%!PS-Adobe-2.0 %%Creator: dvips 5.528 Copyright 1986, 1994 Radical Eye Software %%Title: srinivasan.dvi %%CreationDate: Thu Dec 16 11:36:13 1999 %%Pages: 10 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMR12 CMSS10 CMR10 CMTT10 CMR17 CMR8 CMBX10 CMTI10 %%+ CMBX12 CMR6 CMR9 CMTT9 CMMI10 CMSY10 CMMI8 CMEX10 CMSY8 CMMI6 CMSY6 %%+ CMMI12 %%EndComments %DVIPSCommandLine: dvips -o srinivasan.ps srinivasan.dvi %DVIPSParameters: dpi=300, comments removed %DVIPSSource: TeX output 1999.12.16:1135 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}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 dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put 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 /IE 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 IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /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 dup definefont setfont}B /ch-width{ch-data dup length 5 sub get} B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{ ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 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 dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 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 /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /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 %%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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % 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 (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 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 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec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275AA6F8D39283433935E56A740523E72FA631C1A9DA0C1E9400E4D4B200ABEF380000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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10:42:42 % 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 (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 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 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /arrowup put dup 175 /arrowdown put dup 176 /quotesingle put dup 177 /exclamdown put dup 178 /questiondown put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /visiblespace put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /arrowup put dup 12 /arrowdown put dup 13 /quotesingle put dup 14 /exclamdown put dup 15 /questiondown put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /visiblespace put dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /backslash put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 96 /quoteleft 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 123 /braceleft put dup 124 /bar put dup 125 /braceright put dup 126 /asciitilde put dup 127 /dieresis put dup 128 /visiblespace put dup 160 /space put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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 (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /sterling put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 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/seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi 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 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft 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 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT9 %!PS-AdobeFont-1.1: CMTT9 1.0 %%CreationDate: 1991 Aug 20 16:46:24 % 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 (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 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 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /arrowup put dup 175 /arrowdown put dup 176 /quotesingle put dup 177 /exclamdown put dup 178 /questiondown put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /visiblespace put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /arrowup put dup 12 /arrowdown put dup 13 /quotesingle put dup 14 /exclamdown put dup 15 /questiondown put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /visiblespace put dup 33 /exclam put dup 34 /quotedbl put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk 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 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question 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 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /backslash put dup 93 /bracketright put dup 94 /asciicircum put dup 95 /underscore put dup 96 /quoteleft 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 123 /braceleft put dup 124 /bar put dup 125 /braceright put dup 126 /asciitilde put dup 127 /dieresis put dup 128 /visiblespace put dup 160 /space put readonly def /FontBBox{-6 -233 542 698}readonly def /UniqueID 5000831 def currentdict end currentfile eexec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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove 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 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove 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 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F092 5722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441 FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8 DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F17 8C461553146AB427BDD7DA12534BA078AD3D780414930E72218B3075925CE1192F11FC8530FC D5E3038E3A6A6DB2DCFBAE3B4653E7E02730314E02B54A1E296D2BEF8A79411D9225DAD7B4E6 D6F9CF0688B69BA21193BF1495807E7A196CF14C95A4E02F9CD2DA8CDB2546C6DF52E5247459 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. 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 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 165 /floorleftbig put dup 166 /floorrightbig put dup 167 /ceilingleftbig put dup 168 /ceilingrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 173 /angbracketleftbig put dup 174 /angbracketrightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 177 /slashbig put dup 178 /backslashbig put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 185 /floorleftbigg put dup 186 /floorrightbigg put dup 187 /ceilingleftbigg put dup 188 /ceilingrightbigg put dup 189 /braceleftbigg put dup 190 /bracerightbigg put dup 191 /angbracketleftbigg put dup 192 /angbracketrightbigg put dup 193 /slashbigg put dup 194 /backslashbigg put dup 195 /parenleftBigg put dup 196 /arrowdblbt put dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 4 /floorleftbig put dup 5 /floorrightbig put dup 6 /ceilingleftbig put dup 7 /ceilingrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 14 /slashbig put dup 15 /backslashbig 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 22 /floorleftbigg put dup 23 /floorrightbigg put dup 24 /ceilingleftbigg put dup 25 /ceilingrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 28 /angbracketleftbigg put dup 29 /angbracketrightbigg put dup 30 /slashbigg put dup 31 /backslashbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 36 /floorleftBigg put dup 37 /floorrightBigg put dup 38 /ceilingleftBigg put dup 39 /ceilingrightBigg put dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 42 /angbracketleftBigg put dup 43 /angbracketrightBigg put dup 44 /slashBigg put dup 45 /backslashBigg put dup 46 /slashBig put dup 47 /backslashBig put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex put dup 56 /bracelefttp put dup 57 /bracerighttp put dup 58 /braceleftbt put dup 59 /bracerightbt put dup 60 /braceleftmid put dup 61 /bracerightmid put dup 62 /braceex put dup 63 /arrowvertex put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 70 /unionsqtext put dup 71 /unionsqdisplay put dup 72 /contintegraltext put dup 73 /contintegraldisplay put dup 74 /circledottext put dup 75 /circledotdisplay put dup 76 /circleplustext put dup 77 /circleplusdisplay put dup 78 /circlemultiplytext put dup 79 /circlemultiplydisplay put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 83 /uniontext put dup 84 /intersectiontext put dup 85 /unionmultitext put dup 86 /logicalandtext put dup 87 /logicalortext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 91 /uniondisplay put dup 92 /intersectiondisplay put dup 93 /unionmultidisplay put dup 94 /logicalanddisplay put dup 95 /logicalordisplay put dup 96 /coproducttext put dup 97 /coproductdisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 101 /tildewide put dup 102 /tildewider put dup 103 /tildewidest put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 106 /floorleftBig put dup 107 /floorrightBig put dup 108 /ceilingleftBig put dup 109 /ceilingrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 114 /radicalbigg put dup 115 /radicalBigg put dup 116 /radicalbt put dup 117 /radicalvertex put dup 118 /radicaltp put dup 119 /arrowvertexdbl put dup 120 /arrowtp put dup 121 /arrowbt put dup 122 /bracehtipdownleft put dup 123 /bracehtipdownright put dup 124 /bracehtipupleft put dup 125 /bracehtipupright put dup 126 /arrowdbltp put dup 127 /arrowdblbt put dup 128 /parenleftBigg put dup 160 /space put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC6 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove 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 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /alpha put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 185 /mu put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 190 /sigma put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 194 /chi put dup 195 /psi put dup 196 /tie put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 19 /iota put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 29 /upsilon put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 36 /pi1 put dup 37 /rho1 put dup 38 /sigma1 put dup 39 /phi1 put dup 40 /arrowlefttophalf put dup 41 /arrowleftbothalf put dup 42 /arrowrighttophalf put dup 43 /arrowrightbothalf put dup 44 /arrowhookleft put dup 45 /arrowhookright put dup 46 /triangleright put dup 47 /triangleleft put dup 48 /zerooldstyle put dup 49 /oneoldstyle put dup 50 /twooldstyle put dup 51 /threeoldstyle put dup 52 /fouroldstyle put dup 53 /fiveoldstyle put dup 54 /sixoldstyle put dup 55 /sevenoldstyle put dup 56 /eightoldstyle put dup 57 /nineoldstyle put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 63 /star put dup 64 /partialdiff 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 81 /Q 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 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove 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 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 123 /dotlessi put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /vector put dup 127 /tie put dup 128 /psi put dup 160 /space put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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b(a)g(deterministic)g(algorithm,)e(whic)o (h,)i(giv)o(en)g(an)o(y)g Fj(i)g Fw(and)h Fj(j)s Fw(,)e(can)i (construct)f Fj(s)1441 1122 y Fh(i;j)1496 1115 y Fw(in)g(time)g(p)q (oly)o(\(log)7 b Fi(j)p Fj(S)s Fi(j)h Fw(+)-30 1171 y(log)f Fj(n)13 b Fw(+)g(log)7 b Fj(m)p Fw(\);)20 b(note)f(that)f(represen)o (ting)h Fj(i)f Fw(and)i Fj(j)h Fw(in)d(the)h(natural)f(w)o(a)o(y)g (needs)i(log)7 b Fi(j)p Fj(S)s Fi(j)12 b Fw(+)h(log)7 b Fj(n)19 b Fw(bits.)31 b(F)l(or)-30 1228 y(all)13 b(the)h (constructions)g(of)g(lo)o(w-discrepancy)f(sets)h(surv)o(ey)o(ed)h (here,)f(suc)o(h)h(a)e(constructibilit)o(y)g(prop)q(ert)o(y)g(will)g(b) q(e)-30 1284 y(true.)41 1340 y(A)i(natural)f(sub)q(class)h(of)g Fi(C)504 1324 y Fh(n)501 1352 y(m)549 1340 y Fw(is)g(the)g(follo)o (wing)e(family)h(of)h Fn(ge)n(ometric)h(r)n(e)n(ctangles)p Fw(:)109 1443 y Fi(G)139 1424 y Fh(n)136 1454 y(m)182 1443 y Fw(=)d Fi(f)p Fw([)p Fj(a)290 1450 y Fs(1)309 1443 y Fj(;)8 b(b)350 1450 y Fs(1)368 1443 y Fw(])i Fi(\002)g Fw([)p Fj(a)473 1450 y Fs(2)493 1443 y Fj(;)e(b)534 1450 y Fs(2)552 1443 y Fw(])i Fi(\002)g(\001)e(\001)g(\001)h(\002)h Fw([)p Fj(a)766 1450 y Fh(n)789 1443 y Fj(;)e(b)830 1450 y Fh(n)852 1443 y Fw(])13 b(:)27 b Fi(8)p Fj(i;)8 b Fw(\(\()p Fj(a)1040 1450 y Fh(i)1065 1443 y Fi(\024)13 b Fj(b)1133 1450 y Fh(i)1147 1443 y Fw(\))d Fi(^)g Fw(\()p Fj(a)1257 1450 y Fh(i)1271 1443 y Fj(;)e(b)1312 1450 y Fh(i)1337 1443 y Fi(2)13 b(f)p Fw(0)p Fj(;)8 b Fw(1)p Fj(;)g(:)g(:)f(:)t(;)h(m)i Fi(\000)g Fw(1)p Fi(g)p Fw(\)\))p Fi(g)p Fj(:)-30 1545 y Fw(\(This)17 b(family)f(is)h(sometimes)f(also)h(referred)h(to)e(as)h Fn(axis-p)n(ar)n(al)r(lel)h(r)n(e)n(ctangles)p Fw(.\))25 b(W)l(e)17 b(can)h(analogously)e(de\014ne)-30 1601 y(lo)o (w-discrepancy)22 b(sets)g Fj(S)i Fw(for)e Fi(G)561 1585 y Fh(n)558 1612 y(m)591 1601 y Fw(.)42 b(This)22 b(surv)o(ey)g(will)f (consider)h(the)g(e\016cien)o(t)g(construction)g(of)g(\\small")-30 1658 y(lo)o(w-discrepancy)d(sets)h Fj(S)i Fw(as)e(de\014ned)h(ab)q(o)o (v)o(e.)34 b(W)l(e)20 b(shall)f(consider)h(v)m(arian)o(ts)f(of)g(this)h (basic)f(problem,)i(and)-30 1714 y(applications)14 b(thereof.)41 1771 y(It)22 b(is)g(not)g(hard)g(to)g(sho)o(w)f(that)h(if)g Fj(C)k Fw(is)21 b(a)h(su\016cien)o(tly)g(large)f(constan)o(t)h(and)g (if)g(w)o(e)g(c)o(ho)q(ose)g Fj(C)s(mn=\017)1899 1754 y Fs(2)-30 1827 y Fw(p)q(oin)o(ts)e(indep)q(enden)o(tly)i(from)e Fj(U)5 b Fw(\()p Fi(f)p Fw(0)p Fj(;)j Fw(1)p Fj(;)g(:)g(:)f(:)t(;)h(m) 13 b Fi(\000)h Fw(1)p Fi(g)917 1810 y Fh(n)940 1827 y Fw(\),)22 b(then)f(this)g(random)f(m)o(ulti-set)g Fj(Z)k Fw(of)c(p)q(oin)o(ts)h(is)f(an)-30 1883 y Fj(\017)p Fw(-appro)o (ximation)c(for)g Fi(C)407 1867 y Fh(n)404 1895 y(m)454 1883 y Fw(with)h(high)g(probabilit)o(y)l(.)24 b(Brie\015y)l(,)17 b(consider)g(an)o(y)g(\014xed)h(com)o(binatorial)d(rectangle)-30 1940 y Fj(R)g Fw(=)h Fj(S)99 1947 y Fs(1)130 1940 y Fi(\002)c(\001)c (\001)g(\001)h(\002)j Fj(S)316 1947 y Fh(n)355 1940 y Fi(2)j(C)427 1923 y Fh(n)424 1951 y(m)458 1940 y Fw(.)25 b(A)17 b(Cherno\013-t)o(yp)q(e)f(argumen)o(t)h([12)o(,)f(14])g(sho)o (ws)g(that)h(for)f(an)o(y)h(desired)g(constan)o(t)-30 1996 y Fj(C)5 1980 y Ff(0)30 1996 y Fj(>)c Fw(0,)i(there)g(is)g(a)g (large)f(enough)h(v)m(alue)h(for)f Fj(C)j Fw(suc)o(h)e(that)f(\(1\))f (fails)g(with)g(probabilit)o(y)g(at)g(most)h(2)1730 1980 y Ff(\000)p Fh(C)1784 1968 y Fd(0)1796 1980 y Fh(mn)1866 1996 y Fw(for)-30 2053 y Fj(Z)s Fw(.)26 b(No)o(w,)17 b Fi(C)189 2036 y Fh(n)186 2064 y(m)236 2053 y Fw(has)g(2)342 2036 y Fh(mn)413 2053 y Fw(elemen)o(ts;)h(so,)f(the)g(probabilit)o(y)e (that)i Fj(Z)j Fw(is)d(not)f(an)h Fj(\017)p Fw(-appro)o(ximation)f(for) h Fi(C)1785 2036 y Fh(n)1782 2064 y(m)1832 2053 y Fw(is)g(at)-30 2109 y(most)d(2)104 2093 y Fs(\(2)p Ff(\000)p Fh(C)190 2081 y Fd(0)202 2093 y Fs(\))p Fh(mn)270 2109 y Fw(,)h(a)g(tin)o(y)f (quan)o(tit)o(y)g(if)h Fj(C)688 2093 y Ff(0)713 2109 y Fj(>)e Fw(2.)41 2166 y(Th)o(us,)f(there)g(certainly)g Fn(exists)f Fw(an)h Fj(\017)p Fw(-appro)o(ximation)f(for)h Fi(C)1073 2149 y 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2629 y(m)1907 2617 y Fw(,)p eop %%Page: 3 3 3 2 bop -30 154 a Fw(and)18 b Fj(\017)p Fw(-appro)o(ximations)e(for)h Fi(C)517 138 y Fh(n)514 167 y(m;k)594 154 y Fw(and)h Fi(G)715 138 y Fh(n)712 167 y(m;k)774 154 y Fw(.)27 b(A)18 b(probabilistic)e(construction)g(sho)o(ws)h(that)g(there)h(exists)f(an) -30 211 y Fj(\017)p Fw(-appro)o(ximation)d(of)h(cardinalit)o(y)413 341 y Fj(O)457 269 y Fg( )o( )522 341 y Fj(mk)c Fw(+)g(log)709 269 y Fg( )775 310 y Fj(n)776 372 y(k)802 269 y Fg(!!!)908 341 y Fj(=\017)949 322 y Fs(2)969 269 y Fg(!)1015 341 y Fi(\024)i Fj(O)q Fw(\(\()p Fj(mk)d Fw(+)g Fj(k)f Fw(log)e Fj(n)p Fw(\))p Fj(=\017)1439 322 y Fs(2)1459 341 y Fw(\))-30 474 y(for)14 b Fi(C)66 457 y Fh(n)63 487 y(m;k)139 474 y Fw(\(and)g(hence)h(for)f Fi(G)468 457 y Fh(n)465 487 y(m;k)527 474 y Fw(\).)19 b(The)c(ma)s(jor)d(op)q(en)j(question)f(here) h(is)e(to)h(construct)g(an)g Fj(\017)p Fw(-appro)o(ximation)e(of)-30 535 y(cardinalit)o(y)h(p)q(oly)o(\()p Fj(m)8 b Fw(+)h Fj(k)h Fw(+)e(log)g Fj(n)g Fw(+)h 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Fw(Note)f(that)g Fi(C)206 1045 y Fh(n)203 1073 y(m)249 1062 y Fw(=)f Fi(G)328 1045 y Fh(n)325 1073 y(m)373 1062 y Fw(if)h Fj(m)e Fw(=)h(2.)20 b(Breakthrough)15 b(w)o(ork)g(on)g(lo)o(w-discrepancy)g(sets)g(for)g Fi(C)1552 1045 y Fh(n)1549 1073 y Fs(2)1591 1062 y Fw(w)o(as)f(presen)o (ted)i(in)-30 1118 y([21)o(])g(through)f(a)h(notion)f(of)g Fn(smal)r(l-bias)i(sample)f(sp)n(ac)n(es)p Fw(,)f(whic)o(h)h(will)e(b)q (e)j(in)o(tro)q(duced)f(shortly)l(.)21 b(In)c(particular,)-30 1175 y(the)h(problem)g(of)g(constructing)g(an)g Fj(\017)p Fw(-appro)o(ximation)f(for)g Fi(C)1055 1158 y Fh(n)1052 1188 y Fs(2)p Fh(;k)1119 1175 y Fw(of)h(cardinalit)o(y)f(p)q(oly\()p Fj(k)c Fw(+)f(log)7 b Fj(n)13 b Fw(+)f Fj(\017)1764 1158 y Ff(\000)p Fs(1)1812 1175 y Fw(\))18 b(w)o(as)-30 1231 y(settled)h(in)g(their)f(w)o(ork.)31 b(Let)19 b(us)h(brie\015y)f(surv)o (ey)g(some)g(of)f(the)i(k)o(ey)f(ideas)f(and)i(applications)d(of)i (their)g(and)-30 1288 y(related)c(results.)-30 1409 y Fb(2.1)56 b(F)-5 b(rom)18 b(bias)h(to)g(appro)n(ximation)-30 1495 y Fw(Let)f([)p Fj(`)p Fw(])g(denote)g(the)g(set)g Fi(f)p Fw(1)p Fj(;)8 b Fw(2)p Fj(;)g(:)g(:)f(:)e(;)j(`)p Fi(g)p Fw(;)18 b(log)7 b Fj(x)18 b Fw(will)f(denote)h(log)1092 1506 y Fs(2)1119 1495 y Fj(x)p Fw(.)29 b(T)l(o)18 b(construct)g(an)g Fj(\017)p Fw(-appro)o(ximation)f(for)-30 1551 y Fi(C)-3 1535 y Fh(n)-6 1565 y Fs(2)p Fh(;k)43 1551 y Fw(,)j(w)o(e)f(w)o(an)o(t) f(an)i(e\016cien)o(t)f(construction)g(of)g(a)g(\\small")f(m)o(ultiset)g Fj(S)k Fi(\022)e(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1432 1535 y Fh(n)1473 1551 y Fw(suc)o(h)20 b(that)f(for)g(a)g(v)o(ector)-30 1608 y(\()p Fj(X)26 1615 y Fs(1)45 1608 y Fj(;)8 b(X)104 1615 y Fs(2)123 1608 y Fj(;)g(:)g(:)g(:)t(;)g(X)262 1615 y Fh(n)285 1608 y Fw(\))15 b(sampled)g(according)f(to)h Fj(U)5 b Fw(\()p Fj(S)s Fw(\),)94 1749 y Fi(8)p Fj(j)15 b Fi(2)e Fw([)p Fj(k)q Fw(])i Fi(8f)p Fj(i)326 1756 y Fs(1)345 1749 y Fj(;)8 b(i)382 1756 y Fs(2)401 1749 y Fj(;)g(:)g(:)g(:)d(;)j(i)519 1756 y Fh(j)536 1749 y Fi(g)k(\022)h Fw([)p Fj(n)p Fw(])i Fi(8)p Fw(\()p Fj(b)750 1756 y Fs(1)769 1749 y Fj(;)8 b(b)810 1756 y Fs(2)828 1749 y Fj(;)g(:)g(:)g(:)d(;)j(b) 950 1756 y Fh(j)967 1749 y Fw(\))k Fi(2)h(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1153 1730 y Fh(j)1170 1749 y Fj(;)22 b Fi(j)8 b Fw(Pr)o(\()1313 1693 y Fh(j)1298 1708 y Fg(^)1292 1800 y Fh(`)p Fs(=1)1351 1749 y Fw(\()p Fj(X)1407 1756 y Fh(i)1419 1762 y Fe(`)1448 1749 y Fw(=)13 b Fj(b)1516 1756 y Fh(`)1532 1749 y Fw(\)\))d Fi(\000)g Fw(2)1646 1730 y Ff(\000)p Fh(j)1691 1749 y Fi(j)j(\024)g Fj(\017:)66 b Fw(\(3\))-30 1886 y(\(Setting)14 b Fj(k)g Fw(=)f Fj(n)i Fw(will)f(yield)h(an)g Fj(\017)p Fw(-appro)o(ximation)f(for)h Fi(C)965 1870 y Fh(n)962 1898 y Fs(2)988 1886 y Fw(.\))41 1943 y(A)f(k)o(ey)f(idea)h(in)g([21)o(])f(is)h(to)f(approac)o(h)h(this) f(through)h Fn(smal)r(l-bias)g(sample)h(sp)n(ac)n(es)p Fw(.)j(Giv)o(en)c(a)f(distribution)g Fj(D)-30 1999 y Fw(on)i Fi(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)146 1983 y Fh(n)183 1999 y Fw(and)15 b(an)o(y)g Fj(T)k Fi(\022)13 b Fw([)p Fj(n)p Fw(],)h(de\014ne)450 2099 y(bias)529 2106 y Fh(D)561 2099 y Fw(\()p Fj(T)6 b Fw(\))11 b(=)i Fi(j)8 b Fw(Pr)o(\(\()794 2059 y Fg(M)795 2151 y Fh(i)p Ff(2)p Fh(T)864 2099 y Fj(X)902 2106 y Fh(i)916 2099 y Fw(\))k(=)h(1\))c Fi(\000)i Fw(Pr\(\()1175 2059 y Fg(M)1176 2151 y Fh(i)p Ff(2)p Fh(T)1244 2099 y Fj(X)1282 2106 y Fh(i)1296 2099 y Fw(\))h(=)h(0\))p Fi(j)p Fw(;)-30 2239 y(\()p Fj(X)26 2246 y Fs(1)45 2239 y Fj(;)8 b(X)104 2246 y Fs(2)123 2239 y Fj(;)g(:)g(:)g(:)t(;)g(X)262 2246 y Fh(n)285 2239 y Fw(\))13 b Fi(2)i(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)474 2222 y Fh(n)511 2239 y Fw(is)16 b(a)f(random)h(v)o (ector)f(c)o(hosen)h(according)g(to)f Fj(D)q Fw(,)h(and)g(\\)1489 2207 y Fg(L)1535 2239 y Fw(")f(is)h(the)g(usual)f(X)o(OR)-30 2295 y(op)q(eration.)20 b(De\014ne)c Fj(D)h Fw(to)e(b)q(e)h Fj(k)q Fn(-wise)g Fj(\017)p Fn(-biase)n(d)g Fw(if)f(bias)937 2302 y Fh(D)969 2295 y Fw(\()p Fj(T)6 b Fw(\))12 b Fi(\024)i Fj(\017)i Fw(for)e(all)h Fj(T)21 b Fw(suc)o(h)16 b(that)f Fi(j)p Fj(T)6 b Fi(j)12 b(\024)i Fj(k)q Fw(;)h Fj(D)i Fw(is)e(simply)-30 2352 y(called)h Fj(\017)p Fn(-biase)n(d)h Fw(if)f(it)g(is)g Fj(n)p Fw(-wise)h Fj(\017)p Fw(-biased.)25 b(Via)16 b(F)l(ourier)g(analysis,)f(it)h(is)g(sho)o(wn)h(in)f([21)o(])g (that)g(if)g Fj(D)i Fw(is)e Fj(k)q Fw(-wise)-30 2408 y Fj(\017)p Fw(-biased,)k(then)f(our)g(desired)g(prop)q(ert)o(y)f (\(3\))g(also)g(holds.)30 b(\(Th)o(us,)19 b(in)g(particular,)f(w)o(e)g (ha)o(v)o(e)h(for)f(all)g(distinct)-30 2465 y(indices)d Fj(i)135 2472 y Fs(1)155 2465 y Fj(;)8 b(i)192 2472 y Fs(2)210 2465 y Fj(;)g(:)g(:)g(:)d(;)j(i)328 2472 y Fh(k)363 2465 y Fw(that)433 2523 y Fg(0)433 2598 y(@)594 2567 y(X)470 2663 y Fs(\()p Fh(b)499 2668 y Fm(1)516 2663 y Fh(;b)541 2668 y Fm(2)558 2663 y Fh(;:::)o(;b)622 2669 y Fe(k)641 2663 y Fs(\))p Ff(2f)p Fs(0)p Fh(;)p Fs(1)p Ff(g)761 2653 y Fe(k)785 2607 y Fi(j)g Fw(Pr)o(\()892 2554 y Fh(k)879 2567 y Fg(^)872 2659 y Fh(`)p Fs(=1)932 2607 y Fw(\()p Fj(X)988 2614 y Fh(i)1000 2620 y Fe(`)1029 2607 y Fw(=)13 b Fj(b)1097 2614 y Fh(`)1113 2607 y Fw(\)\))c Fi(\000)h Fw(2)1226 2588 y Ff(\000)p Fh(j)1272 2607 y Fi(j)1285 2523 y Fg(1)1285 2598 y(A)1333 2607 y Fi(\024)j Fw(2)1404 2588 y Fh(k)1426 2607 y Fj(\017:)405 b Fw(\(4\))p eop %%Page: 4 4 4 3 bop -30 154 a Fw(It)15 b(is)g(sho)o(wn)g(in)g([3)o(,)g(21)o(])g (that)g(the)g(left-hand-side)g(of)g(\(4\))f(can)i(in)f(fact)f(b)q(e)i (upp)q(er-b)q(ounded)i(b)o(y)d(2)1668 138 y Fh(k)q(=)p Fs(2)1724 154 y Fj(\017)p Fw(.\))41 211 y(Another)c(in)o(teresting)f (result)g(of)h([21)o(])g(\(using)f(a)h(construction)g(of)g([1)o(]\))f (is)h(the)g(follo)o(wing)e(reduction.)19 b(Supp)q(ose)-30 267 y(w)o(e)e(ha)o(v)o(e)g(an)h(e\016cien)o(t)f(construction)g(of)g(a)g (m)o(ultiset)f Fj(S)j Fi(\022)d(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1128 251 y Fh(n)1167 267 y Fw(with)17 b Fi(j)p Fj(S)s Fi(j)e(\024)i Fj(F)6 b Fw(\()p Fj(n;)i(\017)p Fw(\),)18 b(suc)o(h)f(that)g Fj(U)5 b Fw(\()p Fj(S)s Fw(\))16 b(is)-30 324 y Fj(\017)p Fw(-biased.)35 b(Then,)21 b(for)f(an)o(y)f Fj(k)j Fi(2)f Fw([)p Fj(n)p Fw(],)f(there)g(is)g(also)f(an)h(e\016cien) o(t)f(construction)h(of)f(an)h Fj(S)1589 307 y Ff(0)1621 324 y Fi(\022)h(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1790 307 y Fh(n)1832 324 y Fw(with)-30 380 y Fi(j)p Fj(S)14 364 y Ff(0)25 380 y Fi(j)k(\024)h Fj(F)6 b Fw(\()p Fj(O)q Fw(\()p Fj(k)i Fw(log)g Fj(n)p Fw(\))p Fj(;)g(\017)p Fw(\),)14 b(suc)o(h)h(that)g Fj(U)5 b Fw(\()p Fj(S)719 364 y Ff(0)730 380 y Fw(\))14 b(is)h Fj(k)q Fw(-wise)g Fj(\017)p Fw(-biased.)-30 501 y Fb(2.2)56 b(Constructing)18 b(small-bias)g(spaces)-30 587 y Fw(Ha)o(ving)13 b(seen)h(that)f (small-bias)f(spaces)i(su\016ce)h(to)e(solv)o(e)g(our)g Fj(\017)p Fw(-appro)o(ximation)f(problem)i(for)f Fj(m)g Fw(=)g(2,)g(w)o(e)g(no)o(w)-30 643 y(presen)o(t)19 b(a)g(construction)f (of)h(small-bias)e(spaces)j(due)f(to)g([3)o(].)31 b(W)l(e)19 b(will)f(also)g(surv)o(ey)h(another)g(approac)o(h)g(to)-30 699 y(small-bias)14 b(spaces)h(from)f([21],)g(and)h(sho)o(w)g(a)g (connection)g(to)g(error-correcting)f(co)q(des.)41 756 y(Supp)q(ose)i Fj(m)e Fw(=)g Fi(d)p Fw(log)o(\()p Fj(n=\017)p Fw(\))p Fi(e)p Fw(.)22 b(The)16 b(follo)o(wing)d(construction)i(of)g(a) h(m)o(ultiset)e Fj(S)i Fi(\022)e(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1579 739 y Fh(n)1616 756 y Fw(suc)o(h)16 b(that)f Fj(U)5 b Fw(\()p Fj(S)s Fw(\))-30 812 y(is)19 b Fj(\017)p Fw(-biased,)h(is)f(due)g(to)g([3)o(].)32 b(W)l(e)19 b(will)f(describ)q(e)i Fj(S)h Fw(b)o(y)e(sho)o(wing)f(ho)o (w)h(to)g(generate)g(an)g(elemen)o(t)f(according)-30 869 y(to)g Fj(U)5 b Fw(\()p Fj(S)s Fw(\);)20 b(it)e(will)g(b)q(e)i (immediate)e(then)h(that)g Fi(j)p Fj(S)s Fi(j)e Fw(=)j(2)958 852 y Fs(2)p Fh(m)1009 869 y Fw(,)f(i.e.,)g(that)f Fi(j)p Fj(S)s Fi(j)g Fw(=)i Fj(O)q Fw(\()p Fj(n)1445 852 y Fs(2)1464 869 y Fj(=\017)1505 852 y Fs(2)1525 869 y Fw(\).)31 b(Cho)q(ose)19 b(elemen)o(ts)-30 925 y Fj(x;)8 b(y)21 b Fw(of)e(the)g(\014nite)h (\014eld)g Fj(GF)6 b Fw([2)529 909 y Fh(m)562 925 y Fw(])19 b(indep)q(enden)o(tly)i(and)e(uniformly)g(at)g(random.)33 b(Next)19 b(generate)g(a)h(v)o(ector)-30 982 y Fj(X)c Fw(=)d(\()p Fj(X)128 989 y Fs(1)147 982 y Fj(;)8 b(X)206 989 y Fs(2)224 982 y Fj(;)g(:)g(:)g(:)d(;)j(X)364 989 y Fh(n)387 982 y Fw(\))k Fi(2)h(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)573 965 y Fh(n)608 982 y Fw(b)o(y)14 b(de\014ning)h Fj(X)879 989 y Fh(i)905 982 y Fw(=)e(\()p Fj(x)997 965 y Fh(i)1019 982 y Fi(\001)7 b Fj(y)r Fw(\))15 b(mo)q(d)g(2)f(for)f(eac) o(h)h Fj(i)p Fw(.)19 b(Here,)14 b Fj(x)1597 965 y Fh(i)1625 982 y Fw(denotes)g(raising)-30 1038 y Fj(x)k Fw(to)f(the)g Fj(i)p Fw(th)g(p)q(o)o(w)o(er)h(in)f(the)h(\014eld)g Fj(GF)6 b Fw([2)708 1022 y Fh(m)741 1038 y Fw(];)18 b Fj(x)811 1022 y Fh(i)837 1038 y Fi(\001)11 b Fj(y)19 b Fw(denotes)f(in)o(terpreting)f Fj(x)1347 1022 y Fh(i)1378 1038 y Fw(and)h Fj(y)i Fw(as)d Fj(m)p Fw(-bit)g(strings)g(and)-30 1095 y(taking)d(their)h(dot)g(pro)q(duct.)20 b(This)15 b(v)o(ector)f Fj(X)19 b Fw(represen)o(ts)c(a)g(v)o(ector)f(c)o(hosen)i (according)e(to)h Fj(U)5 b Fw(\()p Fj(S)s Fw(\).)41 1151 y(As)16 b(men)o(tioned)g(ab)q(o)o(v)o(e,)g(it)f(is)h(immediate)g(that)f Fi(j)p Fj(S)s Fi(j)e Fw(=)i(2)1033 1135 y Fs(2)p Fh(m)1084 1151 y Fw(.)23 b(Let)17 b(us)f(quic)o(kly)g(see)h(wh)o(y)f(the)g(ab)q (o)o(v)o(e)g(distri-)-30 1208 y(bution)e(on)g(\()p Fj(X)231 1215 y Fs(1)250 1208 y Fj(;)8 b(X)309 1215 y Fs(2)328 1208 y Fj(;)g(:)g(:)g(:)d(;)j(X)468 1215 y Fh(n)490 1208 y Fw(\))14 b(is)g Fj(\017)p Fw(-biased;)h(w)o(e)f(need)h(to)f(sho)o(w)f (that)h(bias)1266 1215 y Fh(D)1298 1208 y Fw(\()p Fj(T)6 b Fw(\))11 b Fi(\024)i Fj(\017)i Fw(for)f(all)f Fj(T)19 b Fi(\022)13 b Fw([)p Fj(n)p Fw(].)19 b(Fix)13 b(an)o(y)-30 1264 y Fj(T)18 b Fw(=)13 b Fi(f)p Fj(i)102 1271 y Fs(1)122 1264 y Fj(;)8 b(i)159 1271 y Fs(2)177 1264 y Fj(;)g(:)g(:)g(:)d(;)j(i) 295 1271 y Fh(j)312 1264 y Fi(g)k(\022)h Fw([)p Fj(n)p Fw(].)20 b(By)15 b(elemen)o(tary)g(prop)q(erties)f(of)h(sums)g(o)o(v)o (er)g(the)g(\014eld)g Fj(GF)6 b Fw([2)1545 1247 y Fh(m)1578 1264 y Fw(],)15 b(w)o(e)g(ha)o(v)o(e)535 1324 y Fg(M)534 1417 y Fh(`)p Ff(2)p Fh(T)605 1365 y Fj(X)643 1372 y Fh(`)672 1365 y Fw(=)e(\()p Fj(x)764 1346 y Fh(i)776 1351 y Fm(1)805 1365 y Fw(+)e Fj(x)877 1346 y Fh(i)889 1351 y Fm(2)918 1365 y Fw(+)g Fi(\001)d(\001)g(\001)g Fw(+)i Fj(x)1098 1372 y Fh(i)1110 1377 y Fe(j)1128 1365 y Fw(\))g Fi(\001)g Fj(y)17 b Fw(mo)q(d)e(2)p Fj(;)506 b Fw(\(5\))-30 1504 y(where)20 b(the)g(sum)f Fj(t)p Fw(\()p Fj(x)p Fw(\))h(=)g Fj(x)468 1488 y Fh(i)480 1493 y Fm(1)513 1504 y Fw(+)13 b Fj(x)587 1488 y Fh(i)599 1493 y Fm(2)632 1504 y Fw(+)g Fi(\001)8 b(\001)g(\001)j Fw(+)j Fj(x)821 1511 y Fh(i)833 1516 y Fe(j)870 1504 y Fw(is)20 b(tak)o(en)f(in)g Fj(GF)6 b Fw([2)1213 1488 y Fh(m)1246 1504 y Fw(].)33 b(No)o(w)19 b(if)g Fj(t)p Fw(\()p Fj(x)p Fw(\))g(is)g(nonzero)h(for)f (our)-30 1561 y(random)c Fj(x)p Fw(,)h(it)f(is)h(easy)f(to)h(c)o(hec)o (k)g(that)f(the)h(righ)o(t-hand-side)f(of)h(\(5\))f(is)g(equally)g(lik) o(ely)g(to)g(b)q(e)i(0)e(or)h(1.)21 b(On)c(the)-30 1617 y(other)f(hand,)i(if)e Fj(t)p Fw(\()p Fj(x)p Fw(\))h(is)f(zero,)h(the)g (righ)o(t-hand-side)f(of)h(\(5\))f(is)g(0.)24 b(Since)18 b Fj(t)p Fw(\()p Fj(z)r Fw(\))f(is)f(a)g(p)q(olynomial)g(of)g(degree)i (at)-30 1674 y(most)f Fj(n)p Fw(,)h(it)f(has)h(at)f(most)g Fj(n)g Fw(ro)q(ots;)h(th)o(us,)g(Pr\()p Fj(t)p Fw(\()p Fj(x)p Fw(\))e(=)h(0\))f Fi(\024)h Fj(n=)p Fw(2)1133 1657 y Fh(m)1183 1674 y Fi(\024)g Fj(\017)p Fw(.)28 b(This,)18 b(com)o(bined)g(with)f(the)g(ab)q(o)o(v)o(e)-30 1730 y(observ)m(ations,)d(helps)i(sho)o(w)e(that)h(bias)648 1737 y Fh(D)680 1730 y Fw(\()p Fj(T)6 b Fw(\))12 b Fi(\024)h Fj(\017)p Fw(.)41 1786 y(Th)o(us)h(w)o(e)h(ha)o(v)o(e)f(an)h(e\016cien) o(t)f(construction)h(of)f(a)g(m)o(ultiset)g Fj(S)h Fi(\022)e(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1285 1770 y Fh(n)1321 1786 y Fw(with)14 b Fi(j)p Fj(S)s Fi(j)e(\024)h Fj(O)q Fw(\()p Fj(n)1622 1770 y Fs(2)1641 1786 y Fj(=\017)1682 1770 y Fs(2)1702 1786 y Fw(\))i(suc)o(h)g(that)-30 1843 y Fj(U)5 b Fw(\()p Fj(S)s Fw(\))16 b(is)h Fj(\017)p Fw(-biased;)h(a)f (di\013eren)o(t)f(suc)o(h)i(construction)e(with)g Fi(j)p Fj(S)s Fi(j)f(\024)h Fj(O)q Fw(\()p Fj(n=\017)1263 1826 y Fs(3)1283 1843 y Fw(\))h(is)f(presen)o(ted)i(in)f([2)o(].)26 b(F)l(or)16 b Fj(k)q Fw(-wise)-30 1899 y Fj(\017)p Fw(-bias,)f(the)g (reduction)g(of)g([21)o(])g(men)o(tioned)g(at)f(the)i(end)g(of)e Fi(x)p Fw(2.1)h(yields)g(constructions)f(of)h(size)592 1995 y Fj(O)q Fw(\(min)p Fi(f)p Fw(\(\()p Fj(k)7 b Fw(log)h Fj(n)p Fw(\))p Fj(=\017)p Fw(\))983 1976 y Fs(2)1002 1995 y Fj(;)g Fw(\()p Fj(k)g Fw(log)f Fj(n)p Fw(\))p Fj(=\017)1225 1976 y Fs(3)1245 1995 y Fi(g)p Fw(\))p Fj(:)563 b Fw(\(6\))41 2090 y(W)l(e)16 b(no)o(w)f(sk)o(etc)o(h)h(a)f (di\013eren)o(t)g(approac)o(h)h(to)f(small-bias)g(spaces)h(due)g(to)g ([21)o(],)f(whic)o(h)h(has)g(connections)g(to)-30 2146 y(co)q(ding)g(theory)l(.)21 b(An)16 b(e\016cien)o(t)g(construction)f (of)g(a)g(m)o(ulti-set)g Fj(A)e Fi(\022)h(f)p Fw(0)p Fj(;)8 b Fw(1)p Fi(g)1270 2130 y Fh(n)1307 2146 y Fw(with)16 b Fi(j)p Fj(A)p Fi(j)c Fw(=)i(p)q(oly\()p Fj(n)p Fw(\))h(is)h(sho)o(wn) f(in)-30 2203 y([21)o(],)f(suc)o(h)i(that)e(for)h(a)g(certain)g (constan)o(t)f Fj(\014)h(>)e Fw(0,)469 2298 y(for)h(all)h(nonempt)o(y)g Fj(T)j Fi(\022)13 b Fw([)p Fj(n)p Fw(],)22 b(Pr\(\()1080 2258 y Fg(M)1081 2349 y Fh(i)p Ff(2)p Fh(T)1149 2298 y Fj(X)1187 2305 y Fh(i)1201 2298 y Fw(\))12 b(=)h(1\))f Fi(\025)h Fj(\014)r Fw(;)441 b(\(7\))-30 2433 y(\()p Fj(X)26 2440 y Fs(1)45 2433 y Fj(;)8 b(X)104 2440 y Fs(2)123 2433 y Fj(;)g(:)g(:)g(:)t(;)g(X)262 2440 y Fh(n)285 2433 y Fw(\))13 b(is)h(a)g(v)o(ector)f(c)o(hosen)h(according)f(to)h Fj(U)5 b Fw(\()p Fj(A)p Fw(\).)19 b(\(As)13 b(exp)q(ected,)i(a)f (random)f(construction)h(helps)-30 2489 y(sho)o(w)k(the)h Fn(existenc)n(e)e Fw(of)h(suc)o(h)g(an)h Fj(A)p Fw(;)h(the)e(c)o (hallenge)g(is)g(in)h(e\016cien)o(t)f(construction.\))29 b(This)18 b(construction)f(is)-30 2546 y(used)f(as)f(a)f(k)o(ey)i (building)e(blo)q(c)o(k)h(in)g([21)o(])g(in)g(designing)g(small-bias)f 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(y)d(that)i(a)g(giv)o(en)f(edge)i Fi(f)p Fj(i;)8 b(j)s Fi(g)13 b Fw(is)h(cut)i(is)e(giv)o(en)h(b)o(y)161 1819 y(Pr)o(\()p Fj(X)265 1826 y Fh(i)291 1819 y Fw(=)e(1)p Fj(;)23 b(X)436 1826 y Fh(j)466 1819 y Fw(=)13 b(0\))d(+)g(Pr\()p Fj(X)715 1826 y Fh(i)741 1819 y Fw(=)j(0)p Fj(;)22 b(X)885 1826 y Fh(j)915 1819 y Fw(=)13 b(1\))f Fi(\025)h Fw(\(1)p Fj(=)p Fw(4)c Fi(\000)i Fj(\017)p Fw(\))f(+)h(\(1)p Fj(=)p Fw(4)d Fi(\000)j Fj(\017)p Fw(\))i(=)g(\(1)c Fi(\000)i Fj(\016)r Fw(\))p Fj(=)p Fw(2)p Fj(:)-30 1921 y Fw(Th)o(us,)19 b(b)o(y)g(linearit)o(y)d(of)i(exp)q(ectation,)h(the)g(exp)q(ected)h(n)o (um)o(b)q(er)f(of)f(edges)h(cut)f(is)g(at)g(least)g Fj(m)p Fw(\(1)12 b Fi(\000)g Fj(\016)r Fw(\))p Fj(=)p Fw(2.)29 b(So,)-30 1977 y(as)21 b(in)f(\(6\),)h(w)o(e)g(can)g(construct)g(a)f (sample)h(space)g(of)g(size)f Fj(O)q Fw(\(\(log)7 b Fj(n)p Fw(\))p Fj(=\017)1252 1961 y Fs(3)1272 1977 y Fw(\))22 b(=)g Fj(O)q Fw(\(log)7 b Fj(n)p Fw(\))21 b(suc)o(h)g(that)g(at)f (least)-30 2034 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Ff(0)1164 1357 y Fw(=)f(1)p Fj(=)p Fw(p)q(oly)o(\(1)p Fj(=\017)8 b Fw(+)g(\()p Fi(d)p Fj(k)q(=)g Fw(log)o(\(1)p Fj(=\017)p Fw(\))p Fi(e)p Fw(\))1766 1341 y Fs(log)o(\(1)p Fh(=\017)p Fs(\))1890 1357 y Fw(\),)-30 1414 y(an)o(y)14 b Fj(\017)73 1397 y Ff(0)85 1414 y Fw(-appro)o(ximation)f(for)g Fi(G)501 1397 y Fh(n)498 1427 y(m;k)558 1418 y Fd(0)586 1414 y Fw(is)h(also)f(an)i Fj(\017)p Fw(-appro)o(ximation)d(for)i Fi(G)1218 1397 y Fh(n)1215 1427 y(m;k)1278 1414 y Fw(.)19 b(Using)14 b Fj(S)1465 1421 y Fs(1)1499 1414 y Fw(no)o(w)g(giv)o(es)f (the)i(desired)-30 1470 y(construction.)k(These)d(constructions)e(ha)o (v)o(e)h(b)q(een)h(further)f(impro)o(v)o(ed)g(in)g([19)o(])g(to)f(one)h (of)g(cardinalit)o(y)539 1585 y(p)q(oly\(log)7 b Fj(n)k Fw(+)f(1)p Fj(=\017)g Fw(+)g(\(1)p Fj(=\017)p Fw(\))1011 1535 y Fi(p)p 1049 1535 270 2 v 31 x Fs(log)o(\()p Ff(d)p Fh(k)q(=)5 b Fs(log\(1)p Fh(=\017)p Fs(\))p Ff(e)p Fs(\))1320 1585 y Fw(\))p Fj(:)488 b Fw(\(12\))41 1687 y(Tw)o(o)14 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Fs(\()1216 2403 y Fi(p)p 1255 2403 123 2 v 1255 2434 a Fs(log)o(\(1)p Fh(=\017)p Fs(\))o(\))1393 2451 y Fw(\))g(in)g([19)o (].)18 b(These)12 b(approac)o(hes)-30 2507 y(in)o(tro)q(duce)g(certain) g(new)g(ideas)g(and)g(also)f(build)h(on)g([15)o(,)g(18)o(].)19 b(An)12 b Fj(\017)p Fw(-appro)o(ximation)f(for)g Fi(C)1536 2491 y Fh(n)1533 2521 y(m;k)1607 2507 y Fw(with)h(cardinalit)o(y)487 2621 y(p)q(oly\(log)6 b Fj(n)11 b Fw(+)f Fj(m)779 2602 y Fh(O)q Fs(\(log)o(\(1)p Fh(=\017)p Fs(\)\))969 2621 y Fw(+)h(\(1)p Fj(=\017)p Fw(\))1115 2602 y Fs(log)n(\()p Ff(d)p Fh(k)q(=)6 b Fs(log)o(\(1)p Fh(=\017)p Fs(\))p Ff(e)p Fs(\))1386 2621 y Fw(\))p eop %%Page: 8 8 8 7 bop -30 154 a Fw(is)15 b(giv)o(en)f(in)h([8],)f(b)o(y)h(extending)h (an)f(idea)g(of)g([11)o(].)41 211 y(The)22 b(follo)o(wing)e(reductions) i(are)g(also)f(sho)o(wn)h(in)g([8,)f(19].)40 b(Supp)q(ose)24 b(that)d(for)h(all)f(\()p Fj(n;)8 b(m;)g(k)q(;)g(\017)p Fw(\),)21 b(an)h Fj(\017)p Fw(-)-30 267 y(appro)o(ximation)d Fj(S)310 251 y 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