1883). Spisok, 1900, SPb.; 536; Spisok, 1903: 61; Spisok, 1903, sen., SPb.: 254; Spisok, 1904: 51; Spisok, 1905, SPb.: 152. ФОН-ШЛИХТЕН АНАТОЛИЙ ПЕТРОВИЧ (род. 30.03.1849), полков- ник. Произведен в подпоручики _ 7.05.1871, участник военной экспедиции 1873, за боевое отличие поручик _ со старшинством с 15.07.1873, награж- ден орденами Св. Анны 4 ст. с надписью «За храбрость», Св. Станислава 3 374 oTar Jordania ст. с мечами и бантом (1874), штабс-капитан _ 6.08.1875, за отличия в экс- педиции 1875-76 получил ордена Св. Анны 3 ст. с мечами и бантом (1876), Св. Станислава 2 ст. и золотое оружие (1877), капитан _ 10.03.1879, подпол- ковник _ 1.01.1887, за служебные заслуги полковник _ 14.05.1896. Назначен командиром 154 пехотного Дербентского полка _ 25.11.1899. За другие военно-служебные заслуги награжден орденами Св. Влади- мира 4 ст. (1881), Св. Анны 2 ст. (1883), Св. Владимира 3 ст. (1904). Spisok, 1900: 79; Spisok, 1900, SPb.: 547; Spisok, 1902, SPb.: 388; Spisok, 1903: 62; Spisok, 1903, sen., SPb.: 260; Spisok, 1904: 52; Spisok, 1905: 42; Spisok, 1905, SPb.: 156. ФОРТУНАТОВ ПЕТР ВАСИЛЬЕВИЧ (род. 1.07.1852), полковник. Воспитывался в Орловской Бахтина военной гимназии и 2 военном Кон- стантиновском училище. Произведен в прапорщики _ 17.07.1872, подпо- ручик _ 26.12.1873, поручик _ 26.11.1874, штабс-капитан _ 26.12.1877, ка- питан _ 4.12.1883, подполковник _ 15.08.1896, за служебное отличие пол- ковник _ 6.12.1903. Командир 3 батареи Карсской крепостной артиллерии _ 2.01.1897 _ 27.10.1903, назначен командиром 1 батальона Карсской крепостной артил- лерии _ 27.10.1903 За военно-служебные отличия награжден орденами Св. Станислава 3 ст. (1878) и 2 ст. (1893), Св. Анны 3 ст. (1882) и 2 ст. (1896). Spisok, 1904: 80; Spisok, 1904, SPb.: 924; Spisok, 1905: 70; Spisok, 1906, SPb.: 628; Spisok, 1907: 52. ФРОЛОВ МИХАИЛ МИХАЙЛОВИЧ (род. 29.10.1853), полковник. Воспитывался в Сибирском кадетском корпусе, 3 военном Александров- ском и Михайловском училищах. Произведен в подпоручики _ 7.08.1874, поручик _ 3.12.1876, участник Русско-Турецкой войны 1877-78 (контужен в бою), штабс-капитан _ 26.12.1877, награжден орденами Св. Станислава 3 ст. с мечами и бантом, 2 ст. с мечами (1877), Св. Анны 2 ст. с мечами (1878) и чином капитана _ 13.07.1879, подполковник _ 5.02.1894, за служебное от- личие полковник _ 27.01.1901 (в чине по 19.07.1907) ( www.rusgeneral.ru). Командир батальона Кавказской гренадерской артиллерийской брига- ды _ 30.10.1894 _ 27.01.1901, 1 дивизиона 3 резервной артиллерийской бри- гады _ с 27.01.1901, 1 дивизиона 39 артиллерийской бригады _ 15.12.1901. За военно-служебные заслуги награжден орденом Св. Владимира 4 ст. (1885) и 3 ст. (1904). Spisok, 1903: 82; Spisok, 1903, sen., SPb.: 670; Spisok, 1904: 67; Spisok, 1905: 57; Spisok, 1905, SPb.: 539; Spisok, 1906, SPb.: 302. 375 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ФРОЛОВ НИКИТА ИВАНОВИЧ (род. 27.03.1866), полковник. Воспи- тывался в Владикавказской военной прогимназии, Ставропольском казачьем юнкерском училище. Службу начал 9.07.1882, произведен в подпоручики _ 4.08.1885, хорунжий _ 17.07.1886, сотник _ 17.07.1890, подъесаул _ 6.12.1897, капитан _ 6.05.1900, награжден орденом Св. Станислава 2 ст. (1905), за слу- жебные отличия подполковник _ 26.02.1907 и полковник _ 6.12.1910. Занимал должность старшего адъютанта штаба Кавказского военного округа _ 30.07.1907 _ 24.03.1911, Владикавказский уездный воинский на- чальник _ с 24.03.1911. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1906) и Св. Анны 2 ст. (1913). Spisok, 1908: 165; Spisok, 1910: 154; Spisok, 1911: 89; Spisok, 1911, SPb.: 1346; Spisok, 1912, SPb.: 1412: Spisok, 1914, SPb.: 877. ФРОСТ НИКОЛАЙ ВЛАДИМИРОВИЧ (род. 1.12.1852), полковник. Воспитывался во 2 военном Константиновском училище, Нижегород- ском графа Аракчеева военной гимназии. Произведен в подпоручики _ 29.12.1873, поручик _ 26.11.1874, участник Русско-Турецкой войны 1877- 78, штабс-капитан _ 26.12.1877, капитан - 4.12.1883, подполковник _ 15.07.1894, за служебное отличие полковник _ 6.12.1901 (в чине по 1907) (www.rusgeneral.ru). В 1895-1903 службу проходил в Михайловской крепостной артиллерии, командовал 2 батареей там же _ с 9.10.1900. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1876) и 2 ст. (1887), Св. Анны 3 ст. (1881) и 2 ст. (1894), Св. Владимира 4 ст. (1898). Кавалер болгарского ордена «За заслуги» (1883). Spisok, 1895: 185; Spisok, 1901: 123; Spisok, 1903: 85; Spisok, 1903, sen., SPb.; 751. ФУРДУЕВ АЛЕКСАНДР ПАВЛОВИЧ (род. 28.08.1850), полковник. Воспитывался в С.-Петербургском училище Св. Анны и Елисаветрадском кавалерийском юнкерском училище. Произведен в поручики- 27.03.1875, участник Русско-Турецкой войны 1877-78, награжден чином штабс- капитана _ 12.04.1878, орденами Св. Анны 4 ст. с надписью «За храбрость» (1877), Св. Станислава 3 ст. с мечами и бантом (1879), Св. Анны 3 ст. с ме- чами и бантом (1881), ротмистр _ 10.07.1882, подполковник _ 26.02.1895, за служебное отличие полковник _ 26.02.1900. С 15.04.1899 службу проходил в 44 драгунском Нижегородском Е. В. полку, командир Дагестанского конного полка _ c 14.01.1905. 376 oTar Jordania За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1886), Св. Владимира 4 ст. (1897), Св. Анны 2 ст. (1906). Кавалер иностранных орденов: бухарского - Благородной Бухары 3 ст. (1895), персидского _ Льва и Солнца 2 ст. с лентой (1901). Spisok, 1900, SPb.; 867; Spisok, 1903, sen., SPb.: 540; Spisok, 1906, SPb.: 205. ХАДЖИ-ХАН-БЕК. См.: ХАДЖИ-ХАН- СУЛТАНОВ. ХАДЖИ-ХАН-СУЛТАНОВ (ХАДЖИ-ХАН-БЕК) (род. 28.03.1862), полковник. Воспитывался в военной гимназии и Павловском военном учи- лище. Службу начал 30.08.1881, произведен в подпоручики _ 14.08.1884, поручик _ 14.08.1888, штабс-капитан _ 21.11.1891, за отличие награжден чинами капитана _ 15.03.1898, подполковника _ 26.02.1907 и полковника _ 6.12.1912. В 1903-14 служил мировым посредником 1 отдела Нухинского уезда Елизаветпольской губ. Награжден орденом Св. Станислава 3 ст. (1901). Spisok, 1911, SPb.: 143; Spisok, 1913, ch.3, SPb.: 104; Spisok, 1914, SPb.; 1233. ХАЛИЛОВ МИКАЭЕЛЬ МАГОМЕТОВИЧ (род. 18.02.1869), полков- ник. Воспитывался в Ставропольской реальной гимназии и Тифлисском пехот- ном юнкерском училище. Службу начал 10.08.1886, произведен в подпоручики _ 4.07.1889, награжден орденом Св. Станислава 3 ст. (1889), поручик _ 4.07.1893, штабс-капитан _ 1.06.1899, ротмистр _ 4.06.1901, участник Русско-Японской войны 1904-05, награжден орденами Св. Анны 3 ст. с мечами и бантом (1904), Св. Станислава 2 ст. с мечами, Св. Анны 2 ст. с мечами , Св. Владимира 4 ст. с мечами и бантом (1905), за боевое отличие подполковник _ 6.04.1906, награж- ден чином полковника _ 6.12.1910 (в чине по 1917) (www.rusgeneral.ru). С 31.08.1909 занимал должность начальника Кайтаго-Табасаранского округа, начальник Темир-Хан-Шуринского округа _ с 21.11.1913. Spisok, 1907: 169; Spisok, 1910: 143; Spisok, 1911: 88; Spisok, 1911, ch. 3, SPb.: 133; Spisok, 1914, SPb.: 848. ХАН-БАБА-ХАН (род. 3.03.1849), персидский принц, полковник Рус- ской Императорской Армии. Воспитывался дома, с оценкой «Успешно» окончил Офицерскую кавалерийскую школу. Службу начал 19.02.1869, корнет _ 19.02.1869, участник Русско-Турецкой войны 1877-78, поручик _ 3.08.1877, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1879), штабс-капитан _ 1.01.1879, ротмистр _ 6.02.1891, подполковник _ 22.02.1899, за отличие по службе полковник - 23.05.1907. 377 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV С 11.08.1900 службу проходил в 45 драгунском Северском Е. В. Короля Датского Христиана IХ полку, помощник командира того же полка по стро- евой части. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1889) и 2 ст. (1904), Св. Станислава 2 ст. (1895), Св. Владимира 4 ст. с бан- том _ за 25 лет безупречной службы в офицерских чинах (1896). Spisok, 1899: 176; Spisok, 1901: 160; Spisok, 1905: 103; Spisok, 1907: 97; Spisok, 1907, SPb.: 1224; Spisok, 1908: 82. ХАН-ГУССЕЙН-НАХИЧЕВАНСКИЙ (род. 28.07.1863), полковник. Флигель-адъютант императора. Воспитывался в Пажеском Е. В. корпусе, который окончил по 1 разряду. Произведен в корнеты _ 12.08.1883, поручик 30.08.1887, штабс-ротмистр _ 17.04.1894, ротмистр гвардии _ 6.05.1898, полковник _ 6.04.1903 (в чине по 1907) (www.rusgeneral. ru). Участник Рус- ско-Японской войны 1904-05, произведен в флигель-адъютанты императора (1906), награжден орденами Св. Анны 2 ст. с мечами (1904), Св. Владимира 4 ст. с мечами и бантом (1905), 3 ст. с мечами и мечами к ордену Св. Ста- нислава 2 ст. (1906), золотым оружием с надписью «За храбрость» (1905). Командовал 2 Дагестанским конным полком _ с 25.03.1905, 44 драгун- ским Нижегородским Е. В. полком _ 24.11.1905 _ 4.07.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1894) и 2 ст. (1902), Св. Анны 3 ст. (1899). Кавалер иностранных орденов: персидского _ Льва и Солнца 4 ст. (1890) и 2 ст. (1901), Румынской звезды (Офицерский крест, 1895), Австрийской Железной короны 3 ст. (1897). Spisok, 1905: 66; Spisok, 1905, SPb.: 835; Spisok, 1906, SPb.: 575. ХАНЖАЛОВ ИВАН АЛЕКСАНДРОВИЧ (род. 9.05.1856), полков- ник. Воспитывался дома и в 1 Павловском военном училище. Службу на- чал 23.08.1876, участник Русско-Турецкой войны 1877-78, прапорщик _ 16.04.1878, подпоручик _ 20.12.1879, поручик _ 18.12.1880, штабс-капитан _ 23.11.1888, капитан _ 6.05.1894, награжден чинами подполковника _ 26.02.1901 и полковника _ 6.05.1908. В 1891-1905 занимал административные должности в Владикавказском, Грозненском и Хасан-Юртовском округах, Терском областном правлении, на- чальник Венденского _ с 29.12.1905 и Владикавказского _ с 10.04.1906 округов. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1904), Св. Анны 3 ст. (1888) и 2 ст. (1912). Spisok, 1909, ch. 3, SPb.: 92; Spisok, 1910: 77; Spisok, 1910, ch. 3, SPb.: 83; Spisok, 1911: 69; Spisok, 1911, ch. 3, SPb.: 75; Spisok, 1914, SPb.: 324. 378 oTar Jordania ХАТОВ АЛЕКСАНДР СЕРГЕЕВИЧ (род. 3.03.1852), полковник. Вос- питывался в 1 военном Павловском училище. Произведен в прапорщики гвардии _ 13.08.1874, в отставке 1874 _ 1876, с апреля по декабрь 1875 слу- жил по гражданскому ведомству, подпоручик гвардии _ 13.04.1875, поручик гвардии _ 5.07.1876, штабс-капитан _ 7.07.1877, капитан _ 18.12.1878, под- полковник _ 28.02.1892, за служебное отличие полковник _ 6.12.1899. Командир Терско-Дагестанской крепостной артиллерии _ 8.11.1903- 10.12.1905, командующий Карсской крепостной артиллерии - с 10.12.1905. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1880) и 2 ст. (1890), Св. Анны 3 ст. (1889) и 2 ст. (1895). Spisok, 1903, sen., SPb.: 482; Spisok, 1904: 59; Spisok, 1905: 49; Spisok, 1905, SPb.: 354; Spisok, 1906, SPb.: 169. ХЕЛМИЦКИЙ ПАВЕЛ ЛЮДВИГОВИЧ (род. 18.07.1855), полковник. Окончил Николаевскую Академию Генерального штаба по 1 разряду. Про- изведен в подпоручики _ 25.10.1875, поручик _ 9.12.1876, участник Русско- Турецкой войны 1877-78, штабс-капитан _ 18.12.1878, капитан _ 29.03.1885, подполковник _ 9.04.1889, за служебное отличие полковник _ 28.03.1893( в чине по 3.05.1904) (www.rusgeneral.ru). С 1887 занимал военно-административные должностий в Кавказском военном округе; начальник строевого отделения Карсской крепости _ с 26.12.1887, обер-офицер для поручений при штабе Кавказского военного округа _ 18.06.1888_ 9.04.1896, штаб-офицер для особых поручений при командующем войсками Кавказского военного округа _ с 9.04.1889, началь- ник штаба 2 Кавказской казачьей дивизии _ 4.09.1896 _ 24.12.1900, коман- дир 1 Екатерининского полка Кубанского казачьего войска - с 24.12.1900. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1892), Св. Анны 3 ст. (1889) и 2 ст. (1896), Св. Владимира 4 ст. (1899). Spisok, 1894: 126; Spisok, 1897: 89; Spisok, 1900, SPb.: 249; Spisok, 1903: 49; Spisok, 1903, sen., SPb.: 82. ХЕТАГУРОВ ЯКОВ-ЕГОР ГЕРСЕВАНОВИЧ (род. 20.02.1853), пол- ковник. Воспитывался в кадетском корпусе и 2 военном Константиновском училище. Службу начал 1.09.1877, произведен в прапорщики _ 8.08.1879, подпоручик _ 16.12.1880, поручик _ 4.12.1883, штабс-капитан _ 2.03.1890, капитан _ 25.07.1895, получил орден Св. Станислава 2 ст. (1900), участник Русско-Японской войны 1904-05, подполковник _ 3.06.1904, награжден ор- денами Св. Анны 2 ст. с мечами, Св. Владимира 4 ст. с бантом (1905), меча- ми к ордену Св. Станислава 2 ст. (1906), полковник _ 6.12.1910. 379 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Командир Кавказского стрелкового артиллерийского парка _ 17.05.1907 - 4.03.1910, командир Кавказского гренадерского артиллерийского парка с марта по август 1910, в дальнейшем службу проходил в Кавказском грена- дерском Вел. кн. Михаила Николаевича артиллерийской бригаде. Spisok, 1911: 87; Spisok, 1911, SPb.: 1249. ХИРИН ИВАН ВАСИЛЬЕВИЧ (род. 30.04.1853), полковник. Воспиты- вался в Главном реальном немецком и 1 военном Павловском училищах. Про- изведен в подпоручики _ 28.06.1877, поручик _ 16.06.1878, штабс-капитан _ 15.05.1887, капитан _ 30.08.1889, подполковник _ 30.08.1892, полковник _ 6.12.1898. Занимал должность офицера-воспитателя в Тифлисском кадетском кор- пусе _ 16.08.1886 _ 12.11.1898, ротный командир там же - с 12.11.1898. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1885) и 2 ст. (1891), Св. Анны 3 ст. (1888) и 2 ст. (1895), Св. Владимира 4 ст. (1898) и 3 ст. (1901). Кавалер бухарского золотого ордена Благородной Бухары 3 ст. (1893). Spisok, 1899: 102; Spisok, 1900: 90; Spisok, 1900, SPb.; 737; Spisok, 1903: 69; Spisok, 1903, sen., SPb.: 408; Spisok, 1905: 47; Spisok, 1905, SPb.: 286; Spisok, 1907: 38; Spisok, 1907, SPb.: 77; Spisok, 1911, SPb.: 17. ХОВРЕНКО ВЛАДИМИР АЛЕКСАНДРОВИЧ (род. 19.07.1868), пол- ковник. Воспитывался в Владикавказском реальном училище, oкончил во- енные курсы Московского пехотного юнкерского училищах. Службу начал 22.07.1887, произведен в подпоручики _ 9.08.1888, поручик _ 9.08.1892, штабс-капитан _ 6.05.1900, капитан _ 6.05.1901, награжден орденом Св. Станислава 2 ст. (1904), за отличия по службе подполковник _ 1.01.1906 и полковник -14.01.1910 (в последнем чине по 2.04.1917) (www.rusgeneral.ru). Служил на различных штабных должностях в Михайловской крепости, и. д. правителя канцелярии Кавказского окружного интендантского управ- ления _ 1908-10, правитель канцелярии Кавказского военного округа _ с 19.06.1910. Затем служил в другом военном округе. Spisok, 1908: 152; Spisok, 1910: 139; Spisok, 1914, SPb.: 565. ХОДАКОВСКИЙ ИЛЬЯ ИГНАТЬЕВИЧ (род. 12.07.1856), полков- ник. Воспитывался в классической гимназии и Тифлисском пехотном юн- керском училище. Службу начал 2.11.1872, произведен в прапорщики _ 6.12.1876, участник Русско-Турецкой войны 1877-78, военных экспедиций 1880-81 и 1885, подпоручик _ 10.06.1877, награжден орденами Св. Анны 4 ст. с надписью «За храбрость» (1877) и 3 ст. с мечами и бантом (1882), 380 oTar Jordania Св. Станислава 3 ст. с мечами и бантом (1878), поручик _ 24.12.1879, штабс-капитан _ 24.03.1886, капитан _ 2.04.1895, за отличия по службе подполковник _ 26.02.1903 и полковник _ 3.02.1911. С 1.09.1901-3.02.1911 служил Батумским уездным воинским начальни- ком, Екатеринодарский уездный воинский начальник _ с 8.02.1911. За другие военно-служебные заслуги награжден орденами Св. Влади- мира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах, Св. Станислава 2 ст. (1901), Св. Анны 2 ст. (1907). Spisok, 1904: 140; Spisok, 1910: 102; Spisok, 1911: 90; Spisok, 1911, SPb.: 1356; Spisok, 1914, SPb.: 891. ХОДАКОВСКИЙ НИКОЛАЙ ИГНАТЬЕВИЧ (род. 1.03.1851), пол- ковник. Георгиевский кавалер. Воспитывался в гимназии и пехотном юн- керском училище. Произведен в прапорщики _ 4.02.1875, участник Русско- Турецкой войны 1877-78 (контужен в бою), подпоручик _ 10.06.1877, на- гражден орденами Св. Станислава 3 ст. с мечами и бантом, Св. Анны 4 ст. с надписью «За храбрость» (1877), за выдающееся боевое отличие удостоен ордена Св. Георгия 4 ст. (1878), поручик _ 29.01.1879, награжден други- ми боевыми знаками отличия: Св. Анны 3 ст. с мечами и бантом (1879), Св. Владимира 4 ст. с мечами и бантом (1880), Св. Станислава 2 ст. с ме- чами (1881), за служебное отличие капитан _ 25.03.1890, подполковник _ 26.02.1897, награжден чином полковника _ 26.11.1901. Командир 7 Кавказского стрелкового батальона - 19.01.1901 _ 29.07.1904. Затем служил в другом военном округе. Spisok, 1903: 85; Spisok, 1903, sen., SPb.; 737; Spisok, 1904: 70; Spisok, 1905, SPb.: 598. ХОНДЗЫНСКИЙ ИОСИФ-КАЗИМИР АЛЕКСАНДРОВИЧ (род. 20.12.1851), полковник. Окончил Новгородский графа Аракчеева кадет- ский корпус и 3 военное Александровское училище. Произведен в подпо- ручики _ 21.07.1870, участник Русско-Турецкой войны 1877-78, поручик _ 15.06.1877, штабс-капитан _ 17.12.1881, за отличие капитан _ 20.04.1886, подполковник _ 26.02.1892, награжден чином полковника _ 15.09.1903. Командир: 4 Кавказского стрелкового батальона _ 5.04.1904 _ 4.08.1906, 83 пехотного Самурского Е. И. В. Вел. кн. Владимира Александровича пол- ка _ с 8.08.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1895), Св. Анны 3 ст. (1890) и 2 ст. (1900), Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1896) и 3 ст. (1907). 381 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Spisok, 1905: 69; Spisok, 1905, SPb.: 872; Spisok, 1907: 51; Spisok, 1907, SPb.: 418; Spisok, 1908: 44. ХОРАНОВ ИОСИФ ЗАХАРОВИЧ (род. 1842), полковник. Участник Русско-Турецкой войны 1877-78 (контужен в бою), за боевые отличия на- гражден чинами хорунжего, сотника _ 2.11.1877 и есаула 28.11.1878, орде- нами Св. Анны 4 ст. (1877), Св. Станислава 3 ст. с мечами и бантом (1878), Св. Анны 3 ст. с мечами и бантом, Св. Владимира 4 ст. с мечами и бан- том (1879), штабс- ротмистр - 20.01.1880, переименован в подполковники и награжден вензелем Императора Александра II _ 1881 (со старшинством с 30.08.1880), за отличие по службе полковник _ 16.03.1895 (в чине по 31.01.1905) (www.rusgeneral.ru). С конца ХIХ в. по 5.08.1904 занимал должность члена Владикавказско- го окружного по воинским повинностям присутствия. В дальнейшем слу- жил за пределами Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1892), Св. Анны 2 ст. (1896), Св. Владимира 3 ст. (1898). Spisok, 1897: 102; Spisok, 1900: 70; Spisok, 1903: 55; Spisok, 1903, sen., SPb.: 150; Spisok, 1905, SPb.: 80. ХРОСТИЦКИЙ АНАТОЛИЙ ВЛАДИМИРОВИЧ (род. 21.07.1867), полковник. Воспитывался в кадетском корпусе, 1 военном Павловском и Михайловском артиллерийских училищах, окончил Николаевскую Ака- демию Генерального штаба по 1 разряду. Службу начал 1.09.1885, произ- веден в подпоручики _ 9.08.1888, поручик _ 16.12.1890, штабс-капитан _ 28.07.1896, капитан _ 2.06.1899, подполковник _ 6.12.1902, участник Русско-Японской войны 1904-05 (ранен в бою), за отличие полковник _ 11.02.1905 (в чине по 14.11.1914) (www.rusgeneral.ru). Награжден орденами Св. Владимира 4 ст. с мечами и бантом (1904), Св. Станислава 2 ст. с меча- ми, Св. Анны 2 ст. с мечами (1905), золотым оружием (1906). Штаб-офицер при управлении 65 пехотной резервной бригады _ с 16.03.1906, начальник штаба 33 пехотной дивизии _ 4.06.1907 _ 29.12.1909. Затем служил вне Кавказского военного округа. Spisok, 1907: 69; Spisok, 1908: 62; Spisok, 1909, SPb.: 545; Spisok, 1914, SPb.: 84. ЦАРЕВСКИЙ ДМИТРИЙ НИКОЛАЕВИЧ (род. 13.03.1856), полковник. Воспитывался дома, окончил Николаевское инженерное училище по 1 раз- ряду. Участник Русско-Турецкой войны 1877-78, произведен в поручики _ 2.09.1878, награжден орденом Св. Анны 4 ст. с надписью «За храбрость» (1878), 382 oTar Jordania штабс-капитан _ 24.06.1883, капитан _ 30.08.1885, подполковник _ 30.08.1888, за отличие по службе полковник _ 28.061903 (в чине по 1913) (www.rusgeneral.ru). С 1903 _ по январь 1906 служил на Кавказе. Кутаисский уездный во- инский начальник _ 28.07.1903. С января 1906 служил за пределами Кавказ- ского военного округа. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1882) и 2 ст. (1890), Св. Анны 3 ст. (1896) и 2 ст. (1900), Св. Владимира 4 ст. (1906). Spisok, 1904: 78; Spisok, 1905: 68; Spisok, 1905, SPb.: 863; Spisok, 1907: 51; Spisok, 1907, SPb.: 411; Spisok, 1910, SPb.: 188. ЦЕДЕРБЕРГ МИХАИЛ АДОЛЬФОВИЧ (род. 4.11.1843), полков- ник. Участник военных экспедиций 1862-64, произведен в подпоручики _ 19.12.1864, награжден чином поручика _ 5.10.1867, штабс-капитан _ 17.05.1869, за отличие капитан _ 10.12.1874, участник Русско-Турецкой во- йны 1877-78, награжден орденом Св. Анны 3 ст. с мечами и бантом (1878), майор _ 31.01.1879, переименован в подполковники _ 6.05.1884, за отличие полковник _ 5.12.1894 (в чине по 28.02.1902) (www.rusgeneral.ru). Командир 1 Кубанского пластунского батальона _ c 5.12.1894. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1871) и 2 ст. (1884), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1888) и 3 ст. (1899), Св. Анны 2 ст. (1889). Spisok, 1895: 115; Spisok, 1900: 70; Spisok, 1900, SPb.: 385; Spisok, 1902, SPb.: 251. ЦЕЙХАНОВИЧ НИКОЛАЙ ФЕДОРОВИЧ (род. 22.07.1858), полков- ник. Окончил 5 классов Тифлисской классической гимназии, воспитывался в Тифлисском пехотном юнкерском училище, завершил учебу в Офицерской стрелковой школе с оценкой «Успешно». Службу начал 14.12.1876, участник Русско-Турецкой войны 1877-78, за отличие прапорщик _ 25.04.1878, под- поручик _ 6.05.1883, награжден чинами штабс-капитана _ 15.06.1893, капи- тана _ 15.03.1898, подполковника _ 5.10.1904 и полковника _ 31.12.1909 (в чине по 5.08.1916) (www.rusgeneral.ru). В 1905-11 служил в 155 пехотном Кубинском полку, командир156 пе- хотного Елисаветпольского ген. кн. Цицианова полка _ с 23.08.1912. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1902), Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офи- церских чинах (1905), Св. Станислава 2 ст. (1907). Spisok, 1905: 133; Spisok, 1910: 116; Spisok, 1911: 83; Spisok, 1911, SPb.: 1076; Spisok, 1913, SPb.: 671; Spisok, 1914, SPb.: 562. 383 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ЦЕРЕТЕЛИ РОСТОМ ГРИГОРЬЕВИЧ (род. 20.12.1849), князь, пол- ковник. В офицерских чинах с 12.07.1869. Участник Русско-Турецкой во- йны 1877-78. Подполковник _ 26.02.1895. Полковник _ 30.09.1905. В 1895-1905 службу проходил в 44 драгунском Нижегородском Е. В. полку. За военно-служебные заслуги награжден орденами Св. Анны 4 ст. (1877) и 3 ст. (1899), Св. Станислава 3 ст. (1891) и 2 ст. (1903), Св. Владими- ра 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1900). Spisok, 1895: 188; Spisok, 1901: 125; Spisok, 1905: 94; Spisok, 1907: 72; Spisok, 1908: 65. ЦЕРПИЦКИЙ ВИКЕНТИЙ ВИКЕНТЬЕВИЧ (род. 27.11.1850), пол- ковник. Воспитывался во 2 С.-Петербургской военной гимназии, 1 воен- ном Павловском училище, окончил Николаевскую инженерную Академию. Произведен в поручики _ 9.05.1870, подпоручик саперного батальона _ 30.07.1871, поручик _ 22.07.1873, участник Русско-Турецкой войны 1877- 78, за боевое отличие штабс-капитан _ 9.11.1877, награжден орденами Св. Анны 4 ст. (1877), Св. Анны 3 ст. с мечами и бантом (1878), Св. Станислава 2 ст. с мечами (1881), за отличие капитан _ 30.08.1882, майор по армии _ 28.11.1882, переименован в подполковники _ 6.05.1884, награжден чином полковника _ 31.12.1892. Помощник старшего адъютанта штаба Кавказского военного округа _ 26.06.1882 _ 15.11.1884, делопроизводитель по учебной части Тифлисского пехотного юнкерского училища _ 15.11.1884 _ 14.10.1889, командир: 3 Ку- банского пластунского батальона _ с 31.12.1892, 83 пехотного Самурского Е. И. В. Вел. кн. Владимира Александровича полка _ с 2.09.1899. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1873), Св. Анны 2 ст. (1889), Св. Владимира 4 ст. _ за 25 лет без- упречной службы в офицерских чинах (1893) и 3 ст. (1896). Spisok, 1893: 145; Spisok, 1895: 103; Spisok, 1900: 60; Spisok, 1900, SPb.: 237; Spisok, 1902, SPb.: 143; Spisok, 1903, sen., SPb.: 76. ЦИСС ДМИТРИЙ АЛЕКСАНДРОВИЧ (род. 12.09.1870), полковник. Воспитывался в Михайловском Воронежском кадетском корпусе и 1 воен- ном Павловском училище. Службу начал 1.09.1889, произведен в подпору- чики _ 10.08.1890, поручик _ 10.08.1894, штабс-ротмистр _ 6.12.1899, рот- мистр _ 6.12.1900, за отличия награжден чинами подполковника _ 5.09.1905 и полковника _ 6.12.1910. Назначен помощником начальника Тифлисского губернского жандарм- ского управления _ 31.03.1899, Тифлисский полицмейстер _ 25.06.1905, 384 oTar Jordania исполнял должности начальника Ленкоранского _ с 10.02.1906 и Бакин- ского - с 31.10.1907 уездов, Российский пограничный комиссар с Персией (Ираном) _ с 15.04.1909. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1901), Св. Анны 2 ст. (1906). Spisok, 1907: 161; Spisok, 1908: 149; Spisok, 1911, ch. 3, SPb.: 129; Spisok, 1912, ch. 3, SPb.: 121; Spisok, 1913, ch. 3, SPb.: 81; Spisok, 1914, SPb.: 820. ЦИЦИАНОВ МИХАИЛ ИРАКЛИЕВИЧ (род. 17.02.1847), князь. пол- ковник. Георгиевский кавалер. Произведен в подпоручики _ 23.04.1874, участник Русско-Турецкой войны 1877-78 (ранен в бою), поручик _ 4.05.1877, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1877) и чином штабс-капитана за боевое отличие _ 30.10.1877, за выдаю- щиеся подвиги в боях удостоен орденом Св. Георгия 4 ст. и золотым ору- жием (1878), капитан _ 4.11.1882, подполковник _ 26.02.1894, за отличие по службе полковник _ 26.11.1898. Командир 156 пехотного Елисаветпольского ген. кн. Цицианова полка _ c 31.12.1901. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1889), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1894), Св. Анны 2 ст. (1902). Spisok, 1900, SPb.: 717; Spisok, 1902, SPb.: 553; Spisok, 1903: 68; Spisok, 1903, sen., SPb.: 399; Spisok, 1904, SPb.: 311. ЦОПАНОВ АЛЕКСАНДР МИХАЙЛОВИЧ (род. 23.12.1855), полков- ник. Воспитывался в Владикавказском реальном и 2 военном Константи- новском училищах. Службу начал 1.09.1878, произведен в прапорщики - 8.08.1880, подпоручик _ 29.11.1882, поручик _ 1.12.1885, штабс-капитан _ 13.12.1892, капитан _ 13.07.1897, подполковник _ 18.11.1904, награжден орденом Св. Анны 3 ст. (1904), за отличие полковник _ 6.12.1909. Командовал Кавказским резервным артиллерийским парком _ с 11.05.1908, затем службу проходил в 51 артиллерийской бригаде _ с 19.08.1910. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1894), Св. Анны 3 ст. (1904). Spisok, 1905: 144; Spisok, 1908: 128; Spisok, 1909: 690; Spisok, 1910: 90; Spisok, 1911: 82; Spisok, 1911, SPb.: 1031; Spisok, 1913, SPb.: 632. ЦУЛУКИДЗЕ ВАРДЕН ГРИГОРЬЕВИЧ (род. 8.11.1865), князь, пол- ковник. Воспитывался в Тифлисском кадетском корпусе и 3 военном Алек- сандровском училище. Службу начал 26.08.1884, произведен в подпоручики _ 385 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 7.08.1885, поручик _ 7.08.1889, за отличие награжден чином штабс-капитана _ 15.03.1898, капитан _ 6.05.1900, подполковник _ 26.02.1905, полковник _ 6.12.1910 ( в чине по10.04.1916) (www.rusgeneral.ru). В 1905-14 службу проходил в 264 Лорийском и 261 Шемахинском ре- зервных полках. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1902), Св. Анны 3 ст. (1907). Spisok, 1905: 153; Spisok, 1910: 131; Spisok,1911: 97; Spisok, 1914, SPb.: 793. ЦУЛУКИДЗЕ ГЕОРГИЙ ДАВЫДОВИЧ (род. 23.04.1860), князь, пол- ковник. Воспитывался в Елисаветградской военной прогимназии, Тифлис- ском пехотном юнкерском училище, окончил Офицерскую стрелковую шко- лу с оценкой «Успешно». Службу начал 19.07.1876, произведен в прапорщи- ки _ 9.09.1880, подпоручик _ 6.05.1883, поручик _ 6.05.1887, штабс-капитан _ 1.07.1893, капитан _ 6.05.1900, подполковник _ 30.07.1905, полковник _ 6.12.1910 (в чине по18.02.1916) (www.rusgeneral.ru ). Известно, что в 1905-11 служил в 156 Елисаветпольском ген. кн. Цици- анова полку, в 1914 службу проходил в 4 Кавказском стрелковом полку. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1906) и 2 ст. (1910), Св. Анны 3 ст. (1906). Spisok, 1905: 158; Spisok, 1910: 135; Spisok, 1911: 128; Spisok, 1914, SPb.: 810. ЧАВЧАВАДЗЕ АЛЕКСАНДР (СЕМЕН) ИОСИФОВИЧ (род. 3.03.1860), князь, полковник. Воспитывался дома и Кавказской учебной роте. Служ- бу начал 1.04.1877, участник Русско-Турецкой войны 1877-78 и военной экспедиции 1879, произведен в прапорщики _ 30.11.1879, подпоручик _ 26.03.1883, поручик _ 6.05.18887, штабс- ротмистр _ 1.06.1894, ротмистр _ 6.05.1900, участник Русско-Японской войны 1904-05, награжден чином подполковника (войсковой старшина) _ 5.10.1904, за боевое отличие пол- ковник _ 17.07.1906 (в чине по 1910) (www.rusgeneral.ru), удостоен орденов Св. Владимира 4 ст. с бантом, Св. Станислава 2 ст. с мечами, Св. Анны 4 ст. с надписью «За храбрость», Св. Анны 2 ст. с мечами (1905), награжден золотым оружием (1906). В 1904-07 служил в 43 драгунском Тверском полку. Командир Дагестан- ского конного полка _ с 24.09.1907. За военно- служебные заслуги награжден орденами Св. Владимира 4 ст. (1904), Св. Станислава 3 ст. (1905). Spisok, 1904: 143; Spisok, 1905: 119; Spisok, 1907:82; Spisok, 1908: 75; Spisok, 1910: 65; Spisok, 1910, SPb.: 730. 386 oTar Jordania ЧАВЧАВАДЗЕ ИРАКЛИЙ СПИРИДОНОВИЧ (род. 30.08.1851), князь, полковник. В офицерских чинах с 20.07.1877.Участник Русско-Турецкой войны 1877-78. Подполковник _ 7.04.1903. Полковник _ 17.07.1906. В 1907 службу проходил в 43 драгунском, а в 1908 _ 16 драгунском Тверском полках. Spisok, 1907: 82; Spisok, 1908: 75. ЧАНЦЕВ АЛЕКСАНДР НИКОЛАЕВИЧ (род. 23.10.1856), полков- ник. Воспитывался дома и Варшавском пехотном юнкерском училище. Службу начал 25.02.1874, участник Русско-Турецкой войны 1877-78, произведен в прапорщики _ 17.07.1877, награжден чином подпоручика _ 1880 ( со старшинством с 28.08.1879), штабс-капитан _ 15.03.1895, ка- питан-15.03.1898, подполковник - 26.02.1902, за отличие по службе пол- ковник _ 6.12.1911. В 1903-11 служил командиром роты юнкеров Тифлисского пехотного юнкерского училища, назначен командиром батальона Тифлисского Вел. кн. Михаила Николаевича военного училища _ 27.08.1911. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. с мечами и бантом (1880) и 2 ст. (1902), Св. Владимира 4 ст. (1903), Св. Анны 2 ст. (1907). Кавалер иностранных орденов: персидского _ Льва и Солнца 4 ст. (1889), бухарского _ золотого Благородной Бухары 3 ст. (1899), австрийско- го _ Железной короны 3 ст. (1897), сиамского _ Белого Слона (1897), бол- гарского _ Св. Александра 4 ст. (1897). Spisok, 1903: 149; Spisok, 1910: 98; Spisok, 1911: 103; Spisok, 1912, SPb.: 1508; Spisok, 1914, SPb.: 955. ЧАПЛИН ВИКТОР ВИКТОРОВИЧ (род. 15.03.1862), полковник. Воспитывался в Тифлисском реальном и 2 военном Константиновском учи- лищах, окончил Николаевскую Академию Генерального штаба по 2 разряду. Службу начал 1.09.1879, произведен в прапорщики _ 8.08.1881, подпору- чик _ 4.12.1883, поручик _ 1.12.1885, за отличия награжден чинами штабс- капитана _ 30.08.1892 и капитана _ 14.05.1896, подполковник _ 26.02.1901, за служебное отличие полковник _ 1.01.1906 (в чине по 31.12.1914) (www. rusgeneral.ru ). В 1901-05 службу проходил в 78 пехотном Навагинском, 15 гренадер- ском Тифлисском полках, командир 5 Кавказского _ с 28.07.1907 Е. И. В. Вел. кн. Георгия Михайловича и 1 Кавказского _ с 4.04.1908 стрелковых батальонов, командовал 1 Кавказским стрелковым ген.-фельдм. Вел. кн. Михаила Николаевича полком _ с 6.07.1910. 387 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1889) и 2 ст. (1907), Св. Анны 3 ст. (1904) и 2 ст. (1910); Св. Владимира 3 ст.с мечами (1911). Spisok, 1901: 176; Spisok, 1905: 109; Spisok, 1907: 78; Spisok, 1907, SPb.: 1009; Spisok, 1908: 70; Spisok, 1909, SPb.: 709; Spisok, 1910: 63; Spisok, 1910, SPb.: 659: Spisok, 1911: 56; Spisok, 1911, SPb,: 479; Spisok, 1914, SPb.: 136. ЧАУН АНТОН ГЕОРГИЕВИЧ (ГРИГОРЬЕВИЧ) (род. 6.12.1851), пол- ковник. Воспитывался в Ставропольском казенном юнкерском училище, окон- чил Офицерскую кавалерийскую школу с отличием. Произведен в хорунжие _ 30.11.1876, участник Русско-Турецкой войны 1877-78, за боевое отличие награжден чином сотника _ 9.06.1878, орденами Св. Анны 4 ст. с надписью «За храбрость» (1878), подъесаул _ 631.12.1885, за отличие есаул _ 6.05.1889, войсковой старшина _ 26.02.1895, награжден чином полковника _ 15.03.1904. В 1890 _ 93 наказной атаман Кубанского казачьего войска и чиновник для поручений при начальнике Кубанской обл., командир 2 Черноморско- го _ c 25.03.1900, 2 Екатеринодарского _ с 8.06.1902 , 1 Кавказского _ с 15.03.1904 полков. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1883) и 2 ст. (1897), Св. Анны 3 ст. (1884) и 2 ст. (1900), Св. Вла- димира 4 ст. с бантом (1901) и 3 ст. (1906). Spisok, 1904: 84; Spisok, 1905: 73; Spisok, 1905, SPb.: 942; Spisok, 1907: 55; Spisok, 1907, SPb.: 482; Spisok, 1910: 44; Spisok, 1910, SPb.: 237. ЧЕВПЛЯНСКИЙ ФЕДОР ЕМЕЛЬЯНОВИЧ (род. 17.08.1848), полков- ник. Произведен в подпоручики _ 27.11.1873, участник Русско-Турецкой во- йны 1877-78, поручик _ 17.04.1877, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1878), штабс-капитан _ 7.04.1880, капитан _ 30.08.1887, подполковник _ 30.08.1890, за отличие полковник _ 6.12.1902. Начальник съемочного отделения Военно-топографического отдела штаба Кавказского военного округа _ c 24.02.1890. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1880) и 2 ст. (1893), Св. Владимира 4 ст. (1884), Св. Станислава 2 ст. (1887). Spisok, 1901: 111; Spisok, 1903: 89; Spisok, 1903, sen., SPb.: 882. ЧЕКАЛОВ АЛЕКСАНДР ГРИГОРЬЕВИЧ (род. 13.08.1853), полков- ник. Воспитывался в 1 Московской военной гимназии, 3 военном Алексан- дровском училище, окончил курс Офицерской артиллерийской школы. Про- изведен в хорунжие _ 18.08.1873, сотник _ 9.09.1876, награжден чинами еса- ула _ 14.04.1879, войскового старшины _ 3.02.1895 и полковника _ 6.12.1902. 388 oTar Jordania Начальник войсковой оружейной мастерской Кубанского казачьего во- йска _ с 10.03.1893), помощник атамана Темрюкского отдела _ с 9.07.1897, начальник Екатеринодарской военно-фельдшерской школы _ c 27.10.1899. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1882) и 2 ст. (1905), Св. Анны 3 ст. (1887) и 2 ст. (1908). Spisok, 1903: 90; Spisok, 1903, sen., SPb.: 891; Spisok, 1904: 75: Spisok, 1905: 42; Spisok, 1905, SPb.: 751; Spisok, 1907, SPb.: 411; Spisok, 1910, SPb.: 135. ЧЕЛОКАЕВ НИКОЛАЙ ЗААЛОВИЧ (род. 4.02.1841), князь, полков- ник. Воспитывался в частном учебном заведении. Участник военных экс- педиций 1858-60 периода Кавказской войны (1817-64), за боевое отличие награжден чином прапорщика _ 1860 ( старшинство с 1859), прапорщик гвардии _ 9.09.1862, в отставке _ 19.08.1863, на гражданской службе _ 25.08.1870-28.09.1871, переименован в поручики _ 28.09.1871, участник Русско-Турецкой войны 1877-78, штабс-ротмистр гвардии _ 23.01.1878, ротмистр _ 30.08.1880, ранен при исполнении служебных обязанностей (1885), награжден чином полковника _ 9.04.1889. Телавский уездный начальник - с 1.12.1878, инспектор земской стражи Тифлисской губ. - с 15.11.1895, Тианетский уездный воинский начальник _ 10.11.1900. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1870) и 2 ст. (1881), Св. Анны 3 ст. (1872) и 2 ст. (1887), Св. Владимира 4 ст. (1891). Spisok, 1890: 136; Spisok,1895: 72; Spisok, 1897: 62; Spisok, 1900: 48; Spisok, 1901, SPb.: 44; Spisok, 1903: 44; Spisok, 1903, may, SPb.: 22. ЧЕРЕМУШКИН НИКОЛАЙ ТИМОФЕЕВИЧ (род. 27.09.1855), пол- ковник. Воcпитывался в Петровской Полтавской военной гимназии, 1 во- енном Павловском училище, окончил Офицерскую артиллерийскую школу. Службу начал 8.08.1873, подпоручик _ 9.12.1876, участник Русско-Турец- кой войны 1877-78, за боевое отличие поручик _ 26.12.1877, штабс-капитан -18.03.1878, награжден орденами Св. Анны 4 ст. с надписью «За храбрость» (1877), Св. Станислава 3 ст. с мечами и бантом, Св. Владимира 4 ст. с ме- чами и бантом (1878), капитан _ 1.12.1889, подполковник _ 1.10.1897, за отличие по службе полковник _ 20.08.1908. Командир 2 дивизиона Кавказского гренадерского Вел. кн. Михаила Николаевича артиллерийской бригады _ с 20.08.1908. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1894), Св. Анны 2 ст. (1901), Св. Владимира 3 ст. (1911). Spisok, 1910: 78; Spisok, 1911: 70; Spisok, 1911, SPb.: 785; Spisok, 1913: 450. 389 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ЧЕРЕПАНОВ ПЕТР ПЕТРОВИЧ (род. 16.12.1864), полковник. Вос- питывался в Сибирском кадетском корпусе и 2 военном Константиновском училище. Службу начал 1.09.1883, произведен в подпоручики _ 14.08.1884, поручик _ 14.08.1888, штабс-капитан _ 2.04.1895, капитан _ 13.04.1897, подполковник _ 9.04.1900, за отличие по службе награжден чином полков- ника _ 10.04.1911. Офицер-воспитатель Тифлисского кадетского корпуса _ 17.01.1893 _ 1.04.1911, командир роты Тифлисского Вел. кн. Михаила Николаевича ка- детского корпуса _ с 1.04.1911. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1895) и 2 ст. (1903), Св. Анны 3 ст. (1901) и 2 ст. (1907), Св. Владимира 4 ст. (1913). Spisok, 1900: 170; Spisok, 1910: 97; Spisok, 1911: 100; Spisok, 1914, SPb.: 903. ЧЕРКОВ ПАВЕЛ ПЛАТОНОВИЧ (род. 1.11.1846), полковник. Геор- гиевский кавалер. Воспитывался в Воронежском училище и Тифлисском пехотном юнкерском училище. Произведен в подпоручики _ 7.10.1875, участник Русско-Турецкой войны 1877-78 (ранен в бою), за выдающееся боевое отличие награжден орденом Св. Георгия 4 ст. (1878) и другими зна- ками отличия: Св. Владимира 4 ст., Св. Станислава 3 ст. (1877), поручик _ 11.02.1879, штабс-капитан _ 26.01.1880, капитан _ 26.01.1886, подполков- ник _ 26.02.1895. за отличие по службе полковник _ 26.11.1899 (в чине по 6.12.1907) (www.rusgeneral.ru). В разные годы службу проходил в 156 Елисаветпольском, 153 Бакин- ском Е. И. В. Вел. кн. Сергия Михайловича пехотных полках, командовал 14 гренадерским Грузинским ген. Котляревского полком _ 31.12.1901 _ 19.10.1907, и. д. Тифлисского коменданта _ с 19.10.1907. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1891), Св. Анны 2 ст. (1901), Св. Владимира 3 ст. (1905). Spisok, 1900: 93; Spisok, 1900, SPb.: 787; Spisok, 1903: 71; Spisok, 1903, sen., SPb.: 464; Spisok, 1905: 48; Spisok, 1905, SPb.: 337; Spisok, 1907, SPb.: 93. ЧЕРНОГОРОВ ФЕДОР ЕВГЕНИЕВИЧ (род. 15.02.1858), полковник. Окончил 6 классов Самарской классической гимназии и Оренбургское пе- хотное юнкерское училище. Службу начал 20.09.1875, участник Русско-Ту- рецкой войны 1877-78, призведен в прапорщики _ 10.07.1877, награжден орденом Св. Анны 4 ст. с ндписью «За храбрость» (1878), подпоручик _ 15.05.1883, поручик _ 15.05.1887, штабс-капитан _ 15.03.1896, капи- тан _ 6.05.1900, за отличие по службе награжден чином подполковника _ 5.10.1904, полковник _ 6.12.1910 (в чине по 6.03.1917) (www.rusgeneral.ru). 390 oTar Jordania В 1912 служил в 18 пехотном Апшеронском Императрицы Екатерины Великой полку, на 1 марта 1914 показан полковником 83 пехотного Самур- ского полка. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1892), Св. Владимира 4 ст. с бантом (1902), Св. Станислава 2 ст. (1908). Spisok, 1910: 119; Spisok, 1911: 95; Spisok, 1912, SPb.: 1237; Spisok, 1914, SPb.: 735. ЧЕРНОЗУБОВ ФЕДОР ГРИГОРЬЕВИЧ (род. 14.09.1863), полковник. Воспитывался в Пажеском Е. В. корпусе, окончил Николаевскую Академию Генерального штаба по 1 разряду. Службу начал 31.12.1881, произведен в корнеты _ 12.08.1883, поручик _ 30.08.1887, штабс-ротмистр _ 10.04.1889, капитан Генерального штаба _ 26.11.1889, подполковник _ 17.04.1894, за службное отличие полковник _ 5.04.1898 (в чине по 26.12.1908) (www. rusgeneral.ru). С 1901 службу проходил на Кавказе: начальник штаба 1 Кавказской ка- зачьей дивизии _ 17.04.1901 _ 10.12.1902, состоял в распоряжении команду- ющего войсками Кавказского военного округа _ с 10.12.1902. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1890) и 2 ст. (1903), Св. Анны 3 ст. (1895) и 2 ст. (1905). Spisok, 1900: 666; Spisok, 1901: 85; Spisok, 1903: 66; Spisok, 1903, sen., 1903: 355; Spisok, 1904: 54; Spisok, 1905, SPb.: 237; Spisok, 1907, SPb.: 63; Spisok, 1908: 34. ЧЕХОВИЧ АЛЕКСАНДР АЛЕКСАНДРОВИЧ (род. 23.11.1870), пол- ковник. Воспитывался в Владимирском Киевском кадетском корпусе, воен- ном Павловском училище, окончил Александровскую военно-юридическую Академию по 1 разряду. Службу начал 1.09.1889, произведен в подпоручики _ 10.08.1890, поручик _ 10.08.1894, штабс-капитан _ 19.07.1898, капитан _ 19.07.1902, подполковник _ 6.12.1907, за отличие по службе полковник _ 6.12.1911. Помощник военного прокурора Кавказского военно-окружного суда _ 15.03.1908-30.08.1912. В дальнейшем служил вне Каказского военного округа. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1907), Св. Станислава 2 ст. (1910). Spisok, 1910: 165; Spisok, 1914, SPb.: 1043. ЧИВАДЗЕ ДАВИД ТИМОФЕЕВИЧ (род. 10.08.1853), полковник. Воспитывался в Горийском духовном и Тифлисском пехотном юнкерском 391 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV училищах. Службу начал 22.12.1873, участник Русско-Турецкой войны 1877-78 (контужен в бою), награжден Знаком отличия военного ордена Св. Георгия 4 ст. (1877), орденом Св. Станислава 3 ст. с мечами и бантом (1879), подпоручик _ 6.07.1880, штабс-капитан _ 26.02.1886, награжден чином капитана _ 15.03.1891, подполковник _ 26.02.1902, за служебное отличие полковник _ 4.04.1908. Длительное время служил в 153 пехотном Бакинском Е. И. В. Вел. кн. Сергия Михайловича полку. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1896), Св. Станислава 2 ст. (1901), Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1903). Spisok, 1903: 150; Spisok, 1905: 112; Spisok, 1907: 106; Spisok, 1908: 98; Spisok, 1909, SPb.: 1008; Spisok, 1910: 76; Spisok, 1910, SPb.: 945. ЧИЖЕВСКИЙ НИКОЛАЙ КОНСТАНТИНОВИЧ (род. 23.07.1861), полковник. Воспитывался в Полтавской военной прогимназии и Одесском пе- хотном юнкерском училище. Службу начал 8.10.1877, произведен в прапорщики _ 12.01.1881, подпоручик _ 15.03.1883, поручик _ 15.03.18877, штабс-капитан _ 15.03.1892, капитан _ 15.05.1899, за отличие по службе подполковник _ 5.05.1907, полковник _ 6.12.1911( в чине по 20.10.1916) (www.rusgeneral.ru). Служил в 84 Ширванском, 206 Сальянском Е. И. В. Наследника Цеса- ревича пехотных полках. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1893), Св. Анны 3 ст. (1905). Spisok, 1908: 169; Spisok, 1910: 160; Spisok, 1911: 149; Spisok, 1913, SPb.: 413; Spisok, 1914, SPb.: 1025. ЧИЖОВ МИХАИЛ ИВАНОВИЧ (род. 11.01.1857), полковник. Вос- питывался в Смоленской духовний семинарии и Казанском пехотном юн- керском училище. Участник Русско-Турецкой войны 1877-78, награжден орденами Св. Анны 4 ст. с надписью «За храбрость» и Св. Станислава 3 ст. с мечами и бантом (1878), за отличия подпоручик _ 27.06.1879, поручик _ 4.05.1881 и штабс-капитан _ 6.05.1884, капитан _ 23.07.1886, подполков- ник _ 26.02.1892, за служебное отличие полковник _ 6.12.1899 (в чине по 11.12.1908) (www.rusgeneral.ru ). Командовал 253 Грозненским резервным батальоном _ 27.03.1900 _ 7.07.1903, 151 пехотным Пятигорским полком _ 7.07.1903. С июня 1906 слу- жил вне пределов Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1892), Св. Станислава 2 ст. (1895), Св. Владимира 3 ст. (1906). 392 oTar Jordania Spisok, 1900: 95; Spisok, 1900, SPb.: 807; Spisok, 1901: 93; Spisok, 1903, sen., SPb.: 482; Spisok, 1905: 354; Spisok, 1907, SPb.: 98. ЧИКАЛИН ВЛАДИМИР НИКОЛАЕВИЧ (род. 17.09.1853), полков- ник. Георгиевский кавалер. Воспитывался в Михайловской Воронежской военной гимназиии, Михайловском артиллерийском училище. Произведен в поручики _ 9.12.1876, участник Русско-Турецкой войны 1877-78 (конту- жен в бою), за выдающееся боевое отличие награжден орденом Св. Георгия 4 ст. (1878), удостоен других боевых знаков отличия: Св. Станислава 3 ст. с мечами и бантом (1877) и 2 ст. с мечами (1879), Св. Анны 3 ст. с мечами и бантом (1878), награжден чинами штабс-капитана _ 26.12.1877, капитана _ 2.11.1884, подполковника _ 1.10.1895 и полковника _ 13.10.1898 (в чине по 6.12.1906) (www.rusgeneral.ru). В 1895-96 командовал 6 батареей в 39 артиллерийской бригаде _ с 1.10.1895, 4 батареей Кавказского гренадерского Е. И. В. Вел. кн. Михаила Николаевича артиллерийской бригады _ 5.10.1896 -13.10.1898, командир 1 дивизиона Кавказского гренадерского Е. И. В. Вел. кн. Михаила Николае- вича артиллерийской бригады _ с 13.10.1898, командующий 58 артиллерий- ской бригады - с 4.06.1904, командующий Кавказской гренадерской Е. И. В. Вел. кн. Михаила Николаевича бригады _ с 3.09.1904. За другие военно-служебные заслуги награжден орденами Св. Анны 2 ст. (1888), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерсих чинах (1900) и 3 ст. (1903). Spisok, 1899: 100; Spisok, 1900: 88; Spisok, 1903: 68; Spisok, 1903, sen., SPb.: 395; Spisok, 1904: 56; Spisok, 1905: 46; Spisok, 1905, SPb.: 273; Spisok, 1906, SPb.: 120. ЧИКАЛИН КОНСТАНТИН НИКОЛАЕВИЧ (род. 24.10.1858), полков- ник. Воспитывался в Михайловской Воронежской военной гимназии, Михай- ловском артиллерийском училище, окончил Николаевскую инженерную Ака- демию по 1 разряду. Службу начал 12.08.1875, за отличия награжден чинами подпоручика _ 18.04.1878 и штабс-капитана _ 18.12.1883, капитан _ 5.04.1887, подполковник _ 5.04.1898, за отличие по службе полковник _ 19.04.1912. Более 5 лет возглавлял 1 и 5 дистанции Тифлисского отделения Кавказ- ского округа путей сообщения, начальник 2 дистанции того же отделения _ c 16.01.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1890) и 2 ст. (1896), Св. Анны 3 ст. (1894). Spisok, 1911: 101; Spisok, 1912, SPb.: 1212; Spisok, 1914, SPb.: 1145. 393 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ЧИКОВАНИ ВИССАРИОН ПАВЛОВИЧ (род. 13.08.1856), полков- ник. Воспитывался дома и пехотном юнкерском училище. Службу начал 9.12.1876, участник Русско-Турецкой войны 1877-78, награжден Знаком от- личия военного ордена Св. Георгия 4 ст. (1877), произведен в прапорщики _ 19.07.1882, подпоручик _ 14.09.1884, поручик _ 30.08.1888, штабс-капитан _ 21.11.1898, капитан _ 1.01.1901 (старшинство с 6.05.1900), за отличие на- гражден чином подполковника _ 16.07.1905 (старшинство с 5.10.1904), пол- ковник _ 2.04.1911 (в чине по1914) (www.grwar.ru). В 1905-11 служил в 13 лейб-гренадерском Эриванском Е. В. полку. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1894) и 2 ст. (1901), Св. Анны 3 ст. (1896) и 2 ст. (1906), Св. Вла- димира 4 ст. (1906). Spisok, 1905: 160; Spisok, 1909, SPb.: 652; Spisok, 1910: 120; Spisok, 1911: 95; Spisok,1912, SPb.: 1239. ЧИСТЯКОВ СТЕПАН ЕФРЕМОВИЧ (род. 11.01.1845), полковник. Участник военных экспедиций 1863-64, 1878-80, награжден чином сотника _ 26.02.1874, есаул _ 2.02.1881, за отличия по службе войсковой старшина _ 1.01.1890 и полковник _ 6.05.1897. В 1881-85 служил помощником старшего адъютанта войскового штаба Кубанского казачьего войска, старший адъютант там же _ 1885-1893, на- значен старшим помощником атамана Екатеринодарского отдела Кубанской обл. _ 30.01.1893. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1880) и 2 ст. (1888), Св. Анны 3 ст. ((1885) и 2 ст. (1893), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1895). Spisok, 1899: 94; Spisok, 1900: 82; Spisok, 1900, SPb.: 617; Spisok, 1903, may, SPb.: 1903. ЧКОНИЯ КОНСТАНТИН ЛЕВАНОВИЧ (АССАЛОВИЧ) (род. 1.12.1849), полковник. Воспитывался в Кутаисской классической гимназии, окончил Офицерскую кавалерийскую школу с оценкой «Хорошо». Участ- ник Русско-Турецкой войны 1877-78 и военной экспедиции 1879, за боевое отличие переименован из прапорщиков милиции в хорунжие _ 10.09.1877, награжден чином сотника за боевое отличие _ 25.11.1877, удостоен орденов Св. Анны 4 ст. с надписью «За храбрость» (1877), Св. Станислава 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бантом, Св. Владимира 4 ст. с мечами и бантом (1879), за отличия по службе есаул _ 30.08.1880, войсковой старшина _ 14.05.1896 и полковник _ 6.05.1904 (в чине по14.04.1913) (www. rusgeneral.ru). 394 oTar Jordania Назначен заведующим станичным коневодством в Терском казачьем войске _ 22.04.1901. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1886), Св. Анны 2 ст. (1910). Кавалер иностранных орденов: румынского _ Железного креста, пер- сидского _ Льва и Солнца 2 ст. и 4 ст., бухарского _ серебряного Благород- ной Бухары 3 ст. Spisok, 1905: 76; Spisok, 1905, SPb.: 1003; Spisok, 1907: 57; Spisok, 1907, SPb.: 541; Spisok,1911, SPb.: 188; Spisok, 1912, SPb.: 149; Spisok gen., 1913, SPb.: 832. ЧОВПЛЯНСКИЙ ВАСИЛИЙ ЕМЕЛЬЯНОВИЧ (род. 12.04.1850), полковник. Воспитывался в Киевском пехотном юнкерском училище, ко- торое окончил по 1 разряду, с оценкой «Успешнo» завершил учебный курс Офицерской стрелковой школы. Службу начал 20.07.1867, произведен в прапорщики - 24.08.1873, подпоручик _ 26.06.1875, участник Русско-Турец- кой войны 1877-78, поручик _ 9.03.1877, штабс-капитан _ 7.06.1880, капи- тан _ 1.04.1890, подполковник _ 26.02.1897, награжден чином полковника _ 5.10.1904. В 1907 службу проходил в 130 пехотном Херсонском Е. И. В. Вел. кн. Андрея Владимировича полку. За военно-сужебные заслуги награжден орденами Св. Станислава 2 ст. (1892), Св. Анны 2 ст. (1895), Св. Владимира 4 ст. с бантом (1901). Spisok, 1907, SPb.: 663; Spisok, 1908: 55; Spisok, 1910, SPb.: 371. ЧОВПЛЯНСКИЙ ФЕДОР ЕМЕЛЬЯНОВИЧ (род. 1848), полковник. В офицерских чинах с 27.11.1873. Участник Русско-Турецкой войны 1877- 78, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1878). Под- полковник _ 30.08.1890. Полковник _ 6.12.1902. В 1901- 03 служил начальником съемочного отделения Военно-топо- графического отдела Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1880) и 2 ст. (1893), Св. Владимира 4 ст. (1884), Св. Станислава 2 ст. (1893). Spisok, 1901: 111; Spisok, 1903: 89. ЧУРАКОВСКИЙ ЮРИЙ КОНСТАНТИНОВИЧ (род. 17.08.1854), полковник. Воспитывался в Петровской Полтавской военной гимназии и 2 Константиновском училище, которое окончил по 1 разряду. Произведен в подпоручики- 10.08.1873, поручик _ 25.03.1876, участник Русско-Турецкой войны 1877-78, награжден чином штабс-капитана _ 29.09.1877, орденом 395 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Св. Станислава 3 ст. с мечами и бантом (1880), за отличие по службе капи- тан _ 4.11.1882, войсковой старшина _ 14.05.1896, награжден чином пол- ковника _ 27.04.1904. В 1879 _ 1883 служил офицером для поручений при командующем войсками Терской обл. _ 29.06.1879 - 12.03.1883, командир 5 Кубанского пластунского батальона _ 27.04.1904 _ 24.08.1906, назначен командиром 3 Кавказского стрелкового батальона _ 24.08.1906. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1888), Св. Станислава 2 ст. (1895), Св. Владимира 4 ст. с бантом (1901). Spisok, 1905: 75; Spisok, 1905, SPb.: 1000, Spisok, 1907: 56; Spisok, 1907, SPb.: 536. ШАВРОВ НИКОЛАЙ РАФАИЛОВИЧ (род. 4.07.1857), полковник. Воспитывался в Московской классической гимназии и Виленском пехотном юнкерском училище, которое окончил по 1 разряду. Службу начал 24.04.1876, произведен в прапорщики _ 16.04.1878, подпоручик _ 22.09.1879, поручик _ 7.03.1883, за отличия по службе награжден чинами штабс-капитана _ 24.04.1888, капитана _ 30.08.1892, подполковника _ 26.02.1900 и полковни- ка _ 6.12.1903 ( в чине по 1913) (www.rusgeneral.ru). С 1905 служил на Кавказе. Бакинский уездный начальник _ с 20.08.1905. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1884) и 2 ст. (1898), Св. Анны 3 ст. (1895) и 2 ст. (1905), Св. Владимира 4 ст. (1909) и Владимира 3 ст. (1911). Spisok, 1907: 462; Spisok, 1910: 43; Spisok, 1910, SPb.: 225; Spisok, 1911: 40; Spisok, 1911, SPb.: 144; Spisok, 1913, SPb.: 69. ШАМШАДИНОВ АЛИ-АШРАФ-АГА (род. 20.03.1851), полковник. Состоял при войсках Кавказского военного округа. Участник Русско-Турец- кой войны 1877-78. В офицерских чинах с 1877. Есаул _ 5.04.1898. Полков- ник _ 6.12.1903 (в чине по 6.12.1914) (www.rusgeneral.ru). За военно-служебные отличия награжден орденами Св. Станислава 3 ст. (1883) и 2 ст. (1901), Св. Анны 3 ст. (1896) и 2 ст. (1907). Spisok, 1904: 82; Spisok, 1911: 40. ШАНШИЕВ НИКОЛАЙ ШАНШИЕВИЧ (род. 24.01.1862), полковник. Воспитывался во 2 Московской военной гимназии и 3 военном пехотном Алек- сандровском училище. Службу начал 15.08.1880, произведен в подпоручики _ 7.08.1882, поручик _ 7.08.1886, штабс-капитан _ 15.04.1895, за отличие на- гражден чином капитана _ 23.04.1898 (старшинство с 15.03.1898), подполков- ник _ 26.02.1905, полковник _ 6.12.1911 (в чине по 1917) (www.rusgeneral.ru). 396 oTar Jordania Служил в 13 лейб-гренадерском Эриванском царя Михаила Федорови- ча полку. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1900) и 2 ст. (1907), Св. Станислава 2 ст. (1906), Св. Владимира 4 ст. (1912). Spisok, 1905: 150; Spisok, 1910: 128; Spisok, 1911: 123; Spisok, 1914, SPb.: 982. ШАПАРЕВ АРКАДИЙ КОНСТАНТИНОВИЧ (род. 15.03.1870), пол- ковник. Воспитывался в Киевском Владимировском кадетском корпусе, Михайловском артиллерийском училище, окончил Михайловскую артилле- рийскую Академию по 1 разряду. Службу начал 30.08.1887, произведен в хорунжие _ 9.08.1888, сотник _ 9.08.1892, переименован в штабс-капитаны _ 24.02.1902, награжден чином подъесаула _ 20.05.1895, орденом Св. Ста- нислава 3 ст. (1898), капитан _ 6.05.1900, подполковник _ 26.02.1906, за от- личие по службе полковник _ 30.06.1911. В 1906 - 14 служил штаб-офицером по осмотру оружия в Кубанском казачьем войске. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1906), Св. Станислава 3 ст. (1898) и 2 ст. (1912). Spisok, 1907: 166; Spisok, 1910: 142; Spisok, 1914, SPb.: 940. ШАРЫГИН НИКОЛАЙ МИХАЙЛОВИЧ (род. 3.02.1854), полков- ник. Воспитывался в Николаевском кавалерийском училище. Службу на- чал 13.08.1870, произведен в корнеты _ 17.07.1872, поручик _ 23.02.1873, штабс-ротмистр _ 8.09.1875, участник Русско-Турецкой войны 1877-78, на- гражден орденами Св. Станислава 3 ст. с мечами и бантом (1877), Св. Анны 3 ст. с мечами и бантом (1878), подполковник _ 30.08.1899, за отличие по службе полковник _ 16.07.1906. В 1904-07 служил в 43 драгунском Тверском полку, помощник коман- дира того же полка по хозяйственной части - с 7.07.1905, в 1908 показан полковником 16 драгунского Тверского полка. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1881), Св. Анны 2 ст. 1884), Св. Владимира 4 ст. с бантом (1901). Spisok, 1904: 113; Spisok, 1905: 102; Spisok, 1907: 81; Spisok, 1907, SPb.: 1088; Spisok, 1908: 74. ШАХ-РУХ-МИРЗА (род. 15.09.1843), персидский принц. Полковник Императорской Русской армии. Воспитывался дома. Произведен в поручи- ки _ 30.08.1870, корнет гвардии _ 30.08.1870, награжден чином поручика _ 30.08.1873, участник Русско-Турецкой войны 1877-78, за боевое отличие 397 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV награжден чином штабс-ротмистра _ 8.12.1877 и орденами: Св. Владимира 4 ст. с мечами и бантом (1877), Св. Станислава 2 ст. с мечами (1879), рот- мистр, переименован в есаулы _ 30.08.1880, полковник _ 21.04.1891. Служил в лейб-гвардии Казачьем Е. В. полку, прикомандирован к во- йскам Кавказского военного округа _ с 30.08.1880. За другие военно-служебные заслуги награжден орденом Св. Анны 2 ст. (1907). Кавалер персидского ордена Льва и Солнца 2 ст. (1892). Spisok, 1893; 129; Spisok, 1900: 51; Spisok, 1903: 46; Spisok, 1903, sen., SPb.: 41; Spisok, 1905: 37; Spisok, 1905, SPb.: 32; Spisok, 1907, SPb.: 10; Spisok, 1910: 32; Spisok, 1911, SPb.: 3; Spisok, 1914, SPb.: 1. ШАХ-ТАХТИНСКИЙ АБДУЛ-ФЕТ-АГА НАДЖАФ-АЛА-ОГЛЫ (род. 17.10.1858), полковник. Воспитывался в Тифлисском реальном, 2 воен- ном Константиновском училищах, Институте восточных языков, с оценкой «Успешно» завершил курс Офицерской стрелковой школы. Службу начал 1.09.1879, произведен в прапорщики гвардии _ 8.08.1881, подпоручик _ 30.08.1884, поручик _ 8.08.1885, штабс-капитан _ 20.04.1887, за отличие капитан _ 7.08.1889, подполковник _ 26.02.1896, участник Русско-Японской войны 1904-05, награжден орденами Св. Станислава 2 ст. с мечами и Св. Анны 2 ст. с мечами (1906), в отставке с октября 1904 по март 1905, за от- личие по службе полковник _ 31.05.1910. В 1897-13 служил в 77 пехотном Тенгинском Е. И. В. Вел. кн. Алек- сия Александровича полку; 202 пехотном резервном Горийском полку _ с 4.06.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1892), Св. Анны 3 ст. (1900), Св. Владимира 4 ст. с бантом (1909). Кавалер иностранных орденов: персидского _ Льва и Солнца 4 ст. (1889) и 3 ст. (1900), бухарского - золотого Благородной Бухары 2 ст. (1899); награж- ден Знаком Французского общества спасения на водах Верхнего Рейна (1903). Spisok, 1901: 137; Spisok, 1903: 111; Spisok, 1904: 42; Spisok, 1907: 91; Spisok, 1908: 142; Spisok, 1910: 131; Spisok, 1911: 85; Spisok, 1911, SPb.: 1145; Spisok, 1913, SPb.: 722. ШЕБУЕВ АЛЕКСАНДР ПАВЛОВИЧ (род. 27.01.1847), полковник. Произведен в поручики _ 14.11.1868, в отставке _ ноябрь 1868 _ март 1870, штабс-капитан _ 27.03.1873, участник Русско-Турецкой войны 1877-78, капитан _ 13.10.1877, награжден орденом Св. Анны 3 ст. с мечами и бан- том (1878), подполковник _ 1.01.1885, за отличие по службе полковник _ 19.05.1898. 398 oTar Jordania С 1898 служил на Кавказе. Кутаисский уездный воинский начальник _ с 19.05.1898. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1876) и 2 ст. (1880), Св. Анны 2 ст. (1884), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1890). Кавалер иностранных орденов: черногорского _ Кн. Даниила 1-го 3 ст. (1889), прусского _ Прусской короны 2 ст. (1890). Spisok, 1899: 98; Spisok, 1900: 86; Spisok, 1900, SPb.: 695; Spisok, 1901: 86; Spisok, 1903: 67; Spisok, 1903, may., SPb.: 406. ШЕЛКОВНИКОВ ГРИГОРИЙ АРТЕМЬЕВИЧ (род. 28.07.1867), пол- ковник. Воспитывался в Тифлисском кадетском корпусе и 1 военном Пав- ловском училище. Службу начал 31.08.1885, произведен в подпоручики _ 11.08.1886, поручик _ 11.08.1890, штабс-капитан _ 6.05.1900, капитан _ 6.05.1901, за отличие награжден чином подполковника _ 28.02.1907, пол- ковник _ 6.12.1912 (в чине по 30.01.1917) (www.rusgeneral.ru). В 1908-14 служил в 13 лейб-гренадерском Эриванском царя Михаила Федоровича и 77 пехотном Тенгинском полках. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1896) и 2 ст. (1910), Св. Анны 3 ст. (1905). Кавалер бухарского серебряного ордена Благородной Бухары 1 ст. Spisok, 1907: 52; Spisok, 1908: 164; Spisok, 1910: 156; Spisok, 1914, SPb.: 1236. ШЕЛКОВНИКОВ НИКОЛАЙ НИКОЛАЕВИЧ (род. 5.12.1852), пол- ковник. Воспитывался во 2 С.-Петербургской военной гимназии, 2 военном Константиновском училище. Произведен в прапорщики _ 17.07.1872, под- поручик _ 29.12.1873, поручик _ 26.11.1874, штабс-капитан _ 26.12.1877, капитан _ 4.12.1883, подполковник _ 6.06.1896, за отличие по службе пол- ковник _ 6.12.1903. С 1896 службу проходил в Кавказском военном округе. Командир 2 ба- тальона Карсской крепостной артиллерии _ с 3.08.1896. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1895), Св. Анны 3 ст. (1888) и 2 ст. (1899). Spisok, 1897: 182; Spisok, 1903: 114; Spisok, 1904: 80; Spisok, 1905: 70; Spisok, 1905, SPb.: 891; Spisok, 1907: 52; Spisok, 1907, SPb.: 435; Spisok, 1908: 45. ШЕЛХОВСКОЙ АФАНАСИЙ МИХАЙЛОВИЧ (род. 16.01.1861), полковник. Воспитывался в Ставропольской классической гимназии и 1 военном Павловском училище, которое окончил по 1 разряду. Службу на- чал 6.09.1881, произведен в подпоручики _ 12.08.1883, поручик _ 12.08. 399 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 1887, награжден чином подъесаула _ 14.05.1896, войсковой старшина _ 26.02.1904, участник Русско-Японской войны 1904-05, награжден ордена- ми Св. Владимира 4 ст. с мечами и бантом (1906), Св. Анны 2 ст. с мечами (1907), за отличие по службе полковник _ 24.09.1907. Старший помощник атамана Кавказского отдела _ 1897 _ 1899, ко- мандующий Кубанскими 12 пластунским льготным - с 3.06.190), 10 - с 21.08.1906 и 4 - с 24.09.1907 пластунскими батальонами. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1903), Св. Владимира 3 ст. (1910). Spisok, 1908: 83; Spisok, 1909, SPb.: 917; Spisok, 1911, SPb.: 655. ШЕМШУРИН НИКОЛАЙ ПЛАТОНОВИЧ (род. 24.11.1851), полков- ник. Воспитывался в классической гимназии и 2 военном Константиновском училище. Произведен в прапорщики _ 4.08.1875, подпоручик _ 9.12.1876, поручик _ 26.12.1877, штабс-капитан _ 24.10.1881, капитан _ 30.08.1887, подполковник _ 11.10.1897, за отличие по службе полковник _ 6.12.1902 (в чине по 1907) (www.rusgeneral.ru). В 1904-1906 cлужбу проходил в Терско-Дагестанской крепостной ар- тиллерии, назначен командиром Кавказского осадного артиллерийского полка _ с 28.08.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1881) и 2 ст. (1891), Св. Анны 3 ст. (1884) и 2 ст. (1895), Св. Владимира 4 ст. (1899). Spisok, 1899: 164; Spisok, 1903: 89; Spisok, 1904: 75; Spisok, 1904, SPb.: 797; Spisok, 1906, SPb.: 501; Spisok, 1907: 48. ШЕПАТОВСКИЙ ДМИТРИЙ ПЛАТОНОВИЧ (род. 2.10.1864), пол- ковник. Воспитывался в Оренбургском Неплюева кадетском корпусе, 3 во- енном Александровском училище, окончил Офицерскую артиллерийскую школу с оценкой «Успешно». Службу начал 28.08.1883, произведен в под- поручики _ 14.08.1884, поручик _ 14.08.1888, штабс-капитан _ 25.07.1895, капитан _ 27.07.1899, участник Русско-Японской войны 1904-05, подпол- ковник _ 16.06.1905, награжден орденом Св. Анны 2 ст. (1905), за отличие полковник _ 29.03.1913 (в чине по 18.04.1915) (www.rusgeneral.ru). В 1907-11 командовал батареей в Кавказской гренадерской артиллерий- ской бригаде, командир 2 дивизиона Кавказской гренадерской Вел. кн. Ми- хаила Николаевича артиллерийской бригады _ 27.09.1913. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1895), Св. Анны 3 ст. (1901). Spisok, 1907: 155; Spisok, 1910: 132; Spisok, 1911: 126; Spisok, 1914, SPb.: 1294. 400 oTar Jordania ШЕРПУТОВСКИЙ ИВАН ФЕДОРОВИЧ (род. 14.06.1844), полков- ник. Участник военной экспедиции 1864, награжден чином сотника _ 1870, корнет гвардии _ 30.08.1870, за служебное отличие поручик гвардии _ 30.08.1876, участник Русско-Турецкой войны 1877-78, за боевое отличие штабс-ротмистр _ 28.08.1877, награжден орденом Св. Анны 3 ст. с мечами и бантом (1878), за отличие ротмистр - 15.05.1883 и полковник _ 15.06.1891. Командир 1 Сунженско-Владикавказского полка Терского казачьего во- йска _ 26.02.1894 _ 28.08.1895, состоял по Терскому казачьему войску _ с 28.08.1895. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1874) и 2 ст. (1881), Св. Анны 2 ст. (1887), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1892). Кавалер ордена Прусской короны 3 ст. (1890). Spisok, 1893: 133; Spisok, 1894: 113; Spisok, 1897: 78; Spisok, 1900: 52; Spisok, 1900, SPb.: 129; Spisok, 1903, sen., SPb.: 43. ШИДЕЛЬСКИЙ ВЛАДИМИР РОМУАЛЬДОВИЧ (род. 1.04.1850), полковник. Воспитывался в Киевской военной гимназии (окончил 5 кл.), Московском пехотном юнкерском училище, которое окончил по 1 разряду. Произведен в прапорщики _ 23.11.1871, подпоручик _ 2.08.1874, участник Русско-Турецкой войны 1877-78, поручик _ 8.04.1877, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1879), штабс-капитан _ 7.05.1881, капитан _ 3.06.1886, подполковник _ 26.02.1892, за отличие по службе пол- ковник_ 28.03.1904. В 1893 _ 1904 службу проходил в 13 лейб-гренадерском Эриванском Е. В. полку. С августа 1904 выбыл из Кавказского военного округа. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1884) и 2 ст. (1895), Св. Станислава 2 ст. (1891), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1897). Spisok, 1893: 241; Spisok, 1901: 117; Spisok, 1903: 99; Spisok, 1904: 83; Spisok, 1904, SPb.: 977; Spisok, 1906, SPb.: 683. ШИМАНОВСКИЙ ПАВЕЛ НИКИФОРОВИЧ (род. 21 (29).06.1859), полковник. Гергиевский кавалер. Воспитывался в Кишиневском реальном и Тифлисском пехотном юнкерском училищах. Службу начал 8.05.1877, произве- ден в прапорщики _ 25.04.1883, подпоручик _ 30.08.1883, поручик _ 30.08.1888, штабс-капитан _ 24.02.1896, капитан _ 6.05.1900, участник Русско-Японской войны 1904-05 (ранен и контужен), за боевое отличие награжден чином подпол- ковника _ 28.06.1904 (старшинство с 28.09.1904), орденами Св. Анны 3 ст. и 4 ст. с мечами и бантом, Св. Станислава 3 ст. и 2 ст. с мечами (1904). За выдающееся 401 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV боевое отличие награжден орденом Св. Георгия 4 ст. (1908), за отличие по служ- бе полковник _ 26.11.1908 получил орден Св. Владимира 4 ст. (1908). В 1910 служил в 82 пехотном Дагестанском Е. И. В. Вел. кн. Николая Михайловича полку. Spisok, 1907: 125; Spisok, 1908: 114; Spisok, 1910: 79; Spisok, 1910, SPb.: 1019. ШИРОКОВ СЕРГЕЙ ПАВЛОВИЧ (род. 3.07.1846), полковник. Воен- ный инженер. Воспитывался в Константиновском межевом институте, окон- чил Николаевскую инженерную Академию по 1 разряду. Произведен в под- поручики _ 5.12.1867, поручик _ 31.10.1871, штабс-капитан _ 15.12.1874, капитан _ 10.04.1878, подполковник _ 9.04.1889, за отличие по службе на- гражден чином полковника _ 30.08.1893. Начальник Дагестанской инженерной дистанции _ с 14.03.1900. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1879) и 2 ст. (1885), Св. Анны 3 ст. (1883) и 2 ст. (1889), Св. Владимира 4 ст. (1893). Spisok, 1900: 63; Spisok, 1900, SPb.: 284; Spisok, 1900, SPb.: 284; Spisok, 1902: 51; Spisok, 1903: 50; Spisok, 1903, sen., 1903: 94; Spisok, 1904: 44; Spisok, 1905: 37; Spisok, 1905, SPb.: 56. ШИШКО ТИТ-РАЙМУНД-УСТИНОВИЧ (род. 4.01.1853), полковник. Воспитывался в Полоцкой военной гимназии и Рижском пехотном юн- керском училище. Произведен в прапорщики _ 19.12.1873, подпоручик _ 28.05.1875, поручик _ 28.06.1877, штабс-капитан _ 16.06.1878, награжден чином капитана _ 17.04.1880, подполковник _ 1.01.1891, за служебное от- личие полковник _ 1.08.1902. В 1891-1901 служил в 83 пехотном Самурском Е. И. В. Вел. кн. Влади- мира Александровича полку, командовал 253 Грозненским резервным бата- льоном - 16.07.1903 _ 7.01.1905, 156 пехотным Елисаветпольским ген. кн. Цицианова _ 7.01.1905 _ 20.03.1908, 79 пехотным Куринским ген.-фельдм. кн. Воронцова полками. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1885) и 2 ст. (1899), Св. Анны 3 ст. (1895) и 2 ст.(1905). Spisok, 1891: 250; Spisok, 1895: 155; Spisok, 1901: 111; Spisok, 1903: 88; Spisok, 1903, sen., 1903, SPb.: 866; Spisok, 1905: 63; Spisok, 1905, SPb.: 727; Spisok, 1907, SPb.: 305; Spisok, 1908: 41; Spisok, 1910: 38; Spisok, 1910, SPb.: 125. ШКАБИЧ АЛЕКСАНДР ВАСИЛЬЕВИЧ (род. 22.04.1842), полковник. В офицерских чинах с 25.11.1859. Участник Кавказской войны 1817 _ 64, военных экспедиций 1857-59, 1864, за боевое отличие награжден Знаком 402 oTar Jordania отличия военного ордена Св. Георгия 4 ст. (1859), награжден чином под- поручика _ 1.09.1865, поручик _ 7.09.1868, штабс-капитан _ 5.10.1871, за отличие по службе капитан - 14.11.1875, участник Русско-Турецкой войны 1877-78 удостоен боевых наград: Св. Владимира 4 ст. с мечами и бантом (1877), Св. Станислава 2 ст. с мечами (1878), золотым оружием, за боевое отличие получил чин майора _ 1.05.1879, подполковник - 6.05.1884, награж- ден чином полковника _ 25.01.1892. Командовал 2 Кавказской туземной стрелковой дружиной _ с 25.01.1892, затем 260 пехотным резервным Ардаганским полком _ 14.03.1895. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 3 ст. (1869), Св. Анны 2 ст. (1883), Св. Владимира 3 ст. (1896), Знаком отличия за 40 лет образцовой службы (1900). Spisok, 1893:139; Spisok, 1895: 96; Spisok, 1900: 56; Spisok, 1900, SPb.: 166; Spisok, 1901: 56. ШЛИТТЕР МИХАИЛ АЛЕКСАНДРОВИЧ (род. 22.04.1860), пол- ковник. Воспитывался во 2 военном Константиновском училище, которое окончил по 1 разряду, завершил курс восточных языков при Азиатском де- партаменте Министерства иностранных дел. Службу начал 1.09.1877, пра- порщик гвардии _ 9.08.1880, подпоручик _ 30.08.1882, поручик _ 1.01.1885, штабс-капитан армии _ 15.03.1890, за отличие капитан _ 15.03.1890, под- полковник _ 26.02.1901, награжден чином полковника _ 5.10.1904 (в чине по 1912) (www.rusgeneral.ru). C 1906 cлужил на Кавказе. Командовал 2 Кавказской стрелковой бата- реей _ c 4.07.1906; 155 пехотным Кубинским _ 17.04.1908 _ 15.06.1910; 13 лейб-гренадерским Эриванским Е. В._ с 15.06.1910 полками. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1901), Св. Станислава 2 ст. (1908). Spisok, 1901: 175; Spisok, 1903: 144; Spisok, 1904: 126; Spisok, 1905: 82; Spisok, 1906, SPb.: 900; Spisok, 1907: 65; Spisok, 1907, SPb.: 703; Spisok, 1910: 51; Spisok, 1910, SPb.: 404; Spisok, 1911: 47; Spisok, 1912, SPb.: 212. ШЛИТТЕР НИКОЛАЙ ИВАНОВИЧ (род. 13.01.1858), полковник. Военный инженер. Воспитывался в Николаевском инженерном училище, окон- чил Николаевскую инженерную Академию по 1 разряду. Произведен в поручики _ 30.08.1880, штабс-ротистр, переименован в капитаны _ 30.08.1883, подполков- ник _ 30.08.1894, за отличие по службе награжден чином полковника _ 5.04.1898. С 1903 службу проходил в Кавказском военном округе: инспектор ра- бот окружного инженерного управления Кавказского военного округа _ с 16.08.1903. 403 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1888) и 2 ст. (1902), Св. Анны 3 ст. (1893) и 2 ст. (1905), Св. Владимира 4 ст. (1901). Spisok, 1900, SPb.: 677; Spisok, 1902, SPb.: 513; Spisok, 1903, sen., SPb.: 361; Spisok, 1904: 55; Spisok, 1905: 45; Spisok, 1905, SPb.: 243; Spisok, 1907: 37; Spisok, 1907, SPb.: 65; Spisok, 1908: 34, ШНАБЕЛЬ ПЕТР ФЕДОРОВИЧ (род. 28.12.1873), полковник. Воспи- тывался в 1 Московском кадетском корпусе, Михайловском артиллерийском училище, окончил Николаевскую Академию Генерального штаба с допол- нительным курсом по 1 разряду. Службу начал 31.08.1892, произведен в подпоручики _ 7.08.1893, поручик _ 7.08.1897, штабс-капитан _ 23.05.1901, участник Русско-Японской войны 1904-05, капитан _ 28.03.1904, награжден орденами Св. Станислава 3 ст. с мечами и бантом и 2 ст. с мечами (1905), Св. Анны 4 ст. с надписью «За храбрость» и 3 ст. с мечами и бантом, Св. Владимира 4 ст. с мечами и бантом, Св. Анны 2 ст. с мечами (1906), за от- личия по службе подполковник _ 2.04.1906. и полковник_ 6.12.1910 (в чине по 24.09.1917) (www.rusgeneral.ru). В 1909-14 занимал должность старшего адъютанта штаба Кавказского военного округа. Spisok, 1910: 143; Spisok, 1911: 88; Spisok, 1912, SPb.: 1379; Spisok, 1914, SPb.: 847. ШОВСКИЙ НИКОЛАЙ ИВАНОВИЧ (род. 1.05.1852), полковник. Воспитывался в 1 военном Павловском училище, которое окончил по 2 разряду, с оценкой «Успешно» завершил учебу в Офицерской стрелковой школе. Произведен в прапорщики _ 10.08.1873, подпоручик _ 6.07.1875, участник Русско-Турецкой войны 1877-78, поручик _ 2.04.1877, награж- ден орденами Св. Анны 4 ст. с надписью «За храбрость» (1878), Св. Ста- нислава 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бантом (1879), штабс-капитан _ 23.01.1879, награжден чином капитана _ 26.02.1888, ор- деном Св. Станислава 2 ст. с мечами (1895), подполковник _ 26.02.1898, участник Русско-Японской войны 1904-05, награжден чином полковника _ 13.08.1904. Командир 129 пехотного Бессарабского Е. И. В. Вел. кн. Михаила Алек- сандровича полка _ с 29.07.1907. За другие военно-служебные заслуги награжден орденами Св. Влади- мира 4 ст. с бантом (1898), Св. Анны 2 ст. (1903). Spisok, 1906, SPb.: 782; Spisok, 1907, SPb.: 581; Spisok, 1908: 53. 404 oTar Jordania ШПАКОВСКИЙ НИЛ ЛЕОНТЬЕВИЧ (род. 3.01.1845), полковник. Окончил 6 классов Ставропольской классической гимнази и юнкерское пехотное училище. Участник военной экспедиции 1864, награжден чином подпоручика _ 4.03.1869 и поручика _ 12.08.1871, участник Русско-Турец- кой войны 1877-78, штабс-капитан _ 8.07.1877, награжден чном капитана _ 3.10.1877, подполковник _ 1.01.1885, за отличие полковник _ 24.01.1899. Командир Башкадыкларского резервного батальона _ c 13.05.1899. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1874) и 2 ст. (1888), Св. Анны 3 ст. (1881) и 2 ст. (1896), Св. Владимира 4 ст. (1893). Кавалер персидского ордена Льва и Солнца 2 ст. (1901). Spisok, 1899: 103; Spisok, 1900: 91; Spisok, 1900, SPb.: 744; Spisok, 1901: 89; Spisok, 1903, yan, SPb.: 478. ШПИЦБАРТ РУДОЛЬФ-ГЕРМАН КАРЛОВИЧ (род. 19.04.1850), полковник. Воспитывался в Виленском пехотном юнкерском училище. Про- изведен в подпоручики _ 8.06.1875, поручик _ 29.05.1876, участник Рус- ско-Турецкой войны 1877-78 (ранен и контужен в бою), штабс-капитан _ 17.06.1878, награжден орденом Св. Станислава 3 ст. с мечами и бантом (1878), ротмистр _ 1.11.1886, подполковник _ 26.02.1894, за отличие по службе награжден чином полковника _ 27.10.1901. Начальник Терского областного жандармского управления _ с 29.09.1901. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1898), Св. Владимира 4 ст. _ за 25 лет безупречной службы в офицерских чинах (1899) и 3 ст. (1904). Spisok, 1902, SPb.: 900; Spisok, 1903: 84; Spisok, 1903, sen., SPb.: 735; Spisok, 1904: 70; Spisok, 1904, SPb.: 637; Spisok, 1906, SPb.: 346. ШТЕРНБЕРГ ЭМИЛИЙ КАРЛОВИЧ (род. 6.04.1860), полковник. Воспитывался в 3 С.-Петербургской гимназии, Николаеском инженерном училище. Произведен в поручики - 1.01.1885, штабс-капитан _ 30.08.1889, капитан _ 30.08.1891, подполковник _ 30.08.1894, за отличие по службе полковник _ 6.12.1901 (в чине по 13.04.1908)( www.rusgeneral. ru). Участник Русско-Японской войны 1904-05. В 1907-08 служил корпусным интендантом 1 Кавказского армейского корпуса. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1896), Св. Станислава 2 ст. (1906). Spisok, 1903, sen., SPb.: 752; Spisok, 1905, SPb.: 611; Spisok, 1906, SPb: 360; Spisok, 1907: 45; Spisok, 1907, SPb.: 211; Spisok, 1908: 39. 405 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ШТУБЕНДОРФ АЛЕКСЕЙ ОТТОВИЧ (род. 19.04.1877), полковник. Воспитывался в Пажеском Е. В. корпусе, окончил Николаевскую Академию Генерального штаба по 1 разряду. Службу начал 1.09.1894, подпоручик _ 12.08.1896, поручик _ 12.08.1900, участник Русско-Японской войны 1904-05, штабс-капитан гвардии, капитан Генерального штаба _ 31.05.1904, подпол- ковник _ 29.03.1909, за отличие по службе награжден чином полковника _ 25.03.1912 (в чине по 2.04.1917) (www.rusgeneral.ru). Штаб-офицер для поручений при штабе 3 Кавказского армейского кор- пуса _ 6.12.1911 _ 15.01.1913. Затем служил в другом военном округе. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1907), Св. Анны 3 ст. (1909). Spisok, 1913, SPb.: 1198; Spisok, 1914, SPb.: 1131. ШТУС АЛФФРЕД КАРЛОВИЧ (род. 10.12.1853), полковник. Про- изведен в хорунжие _ 10.08.1873, участник Русско-Турецкой войны 1877-78, военных экспедиций 1879-80, сотник _ 10.05.1877, награжден чинами еса- ула _ 1881, войскового старшины _ 14.08.1897, участвовал в Русско-Япон- ской войне 1904-05, за отличие полковник _ 6.05.1904, удостоен орденом Св. Владимира 4 ст. с мечами и бантом (1906). Командир 4 Кубанской казачьей батареи _ 14.08.1897-20.11.1904, ко- мандовал Кавказским казачьим артиллерийским дивизионом _20.11.1904- 26.07.1906, прикомандрован к штабу Кавказского военного округа _ 26.07.1906, назначен командиром 1 Волгского полка Терского казачьего во- йска _ 3.06.1907. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1888) и 2 ст. (1896), Св. Анны 2 ст. (1901). Кавалер бухарского ордена Благородной Бухары 3 ст. (1900). Spisok, 1905: 76; Spisok, 1905, SPb.: 1004; Spisok, 1907: 57; Spisok, 1907, SPb.: 542. ШУБИНСКИЙ ГРИГОРИЙ (ГЕОРГИЙ) НИКОЛАЕВИЧ (род. 5.11.1873), полковник. Воспитывался в Владимирском Киевском кадетском корпусе, 3 военном Александровском училище, окончил Александровскую военно-юридическую Академию по 1 разряду. Службу начал 1 сентября 1892, произведен в подпоручики _ 7.08.1893, поручик _ 7.08.1897, штабс- капитан _ 23.05.1901, капитан _ 6.04.1903, подполковник _ 2.04.1906, за от- личие по службе полковник _ 18.04.1910. До 1909 служил вне пределов Кавказского военного округа, назначен помощником военного прокурора Кавказского военного окружного суда _ 14.02.1909. 406 oTar Jordania За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1904) и 2 ст. (1912), Св. Анны 3 ст. (1906). Spisok, 1910: 143; Spisok, 1911: 84; Spisok, 1911, SPb.: 1118; Spisok, 1912, SPb.: 1016; Spisok, 1913, SPb.: 703; Spisok, 1914, SPb.: 596; ШУБИНСКИЙ ПЕТР ПЕТРОВИЧ (род. 25.02.1855), полковник. Вос- питывался дома и Тверском кавалерийском юнкерском училище. Службу начал 16.05.1876, произведен в корнеты _ 16.04.1878, награжден чином по- ручика _ 18.02.1882, штабс-ротмистр _ 31.03.1891, за служебные отличия награжден чинами ротмистра _ 31.03.1891, подполковника _ 26.02.1899 и полковника _ 6.12.1905. В 1896-97 занимал должность обер-офицера для особых поручений при Кутаисском военном губернаторе, начальник Артвинского _ c 2.07.1898, Гу- нибского _ c 2.05.1905, Закатальского _ с 19.05.1906 округов, помощник Бакинского градоначальника _ 2.12.1906-24.03.1909, помощник военного губернатора Батумской обл. _ 24.03.1909 - 5.11.1910, штаб-офицер для по- ручений при наместнике на Кавказе _ с 5.11.1910. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1887), Св. Анны 3 (1895) и 2 ст. (1909). Spisok, 1899: 175; Spisok, 1904: 113; Spisok, 1907: 73; Spisok, 1907, SPb.: 1089; Spisok, 1908: 66; Spisok, 1909, ch. 3, SPb.: 46; Spisok, 1910: 59; Spisok, 1911: 53; Spisok, 1911, SPb.: 419. ШУВАЛОВ АНДРЕЙ ПЕТРОВИЧ (род. 11.11.1865), граф. Флигель- адъютант. Полковник. Воспитывался в Императорском лицее Цесаревича Николая, сдал экзамен на получение чина офицера гвардии во 2 военном Константиновском училище, окончил Николаевское кавалерийское учи- лище. Произведен в корнеты _ 7.08.1887, поручик _ 30.08.1891, штабс- ротмистр _ 6.12.1895, флигель-адъютант (1897), ротмистр _ 6.12.1899, полковник _ 6.04.1903 (в чине по 25.031912) (www.rusgeneral.ru). Участник Русско - Японской войны 1904-05, награжден орденами Св. Анны 2 ст. с ме- чами, Св. Владимира 3 ст. с мечами (1905), мечами к ордену Св. Станислава 2 ст., золотым оружием и орденом Св. Владимира 4 ст. с мечами и бантом (1906). С 3.10. по 27.11.1898 состоял в распоряжении Военного Министерства. В 1899 - 1904 службу проходил во 2 Дагестанском полку, командир Терско- Кубанского конного полка _ 27.11.1904 _ 29.06.1906, состоял по армейской кавалерии _ 29.06.- 26.11. 1906. За другие военно-служебные заслуги награжден орденом Св. Станисла- ва 3 ст. (1900) и 2 ст. (1903). 407 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Кавалер иностранных орденов: черногорского _ Кн. Даниила I 4 ст. (1889), Германской Короны 4 ст., французских _ Почетного Легиона (Кава- лерийский крест) и знака Академической Пальмы (1895), бухарского _ золо- того Благородной Бухары 3 ст. (1896), сиамского _ Сиамской Короны (1897), китайского _ Дракона 2 и 3 классов (1898), Румынской Звезды 4 ст. (1899), мекленбург-шверинского _ Венедской Короны (Кавалерийский крест) 4 ст., итальянского _ Итальянской Короны (1902), прусского _ Прусской Короны 2 ст. и австрийского _ Франца-Иосифа (Командорский крест) 2 ст. (1903). Spisok, 1903, sen., SPb.: 969; Spisok, 1905: 67; Spisok, 1905, SPb.: 837; Spisok, 1907, SPb.: 393; Spisok, 1910, SPb.: 177; Spisok, 1912, SPb.: 80. ШУКСТ ГЕОРГИЙ (ГРИГОРИЙ) ВАСИЛЬЕВИЧ (род. 4.04.1853), полковник. Воспитывался в Псковской военной прогимназии, Рижском пе- хотном юнкерском училище, с оценкой «Успешно» окончил Офицерскую стрелковую школу. Службу начал 6.06.1869, произведен в прапорщики _ 14.11.1876, подпоручик _ 28.03.1878, поручик _ 2.08. 1879, награжден чином штабс-капитана _ 1881, капитан _ 25.03.1889, подполковник _ 26.02.1895, за отличие полковник _ 19.09.1908. Александропольский уездный воинский начальник _ с 19.09.1908. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1902), Св. Анны 2 ст. (1908), Св. Владимира 4 ст. (1911). Spisok, 1909, SPb.: 1065; Spisok, 1910: 78; Spisok, 1911: 70; Spisok, 1911, SPb.: 791; Spisok, 1912, SPb.: 697; Spisok, 1913, SPb.: 454; Spisok, 1914, SPb.: 334. ШУЛЬЦ ИВАН АЛЕКСАНДРОВИЧ (род. 6.03.1860), полковник. Воспитывался в Ярославской военной прогимназии, Тифлисском пехот- ном юнкерском училище, окончил Офицерскую стрелковую школу с оцен- кой “Отлично». Службу начал 11.08.1878, произведен в прапорщики _ 10.09.1881, подпоручик _ 30.08.1884, поручик _ 30.08.1888, штабс-капитан _ 15.03.1898, капитан _ 24.09.1900 (старшинство с 6.05.1900), за отличие награжден чином подполковника _ 26.02.1905, полковник _ 2.12.1912. В 1905-14 служил в 15 гренадерском Тифлисском Е. И. В. Вел. кн. Кон- стантина Константиновича полку и 14 гренадерском Грузинском Е. И. В. Наследника Цесаревича полку. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1898), Св. Анны 3 ст. (1904) и 2 ст. (1907). Spisok, 1905: 152; Spisok, 1910: 124; Spisok, 1911: 119; Spisok, 1914, SPb.: 1204. 408 oTar Jordania ЩЕГЛОВИТОВ НИКОЛАЙ АНДРЕЕВИЧ (род. 18.12.1849), полков- ник. Воспитывался в Виленском пехотном юнкерском училище. Произве- ден в подпоручики _ 16.04.1871, поручик _ 16.06.1872, штабс-капитан _ 21.06.1877, капитан _ 19.09.1879, подполковник _ 5.04.1887, за отличие по службе награжден чином полковника _ 6.12.1900. Ротный командир Тифлисского кадетского корпуса _ 12.07.1900 _ 7.11.1903, мировой посредник 2 отдела Новобаязетского уезда _ с 7.11.1903. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1884) и 2 ст. (1892), Св. Анны 3 ст. (1888) и 2 ст. (1895). Spisok, 1901: 101; Spisok, 1903: 79; Spisok, 1903, sen., SPb.: 613; Spisok, 1904: 65; Spisok, 1905, SPb.: 486. ЩЕРБАКОВ РОСТИСЛАВ ПАВЛОВИЧ (род. 1.10.1859), полковник. Воспитывался в Михайловской Воронежской военной гимназии, 3 военном Александровском училище, которое окончил по 1 разряду, выпускник Ни- колаевской Академии Генерального штаба, курс которой завершил по 2 раз- ряду. Службу начал 26.08.1877, произведен в прапорщики _ 8.08.1879, под- поручик _ 18.12.1880, поручик _ 4.12.1883, штабс-ротмистр _ 30.08.1890, подполковник _ 26.02.1901, за отличие по службе полковник _ 13.02.1907. Начальник отдела Минеральных Вод Владикавказского жандармского полицейского управления железных дорог _ 23.03.1896, и. д. начальника Бакинского жандармского управления _ 7.01.1907, начальник того же жан- дармского управления _ 19.02. _ 20.11.1907. В дальнейшем служил вне Кав- казского военого округа. Награжден орденами Св. Станислава 3 ст. (1898), Св. Анны 3 ст. (1904), Св. Владимира 4 ст. (1905). Spisok, 1907: 86; Spisok, 1907, ch. 3, SPb.: 111; Spisok, 1908: 80; Spisok, 1910, ch. 3, SPb.: 63; Spisok, 1912, ch. 3, SPb.: 49; Spisok, 1914, ch. 3, SPb.: 205. ЩЕРБИНА ГРИГОРИЙ ЯКОВЛЕВИЧ (род. 10.01.1855), полковник. Воспитывался в Михайловской Воронежской военной гимназии, Павлов- ском военном училище, которое окончил по 2 разряду, завершил курс Офи- церской кавалерийской школы. Службу начал 10.08.1872, награжден чином хорунжего _ 7.08.1874, участник Русско-Турецкой войны 1877-78, за боевое отличие сотник _ 9.07.1878, за отличия по службе есаул _ 6.05.1882, войско- вой старшина _ 14.05.1896 и полковник _ 20.11.1904. Командовал 2 Таманским (с 4.07.1901), 1 Хоперским Ее И. В. Вел. кн. Анастасии Михайловны (с 20.11.1904), 1 Лабинским ген. Засса (с 20.05.1906) полками Кубанского казачьего войска. 409 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV За военно-служебные заслуги награжден орденами Св. Владимира 4 ст. с бантом _ за 25 лет безупречной службы в офицерских чинах (1900), Св. Станислава 3 ст. (1899) и 2 ст. (1904), Св. Анны 2 ст. (1907). Кавалер персидского ордена Льва и Солнца 2 ст. (1900). Spisok, 1905: 83; Spisok, 1905, SPb.: 1093; Spisok, 1907: 65; Spisok, 1907, SPb.: 722; Spisok, 1908: 59. ЩЕТКИН НИКОЛАЙ ОСИПОВИЧ (ИОСИФОВИЧ) (род. 8.04.1860), полковник. Воспитывался в Николаевском инженерном училище, Нико- лаевской Академии Генерального штаба, которую окончил по 1 разряду. Произведен в подпоручики _ 8.08.1880, поручик _ 1.01.1885, награжден чином штабс-капитана _ 22.05.1891, капитан _ 28.03.1893, подполков- ник _ 5.04.1898, за отличие по службе полковник _ 14.02.1902 (в чине по 13.04.1908) (www.rusgeneral.ru). Штаб-офицер для поручений и астрономических работ при Военно-То- пографическом отделе Кавказского военного округа _ 2.06.1901 -28.04.1903. В дальнейшем служил вне Кавказского военного округа. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1886) и 2 ст. (1898), Св. Анны 3 ст. (1895). Spisok, 1903: 86; Spisok, 1903, sen., SPb.: 817; Spisok, 1905, SPb.: 676; Spisok, 1907, SPb.: 261. ЭГГЕРТ ВИКТОР ВИКТОРОВИЧ (род. 7.11.1867), полковник. Вос- питывался в Оренбургском Неплюева кадетском корпусе, Павловском во- енном училище, которое окончил по 1 разряду, выпускник Николаевской Академии Генерального штаба. Произведен в подпоручики _ 11.08.1886, поручик _ 11.08.1890, штабс-капитан _ 20.05.1893, капитан _ 2.04.1895, подполковник _ 6.12.1899, за отличие полковник _ 6.12.1903 (в чине по 3.03.1912) (www.rusgeneral.ru). С 1900 служил на Кавказе: штаб-офицер для поручений при штабе Кав- казского военного округа _ с 31.01.1900, старший адъютантом штаба того же округа _ 2.12.1900 _ 25.12.1903, штаб-офицер при управлении 66 пехот- ной резервной бригады _ с 25.12.1903, командир 77 пехотного Тенгинского Е. И. В. Вел. кн. Алексия Александровича полка _ c 21.01.1906. За военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1898), Св. Станислава 2 ст. (1899), Св. Анны 2 ст. (1902), Св. Владимира 4 cт. (1905) и 3 ст. (1909). Кавалер иностранных орденов: бухарского _ золотого ордена Благород- ной Бухары 3 ст. (1898), персидского _ Льва и Солнца 2 ст. (1902). 410 oTar Jordania Spisok, 1901: 163; Spisok, 1904: 81; Spisok, 1904, SPb.: 951; Spisok, 1905: 71; Spisok, 1907, SPb.: 583; Spisok, 1908: 46; Spisok, 1910: 42; Spisok, 1910, SPb.: 221; Spisok, 1911: 39; Spisok, 1912, SPb.: 104. ЭЛЛИОТ ФРИДРИХ ИВАНОВИЧ (род. 28.08.1849), полковник. Вос- питывался в 1 военном Павловском училище, произведен в прапорщики гвардии _ 26.02.1871, подпоручик _ 30.08.1872, поручик _ 4.04.1876, участ- ник Русско-Турецкой войны 1877-78, награжден орденами Св. Анны 4 ст., Св. Станислава 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бан- том (1878), штабс-капитан _ 30.08.1878, капитан _ 24.03.1885, полковник _ 30.08.1891 (в чине по18.12.1902) (www.rusgeneral.ru). Командир 82 пехотного Дагестанского Е. И. В. Вел. кн. Николая Михай- ловича полка _ с 9.11.1895 и начальник Грозненского военноо госпиталя _ с 26.08.1896. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1884), Св. Анны 2 ст. (1888), Св. Владимира 4 ст. (1891) и 3 ст. (1898). Spisok, 1897: 81; Spisok, 1900: 55; Spisok, 1900, SPb.: 157; Spisok, 1902: 46; Spisok, 1902, SPb.: 91. ЭЛЬСНЕР ЕВГЕНИЙ ФЕЛИКСОВИЧ (род. 12.12.1867), полковник. Воспитывался в Тифлисском кадетском корпусе, Михайловском артилле- рийском училище, окончил Николаевскую Академию Генерального штаба по 1 разряду. Произведен в подпоручики _ 11.08.1886, поручик _ 11.08.1890, награжден чином штабс-капитана _ 20.05.1895, капитан Генерального штаба _ 13.04.1897, подполковниик _ 1.04.1901, за отличие полковник _ 17.04.1905 (в чине по 10.04.1911) (www.rusgeneral.ru). В 1896 _ 1901 служил обер-офицером для поручений при штабе Кав- казского военного округа, старший адъютант там же - 1901-04, назначен началником штаба 6 округа Отдельного корпуса пограничной стражи _ 16.07.1904, непродолжительное время исполнял должность Ставропольско- го губернатора _ 20.02. - 25.08.1906. Затем служил вне Кавказского военно- го округа. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1897) и 2 ст. (1903), Св. Анны 3 ст. (1901). Кавалер персидского ордена Льва и Солнца 2 ст. (1903). Spisok, 1901: 176; Spisok, 1903: 145: Spisok, 1905: 87; Spisok, 1906, SPb.: 1060; Spisok, 1909, SPb.: 586; Spisok, 1911, SPb.: 381. ЭМИР-КАЗЫМ-МИРЗА (род. 1.05.1855), персидский принц, полковник Русской Императорской армии. Воспитывался в доме родителей, военной 411 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV кавалерийской Кавказской учебной роте, окончил Офицерскую кавалерий- скую щколу с оценкой «Успешно». Службу начал 16.12.1873, произведен в корнеты _ 16.12.1873, участник Русско-Турецкой войны 1877-78 (ранен в бою), поручик _ 3.05.1877, награжден орденами Св. Анны 4 ст. с надписью « За храбрость» (1877), Св. Станислава 3 ст. с мечами и бантом (1878), Св. Станислава 2 ст. с мечами (1879), Св. Анны 2 ст. с мечами (1881), штабс- ротмистр _ 24.03.1881, ротмистр _ 25.10.1882, подполковник - 26.02.1895, участник Русско-Японской войны 1904-05, полковник _ 6.12.1904 , за бое- вые отличия награжден золотым оружием (1906), мечами и бантом к ордену Св. Владимира 4 ст. (1907). Служил в 44 драгунском Нижегородском Е. В. полку, командирован в штаб Кавказского военного округа _ 22.11.1906. За другие военно-служебные заслуги награжден орденами Св. Анны 3 ст. (1879) и 2 ст. (1881), Владимира 4 ст. (1888). Кавалер иностранных орденов: персидского _ Льва и Солнца 4 ст. (1890) и 2 ст. с лентой (1901), бухарского _ золотого ордена Благородной Бухары 3 ст. (1895). Spisok, 1895: 188; Spisok, 1901: 125; Spisok, 1905, SPb.: 1102; Spisok, 1907: 66; Spisok, 1907, SPb.: 870; Spisok, 1908: 59. ЭНКЕЛ АКСЕЛЬ-ВОЛЬДЕМАР КАРЛОВИЧ (род. 4.09.1866), пол- ковник. воспитывался в Финляндском кадетском корпусе, окончил Ни- колаевскую Академию Генеральногго штаба по 2 разряду. Службу начал 11.04.1886, произведен в подпоручики _ 7.08.1885, поручик _ 7.08.1889, штабс-капитан _ 29.07.1895, капитан _ 6.05.1900, подполковник _ 26.02.1905, за отличие по службе полковник _ 3.12.1908. Служил старшим помощником Шушинского уездного начальника, и. д. Нахичеванского уездного начальника _ с 27.10.1900, и. д. мирового посред- ника 3 отдела Эчмиадзинского уезда _ с 22. 12.1905, Лечхумский уездный начальник Кутаисской губ. _ 31.01.1907. За военно-служебные заслуги награжден орденами Св. Владимира 4 ст. (1903), Св. Станислава 2 ст. (1907), Св. Анны 2 ст. (1909). Spisok, 1910: 80; Spisok, 1911: 72; Spisok, 1911, ch. 3, SPb.: 80; Spisok, 1914, SPb.: 344. ЭФЕНДИЕВ СУЛЕЙМАН-БЕК (род. 5.10.1864), полковник. Воспи- тывался в реальном и Елисаветпольском кавалерийском училищах. Службу начал 14.05.1885, произведен в корнеты _ 18.05.1887, поручик _ 18.05.1891, штабс-ротмистр _ 15.03.1896, ротмистр _ 15.03.1899, за отличия по службе подполковник _ 26.02.1908 и полковник _ 6.12.1912. 412 oTar Jordania В 1907-14: инспектор Закавказской полицейской стражи _ с 28.02.1907. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1900), Св. Анны 3, Св. Владимира 4 ст. (1908), Св. Анны 2 ст. (1909). Spisok, 1910: 168; Spisok, 1911: 157; Spisok, 1913, ch. 3, SPb.: 106; Spisok, 1914, SPb.: 1249. ЮДИН ПЕТР ИВАНОВИЧ (род. 24.08.1847), полковник. Воспиты- вался в Тифлисском пехотном юнкерском училище, с оценкой «Успеш- но» окончил Офицерскую стрелковую школу. Произведен в прапорщики _ 16.09.1871, подпоручик _ 30.11.1875, участник Русско-Турецкой войны 1877-78, поручик _ 8.07.1877, за боевое отличие штабс-капитан _ 19.02.1880, награжден чином капитана _ 12.05.1881, подполковник _ 26.02.1892, за слу- жебное отличие полковник _ 13.01.1903. В 1893-1904 служил в 80 пехотном Кабардинском ген.-фельдм. кн. Ба- рятинского полку, назначен командиром 7 Кавказского стрелкового батальо- на _ 29.07.1904. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1884) и 2 ст. (1896), Св. Анны 3 ст. (1889) и 2 ст. (1906), Св. Владимира 4 ст. с бантом (1897). Spisok, 1893: 238; Spisok, 1901: 116; Spisok, 1903: 91; Spisok, 1903, sen., SPb.: 933; Spisok, 1904: 76; Spisok, 1905: 66: Spisok, 1906, SPb.: 540; Spisok, 1907: 50. ЮНГЕР ВЛАДИМИР ГУСТАВОВИЧ (род. 28.08.1864), полков- ник. Воспитывался в Николаевском инженерном училище, окончил Ни- колаевскую инженерную Академию. Службу начал 13.09.1885, произве- ден в подпоручики _ 11.01.1886, поручик _ 11.08.1890, штабс-капитан _ 26.11.1892, капитан _ 6.12.1895, участник военной экспедиции 1900, на- гражден орденом Св. Станислава 3 ст. (1900), подполковник _ 3.12.1903, за служебное отличие полковник _ 11.03.1908 (в чине по 6.12.1914) (www.rusgeneral.ru). Командир Кавказского железнодорожного батальона _ 11.03.1908. За другие военно-служебные заслуги награжден орденами Св. Станис- лава 2 ст. (1905), Св. Анны 2 ст. (1911). Spisok, 1908: 84; Spisok, 1909, SPb.: 1001; Spisok, 1910: 75; Spisok, 1911: 68; Spisok, 1911, SPb.: 736; Spisok, 1914, SPb.: 293. ЮРОВ ДМИТРИЙ ВАСИЛЬЕВИЧ (род. 28.09.1855), полковник. Участ- ник Русско-Турецкой войны 1877-78, поручик _ 13.05.1877, за боевое отличие награжден чином штабс-капитана _ 12.04.1878 и орденами Св. Станислава 413 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бантом (1877), Св. Вла- димира 4 ст. с мечами и бантом, Св. Анны 4 ст. (1878), Св. Станислава 2 ст. с мечами (1879), капитан _ 16.071881, за отличия по службе награжден чинами подполковника - 1.01.1889 и полковника _ 30.08.1894 (в чине по 6.04.1903) (www.rusgeneral.ru). С 1879 занимал различные адъютантские должности в Кавказском во- енном округе: старший адъютант штаба округа _ 1888-1900, и. д. комендан- та и начальника военного госпиталя Абас-Тумана (Абастумани). За другие военно-служебные заслуги награжден орденами .Св. Анны 2 ст. (1884), Св. Владимира 3 ст. (1896). Spisok, 1895: 113; Spisok, 1900: 68; Spisok, 1900, SPb.: 358; Spisok, 1902: 155; Spisok, 1902, SPb.: 226; Spisok, 1903: 54. ЯГИМОВСКИЙ ФЕРДИНАНД-ИВАН АВГУСТИНОВИЧ (род. 30.05.1852), полковник. Произведен в поручики _ 13.04.1875, участник Русско-Турецкой войны 1877-78 (ранен в бою), штабс-капитан- 30.08.1878, награжден орденами Св. Станислава 3 ст. с мечами и бантом (1877), Св. Анны 3 ст. с мечами и бантом, Св. Станислава 2 ст. с мечами и Св. Влади- мира 4 ст. с мечами и бантом (1878), капитан _ 30.08.1883, подполковник _ 30.08.1890, в запасе _ 16.05.1895-4.04.1896, полковник _ 4.04.1896 (в чине по 1907) (www.rusgeneral.ru). Командир 256 Гунибского резервного батальона _ 9.05.1897-8.05.1902. В последующие годы служил за пределами Кавказского военного округа. За военно-служебные заслуги награжден орденами Св. Анны 2 ст. (1887), Св. Владимира 3 ст. (1900). Кавалер иностранных орденов: Прусской Короны 3 ст. с мечами (1881), персидского _ Льва и Солнца 2 ст. (1903). Spisok, 1899: 89; 1900; 78; Spisok, 1900, SPb.: 526; Spisok, 1904, SPb.: 170; Spisok, 1906, SPb.: 63. ЯГОДКИН ПАВЕЛ ЯКОВЛЕВИЧ (род. 2.06.1867), полковник. Вос- питывался в Ставропольской гимназии, Московском пехотном юнкерском училище, окончил Николаевскую Академию Генерального штаба по 1 раз- ряду. Службу начал 22.09.1887, произведен в хорунжие _ 9.08.1888, сот- ник _ 9.08.1892, подъесаул _ 19.05.1897, капитан _ 18.04. подполковник _ 6.04.1903, за отличие по службе полковник _ 22.04.1907 (в чине по 1913) (www.rusgeneral.ru). С 1910 службу проходил в Кавказском военном округе: командир 1 Ека- теринодарского кошевого атамана Ченеги полка Кубанского казачьего во- йска _ с 28.07.1910. 414 oTar Jordania За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1901) и 2 ст. (1910), Св. Анны 3 ст. (1905). Spisok, 1907, SPb.: 1207; Spisok, 1909, SPb.: 882; Spisok, 1911: 63; Spisok, 1911, SPb.: 628; Spisok, 1913, SPb.: 337. ЯЖИНСКИЙ НИКОЛАЙ НЕСТОРОВИЧ (род. 2.02.1864), полков- ник. Воспитывался в Александровской гимназии, Михайловском артилле- рийском училище, окончил Михайловскую артиллерийскую Академию по 1 разряду и Офицерскую артиллерийскую школу с оценкой «Успешно». Службу начал 31.08.1882, подпоручик _ 12.08.1882, поручик _ 12.08.1887, награжден чином штабс-капитана _ 7.06.1890, капитан, штабс-капитан гвардии _ 2.04.1895, капитан гвардии- подполковник _ 6.12.1897, награж- ден орденом Св. Анны 3 ст. (1903), участник Русско-Японской войны 1904- 05, награжден орденом Св. Станислава 2 ст. с мечами (1905), за отличие по службе полковник _ 19.05.1910 (в чине по 3.06.1917) (www.rusgeneral.ru). Командир 6 батареи 21 Артиллерийской бригады _ 13.03.1906- 19.05.1910, командовал 1 дивизионом той же бригады _ 20.04.1912, 2.02.1914. Spisok, 1908: 87; Spisok, 1910: 93; Spisok, 1911: 84; Spisok, 1911: 1140; Spisok, 1914, SPb.: 609. ЯЗЫКОВ АЛЕКСАНДР ПЕТРОВИЧ (род. 28.05.1859), полковник. Произведен в подпоручики _ 30.08.1884, поручик _ 6.02.1885, штабс- капитан _ 9.03.1890, капитан _ 1.04.1890, за отличие по службе полковник _ 21.01.1898 (в чине по 2.04.1906) (www.rusgeneral.ru). Начальник Закатальского округа (по 24.02.1903), помощник военных губернаторов Дагестанской обл. _ 24.02.1903-8.11.1904 и Батумской обл. _ с 8.11.1904. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1891) и 2 ст. (1901), Св. Владимира 4 ст. (1895), Св. Анны 2 ст. (1904). Spisok, 1899: 97; Spisok, 1900: 85; Spisok, 1900, SPb.: 654; Spisok, 1903: 65; Spisok, 1903, sen., SPb.: 342; Spisok, 1904: 54; Spisok, 1904, SPb.: 258; Spisok, 1905, SPb.: 225. ЯКОБИ ФЕДОР НИКОЛАЕВИЧ (род. 28.06.1847), полковник. Вос- питывался в 1 кадетском корпусе и 1 военном Павловском училище. Про- изведен в прапорщики артиллерии _ 20.10.1868, подпоручик _ 31.09.1869, поручик _ 31.10.1871, штабс-капитан _ 29.12.1873, капитан _ 26.12.1877, подполковник _ 7.02.1890, полковник _ 30.12.1899. Командир 1 дивизиона 21 Артиллерийской бригады _ с 30.12.1899. 415 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1874) и 2 ст. (1884), Св. Анны 3 ст. (1880) и 2 ст. (1896), Св. Владимира 4 ст. (1892). Spisok, 1900: 96; Spisok, 1900, SPb.: 841; Spisok, 1901: 94; Spisok, 1903: 74; Spisok, 1903, sen., SPb.: 516, Spisok, 1904: 60; Spisok, 1904, SPb: 426; Spisok, 1905, SPb.: 387. ЯКОВЛЕВ АЛЕКСАНДР КОНСТАНТИНОВИЧ (род. 13.11.1862), полковник. В офицерских чинах с 1882. За отличие по службе награжден чином войскового старшины _ 26.02.1903, полковник _ 6.05.1909. В 1904-07 служил адъютантом, затем старшим адъютантом штаба Кавказского военного округа, назначен командиром 2 Волгского полка _ 6.01.1907, командовал льготным составом того же полка _ 30.07.1908, командир 2 Кизляро-Гребенского полка Терского казачьего войска _ с 4.01.1909. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1885) и 2 ст. (1905), Св. Анны 3 ст. (1899). Spisok, 1904: 140; Spisok, 1905: 117; Spisok, 1909: 127; Spisok, 1909, SPb.: 301; Spisok, 1910: 87; Spisok, 1911: 79. ЯКУТИН ВЛАДИМИР ПАВЛОВИЧ (род. 7.08.1847), полковник. В офицерских чинах с 1871. За отличие по службе награжден чином штабс- капитана _ 26.06.1872, участник Русско-Турецкой войны 1877-78, капитан _ 28.06.1877, награжден орденами Св. Владимира 4 ст. с мечами и бантом (1877), Св. Станислава 2 ст. с мечами (1878), золотым оружием (1877), участник военной экспедиции 1881, за отличия награжден чинами подпол- ковника _ 1.01.1885 и полковника _ 26.05.1897. Командир: 4 Кавказского стрелкового батальона _ 6.05.1897-15.12.1899; 263 пехотного резервного Новобаязетского полка _ 15.12.1899 - 27.02.1904. В дальнейшем службу проходил вне Кавказского военного округа. За другие военно-служебные заслуги награжден орденом Св. Анны 2 ст. (1888). Кавалер иностранных орденов: бухарского _ золотого Благородной Бу- хары 2 ст. (1900), персидского _ Льва и Солнца 2 ст. (1902). Spisok, 1899: 94; Spisok, 1900: 82; Spisok, 1900, SPb.: 619; Spisok, 1901: 83; Spisok, 1903: 64; Spisok, 1903, sen., SPb.: 314; Spisok, 1905, SPb.: 200. ЯНКОВСКИЙ КАЗИМИР ИГНАТЬЕВИЧ (род. 15.02.1839), полков- ник. Военный инженер. Окончил Николаевскую инженерную Академию по 1 разряду. Произведен в подпоручики _ 22.07.1859, поручик _ 14.09.1860, 416 oTar Jordania штабс-капитан _ 17.04.1863, подполковник _ 24.05.1876, участник кампа- нии 1877, награжден орденом Св. Анны 2 ст. с мечами (1878), за отличие полковник _ 20.04.1880. Начальник Терской инженерной дистанции _ 16.06.1878-1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1868) и 2 ст. (1873), Св. Анны 3 ст. (1871), Св. Владимира 4 ст. _ за 25 лет образцовой службы в офицерских чинах (1885) и 3 ст. (1886), Знаком отли- чия за 40 лет образцовой службы (1899). Кавалер ордена Благородной Бухары 2 ст. (1898). Spisok, 1900, SPb.: 7; Spisok, 1902, SPb.: 7; Spisok, 1903, sen., SPb.: 4; Spisok, 1906, SPb.: 3. ЯННАУ ПАВЕЛ КОНСТАНТИНОВИЧ (род. 6.11.1851), полковник. Участник Русско-Турецкой войны 1877-78 и военной экспедиции 1879, подпоручик _ 12..06.1877, за боевое отличие поручик _ со старшинством с 28.08.1879, награжден орденами Св. Станислава 3 ст с мечами и бантом, Св. Анны 3 ст. с мечами и бантом (1878), за отличия по службе штабс-капитан _ 4.11.1882, капитан _ 26.02.1886, подполковник _ 1.01.1891, полковник _ 6.12.1895 (в чине по 1905) (www.rusgeneral.ru). Старший помощник старшего адъютанта штаба Кавказского воен- ного округа _ с 29.09.1884, старший адъютант того же военного округа _ 21.09.1894-17.01.1905, назначен начальником Тифлисского военного госпи- таля _ 17.01.1905. За военно-служебные заслуги награжден орденами Св. Станислава 2 ст. (1898), Св. Анны 2 ст. (1901). Кавалер персидского ордена Льва и Солнца 2 ст. (1903). Spisok, 1902, SPb.: 328; Spisok, 1903, sen., SPb.: 204; Spisok, 1905, SPb.: 117. ЯРЧЕНКО ЕФИМ ИВАНОВИЧ (род. 1.04.1857), полковник. Вос- питывался дома и Тифлисском пехотном юнкерском училище. Службу начал 4.12.1873, произведен в прапорщики _ 16.04.1878, участник во- енных экспедиций 1879-1881, награжден орденами Св. Станислава 3 ст. с мечами и бантом, Св. Анны 3 ст. с мечами и бантом (1881), подпоручик _ 19.02.1881, поручик _ 19.02.1885, штабс-капитан _ 15.03.1891, капи- тан _ 15.03.1896, участник Русско-Японской войны 1904-05, награжден орденом Св. Станислава 2 ст. (1905), подполковник _ 26.02.1905, полков- ник _ 6.12.1910. С 1873 службу проходил в 84 пехотном Ширванском Е. В. полку. За военно-служебные заслуги награжден орденами Св. Владимира 4 ст. с бантом (1904), Св. Анны 2 ст. (1910). 417 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Spisok, 1905: 148; Spisok, 1910: 127; Spisok, 1911: 96; Spisok, 1912, SPb.: 1293; Spisok, 1913, SPb .: 903. ЯСНОПОЛЬСКИЙ ГРИГОРИЙ ПЕТРОВИЧ (род. 21.02.1862), пол- ковник. Воспитывался в Императорском Гатчинском сиротском институте и 1 военном Павловском училище, которое окончил по 1 разряду. Служ- бу начал 31.08.1881, произведен в подпоручики _ 12.08.1883, поручик _ 12.08.1887, штабс-капитан _ 24.03.1896, капитан _ 5.04.1898, подполковник _ 1.04.1901, за отличие по службе награжден чином полковника _ 6.12.1905. С 1904 служил на Кавказе; состоял для поручений Кавказского окруж- ного интендантского управления _ с 1.06.1904, начальник отдела там же _ c 6.12.1905, главный смотритель Ставропольского вещевого склада Кавказ- ского военного округа _ с 28.10.1906. За военно-служебные заслуги награжден орденами Св. Станислава 3 ст. (1897), Св. Анны 3 ст. (1901). Spisok, 1907: 74; Spisok, 1907, ch. 3, SPb.: 63; Spisok, 1908: 67; Spisok, 1910: 60; Spisok, 1910, ch., 2, SPb.: 31. Список использованных и учтенных источников: 1. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 22-e yanvarya 1885 goda. Tiflis, 1885. 2. Spisok generalam i shtab-ofitseram Kavkazskoy armii i voisk k onym prikomandirovannikh. Ispravlen po 28-e ynvarya 1886 goda. Tiflis, 1886. 3. Spisok generalam i shtab-ofitseram Kavkazskoy armii i voisk k onym prikomandirovannikh. Ispravlen po 6-e marta 1887 goda. Tiflis, 1887. 4. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 25-e fevralya 1889 goda. Tiflis, 1889. 5. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 15-e fevralya 1890. Tiflis, 1890. 6. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 10-e fevralya 1891 goda. Tiflis, 1891. 7. Spisok generalam i stab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 1-e marta 1893 goda. Tiflis, 1893. 8. Spisok generalam i stab-ofitseram Kavkazskogo voennogo okruga. Isphavlen po 1-e marta 1894 goda. Tiflis, 1894. 9. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 15-e aprelya 1895 goda. Tiflis, 1895. 10. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 15-e aprelya 1897 goda. Tiflis, 1897. 418 oTar Jordania 11. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 7-e maya 1899 goda. Tiflis, 1899. 12. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 9-e aprelya 1900 goda. Tiflis, 1900. 13. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 9-e maya 1901. Tiflis, 1901. 14. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 20-e marta 1902 goda. Tiflis, 1902. 15. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 1-e marta 1903 goda. Tiflis, 1903. 16. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 1-e aprelya 1904 goda. Tiflis, 1904. 17. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 1-e sentyabrya 1905 goda. Tiflis, 1906. 18. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 17-e fevralya 1907 goda. Tiflis, 1907. 19. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 15-e marta 1908 goda. Tiflis, 1908. 20. Spisok generalam i shtab-ofitseram Kavkazskogo voennogo okruga. Ispravlen po 1-e yanvarya 1910 goda. Tiflis, 1910. 21. Spisok generalam i shtab-ofitseram Kavkazskogo voenngo okruga. Ispravlen po 1-e maya 1911 goda. Tiflis, 1911. 22. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e sentyabrya 1900, SPb., 1900. 23. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e maya 1901, SPb., 1901. 24. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e ynvarya 1902, SPb., 1902. 25. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e yanvarya 1903, SPb., 1903. 26. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e maya 1903. SPb., 1903. 27. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e sentyabrya. 1903, SPb., 1903. 28. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e sentyabrya 1904, SPb., 1904. 29. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e yanvarya. 1905, SPb., 1905. 30. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e noyabrya. 1907, SPb., 1907. 31. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e noyabrya 1907, SPb., 1907. 32. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e noyabrya 1909, SPb., 1909. 33. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e marta 1910, SPb., 1910. 34. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e marta 1911, SPb., 1911. 35. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e marta 1912, SPb., 1912. 36. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e marta 1913, SPb., 1913. 419 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV 37. Spisok polkovnikam po starshinstvu. Sostavlen po 1-e marta 1914, SPb., 1914. 38. Spisok polkovnikam po starshinstvu. Na 1 avgusta 1916, Pt., 1916. 39. Spisok generalam po starshinstvu.Ch. I _ III. Sostavlen po 1-e iylya. 1913, SPb., 1913. 40. Spisok generalam po starshinstvu. Ispravlen po 19-e iylya 1916, Pt., 1916. 41. Spisok podpolkovnikam po starshinstvu. Sostavlen po 25-e fevralya 1901, SPb., 1901. 42. Spisok podpolkovnikam po starshinstvu. Ch. I-III. Sostavlen po 1-e marta 1909, SPb., 1909. 43. Spisok podpolkovnikam po starshinstvu. Ch. I-III. Sostavlen po 15-e maya 1913. SPb., 1913. 44. www.rusgeneral.ru 45. www.ourbaki.com 46. www.grwar.ru 420 oTar Jordania kavkasiis armia oficerTa biografiebSi polkovnikebi (1901-1914 ww.) reziume naSromSi Seswavlilia im polkovnikebis biografiebi, romle- bic 1901-1914 ww. samxedro samsaxurs gadiodnen kavkasiis armia- Si. 1901-1911 ww. kavkasiis samxedro olqis generalTa da Stab- oficerTa `siebis~ mixedviT kavkasiis armiaSi msaxurobda 1901 w. (maisi) aranakleb 235, 1903 w. (1 marti) _ 229, 1904 (1 aprili) _ 218, 1905 w. (1 seqtemberi) _ 221, 1907 w. (Tebervali) _ 257, 1908 w. (mar- ti) _ 249, 1910 w. (1 ianvari) _ 276, 1911 w. (1 maisi) _ 270 polkoniki. kavkasiis armiis polkovnikebi monawileobdnen 1877-1878 ww. ruseT-TurqeTis, 1904-05 ww. ruseT-iaponiis omebSi, Sua aziis da- pyrobaSi, CineTSi laSqrobasa da sxva samxedro kampaniaSi. samxe- dro brZolebSi gamoCenili mamacobisaTvis 30-ze met polkovniks miRebuli hqonda wminda giorgis IV xarisxis ordeni. 1901-1914 ww. sagrZnoblad gaizarda oficerTa ganaTle- bis done. aRniSnul periodSi kavkasiis armiaSi msaxurobda ara nakleb 179 polkovniki, romelTac umaRlesi samxedro ganaTle- ba miRebuli qondaT nikolozis generaluri Stabis (101 ofice- ri), nikolozis sainJinero (45), aleqsandres samxedro-iuridiuli (18), moskovis saartilerio (15) akademiebSi. polkovnikTa Soris iyvnen agreTve moskovisa da varSavis universitetebis, moskovis arqeologiuri, aRmosavluri enebis, teqnologiuri institutebis kursdamTavrebulni. 1901-1914 ww. kavkasiis armiis polkovnikebdan 325 oficeri ru- seTis armiis cnobili moRvawe gaxda. maT Soris 6 infanteriis generali, 5 _ kavaleriis generali, 1 _ artileriis generali, 67 _ general-leiteneti da 246 _ general-maiori. 421 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Otar Zhordania CAUCASUS ARMY IN THE OFFICERS’ BIOGRAPHIES COLONELS (1901-1914) Summary Biographies of those colonels are studied in the work, who served during 1901-1914 years in Caucasian Army. According to the Caucasian military region Colonels’ and Staff-officers’ “lists”, at least 235 served in Caucasian Army in 1901 (1 May), 229 _ in 1903 (1 March), 218 _ in 1904 (1 April), 221 _ in 1905 (1 September), 257 _ in 1907 (February), 249 _ in 1908 (March), 276 _ in 1910 (1 January), 270 _ in 1911 (1 May). Caucasian Army Colonels took part in Russia-Turkey 1877-1878, Russia- Japan 1904-05 wars, in conquest of Middle Asia, in marching through China and other military campaigns. For bravery displayed in military battles, more than 30 colonels had Fourth Degree order of Saint George. In 1901-1914 the level of education amongst the officers increased signifi- cantly. In aforementioned period at least 179 colonels served in Caucasian Army, who received higher military education at General headquarters of Nicholas (101 officers), Nicholas engineering (45), at Aleksandre Military-Law (18), Moscow artillery (15) Academies. Among the colonels also were the graduates of Moscow and Warsaw Universities, Moscow Archeological, Eastern Languages, Technical Universities. In 1901-1914, from the Caucasian Army colonels 325 officers, became the prominent figures of Russian Army. Including 6_ Infantry Generals, 5 _ Cavalry Generals, 1 Artillery General, 67 _ General Lieutenants and 246 General Majors. 422 avtorTa Sesaxeb adamia zoia, filologiis doqtori, cxum-afxazeTis mecniere baTa akademiis rusuli enisa da literaturis institutis wamyva ni mecnieri TanamSromeli, eqvTime TayaiSvilis saswavlo univer sitetis profesori; alania diana, filologiis mecnierebaTa doqtori, cxum-afxa zeTis mec. akademiis rusuli enisa da literaturis institutis direqtori, soxumis saxelmwifo universitetis profesori; amaRlobeli xaTuna, filosofiis doqtori, soxumis saxelmwi fo universitetis asocirebuli porfesori; arqimandriti Sio (kvaracxelia), Tbilisis samebis taZari; bendeliani medea, istoriis doqtori, soxumis saxelmwifo universitetis asistent-profesori, cxum-afxazeTis mecniere baTa akademiis religiaTmcodneobis institutis wamyvani mecnie ri TanamSromeli; gabedava meri, istoriis doqtori, cxum-afxazeTis mecniere baTa akademiis mTavari swavluli mdivani, soxumis saxelmwifo universitetis asocirebuli profesori; gaxokiZe ramaz, ivane javaxiSvilis saxelobis Tbilisis saxel mwifo universiteti; daviTaSvili TinaTin, ivane javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti; esebua eka, biologiis doqtori, soxumis saxelmwifo universi tetis asistent-profesori; vardoSvili eka, filologiis doqtori, ivane javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis asocirebuli profesori, cxum-afxazeTis mecnierebaTa akademiis wevr-kores pondenti; zarandia jandri, soxumis saxelmwifo universitetis asoci rebuli profesori, ekonomikis akademiuri doqtori; TavxeliZe ilia, ivane javaxiSvilis saxelobis Tbilisis saxelmwifo universiteti, zust da sabunebismetyvelo mecnie rebaTa fakulteti, maTematikis departamenti; kvaracxelia medea, filologiis doqtori, soxumis saxelmwi fo universiteti; mania qeTevan, istoriis doqtori; marRania joni, filologiis doqtori, soxumis saxelmwifo universiteti; maxaraSvili irma, biznesis administrirebis akademiuri do 423 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV qtori, kavkasiis saerTaSoriso universitetis dekani; melaZe hamlet, wminda andria pirvelwodebulis qarTuli uni versiteti. saqarTvelo; melaZe iulia, wminda andria pirvelwodebulis qarTuli uni versiteti, Tbilisi, saqarTvelo; meunargia Tengiz, ivane javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis ilia vekuas saxelobis gamoyenebiTi maTematikis instituti; msxilaZe antonina, qimiis akademiuri doqtori, soxumis saxel mwifo universitetis sabunebismetyvelo mecnierebebisa da jan dacvis fakulteti, qimiis mimarTuleba; mosia tite, filologiis mecnierebaTa doqtori, soxumis saxel mwifo universitetis profesori, cxum-afxazeTis mecnierebaTa akademiis qarTuli enisa da literaturis institutis direqtori; pavliaSvili qeTevan, istoriis mecnierebaTa doqtori, profe sori, cxum-afxazeTis mecnierebaTa akademiis religiaTmcodneo bis institutis direqtori; pinelasi sandra, samxedro akademia, zust da sabunebismetyve lo mecnierebaTa departamenti, amadora, portugalia; Jordania oTari, istoriis mecnierebaTa doqtori, profes ori, cxum-afxazeTis mecnierebaTa akademiis d. gulias saxelobis istoriis, enisa da kulturis institutis direqtori; svaniZe lia, fsiqologiis doqtori,soxumis saxelmwifo uni versitetis asocirebuli profesori, cxum-afxazeTis mecniere Ta akademiis pedagogikisa da fsiqologiis institutis wamyvani mecnier-TanamSromeli; sulava leila, fizika-maTematikis mecnierebaTa akademiuri doqtori, soxumis saxelmwifo universiteti; tabataZe lali, qimiis akademiuri doqtori, soxumis saxelmwi fo universitetis sabunebismetyvelo mecnierebebisa da jandac vis fakulteti, qimiis mimarTuleba; uSveriZe nona, filologiis doqtori, cxum-afxazeTis mecnie rebaTa akademiis ucxo enaTa institutis direqtori; faCulia zurab, qimiis akademiuri doqtori, soxumis saxelmwi fo universitetis sabunebismetyvelo mecnierebebisa da jandac vis fakulteti, qimiis mimarTuleba; qarCava gulnara, biologiis mecnierebaTa doqtori, soxumis saxelmwifo universitetis profesori, cxum-afxazeTis mecniere baTa akademiis biologiisa da ekologiis institutis direqtori; Rvinjilia cira, baTumis saxelmwifo universiteti; 424 Selia manana, ganaTlebis doqtori, soxumis saxelmwifo univer siteti, cxum-afxazeTis mecnierebaTa akademiis ucxo enaTa insti tutis wamyvani mecnier-TanamSromeli; Sengelia naTia, soxumis saxelmwifo universiteti; CilaCava Temur, fizika-maTematikis mecnierebaTa doqtori, cxum-afxazeTis mecnierebaTa akademiis vice-prezidenti, soxu mis saxelmwifo universitetis gamoyenebiTi maTematikis profe sori; wereTeli avTandil, istoriis magistri; cicqiSvili marat, biologiisa da fizika-maTematikis mecnie rebaTa doqtori, soxumis saxelmwifo universitetis asocirebu li profesori. saqarTvelos ekologiur mecnierebaTa akademiis prezideti; cicqiSvili mariam, ekologiis mimarTulebis doqtoranti, soxumis saxelmwifo universiteti; Wanturia mineda, qimiis akademiuri doqtori, soxumis saxel mwifo universitetis sabunebismetyvelo mecnierebebisa da jan dacvis fakulteti, qimiis mimarTuleba, cxum-afxazeTis mecnie rebaTa akademiis qimiis institutis direqtori; xuxua gulnazi, pedagogikis mecnierebaTa doqtori, cxum- afxazeTis mecniereTa akademiis pedagogikisa da fsiqologiis institutis direqtori, soxumis saxelmwifo universitetis pro fesori; jaiani marine, filologiis doqtori, soxumis saxelmwifo universiteti; jinjixaZe giorgi, pedagogikis doqtori, soxumis saxelmwifo universiteti; jinjixaZe jemal, pedagogikis mecnierebaTa doqtori, soxumis saxelmwifo universitetis profesori, cxum-afxazeTis mecnie rebaTa akademiis akademikosi. 425 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV OUTHORS Adamia Zoia, PhD (Philology), Professor at E. Takaishvili Teaching Uni- versity, Leading Scientific Worker of Institute of Russian Language and Litera- ture, at Tskhum-Abkhazian Academy of Sciences; Alania Diana, Doctor of Sciences (Philology), Director of Institute of Rus- sian Language and Literature at Tskhum-Abkhazian Academy of Sciences; Amaghlobeli Khatuna, PhD of Philosophy, Associate Professor of Sokhumi State University; Archimandrite Shio (Kvaratskhelia), Tbilisi Trinity Cathedral; Bendeliani Medea, PhD (History), Assistant Professor at Sokhumi State University, Leading Scientific Worker Religion Studies Institute at Tskhum-Ab- khazian Academy of Sciences; Chanturia Mineda, PhD (Chemistry), Direction of Chemistry of Natural Sciences and Health Faculty of Sokhumi State University, Director of Institute of Chemistry at Tskhum-Abkhazian Academy of Sciences; Chilachava Temur, Doctor of Sciences (Physics - Mathematics), Vice-Pres- ident of Tskhum-Abkhazian Academy of Sciences, Professor at Sokhumi State University, Tbilisi, Georgia; Davitashvili Tinatin, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia; Esebua Eka, PhD (Biology), Assistant Professor at Sokhumi State University; Gabedava Meri, PhD (History), Chief Scientific Secretary of Tskhum-Abkha- zian Academy of Sciences, Associate Professor of Sokhumi State University; Gakhokidze Ramaz , Ivane Javakhishvili Tbilisi State University; Gvinjilia Tsira, Batumi state Maritime Academy, Batumi, Georgia; Jaiani Marine, PhD (Philology), Sokhumi State University; Jinjikhazde Giorgi, PhD (Pedagogy), Sokhumi State University; Jinjikhadze Jemal, Doctor of Sciences (Pedagogy), Professor of Sokhumi State University, Leading Scientist of Pedagogy and Psychology Institute at Tskhum-Abkhazian Academy of Sciences, Academician; Karchava Gulnara, Doctor of Sciences (Biology), Professor at Sokhumi State University, Director of Institute of Biology and Ecology at Tskhum-Abkha- zian Academy of Sciences, Academician; Khukua Gulnaz, PhD (Pedagogy), Professor of Sukhumi State University, Director of Institute of Pedagogy and Psychology Institute at Tskhum-Abkhazian Academy of Sciences; Kvaratskhelia Medea, PhD (Philology), Sokhumi State University; Mania Ketevan, PhD (History); Marghania Joni, PhD (Philology), Sokhumi State University; 426 Makharashvili Irma, PhD (Business Administration), Dean at Caucasus International University; Meladze Hamlet, St. Andrew the First Called Georgian University, Tbilisi, Georgia; Meladze Iulia, St. Andrew the First Called Georgian University, Tbilisi, Georgia; Meunargia Tengiz, Ilia Vekua Institute of Applied Mathematics at Ivane Javakhishvili Tbilisi State University; Mosia Tite, Doctor of Sciences (Philology), Professor at Sokhumi State University, Director of Institute of Georgian Language and Literature at Tskhum- Abkhazian Academy of Sciences; Mskhiladze Antonina, PhD (Chemistry), Direction of Chemistry of Natural Sciences and Health Faculty of Sokhumi State University; Pachulia Zurab, PhD (Chemistry), Direction of Chemistry of Natural Sci- ences and Health Faculty of Sokhumi State University; Pavliashvili Ketevan, Doctor of Sciences (History), Professor, Director of Religion Studies Institute at Tskhum-Abkhazian Academy of Sciences; Pinelas Sandra, Military Academy,Department of Exact and Natural Sci- ences; Portugal; Shelia Manana, PhD (Pedagogical Sciences), Professor at Sokhumi State University, Leading Research Worker of Foreign Languages Institute at Tskhum- Abkhazian Academy of Sciences; Shengelia Natia, Sokhumi State University; Sulava Leila, PhD (Physics -Mathematics), Sokhumi State University; Svanidze Lia, PhD (Psychology), Associate Professor of Sukhumi State University, Leading Research Worker of Pedagogy and Psychology Institute at Tskhum-Abkhazian Academy of Sciences; Tabatazde Lali, PhD (Chemistry), Direction of Chemistry of Natural Sci- ences and Health Faculty of Sokhumi State University; Tavkhelidze Ilia, Ivane Javakhishvili Tbilisi State University, Faculty of Ex- act and Natural Sciences, Department of Mathematics; Tsereteli Avtandil, Master of History; Tsitskishvili Marat, Doctor of Sciences (Biology; Physics - Mathematics), Associate Professor at Sokhumi State University, President of Ecological Sci- ences Academy of Georgia; Tsitskishvili Mariam, Doctoral Student (Ecology), Sokhumi State University; Ushveridze Nonna (Nazi), PhD (Philology), Director of Institute of Foreign Languages at Tskhum-Abkhazian Academy of Sciences; Vardoshvili Eka, PhD (Philology), Associate Professor of Ivane Javakhish- vili Tbilisi State University, Corresponding Member of Tskhum-Abkhazian Acad- 427 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV emy of Sciences; Zarandia Jandri, PhD (Economics), Associate Professor of Sokhumi State University, Leading Research worker of Economics and Business Administration Institute at Tskhum-Abkhazian Academy of Sciences; Zhordania Otar, Doctor of Sciences (History), Director of D. Gulia In- stitute of History, Language and Culture at Tskhum-Abkhazian Academy of Sci- ences. 428 sarCevi ilia vekua _ 110 Ilia Vekua _ 110 Temur CilaCava akademikos ilia vekuas cxovreba da moRvaweoba...... 6 Academician Ilia Vekua ...... 17 Tengiz meunargia eZRvneba akademikos ilia vekuas 110 wlisTavs...... 20 Tengiz Meunargia It is Devoted to the 110 Anniversary of the Academician Iliya Vekua ...... 27 gamoyenebiTi maTematika Applied Mathematics Sandra Pinelas, Ilia Tavkhelidze Some Remarks about Bulk links Which Appear afterCutting of Generalalized Mobius-Listing’s Bodies n ...... 28 GML6 sandra pinelasi, ilia TavxeliZe SeniSvnebi n _ ganzogadebuli mebius-listingis gaWris GML6 Sedegad warmoqmnili moculobiTi xlarTebis Sesaxeb...... 48 Tinatin Davitashvili, Hamlet Meladze, Iulia Meladze Nonlocal Contact Problem for Nonhomogeneous Second order Ordinary Differential Equations...... 49 TinaTin daviTaSvili, hamlet melaZe, iulia melaZe aralokaluri sakontaqto amocana meore rigis araerTgvarovani diferencialuri gantolebebisaTvis...... 58 maTematikuri modelireba Mathematical Modeling Temur Chilachava About Some First Integrals of Nonlinear System of the Differential Equations Describing Process of Two_Level Assimilation...... 59 Temur CilaCava ordoniani asimilaciis procesis aRmweri arawrfivi diferencialuri gantolebaTa sistemis zogierTi pirveli integralebis Sesaxeb...... 78 429 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV Temur Chilachava, Tsira Gvinjilia About Some Exact Solutions of Nonlinear Systems of Differential Equations Describing Interference of Fundamental and Applied Reaserches ...... 79 Temur CilaCava, cira Rvinjilia fundamenturi da gamoyenebiTi kvlevebis urTierTgavlenis aRmweri arawrfivi diferencialuri gantolebaTa sistemis zogierTi zusti amonaxsnis Sesaxeb ...... 91 maTematikuri da kompiuteruli modelireba Mathematical and Computer Modeling nugzar kereseliZe informaciuli omis gaerTianebuli maTematikuri da kompiuteruli modelebi...... 92 Nugzar Kereselidze The United Matematical and Computer Models of Information Warfare ...... 107 Leila Sulava Computer Modeling of Three-Party Elections Taking into Account Demografic Factor...... 110 leila sulava sampartiuli arCevnebis kompiuteruli modelireba demografiuli faqtoris gaTvaliswinebiT...... 124 qimia Chemistry Mineda Chanturia, Antonina Mskhiladze Some Aspects of Problem-Based Teaching in the Chemical Kinetics...... 125 mineda Wanturia, antonina msxilaZe problemaze dafuZnebuli qimiuri kinetikis swavlebis zogierTi aspeqti ...... 136 Natia Shengelia, Zurab Pachulia, Lali Tabatazde, Ramaz Gakhokidze Modelling of the Glycolsylation Principle by Quantum-Chemical Method...... 138 naTia Sengelia, zurab faCulia, lali tabataZe, ramaz gaxokiZe kvantur-qimiuri meTodiT glikozilirebis principis modelireba...... 146 430 ekologia Ecology Marat Tsitskishvili, Gulnara Karchava, Mariam Tsitskishvili, Eka Esebua Regional Parameterisation of Atmospheric Transfer for Reduction Radioactive Pollution ...... 147 marat cicqiSvili, gulnara qarCava, mariam cicqiSvili, eka esebua atmosferuli gadatanis regionaluri parametrizacia radiaciuli daWuWyianebis Sesamcireblad...... 152 enaTmecniereba Linguistics manana Selia toponimuri warmoSobis ferTa Seferilobebi Tanamedrove inglisur enaSi...... 153 Manana Shelia Colour Shades of Toponymic Origin in Modern English Language...... 163 Nonna Ushveridze Some Aspects of Formation National (English) Language ...... 164 nona uSveriZe erovnuli (inglisuri) enis formirebis zogierTi aspeqti...... 169 Диана Алания Русский язык в Грузии в XXI веке (статус и положение)...... 170 diana alania rusuli ena saqarTveloSi XXI saukuneSi (mdgomareoba da statusi)...... 172 Diana Alaniya The Position and Status of the Russian Language in Georgia in the XXI Century ...... 173 literaturaTmcodneoba Lliterature Studies tite mosia rusTavelis mijnurobis Teoriis interpretaciebidan...... 174 Tite Mosia From Tthe Interpretation of Rustaveli’s Romance Theory ...... 185 431 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV marine jaiani `vefxistyaosani~ da afxazeTi (`rusTveli msoflio literaturaSi~, mesame tomSi gamoqveynebuli rusTvelologiuri masalis mixedviT)...... 186 Marine Jaiani The Knight in the Panther’s Skin and Abkhazia (According to Rustvelological Material Published in Volume III, Rustaveli in World Literature)...... 193 joni marRania vladimer misabiSvilis moTxrobebis mxatvruli samyaro...... 194 Joni Marghania Artistic World of Vladimer Misabishvili’s Stories ...... 198 eka vardoSvili qarTveli qalis saxe germanul dramatul xelovnebaSi...... 199 Eka Vardoshvili Georgian Woman’s Face in German Dramatic Art...... 204 medea kvaracxe lia `sabav S vo lite ra tu ra yvela ze sarw mu no eb ri vi dargi a~ ...... 205 Medea Kvaratskhelia “Children’s Literature is the most Reliable Source”...... 210 Зоя Адамия Переводы Произведений Пушкина на Грузинский язык...... 211 zoia adamia aleqsan d re puSki nis nawar mo e be bis Targ ma ni qarTul enaze ...... 214 Zoia Adamia The Translations of Pushkin’s Works into Georgian ...... 215 religiaTmcodneoba Religion Studies qeTe van pavli aS vi li saqar T ve los samo ci qu lo ekle si is avto ke fa li is aRd ge nis erovnul - sa xel m wi fo eb ri vi mniSv ne lo ba (1917 weli) ...... 216 Ketevan Pavliashvili The National-State Meaning of the Georgian Orthodox Church Autocephaly Re-Establishment ...... 225 medea bendeliani saqarTvelos samociqulo eklesiisTvis teritoriuli avtokefaliis miniWebis sakiTxi 432 sabWoTa sistemaSi (1943 weli)...... 226 Medea Bendeliani The Issue of Territorial Autocepaly Recognition for the Apostolic Church of Georgian in the Soviet System ...... 231 arqimandriti Sio (kvaracxelia) asketizmis warmarTuli da ZvelaRTqmiseuli elementebi ...... 232 Archimandrite Shio (Kvaratskhelia) Pagan and the Old Testament Elements of Asceticism ...... 238 avTan dil were Te li romis ekle si is saek le sio damo ki de bu le bis sakiTxi da msoflio avto ri te tu lo bis Tavi se bu re be bi I-V sau ku ne eb is dasav leT Si (pati vi sa da Zala uf le bis sakiTxi) ...... 239 Avtandil Tsereteli The Issue of Ecclesiastical Dependence of Roman Church and the Peculiarities of Worldly Authority in the West in the I-V Centuries (Issue of Honor and Power)...... 246 istoria History qeTevan mania daviT yolbaia da polonuri qarTvelologia...... 247 Ketevan Mania David Kolbaia and Georgian Studies in Poland ...... 257 socialuri da politikuri mecnierebani Social and Political Sciences xaTuna amaRlobeli religiis analizi marqsis, veberisa da diurkemis SexedulebaTa SedarebiT...... 258 Khatuna Amaghlobeli Analysis of Religion Based on Thoughts of Marx, Weber and Dukheim ...... 262 Meri Gabedava The Challenge of Confidence-Building and Reconciliation Process in the Post-Conflict Georgia...... 263 meri gabedava ndobis aRdgenisa da Serigebis procesis gamowvevebi postkonfliqtur saqarTveloSi...... 270 433 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV ekonomika Economics jandri zarandia, irma maxaraSvili kidev erTxel klasteruli menejmentis Sesaxeb...... 271 Jandri Zarandia, Irma Makharashvili Once More About Cluster Management ...... 278 pedagogika da meTodika Pedagogy and Methodology jemal jinjixaZe maTematikis gakveTilebze esTetikuri aRzrdis sakiTxisaTvis...... 279 Jemal Jinjikhadze Aesthetic Education on the Lessons of Mathematics...... 313 giorgi jinjixaZe agebaze amocanebis amoxsna _ nabiji logikuri azrovnebis ganviTarebisken...... 314 Giorgi Jinjikhadze Solving Tasks by Drawing _ a Step Towards Development of Logical Thinking ...... 319 gulnaz xuxua moraluri devianturoba da maTi sakoreqcio pedagogiur RonisZiebaTa sistema...... 320 Gulnaz Khukhua Moral Deviation and System of their Correctional Pedagogical Measurements...... 338 fsiqologia Psychology lia svaniZe adamianis nervul-fsiqikuri Taviseburebebis TviTregulireba, rogorc Tandayolili da SeZenili unarebis daxvewis saSualeba...... 339 Lia Svanidze Self- Adjustment of Neuropsychic and Physiological Peculiarities as the Means of Improvement and Perfection of Natural and Acquired Skills...... 347 434 masalebi biobibliografiuli leqsikonisaTvis Materials for Biobibliographical Dictionary Отар Жордания Кавказская армия в биографиях ее офицеров Полковники (1901-1914 гг.) ...... 348 oTar Jordania kavkasiis armia oficerTa biografiebSi polkovnikebi (1901-1914 ww.)...... 421 Otar Zhordania Caucasus Army in the Officers’ Biographies Colonels (1901-1914) ...... 422 avtorTa Sesaxeb...... 423 Authors...... 426 435 cxum-afxazeTis mecnierebaTa akademiis Sromebi, XIII-XIV daibeWda: gamomcemloba `saari~, q. Tbilisi, Tevdore mRvdlis #57 577 50 62 27 E-mail: [email protected] 436