Content-Type: multipart/mixed; boundary="-------------0211201106232" This is a multi-part message in MIME format. ---------------0211201106232 Content-Type: text/plain; name="02-471.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-471.keywords" random operators, localization ---------------0211201106232 Content-Type: application/postscript; name="dss_discrete_73.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="dss_discrete_73.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: dss_discrete_73.dvi %%CreationDate: Wed Nov 20 10:39:34 2002 %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMR8 CMCSC10 CMMI8 CMR6 MSBM7 CMSY8 CMR10 CMMI10 %%+ CMMI7 MSBM10 CMSY10 CMR7 CMR5 CMTI8 CMEX10 CMMI5 CMTI10 CMSY7 MSAM10 %%+ CMMI6 CMBX7 CMBX5 CMBX8 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf dss_discrete_73 %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2002.11.20:1039 %%BeginProcSet: tex.pro %! /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 %! % 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) 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 161 /parenleftbig put dup 162 /parenrightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 195 /parenleftBigg put dup 33 /parenrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 62 /braceex put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 79 /circlemultiplydisplay put dup 80 /summationtext put dup 83 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX5 %!PS-AdobeFont-1.1: CMBX5 1.0 %%CreationDate: 1991 Aug 20 16:35:12 % 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 (CMBX5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX5 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 115 /s put readonly def /FontBBox{-40 -250 1483 756}readonly def /UniqueID 5000763 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % 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 (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 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 106 /j put dup 115 /s put readonly def /FontBBox{-55 -250 1289 751}readonly def /UniqueID 5000765 def currentdict end currentfile eexec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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 115 /s put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 164 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 161 /minus put dup 167 /plusminus put dup 183 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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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 175 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 65 /A put dup 68 /D put dup 70 /F put dup 71 /G put dup 73 /I put dup 76 /L 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 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 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{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % 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 (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 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 78 /N put dup 90 /Z put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 105 /i put dup 106 /j put dup 110 /n put dup 114 /r put dup 115 /s put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % 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 (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 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 182 /acute put dup 46 /period put dup 65 /A 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 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 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 119 /w put dup 121 /y put dup 196 /dieresis 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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 61 /equal put dup 101 /e put dup 112 /p put dup 114 /r put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 44 /comma 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 61 /equal put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G 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 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 90 /Z put dup 94 /circumflex put dup 101 /e put dup 112 /p put dup 114 /r put readonly def /FontBBox{-27 -250 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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 69 /E put dup 78 /N put dup 80 /P put dup 82 /R put dup 90 /Z put dup 92 /hatwider put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 33 /omega put dup 59 /comma put dup 62 /greater put dup 65 /A put dup 66 /B put dup 68 /D put dup 72 /H put dup 73 /I put dup 78 /N put dup 80 /P put dup 84 /T put dup 86 /V put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % 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 (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 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 174 /alpha put dup 176 /gamma put dup 180 /eta put dup 184 /lambda put dup 186 /nu put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 193 /phi put dup 194 /chi put dup 33 /omega 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 69 /E 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 80 /P put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 96 /lscript 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 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n 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 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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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 39 /quoteright 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 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 64 /at 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 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N 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 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 dup 122 /z put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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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 162 /Delta put dup 164 /Lambda put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 181 /grave put dup 182 /acute put dup 34 /quotedblright put dup 35 /numbersign 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 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 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 92 /quotedblleft 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 dup 124 /emdash put dup 126 /tilde put dup 196 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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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 183 /lessequal put dup 87 /W put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 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 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 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 186 /nu put dup 58 /period put dup 59 /comma put dup 96 /lscript put dup 106 /j put dup 109 /m put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 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 174 /ff put dup 175 /fi put dup 181 /grave 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 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 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z 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 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 dup 123 /endash put dup 196 /dieresis put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % 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 (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 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 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 54 /six put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 73 /I 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 87 /W put dup 90 /Z 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 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 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put readonly def /FontBBox{-301 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437 437 486 12[680 534 693 729 644 729 705 851 596 1[498 365 705 735 620 644 717 680 1[705 18[292 26[486 19[{}43 885.568 /CMTI8 rf /Fm 141[300 1[415 10[338 39[569 10[377 377 377 4[569 43[{}8 553.48 /CMR5 rf /Fn 141[346 1[489 10[394 6[441 3[537 2[892 2[632 489 643 2[680 653 796 547 677 1[320 1[685 571 595 666 632 1[653 3[680 2[251 441 441 441 441 441 441 441 441 441 441 1[251 1[251 680 1[346 346 40[{}38 774.872 /CMR7 rf /Fo 145[553 2[553 307 430 430 553 553 9[738 4[1093 2[603 670 12[796 3[727 6[553 4[0 3[738 1107 7[1107 7[1107 6[861 4[861 861 12[861 861 3[861 307 861{}27 1106.96 /CMSY10 rf /Fp 163[2583 1[738 7[799 1[676 1[799 8[738 1[799 67[{}7 1106.96 /MSBM10 rf /Fq 139[334 418 411 1[456 1[547 786 1[471 366 313 4[461 1[389 480 371 9[523 1[523 3[564 1[701 4[392 725 3[724 1[669 666 2[692 2[263 25[558 33[{}25 774.872 /CMMI7 rf /Fr 133[515 2[792 537 634 400 519 499 494 557 1[664 972 1[576 456 381 1[528 542 515 576 479 475 585 461 7[917 1045 646 756 647 679 2[711 1[889 1074 753 940 614 487 920 870 1[817 916 791 840 830 2[861 553 861 307 307 24[689 1[693 660 2[633 572 631 1[547 1[646 3[550 3[573 1[708 11[{}58 1106.96 /CMMI10 rf /Fs 133[556 679 679 925 679 679 654 507 667 704 617 704 679 827 568 704 1[335 679 710 593 617 691 654 642 679 9[1224 2[870 676 886 1[821 2[1095 756 2[449 2[789 821 2[853 901 25[354 39[{}38 1106.96 /CMCSC10 rf /Ft 128[553 553 1[1107 1[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[307 553 307 3[1138 1[830 799 615 815 1[753 861 830 1015 692 861 569 400 830 869 723 753 846 799 784 830 3[861 1[307 307 553 553 553 553 553 553 553 553 553 553 553 307 369 307 861 1[430 430 307 3[922 553 14[553 553 2[922 922 615 615 646 799 6[769 1[922 1[{}86 1106.96 /CMR10 rf /Fu 168[934 66[732 20[{}2 885.568 /CMSY8 rf /Fv 165[590 90[{}1 885.568 /MSBM7 rf /Fw 205[406 406 49[{}2 664.176 /CMR6 rf /Fx 146[832 2[381 9[384 36[261 261 34[463 23[{}6 885.568 /CMMI8 rf /Fy 133[445 543 2[543 543 523 405 533 1[494 563 543 661 455 563 1[268 543 568 474 494 553 523 514 543 11[721 696 541 2[657 1[721 876 605 1[502 359 3[657 734 696 683 721 748 4[283 283 490 490 490 1[490 490 490 490 490 490 1[283 335 283 44[{}51 885.568 /CMCSC10 rf /Fz 128[470 3[470 418 497 497 680 497 523 366 371 367 497 523 470 523 784 261 497 1[261 523 470 288 418 523 418 523 470 3[261 1[261 575 705 1[966 705 705 680 523 692 1[640 732 705 862 588 731 483 339 705 738 614 640 718 680 666 705 3[732 2[261 470 470 470 470 470 470 470 470 470 470 1[261 314 261 732 1[366 366 261 20[470 5[523 549 11[{}75 885.568 /CMR8 rf /FA 136[919 2[495 502 524 1[707 636 707 1061 354 672 389 354 707 636 1[583 707 566 1[619 6[778 2[1316 2[886 707 955 1[870 956 996 1208 766 2[483 2[801 836 976 919 1[962 6[354 3[636 636 1[636 636 636 2[354 46[{}41 1106.96 /CMBX10 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 8000dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 9276 9544 a FA(LOCALIZA)-106 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b(+)f Fr(b)p Ft(\()p Fr(z)49 b Ft(\))p Fr(\301)30650 65170 y Fg(\241)31397 65004 y Ft(\()p Fr(n)247 b Fo(\241)f Fr(m)g Ft(+)g Fr(p;)184 b(z)49 b Ft(\))1108 b(for)369 b Fr(n)308 b Fo(\270)f Fr(m:)6075 66884 y Ft(Since)442 b Fr(\301)9698 67050 y Fg(\247)10887 66884 y Ft(are)g(linearly)h(indep) 31 b(enden)-31 b(t)443 b(for)f Fr(z)477 b Fo(2)429 b Fr(S)64 b Ft(,)461 b(this)442 b(de\257nes)f Fr(a)p Ft(\()p Fr(z)49 b Ft(\))443 b(and)f Fr(b)p Ft(\()p Fr(z)49 b Ft(\))443 b(uniquely)-92 b(.)6075 68213 y(The)506 b(n)-31 b(um)g(b)31 b(ers)506 b Fr(t)p Ft(\()p Fr(z)49 b Ft(\))535 b(=)h(1)p Fr(=a)p Ft(\()p Fr(z)49 b Ft(\))507 b(and)g Fr(r)31 b Ft(\()p Fr(z)49 b Ft(\))536 b(=)f Fr(b)p Ft(\()p Fr(z)49 b Ft(\))p Fr(=a)p Ft(\()p Fr(z)g Ft(\))508 b(are)e(discrete)f (analogues)j(of)f(the)6075 69541 y(classical)380 b(transmission)f(and)g (re\260ection)g(co)31 b(e\261cien)-31 b(ts,)382 b(at)e(least)f(if)g Fr(V)35289 69707 y Fn(p)24 b(er)36919 69541 y Ft(=)323 b(0.)520 b(In)378 b(particular,)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 6075 3345 a Fn(10)10851 b(D.)298 b(D)-24 b(AMANIK,)300 b(R.)e(SIMS,)g(AND)h(G.)f(STOLZ)6075 6001 y Ft(v)-61 b(anishing)332 b(of)g Fr(b)g Ft(is)f(equiv)-61 b(alen)-31 b(t)334 b(to)e(v)-61 b(anishing)333 b(of)f(the)g (re\260ection)g(co)31 b(e\261cien)-31 b(t.)482 b(Th)-31 b(us)331 b Fr(b)h Ft(and)g Fr(u)45191 6167 y Fn(+)6075 7330 y Ft(tak)-31 b(e)424 b(on)f(the)h(role)f(of)h(a)f(\(mo)31 b(di\257ed\))425 b(re\260ection)f(co)31 b(e\261cien)-31 b(t)425 b(and)e(Jost)h(solution)g(relativ)-31 b(e)425 b(to)6075 8658 y(the)369 b(p)31 b(erio)g(dic)370 b(bac)-31 b(kground)370 b Fr(V)18842 8824 y Fn(p)24 b(er)20149 8658 y Ft(,)370 b(resp)31 b(ectiv)-31 b(ely)-92 b(.)7403 10137 y(Since)310 b(for)g Fr(\270)d Fo(2)g Ft(\()p Fr(a;)184 b(b)p Ft(\),)324 b(w)-31 b(e)311 b(kno)-31 b(w)310 b Fr(\301)21970 10303 y Fg(\241)22717 10137 y Ft(\()p Fr(n;)184 b(\270)p Ft(\))310 b(=)p 26856 9174 4058 45 v 307 w Fr(\301)27516 10303 y Fn(+)28251 10137 y Ft(\()p Fr(n;)184 b(\270)p 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Ft(Using)349 b(constancy)h(of)f(the)h (non-zero)f(W)-92 b(ronskian)349 b Fr(\301)28039 17986 y Fn(+)28773 17820 y Ft(\()p Fr(n)206 b Ft(+)g(1\))p Fr(\301)32783 17986 y Fg(\241)33530 17820 y Ft(\()p Fr(n)p Ft(\))h Fo(\241)e Fr(\301)36987 17986 y Fg(\241)37734 17820 y Ft(\()p Fr(n)h Ft(+)g(1\))p Fr(\301)41744 17986 y Fn(+)42479 17820 y Ft(\()p Fr(n)p Ft(\),)355 b(w)-31 b(e)6075 19148 y(arriv)g(e)369 b(at)h(the)g(familiar)h(relation)6075 22325 y(\(5.16\))12106 b Fo(j)p Fr(a)p Ft(\()p Fr(\270)p Ft(\))p Fo(j)23712 21868 y Fn(2)24456 22325 y Fo(\241)246 b(j)p Fr(b)p Ft(\()p Fr(\270)p Ft(\))p Fo(j)28158 21868 y Fn(2)28964 22325 y Ft(=)307 b(1)p Fr(;)6075 24174 y Ft(for)369 b Fr(\270)307 b Fo(2)h Ft(\()p Fr(a;)184 b(b)p Ft(\),)371 b(corresp)31 b(onding)370 b(to)g Fo(j)p Fr(r)31 b Fo(j)22470 23772 y Fn(2)23213 24174 y Ft(+)246 b Fo(j)p Fr(t)p Fo(j)25334 23772 y Fn(2)26139 24174 y Ft(=)307 b(1.)6075 26198 y FA(Prop)35 b(osition)353 b(5.1.)497 b Fr(a)p Ft(\()p Fo(\242)p Ft(\))339 b Fh(and)e Fr(b)p Ft(\()p Fo(\242)p Ft(\))p Fh(,)352 b(de\257ne)-57 b(d)338 b(on)g Fr(S)401 b Fh(as)337 b(ab)-57 b(ove,)351 b(ar)-57 b(e)338 b(algebr)-57 b(aic)338 b(functions)h(with)6075 27527 y(singularities)396 b(only)h(p)-57 b(ossible)396 b(at)g(the)f(b)-57 b(oundaries)397 b(of)f(stability)g(intervals.)6075 29551 y(Pr)-57 b(o)g(of.)554 b Ft(Recall)370 b(that)h Fr(u)15912 29717 y Fn(+)17015 29551 y Ft(is)f(the)f(solution)i(of)456 b(\(5.13\))372 b(with)16434 31090 y Fk(\265)17803 31975 y Fr(u)18437 32141 y Fn(+)19171 31975 y Ft(\(1)p Fr(;)184 b(z)49 b Ft(\))17803 33304 y Fr(u)18437 33470 y Fn(+)19171 33304 y Ft(\(0)p Fr(;)184 b(z)49 b Ft(\))22195 31090 y Fk(\266)23317 32651 y Ft(=)24485 31090 y Fk(\265)25854 31975 y Fr(\301)26514 32141 y Fn(+)27248 31975 y Ft(\(1)p Fr(;)184 b(z)49 b Ft(\))25854 33304 y Fr(\301)26514 33470 y Fn(+)27248 33304 y Ft(\(0)p Fr(;)184 b(z)49 b Ft(\))30272 31090 y Fk(\266)31394 32651 y Ft(=)307 b Fr(v)33099 32817 y Fn(+)33834 32651 y Ft(\()p Fr(z)49 b Ft(\))p Fr(:)6075 35134 y Ft(Th)-31 b(us)375 b(\()p Fr(u)9949 35300 y Fn(+)10684 35134 y Ft(\()p Fr(m)246 b Ft(+)g(1)p Fr(;)184 b(z)49 b Ft(\))p Fr(;)184 b(u)16602 35300 y Fn(+)17339 35134 y Ft(\()p Fr(m;)g(z)49 b Ft(\)\))20658 34578 y Fq(t)21423 35134 y Ft(is)375 b(algebraic)h(in)g Fr(S)438 b Ft(with)376 b(singularities)h(only)f(p)31 b(ossible)375 b(at)6075 36463 y Fr(a)331 b Ft(and)h Fr(b)p Ft(,)339 b(that)333 b(is,)339 b(the)332 b(b)31 b(oundaries)331 b(of)h(the)g(stabilit)-31 b(y)334 b(in)-31 b(terv)-61 b(al.)482 b(As)331 b(w)-31 b(as)332 b(determined)g(b)31 b(efore,)6075 37822 y(the)456 b(same)g(is)g(true)g(for)g(b)31 b(oth)456 b(\()q Fr(\301)20127 37988 y Fg(\247)20873 37822 y Ft(\()p Fr(p)247 b Ft(+)f(1)p Fr(;)184 b(z)49 b Ft(\))p Fr(;)184 b(\301)26403 37988 y Fg(\247)27152 37822 y Ft(\()p Fr(p;)g(z)49 b Ft(\)\))30056 37265 y Fq(t)30446 37822 y Ft(.)752 b(By)456 b(the)h(de\257nition)g(of) g Fr(a)p Ft(\()p Fr(z)49 b Ft(\))456 b(and)6075 39150 y Fr(b)p Ft(\()p Fr(z)49 b Ft(\),)370 b(w)-31 b(e)369 b(ha)-31 b(v)g(e)6075 42940 y(\(5.17\))11219 41380 y Fk(\265)12587 42265 y Fr(a)p Ft(\()p Fr(z)49 b Ft(\))12642 43593 y Fr(b)p Ft(\()p Fr(z)g Ft(\))15150 41380 y Fk(\266)16272 42940 y Ft(=)17441 41380 y Fk(\265)18809 42265 y Fr(\301)19469 42431 y Fn(+)20204 42265 y Ft(\()p Fr(p)246 b Ft(+)g(1)p Fr(;)184 b(z)49 b Ft(\))1108 b Fr(\301)26350 42431 y Fg(\241)27097 42265 y Ft(\()p Fr(p)247 b Ft(+)f(1)p Fr(;)184 b(z)49 b Ft(\))19762 43593 y Fr(\301)20422 43759 y Fn(+)21157 43593 y Ft(\()p Fr(p;)184 b(z)49 b Ft(\))3015 b Fr(\301)27304 43759 y Fg(\241)28050 43593 y Ft(\()p Fr(p;)184 b(z)49 b Ft(\))32030 41380 y Fk(\266)32845 41609 y Fg(\241)p Fn(1)34218 41380 y Fk(\265)35587 42265 y Fr(u)36221 42431 y Fn(+)36955 42265 y Ft(\()p Fr(m)247 b Ft(+)e(1)p Fr(;)184 b(z)49 b Ft(\))36540 43593 y Fr(u)37174 43759 y Fn(+)37908 43593 y Ft(\()p Fr(m;)184 b(z)49 b Ft(\))42303 41380 y Fk(\266)43303 42940 y Fr(;)6075 45392 y Ft(and)369 b(so)g(w)-31 b(e)370 b(are)f(done.)29418 b Ff(\244)6075 47464 y FA(Lemma)424 b(5.2.)553 b Fh(If)397 b Fr(b)p Ft(\()p Fr(\270)p Ft(\))308 b(=)f(0)397 b Fh(for)f(al)57 b(l)395 b Fr(\270)307 b Fo(2)h Ft(\()p Fr(a;)184 b(b)p Ft(\))p Fh(,)398 b(then)f Fr(V)553 b Ft(=)307 b Fr(V)32666 47630 y Fn(p)24 b(er)33974 47464 y Fh(.)6075 49488 y(Pr)-57 b(o)g(of.)554 b Ft(Supp)31 b(ose)381 b(that)i Fr(b)p Ft(\()p Fr(\270)p Ft(\))329 b(=)f(0)381 b(for)h(all)h Fr(\270)327 b Fo(2)h Ft(\()p Fr(a;)184 b(b)p Ft(\),)387 b(and)382 b(hence)f(all)i Fr(z)376 b Fo(2)328 b Fr(S)445 b Ft(b)-31 b(y)382 b(analyticit)-31 b(y)-92 b(.)6075 50816 y(W)g(e)392 b(kno)-31 b(w)394 b(then)f(that)h(for)f(ev)-31 b(ery)393 b Fr(\270)346 b Fo(2)h Ft(\()p Fr(a;)184 b(b)p Ft(\))395 b(and)e Fr(\264)386 b(>)347 b Ft(0,)400 b(the)393 b(Jost)g(solution)h Fr(u)40172 50982 y Fn(+)40907 50816 y Ft(\()p Fr(n;)184 b(\270)263 b Ft(+)f Fr(i\264)40 b Ft(\))6075 52145 y(is)497 b Fr(a)p Ft(\()p Fr(\270)332 b Ft(+)f Fr(i\264)40 b Ft(\))p Fr(\301)12562 52311 y Fn(+)13297 52145 y Ft(\()p Fr(n)332 b Fo(\241)g Fr(m)f Ft(+)g Fr(p;)184 b(\270)332 b Ft(+)g Fr(i\264)40 b Ft(\))497 b(\(for)h(all)h Fr(n)521 b Fo(\270)g Fr(m)p Ft(\),)531 b(that)498 b(is,)530 b Fr(u)36995 52311 y Fn(+)38227 52145 y Ft(is)497 b(exp)31 b(onen)-31 b(tially)6075 53473 y(deca)g(ying)417 b(in)g(this)f(region)h(of)g(the)f(upp)31 b(er)415 b(half-plane.)635 b(Th)-31 b(us)416 b Fr(u)33256 53639 y Fn(+)34407 53473 y Ft(is)g(the)g(W)-92 b(eyl)416 b(solution)i(for)6075 54801 y(the)440 b(p)31 b(erturb)g(ed)439 b(equation)i(\(5.13\))s(.)705 b(W)-92 b(e)439 b(ma)-31 b(y)441 b(therefore)f(calculate)i(the)e(W)-92 b(eyl-Titc)-31 b(hmarsh)6075 56130 y Fr(m)p Ft(-function,)371 b Fr(m)13031 56296 y Fq(V)13799 56130 y Ft(,)f(for)f(\(5.13\))j(on)d(the)h (half-line)h([1)p Fr(;)184 b Fo(1)p Ft(\),)18269 59668 y Fr(m)19241 59834 y Fq(V)20010 59668 y Ft(\()p Fr(\270)246 b Ft(+)g Fr(i\264)40 b Ft(\))1107 b(=)27048 58920 y Fr(u)27682 59086 y Fn(+)28417 58920 y Ft(\(1)p Fr(;)184 b(\270)247 b Ft(+)f Fr(i\264)40 b Ft(\))p 27048 59414 6245 45 v 27048 60428 a Fr(u)27682 60594 y Fn(+)28417 60428 y Ft(\(0)p Fr(;)184 b(\270)247 b Ft(+)f Fr(i\264)40 b Ft(\))24947 62726 y(=)27048 61977 y Fr(\301)27708 62143 y Fn(+)28442 61977 y Ft(\(1)p Fr(;)184 b(\270)248 b Ft(+)e Fr(i\264)40 b Ft(\))p 27048 62472 6271 45 v 27048 63486 a Fr(\301)27708 63652 y Fn(+)28442 63486 y Ft(\(0)p Fr(;)184 b(\270)248 b Ft(+)e Fr(i\264)40 b Ft(\))24947 65035 y(=)1107 b Fr(m)27887 65201 y Fq(V)28410 65312 y Fm(p)19 b(er)29593 65035 y Ft(\()p Fr(\270)246 b Ft(+)g Fr(i\264)40 b Ft(\))p Fr(;)6075 66884 y Ft(where)384 b(the)h(latter)h(is)e(the)h Fr(m)p Ft(-function)h(of)471 b(\(4.7\))387 b(on)d([1)p Fr(;)184 b Fo(1)p Ft(\))387 b(\(whic)-31 b(h)386 b(is)e(the)h(same)g(as)g(the)f Fr(m)p Ft(-)6075 68213 y(function)258 b(of)343 b(\(5.13\))260 b(on)d([)p Fr(m)21 b Ft(+)g(1)p Fr(;)184 b Fo(1)p Ft(\)\).)458 b(As)256 b(the)h Fr(m)p Ft(-functions)h(are)f(analytic)i(in)e(the)g(en) -31 b(tire)257 b(upp)31 b(er)6075 69541 y(half-plane,)393 b(w)-31 b(e)387 b(conclude)g(that)h Fr(m)21142 69707 y Fq(V)21911 69541 y Ft(\()p Fr(z)49 b Ft(\))337 b(=)f Fr(m)25841 69707 y Fq(V)26364 69818 y Fm(p)19 b(er)27547 69541 y Ft(\()p Fr(z)49 b Ft(\))387 b(for)f(all)i Fr(z)d Fo(2)336 b Fp(C)35397 69139 y Fn(+)36133 69541 y Ft(.)544 b(Th)-31 b(us,)392 b(b)-31 b(y)387 b(standard)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 8519 3345 a Fn(LOCALIZA)-71 b(TION)387 b(F)-24 b(OR)388 b(DISCRETE)f(ONE)h(DIMENSIONAL)h(RANDOM)g(W)-24 b(ORD)387 b(MODELS)1563 b(11)6075 6001 y Ft(results)386 b(from)h(in)-31 b(v)g(erse)386 b(sp)31 b(ectral)387 b(theory)f(\(see,) 391 b(e.g.,)i([17)q(]\),)f(w)-31 b(e)387 b(conclude)g(that)h Fr(V)581 b Ft(=)336 b Fr(V)43063 6167 y Fn(p)24 b(er)44757 6001 y Ft(on)6075 7330 y([1)p Fr(;)184 b Fo(1)p Ft(\).)495 b(Since)369 b(they)h(coincide)g(on)f(\()p Fo(\2411)p Fr(;)184 b Ft(0])372 b(b)-31 b(y)369 b(de\257nition,)j(w)-31 b(e)369 b(get)h Fr(V)553 b Ft(=)308 b Fr(V)38300 7496 y Fn(p)24 b(er)39607 7330 y Ft(.)5150 b Ff(\244)7403 9424 y Ft(Th)-31 b(us,)313 b(if)299 b(w)-31 b(e)298 b(restrict)h(our)f (atten)-31 b(tion)301 b(to)e(the)f(case)g Fr(V)553 b Fo(6)p Ft(=)308 b Fr(V)31713 9590 y Fn(p)24 b(er)33020 9424 y Ft(,)313 b(w)-31 b(e)298 b(kno)-31 b(w)300 b(that)f Fo(f)p Fr(\270)308 b Fo(2)f Ft(\()p Fr(a;)184 b(b)p Ft(\))310 b(:)6075 10753 y Fr(b)p Ft(\()p Fr(\270)p Ft(\))e(=)f(0)p Fo(g)370 b Ft(is)f(\257nite.)7403 12081 y(No)-31 b(w)474 b(w)-31 b(e)473 b(consider)g(a)f(gap.)804 b(T)-92 b(ak)-31 b(e)474 b Fr(\256)i Ft(suc)-31 b(h)473 b(that)h Fo(\2411)479 b(\267)h Fr(\256)k(<)c(a)g(<)g(b)473 b Ft(and)g(\()p Fr(\256)t(;)184 b(a)p Ft(\))474 b(is)f(a)6075 13409 y(maximal,)395 b(non-trivial)389 b(gap)f(in)g(the)f(sp)31 b(ectrum)387 b(of)g Fr(H)28784 13575 y Fn(0)29668 13409 y Ft(\(if)h Fr(a)338 b Ft(=)f(inf)271 b Fr(\276)40 b Ft(\()p Fr(H)36806 13575 y Fn(0)37303 13409 y Ft(\),)392 b(then)387 b Fr(\256)342 b Ft(=)337 b Fo(\2411)p Ft(\).)6075 14738 y(W)-92 b(e)345 b(note)h(that)h(there)e(is)h(also)g(a)g(gap)g(\()p Fr(b;)184 b Fo(1)p Ft(\))348 b(where)d Fr(b)307 b Ft(=)h(sup)o(\()p Fr(\276)40 b Ft(\()p Fr(H)34357 14904 y Fn(0)34854 14738 y Ft(\)\).)486 b(The)346 b(analysis)h(of)f(this)6075 16066 y(gap)337 b(is)f(iden)-31 b(tical)339 b(to)e(the)g(case)f Fr(\256)312 b Ft(=)c Fo(\2411)336 b Ft(b)31 b(elo)-31 b(w,)344 b(excepting)338 b(that)g(w)-31 b(e)337 b(analytically)j(con) -31 b(tin)g(ue)6075 17395 y(to)370 b(the)f(righ)-31 b(t)370 b(rather)f(than)h(the)g(left.)493 b(Consider)370 b(the)f(follo)-31 b(wing)373 b(split)d(strip:)15178 20123 y Fr(S)15921 19666 y Fg(0)16538 20123 y Ft(:=)308 b Fo(f)p Fr(z)357 b Ft(=)307 b Fr(\270)246 b Ft(+)g Fr(i\264)347 b Ft(:)308 b Fr(\256)k(<)307 b(\270)g(<)h(b;)184 b(\264)348 b Fo(2)307 b Fp(R)p Fo(g)247 b(n)f Ft([a)q Fr(;)184 b Ft(b)q(\))p Fr(:)6075 21755 y Ft(F)-92 b(or)385 b Fr(i)336 b Ft(=)f(1)p Fr(;)184 b Ft(2,)393 b(let)386 b Fr(\275)14475 21921 y Fq(i)14844 21755 y Ft(\()p Fr(z)49 b Ft(\))386 b(b)31 b(e)386 b(the)g(branc)-31 b(hes)386 b(of)472 b(\(4.8\))389 b(with)e Fo(j)p Fr(\275)32151 21921 y Fn(1)32648 21755 y Ft(\()p Fr(z)49 b Ft(\))p Fo(j)337 b Fr(<)e Ft(1)386 b(and)g Fo(j)p Fr(\275)39899 21921 y Fn(2)40397 21755 y Ft(\()p Fr(z)49 b Ft(\))p Fo(j)336 b Fr(>)g Ft(1)386 b(for)6075 23083 y(all)309 b Fr(z)356 b Fo(2)307 b Fr(S)10210 22682 y Fg(0)10521 23083 y Ft(,)320 b(whic)-31 b(h)309 b(are)f(w)-31 b(ell)309 b(de\257ned)f(since)g([)p Fr(a;)184 b(b)p Ft(\))310 b(is)e(excluded.)473 b(W)-92 b(e)307 b(\257rst)g(note)i(that)g Fr(\275)42645 23249 y Fn(1)43450 23083 y Ft(=)e Fr(\275)45190 23249 y Fn(+)6075 24412 y Ft(on)378 b(the)g(upp)31 b(er)377 b(half)i(of)f Fr(S)64 b Ft(,)380 b(but)e Fr(\275)20216 24578 y Fn(1)21035 24412 y Ft(=)322 b Fr(\275)22790 24578 y Fg(\241)23915 24412 y Ft(on)378 b(the)g(lo)-31 b(w)g(er)380 b(half)e(of)h Fr(S)64 b Ft(.)518 b(Secondly)-92 b(,)381 b(as)d(b)31 b(efore,)380 b(it)6075 25740 y(can)403 b(b)31 b(e)403 b(seen)g(that)i Fr(\275)15123 25906 y Fq(i)15895 25740 y Ft(are)e(algebraic)i(in)f Fr(S)24557 25338 y Fg(0)24867 25740 y Ft(.)595 b(They)404 b(ha)-31 b(v)g(e,)413 b(at)404 b(most,)414 b(singularities)405 b(at)f Fr(\256)t Ft(,)413 b Fr(a)p Ft(,)6075 27068 y(and)317 b Fr(b)p Ft(,)328 b(and)317 b(therefore)h(they)f(ma)-31 b(y)319 b(b)31 b(e)316 b(con)-31 b(tin)g(ued)319 b(analytically)j(across)316 b(\()p Fr(a;)184 b(b)p Ft(\).)478 b(In)316 b(particular,)6075 28397 y Fr(\275)6647 28563 y Fq(i)7385 28397 y Ft(is)369 b(the)g(analytic)j(con)-31 b(tin)g(uation)372 b(of)e Fr(\275)22845 28563 y Fq(j)23312 28397 y Ft(,)f(where)g Fr(i;)184 b(j)372 b Fo(2)308 b(f)p Ft(1)p Fr(;)184 b Ft(2)p Fo(g)372 b Ft(with)e Fr(i)308 b Fo(6)p Ft(=)f Fr(j)63 b Ft(.)7403 29725 y(F)-92 b(or)629 b Fr(z)789 b Fo(2)741 b Fr(S)13176 29323 y Fg(0)13486 29725 y Ft(,)695 b(c)-31 b(ho)31 b(ose)630 b(eigen)-31 b(v)g(ectors)631 b Fr(v)25247 29891 y Fq(i)25615 29725 y Ft(\()p Fr(z)49 b Ft(\))741 b(=)h(\()p Fr(c)30292 29891 y Fq(i)30661 29725 y Ft(\()p Fr(z)49 b Ft(\))p Fr(;)184 b Ft(1\))33559 29323 y Fq(t)34580 29725 y Ft(of)630 b Fr(g)36629 29891 y Fn(0)37125 29725 y Ft(\()p Fr(z)49 b Ft(\))630 b(corresp)31 b(onding)6075 31054 y(to)622 b Fr(\275)8252 31220 y Fq(i)8621 31054 y Ft(\()p Fr(z)49 b Ft(\),)686 b(analogously)624 b(to)f(\(4.10\).)1253 b(T)-92 b(aking)623 b Fr(\301)27886 31220 y Fq(i)28876 31054 y Ft(to)f(b)31 b(e)621 b(the)h(solutions)i(of) 708 b(\(4.7\))624 b(with)6075 32382 y(\()p Fr(\301)7165 32548 y Fq(i)7533 32382 y Ft(\(1)p Fr(;)184 b(z)49 b Ft(\))p Fr(;)184 b(\301)11152 32548 y Fq(i)11523 32382 y Ft(\(0)p Fr(;)g(z)49 b Ft(\)\))14421 31980 y Fq(t)15314 32382 y Ft(=)501 b Fr(v)17213 32548 y Fq(i)17581 32382 y Ft(\()p Fr(z)49 b Ft(\))486 b(for)f Fr(z)550 b Fo(2)500 b Fr(S)24347 31980 y Fg(0)24658 32382 y Ft(,)514 b(w)-31 b(e)486 b(see)e(again)j(that)g Fr(\301)35373 32548 y Fn(1)35869 32382 y Ft(\()p Fo(\242)p Fr(;)184 b(z)49 b Ft(\))487 b(\(resp.,)515 b Fr(\301)42775 32548 y Fn(2)43271 32382 y Ft(\()p Fo(\242)p Fr(;)184 b(z)49 b Ft(\)\))6075 33710 y(is)428 b(in)g Fr(`)9058 33309 y Fn(2)9983 33710 y Ft(near)g(+)p Fo(1)g Ft(\(resp.,)444 b Fo(\2411)p Ft(\),)g(that)429 b(is,)444 b(they)428 b(are)h(the)f(W)-92 b(eyl)428 b(solutions.)672 b(Set)428 b Fr(u)42579 33876 y Fq(i)43376 33710 y Ft(to)h(b)31 b(e)6075 35039 y(the)369 b(Jost)h(solutions)g(of)456 b(\(5.13\))372 b(satisfying)6075 38619 y(\(5.18\))1947 b Fr(u)11482 38785 y Fq(i)11850 38619 y Ft(\()p Fr(n;)184 b(z)49 b Ft(\))310 b(=)15907 37058 y Fk(\275)26379 37944 y Fr(\301)27039 38110 y Fq(i)27407 37944 y Ft(\()p Fr(n;)184 b(z)49 b Ft(\))10405 b Fr(n)308 b Fo(\267)g Ft(1)17291 39272 y Fr(a)17876 39438 y Fq(i)18244 39272 y Ft(\()p Fr(z)49 b Ft(\))p Fr(\301)20328 39438 y Fq(i)20697 39272 y Ft(\()p Fr(n)247 b Fo(\241)f Fr(m)g Ft(+)g Fr(p;)184 b(z)49 b Ft(\))247 b(+)f Fr(b)29341 39438 y Fq(i)29709 39272 y Ft(\()p Fr(z)49 b Ft(\))p Fr(\301)31793 39438 y Fq(j)32260 39272 y Ft(\()p Fr(n)247 b Fo(\241)e Fr(m)h Ft(+)g Fr(p;)184 b(z)49 b Ft(\))1108 b Fr(n)308 b Fo(\270)g Fr(m)6075 41150 y Ft(for)427 b Fr(z)453 b Fo(2)404 b Fr(S)10680 40748 y Fg(0)11418 41150 y Ft(and)427 b(the)h(same)g Fr(i;)184 b(j)491 b Ft(con)-31 b(v)g(en)g(tion)430 b(used)d(ab)31 b(o)-31 b(v)g(e.)668 b(As)427 b(in)h(\(5.17\))i(ab)31 b(o)-31 b(v)g(e,)443 b(one)428 b(sees)6075 42478 y(that)420 b Fr(a)9108 42644 y Fn(1)9605 42478 y Ft(\()p Fr(z)49 b Ft(\))420 b(and)g Fr(b)14127 42644 y Fn(1)14623 42478 y Ft(\()p Fr(z)49 b Ft(\))420 b(are)f(algebraic)j(in)d Fr(S)25177 42077 y Fg(0)25487 42478 y Ft(.)644 b(In)419 b(fact,)433 b(in)420 b(the)g(upp)31 b(er)418 b(half)j Fr(S)39857 42644 y Fn(+)41011 42478 y Ft(of)f Fr(S)64 b Ft(,)432 b(they)6075 43807 y(coincide)279 b(with)g Fr(a)p Ft(\()p Fr(z)49 b Ft(\))278 b(and)h Fr(b)p Ft(\()p Fr(z)49 b Ft(\),)297 b(since)278 b(for)g Fr(z)356 b Fo(2)307 b Fr(S)26328 43973 y Fn(+)27063 43807 y Ft(,)296 b(w)-31 b(e)279 b(ha)-31 b(v)g(e)279 b(that)g Fr(v)34510 43973 y Fn(+)35245 43807 y Ft(\()p Fr(z)49 b Ft(\))278 b(and)g Fr(v)39545 43973 y Fn(1)40041 43807 y Ft(\()p Fr(z)49 b Ft(\))278 b(coincide.)6075 45135 y(Th)-31 b(us)351 b Fr(a)9446 45301 y Fn(1)9943 45135 y Ft(\()p Fr(z)49 b Ft(\))351 b(and)g Fr(b)14327 45301 y Fn(1)14824 45135 y Ft(\()p Fr(z)49 b Ft(\))351 b(are)g(analytic)j(con)-31 b(tin)g(uations)354 b(of)d(the)h(restrictions)f(of)h Fr(a)p Ft(\()p Fr(z)49 b Ft(\))351 b(and)h Fr(b)p Ft(\()p Fr(z)49 b Ft(\))6075 46464 y(to)422 b Fr(S)8159 46630 y Fn(+)8894 46464 y Ft(.)650 b(Similarly)-92 b(,)438 b(it)422 b(is)g(seen)f(that)i Fr(a)22658 46630 y Fn(2)23155 46464 y Ft(\()p Fr(z)49 b Ft(\))422 b(and)g Fr(b)27681 46630 y Fn(2)28178 46464 y Ft(\()p Fr(z)49 b Ft(\))422 b(are)f(analytic)k(con)-31 b(tin)g(uations)425 b(of)d(the)6075 47792 y(restrictions)g(of)h Fr(a)p Ft(\()p Fr(z)49 b Ft(\))422 b(and)h Fr(b)p Ft(\()p Fr(z)49 b Ft(\))422 b(to)h(the)f(lo)-31 b(w)g(er)423 b(half)g Fr(S)29363 47958 y Fg(\241)30532 47792 y Ft(of)g Fr(S)64 b Ft(.)650 b(Th)-31 b(us,)436 b Fr(a)37309 47958 y Fn(1)37806 47792 y Ft(\()p Fr(z)49 b Ft(\),)436 b Fr(b)40448 47958 y Fn(1)40945 47792 y Ft(\()p Fr(z)49 b Ft(\),)436 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65811 y Fr(g)22129 65977 y Fn(0)22626 65811 y Ft(\()p Fr(\270)p Ft(\))308 b(=)g Fr(M)121 b Ft(\()p Fr(w)28026 65977 y Fn(0)28523 65811 y Fr(;)184 b(\270)p Ft(\))p Fr(;)6075 67676 y Ft(corresp)31 b(onding)369 b(to)h(the)f(p)31 b(erio)g(dic)370 b(problem)g(\(4.7\))h (and)f(the)f(matrix)21755 69541 y Fr(g)22283 69707 y Fn(1)22780 69541 y Ft(\()p Fr(\270)p Ft(\))308 b(=)f Fr(M)121 b Ft(\()p Fr(w)28179 69707 y Fn(1)28677 69541 y Fr(;)184 b(\270)p Ft(\))p eop end %%Page: 12 12 TeXDict begin 12 11 bop 6075 3345 a Fn(12)10851 b(D.)298 b(D)-24 b(AMANIK,)300 b(R.)e(SIMS,)g(AND)h(G.)f(STOLZ)6075 6001 y Ft(describing)389 b(the)f(lo)31 b(cal)390 b(p)31 b(erturbation,)395 b(corresp)31 b(onding)389 b(to)g(the)f(p)31 b(erturb)g(ed)388 b(di\256erence)g(equa-)6075 7330 y(tion)459 b(\(5.13\))r(.)758 b(In)457 b(corresp)31 b(ondence)457 b(with)h(the)g(previous)g(sections,)481 b(w)-31 b(e)458 b(tak)-31 b(e)458 b Fr(H)40397 7496 y Fn(0)41351 7330 y Ft(to)h(b)31 b(e)457 b(the)6075 8658 y(op)31 b(erator)323 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b(Impro)-31 b(v)g(ed)470 b(v)-31 b(er-)6075 65556 y(sions,)337 b(whic)-31 b(h)330 b(sho)-31 b(w)330 b(that)g(strong)g(dynamical)h(lo) 31 b(calization)333 b(as)c(in)g(Theorem)h(2.3)g(is)f(obtained)6075 66884 y(through)483 b(m)-31 b(ultiscale)485 b(analysis,)512 b(w)-31 b(ere)483 b(recen)-31 b(tly)483 b(pro)-31 b(vided)483 b(in)g([8)q(])g(and)f([10)r(].)832 b(While)483 b(these)6075 68213 y(pap)31 b(ers)317 b(are)h(written)h(for)f(con)-31 b(tin)g(uum)321 b(op)31 b(erators,)329 b(they)318 b(b)31 b(oth)319 b(note)g(that)g(their)f(results)g(apply)6075 69541 y(to)370 b(lattice)h(mo)31 b(dels)370 b(as)f(w)-31 b(ell.)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 6075 3345 a Fn(14)10851 b(D.)298 b(D)-24 b(AMANIK,)300 b(R.)e(SIMS,)g(AND)h(G.)f(STOLZ)23432 6001 y Fs(Appendix)7403 7994 y Ft(The)500 b(aim)i(of)e(this)h(app)31 b(endix)500 b(is)g(to)h(pro)-31 b(v)g(e)501 b(Prop)31 b(osition)502 b(2.1.)886 b(W)-92 b(e)500 b(will)h(start)g(b)-31 b(y)500 b(pro-)6075 9322 y(viding)486 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Ft(\(A.15\))4816 b(lim)13650 30766 y Fq(d)p Fg(!1)16204 29294 y Ft(1)p 16193 29789 577 45 v 16193 30802 a Fr(d)17655 28659 y Fq(d)17086 28991 y Fk(X)17140 31375 y Fq(`)p Fn(=1)20115 28991 y Fk(X)18870 31418 y Fd(j)19179 31529 y Fc(s)19569 31418 y Fg(2)p Fq(P)119 b Fn(\()p Fq(`;m)p Fn(\))23144 30043 y Fr(\272)23691 30209 y Fq(j)24057 30320 y Fm(1)24790 30043 y Fo(\242)246 b Fr(\272)25890 30209 y Fq(j)26256 30320 y Fm(2)26990 30043 y Fo(\242)g Fr(:)184 b(:)g(:)249 b Fo(\242)d Fr(\272)30181 30209 y Fq(j)30547 30320 y Fj(s)31337 30043 y Ft(=)34997 29294 y(1)p 32638 29789 5273 45 v 32638 29981 a Fk(P)33806 30255 y Fq(m)33806 31144 y(j)45 b Fn(=1)35578 30812 y Fr(j)309 b Fo(\242)247 b Fr(\272)37444 30978 y Fq(j)38043 30043 y Fr(:)6075 33438 y Fh(Pr)-57 b(o)g(of.)554 b Ft(F)-92 b(or)369 b(eac)-31 b(h)369 b Fr(`)308 b Fo(2)f Fp(N)p Ft(,)370 b(de\257ne)6075 35694 y(\(A.16\))9069 b Fr(A)19077 35860 y Fq(`)19810 35694 y Ft(:=)22532 34642 y Fk(X)21286 37068 y Fd(j)21595 37179 y Fc(s)21986 37068 y Fg(2)p Fq(P)119 b Fn(\()p Fq(`;m)p Fn(\))25560 35694 y Fr(\272)26107 35860 y Fq(j)26473 35971 y Fm(1)27207 35694 y Fo(\242)246 b Fr(\272)28307 35860 y Fq(j)28673 35971 y Fm(2)29407 35694 y Fo(\242)g Fr(:)184 b(:)g(:)248 b Fo(\242)f Fr(\272)32598 35860 y Fq(j)32964 35971 y Fj(s)33446 35694 y Fr(;)6075 39080 y Ft(and)369 b(for)g(an)-31 b(y)370 b Fr(z)356 b Fo(2)308 b Fp(C)369 b Ft(with)i Fo(j)p Fr(z)49 b Fo(j)308 b Fr(<)f Ft(1,)370 b(set)6075 42063 y(\(A.17\))22043 41771 y(~)21898 42063 y Fr(\301)p Ft(\()p Fr(z)49 b Ft(\))308 b(:=)26124 40679 y Fg(1)25766 41011 y Fk(X)25819 43394 y Fq(`)p Fn(=1)27549 42063 y Fr(A)28379 42229 y Fq(`)28805 42063 y Fr(z)29369 41606 y Fq(`)29794 42063 y Fr(:)6075 45151 y Ft(Clearly)-92 b(,)14740 47780 y(~)14595 48072 y Fr(\301)o Ft(\()p Fr(z)49 b Ft(\))308 b(=)18513 46689 y Fg(1)18155 47021 y Fk(X)18208 49404 y Fq(`)p Fn(=1)21183 47021 y Fk(X)19938 49447 y Fd(j)20247 49558 y Fc(s)20637 49447 y Fg(2)p Fq(P)119 b Fn(\()p Fq(`;m)p Fn(\))24212 48072 y Fr(\272)24759 48238 y Fq(j)25125 48349 y Fm(1)25858 48072 y Fo(\242)247 b Fr(\272)26959 48238 y Fq(j)27325 48349 y Fm(2)28058 48072 y Fo(\242)g Fr(:)184 b(:)g(:)248 b Fo(\242)f Fr(\272)31250 48238 y Fq(j)31616 48349 y Fj(s)32097 48072 y Fr(z)32661 47615 y Fq(`)16986 52022 y Ft(=)18513 50638 y Fg(1)18155 50971 y Fk(X)18185 53315 y Fq(s)p Fn(=1)20505 50638 y Fq(m)20098 50971 y Fk(X)19938 53328 y Fq(j)20304 53439 y Fm(1)20736 53328 y Fn(=1)22042 52022 y Fr(:)184 b(:)g(:)24082 50638 y Fq(m)23675 50971 y Fk(X)23518 53328 y Fq(j)23884 53439 y Fj(s)24310 53328 y Fn(=1)25615 52022 y Fr(\272)26162 52188 y Fq(j)26528 52299 y Fm(1)27262 52022 y Fo(\242)246 b Fr(\272)28362 52188 y Fq(j)28728 52299 y Fm(2)29462 52022 y Fo(\242)g Fr(:)184 b(:)g(:)249 b Fo(\242)d Fr(\272)32653 52188 y Fq(j)33019 52299 y Fj(s)33501 52022 y Fr(z)34065 50984 y Fb(P)34995 51231 y Fj(s)34995 51814 y(r)19 b Fm(=1)36538 51565 y Fq(j)36904 51676 y Fj(r)16986 56362 y Ft(=)18513 54978 y Fg(1)18155 55310 y Fk(X)18185 57654 y Fq(s)p Fn(=1)19938 54137 y Fk(0)19938 56129 y(@)21313 54978 y Fq(m)20907 55310 y Fk(X)20940 57668 y Fq(j)45 b Fn(=1)22690 56362 y Fr(\272)23237 56528 y Fq(j)23703 56362 y Fr(z)24267 55905 y Fq(j)24733 54137 y Fk(1)24733 56129 y(A)25702 54366 y Fq(s)16986 60349 y Ft(=)19241 58604 y Fk(P)20409 58878 y Fq(m)20409 59767 y(j)g Fn(=1)22181 59435 y Fr(\272)22728 59601 y Fq(j)23194 59435 y Fr(z)23758 59033 y Fq(j)p 18287 60095 6890 45 v 18287 61118 a Ft(1)247 b Fo(\241)20194 60287 y Fk(P)21362 60561 y Fq(m)21362 61450 y(j)45 b Fn(=1)23134 61118 y Fr(\272)23681 61284 y Fq(j)24147 61118 y Fr(z)24711 60798 y Fq(j)25495 60349 y Fr(:)6075 63247 y Ft(T)-92 b(ak)-31 b(e)370 b Fr(A)9580 63413 y Fn(0)10384 63247 y Ft(:=)308 b(0)370 b(and)f(consider)21205 64877 y Fr(\301)p Ft(\()p Fr(z)49 b Ft(\))308 b(:=)g(\(1)246 b Fo(\241)g Fr(z)49 b Ft(\))28548 64585 y(~)28403 64877 y Fr(\301)p Ft(\()p Fr(z)g Ft(\))p Fr(:)6075 66831 y Ft(It)369 b(is)g(clear)h(that)g(b)31 b(oth)16192 66539 y(~)16047 66831 y Fr(\301)368 b Ft(and)i Fr(\301)e Ft(are)h(analytic)j (in)d Fo(j)p Fr(z)49 b Fo(j)308 b Fr(<)g Ft(1.)7403 68159 y(Observ)-31 b(e)484 b(that)i(the)f(set)g Fr(J)606 b Ft(:=)500 b Fo(f)p Fr(j)564 b Ft(:)500 b Fr(\272)23966 68325 y Fq(j)24933 68159 y Fr(>)g Ft(0)p Fo(g)485 b Ft(is)g(relativ)-31 b(ely)487 b(prime)e(if)g(and)g(only)h(if)f(the)6075 69501 y(equation)10595 68671 y Fk(P)11763 68944 y Fq(m)11763 69833 y(j)45 b Fn(=1)13535 69501 y Fr(\272)14082 69667 y Fq(j)14548 69501 y Fr(z)15112 69099 y Fq(j)15886 69501 y Ft(=)307 b(1)370 b(has)f(exactly)h(one)g(solution)h(\()p Fr(z)356 b Ft(=)308 b(1\))370 b(on)f(the)h(unit)g(circle.)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 6075 3345 a Fn(18)10851 b(D.)298 b(D)-24 b(AMANIK,)300 b(R.)e(SIMS,)g(AND)h(G.)f(STOLZ)7403 6001 y Ft(W)-92 b(e)377 b(ma)-31 b(y)379 b(conclude)f(that)h(if)f Fr(J)484 b Ft(is)378 b(relativ)-31 b(ely)380 b(prime,)h(then)d Fr(\301)f Ft(is)g(analytic)j(in)e(a)g(neigh)-31 b(b)31 b(or-)6075 7330 y(ho)g(o)g(d)369 b(of)h 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Fd(j)21595 26574 y Fc(s)21986 26463 y Fg(2)p Fq(P)119 b Fn(\()p Fq(`;m)p Fn(\))25623 25088 y Ft(~)-616 b Fr(\272)26107 25254 y Fq(j)26473 25365 y Fm(1)27207 25088 y Fo(\242)309 b Ft(~)-616 b Fr(\272)28307 25254 y Fq(j)28673 25365 y Fm(2)29407 25088 y Fo(\242)246 b Fr(:)184 b(:)g(:)248 b Fo(\242)310 b Ft(~)-616 b Fr(\272)32598 25254 y Fq(j)32964 25365 y Fj(s)33446 25088 y Fr(;)6075 28166 y Ft(one)369 b(sees)f(that)19156 30004 y Fr(A)19986 30170 y Fq(`)20719 30004 y Ft(=)21888 28443 y Fk(\275)23271 29306 y Ft(0)1851 b(if)27011 28870 y Fq(`)p 26823 29051 748 45 v 26823 29688 a(D)28133 29306 y Fr(=)-676 b Fo(2)308 b Fp(N)23563 30444 y Ft(~)23271 30724 y Fr(A)24101 30890 y Fq(j)25675 30724 y Ft(if)27011 30288 y Fq(`)p 26823 30469 V 26823 31105 a(D)28010 30724 y Ft(=)g Fr(j)371 b Fo(2)307 b Fp(N)p Fr(:)6075 32289 y Ft(Th)-31 b(us)17317 34487 y(lim)16973 35210 y Fq(d)p Fg(!1)19527 33738 y Ft(1)p 19516 34233 577 45 v 19516 35247 a Fr(d)20979 33104 y Fq(d)20410 33436 y Fk(X)20463 35819 y Fq(`)p 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32241 40187 a Fk(P)33410 40460 y Fq(m)33410 41349 y(j)g Fn(=1)35182 41017 y Fr(j)309 b Fo(\242)246 b Fr(\272)37047 41183 y Fq(j)37646 40248 y Fr(;)6075 43215 y Ft(whic)-31 b(h)370 b(completes)g(our)f(pro)31 b(of.)25910 b Ff(\244)22773 45631 y Fs(References)6545 47402 y Fz([1])472 b(S.)431 b(de)f(Bi)-26 b(\265)-444 b(evre)431 b(and)f(F.)h(Germinet,)460 b(Dynamical)432 b(lo)26 b(calization)434 b(for)d(the)f(random)h(dimer)f(Sc)-26 b(hr\304)-470 b(odinger)8009 48509 y(op)26 b(erator,)315 b Fl(J.)340 b(Stat.)f(Phys.)312 b Fa(98)j Fz(\(2000\),)h(1135{1148)6545 49616 y([2])472 b(P)-78 b(.)315 b(Bougerol)i(and)f(J.)g(Lacroix,)h Fl(Pr)-49 b(o)g(ducts)342 b(of)g(R)-49 b(andom)342 b(Matric)-49 b(es)342 b(with)e(Applic)-49 b(ations)341 b(to)h(Schr\304)-486 b(odinger)8009 50723 y(Op)-49 b(er)g(ators)p Fz(,)313 b(Birkh\304)-470 b(auser,)314 b(Boston{Stuttgart)h(\(1985\))6545 51830 y([3])472 b(R.)466 b(Carmona,)504 b(A.)465 b(Klein,)505 b(and)465 b(F.)g(Martinelli,)505 b(Anderson)465 b(lo)26 b(calization)469 b(for)c(Bernoulli)h(and)f(other)8009 52936 y(singular)314 b(p)26 b(oten)-26 b(tials,)316 b Fl(Commun.)341 b(Math.)e(Phys.)312 b Fa(108)j Fz(\(1987\),)h(41{66)6545 54043 y([4])472 b(R.)293 b(Carmona)g(and)g(J.)g(Lacroix,)298 b Fl(Sp)-49 b(e)g(ctr)g(al)322 b(The)-49 b(ory)321 b(of)f(R)-49 b(andom)321 b(Schr\304)-486 b(odinger)321 b(Op)-49 b(er)g(ators)p Fz(,)296 b(Birkh\304)-470 b(auser,)8009 55150 y(Basel{Berlin)316 b(\(1990\))6545 56257 y([5])472 b(D.)267 b(Damanik,)276 b(Gordon-t)-26 b(yp)26 b(e)266 b(argumen)-26 b(ts)266 b(in)g(the)g(sp)26 b(ectral)267 b(theory)e(of)h(one-dimensional)i (quasicrystals,)8009 57364 y(in)255 b Fl(Dir)-49 b(e)g(ctions)286 b(in)f(Mathematic)-49 b(al)286 b(Quasicrystals)p Fz(,)264 b(Eds.)256 b(M.)f(Baak)-26 b(e,)268 b(R.)255 b(V.)h(Mo)26 b(o)g(dy)-78 b(,)267 b(CRM)254 b(Monograph)8009 58471 y(Series)314 b Fa(13)p Fz(,)h(AMS,)e(Pro)-26 b(vidence,)314 b(RI)f(\(2000\),)j(277{305)6545 59578 y([6])472 b(D.)303 b(Damanik,)i(R.)e(Sims,)i(and)d(G.)h(Stolz,)i(Lo)26 b(calization)305 b(for)d(one-dimensional,)k(con)-26 b(tin)g(uum,)305 b(Bernoulli-)8009 60685 y(Anderson)313 b(mo)26 b(dels,)315 b Fl(Duke)341 b(Math.)e(J.)314 b Fa(114)h Fz(\(2002\),)g(59{100)6545 61792 y([7])472 b(D.)467 b(Damanik)g(and)f(B.)h(Solom)-26 b(y)g(ak,)505 b(Some)466 b(high-complexit)-26 b(y)467 b(Hamiltonians)h(with)e(purely)f(singular)8009 62899 y(con)-26 b(tin)g(uous)314 b(sp)26 b(ectrum,)314 b Fl(A)-24 b(nn.)340 b(Henri)h(Poinc)-49 b(ar)-24 b(\266)-462 b(e)380 b Fa(3)314 b Fz(\(2002\),)i(99{105)6545 64006 y([8])472 b(D.)407 b(Damanik)g(and)f(P)-78 b(.)406 b(Stollmann,)430 b(Multi-scale)407 b(analysis)g(implies)h(strong)e(dynamical)h(lo)26 b(calization,)8009 65113 y Fl(Ge)-49 b(om.)340 b(F)-73 b(unct.)341 b(A)-24 b(nal.)313 b Fa(11)h Fz(\(2001\),)i(11{29)6545 66220 y([9])472 b(H.)244 b(v)-26 b(on)244 b(Dreifus)g(and)f(A.)i (Klein,)258 b(A)244 b(new)g(pro)26 b(of)244 b(of)g(lo)26 b(calization)247 b(in)d(the)g(Anderson)f(tigh)-26 b(t)245 b(binding)f(mo)26 b(del,)8009 67327 y Fl(Commun.)341 b(Math.)e(Phys.)312 b Fa(124)j Fz(\(1989\),)h(285{299)6075 68434 y([10])472 b(F.)330 b(Germinet)g(and)g(A.)g(Klein,)335 b(Bo)26 b(otstrap)331 b(m)-26 b(ultiscale)332 b(analysis)f(and)f(lo)26 b(calization)334 b(in)c(random)g(media,)8009 69541 y Fl(Commun.)341 b(Math.)e(Phys.)312 b Fa(222)j Fz(\(2001\),)h(415{448)p eop end %%Page: 19 19 TeXDict begin 19 18 bop 8519 3345 a Fn(LOCALIZA)-71 b(TION)387 b(F)-24 b(OR)388 b(DISCRETE)f(ONE)h(DIMENSIONAL)h(RANDOM)g(W)-24 b(ORD)387 b(MODELS)1563 b(19)6075 6001 y Fz([11])472 b(S.)343 b(Jitomirsk)-52 b(a)-26 b(y)g(a,)352 b(H.)344 b(Sc)-26 b(h)g(ulz-Baldes,)351 b(and)343 b(G.)h(Stolz,)352 b(Delo)26 b(calization)347 b(in)d(random)f(p)26 b(olymer)344 b(mo)26 b(dels,)8009 7108 y(preprin)-26 b(t)312 b(\(2002\),)k(a)-26 b(v)-52 b(ailable)315 b(at)f(mp-arc)g(02-267)6075 8215 y([12])472 b(T.)524 b(Kato,)577 b Fl(Perturb)-49 b(ation)536 b(The)-49 b(ory)535 b(for)g(Line)-49 b(ar)536 b(Op)-49 b(er)g(ators)p Fz(,)576 b(Springer-V)-78 b(erlag,)577 b(Berlin{Heidelb)26 b(erg)8009 9322 y(\(1966\))6075 10429 y([13])472 b(W.)307 b(Kirsc)-26 b(h,)308 b(On)f(a)g(class)h(of)e (random)h(Sc)-26 b(hr\304)-470 b(odinger)307 b(op)26 b(erators,)309 b Fl(A)-49 b(dv.)334 b(in)f(Appl.)g(Math.)306 b Fa(6)h Fz(\(1985\),)j(177{)8009 11536 y(187)6075 12643 y([14])472 b(K.)314 b(Knopp,)f Fl(The)-49 b(ory)340 b(of)g(F)-73 b(unctions)p Fz(,)314 b(V)-78 b(ol.)314 b(I)26 b(I,)314 b(Do)-26 b(v)g(er,)314 b(New)f(Y)-78 b(ork)313 b(\(1947\))6075 13750 y([15])472 b(K.)314 b(P)-26 b(etersen,)314 b Fl(Er)-49 b(go)g(dic)340 b(the)-49 b(ory)p Fz(,)314 b(Cam)-26 b(bridge)314 b(Univ)-26 b(ersit)g(y)312 b(Press,)i(Cam)-26 b(bridge)314 b(\(1983\))6075 14857 y([16])472 b(C.)523 b(Sh)-26 b(ubin,)574 b(R.)523 b(V)-78 b(akilian,)577 b(and)522 b(T.)h(W)-78 b(ol\256,)576 b(Some)523 b(harmonic)h(analysis)g(questions)f(suggested) h(b)-26 b(y)8009 15964 y(Anderson-Bernoulli)314 b(mo)26 b(dels,)315 b Fl(Ge)-49 b(om.)340 b(F)-73 b(unct.)340 b(A)-24 b(nal.)314 b Fa(8)g Fz(\(1998\),)i(932{964)6075 17071 y([17])472 b(G.)451 b(T)-78 b(esc)-26 b(hl,)485 b Fl(Jac)-49 b(obi)468 b(Op)-49 b(er)g(ators)467 b(and)h(Completely)g (Inte)-49 b(gr)g(able)469 b(Nonline)-49 b(ar)468 b(L)-49 b(attic)g(es)p Fz(,)485 b(Mathematical)8009 18178 y(Surv)-26 b(eys)312 b(and)i(Monographs)g Fa(72)p Fz(,)h(AMS,)e(Pro)-26 b(vidence,)314 b(RI)f(\(2000\))6075 19285 y([18])472 b(P)-78 b(.)313 b(W)-78 b(alters,)315 b Fl(A)-24 b(n)340 b(Intr)-49 b(o)g(duction)341 b(to)f(Er)-49 b(go)g(dic)341 b(The)-49 b(ory)p Fz(,)313 b(Springer-V)-78 b(erlag,)314 b(New)f(Y)-78 b(ork{Berlin)314 b(\(1982\))7403 21360 y Fy(Dep)-59 b(ar)g(tment)358 b(of)f(Ma)-59 b(thema)g(tics)358 b(253-37,)g(Calif)-20 b(ornia)357 b(Institute)h(of)f(Technology,)k(P) -77 b(asadena,)6075 22467 y(CA)334 b(91125,)e(USA;)i(Email:)437 b(d)-20 b(amanik@its.cal)-59 b(tech.edu)7403 24349 y(Dep)g(ar)g(tment) 238 b(of)e(Ma)-59 b(thema)g(tics,)257 b(Princeton)237 b(University,)256 b(Princeton,)h(NJ)235 b(08544,)253 b(USA;)236 b(Email:)6075 25456 y(rsims@princeton.edu)7403 27338 y(Dep)-59 b(ar)g(tment)298 b(of)f(Ma)-59 b(thema)g(tics,)306 b(University)297 b(of)f(Alabama)h(a)-59 b(t)297 b(Birmingham,)304 b(Birmingham,)f(AL)6075 28445 y(35394-1170,)329 b(USA;)334 b(Email:)438 b(stolz@ma)-59 b(th.uab.edu)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0211201106232--