DOCSLIB.ORG

Principle and Equipartition of Energy for the Modified Wave

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Principle and Equipartition of Energy for the Modified Wave Annales Mathematiques Blaise Pascal 1 2 comma 1 47 hyphen 1 60 open parenthesis 2 0 0 5 closing parenthesis nnoindentHuygens quoterightAnnales .. Mathematiques principle .. and .. Blaise equipartition Pascal .. of 1 2 , 1 47 − 1 60 ( 2 0 0 5 ) energy .. for .. the .. modified .. wave .. equation n centerlineassociated ..fHuygens to .. a .. generalized ' nquad ..p radial r i n c i .. p l Laplacian e nquad and nquad equipartition nquad o f g Jamel El Kamel n centerlineChokri Yacoubf energy nquad f o r nquad the nquad modified nquad wave nquad equation g Abstract n centerlineIn this paperf a we sAnnales s considero c i a t e Mathematiques d thenquad modifiedto Blaise wavenquad equation Pascala nquad1 associated 2 , 1generalized 47 - 1 60 ( 2 0 0 5n ) quad r a d i a l nquad Laplacian g with a classHuygens of radial Laplacians ' L principle generalizing the radial and part of equipartition of n centerlinethe Laplaceenergyf endashJamel Beltrami El Kamel for operatorg the on hyperbolic modified spaces or Damek endash wave Ricci equation spaces period We show that the Huygens quoteright principle and the equipartition of n centerlineenergyassociated holdf ifChokri the inverse Yacoub of the tog Harish a endash generalized Chandra c endash function radial is a poly hyphen Laplacian nomial and that these two properties hold asymptoticallyJamel El otherwise Kamel period n centerlineSimilar resultsf Abstract were establishedg previously by BransonChokri comma Yacoub Olafsson and Schlichtkrull in the case of noncompact symmetricAbstract spaces period n centerline1 .. Introductionf In thisIn this paper paper we we consider consider the the modified modified wave wave equation equation associated associated g In Euclidean spacewith X = Ra class to the of power radial of nLaplacians of odd dimensionL generalizing comma any the solution radial u part openof parenthesis x comman centerline t closingf with parenthesisthe Laplacea class to the { of Beltrami radial operator Laplacians on hyperbolic $ L $ spacesgeneralizing or Damek the { Ricci radial part of g wave equation spaces . We show that the Huygens ' principle and the equipartition of n centerlineCapital Deltaf theenergy sub x Laplace u open hold parenthesis if−− theBeltrami inverse x comma of operator the t closing Harish parenthesis on { Chandrahyperbolic = partialdiffc { spaces function to the or power is Damek a poly of partialdiff−− - R i c c i g sub t to the power ofnomial 2 to the and power that of 2these u open two parenthesis properties x comma hold asymptotically t closing parenthesis otherwise . n centerlineis determinedf spaces bySimilar the value . We results of show its in were i-line that established tial the data Huygens in an previously arbitrarily ' principle by thin Branson shell and around , the Olafsson equipartition and of g the sphere S open parenthesisSchlichtkrull x comma in bar the t case bar closing of noncompact parenthesis symmetric period .. This spaces is Huygens . quoteright principlen centerline periodf ..energy Moreover1 hold Introduction the total if the energy inverse of the Harish −− Chandra c −− function is a poly − g Equation: open parenthesis 1 period 1 closing parenthesisn .. E open parenthesis u closing parenthesis = 2 to n centerline f nomialIn and Euclidean that these space twoX = propertiesR of odd dimension hold asymptotically , any solution otherwiseu(x; t) to . g the power of 1 integralthe sub R n vextendsingle-vextendsingle-vextendsingle-vextendsingle partialdiff to the power of partialdiff t to thewave power equation of u open parenthesis x comma t closing parenthesis vextendsingle-vextendsingle- vextendsingle-vextendsinglen centerline f Similar results to the power were of 2 established dx plus 2 to the previously power of 1 integral by Branson sub R n ,bar Olafsson nabla sub andx u g open parenthesis x comma t closing parenthesis bar to the power@ 2 of 2 dx ∆xu(x; t) = @ t2 u(x; t) n centerlinesplits eventuallyf Schlichtkrull equally into its inkinetic the and case potential of noncompact components if symmetric the initial spaces . g data are compactlyis determined supported period by the.. See value Duffin of open its square in i − bracketline tial 7 closing data square in an bracket arbitrarily and Branson opennnoindent square bracket1 nquadthin 3 closingIntroduction shell square around bracket the period sphere S(x; j t j): This is Huygens ' principle . Similar results wereMoreover established the bytotal Branson energy comma Helgason comma Olafsson comma Schlicht hyphen n hspacekrull in∗fn openf i l square l g In bracket Euclidean 4 closing space square $X bracket = comma R^ openf n squareg$ of bracket odd 8dimension closing square , any bracket solution comma$u open ( square x , bracket t 1 2 )$tothe closing squareZ bracket for the modifiedZ wave equation on Riemannian symmetric 1 @ u(x; 2 1 2 147 E(u) = 2 j@ t t)j dx + 2 j rxu(x; t) j dx (1:1) nnoindent wave equation Rn Rn splits eventually equally into its kinetic and potential components if the n [ nDelta f xinitialg u data ( are x compactly , t supported ) = n .partial See Duffin^f n partial [ 7 ] andg Branson^f 2 g f [ t ^f 2 gg u ( x ,3 ] t . ) n ] Similar results were established by Branson , Helgason , Olafsson , Schlicht - krull in [ 4 ] , [ 8 ] , [ 1 2 ] for the modified wave equation on nnoindent is determinedRiemannian by symmetric the value of its in $ i−line $ tial data in an arbitrarily thin shell around thesphere $S ( x , nmid t nmid147 ) . $ nquad This is Huygens ' principle . nquad Moreover the total energy n begin f a l i g n ∗g E ( u ) = 2 ^f 1 g n int f R n g narrowvert n partial ^f n partial g t ^f u ( x , g t ) narrowvert ^f 2 g dx + 2 ^f 1 g n int f R n g nmid nnabla f x g u ( x , t ) nmid ^f 2 g dx n tag ∗f$ ( 1 . 1 ) $g nendf a l i g n ∗g nnoindent splits eventually equally into its kinetic and potential components if the initial data are compactly supported . nquad See Duffin [ 7 ] and Branson [ 3 ] . Similar results were established by Branson , Helgason , Olafsson , Schlicht − krull in [ 4 ] , [ 8 ] , [ 1 2 ] for the modified wave equation on Riemannian symmetric n centerline f147 g J period Elkamel comma .. Ch period .. Yacoub n centerlinespaces of noncompactfJ . Elkamel type X ,=n Gquad slashCh K comma . nquad underYacoub the assumptionsg that dim X is o dd and G has only one conjugacy class of Cartan subgroups period .. Otherwise nnoindentthese phenomenaspaces may of not noncompact hold strictly type speaking $X comma = but G they do/ asymptotically K , $ under comma the assumptions that dim $ Xas $ shown by Branson comma Olafsson and Schlichtkrull in open square bracket 5 closing square bracket period nnoindentThis paperis is devoted o dd and to another $ G setting$ has comma only which one is conjugacy known to share class features of Cartan subgroups . nquad Otherwise thesewith the phenomena previous one may period not .. hold SpecificallyJ . strictly Elkamel we consider speaking , the Ch modified . , but Yacoubwave they equation do asymptotically , asEquation: shown by open Bransonspaces parenthesis of , noncompact 1Olafsson period 2 closing and type Schlichtkrull parenthesisX = G=K; ..under L sub in xthe u [ open assumptions5 ] parenthesis . that x comma dim tX closing parenthesis = partialdiffis o dd to andthe powerG has of only partialdiff one conjugacy sub t to the class power of of Cartan 2 to the powersubgroups of 2 u . open Oth- parenthesis xThis comma paper t closing is parenthesiserwise devoted these to another phenomena setting may not , which hold strictly is known speaking to share , but features they do withwith theinitial previous dataasymptotically one . nquad , as shownSpecifically by Branson we consider , Olafsson the and modified Schlichtkrull wave in [ equation 5 Equation: open]. parenthesis 1 period 3 closing parenthesis .. u open parenthesis x comma 0 closing parenthesis =n begin f 0 openf a l i parenthesis g n ∗g This x closing paper parenthesis is devoted comma to another partialdiff setting to the , power which of is partialdiff known tto vextendsingle- share vextendsingle-vextendsingle-vextendsingleL f x g ufeatures ( x with , the t previous sub) t = = one0 un partial open . Specificallyparenthesis^f n partial x we comma considerg t^f closing2 theg parenthesisf modifiedt ^f 2 =gg f 1 openu parenthesis( x , xwave closing t equation parenthesis ) n tag ∗f$ ( 1 . 2 ) $g nendassociatedf a l i g n ∗g to certain second order differential operators Equation: open parenthesis 1 period 4 closing parenthesis ..@ 2 Lu = dx to the power of d to the power of 2 unnoindent sub 2 plus Awith sub A initial open parenthesis data to the powerLxu of(x; prime t) = @ subt2 u x(x; closing t) parenthesis to the power (1:2) of open parenthesis x closingwith parenthesis initial datadx to the power of du plus rho to the power of 2 u n beginon ..f opena l i g parenthesisn ∗g 0 comma plus infinity closing parenthesis period .. Following Cheacutebli and Trim egraveu(x,0)=f0(x), che comma we a-s sume that the function n partial ^f n partial g t narrowvert f t = 0 g u(x,t)=f1(x) n tag ∗f$ ( A open parenthesis x closing parenthesis behaves as follows@ : u(x; 0) = f0(x);@ tjt=0u(x; t) = f1(x) (1:3) 1bullet . A 3 open ) parenthesis $g x closing parenthesis thicksim x to the power of 2 alpha plus 1 as x searrow 0 commanendf a where l i g n ∗g alphaassociated greater minus to 2certain to the power second of order1 period differential .. More precisely operators Equation: open parenthesis 1 period 5 closing parenthesis .. A open parenthesis x closing parenthesis = x tonnoindent
Load more

Recommended publications
  • Brand Book Cover 2021.Pub
    RR PP Commissioner QQ BB BB Rਤਦਨਲਲ਼ਤ਱ਤਣ B਱ਠਭਣਲ ਠਲ ਮਥ MARCH 31, 2021 REMEMBER TO REGISTER YOUR BRAND 2021 BRAND RENEWAL YEAR Alabama Law requires any livestock owner who uses a brand to identify their livestock must register their brand with the Alabama Department of Agriculture and Industries. Brands are renewed every three years. Renewals Start September 2021. Pursuant to §2-15-21 & §2-15-23 Code of Alabama 1975 S B S 1445 Federal Drive · Montgomery, Alabama 36107-1123 Rick Pate 334-240-7304 · 800-642-7761 Ext. 7304 Commissioner APPLICATION FOR LIVESTOCK BRAND REGISTRATION FOR REGISTRATION PERIOD OCTOBER 1, 2028—SEPTEMBER 30, 2021 (Please Print or Type) Date: __________________ Name: _________________________________________________________________ Business Name: _________________________________________________________________ Address: _________________________________________________________________ (Street) (City) (State) (Zip) Phone: ___________________________ E-Mail: _____________________________ County: _______________________ Livestock Type: ___________________________ Signature: _____________________________________________________________________ I hereby make application for a recorded brand to be used on livestock. IMPORTANT NOTICE Do not have irons made or brand any stock until you have received your brand certificate. BRAND EXAMPLES WITH VERBAL DESCRIPTIONS RJ LJ LJ - Left Jaw RJ - Right Jaw THERE IS A RECORDING FEE OF $ 20.00 FOR THE FIRST LOCATION AND A $ 4.00 FEE FOR EACH ADDITIONAL LOCATION. CIRCLE LOCATION YOU WISH TO RESERVE RH LH RR LR RS LS RJ LJ 1st Choice 2nd Choice 3rd Choice Verbal Description: 1st Choice _______________________________________________ 2nd Choice _______________________________________________ 3rd Choice _______________________________________________ Duplicate brands cannot be registered. Give your second and third choices to save any delays in the event your first choice has been already registered. Draw your brand exactly as it will appear on the animal.
    [Show full text]
  • The Unicode Standard, Version 6.1 This File Contains an Excerpt from the Character Code Tables and List of Character Names for the Unicode Standard, Version 6.1
    Latin Extended-D Range: A720–A7FF The Unicode Standard, Version 6.1 This file contains an excerpt from the character code tables and list of character names for The Unicode Standard, Version 6.1. Characters in this chart that are new for The Unicode Standard, Version 6.1 are shown in conjunction with any existing characters. For ease of reference, the new characters have been highlighted in the chart grid and in the names list. This file will not be updated with errata, or when additional characters are assigned to the Unicode Standard. See http://www.unicode.org/errata/ for an up-to-date list of errata. See http://www.unicode.org/charts/ for access to a complete list of the latest character code charts. See http://www.unicode.org/charts/PDF/Unicode-6.1/ for charts showing only the characters added in Unicode 6.1. See http://www.unicode.org/Public/6.1.0/charts/ for a complete archived file of character code charts for Unicode 6.1. Disclaimer These charts are provided as the online reference to the character contents of the Unicode Standard, Version 6.1 but do not provide all the information needed to fully support individual scripts using the Unicode Standard. For a complete understanding of the use of the characters contained in this file, please consult the appropriate sections of The Unicode Standard, Version 6.1, online at http://www.unicode.org/versions/Unicode6.1.0/, as well as Unicode Standard Annexes #9, #11, #14, #15, #24, #29, #31, #34, #38, #41, #42, and #44, the other Unicode Technical Reports and Standards, and the Unicode Character Database, which are available online.
    [Show full text]
  • Abbreviations and Conversions Page 1 of 2 Latin Abbreviations
    Abbreviations and Conversions Latin Abbreviations Abbreviation Meaning Latin ad.lib. freely as wanted ad libitum aq. water aqua b.i.d. twice a day bis in die cap. capsule capula c with bar on top with cum div. divide divide eq.pts. equal parts equalis partis gtt. a drop gutta h. hour hora no. number numero O. pint octarius p.r.n. as occasion requires pro re nata q.s. a sufficient quantity quantum sufficiat q4h every 4 hours quaque 4 hora q6h every 6 hours quaque 6 hora q1d every day quaque 1 die q1w every week q.i.d. four times a day quater in die s.i.d. once a day semel in die Sig., S. write on the label signa stat. immediately statim tab. a tablet tabella t.i.d. three times a day ter in die The Apothecaries' System The Metric System Weight Weight 20 grains (gr) 1 scruple ( ) 1 picogram (pg) 10-12 gram 3 scruples 1 dram( ) = 60 grains 1000 picograms 1 nanogram (ng) or 10-9 gram 8 drams 1 ounce ( ) = 480 grains 1000 nanograms 1 microgram (ug) or 10-6 gram Volume 1000 micrograms 1 milligram (mg) or 10-3 gram 60 minims (m) 1 fluid dram ( ) 1000 milligrams 1 gram (g) 8 fluid drams 1 fluid ounce ( ) 1000 grams 1 kilogram (kg) 16 fluid ounces 1 pint (O.) Volume Know eqivalents in bold faced type 1000 milliliters (ml) 1 liter (L) Be able to interconvert all of these values Prefixes for volumes correspond to those for weight. Page 1 of 2 Abbreviations and Conversions Conversion Equivalents Approximate Exact 1 milligram 1/60 grain 1/65 grain 1 gram 15 grains 15.432 grains 1 kilogram 2.2 pounds* 2.2 pounds* 1 milliliter 15 minims 16.23 minims 1 liter 1 quart 1.06 quarts or 33.8 fluid ounces 1 grain 60 milligrams 65 milligrams 1 dram 4 grams 3.88 grams 1 ounce 30 grams 31.1 grams 1 pound* 450 grams 454 grams 1 minim 0.06 milliliter 0.062 milliliter 1 fluid dram 4 milliliters 3.7 milliliters 1 fluid ounce 30 milliliters 29.57 milliliters 1 pint 500 milliliters 473 milliliters 1 quart 1000 milliliters 946 milliliters 1 drop 1 minim 1 teaspoonful 5 milliliters 1 dessertspoonful 8 milliliters 1 tablespoonful 15 milliliters Know equivalents in bold face type.
    [Show full text]
  • New Constraints on the Galactic Bar I
    Draft version November 7, 2018 A Preprint typeset using LTEX style emulateapj v. 08/22/09 NEW CONSTRAINTS ON THE GALACTIC BAR I. Minchev1, J. Nordhaus1,2 and A. C. Quillen1 Draft version November 7, 2018 ABSTRACT Previous work has related the Galactic Bar to structure in the local stellar velocity distribution. Here we show that the Bar also influences the spatial gradients of the velocity vector via the Oort constants. By numerical integration of test-particles we simulate measurements of the Oort C value in a gravitational potential including the Galactic Bar. We account for the observed trend that C is increasingly negative for stars with higher velocity dispersion. By comparing measurements of C with our simulations we improve on previous models of the Bar, estimating that the Bar pattern speed is Ωb/Ω0 =1.87 ± 0.04, where Ω0 is the local circular frequency, and the Bar angle lies within ◦ ◦ 20 6 φ0 6 45 . We find that the Galactic Bar affects measurements of the Oort constants A and B less than ∼ 2 km/s/kpc for the hot stars. Subject headings: 1. INTRODUCTION Assuming the Galactic Bar affects the shape of the The Galaxy is often modeled as an axisymmetric disk. distribution function of the old stellar population in the With the ever increasing proper motion and radial ve- SN, an additional constraint on the Bar can be provided locity data, it is now apparent that nonaxisymmetric by considering the values derived for the Oort constant effects cannot be neglected (nonzero Oort constant C, C. In other words, in addition to relating the dynamical Olling & Dehnen 2003, hereafter O&D; nonzero vertex influence of the Bar to the local velocity field, C provides deviation, Famaey et al.
    [Show full text]
  • Preliminary Proposal to Encode Additional Dialectology Latin Characters
    Preliminary proposal to encode additional dialectology Latin characters Denis Moyogo Jacquerye <[email protected]> 2013-08-01 1. Background The recent addition of the German dialectology symbols to Unicode raises the question of other dialectology transcription systems being encoded. Romance dialectology transcription systems were created in the late 19th century or early 20th, in the same period as German dialectology systems or the International Phonetic Alphabet (IPA). Besides the Böhmer-Ascoli transcription from which the Teuthonista transcription is derived, another major transcription systems is the Rousselot-Gilliéron (French) system, and other systems have borrewed from these such as the Revista de Filología española (Spanish) system or the Romanian dialectology system. These transcription systems have been used, adapted or extended in a relatively large quantity of dialectology works (French, Spanish and Portuguese, Italian, and Romanian), some of these are being digitized and require standardized characters. More recent transcription systems were developped in the second half of the 20th century, on the basis of these transcription systems and the IPA, to accomodate larger second generation dialectology works (European: ALE, Mediteranean: ALM, Romance languages: ALiR, and others), some of these require additional characters to be encoded. The characters being proposed are used mostly in Romance languages dialectology works but not exclusively, they are also used in transcription of other linguistic families present in the areas covered by these works. The characters needed for several other dialectology transcription systems, such as the Swedish, Danish and Norwegian systems would require further work and is out of the scope of this proposal. This proposal aims to encode the missing characters needed for these transcription systems and questions the current encoding model for superscript diacritic letters with diacritics (nested letters) given their heavy use in some transcription systems.
    [Show full text]
  • Revised Proposal to Encode Characters
    ISO/IEC JTC1 SC2 WG2 N3981 Universal Multiple-Octet Coded Character Set International Organization for Standardization Organisation Internationale de Normalisation Международная организация по стандартизации Doc Type: Working Group Document Title: Revised Proposal to encode characters for the English Phonotypic Alphabet (EPA) in the UCS Source: German NB Author: Karl Pentzlin Status: National Body Contribution Action: For consideration by JTC1/SC2/WG2 and UTC Date: 2011-01-18 Replaces: L2/10-229R, L2/10-403 Major changes compared with L2/10-229R (submitted to the UTC 2010-08-04): – The section 2.3 “Casing issues” is completely rewritten (based on the UTC feedback on Rev. 1). – The formal case pairing reflected in the character properties was rearranged considering the naming and the shape of the characters, rather than the special use in any EPA variant. – Variation sequences are no longer proposed. – In consequence of this, some characters were renamed, and the whole set was rearranged. – Three lower case forms from other sources were added, to accomplish the case pairing in the light of the valid stability policies (see the detailed explanations in the new section 2.3). – It is proposed to group capital letters without lowercase counterparts together, employing the otherwise unusable area in the “Alphabetic Presentation Forms” block. – One punctuation mark was added (an “inverted wiggly exclamation mark” was found in the sources). – In section 2.5 “Special issues on single characters”, paragraphs were added for characters where questions were raised in the UTC feedback. – The code positions of the punctuation marks were shifted to prevent overlapping with other proposals.
    [Show full text]
  • Proposal to Encode Additional Dialectology Latin Characters
    Proposal to encode additional dialectology Latin characters Denis Moyogo Jacquerye <[email protected]> 2014-08-06 Revision 1 Replaces L2/13-172 1. Background The recent addition of the German dialectology symbols to Unicode raises the question of other dialectology transcription systems being encoded. Romance dialectology transcription systems were created in the late 19th century or early 20th, in the same period as German dialectology systems or the International Phonetic Alphabet (IPA). Besides the Böhmer-Ascoli transcription from which the Teuthonista transcription is derived (both used in German dialectology), another major transcription systems is the French Rousselot-Gilliéron system. Other systems have borrowed from these such as the Spanish Revista de Filología española system or the Romanian dialectology system. These transcription systems have been used, adapted or extended in a relatively large quantity of dialectology works (French, Spanish and Portuguese, Italian, and Romanian), some of these are being digitized and would require standardized characters. More recent transcription systems were developped in the second half of the 20th century, based on these earlier transcription systems and the IPA, to accomodate larger second generation dialectology works (European: ALE, Mediteranean: ALM, Romance languages: ALiR, and others), some of these require additional characters to be encoded. The characters being proposed are used mostly in Romance languages dialectology works but not exclusively, they are also used in transcription of other linguistic families present in the areas covered by these works. The characters needed for several other dialectology transcription systems, such as the Swedish, Danish and Norwegian systems would require further work and are out of the scope of this proposal.
    [Show full text]
  • A New Method for Determining the Milky Way Bar Pattern Speed
    Mem. S.A.It. Vol. 00, 189 c SAIt 2008 Memorie della New method for determining the Milky Way bar pattern speed I. Minchev1, J. Nordhaus2 and A. C. Quillen3 1 Observatoire Astronomique, Universit´ede Strasbourg, Strasbourg, France 2 Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA 3 Department of Physics and Astronomy, University of Rochester, Rochester, NY, USA Abstract. Previous work has related the Galactic bar to structure in the local stellar ve- locity distribution. Here we show that the bar also influences the spatial gradients of the velocity vector via the Oort constants. By numerical integration of test-particles we sim- ulate measurements of the Oort C value in a gravitational potential including the Galactic bar. We account for the observed trend that C is increasingly negative for stars with higher velocity dispersion. By comparing measurements of C with our simulations we improve on previous models of the bar, estimating that the bar pattern speed is Ωb/Ω0 = 1.87 ± 0.04, ◦ ◦ where Ω0 is the local circular frequency, and the bar angle lies within 20 6 φ0 6 45 . We find that the Galactic bar affects measurements of the Oort constants A and B less than ∼ 2 km s−1 kpc−1 for the hot stars. 1. Introduction as orientation and pattern speed, have only been inferred indirectly from observations of The Galaxy is often modeled as an ax- the inner Galaxy (e.g., Blitz & Spergel 1991; isymmetric disk. With the ever increasing Weinberg 1992). proper motion and radial velocity data, it is now apparent that non-axisymmetric effects However, the bar has also been found to cannot be neglected (nonzero Oort constant affect the local velocity distribution of stars.
    [Show full text]
  • Unibook Document
    Title: Additional repertoire Amendment 2.3 to ISO/IEC 10646:2014 (4th edition) Date: 2015-01-31 L2/15-028R WG2 N4658 Source: Michel Suignard, project editor Status: Project Editor's summary of the character repertoire addition as of January 2015 Action: For review by WG2 and UTC experts Distribution: WG2 and UTC Replaces: WG2 N4651 Status This document presents a summary of all characters that constitute the tentative repertoire of the amendment 2.3 to ISO/IEC 10646:2014, with code positions, representative glyphs and character names. In this document, the names and code positions are shown as a result of the disposition of comments on PDAM2.2, document WG2 N4656, including some Emoji character names and code positions currently approved by UTC for future versions of the Unicode Standard. Manner of Presentation The character names and code points shown are the same for Unicode and ISO/IEC 10646, including annotations. Contents This document lists 7328 characters. The following list shows all 25 blocks (existing or new) to which characters are proposed to be added, these new proposed characters are higlighted in yellow. Existing characters from ISO/IEC 10646:2014 (4th edition), for which glyph corrections have been requested are shown highlighted in blue. Blocks which have only glyph corrections are not listed. 08A0-08FF Arabic Extended-A See document L2/13-130R L2/13-223 WG2 N4474 L2/14-105 L2/14-293 N4589 N4592 N4597 0C80-0CFF Kannada See document: WG2 N4591 L2/014-153 0D00-0D7F Malayalam See document WG2 N4428 N4429 L2/013-063 L2/013-051
    [Show full text]
  • 1 . Introduction to Systematically Pass to the L Imit in a Product Of
    ISSN sub w ww divided by hline to the power of B to the power of hline from hline to Banach a n sub : sub period 1 e 735 m i s hyphenn begin 8787f a l i periodg n ∗g sub d e slash j open parenthesis o electronic u r n al s slash B closing parenthesis sub J M A slash to the power ofISSN a c h ^ Jf subB J ^f period n r u l Math e f3em ogf u r0.4 n apt periodg ^f sub n r u l l Anale f3em ogf f period0.4 pt 5g M g af tBanach open parenthesisgg a 20 n h eg 1f mw 1 an closingf r a c f parenthesisww gf n r u l e f3emgf0.4 pt g gg^f a tc sub h i to the J powerf J g of comma. Math sub c nof ao l period u 1 r A comma n a subg n. 1 subf al 0g l 1Anal y endashf subo s i f 1g s 35. Capital 5 Sigmaf M hyphen a g t ( 20 f h e g 1 f m g 1 f a g ) f t g^f , g f ; i g f c g no f a l g . 1 f A g CONVERGENCE B Banach ana chJJ:Matho urna:l Analof :5Mat(20he1m1a)ticnoal: 1A;n1a0l1y −−si1s35 ISSNw ww , GABRIELf n g 1 NGUETSENGf a g 0 tof thel powerg ::1e1735 ofmisf 1−y AND8787g:de NILS −−=j(oelectronic SVANSTEDTf surnals i =Bg)J to1MA thef powers =g of35 2 *g f : f .
    [Show full text]
  • Technical and Production Information Shalin Liu Performance Center 37 Main Street - Rockport, MA 01966
    ….the distinctive sound of Rockport Shalin Liu Performance Center at Rockport Music Technical and Production Information Shalin Liu Performance Center 37 Main Street - Rockport, MA 01966 Please direct all enquiries to Production Services phone 978.546.7391 x 130 email: [email protected] www.rockportmusic.org The information contained in this document is given in good faith and is believed to be correct at the time of preparation. While every effort is made to fulfill presenters’ requirements from in-house stock, no guarantee is made that the equipment listed will be available for a particular event. Availability is subject to change due to the requirements of Rockport Music. Revised: April 2019 Shalin Liu Performance Center Concert Hall CONTENTS GENERAL INFORMATION ......................................................................................................................... 5 SHALIN LIU PERFORMANCE CENTER ......................................................................................................... 5 Seating ...................................................................................................................................................... 6 Seating Capacities ................................................................................................................................. 6 Recommended Tiers ............................................................................................................................. 6 Seating Chart ............................................................................................................................................
    [Show full text]
  • Proposal to Encode Additional Dialectology Latin Characters
    Proposal to encode additional dialectology Latin characters Denis Moyogo Jacquerye <[email protected]> 2014-07-28 1. Background The recent addition of the German dialectology symbols to Unicode raises the question of other dialectology transcription systems being encoded. Romance dialectology transcription systems were created in the late 19th century or early 20th, in the same period as German dialectology systems or the International Phonetic Alphabet (IPA). Besides the Böhmer-Ascoli transcription from which the Teuthonista transcription is derived (both used in German dialectology), another major transcription systems is the French Rousselot-Gilliéron system, and other systems have borrowed from these such as the Spanish Revista de Filología española system or the Romanian dialectology system. These transcription systems have been used, adapted or extended in a relatively large quantity of dialectology works (French, Spanish and Portuguese, Italian, and Romanian), some of these are being digitized and would require standardized characters. More recent transcription systems were developped in the second half of the 20th century, based on these earlier transcription systems and the IPA, to accomodate larger second generation dialectology works (European: ALE, Mediteranean: ALM, Romance languages: ALiR, and others), some of these require additional characters to be encoded. The characters being proposed are used mostly in Romance languages dialectology works but not exclusively, they are also used in transcription of other linguistic families present in the areas covered by these works. The characters needed for several other dialectology transcription systems, such as the Swedish, Danish and Norwegian systems would require further work and are out of the scope of this proposal.
    [Show full text]