(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvips 5.521-sst Copyright 1986, 1993 Radical Eye Software %%Title: #tmp#driver12.dvi %%CreationDate: Tue Apr 16 16:59:10 1996 %%Pages: 39 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Optima-Bold Optima Times-Roman Times-Italic RMTMI %%+ Times-BoldItalic MTEX MTSY MSBM10 EUFM10 Optima-BoldOblique CMSY10 %%+ Times-Bold %%EndComments %DVIPSCommandLine: dvips -Paristophanes #tmp#driver12 -och12.ps %DVIPSSource: TeX output 1996.04.16:1658 %%BeginProcSet: hooks.pro /pre-hook{currentdict 2 index known{4 array cvx dup 1 /exec load put dup 3 /exec load put dup 0 4 -1 roll put dup 2 3 index load put def}{def}ifelse} bind def /post-hook{currentdict 2 index known{4 array cvx dup 1 /exec load put dup 3 /exec load put dup 2 4 -1 roll put dup 0 3 index load put def}{def} ifelse}bind def %%EndProcSet %%BeginProcSet: overprnt.pro /setoverprint where{pop}{/setoverprint{pop}def}ifelse %%EndProcSet %%BeginProcSet: ljbugfix.pro /rmoveto{currentpoint 3 -1 roll add 3 1 roll add exch moveto}bind def /rlineto {currentpoint 3 -1 roll add 3 1 roll add exch lineto}bind def %%EndProcSet %%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 round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /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 sub]{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 userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /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 newpath 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: Optima-Bold FontDirectory/Optima-Bold known{/Optima-Bold findfont dup /UniqueID known{dup /UniqueID get 35888 eq exch /FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontInfo 10 dict dup begin /version (001.004) readonly def /Notice (Copyright (c) 1985, 1987, 1988, 1989, 1991 Adobe Systems Incorporated. All Rights Reserved.Optima is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /Copyright ( The digitally encoded machine readable outline data for producing the Typefaces provided as part of your laser printer is copyrighted (c) 1981 Linotype-Hell AG and/or its subsidiaries. All Rights Reserved. This data is the property of Linotype-Hell AG and may not be reproduced, used, displayed, modified, disclosed or transferred without the express written approval of Linotype-Hell AG. 12 Optima* Bold 07203 ) readonly def /FullName (Optima Bold) readonly def /FamilyName (Optima) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /Optima-Bold def /Encoding StandardEncoding def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /UniqueID 35888 def /FontBBox{-97 -271 1000 921}readonly def currentdict end currentfile eexec 5045911D6885A589EA795B707643D10C3569BF44D0A9F86E5AAEF0927B53DF82DE76B5E023F5 ADEB003193A4FC93600F351728951570B19C374806CB0F7989F3060C1D60B1700720E5D36C82 AD12716371C01ABEA50360F4BB2037757CF8FBCE2A0A8549C48831871EA54C91A76354A5A5FE CACB0680DC9759DA49F7E05DC1995CB754387F2B4CB1B05856190BDBF7F90EB28119F521D296 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{restore}if %%EndFont %%BeginFont: Optima FontDirectory/Optima known{/Optima findfont dup /UniqueID known{dup /UniqueID get 35882 eq exch /FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontInfo 10 dict dup begin /version (001.004) readonly def /Notice (Copyright (c) 1985, 1987, 1989, 1991 Adobe Systems Incorporated.All Rights Reserved.Optima is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /Copyright ( The digitally encoded machine readable outline data for producing the Typefaces provided as part of your laser printer is copyrighted (c) 1981 Linotype-Hell AG and/or its subsidiaries. All Rights Reserved. This data is the property of Linotype-Hell AG and may not be reproduced, used, displayed, modified, disclosed or transferred without the express written approval of Linotype-Hell AG. 12 Optima* Roman 05203 ) readonly def /FullName (Optima Roman) readonly def /FamilyName (Optima) readonly def /Weight (Roman) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /Optima def /Encoding StandardEncoding def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /UniqueID 35882 def /FontBBox{-78 -271 1000 919}readonly def currentdict end currentfile eexec 52FC911D14EF07EEDE272D967D998ECF170C7A49B4742449F7A2B2D15321716077635826D058 0683C2E7F477476C7AB1C34122963F797A24BB5A3E9BB6689B3F9B7E36D8FD5A492B9E2E0DE4 F77C77F2D348900B40279FBA9DC9EB19A5802FD0B1B4B1E3497F2D522D8AD57EB08C2D6B08CA 1BE1CAFCD41FAEAA2478904DADDA27B59AB7705622E89F03846B7C3CA47A1CC1C3521D8A6D0B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark {restore}if %%EndFont %%BeginFont: RMTMI % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation) readonly def /FullName (RMTMI) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle -14.036 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /RMTMI 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 /Omega1 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 /parenleft put dup 47 /parenright put dup 48 /Gamma1 put dup 49 /Delta1 put dup 50 /Theta1 put dup 51 /Lambda1 put dup 52 /Xi1 put dup 53 /Pi1 put dup 54 /Sigma1 put dup 55 /Upsilon1 put dup 56 /Phi1 put dup 57 /Psi1 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 91 /flat put dup 92 /natural put dup 93 /sharp put dup 94 /slurbelow put dup 95 /slurabove put dup 96 /lscript put dup 118 /v put dup 119 /w put dup 124 /dotlessj put dup 125 /weierstrass put dup 126 /kappa1 put dup 127 /Omega1 put dup 160 /space put dup 128 /psi put readonly def /FontBBox{0 -213 987 680}readonly def /UniqueID 5018946 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MTEX % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation) readonly def /FullName (MTEX) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /MTEX 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 128 /parenleftBigg 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 159 /radical put dup 160 /space put readonly def /FontBBox{-23 -2958 1456 766}readonly def /UniqueID 5018948 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D70C1E2528F01045F8CAEC9829F31D648C8D0A29EA851 AF41C327A0D569ABAAFE5AFE94DAD818C312D3CEE72F1ACEA0B701B6A5608521A2866790BDD577 6D6CD0C7D971B9A48B96AA970DCBB8B76EDCB90DA356DC2529B665EB4BB80AC4F5B0F4C0ED7686 1E399638AD3DB1BE4759C78D4F2E81A2FF688D366B91D729D63AB5FC9556FE10A07B81904D879A 7446DA82DC107FF41B0E3B7C2245D57B2EE9BAB31ECCFE9B79E3EC32CB1F10C622F4BCE18DF0E5 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MTSY % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation) readonly def /FullName (MTSY) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /MTSY 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 /tie put dup 66 /openbullet1 put dup 67 /plus put dup 68 /equal put dup 69 /vector put dup 70 /triangleright put dup 71 /triangleleft put dup 72 /equal1 put dup 73 /semicolon put dup 74 /grave put dup 75 /acute put dup 76 /caron put dup 77 /breve put dup 78 /macron put dup 79 /circumflex put dup 80 /dotaccent put dup 81 /tilde put dup 82 /dieresis put dup 83 /overbar 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 /radical1 put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 160 /space put dup 128 /arrowleft put readonly def /FontBBox{0 -954 1043 796}readonly def /UniqueID 5018947 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D70C1E2528F01045F8CAEC9829F31D648C8D0A29EA851 AF41C327A0D569ABAAFE5AFE94DAD818C312D3CEE72F1ACEA0B701B6A5608521A2866790BDD577 6D6CD0C7D971B9A48B96AA970DCBB8B76EDCB90DA356DC2529B665EB4BB80AC4F5B0F4C0ED7686 1E399638AD3DB1BE4759C78D4F2E81A2FF688D366B91D729D63AB5FC9556FE10A07B81904D879A 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cleartomark %%EndFont %%BeginFont: MSBM10 % Copyright (C) 1991, 1992 Y&Y. All rights reserved. % Copyright (C) 1991, 1992 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Math Symbol fonts were designed by the American Mathematical Society) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /lessornotequal put dup 162 /greaterornotequal put dup 163 /notlessequal put dup 164 /notgreaterequal put dup 165 /notless put dup 166 /notgreater put dup 167 /notprecedes put dup 168 /notfollows put dup 169 /lessornotdbleql put dup 170 /greaterornotdbleql put dup 173 /notlessorslnteql put dup 174 /notgreaterorslnteql put dup 175 /lessnotequal put dup 176 /greaternotequal put dup 177 /notprecedesoreql put dup 178 /notfollowsoreql put dup 179 /precedeornoteqvlnt put dup 180 /followornoteqvlnt put dup 181 /lessornotsimilar put dup 182 /greaterornotsimilar put dup 183 /notlessdblequal put dup 184 /notgreaterdblequal put dup 185 /precedenotslnteql put dup 186 /follownotslnteql put dup 187 /precedenotdbleqv put dup 188 /follownotdbleqv put dup 189 /lessnotdblequal put dup 190 /greaternotdblequal put dup 191 /notsimilar put dup 192 /notapproxequal put dup 193 /upslope put dup 194 /downslope put dup 195 /notsubsetoreql put dup 196 /epsiloninv put dup 0 /lessornotequal put dup 1 /greaterornotequal put dup 2 /notlessequal put dup 3 /notgreaterequal put dup 4 /notless put dup 5 /notgreater put dup 6 /notprecedes put dup 7 /notfollows put dup 8 /lessornotdbleql put dup 9 /greaterornotdbleql put dup 10 /notlessorslnteql put dup 11 /notgreaterorslnteql put dup 12 /lessnotequal put dup 13 /greaternotequal put dup 14 /notprecedesoreql put dup 15 /notfollowsoreql put dup 16 /precedeornoteqvlnt put dup 17 /followornoteqvlnt put dup 18 /lessornotsimilar put dup 19 /greaterornotsimilar put dup 20 /notlessdblequal put dup 21 /notgreaterdblequal put dup 22 /precedenotslnteql put dup 23 /follownotslnteql put dup 24 /precedenotdbleqv put dup 25 /follownotdbleqv put dup 26 /lessnotdblequal put dup 27 /greaternotdblequal put dup 28 /notsimilar put dup 29 /notapproxequal put dup 30 /upslope put dup 31 /downslope put dup 32 /notsubsetoreql put dup 33 /notsupersetoreql put dup 34 /notsubsetordbleql put dup 35 /notsupersetordbleql put dup 36 /subsetornotdbleql put dup 37 /supersetornotdbleql put dup 38 /subsetornoteql put dup 39 /supersetornoteql put dup 40 /subsetnoteql put dup 41 /supersetnoteql put dup 42 /notsubseteql put dup 43 /notsuperseteql put dup 44 /notparallel put dup 45 /notbar put dup 46 /notshortbar put dup 47 /notshortparallel put dup 48 /notturnstile put dup 49 /notforces put dup 50 /notsatisfies put dup 51 /notforcesextra put dup 52 /nottriangeqlright put dup 53 /nottriangeqlleft put dup 54 /nottriangleleft put dup 55 /nottriangleright put dup 56 /notarrowleft put dup 57 /notarrowright put dup 58 /notdblarrowleft put dup 59 /notdblarrowright put dup 60 /notdblarrowboth put dup 61 /notarrowboth put dup 62 /dividemultiply put dup 63 /emptyset put dup 64 /notexistential 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 /hatwide put dup 92 /hatwider put dup 93 /tildewide put dup 94 /tildewider put dup 96 /Finv put dup 97 /Gmir put dup 102 /Omegainv put dup 103 /eth put dup 104 /equalorsimilar put dup 105 /beth put dup 106 /gimel put dup 107 /daleth put dup 108 /lessdot put dup 109 /greaterdot put dup 110 /multicloseleft put dup 111 /multicloseright put dup 112 /barshort put dup 113 /parallelshort put 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cleartomark %%EndFont %%BeginFont: EUFM10 % Copyright (C) 1991, 1992 Y&Y. All rights reserved. % Copyright (C) 1991, 1992 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Euler fonts were designed by Hermann Zapf) readonly def /FullName (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 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 /dnos put dup 162 /dalt put dup 163 /fnos put dup 164 /falt put dup 165 /galt put dup 166 /kalt put dup 167 /talt put dup 168 /ualt put dup 181 /quoteleft put dup 182 /quoteright put dup 195 /space put dup 196 /onealt put dup 0 /dnos put dup 1 /dalt put dup 2 /fnos put dup 3 /falt put dup 4 /galt put dup 5 /kalt put dup 6 /talt put dup 7 /ualt put dup 18 /quoteleft put dup 19 /quoteright put dup 32 /space put dup 33 /exclam put dup 38 /ampersand put dup 39 /quotesingle put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /minus put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question 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 93 /bracketright put dup 94 /asciicircum 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 125 /quotedbl put dup 127 /onealt put dup 128 /space put dup 160 /space put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueID 5031986 def currentdict end currentfile eexec 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F09257 22787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC8 37ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6 CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553 146AB427BDD7DA12534BA078AD3D780414930DA4F8D58AB16340DDF86E6DC542E7BE73FD188156 895E7823FE8248E3DC76897AB879E894CDC338E3FF3C74898E2F6EDB6CFC7B82D7CA3800B2B451 BEF3DBF52DCF502183FA4675FC21AE77258D5AC714BF54FB2C27DECF3E29CAA276AD8ED566295A 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: Optima-BoldOblique 11 dict begin /FontInfo 10 dict dup begin /version (001.004) readonly def /Notice (Copyright (c) 1985, 1987, 1988, 1989, 1991 Adobe Systems Incorporated. All Rights Reserved.Optima is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /Copyright ( The digitally encoded machine readable outline data for producing the Typefaces provided as part of your laser printer is copyrighted (c) 1981 Linotype-Hell AG and/or its subsidiaries. All Rights Reserved. This data is the property of Linotype-Hell AG and may not be reproduced, used, displayed, modified, disclosed or transferred without the express written approval of Linotype-Hell AG. 12 Optima* Bold 07203 ) readonly def /FullName (Optima Bold Oblique) readonly def /FamilyName (Optima) readonly def /Weight (Bold) readonly def /ItalicAngle -11 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /Optima-BoldOblique def /Encoding StandardEncoding def /PaintType 0 def /FontType 1 def /FontMatrix [0.001000 0 .19438E-3 0.001 0 0] readonly def /UniqueID 35891 def /FontBBox{-97 -271 1000 921}readonly def currentdict end currentfile eexec 6D56D757136FE5001B5A4163003A8EAED86B3181CF664A28D99309DDAE21A84497ECDAE6FB96 1B36E6BD1C8A138D3D2C7FD6A917D9C5CCEA974AA1E977CECE8A4C8EAB10E0979AFA7702E685 4EC753D486CF601A9C4EE984559E2B10389810EFD1036DE9F711711A235C96E326413F85A29A 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) 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 5000820 def 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4314 y(dom)c(variables)f(\(such)h(as)h(the)f(mean)g(ener)o(gy)e(of)i(a) h(con\256guration\).)c(Computations)i(of)h(this)807 4414 y(kind)20 b(are)g(typically)f(known)g(as)i(\252Monte)e(Carlo)i (experiments.\272)p Black 657 4543 a FK(III.)p Black 33 w FN(Combinatorial)k(optimization)p FO(:)g(here)h FM(\012)33 b FO(is)28 b(the)e(set)h(of)f(feasible)g(solutions)g(to)h (an)f(opti-)807 4642 y(mization)13 b(problem,)e(and)i FM(\031)22 b FO(is)15 b(a)f(distribution)d(that)j(assigns,)g(in)f(some) g(natural)g(way)-5 b(,)13 b(higher)807 4742 y(weight)18 b(to)g(solutions)f(with)i(a)f(better)g(objective)e(function)h(value.)g (Sampling)g(from)g FM(\031)26 b FO(thus)807 4842 y(favors)19 b(better)g(solutions.)g(An)g(example)g(of)g(this)h(approach)d(is)k(the) e(popular)f(optimization)807 4941 y(heuristic)i(known)f(as)i (\252simulated)e(annealing.\272)p Black Black eop %%Page: 484 3 %%BeginPageSetup /platenumber 1 def %%EndPageSetup 484 2 bop Black Black 36 -125 3 150 v 36 5674 V -162 -75 150 3 v 3912 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b FO(.)24 b(The)448 1171 y(Markov)g(chain)h(is)i(designed)d (to)i(be)g FN(er)m(godic)p FO(,)e(i.e.,)h(the)h(probability)e (distribution)g(over)g FM(\012)33 b FO(con-)448 1271 y(ver)o(ges)21 b(asymptotically)f(to)i FM(\031)8 b FO(,)22 b(regardless)f(of)g(the)h(initial)g(state.)g(Moreover)m(,)d(its)j (transitions)f(cor)n(-)448 1371 y(respond)29 b(to)h(simple)f(random)f (perturbations)g(of)h(structures)h(in)g FM(\012)7 b FO(,)29 b(and)g(hence)g(are)h(simple)g(to)448 1470 y(simulate.)20 b(Now)f(we)h(may)f(sample)h(from)e FM(\031)28 b FO(as)21 b(follows:)e(starting)g(from)g(an)g(arbitrary)f(state)j(in)e FM(\012)7 b FO(,)448 1570 y(simulate)20 b(the)f(Markov)f(chain)h(for)g (some)g(number)m(,)g FL(T)13 b FO(,)19 b(of)g(steps,)h(and)f(output)f (the)i(\256nal)f(state.)h(The)448 1670 y(er)o(godicity)g(means)h(that,) g(by)g(taking)i FL(T)35 b FO(lar)o(ge)20 b(enough,)f(we)j(can)f(ensure) g(that)h(the)f(distribution)f(of)448 1769 y(the)h(output)d(state)j(is)h 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b FF(D)568 1755 y FL(M)18 b FF(\000)11 b FM(.)6 b FL(X)19 b FF(\010)11 b FL(Y)h FM(/)p FO(,)20 b(which)f(is)h(immediate)f(from)f(the)h(de\256nition)g (of)g(the)g(paths.)g(Hence,)24 b FL(X)29 b FO(and)19 b FL(Y)31 b FO(can)563 1854 y(be)20 b(uniquely)e(recovered)g(from)h FM(\021)1546 1866 y FH(t)1572 1854 y FM(.)6 b FL(X)g FM(;)j FL(Y)j FM(/)p FO(,)21 b(so)f FM(\021)1970 1866 y FH(t)2017 1854 y FO(is)h(injective.)712 1954 y(W)-7 b(e)16 b(are)f(almost)g(done.)e(However)m(,)h(the)g(fact)h(that)g FM(\021)2164 1966 y FH(t)2206 1954 y FO(is)g(injective)g(is)h(not)e (suf)o(\256cient)g(in)h(this)h(case)563 2053 y(because,)23 b(in)h(contrast)g(to)h(the)f(hypercube)e(example,)h(the)h(stationary)g (distribution)e FM(\031)3098 2065 y FI(\025)3159 2053 y FO(is)j(highly)563 2153 y(non-uniform.)13 b(What)k(we)g(require)f(in) h(addition)f(is)i(that)f FM(\021)2215 2165 y FH(t)2258 2153 y FO(be)g(\252weight-preserving,\272)d(in)j(the)g(sense)563 2253 y(that)26 b FL(Q)t FM(.)p FL(t)7 b FM(/\031)920 2265 y FI(\025)956 2253 y FM(.\021)1030 2265 y FH(t)1056 2253 y FM(.)f FL(X)g FM(;)j FL(Y)j FM(//)19 b FF(\031)f FM(\031)1458 2265 y FI(\025)1494 2253 y FM(.)6 b FL(X)i FM(/\031)1671 2265 y FI(\025)1707 2253 y FM(.)p FL(Y)k FM(/)p FO(.)20 b(More)g(precisely)-5 b(,)19 b(we)h(will)h(show)f(in)h (a)f(moment)f(that)1312 2406 y FM(\031)1362 2418 y FI(\025)1397 2406 y FM(.)6 b FL(X)i FM(/\031)1574 2418 y FI(\025)1611 2406 y FM(.)p FL(Y)k FM(/)18 b FF(\024)g FO(2)p FF(j)6 b FL(E)h FF(j)p FM(\025)2029 2371 y FG(0)2048 2363 y FE(2)2087 2406 y FL(Q)t FM(.)p FL(t)g FM(/\031)2293 2418 y FI(\025)2330 2406 y FM(.\021)2404 2418 y FH(t)2430 2406 y FM(.)f FL(X)g FM(;)j FL(Y)j FM(//:)507 b FO(\(12.12\))563 2558 y(First,)20 b(let)h(us)g(see)f(why)g(we)h(need)e(a)i(bound)d(of)i (this)h(form)e(in)h(order)f(to)h(estimate)39 b(\305)-46 b FM(\032)5 b FO(.)21 b(W)-7 b(e)21 b(have)1028 2685 y(1)p 967 2724 163 4 v 973 2802 a FL(Q)t FM(.)p FL(t)7 b FM(/)1167 2664 y FJ(X)1149 2830 y FI(\015)1181 2839 y Fq(X)e(Y)1244 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