Content-Type: multipart/mixed; boundary="-------------0803121232921" This is a multi-part message in MIME format. ---------------0803121232921 Content-Type: text/plain; name="08-45.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="08-45.keywords" Jacobi matrices, Subordinacy theory, Asymptotics of generalized eigenvectors ---------------0803121232921 Content-Type: application/postscript; name="Naboko-Simonov.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Naboko-Simonov.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software %%Title: double_root.dvi %%CreationDate: Wed Mar 12 20:28:17 2008 %%Pages: 17 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMBX12 CMR10 CMCSC10 CMR12 CMTI10 CMR9 CMMI12 CMMI8 %%+ CMEX10 CMSY10 CMR8 CMSY8 CMMI6 CMR6 CMSY6 MSBM10 CMTI12 MSAM10 %%+ CMTT10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 double_root %DVIPSParameters: dpi=8000 %DVIPSSource: TeX output 2007.08.29:2000 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro 0 0 %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 80 /summationtext put dup 81 /producttext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 113 /radicalBig put dup 114 /radicalbigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 50 /two put dup 58 /colon put dup 59 /semicolon put dup 65 /A put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-36 -251 1103 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 78 /N put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 61 /equal put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5 D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D 23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8 D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B 93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711 6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4 EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953 CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE 00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5 B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA 99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904 A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB 11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5 50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB6CCCC950AF F6A29F479A2D64381EEF89EDD5FF9B5592CE8F4EE8E3BA1E6E9AA35F5FC82629 E25D1F36DF188864FB57F960F508173D284660BD33334C022E06D6B3CDBC272B C8FD6324218C00DD1EF4C0BB2098AE7AC732209CA00AFBDDCA81147BF7673CB0 59C3EFC6DCE1B7F5FAB8C1610BF6CB38917B9D477E87726C65A520B2BE0595A9 5F960B111E818479CE2811F45966785F205D344E4DFE632C06705CBB5B4EEC20 E731D7DA971EABC6923DED1B3A663BB16F453CA20BA20D3A281DD2BB0ADAA592 F1B999078F84D0D1A4DD09AA5DF4302706CEDECCCFB5848F36129332C1E9A869 54116686708EC8A88F7781E0C1A46B8B574D361E4074793BBF153765FA9C0D7F 84E95E19CCFFC94EF6B1B81410768FB00B807C36EB7B60E8B6ED08482E48A374 ACC5DD9FA74812ED51E4F3A24242557F0DD3531BA0B8D7BD21B6AFDC54EEFEC6 FF6C3753FFD7A707F66FFAB2D8F59A6C04A297B207D3E8EDE2ABB5B330571A27 27C0D2BF072FF52A98A14AF6E28E83C74E03C10F3B81A3F277B8B06F9647E2C8 748F5423DF06DFBD8A517659A7643478C383C67187BA84CAB4D8A3126AE67DCF 0CFCC199CB90813C574E89E1C0F36910617BF5A6B7346518B4A8AD5413786272 C4150BA540BBFA790937A21E69E30E660F47954569BCB2403BECA5EF2F0FBDA7 A30F92EE880A46FA758722A0857F6BE3FC83451BFA922B5FE7BB3BD45F6742CA 1F49D028C96BDF89DAEECBF33BF189E8C5509AF397FB3BCD64972870FD3F3C69 00D36D213E8BCCF605B9515F632B4838A823273C6D2D93789BBE6524E0CD4551 6D1BFCA0BC5EDF2D025B7CA2A6EC2BB85B2427947ED75442F121CD9A3BB94F76 7A5C335020C575AA8E73CBA2010078A140F542EA5F8AEBDB01BFEB3D7DF9E8D3 DA6EC07AEC0C5D3D603839EB10E4A666D010C80DD4FBD0857FE2E643216B8333 2FA960AA75783C511880043B40C12194F6C56D5EC666269CD720FB2E9746EE39 770C31C2D6D6E6445F3ACBFB3E46742B637EFEA252BDA1436D3B4F5198B5587F 758EC8390CF47722E4E56C8FE755EE7FC2796BC09B474B2573994941AFC33BB5 31A22EA7E243745B2B427AF2188349A0F4D04E49BE1F1F45A004727025345055 CE7C5D93D1E8D0CBAEA1C9191BD7FC8BE718D64D42788E1C77E2A2B478ACF0AB 1D09EDE6E1D0E95BD8988065EA9017895978CE9A7A95A8A47FFEDEB4B93630BF BE28B3B41E949C9429877A204C6D7701504F6E2DD1CD7C13473D4EFE20C1F126 C190E44B8DA28D5A467262660999275CE40DA2D01EF502718A88618EBEA075D3 C87298652D0F1989EBD00B1C8F9900CEDDA7097523E3FB0F92A12DB8F2387CA8 80C7B6116F614898923E01FAB2950DEBB6211C8628BDDC8F7DFB51353879CFC0 2596966CDF1EEBFF75DE6D1428B27B3DD1065C2B3EA821BA72FD963B7EC6741A 543384ED11BF4600949A017C39D384A18EEDECDD568B2364271DDF72A81F68A6 BD6559809003A1085A490B868812C9EE243BF2B926940CA01679747CD4209B55 836499414EDB7DBB 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 14 /delta put dup 61 /slash put dup 108 /l put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 33 /arrowright put dup 49 /infinity put dup 54 /negationslash put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 58 /colon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 100 /d put dup 105 /i put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 6 /plusminus put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 74 /J put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 21 /lambda put dup 59 /comma put dup 61 /slash put dup 65 /A put dup 66 /B put dup 78 /N put dup 86 /V put dup 97 /a put dup 98 /b put dup 102 /f put dup 105 /i put dup 107 /k put dup 108 /l put dup 110 /n put dup 112 /p put dup 113 /q put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 21 /lambda put dup 22 /mu put dup 27 /sigma put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 88 /X put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 4391C9DF440285B8FC159D0E98D4258FC57892DCC57F7903449E07914FBE9E67 3C15C2153C061EB541F66C11E7EE77D5D77C0B11E1AC55101DA976CCACAB6993 EED1406FBB7FF30EAC9E90B90B2AF4EC7C273CA32F11A5C1426FF641B4A2FB2F 4E68635C93DB835737567FAF8471CBC05078DCD4E40E25A2F4E5AF46C234CF59 2A1CE8F39E1BA1B2A594355637E474167EAD4D97D51AF0A899B44387E1FD933A 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 45 /hyphen put dup 46 /period put dup 67 /C put dup 69 /E put dup 75 /K put dup 77 /M put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 52 /four put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 73 /I put dup 74 /J put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 88 /X put dup 89 /Y put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put readonly def /FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39139632 55387786 1000 8000 8000 (double_root.dvi) @start /Fa 134[581 2[581 581 1[581 581 1[581 581 581 581 581 581 1[581 581 581 1[581 2[581 581 32[581 17[581 46[{}19 1106.96 /CMTT10 rf /Fb 174[889 81[{}1 885.568 /CMEX10 rf /Fc 252[1033 3[{}1 1328.35 /MSAM10 rf /Fd 134[631 598 863 598 697 432 531 548 598 664 664 731 1063 332 598 1[399 664 598 399 598 664 598 598 664 9[1298 2[930 731 948 1[881 1[966 1[815 2[501 966 1[848 1[981 2[966 5[399 399 7[664 3[399 465 399 2[531 531 5[664 19[1146 1[731 797 11[{}48 1328.35 /CMTI12 rf /Fe 177[959 10[959 67[{}2 1328.35 /MSBM10 rf /Ff 249[640 5[640{}2 664.176 /CMSY6 rf /Fg 194[621 8[406 406 406 406 406 4[621 43[{}7 664.176 /CMR6 rf /Fh 145[511 1[267 46[424 46[376 2[534 11[{}5 664.176 /CMMI6 rf /Fi 143[784 57[0 4[941 15[941 26[732 5[732{}6 885.568 /CMSY8 rf /Fj 139[366 371 367 8[261 4[523 418 5[261 1[261 29[732 2[261 5[470 470 470 470 470 4[732 1[366 366 40[{}18 885.568 /CMR8 rf /Fk 148[664 369 2[664 664 27[900 19[0 3[886 1328 15[1328 8[1033 2[1033 1033 2[1033 1[664 8[1033 2[664 1033 369 1033{}19 1328.35 /CMSY10 rf /Fl 141[1328 1328 23[1697 1919 6[1255 1402 12[1162 1162 1162 1162 14[1162 1162 12[775 775 1052 1052 4[996 996 4[701 701 978 978 793 793 2[738 443 10[609 609{}28 1328.35 /CMEX10 rf /Fm 133[438 8[420 474 1[571 1[281 490 1[320 2[452 3[403 500 10[548 7[747 11[710 705 3[470 1[261 37[549 6[416 485 1[604 11[{}20 885.568 /CMMI8 rf /Fn 133[604 634 1[930 629 740 2[586 577 653 625 776 1[387 676 5[603 1[560 553 683 7[755 1079 1[758 1[762 800 990 1030 838 994 1042 1258 885 1107 719 574 2[842 1[1080 931 988 975 2[1012 650 1012 361 361 30[739 4[783 759 6[576 675 734 827 11[{}48 1328.35 /CMMI12 rf /Fo 166[768 2[768 768 740 569 754 1[697 796 768 938 640 796 1[370 768 803 1[697 782 740 725 768 7[512 512 512 512 512 512 512 512 512 512 48[{}30 996.264 /CMR9 rf /Fp 134[537 1[736 1[594 368 453 467 1[566 566 622 905 283 1[339 339 566 2[509 566 509 509 566 13[622 5[993 1[851 5[751 1[792 20[339 396 32[622 12[{}27 1106.96 /CMTI10 rf /Fq 133[667 815 815 1[815 815 785 608 800 1[741 844 815 992 682 844 1[401 815 1[711 741 829 785 770 815 12[1044 1[1063 1[985 2[1314 2[753 539 5[1044 1[1081 6[424 11[424 502 45[{}33 1328.35 /CMCSC10 rf /Fr 133[578 686 686 939 686 723 506 513 506 686 723 650 723 1084 361 686 397 361 723 650 397 578 723 578 723 650 3[361 1[361 3[1336 1[975 939 723 957 1[885 1012 975 1192 813 1011 668 469 975 1021 849 885 993 939 921 975 3[1012 1[361 361 650 650 650 650 650 650 650 650 650 650 1[361 434 361 1012 1[506 506 361 4[650 19[1084 1[723 759 11[{}73 1328.35 /CMR12 rf /Fs 134[679 2[679 679 654 507 667 1[617 704 679 827 568 704 1[335 679 710 593 617 1[654 642 679 11[901 1[676 2[821 2[1095 3[449 4[918 2[901 7[612 612 3[612 2[612 612 1[354 418 354 44[{}35 1106.96 /CMCSC10 rf /Ft 128[553 4[492 584 584 799 584 615 430 437 434 584 615 553 615 922 307 584 338 307 615 553 338 492 615 492 615 553 3[307 1[307 676 830 1[1138 830 830 799 615 815 1[753 861 830 1015 692 861 569 400 830 869 723 753 846 799 784 830 6[307 553 553 553 553 553 553 553 553 553 553 553 307 369 307 2[430 430 5[553 21[615 646 11[{}73 1106.96 /CMR10 rf /Fu 136[1079 2[581 589 610 1[830 747 830 1245 415 789 1[415 830 747 1[682 830 664 1[726 7[1128 1128 2[1148 1039 830 1115 1[1021 1122 1168 1418 898 1[772 557 1168 1[939 981 1145 1079 1062 1128 6[415 5[747 747 747 747 2[415 4[581 581 40[{}45 1328.35 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin 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Fn(u)17349 10187 y Fm(n)p Fj(+1)19473 9988 y Fr(+)295 b Fn(F)21622 10187 y Fj(1)22148 9988 y Fr(\()p Fn(n)p Fr(\))p Fn(u)24676 10187 y Fm(n)25598 9988 y Fr(+)g Fn(F)27747 10187 y Fj(2)28272 9988 y Fr(\()p Fn(n)p Fr(\))p Fn(u)30800 10187 y Fm(n)p Fi(\000)p Fj(1)32998 9988 y Fr(=)369 b(0)p Fn(:)6075 12424 y Fr(The)433 b(latter)h(has)g(t) -36 b(w)g(o)433 b("appro)-36 b(ximate)435 b(solutions")f(of)g(the)f (form)21975 15002 y Fn(z)22638 14454 y Fi(\006)22579 15330 y Fm(n)23794 15002 y Fr(=)369 b Fn(n)25951 14454 y Fm(\015)26544 15002 y Fn(e)27147 14454 y Fi(\006)p Fm(An)29155 14141 y Fh(\016)29664 15002 y Fn(;)6075 17456 y Fr(with)433 b Fn(\015)441 b Fr(=)369 b Fk(\000)12700 16933 y Fm(\013)p 12700 17151 605 54 v 12767 17914 a Fj(4)13437 17456 y Fr(,)434 b Fn(\016)419 b Fr(=)368 b(1)296 b Fk(\000)19014 16933 y Fm(\013)p 19014 17151 V 19081 17914 a Fj(2)19751 17456 y Fr(,)434 b Fn(A)369 b Fr(=)23404 16933 y Fm(B)p 23404 17151 754 54 v 23555 17914 a(\016)24290 17456 y Fr(.)578 b(This)434 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y(structure)468 b(of)j(the)f("solution")h(one)f(can)g(determine)g(unkno)-36 b(wn)469 b(v)-72 b(alues)471 b(of)g Fn(\015)72 b Fr(,)479 b Fn(\016)6075 28666 y Fr(and)423 b Fn(A)g Fr(from)h(the)f(condition)g (of)h(cancellation)g(of)g(all)h(decreasing)e(terms)g(in)g(\(8\))6075 30216 y(up)432 b(to)i(the)f(order)g Fn(O)36 b Fr(\()p Fn(n)17491 29734 y Fi(\000)p Fj(2)p Fm(\013)19354 30216 y Fr(\).)578 b(The)433 b(equation)i(\(8\))e(implies)h(that)6075 32929 y(\(9\))7403 33613 y Fl(\022)9425 34689 y Fn(z)10088 34207 y Fi(\006)10029 35018 y Fm(n)8934 36239 y Fn(z)9597 35689 y Fi(\006)9538 36565 y Fm(n)p Fj(+1)11921 33613 y Fl(\023)13267 35486 y Fr(=)14648 33613 y Fl(\022\022)18926 34689 y Fr(0)4646 b(1)17157 36239 y Fk(\000)p Fn(F)19032 36438 y Fj(2)19558 36239 y Fr(\()p Fn(n)p Fr(\))1107 b Fk(\000)p Fn(F)24328 36438 y Fj(1)24854 36239 y Fr(\()p Fn(n)p Fr(\))27196 33613 y Fl(\023)28469 35486 y Fr(+)29775 33613 y Fl(\022)31307 34689 y Fr(0)3122 b(0)31307 36239 y(0)1107 b Fn(O)36 b Fr(\()p 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b(from)h(the)e(fact)h(of)h(mo)36 b(di\014ed)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 12328 3345 a Fo(ONE)443 b(MODEL)i(IN)e(CRITICAL)e (HYPERBOLIC)h(SITUA)-85 b(TION)5738 b(9)6075 6001 y Fr(wronskian)434 b(p)36 b(ersistence\),)433 b(w)-36 b(e)434 b(obtain)6075 9305 y(\(10\))2122 b Fn(S)11386 8757 y Fi(\000)p Fj(1)11309 9634 y Fm(n)p Fj(+1)13137 9305 y Fn(N)14179 9504 y Fm(n)14805 9305 y Fn(S)15605 9504 y Fm(n)16600 9305 y Fr(=)369 b Fn(I)399 b Fr(+)21492 8407 y(1)p 20394 9000 2848 54 v 20394 10216 a Fn(n)21170 9833 y Fj(3)p Fm(\013=)p Fj(2)23595 7432 y Fl(\022)26922 8508 y Fn(O)36 b Fr(\(1\))2902 b Fn(e)33119 8026 y Fj(2)p Fm(An)34865 7714 y Fh(\016)35375 8508 y Fn(O)36 b Fr(\(1\))25127 10229 y Fn(e)25730 9747 y Fi(\000)p Fj(2)p Fm(An)28208 9434 y Fh(\016)28717 10229 y Fn(O)g Fr(\(1\))2537 b Fn(O)36 b Fr(\(1\))38621 7432 y Fl(\023)39967 9305 y Fr(=:)369 b Fn(K)42816 9504 y Fm(n)43442 9305 y Fn(:)7403 12535 y Fr(The)528 b(calculations)g(pro)36 b(duced)527 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b(es)6075 32059 y Fn(S)6875 32258 y Fm(n)7966 32059 y Fd(gives)7182 35550 y Fn(S)8059 35001 y Fi(\000)p Fj(1)7982 35878 y Fm(n)p Fj(+1)10032 33677 y Fl(\022)13332 34753 y Fr(0)4646 b(1)11563 36302 y Fk(\000)p Fn(F)13438 36501 y Fj(2)13964 36302 y Fr(\()p Fn(n)p Fr(\))1107 b Fk(\000)p Fn(F)18734 36501 y Fj(1)19260 36302 y Fr(\()p Fn(n)p Fr(\))21601 33677 y Fl(\023)22800 35550 y Fn(S)23600 35749 y Fm(n)24596 35550 y Fr(=)30479 34651 y(1)p 26109 35244 9391 54 v 26109 36488 a Fn(z)26772 36105 y Fi(\000)26713 36817 y Fm(n)27560 36488 y Fn(z)28223 35939 y Fj(+)28164 36814 y Fm(n)p Fj(+1)30288 36488 y Fk(\000)295 b Fn(z)32279 36105 y Fj(+)32220 36817 y Fm(n)33067 36488 y Fn(z)33730 35939 y Fi(\000)33671 36814 y Fm(n)p Fj(+1)6075 39331 y Fk(\002)7108 37458 y Fl(\022)8639 38534 y Fn(z)9302 38052 y Fi(\000)9243 38862 y Fm(n)10090 38534 y Fn(z)10753 37984 y Fj(+)10694 38859 y Fm(n)p Fj(+1)12818 38534 y Fr(+)g Fn(z)14788 38052 y Fj(+)14729 38862 y Fm(n)15575 38534 y Fr(\()p Fn(F)16923 38733 y 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b(r)-66 b(e)g(duc)g(es)464 b(to)h(the)f(fol)66 b(lowing)465 b(one)7182 49079 y Fn(I)399 b Fr(+)13965 48180 y(1)p 9595 48773 V 9595 50018 a Fn(z)10258 49634 y Fi(\000)10199 50346 y Fm(n)11045 50018 y Fn(z)11708 49468 y Fj(+)11649 50343 y Fm(n)p Fj(+1)13773 50018 y Fk(\000)295 b Fn(z)15764 49634 y Fj(+)15705 50346 y Fm(n)16552 50018 y Fn(z)17215 49468 y Fi(\000)17156 50343 y Fm(n)p Fj(+1)7236 52860 y Fk(\002)8564 50987 y Fl(\022)10612 52063 y Fn(z)11275 51581 y Fj(+)11216 52391 y Fm(n)12062 52063 y Fr(\()p Fn(z)13231 51513 y Fi(\000)13172 52388 y Fm(n)p Fj(+1)15296 52063 y Fr(+)g Fn(F)17445 52262 y Fj(1)17971 52063 y Fn(z)18634 51581 y Fi(\000)18575 52391 y Fm(n)19717 52063 y Fr(+)f Fn(F)21865 52262 y Fj(2)22391 52063 y Fn(z)23054 51513 y Fi(\000)22995 52388 y Fm(n)p Fi(\000)p Fj(1)24824 52063 y Fr(\))2140 b Fn(z)28133 51581 y Fj(+)28074 52391 y Fm(n)28920 52063 y Fr(\()p Fn(z)30089 51513 y Fj(+)30030 52388 y Fm(n)p Fj(+1)32154 52063 y Fr(+)295 b Fn(F)34303 52262 y Fj(1)34829 52063 y 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Fn(e)37757 66873 y Fj(2)p Fm(An)39503 66561 y Fh(\016)40012 67355 y Fn(O)36 b Fr(\(1\))29764 69076 y Fn(e)30367 68594 y Fi(\000)p Fj(2)p Fm(An)32845 68281 y Fh(\016)33354 69076 y Fn(O)g Fr(\(1\))2537 b Fn(O)36 b Fr(\(1\))43258 66279 y Fl(\023)44457 68152 y Fn(:)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 6075 3345 a Fo(10)7817 b(SER)-28 b(GUEI)340 b(NABOK)-28 b(O)341 b(AND)g(SER)-28 b(GEY)340 b(SIMONO)-28 b(V)7403 6001 y Fr(The)481 b(problem)f(no)-36 b(w)481 b(is)g(the)f(gro)-36 b(wing)481 b(exp)36 b(onen)-36 b(t)480 b(in)h(the)f(upp)36 b(er-righ)-36 b(t)479 b(en)-36 b(try)6075 7551 y(of)533 b(the)f(matrix,)558 b(whic)-36 b(h)533 b(lea)-36 b(v)g(es)534 b(no)e(c)-36 b(hance)532 b(to)h(call)h(the)e(remainder)g(small)h(in)6075 9101 y(an)-36 b(y)391 b(sense.)563 b(But)390 b(this)h(exp)36 b(onen)-36 b(t)390 b(can)g(b)36 b(e)391 b(comp)36 b(ensated)390 b(b)-36 b(y)390 b(the)g(deca)-36 b(ying)391 b(one)6075 10651 y(in)433 b(the)g(lo)-36 b(w)g(er-left)435 b(en)-36 b(try)433 b(as)h(w)-36 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b(we)c(assume)h(the)e(notation)g(for)6075 26944 y(the)483 b(pr)-66 b(o)g(duct)13336 25682 y Fm(N)13130 25947 y Fl(Q)12870 28073 y Fm(n)p Fj(=1)14865 26944 y Fn(a)15548 27143 y Fm(n)16658 26944 y Fd(me)g(aning)22859 25947 y Fl(Q)21857 28112 y Fm(n)p Fj(:)157 b Fm(a)23346 28223 y Fh(n)23913 28112 y Fi(6)p Fj(=0)25336 26944 y Fn(a)26019 27143 y Fm(n)26645 26944 y Fd(.)654 b(We)483 b(also)i(use)f(the)g (notation)e Fn(l)42856 26462 y Fj(1)43866 26944 y Fd(and)6075 29581 y Fn(D)7191 29099 y Fj(1)8304 29581 y Fd(for)587 b(the)h(matrix)e(se)-66 b(quenc)g(es,)616 b(i.e.)964 b(the)588 b(se)-66 b(quenc)g(e)585 b(of)j(matric)-66 b(es)586 b Fk(f)p Fn(M)42806 29780 y Fm(n)43433 29581 y Fk(g)44097 29099 y Fi(1)44097 29909 y Fm(n)p Fj(=1)6075 31130 y Fd(b)-66 b(elongs)464 b(to)9051 33611 y Fk(\017)554 b Fn(l)10685 33129 y Fj(1)11211 33611 y Fd(,)465 b(i\013)14151 32349 y Fi(1)13921 32615 y Fl(P)13735 34740 y Fm(n)p Fj(=1)15730 33611 y Fk(k)p Fn(M)17652 33810 y Fm(n)18279 33611 y Fk(k)369 b Fn(<)f Fk(1)p Fd(,)9051 36760 y Fk(\017)554 b Fn(D)11385 36278 y Fj(1)11911 36760 y Fd(,)464 b(i\013)14851 35498 y Fi(1)14620 35763 y Fl(P)14435 37889 y Fm(n)p Fj(=1)16429 36760 y Fk(k)p Fn(M)18351 36959 y Fm(n)p Fj(+1)20475 36760 y Fk(\000)296 b Fn(M)23062 36959 y Fm(n)23688 36760 y Fk(k)370 b Fn(<)e Fk(1)p Fd(.)7403 39903 y Fr(Consider)434 b(a)g(linear)g(di\013erence)e(system)6075 42870 y(\(12\))15106 40997 y Fl(\022)16637 42073 y Fn(u)17377 42272 y Fm(n)p Fj(+1)16693 43622 y Fn(v)17322 43821 y Fm(n)p Fj(+1)19760 40997 y Fl(\023)21107 42870 y Fr(=)368 b(\()p Fn(I)399 b Fr(+)295 b Fn(p)25926 43069 y Fm(n)26552 42870 y Fn(V)27310 43069 y Fm(n)28232 42870 y Fr(+)g Fn(R)30529 43069 y Fm(n)31155 42870 y Fr(\))31882 40997 y Fl(\022)33413 42073 y Fn(u)34153 42272 y Fm(n)33469 43622 y Fn(v)34098 43821 y Fm(n)35333 40997 y Fl(\023)36533 42870 y Fn(;)6075 45910 y Fr(supp)36 b(osing)489 b(it)g (non-degenerate,)503 b(i.e.)746 b(det\()p Fn(I)437 b Fr(+)333 b Fn(p)30728 46109 y Fm(n)31354 45910 y Fn(V)32112 46109 y Fm(n)33071 45910 y Fr(+)g Fn(R)35406 46109 y Fm(n)36033 45910 y Fr(\))463 b Fk(6)p Fr(=)h(0)490 b(for)g(ev)-36 b(ery)490 b Fn(n)6075 47459 y Fr(\(this)433 b(means)g(that)g(the)g (system)h(has)g(t)-36 b(w)g(o)434 b(linearly)g(indep)36 b(enden)-36 b(t)432 b(solutions\).)6075 49858 y Fu(Theorem)540 b(2.)572 b Fd(\(se)-66 b(e)498 b Fr([9)q(])g Fd(wher)-66 b(e)498 b(the)f(the)h(essential)f(p)-66 b(art)498 b(of)f(the)h(The)-66 b(or)g(em)497 b(has)6075 51407 y(b)-66 b(e)g(en)463 b(pr)-66 b(ove)g(d\).)7403 52957 y(L)g(et)9051 55179 y Fk(\017)554 b Fn(p)10922 55378 y Fm(n)11917 55179 y Fk(!)369 b Fr(0)465 b Fd(b)-66 b(e)465 b(a)564 b Fr(p)36 b(ositiv)-36 b(e)466 b Fd(se)-66 b(quenc)g(e)463 b(with)30915 53917 y Fi(1)30684 54183 y Fl(P)30499 56309 y Fm(n)p Fj(=1)32493 55179 y Fn(p)33146 55378 y Fm(n)34141 55179 y Fr(=)369 b(+)p Fk(1)p Fd(.)9051 57605 y Fk(\017)554 b(f)p Fn(V)11691 57804 y Fm(n)12318 57605 y Fk(g)586 b(2)g Fn(D)16156 57123 y Fj(1)17264 57605 y Fd(b)-66 b(e)582 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y Fm(n)17224 68284 y Fr(=)18605 66012 y Fl( )20229 66623 y Fm(n)19666 67022 y Fl(Y)19656 69851 y Fm(k)24 b Fj(=1)21372 68284 y Fr([1)296 b(+)f Fn(p)24639 68483 y Fm(k)25207 68284 y Fn(\026)25990 68483 y Fj(1)p Fm(;)p Fj(2)27248 68284 y Fr(\()p Fn(k)45 b Fr(\)])29342 66012 y Fl(!)30615 68284 y Fr(\()31121 67712 y Fk(\000)-1033 b(!)31483 68284 y Fn(e)32449 68483 y Fj(1)p Fm(;)p Fj(2)34002 68284 y Fr(+)294 b Fn(o)p Fr(\(1\)\))p Fn(;)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 12328 3345 a Fo(ONE)443 b(MODEL)i(IN)e (CRITICAL)e(HYPERBOLIC)h(SITUA)-85 b(TION)5226 b(13)6075 6001 y Fd(wher)-66 b(e)451 b Fn(\026)10514 6200 y Fj(1)11492 6001 y Fd(and)h Fn(\026)14786 6200 y Fj(2)15763 6001 y Fd(\(R)-66 b(e)452 b Fn(\026)19009 6200 y Fj(1)19903 6001 y Fk(\024)369 b Fd(R)-66 b(e)451 b Fn(\026)24019 6200 y Fj(2)24545 6001 y Fd(\))h(ar)-66 b(e)452 b(the)f(eigenvalues)g (of)h(the)g(matrix)e Fn(V)290 b Fd(,)6075 6979 y Fk(\000)-1033 b(!)6437 7551 y Fn(e)7403 7750 y Fj(1)8295 7551 y Fd(and)10721 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26712 y(Theorem)433 b(for)i(a)e(system)h(of)h(a)e(sp)36 b(ecial)435 b(form)6075 29549 y(\(13\))12944 27676 y Fl(\022)14475 28752 y Fn(u)15215 28951 y Fm(n)p Fj(+1)14531 30302 y Fn(v)15160 30501 y Fm(n)p Fj(+1)17597 27676 y Fl(\023)18944 29549 y Fr(=)20325 27676 y Fl(\022)21303 29549 y Fn(I)399 b Fk(\000)23604 27676 y Fl(\022)25135 28752 y Fn(q)25712 28951 y Fm(n)27445 28752 y Fr(0)25412 30302 y(0)1383 b(0)28649 27676 y Fl(\023)29922 29549 y Fr(+)295 b Fn(R)32219 29748 y Fm(n)32845 27676 y Fl(\023)221 b(\022)35576 28752 y Fn(u)36316 28951 y Fm(n)35632 30302 y Fn(v)36261 30501 y Fm(n)37496 27676 y Fl(\023)38695 29549 y Fn(:)6075 32387 y Fr(The)306 b(meaningful)g(part)g(of)h(this)f (system)g(is)g(diagonal)i(and)d(the)h(larger)h(eigen)-36 b(v)-72 b(alue)6075 33936 y(of)429 b(the)f(corresp)36 b(onding)428 b(matrix)h Fn(V)718 b Fr(is)429 b(exactly)h(zero.)577 b(In)428 b(what)h(follo)-36 b(ws)430 b(w)-36 b(e)429 b(will)6075 35486 y(use)448 b(the)g(follo)-36 b(wing)451 b(statemen)-36 b(t)447 b(\(its)i(pro)36 b(of)449 b(can)g(b)36 b(e)448 b(found)g(in)h(the)f(v)-36 b(ery)449 b(end)f(of)6075 37036 y(the)433 b(App)36 b(endix\).)6075 39149 y Fu(Lemma)499 b(1.)553 b Fd(L)-66 b(et)9051 41307 y Fk(\017)554 b Fn(q)10846 41506 y Fm(n)11841 41307 y Fk(!)369 b Fr(0)465 b Fd(b)-66 b(e)464 b(such)i(a)564 b Fr(p)36 b(ositiv)-36 b(e)466 b Fd(se)-66 b(quenc)g(e)464 b(that)33628 40045 y Fi(1)33398 40311 y Fl(P)33212 42436 y Fm(n)p Fj(=1)35207 41307 y Fn(q)35784 41506 y Fm(n)36779 41307 y Fr(=)368 b(+)p Fk(1)p Fd(.)9051 43733 y Fk(\017)554 b(f)p Fn(R)11923 43932 y Fm(n)12549 43733 y Fk(g)369 b(2)g Fn(l)15253 43251 y Fj(1)16244 43733 y Fd(b)-66 b(e)464 b(a)i Fr(2)295 b Fk(\002)g Fr(2)466 b Fd(matrix)d(se)-66 b(quenc)g(e.)6075 45554 y(Then)464 b(ther)-66 b(e)464 b(exists)g(a)h(solution)g(of)g(the) g(system)564 b Fr(\(13\))p Fd(of)465 b(the)f(form)19110 46592 y Fl(\022)20641 47668 y Fn(u)21381 47867 y Fm(n)20697 49218 y Fn(v)21326 49417 y Fm(n)22561 46592 y Fl(\023)23908 48465 y Fr(=)25288 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Fj(1)33145 68607 y Fm(n)34584 68279 y Fn(:)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 6075 3345 a Fo(14)7817 b(SER)-28 b(GUEI)340 b(NABOK)-28 b(O)341 b(AND)g(SER)-28 b(GEY)340 b(SIMONO)-28 b(V)7403 6001 y Fr(Without)590 b(loss)h(of)g(generalit)-36 b(y)591 b(w)-36 b(e)590 b(ma)-36 b(y)591 b(consider)f(all)h(the)f (matrices)g Fk(f)p Fn(V)44634 6200 y Fm(n)45261 6001 y Fk(g)6075 7551 y Fr(to)554 b(b)36 b(e)553 b(diagonalizable.)940 b(General)554 b(case)g(can)g(b)36 b(e)553 b(reduced)g(to)g(that)h(one)f (b)-36 b(y)554 b(a)6075 9101 y(prop)36 b(er)377 b(correction)g(of)h (the)f(sequence)h Fn(R)26121 9300 y Fm(n)27124 9101 y Fr(for)g(\014nitely)g(man)-36 b(y)378 b(v)-72 b(alues)378 b(of)g Fn(n)g Fr(only)-108 b(.)6075 10651 y(In)517 b(what)g(follo)-36 b(ws)519 b(w)-36 b(e)517 b(supp)36 b(ose)516 b(for)i(the)e(notation)h (con)-36 b(v)g(enience)517 b(that)g(all)h(the)6075 12200 y(matrices)526 b Fn(V)12135 12399 y Fm(n)13287 12200 y Fr(are)h(diagonalizable.)857 b(F)-108 b(ollo)-36 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Fr(\))17833 20482 y Fl(\022)18811 22355 y Fn(I)399 b Fr(+)295 b Fn(p)21744 22554 y Fm(n)22591 20482 y Fl(\022)24123 21558 y Fn(\026)24906 21757 y Fj(1)25431 21558 y Fr(\()p Fn(n)p Fr(\))2330 b(0)25346 23108 y(0)g Fn(\026)29109 23307 y Fj(2)29634 23108 y Fr(\()p Fn(n)p Fr(\))31976 20482 y Fl(\023\023)34227 22355 y Fr(+)294 b Fn(T)36476 21806 y Fi(\000)p Fj(1)36295 22683 y Fm(n)p Fj(+1)38124 22355 y Fn(R)39114 22554 y Fm(n)39741 22355 y Fn(T)40503 22554 y Fm(n)25675 26041 y Fr(=)369 b Fn(I)399 b Fr(+)295 b Fn(p)29989 26240 y Fm(n)30836 24168 y Fl(\022)32368 25244 y Fn(\026)33151 25443 y Fj(1)33676 25244 y Fr(\()p Fn(n)p Fr(\))2330 b(0)33591 26794 y(0)g Fn(\026)37354 26993 y Fj(2)37879 26794 y Fr(\()p Fn(n)p Fr(\))40221 24168 y Fl(\023)41494 26041 y Fr(+)295 b Fn(Q)43831 26240 y Fm(n)44457 26041 y Fn(;)6075 28960 y Fr(where)8032 31620 y Fn(Q)9062 31819 y Fm(n)10057 31620 y Fr(=)368 b Fn(T)12380 31072 y Fi(\000)p Fj(1)12199 31949 y Fm(n)p Fj(+1)14028 31620 y Fr(\()p Fn(T)15296 31819 y Fm(n)16218 31620 y Fk(\000)295 b Fn(T)18308 31819 y Fm(n)p Fj(+1)20137 31620 y Fr(\))20864 29747 y Fl(\024)21566 31620 y Fn(I)399 b Fr(+)295 b Fn(p)24499 31819 y Fm(n)25346 29747 y Fl(\022)26877 30823 y Fn(\026)27660 31022 y Fj(1)28186 30823 y Fr(\()p Fn(n)p Fr(\))2330 b(0)28100 32373 y(0)h Fn(\026)31864 32572 y Fj(2)32389 32373 y Fr(\()p Fn(n)p Fr(\))34731 29747 y Fl(\023)o(\025)36705 31620 y Fr(+)294 b Fn(T)38954 31072 y Fi(\000)p Fj(1)38773 31949 y Fm(n)p Fj(+1)40602 31620 y Fn(R)41592 31819 y Fm(n)42219 31620 y Fn(T)42981 31819 y Fm(n)43607 31620 y Fn(:)6075 34669 y Fr(b)36 b(elongs)441 b(to)h Fn(l)12764 34187 y Fj(1)13732 34669 y Fr(b)36 b(ecause)441 b(the)f(sequence)i Fk(f)p Fn(T)27624 34868 y Fm(n)28250 34669 y Fk(g)383 b(2)e Fn(D)31680 34187 y Fj(1)32648 34669 y Fr(and)440 b(the)h(limit)765 b(lim)40547 35466 y Fm(n)p Fi(!1)43221 34669 y Fn(T)43983 34868 y Fm(n)45051 34669 y Fr(is)6075 36762 y(in)-36 b(v)g(ertible)380 b(\(hence)f(norms)g Fk(k)p Fn(T)21293 36280 y Fi(\000)p Fj(1)21112 37091 y Fm(n)22551 36762 y Fk(k)h Fr(are)g(b)36 b(ounded\).)559 b(Therefore)381 b(the)e(c)-36 b(hronolog-)6075 38312 y(ical)434 b(pro)36 b(duct)433 b(equals)7976 40206 y Fm(n)7412 40605 y Fl(Y)7403 43434 y Fm(k)24 b Fj(=1)9119 41867 y Fr(\()p Fn(I)399 b Fr(+)295 b Fn(p)12558 42066 y Fm(k)13126 41867 y Fn(V)13884 42066 y Fm(k)14749 41867 y Fr(+)g Fn(R)17046 42066 y Fm(k)17614 41867 y Fr(\))11568 46389 y(=)368 b Fn(T)13710 46588 y Fm(n)p Fj(+1)15761 44118 y Fl( )17385 44729 y Fm(n)16822 45127 y Fl(Y)16812 47956 y Fm(k)24 b Fj(=1)18750 44516 y Fl(\024)19451 46389 y Fn(I)399 b Fr(+)295 b Fn(p)22384 46588 y Fm(k)23174 44516 y Fl(\022)24705 45592 y Fn(\026)25488 45791 y Fj(1)26013 45592 y Fr(\()p Fn(k)45 b Fr(\))2302 b(0)25900 47142 y(0)h Fn(\026)29636 47341 y Fj(2)30161 47142 y Fr(\()p Fn(k)45 b Fr(\))32448 44516 y Fl(\023)33721 46389 y Fr(+)294 b Fn(Q)36057 46588 y Fm(k)36626 44516 y Fl(\025)37327 44118 y(!)38600 46389 y Fn(T)39543 45841 y Fi(\000)p Fj(1)39362 46718 y(1)10469 50912 y Fr(=)11849 48640 y Fl( )13473 49251 y Fm(n)12910 49650 y Fl(Y)12901 52479 y Fm(k)24 b Fj(=1)14617 50912 y Fr(\(1)295 b(+)g Fn(p)18028 51111 y Fm(k)18596 50912 y Fn(\026)19379 51111 y Fj(2)19905 50912 y Fr(\()p Fn(k)45 b Fr(\)\))22144 48640 y Fl(!)23416 50912 y Fn(T)24178 51111 y Fm(n)p Fj(+1)26229 48640 y Fl( )27853 49251 y Fm(n)27289 49650 y Fl(Y)27280 52479 y Fm(k)24 b Fj(=1)29217 49039 y Fl(\024)29919 50912 y Fn(I)399 b Fk(\000)32220 49039 y Fl(\022)33751 50115 y Fn(q)34328 50314 y Fm(k)36004 50115 y Fr(0)33999 51665 y(0)1355 b(0)37208 49039 y Fl(\023)38481 50912 y Fr(+)295 b Fn(P)40626 51111 y Fm(k)41195 49039 y Fl(\025)41896 48640 y(!)43169 50912 y Fn(T)43931 51111 y Fj(1)44457 50912 y Fn(;)6075 54268 y Fr(where)433 b(w)-36 b(e)434 b(used)f(the)g(follo)-36 b(wing)436 b(notations)8254 57156 y Fn(q)8831 57355 y Fm(n)9826 57156 y Fr(:=)11701 56257 y Fn(p)12354 56456 y Fm(n)12980 56257 y Fr(\()p Fn(\026)14269 56456 y Fj(2)14794 56257 y Fr(\()p Fn(n)p Fr(\))295 b Fk(\000)h Fn(\026)18989 56456 y Fj(1)19514 56257 y Fr(\()p Fn(n)p Fr(\)\))p 11701 56850 10108 54 v 13441 58067 a(1)f(+)g Fn(p)16346 58266 y Fm(n)16972 58067 y Fn(\026)17755 58266 y Fj(2)18280 58067 y Fr(\()p Fn(n)p Fr(\))22310 57156 y Fk(\030)369 b Fn(p)24365 57355 y Fm(n)24991 57156 y Fr(\()p Fn(\026)26280 57355 y Fj(2)27100 57156 y Fk(\000)296 b Fn(\026)29212 57355 y Fj(1)29737 57156 y Fr(\))p Fn(;)655 b(P)32097 57355 y Fm(n)33093 57156 y Fr(:=)37956 56257 y(1)p 34967 56850 6628 54 v 34967 58067 a(1)296 b(+)f Fn(p)37873 58266 y Fm(n)38499 58067 y Fn(\026)39282 58266 y Fj(2)39807 58067 y Fr(\()p Fn(n)p Fr(\))41728 57156 y Fn(Q)42758 57355 y Fm(n)43384 57156 y Fn(:)6075 60056 y Fr(Since)662 b(w)-36 b(e)662 b(consider)g(the)g(h)-36 b(yp)36 b(erb)g(olic)663 b(case)f(discr)p Fn(V)1048 b(>)758 b Fr(0,)720 b(the)662 b(eigen)-36 b(v)-72 b(alues)6075 61762 y Fn(\026)6858 61961 y Fj(1)7383 61762 y Fr(\()p Fn(n)p Fr(\))p Fn(;)221 b(\026)10536 61961 y Fj(2)11062 61762 y Fr(\()p Fn(n)p Fr(\))687 b(=)15368 61239 y Fj(tr)p Fm(V)16649 61350 y Fh(n)p 15368 61457 1848 54 v 16057 62220 a Fj(2)17771 61762 y Fk(\006)19359 60505 y Fi(p)p 20143 60505 3055 40 v 699 x Fj(discr)p Fm(V)22631 61315 y Fh(n)p 19359 61457 3839 54 v 21043 62220 a Fj(2)23951 61762 y Fr(are)621 b(real)f(for)h(large)h(v)-72 b(alues)620 b(of)i Fn(n)p Fr(.)1139 b(Again)6075 63327 y(without)487 b(loss)h(of)g(generalit)-36 b(y)488 b(\(b)-36 b(y)487 b(c)-36 b(hanging)487 b(sequence)g Fn(P)35238 63526 y Fm(n)36352 63327 y Fr(for)h(\014nitely)f(man)-36 b(y)6075 64877 y(v)-72 b(alues)489 b(of)h Fn(n)p Fr(\))f(w)-36 b(e)489 b(ma)-36 b(y)490 b(supp)36 b(ose)488 b(the)h(p)36 b(ositiv)-36 b(eness)489 b(of)h Fn(\026)34912 65076 y Fj(2)35437 64877 y Fr(\()p Fn(n)p Fr(\))333 b Fk(\000)g Fn(\026)39707 65076 y Fj(1)40233 64877 y Fr(\()p Fn(n)p Fr(\))489 b(for)g(all)6075 66427 y Fn(n)369 b Fr(=)g(1)p Fn(;)221 b Fr(2)p Fn(;)g Fr(3)p Fn(;)g(:::)p Fr(.)545 b(So)322 b(the)g(conditions)g(of)i(Lemma)e(1)g(are)h(satis\014ed)f(for) h(the)f(system)6075 68722 y(with)516 b(co)36 b(e\016cien)-36 b(t)516 b(matrices)h Fn(I)455 b Fk(\000)22979 66849 y Fl(\022)24510 67925 y Fn(q)25087 68124 y Fm(n)26820 67925 y Fr(0)24786 69474 y(0)1384 b(0)28024 66849 y Fl(\023)29353 68722 y Fr(+)351 b Fn(P)31554 68921 y Fm(n)32181 68722 y Fr(.)826 b(Therefore)516 b(the)g(original)p eop end %%Page: 15 15 TeXDict begin 15 14 bop 12328 3345 a Fo(ONE)443 b(MODEL)i(IN)e (CRITICAL)e(HYPERBOLIC)h(SITUA)-85 b(TION)5226 b(15)6075 6001 y Fr(system)434 b(\(12\))f(has)h(a)g(solution)g(of)g(the)f(form) 7403 8001 y Fl( )9027 8612 y Fm(n)8464 9010 y Fl(Y)8455 11839 y Fm(k)24 b Fj(=1)10170 10272 y Fr([1)296 b(+)f Fn(p)13437 10471 y Fm(k)14006 10272 y Fn(\026)14789 10471 y Fj(2)15314 10272 y Fr(\()p Fn(k)45 b Fr(\)])17408 8001 y Fl(!)18681 10272 y Fn(T)19443 10471 y Fm(n)p Fj(+1)21493 8399 y Fl(\024\022)23726 9475 y Fr(0)23726 11025 y(1)24930 8399 y Fl(\023)26203 10272 y Fr(+)294 b Fn(o)p Fr(\(1\))29796 8399 y Fl(\025)25043 14795 y Fr(=)26424 12523 y Fl( )28048 13134 y Fm(n)27485 13533 y Fl(Y)27476 16362 y Fm(k)24 b Fj(=1)29191 14795 y Fr([1)296 b(+)f Fn(p)32458 14994 y Fm(k)33027 14795 y Fn(\026)33810 14994 y Fj(2)34335 14795 y Fr(\()p Fn(k)45 b Fr(\)])36429 12523 y Fl(!)37702 14795 y Fr(\()38208 14223 y Fk(\000)-1033 b(!)38571 14795 y Fn(e)39536 14994 y Fj(2)40357 14795 y Fr(+)295 b Fn(o)p Fr(\(1\)\))p Fn(;)6075 19647 y Fr(b)36 b(ecause)344 b Fn(T)11560 19846 y Fm(n)p Fj(+1)13611 17774 y Fl(\022)15142 18850 y Fr(0)15142 20400 y(1)16346 17774 y Fl(\023)17693 19647 y Fr(=)19073 19075 y Fk(\000)-1033 b(!)19436 19647 y Fn(e)20402 19846 y Fj(2)21041 19647 y Fr(+)114 b Fn(o)p Fr(\(1\))345 b(with)g(some)30843 19075 y Fk(\000)-1033 b(!)31206 19647 y Fn(e)32172 19846 y Fj(2)32697 19647 y Fr(,)363 b(a)345 b(non-zero)g(eigen)-36 b(v)g(ector)6075 21942 y(of)627 b(the)f(matrix)h Fn(V)915 b Fr(corresp)36 b(onding)626 b(to)h(the)f(eigen)-36 b(v)-72 b(alue)627 b Fn(\026)36227 22141 y Fj(2)36752 21942 y Fr(.)1157 b(The)627 b(last)g(fact)6075 23492 y(follo)-36 b(ws)515 b(from)f(Prop)36 b(osition)514 b(1)f(immediately)-108 b(.)819 b(It)513 b(is)h(clear)g(that)f(this)g(solution)6075 25204 y(pla)-36 b(ys)554 b(the)f(role)i(of)f(the)g(solution)23539 24632 y Fk(\000)-1033 b(!)23833 25204 y Fn(u)24867 24525 y Fj(\(2\))24867 25340 y Fm(n)26125 25204 y Fr(.)939 b(This)554 b(completes)g(the)g(pro)36 b(of)554 b(of)h(the)6075 26754 y(Theorem.)33398 b Fc(\003)6075 29670 y Fd(Pr)-66 b(o)g(of.)552 b Fr(of)434 b(Lemma)g(1.)7403 31220 y(One)506 b(can)g(assume)g(0)493 b Fn(<)f(q)20470 31419 y Fm(n)21589 31220 y Fn(<)g Fr(1)506 b(for)h(ev)-36 b(ery)507 b Fn(n)g Fr(without)f(loss)g(of)h(generalit)-36 b(y)-108 b(.)6075 33515 y(In)-36 b(tro)36 b(duce)586 b(the)h(notation)g(for)g(matrix)h (en)-36 b(tries)587 b Fn(R)31694 33714 y Fm(n)32951 33515 y Fr(=:)34954 31642 y Fl(\022)36485 32718 y Fr(\()p Fn(r)37577 32917 y Fj(11)38573 32718 y Fr(\))39079 32917 y Fm(n)40812 32718 y Fr(\()p Fn(r)41904 32917 y Fj(12)42901 32718 y Fr(\))43407 32917 y Fm(n)36485 34267 y Fr(\()p Fn(r)37577 34466 y Fj(21)38573 34267 y Fr(\))39079 34466 y Fm(n)40812 34267 y Fr(\()p Fn(r)41904 34466 y Fj(22)42901 34267 y Fr(\))43407 34466 y Fm(n)44586 31642 y Fl(\023)45564 33515 y Fr(.)6075 35810 y(F)-108 b(or)433 b(an)-36 b(y)434 b(natural)f Fn(n)16190 36009 y Fj(1)17085 35810 y Fn(<)369 b(n)19242 36009 y Fj(2)7403 37682 y Fl(\015)7403 38479 y(\015)7403 39276 y(\015)7403 40073 y(\015)7403 40870 y(\015)8792 38341 y Fm(n)9363 38464 y Fg(2)8460 38745 y Fl(Y)8141 41534 y Fm(n)p Fj(=)p Fm(n)10015 41657 y Fg(1)10697 38134 y Fl(\024)11398 40007 y Fn(I)400 b Fk(\000)13700 38134 y Fl(\022)15231 39210 y Fn(q)15808 39409 y Fm(n)17541 39210 y Fr(0)15508 40759 y(0)1383 b(0)18745 38134 y Fl(\023)20018 40007 y Fr(+)295 b Fn(R)22315 40206 y Fm(n)22941 38134 y Fl(\025)23642 37682 y(\015)23642 38479 y(\015)23642 39276 y(\015)23642 40073 y(\015)23642 40870 y(\015)24749 40007 y Fk(\024)26803 38341 y Fm(n)27374 38464 y Fg(2)26470 38745 y Fl(Y)26151 41534 y Fm(n)p Fj(=)p 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