ÓÀØÀÒÈÅÄËÏÓ ÌÀÈÄÌÀÔÉÊÏÓÈÀ ÊÀÅÛÉÒÉÓ III ÓÀÄÒÈÀÛÏÒÉÓÏ ÊÏÍ×ÄÒÄÍÝÉÀ III INTERNATIONAL CONFERENCE OF THE GEORGIAN MATHEMATICAL UNION ÈÄÆÉÓÄÁÉÓ ÊÒÄÁÖËÉ BOOK OF ABSTRACTS ÁÀÈÖÌÉ, 2 – 9 ÓÄØÔÄÌÁÄÒÉ Batumi, September 2 – 9 2012 Organizing Committee: Baladze Vladimer (Vice Chairman), Beridze Anzor (Vice Chairman), Davitashvili Tinatin (Scientific Secretary), Duduchava Roland (Chairman), Kadeishvili Tornike, Kvaratskhe- lia Vakhtang, Makharadze Shota, Meladze Hamlet (Vice Chairman), Natroshvili David, Tarieladze Vaja (Chairman of Program Committee) ÓÀÏÒÂÀÍÉÆÀÝÉÏ ÊÏÌÉÔÄÔÉ: ÁÀËÀÞÄ ÅËÀÃÉÌÄÒ (ÈÀÅÌãÃÏÌÀÒÉÓ ÌÏÀÃÂÉËÄ), ÁÄÒÉÞÄ ÀÍÆÏÒ (ÈÀÅÌãÃÏÌÀÒÉÓ ÌÏÀÃÂÉËÄ), ÃÀÅÉÈÀÛÅÉËÉ ÈÉÍÀÈÉÍ (ÓßÀÅËÖËÉ ÌÃÉÅÀÍÉ), ÃÖÃÖÜÀÅÀ ÒÏËÀÍà (ÈÀÅÌãÃÏÌÀÒÄ), ÊÅÀÒÀ- ÝáÄËÉÀ ÅÀáÔÀÍÂ, ÌÀáÀÒÀÞÄ ÛÏÈÀ, ÌÄËÀÞÄ äÀÌËÄÔ (ÈÀÅÌãÃÏÌÀÒÉÓ ÌÏÀÃÂÉËÄ), ÍÀÔÒÏ- ÛÅÉËÉ ÃÀÅÉÈ, ÔÀÒÉÄËÀÞÄ ÅÀÑÀ (ÓÀÐÒÏÂÒÀÌÏ ÊÏÌÉÔÄÔÉÓ ÈÀÅÌãÃÏÌÀÒÄ), ØÀÃÄÉÛÅÉËÉ ÈÏÒÍÉÊÄ Programm Committee: Baladze V., Chilachava T., Duduchava R., Goginava Z., Gogishvili G., Gvazava J., Jangve- ladze T., Japaridze G., Jibladze M., Kadeishvili T., Kharazishvili A., Khimshiashvili G., Kvinikadze M., Kvinikhidze A., Mania M., Meladze H., Nadaraia E., Natroshvili D., Omanadze R., Oniani G., Oturanc G., Pkhakadze K., Rabinovich V., Rukhaia Kh., Sokhadze G., Giorgashvili L., Tarieladze V. (Chairman), Vakhania N. ÓÀÐÒÏÂÒÀÌÏ ÊÏÌÉÔÄÔÉ: ÁÀËÀÞÄ Å., ÜÉËÀÜÀÅÀ È., ÃÖÃÖÜÀÅÀ Ò., ÂÏÂÉÍÀÅÀ Æ., ÂÏÂÉÛÅÉËÉ Â., ÂÅÀÆÀÅÀ ã., ãÀÍÂÅÄËÀÞÄ È., ãÀ×ÀÒÉÞÄ Â., ãÉÁËÀÞÄ Ì., ØÀÃÄÉÛÅÉËÉ È., áÀÒÀÆÉÛÅÉËÉ À., áÉÌÛÉÀÛÅÉËÉ Â., ÊÅÉÍÉÊÀÞÄ Ì., ÊÅÉÍÉáÉÞÄ À., ÌÀÍÉÀ Ì., ÌÄËÀÞÄ ä., ÍÀÃÀÒÀÉÀ Ä., ÍÀÔÒÏÛÅÉËÉ Ã., ÏÌÀÍÀÞÄ Ò., ÏÍÉÀÍÉ Â., ÏÈÖÒÀÍ Â., ×áÀÊÀÞÄ Ê., ÒÀÁÉÍÏÅÉÜÉ Å., ÒÖáÀÉÀ á., ÓÏáÀÞÄ Â., ÂÉÏÒÂÀÛÅÉ- ËÉ Ë., ÔÀÒÉÄËÀÞÄ Å. (ÈÀÅÌãÃÏÌÀÒÄ), ÅÀáÀÍÉÀ Í. Contents Our Calendar - ÜÅÄÍÉ ÊÀËÄÍÃÀÒÉ 21 Stefan Banach in Tbilisi (On the occasion of his 120-th Birthday Anniversary) . 21 ÐÒÏ×ÄÓÏÒÉ ÀËÄØÓÉ ÂÏÒÂÉÞÄ (ÃÀÁÀÃÄÁÉÃÀÍ 105 ßËÉÓÈÀÅÉÓÀÃÌÉ) ........ 27 Prefessor Alexi Gorgidze (To the 105-th Birthday Anniversary) . 29 Professor George Lomadze (To the 100-th Birthday Anniversary) . 31 ÐÒÏ×ÄÓÏÒÉ ÄËÉÆÁÀÒ ßÉÈËÀÍÀÞÄ (ÃÀÁÀÃÄÁÉÃÀÍ 100 ßËÉÓÈÀÅÉÓÀÃÌÉ) ...... 35 Professor Elizbar Citlanadze (To the 100th Birthday Anniversary) . 36 Anniversaries - ÜÅÄÍÉ ÉÖÁÉËÀÒÄÁÉ 37 ÂÀÉÏÆ áÀÔÉÀÛÅÉËÉ – 90 ............................... 37 Gaioz Khatiashvili – 90 . 39 ÐÒÏ×ÄÓÏÒÉ ÃÀÅÉÈ ÂÏÒÃÄÆÉÀÍÉ – 75 ....................... 41 Professor David Gordeziani – 75 . 47 ÓÄÒÂÏ ÜÏÁÀÍÉÀÍÉ – 70 ................................ 49 Sergei (Sergo) Chobanyan – 70 . 51 Plenary Talks 53 ÐËÄÍÀÒÖËÉ ÌÏáÓÄÍÄÁÄÁÉ 53 Dionys Baeriswyl, Quantum XX chain with interface . 55 ÃÉÏÍÉÓ ÁÀÄÒÉÓÅÉËÉ, ÄÒÈÂÀÍÆÏÌÉËÄÁÉÀÍÉ ÓÐÉÍÉ XX-ÌÏÃÄËÉ ÂÀÃÀÁÌÉÓ ßÄÒÔÉËÉÈ 55 Vladimer Baladze, Coshape theory and its applications . 55 ÅËÀÃÉÌÄÒ ÁÀËÀÞÄ, ÊÏÛÄÉÐÄÁÉÓ ÈÄÏÒÉÀ ÃÀ ÌÉÓÉ ÂÀÌÏÚÄÍÄÁÄÁÉ .......... 55 3 4 September 2–9, Batumi, Georgia Sergei Chobanyan, Shlomo Levental, On the distribution of the Steinitz functional . 56 ÓÄÒÂÄÉ ÜÏÁÀÍÉÀÍÉ, ÛËÏÌÏ ËÄÅÄÍÔÀËÉ, ÛÔÀÉÍÉÝÉÓ ×ÖÍØÝÉÏÍÀËÉÓ ÂÀÍÀßÉËÄÁÉÓ ÛÄÓÀáÄÁ ..................................... 56 David Gordeziani, Mathematical modelling and numerical solution of some problems of water pollution and filtration problems of liquids . 56 ÃÀÅÉÈ ÂÏÒÃÄÆÉÀÍÉ, ßÚËÉÓ ÃÀÁÉÍÞÖÒÄÁÉÓÀ ÃÀ ÓÉÈáÄÈÀ ×ÉËÔÒÀÝÉÉÓ ÆÏÂÉÄÒÈÉ ÀÌÏÝÀÍÉÓ ÌÀÈÄÌÀÔÉÊÖÒÉ ÌÏÃÄËÉÒÄÁÀ ÃÀ ÒÉÝáÅÉÈÉ ÀÌÏáÓÍÀ ........ 56 Inna Grusha, Giorgi Japaridze, Effective Hamiltonian for the half-filled spin-asymmetric Hubbard chain with strong and alternating on-site repulsion 58 ÉÍÀ ÂÒÖÛÀ, ÂÉÏÒÂÉ ãÀ×ÀÒÉÞÄ, Ä×ÄØÔÖÒÉ ÓÐÉÍÖÒÉ äÀÌÉËÔÏÍÉÀÍÉ ÄÒÈÂÀÍÆÏÌÉËÄ- ÁÉÀÍÉ ÍÀáÄÅÒÀÃÛÄÅÓÄÁÖËÉ ÓÐÉÍ-ÀÓÉÌÄÔÒÖËÉ äÀÁÀÒÃÉÓ ÌÏÃÄËÉÓÀÈÅÉÓ, ËÖß ÃÀ ÊÄÍÔ ÊÅÀÍÞÄÁÆÄ ÂÀÍÓáÅÀÅÄÁÖËÉ ÞËÉÄÒÉ ÂÀÍÆÉÃÅÉÓ ÐÉÒÏÁÄÁÛÉ ...... 58 Tornike Kadeishvili, Homotopy algebras in topological field theory . 58 ÈÏÒÍÉÊÄ ØÀÃÄÉÛÅÉËÉ, äÏÌÏÔÏÐÉÖÒÉ ÀËÂÄÁÒÄÁÉ ÅÄËÉÓ ÔÏÐÏËÏÂÉÖÒ ÈÄÏ- ÒÉÀÛÉ ...................................... 58 Leonard Mdzinarishvili, Continuous homologies and cohomologies . 59 ËÄÏÍÀÒà ÌÞÉÍÀÒÉÛÅÉËÉ, ÖßÚÅÄÔÉ äÏÌÏËÏÂÉÄÁÉ ÃÀ ÊÏäÏÌÏËÏÂÉÄÁÉ ...... 59 ÊÏÍÓÔÀÍÔÉÍÄ ×áÀÊÀÞÄ, ØÀÒÈÖËÉ ÄÍÉÓ ÔÄØÍÏËÏÂÉÆÄÁÖËÉ ÀÍÁÀÍÉÓ ÛÄÌÖÛÀÅÄÁÉÓ ÌÉÆÍÄÁÉ ÃÀ ÐÒÏÁËÄÌÄÁÉ ............................ 59 Konstantine Pkhakadze, The aims and problems of creation of the techno- logical alphabet of the Georgian language . 59 Vladimir S. Rabinovich, Diffraction problems on periodic metric graphs . 60 ÅËÀÃÉÌÄÒ Ó. ÒÀÁÉÍÏÅÉÜÉ, ÃÉ×ÒÀØÝÉÉÓ ÀÌÏÝÀÍÄÁÉ ÐÄÒÉÏÃÖË ÌÄÔÒÉÊÖË ÂÒÀ×ÄÁÆÄ 60 áÉÌÖÒÉ ÒÖáÀÉÀ, ËÀËÉ ÔÉÁÖÀ, ÂÄËÀ àÀÍÊÅÄÔÀÞÄ, ÖÒÀÍÂÏ ÊÅÀÍÔÏÒÖËÉ ÈÄÏÒÉÀ 61 Khimuri Rukhaia, Lali Tibua, Gela Chankvetadze, Unranked theory with quantifiers . 61 Elias Wegert, On boundary value problems in circle packing . 62 ÄËÉÀÓ ÅÄÂÄÒÔÉ, ßÒÄÄÁÉÓ ÜÀËÀÂÄÁÉÓ ÐÒÏÁËÄÌÀÓÈÀÍ ÃÀÊÀÅÛÉÒÄÁÖËÉ ÓÀÓÀÆÙÅÒÏ ÀÌÏÝÀÍÄÁÉ .................................... 62 Real and Complex Analysis 63 ÍÀÌÃÅÉËÉ ÃÀ ÊÏÌÐËÄØÓÖÒÉ ÀÍÀËÉÆÉ 63 George Akhalaia, Nino Manjavidze, Generalized analytic functions . 65 ÂÉÏÒÂÉ ÀáÀËÀÉÀ, ÍÉÍÏ ÌÀÍãÀÅÉÞÄ, ÂÀÍÆÏÂÀÃÏÄÁÖËÉ ÀÍÀËÉÆÖÒÉ ×ÖÍØÝÉÄÁÉ ... 65 2–9 ÓÄØÔÄÌÁÄÒÉ, ÁÀÈÖÌÉ, ÓÀØÀÒÈÅÄËÏ 5 Leri Bantsuri, On the relationship between conditions of differentiability and existence of generalized gradient . 65 ËÄÒÉ ÁÀÍÝÖÒÉ, ÃÉ×ÄÒÄÍÝÉÒÄÁÀÃÏÁÉÓÀ ÃÀ ÂÀÍÆÏÂÀÃÄÁÖËÉ ÂÒÀÃÉÄÍÔÉÓ ÀÒÓÄÁÏÁÉÓ ÐÉÒÏÁÄÁÓ ÛÏÒÉÓ ÌÉÌÀÒÈÄÁÉÓ ÛÄÓÀáÄÁ ..................... 65 Grigor Barsegian, Idea of complex conjugacy in differential geometry. Ar- gument variation principle and Nevanlinna type results for conjugate surfaces . 66 ÂÒÉÂÏÒÉ ÁÀÒÓÄÂÉÀÍÉ, ÊÏÌÐËÄØÓÖÒÀà ÛÄÖÙËÄÁÖËÏÁÉÓ ÉÃÄÀ ÃÉ×ÄÒÄÍÝÉÀËÖÒ ÂÄÏÌÄÔÒÉÀÛÉ. ÀÒÂÖÌÄÍÔÉÓ ÝÅËÉËÄÁÉÓ ÐÒÉÍÝÉÐÉ ÃÀ ÍÄÅÀÍËÉÍÀÓ ÔÉÐÉÓ ÈÄÏÒÄÌÄÁÉ ÛÄÖÙËÄÁÖËÉ ÆÄÃÀÐÉÒÄÁÉÓÀÈÅÉÓ .................. 66 Natela Chachava, Ilia Lomidze, Classification of Hermitian Matrices with Their Polynomial Invariants . 67 ÍÀÈÄËÀ ÜÀÜÀÅÀ, ÉËÉÀ ËÏÌÉÞÄ, ÄÒÌÉÔÖËÉ ÌÀÔÒÉÝÄÁÉÓ ÊËÀÓÉ×ÉÝÉÒÄÁÀ ÌÀÈÉ ÐÏËÉÍÏÌÖÒÉ ÉÍÅÀÒÉÀÍÔÄÁÉÈ .......................... 67 Omar Dzagnidze, Irma Tsivtsivadze, The representation of an indefinite integral with a parameter by double exponential series . 68 ÏÌÀÒ ÞÀÂÍÉÞÄ, ÉÒÌÀ ßÉÅßÉÅÀÞÄ, ÐÀÒÀÌÄÔÒÉÓ ÛÄÌÝÅÄËÉ ÂÀÍÖÓÀÆÙÅÒÄËÉ ÉÍÔÄÂÒÀËÉÓ ßÀÒÌÏÃÂÄÍÀ ÄØÓÐÏÍÄÍÔÖÒÉ ÏÒÌÀÂÉ ÌßÊÒÉÅÉÈ ................ 68 ÏÌÀÒ ÂÉÅÒÀÞÄ, ÆÏÂÉÄÒÈÉ ÔÉÐÉÓ ×ÖÍØÝÉÏÍÀËÖÒÉ ÂÀÍÔÏËÄÁÄÁÉ ......... 69 Omar Givradze, Some types of functional equations . 69 ÄÒÄÊËÄ ãÀ×ÀÒÉÞÄ, ÐÖÀÓÏÍÉÓ ÂÀßÀÒÌÏÄÁÖËÉ ÉÍÔÄÂÒÀËÉÓ ÓÀÓÀÆÙÅÒÏ ÌÍÉÛÅÍÄ- ËÏÁÄÁÉÓ ÛÄÓÀáÄÁ ................................ 70 Erekle Japharidze, On boundary values of differentiated Poisson integral . 70 Shadiman Kheladze, On the metric kernel and shell problem . 70 ÛÀÃÉÌÀÍ áÄËÀÞÄ, ÌÄÔÒÉÊÖËÉ ÂÖËÉÓÀ ÃÀ ÂÀÒÓÉÓ ÛÄÓÀáÄÁ ............. 70 Ilia Lomidze, Jimsher Javakhishvili, At the tetrad representation of the Lorentz group . 70 ÉËÉÀ ËÏÌÉÞÄ, ãÉÌÛÄÒ ãÀÅÀáÉÛÅÉËÉ, ËÏÒÄÍÝÉÓ ãÂÖ×ÉÓ ÔÄÔÒÀÃÖËÉ ßÀÒÌÏÃÂÄ- ÍÉÓ ÛÄÓÀáÄÁ ................................... 70 George Makatsaria, Liouville theorems for the systems of elliptic equations 72 ÂÉÏÒÂÉ ÌÀØÀÝÀÒÉÀ, ËÉÖÅÉËÉÓ ÔÉÐÉÓ ÈÄÏÒÄÌÄÁÉ ÄËÉ×ÓÖÒ ÂÀÍÔÏËÄÁÀÈÀ ÓÉÓ- ÔÄÌÄÁÉÓÀÈÅÉÓ .................................. 72 ÂÉÂËÀ ÏÍÉÀÍÉ, ÂÏÂÉ ÈÄÈÅÀÞÄ, ÄÒÈÄÖËÏÅÀÍ ßÒÄÛÉ ãÀÌÄÁÀÃÉ ÂÒÀÃÉÄÍÔÉÓ ÌØÏÍÄ äÀÒÌÏÍÉÖËÉ ×ÖÍØÝÉÄÁÉÓ ÓÀÓÀÆÙÅÒÏ ÈÅÉÓÄÁÄÁÉ ................ 72 Gigla Oniani, Gogi Tetvadze, Boundary values of harmonic functions in unit ball with summable gradient . 72 6 September 2–9, Batumi, Georgia ÂÉÂËÀ ÏÍÉÀÍÉ, ÉÒÌÀ ßÉÅßÉÅÀÞÄ, Ap ÓÉÅÒÝÉÓ ×ÖÍØÝÉÄÁÉÓ ÐÀÒÀÌÄÔÒÖËÉ ßÀÒÌÏÃ- ÂÄÍÉÓÀ ÃÀ ÍÖËÏÅÀÍÉ ÓÉÌÒÀÅËÄÄÁÉÓ ÛÄÓÀáÄÁ ................. 73 Gigla Oniani, Irma Tsivtsivadze, On parametric representation and zero sets of functions from the space Ap ...................... 73 Giorgi Oniani, Divergence of Fourier series with respect to systems of products of bases . 74 ÂÉÏÒÂÉ ÏÍÉÀÍÉ, ÁÀÆÉÓÈÀ ÍÀÌÒÀÅËÉÓ ÓÀáÉÓ ÓÉÓÔÄÌÄÁÉÓ ÌÉÌÀÒÈ ×ÖÒÉÄÓ ÌßÊÒÉÅÄÁÉÓ ÂÀÍÛËÀÃÏÁÉÓ ÛÄÓÀáÄÁ .............................. 74 Gogi R. Pantsulaia, Givi P. Giorgadze, A description of behaviors of some phase motions in R1 in terms of ordinary and standard “Lebesgue measures” . 75 ÂÏÂÉ ×ÀÍÝÖËÀÉÀ, ÂÉÅÉ ÂÉÏÒÂÀÞÄ, R1 ÓÉÅÒÝÄÆÄ ÂÀÍÓÀÆÙÅÒÖËÉ ÆÏÂÉÄÒÈÉ ×ÀÆÖÒÉ ÌÏÞÒÀÏÁÉÓ ÚÏ×ÀØÝÄÅÉÓ ÀÙßÄÒÀ ÓÔÀÍÃÀÒÔÖËÉ ÃÀ ÏÒÃÉÍÀËÖÒÉ ``ËÄÁÄÂÉÓ ÆÏÌÉÓ'' ÔÄÒÌÉÍÄÁÛÉ ......................... 75 Shakro Tetunashvili, On Cantor’s functionals . 76 ÛÀØÒÏ ÔÄÔÖÍÀÛÅÉËÉ, ÊÀÍÔÏÒÉÓ ×ÖÍØÝÉÏÍÀËÈÀ ÛÄÓÀáÄÁ .............. 76 Salaudin Umarkhadzhiev, Boundedness of linear operators from generalized grand Lebesque spaces to generalized grand Morrey spaces . 77 ÓÀËÀÖÃÉÍ ÖÌÀÒáÀãÉÄÅÉ, ÂÀÍÆÏÂÀÃÄÁÖËÉ ÂÒÀÍà ËÄÁÄÂÉÓ ÓÉÅÒÝÉÃÀÍ ÂÀÍÆÏÂÀÃÄ- ÁÖË ÂÒÀÍà ÌÏÒÉÓ ÓÉÅÒÝÄÛÉ ÌÏØÌÄÃÉ ßÒ×ÉÅÉ ÏÐÄÒÀÔÏÒÄÁÉÓ ÛÄÌÏÓÀÆÙÅ- ÒÖËÏÁÀ ..................................... 77 Topology, Algebra and Number Theory 79 ÔÏÐÏËÏÂÉÀ, ÀËÂÄÁÒÀ ÃÀ ÒÉÝáÅÈÀ ÈÄÏÒÉÀ 79 Malkhaz Bakuradze, Morava K-theory atlas for finite groups . 81 ÌÀËáÀÆ ÁÀÊÖÒÀÞÄ, ÌÏÒÀÅÀÓ K-ÈÄÏÒÉÉÓ ÀÔËÀÓÉ ÓÀÓÒÖËÉ ãÂÖ×ÄÁÉÓÀÈÅÉÓ ... 81 Vladimer Baladze, On homology and shape theories of compact Hausdorff spaces . 82 ÅËÀÃÉÌÄÒ ÁÀËÀÞÄ, äÀÖÓÃÏÒ×ÉÓ ÊÏÌÐÀØÔÖÒ ÓÉÅÒÝÄÈÀ äÏÌÏËÏÂÉÖÒÉ ÃÀ ÛÄÉÐÖÒÉ ÈÄÏÒÉÄÁÉÓ ÛÄÓÀáÄÁ ............................... 82 Vladimer Baladze, Ruslan Tsinaridze, On normal homology and coho- mology theories . 83 ÅËÀÃÉÌÄÒ ÁÀËÀÞÄ, ÒÖÓËÀÍ ÝÉÍÀÒÉÞÄ, ÍÏÒÌÀËÖÒÉ äÏÌÏËÏÂÉÉÓÀ ÃÀ ÊÏäÏÌÏ- ËÏÂÉÉÓ ÈÄÏÒÉÄÁÉÓ ÛÄÓÀáÄÁ .......................... 83 2–9 ÓÄØÔÄÌÁÄÒÉ, ÁÀÈÖÌÉ, ÓÀØÀÒÈÅÄËÏ 7 Sadi Bayramov, Ciğdem Gunduz (Aras), Separable and compact soft topological space . 84 ÓÀÃÉ ÁÀÉÒÀÌÏÅÉ, ÜÉÂÃÄÌ ÂÖÍÃÖÆÉ (ÀÒÀÓÉ), ÓÄÐÀÒÀÁÄËÖÒÉ ÃÀ ÊÏÌÐÀØÔÖÒÉ ÒÁÉËÉ ÔÏÐÏËÏÂÉÖÒÉ ÓÉÅÒÝÄÄÁÉ ........................... 84 Anzor Beridze, Partial continuity of strong homology group of continuous map ....................................... 85 ÀÍÆÏÒ ÁÄÒÉÞÄ, ÖßÚÅÄÔÉ ÀÓÀáÅÉÓ ÞËÉÄÒÉ äÏÌÏËÏÂÉÉÓ ãÂÖ×ÉÓ ÍÀßÉËÏÁÒÉÅ ÖßÚÅÄÔÏÁÀ .................................... 85 Vakhtang Beridze, Solution Bitsadze–Samarski