Content-Type: multipart/mixed; boundary="-------------0102271755181" This is a multi-part message in MIME format. ---------------0102271755181 Content-Type: text/plain; name="01-80.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="01-80.keywords" random Schr\"odinger operator, Wegner estimate, spectral shift function, Anderson localization ---------------0102271755181 Content-Type: application/postscript; name="Combes-Hislop-Nakamura.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Combes-Hislop-Nakamura.ps" %!PS-Adobe-3.0 %%Title: (Wegner-final.tex) %%Creator: (Textures\250: AdobePS 8.7.0) %%CreationDate: (8:43 AM 2001\224N 2\214\216 28\223\372 \220\205\227j\223\372) %%For: (Shu Nakamura) %%Pages: 26 %%DocumentFonts: CMR10 CMBX10 CMR8 CMR6 CMMI10 CMMI8 CMSY10 CMR9 CMTI10 CMBX12 CMEX10 CMSY8 CMR12 CMMI12 CMMI6 LASY10 CMSY6 %%DocumentNeededResources: %%DocumentSuppliedResources: font CMR10 CMBX10 CMR8 CMR6 CMMI10 CMMI8 CMSY10 CMR9 CMTI10 CMBX12 CMEX10 CMSY8 CMR12 CMMI12 CMMI6 LASY10 CMSY6 %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: (Default) 595 842 0 () () %RBINumCopies: 1 %RBINupNess: 1 1 %ADO_ImageableArea: 6 7 590 836 %RBIDocumentSuppliedFonts: CMR10 CMBX10 CMR8 CMR6 CMMI10 CMMI8 CMSY10 CMR9 CMTI10 CMBX12 CMEX10 CMSY8 CMR12 CMMI12 CMMI6 LASY10 CMSY6 %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults userdict/dscInfo 5 dict dup begin /Title(Wegner-final.tex)def /Creator(Textures\250: AdobePS 8.7.0)def /CreationDate(8:43 AM 2001\224N 2\214\216 28\223\372 \220\205\227j\223\372)def /For(Shu Nakamura)def /Pages 26 def end put %%BeginProlog %%BeginFeature: *JobPatchFile 0 countdictstack[{ false /resourcestatus where { pop /CIDParams /ProcSet 2 copy resourcestatus { pop pop findresource /SetBuildCompatible get exec } { pop pop pop } ifelse } { pop } ifelse } stopped cleartomark countdictstack exch sub dup 0 gt { {end} repeat }{ pop }ifelse %%EndFeature /md 248 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: lw8_feature-1.01 %%Copyright: Copyright 1990-1999 Adobe Systems Incorporated and Apple Computer Incorporated. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f42/CMR10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f54 f42 12 scf fc %%BeginResource: font 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f76/CMBX10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f88 f76 12 scf fc %%BeginResource: font 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 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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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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f109/CMR8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f120 f109 12 scf fc %%BeginResource: font 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f141/CMR6 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f152 f141 12 scf fc %%BeginResource: font CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F0925722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553146AB427BDD7DA12534BA078AD3D780414930DA4F8D58ABEFD45DB119B10EB409DD897923C6E705479464A4B31 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15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/omega pd 34/epsilon pd 35/theta1 pd 36/pi1 pd 37/rho1 pd 38/sigma1 pd 39/phi1 pd 40/arrowlefttophalf pd 41/arrowleftbothalf pd 42/arrowrighttophalf pd 43/arrowrightbothalf pd 44/arrowhookleft pd 45/arrowhookright pd 46/triangleright pd 47/triangleleft pd 48/zerooldstyle pd 49/oneoldstyle pd 50/twooldstyle pd 51/threeoldstyle pd 52/fouroldstyle pd 53/fiveoldstyle pd 54/sixoldstyle pd 55/sevenoldstyle pd 56/eightoldstyle pd 57/nineoldstyle pd 58/period pd 59/comma pd 60/less pd 61/slash pd 62/greater pd 63/star pd 64/partialdiff pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/flat pd 92/natural pd 93/sharp pd 94/slurbelow pd 95/slurabove pd 96/lscript pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/dotlessi pd 124/dotlessj pd 125/weierstrass pd 126/vector pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/alpha pd 175/beta pd 176/gamma pd 177/delta pd 178/epsilon1 pd 179/zeta pd 180/eta pd 181/theta pd 182/iota pd 183/kappa pd 184/lambda pd 185/mu pd 186/nu pd 187/xi pd 188/pi pd 189/rho pd 190/sigma pd 191/tau pd 192/upsilon pd 193/phi pd 194/chi pd 195/psi pd 196/tie pd :esr /f186 f174 12 scf fc %%BeginResource: font 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 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F0925722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553146AB427BDD7DA12534BA078AD3D780414930E72218B3075925CE1192F11FC8530FCD5E3038E3A6A6DB2DCFBAE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f207/CMMI8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/omega pd 34/epsilon pd 35/theta1 pd 36/pi1 pd 37/rho1 pd 38/sigma1 pd 39/phi1 pd 40/arrowlefttophalf pd 41/arrowleftbothalf pd 42/arrowrighttophalf pd 43/arrowrightbothalf pd 44/arrowhookleft pd 45/arrowhookright pd 46/triangleright pd 47/triangleleft pd 48/zerooldstyle pd 49/oneoldstyle pd 50/twooldstyle pd 51/threeoldstyle pd 52/fouroldstyle pd 53/fiveoldstyle pd 54/sixoldstyle pd 55/sevenoldstyle pd 56/eightoldstyle pd 57/nineoldstyle pd 58/period pd 59/comma pd 60/less pd 61/slash pd 62/greater pd 63/star pd 64/partialdiff pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/flat pd 92/natural pd 93/sharp pd 94/slurbelow pd 95/slurabove pd 96/lscript pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/dotlessi pd 124/dotlessj pd 125/weierstrass pd 126/vector pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/alpha pd 175/beta pd 176/gamma pd 177/delta pd 178/epsilon1 pd 179/zeta pd 180/eta pd 181/theta pd 182/iota pd 183/kappa pd 184/lambda pd 185/mu pd 186/nu pd 187/xi pd 188/pi pd 189/rho pd 190/sigma pd 191/tau pd 192/upsilon pd 193/phi pd 194/chi pd 195/psi pd 196/tie pd :esr /f219 f207 12 scf fc %%BeginResource: font CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 %%EndResource /f241/CMSY10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/arrowright pd 34/arrowup pd 35/arrowdown pd 36/arrowboth pd 37/arrownortheast pd 38/arrowsoutheast pd 39/similarequal pd 40/arrowdblleft pd 41/arrowdblright pd 42/arrowdblup pd 43/arrowdbldown pd 44/arrowdblboth pd 45/arrownorthwest pd 46/arrowsouthwest pd 47/proportional pd 48/prime pd 49/infinity pd 50/element pd 51/owner pd 52/triangle pd 53/triangleinv pd 54/negationslash pd 55/mapsto pd 56/universal pd 57/existential pd 58/logicalnot pd 59/emptyset pd 60/Rfractur pd 61/Ifractur pd 62/latticetop pd 63/perpendicular pd 64/aleph pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/union pd 92/intersection pd 93/unionmulti pd 94/logicaland pd 95/logicalor pd 96/turnstileleft pd 97/turnstileright pd 98/floorleft pd 99/floorright pd 100/ceilingleft pd 101/ceilingright pd 102/braceleft pd 103/braceright pd 104/angbracketleft pd 105/angbracketright pd 106/bar pd 107/bardbl pd 108/arrowbothv pd 109/arrowdblbothv pd 110/backslash pd 111/wreathproduct pd 112/radical pd 113/coproduct pd 114/nabla pd 115/integral pd 116/unionsq pd 117/intersectionsq pd 118/subsetsqequal pd 119/supersetsqequal pd 120/section pd 121/dagger pd 122/daggerdbl pd 123/paragraph pd 124/club pd 125/diamond pd 126/heart pd 127/.notdef pd 128/.notdef pd 161/minus pd 162/periodcentered pd 163/multiply pd 164/asteriskmath pd 165/divide pd 166/diamondmath pd 167/plusminus pd 168/minusplus pd 169/circleplus pd 170/circleminus pd 173/circlemultiply pd 174/circledivide pd 175/circledot pd 176/circlecopyrt pd 177/openbullet pd 178/bullet pd 179/equivasymptotic pd 180/equivalence pd 181/reflexsubset pd 182/reflexsuperset pd 183/lessequal pd 184/greaterequal pd 185/precedesequal pd 186/followsequal pd 187/similar pd 188/approxequal pd 189/propersubset pd 190/propersuperset pd 191/lessmuch pd 192/greatermuch pd 193/precedes pd 194/follows pd 195/arrowleft pd 196/spade pd :esr /f253 f241 12 scf fc %%BeginResource: font 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 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B448685BDD20EB05D5E7C2126132E33A59A7170609DCF4871A5D023C9EF5 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cleartomark %%EndResource /f274/CMR9 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f285 f274 12 scf fc %%BeginResource: font 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 8053514D28EC28DA1630165FAB262882D3FFD20326947B1065649B533EB5E9E3A88A87FE987918A687950B26F647D6E08BF14D983ED1D4A8CA1E2DA8D985F9442EB916F5B6ED0697AC7C33E1E36A3BF460D34CE45F1631871097CB04F18E38894CF4AC1538EB19481311D24FE3BE7BEAA4A3730E8B4831FE59D6D9CE2E46116B629C7BA2F9CE3ECBA2F43BC162A5A077CA1B2882A42AFDCEC3F4B75B5D63E0BC8E5DC95257766D8EA467AD9CBAF47BE60F797580CCED6884B3A68F70C91F4FDF80FD00ED9139E7F480 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cleartomark %%EndResource /f307/CMTI10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/sterling pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f319 f307 12 scf fc %%BeginResource: font 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 /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{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486BE79011D1F5BFAE5C1F476EE6F05EB1D2CAEB269958B194521197B3 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f341/CMBX12 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f353 f341 12 scf fc %%BeginResource: font 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f375/CMEX10 :bsr 32/space pd :esr /f387 f375 12 scf fc %%BeginResource: font 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 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f408/CMSY8 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/arrowright pd 34/arrowup pd 35/arrowdown pd 36/arrowboth pd 37/arrownortheast pd 38/arrowsoutheast pd 39/similarequal pd 40/arrowdblleft pd 41/arrowdblright pd 42/arrowdblup pd 43/arrowdbldown pd 44/arrowdblboth pd 45/arrownorthwest pd 46/arrowsouthwest pd 47/proportional pd 48/prime pd 49/infinity pd 50/element pd 51/owner pd 52/triangle pd 53/triangleinv pd 54/negationslash pd 55/mapsto pd 56/universal pd 57/existential pd 58/logicalnot pd 59/emptyset pd 60/Rfractur pd 61/Ifractur pd 62/latticetop pd 63/perpendicular pd 64/aleph pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/union pd 92/intersection pd 93/unionmulti pd 94/logicaland pd 95/logicalor pd 96/turnstileleft pd 97/turnstileright pd 98/floorleft pd 99/floorright pd 100/ceilingleft pd 101/ceilingright pd 102/braceleft pd 103/braceright pd 104/angbracketleft pd 105/angbracketright pd 106/bar pd 107/bardbl pd 108/arrowbothv pd 109/arrowdblbothv pd 110/backslash pd 111/wreathproduct pd 112/radical pd 113/coproduct pd 114/nabla pd 115/integral pd 116/unionsq pd 117/intersectionsq pd 118/subsetsqequal pd 119/supersetsqequal pd 120/section pd 121/dagger pd 122/daggerdbl pd 123/paragraph pd 124/club pd 125/diamond pd 126/heart pd 127/.notdef pd 128/.notdef pd 161/minus pd 162/periodcentered pd 163/multiply pd 164/asteriskmath pd 165/divide pd 166/diamondmath pd 167/plusminus pd 168/minusplus pd 169/circleplus pd 170/circleminus pd 173/circlemultiply pd 174/circledivide pd 175/circledot pd 176/circlecopyrt pd 177/openbullet pd 178/bullet pd 179/equivasymptotic pd 180/equivalence pd 181/reflexsubset pd 182/reflexsuperset pd 183/lessequal pd 184/greaterequal pd 185/precedesequal pd 186/followsequal pd 187/similar pd 188/approxequal pd 189/propersubset pd 190/propersuperset pd 191/lessmuch pd 192/greatermuch pd 193/precedes pd 194/follows pd 195/arrowleft pd 196/spade pd :esr /f420 f408 12 scf fc %%BeginResource: font 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 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486858B2A4B5A0CC2E1BF4E2A4A0E748483C3BCF5DE47CC5260A3A967C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f441/CMR12 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f453 f441 12 scf fc %%BeginResource: font 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 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F0925722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553146AB427BDD7DA12534BA078AD3D780414930E72218B3075925CE1192F11FC8530FCD5E3038E3A6A6DB2DCFBAE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndResource /f475/CMMI12 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/.notdef pd 33/omega pd 34/epsilon pd 35/theta1 pd 36/pi1 pd 37/rho1 pd 38/sigma1 pd 39/phi1 pd 40/arrowlefttophalf pd 41/arrowleftbothalf pd 42/arrowrighttophalf pd 43/arrowrightbothalf pd 44/arrowhookleft pd 45/arrowhookright pd 46/triangleright pd 47/triangleleft pd 48/zerooldstyle pd 49/oneoldstyle pd 50/twooldstyle pd 51/threeoldstyle pd 52/fouroldstyle pd 53/fiveoldstyle pd 54/sixoldstyle pd 55/sevenoldstyle pd 56/eightoldstyle pd 57/nineoldstyle pd 58/period pd 59/comma pd 60/less pd 61/slash pd 62/greater pd 63/star pd 64/partialdiff pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/flat pd 92/natural pd 93/sharp pd 94/slurbelow pd 95/slurabove pd 96/lscript pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/dotlessi pd 124/dotlessj pd 125/weierstrass pd 126/vector pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/alpha pd 175/beta pd 176/gamma pd 177/delta pd 178/epsilon1 pd 179/zeta pd 180/eta pd 181/theta pd 182/iota pd 183/kappa pd 184/lambda pd 185/mu pd 186/nu pd 187/xi pd 188/pi pd 189/rho pd 190/sigma pd 191/tau pd 192/upsilon pd 193/phi pd 194/chi pd 195/psi pd 196/tie pd :esr /f487 f475 12 scf fc %%BeginResource: font 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 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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 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F0925722787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC837ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553146AB427BDD7DA12534BA078AD3D780414930E72218B3075925CE1192F11FC8530FCD5E3038E3A6A6DB2DCFBAE 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pd 3/a3 pd 4/a4 pd 32/.notdef pd 40/a40 pd 41/a41 pd 42/a42 pd 43/a43 pd 48/a48 pd 49/a49 pd 50/a50 pd 51/a51 pd 58/a58 pd 59/a59 pd 60/a60 pd 61/a61 pd :esr /f554 f542 12 scf fc %%BeginResource: font 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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54 (b)s 59.779 (y)s 7 f 309.674 y 176.901 (H)s 8 f 305.153 y 186.893 (A)s 4 f 312.381 y 186.003 (0)s 2 f 309.674 y 196.801 (=)s 208.36 (\050)s 10 f 212.618 (\241)s 7 f 221.135 (i)s 10 f 224.907 (r)s 236.465 (\241)s 7 f 247.415 (A)s 2 f 255.628 (\051)s 4 f 305.153 y 259.886 (2)s 2 f 309.674 y 267.07 (+)s 7 f 278.02 (W)s 288.057 (;)s 2 f 391.492 (\0501.4\051)s 328.837 y 54 (where)s 7 f 85.937 (A)s 2 f 98.073 (is)s 109.358 (a)s 118.756 (v)s 124.231 (ector)s 151.91 (p)s 158.298 (oten)s 178.677 (tial)s 198.417 (with)s 7 f 223.632 (A)s 10 f 235.342 (2)s 7 f 246.14 (L)s 4 f 324.863 y 253.592 (2)s 8 f 332.019 y 253.592 (l)s 256.224 (oc)s 2 f 328.837 y 264.514 (\050)s 7 f 268.772 (I)s 271.16 (R)s 8 f 324.863 y 279.558 (d)s 2 f 328.837 y 284.432 (\051)s 288.69 (,)s 295.724 (and)s 7 f 317.289 (W)s 2 f 332.649 (=)s 7 f 344.663 (W)s 4 f 330.479 y 355.005 (+)s 10 f 328.837 y 364.732 (\241)s 7 f 375.864 (W)s 11 f 330.479 y 386.206 (\241)s 2 f 328.837 y 397.241 (is)s 408.525 (a)s 342.437 y 54 (bac)s 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(lattice)s 106.124 (p)s 112.511 (oin)s 126.807 (ts)s 138.938 (in)s 151.616 (the)s 170.378 (region)s 203.162 (\244)s 210.766 (,)s 217.381 (so)s 230.728 (that)s 366.869 y 255.421 (\176)s 369.637 y 254.357 (\244)s 10 f 265.002 (\264)s 2 f 276.561 (\244)s 10 f 286.405 (\134)s 7 f 295.945 (Z)s 298.728 (Z)s 8 f 365.663 y 306.986 (d)s 2 f 369.637 y 311.86 (.)s 319.736 (F)s 325.972 (or)s 339.289 (an)s 350.543 (y)s 7 f 359.876 (k)s 10 f 368.962 (2)s 7 f 379.304 (Z)s 382.087 (Z)s 8 f 365.663 y 390.345 (d)s 2 f 369.637 y 395.219 (,)s 401.833 (let)s 383.237 y 54 (\244)s 8 f 384.932 y 61.604 (L)s 2 f 383.237 y 67.885 (\050)s 7 f 72.143 (k)s 2 f 78.188 (\051)s 85.728 (denote)s 120.642 (the)s 139.132 (cub)s 156.469 (e)s 164.617 (of)s 176.719 (side)s 198.311 (length)s 7 f 231.4 (L)s 2 f 242.133 (cen)s 257.646 (tered)s 285.291 (at)s 298.305 (p)s 304.692 (oin)s 318.988 (t)s 7 f 326.528 (k)s 10 f 335.615 (2)s 7 f 345.956 (Z)s 348.739 (Z)s 8 f 379.263 y 356.997 (d)s 2 f 383.237 y 361.871 (.)s 369.656 (The)s 391.796 (lo)s 400.617 (cal)s 396.837 y 54 (p)s 60.388 (erturbation)s 118.24 (in)s 131.015 (the)s 149.873 (Anderson-t)s 202.89 (yp)s 215.056 (e)s 223.573 (mo)s 238.477 (del)s 256.119 (is)s 267.13 (de)s 278.08 (\257ned)s 304.847 (b)s 310.626 (y:)s 7 f 419.561 y 149.661 (V)s 4 f 421.256 y 156.049 (\244)s 2 f 419.561 y 162.443 (\050)s 7 f 166.702 (x)s 2 f 172.96 (\051)s 180.26 (=)s 0 f 409.824 y 191.824 (X)s 8 f 433.878 y 191.818 (i)s 11 f 194.712 (2)s 4 f 431.856 y 201.201 (\176)s 433.878 y 200.379 (\244)s 7 f 419.561 y 208.098 (\270)s 8 f 421.204 y 214.486 (i)s 2 f 419.561 y 217.88 (\050)s 7 f 222.138 (!)s 2 f 229.347 (\051)s 7 f 233.605 (u)s 8 f 421.204 y 239.874 (i)s 2 f 419.561 y 243.268 (\050)s 7 f 247.526 (x)s 10 f 256.217 (\241)s 7 f 267.167 (i)s 10 f 273.373 (\241)s 7 f 284.323 (\273)s 8 f 421.204 y 289.114 (i)s 2 f 419.561 y 292.508 (\050)s 7 f 296.766 (!)s 11 f 415.04 y 303.975 (0)s 2 f 419.561 y 306.78 (\051)s 311.039 (\051)s 7 f 315.297 (;)s 2 f 391.492 (\0501.5\051)s 453.925 y 54 (pro)s 69.543 (vided)s 98.04 (the)s 115.892 (random)s 155.065 (v)s 160.236 (ariables)s 7 f 199.47 (\273)s 8 f 455.568 y 204.261 (i)s 2 f 453.925 y 207.655 (\050)s 7 f 211.913 (!)s 11 f 449.952 y 219.122 (0)s 2 f 453.925 y 221.927 (\051)s 226.186 (,)s 232.072 (mo)s 246.976 (deling)s 278.211 (thermal)s 317.992 (vibrations,)s 371.724 (are)s 388.998 (small)s 467.525 y 54 (enough)s 91.676 (so)s 105.08 (the)s 123.898 (p)s 130.286 (ositivit)s 163.196 (y)s 172.585 (condition)s 220.603 (\050H3\051)s 246.417 (\050giv)s 264.667 (en)s 279.227 (ahead\051)s 315.078 (holds.)s 347.975 (The)s 370.443 (functions)s 7 f 481.125 y 54 (u)s 8 f 482.768 y 60.268 (i)s 2 f 481.125 y 66.378 (are)s 83.723 (nonnegativ)s 136.04 (e)s 143.622 (and)s 163.979 (compactly)s 215.665 (supp)s 238.538 (orted)s 266.225 (in)s 278.066 (a)s 286.256 (neigh)s 311.502 (b)s 317.889 (orho)s 339.516 (o)s 345.295 (d)s 354.093 (of)s 365.629 (the)s 383.553 (origin.)s 494.725 y 54 (They)s 81.508 (need)s 106.279 (not)s 124.967 (b)s 131.355 (e)s 139.092 (of)s 150.784 (the)s 168.863 (form)s 7 f 193.969 (u)s 8 f 496.368 y 200.237 (i)s 2 f 494.725 y 203.631 (\050)s 7 f 207.889 (x)s 2 f 214.148 (\051)s 221.448 (=)s 7 f 233.006 (u)s 2 f 239.274 (\050)s 7 f 243.533 (x)s 2 f 249.791 (\051)s 254.049 (,)s 260.118 (for)s 276.098 (some)s 302.755 (\257xed)s 7 f 328.438 (u)s 2 f 334.707 (,)s 340.775 (since)s 366.824 (ergo)s 387.233 (dicit)s 408.221 (y)s 508.326 y 54 (pla)s 68.296 (ys)s 81.366 (no)s 95.895 (role)s 116.539 (in)s 128.635 (the)s 146.815 (W)s 157.157 (egner)s 185.708 (estimate.)s 233.601 (F)s 239.837 (or)s 252.572 (the)s 270.752 (breather-t)s 318.567 (yp)s 330.733 (e)s 338.571 (mo)s 353.476 (del,)s 373.616 (the)s 391.796 (lo)s 400.617 (cal)s 521.926 y 54 (p)s 60.388 (oten)s 80.767 (tial)s 100.233 (is)s 111.244 (de)s 122.194 (\257ned)s 148.961 (b)s 154.74 (y)s 7 f 544.65 y 166.973 (V)s 4 f 546.345 y 173.361 (\244)s 2 f 544.65 y 179.755 (\050)s 7 f 184.014 (x)s 2 f 190.272 (\051)s 197.572 (=)s 0 f 534.912 y 209.135 (X)s 8 f 558.967 y 209.13 (i)s 11 f 212.024 (2)s 4 f 556.944 y 218.513 (\176)s 558.967 y 217.691 (\244)s 7 f 544.65 y 225.41 (u)s 8 f 546.293 y 231.679 (i)s 2 f 544.65 y 235.073 (\050)s 7 f 239.331 (\270)s 8 f 546.293 y 245.718 (i)s 2 f 544.65 y 249.112 (\050)s 7 f 253.371 (!)s 2 f 260.58 (\051)s 264.838 (\050)s 7 f 269.096 (x)s 10 f 277.788 (\241)s 7 f 288.738 (i)s 2 f 292.51 (\051)s 296.768 (\051)s 391.492 (\0501.6\051)s 578.2 y 54 (The)s 77.363 (single-site)s 128.831 (p)s 135.218 (oten)s 155.597 (tials)s 7 f 180.238 (u)s 8 f 579.843 y 186.506 (i)s 2 f 578.2 y 194.405 (m)s 203.226 (ust)s 222.391 (satisfy)s 257.434 (a)s 267.413 (repulsivit)s 311.913 (y)s 322.197 (condition)s 371.11 (stated)s 404.875 (in)s 591.8 y 54 (Hyp)s 74.379 (othesis)s 111.71 (\050H3\051.)s 145.777 (W)s 156.118 (e)s 165.953 (remark)s 204.744 (that)s 229.787 (the)s 249.963 (dep)s 267.301 (endence)s 309.985 (of)s 323.774 (the)s 343.95 (Anderson-t)s 396.967 (yp)s 409.133 (e)s 621.8 y 231.263 (2)s do-end end endp showpage %%PageTrailer %%Page: 4 4 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 4 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f120 sf ( )S -993 -1000 :M f186 sf ( )S -985 -1000 :M f219 sf ( )S -977 -1000 :M f253 sf ( )S -965 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (p)s 60.388 (oten)s 80.767 (tial)s 100.152 (on)s 115.28 (the)s 134.057 (random)s 174.157 (v)s 179.327 (ariables)s 10 f 219.488 (f)s 7 f 224.963 (\270)s 8 f 76.784 y 231.35 (k)s 2 f 75 y 236.489 (\050)s 7 f 240.748 (!)s 2 f 247.956 (\051)s 10 f 255.256 (j)s 7 f 261.34 (k)s 10 f 270.427 (2)s 2 f 72.232 y 281.833 (\176)s 75 y 280.768 (\244)s 10 f 288.372 (g)s 2 f 297.416 (is)s 308.346 (linear,)s 341.77 (and)s 362.981 (hence)s 393.317 (ana-)s 88.6 y 54 (lytic,)s 81.405 (whereas)s 122.52 (the)s 141.036 (dep)s 158.374 (endence)s 199.398 (of)s 211.526 (the)s 230.042 (breather-t)s 277.857 (yp)s 290.023 (e)s 298.197 (p)s 304.585 (oten)s 324.964 (tial)s 344.088 (on)s 358.954 (the)s 377.47 (random)s 102.2 y 54 (v)s 59.171 (ariables)s 10 f 99.837 (f)s 7 f 105.312 (\270)s 8 f 103.984 y 111.7 (k)s 2 f 102.2 y 116.838 (\050)s 7 f 121.097 (!)s 2 f 128.306 (\051)s 10 f 136.314 (j)s 7 f 143.105 (k)s 10 f 152.9 (2)s 2 f 99.432 y 165.014 (\176)s 102.2 y 163.95 (\244)s 10 f 171.554 (g)s 2 f 181.104 (is)s 192.54 (nonanalytic)s 252.277 (when)s 281.294 (the)s 300.577 (single-site)s 351.615 (p)s 358.003 (oten)s 378.382 (tials)s 7 f 402.593 (u)s 8 f 103.984 y 408.861 (k)s 2 f 115.8 y 54 (ha)s 65.254 (v)s 70.729 (e)s 79.237 (compact)s 123.029 (supp)s 145.902 (ort.)s 167.83 (When)s 199.759 (the)s 218.609 (sum)s 241.778 (in)s 254.545 (\0501.5\051)s 280.695 (or)s 294.1 (\0501.6\051)s 320.25 (extends)s 360.149 (o)s 365.32 (v)s 370.795 (er)s 383.592 (all)s 398.792 (the)s 129.4 y 54 (lattice)s 87.341 (p)s 93.729 (oin)s 108.024 (ts)s 7 f 120.135 (Z)s 122.918 (Z)s 8 f 125.426 y 131.176 (d)s 2 f 129.4 y 136.05 (,)s 142.648 (w)s 150.252 (e)s 158.651 (write)s 7 f 186.548 (V)s 8 f 131.043 y 192.935 (!)s 2 f 129.4 y 202.54 (for)s 219.183 (the)s 237.924 (p)s 244.311 (oten)s 264.69 (tial)s 284.04 (and)s 7 f 305.214 (H)s 8 f 125.426 y 315.206 (X)s 132.107 y 314.316 (!)s 2 f 129.4 y 323.322 (,)s 329.919 (with)s 354.744 (the)s 373.485 (op)s 385.347 (erator)s 143 y 54 (for)s 7 f 70.423 (X)s 2 f 83.395 (=)s 7 f 94.954 (A)s 2 f 106.479 (giv)s 120.471 (en)s 134.734 (b)s 140.513 (y)s 149.606 (\0501.2\051)s 175.427 (with)s 7 f 200.032 (V)s 4 f 144.695 y 206.42 (\244)s 2 f 143 y 216.127 (replaced)s 259.012 (b)s 264.792 (y)s 7 f 273.884 (V)s 8 f 144.643 y 280.271 (!)s 2 f 143 y 286.344 (,)s 292.766 (and)s 313.721 (similarly)s 358.188 (for)s 7 f 374.61 (X)s 2 f 387.583 (=)s 7 f 399.141 (M)s 2 f 410.958 (.)s 156.6 y 71 (W)s 81.342 (e)s 89.501 (will)s 109.827 (put)s 129.545 (conditions)s 181.565 (of)s 193.678 (the)s 212.179 (random)s 252.002 (v)s 257.173 (ariables)s 7 f 297.057 (\270)s 8 f 158.384 y 303.444 (k)s 2 f 156.6 y 308.583 (\050)s 7 f 312.842 (!)s 2 f 320.05 (\051)s 327.601 (and)s 348.536 (the)s 367.037 (single-site)s 170.2 y 54 (p)s 60.388 (oten)s 80.767 (tials)s 7 f 104.354 (u)s 8 f 171.984 y 110.623 (k)s 2 f 170.2 y 115.762 (.)s 123.604 (W)s 133.945 (e)s 142.264 (note)s 166.399 (that)s 189.925 (the)s 208.585 (W)s 218.927 (egner)s 247.959 (estimate)s 291.622 (is)s 302.434 (a)s 311.361 (lo)s 320.182 (cal)s 337.017 (estimate)s 380.679 (so)s 393.925 (that)s 183.8 y 54 (for)s 70.71 (a)s 79.785 (\257nite)s 107.719 (region)s 140.55 (\244)s 10 f 151.196 (\275)s 7 f 162.754 (I)s 165.142 (R)s 8 f 179.826 y 173.541 (d)s 2 f 183.8 y 178.414 (,)s 185.066 (only)s 209.046 (a)s 218.121 (\257nite)s 246.055 (n)s 251.834 (um)s 266.738 (b)s 273.126 (er)s 285.882 (of)s 298.303 (single-site)s 348.867 (p)s 355.254 (oten)s 375.633 (tials)s 399.37 (are)s 197.4 y 54 (in)s 62.821 (v)s 68.296 (olv)s 82.288 (ed.)s 101.146 (W)s 111.488 (e)s 120.004 (denote)s 155.288 (the)s 174.146 (ball)s 195.438 (of)s 207.908 (radius)s 7 f 240.85 (R)s 252.29 (\076)s 2 f 263.848 (0)s 272.973 (ab)s 284.836 (out)s 304.303 (the)s 323.161 (origin)s 354.216 (b)s 359.996 (y)s 7 f 369.425 (B)s 2 f 378.28 (\050)s 7 f 382.538 (R)s 2 f 390.937 (\051)s 395.195 (.)s 223 y 48.221 (\050H1a\051)s 81.375 (The)s 104.889 (self-adjoin)s 153.312 (t)s 162.226 (op)s 174.089 (erator)s 7 f 207.397 (H)s 8 f 219.026 y 217.389 (X)s 4 f 225.782 y 216.499 (0)s 2 f 223 y 230.16 (is)s 242.177 (essen)s 266.327 (tially)s 295.621 (self-adjoin)s 344.044 (t)s 352.958 (on)s 7 f 369.172 (C)s 11 f 219.026 y 377.781 (1)s 4 f 225.782 y 376.998 (0)s 2 f 223 y 386.781 (\050)s 7 f 391.04 (I)s 393.427 (R)s 8 f 219.026 y 401.826 (d)s 2 f 223 y 406.7 (\051)s 410.958 (,)s 236.6 y 81.375 (for)s 7 f 98.69 (X)s 2 f 112.588 (=)s 7 f 125.072 (A)s 2 f 137.49 (and)s 159.337 (for)s 7 f 176.652 (X)s 2 f 190.55 (=)s 7 f 203.034 (M)s 2 f 214.851 (.)s 224.425 (The)s 247.489 (op)s 259.351 (erator)s 7 f 292.209 (H)s 8 f 232.626 y 302.201 (X)s 4 f 239.382 y 301.311 (0)s 2 f 236.6 y 314.522 (is)s 326.088 (semi-b)s 357.478 (ounded)s 396.358 (and)s 250.2 y 81.375 (has)s 100.931 (an)s 116.168 (op)s 128.031 (en)s 142.659 (sp)s 153.366 (ectral)s 183.841 (gap.)s 208.869 (That)s 236.272 (is,)s 250.361 (there)s 278.403 (exist)s 304.346 (constan)s 340.603 (ts)s 10 f 352.859 (\241)s 361.376 (1)s 7 f 375.415 (\074)s 387.021 (M)s 4 f 251.843 y 397.644 (0)s 10 f 250.2 y 405.483 (\267)s 7 f 263.8 y 81.375 (C)s 4 f 265.443 y 89.201 (0)s 10 f 263.8 y 96.993 (\267)s 7 f 108.551 (B)s 11 f 265.443 y 116.857 (\241)s 7 f 263.8 y 127.01 (\074)s 138.568 (B)s 4 f 265.443 y 146.874 (+)s 7 f 263.8 y 157.026 (\074)s 168.585 (C)s 4 f 265.443 y 176.411 (1)s 10 f 263.8 y 184.203 (\267)s 195.761 (1)s 2 f 210.361 (so)s 223.805 (that)s 7 f 247.53 (\276)s 2 f 254.18 (\050)s 7 f 258.438 (H)s 4 f 265.443 y 267.541 (0)s 2 f 263.8 y 272.291 (\051)s 10 f 279.591 (\275)s 2 f 291.149 ([)s 7 f 294.191 (M)s 4 f 265.443 y 304.814 (0)s 7 f 263.8 y 309.564 (;)s 10 f 314.43 (1)s 2 f 325.38 (\051)s 329.639 (,)s 336.33 (and)s 7 f 288.4 y 152.763 (\276)s 2 f 159.413 (\050)s 7 f 163.671 (H)s 4 f 290.043 y 172.773 (0)s 2 f 288.4 y 177.524 (\051)s 10 f 184.215 (\134)s 2 f 193.948 (\050)s 7 f 198.207 (C)s 4 f 290.043 y 206.033 (0)s 7 f 288.4 y 210.783 (;)s 215.65 (C)s 4 f 290.043 y 223.476 (1)s 2 f 288.4 y 228.226 (\051)s 235.526 (=)s 247.084 (\050)s 7 f 251.343 (C)s 4 f 290.043 y 259.169 (0)s 7 f 288.4 y 263.919 (;)s 268.785 (B)s 11 f 290.043 y 277.091 (\241)s 2 f 288.4 y 284.202 (])s 10 f 289.677 ([)s 2 f 299.411 ([)s 7 f 302.452 (B)s 4 f 290.043 y 310.758 (+)s 7 f 288.4 y 317.869 (;)s 322.736 (C)s 4 f 290.043 y 330.562 (1)s 2 f 288.4 y 335.312 (\051)s 7 f 339.57 (:)s 2 f 317.5 y 47.613 (\050H1b\051)s 81.375 (The)s 104.889 (self-adjoin)s 153.312 (t)s 162.226 (op)s 174.089 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157.846 (prior)s 184.98 (results)s 220.113 (on)s 235.628 (the)s 254.793 (W)s 265.134 (egner)s 294.671 (estimate)s 338.838 (for)s 355.904 (m)s 364.725 (ultidimen-)s 585.83 y 54 (sional,)s 88.718 (con)s 104.838 (tin)s 117.918 (uous)s 144.001 (Sc)s 154.646 (hr)s 165.019 (\304)s 165.019 (odinger)s 204.454 (op)s 216.317 (erators.)s 258.613 (Kotani)s 295.585 (and)s 317.349 (Simon)s 351.28 ([25)s 365.271 (])s 372.435 (pro)s 387.978 (v)s 393.453 (ed)s 408.525 (a)s 621.8 y 231.263 (4)s do-end end endp showpage %%PageTrailer %%Page: 6 6 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 6 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f120 sf ( )S -993 -1000 :M f186 sf ( )S -985 -1000 :M f219 sf ( )S -977 -1000 :M f253 sf ( )S -965 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (W)s 64.342 (egner)s 93.659 (estimate)s 137.606 (with)s 162.634 (a)s 10 f 171.846 (j)s 2 f 174.887 (\244)s 10 f 182.492 (j)s 2 f 185.533 (-dep)s 206.521 (endence)s 247.974 (for)s 264.82 (Anderson)s 313.969 (mo)s 328.873 (dels)s 350.92 (with)s 375.949 (o)s 381.119 (v)s 386.595 (erlap-)s 88.6 y 54 (ping)s 77.967 (single-site)s 128.214 (p)s 134.601 (oten)s 154.981 (tials.)s 182.903 (This)s 207.539 (condition)s 255.231 (w)s 262.835 (as)s 275.913 (remo)s 299.364 (v)s 304.839 (ed)s 319.072 (and)s 339.998 (extensions)s 392.374 (w)s 399.978 (ere)s 102.2 y 54 (made)s 83.855 (to)s 97.894 (the)s 117.408 (band-edge)s 170.38 (case)s 194.212 (in)s 207.643 ([5)s 216.159 (])s 223.506 (and)s 245.453 ([1)s 253.97 (].)s 266.886 (An)s 285.487 (extension)s 334.565 (to)s 348.604 (m)s 357.425 (ultiplicativ)s 409.133 (e)s 115.8 y 54 (p)s 60.388 (erturbations)s 122.266 (w)s 129.87 (as)s 143.02 (made)s 171.927 (in)s 184.408 ([9)s 192.925 (,)s 199.323 (11)s 210.273 (,)s 216.671 (12)s 227.621 (,)s 234.019 (13)s 244.969 (].)s 255.821 (These)s 287.222 (metho)s 317.334 (ds)s 331.093 (require)s 367.665 (a)s 376.496 (sp)s 387.203 (ectral)s 129.4 y 54 (a)s 59.171 (v)s 64.646 (eraging)s 103.481 (theorem)s 146.575 (\050cf.)s 166.218 ([7)s 174.734 (])s 181.906 (and)s 203.678 (references)s 254.467 (therein\051.)s 301.563 (W)s 311.904 (egner\047s)s 348.976 (original)s 389.028 (pro)s 405.179 (of)s 143 y 54 ([32)s 67.992 (])s 73.994 (for)s 90.065 (Anderson)s 138.438 (mo)s 153.343 (dels)s 174.614 (did)s 192.784 (not)s 211.562 (require)s 247.738 (sp)s 258.444 (ectral)s 288.203 (a)s 293.373 (v)s 298.848 (eraging.)s 341.233 (F)s 347.468 (ollo)s 364.197 (wing)s 389.667 (W)s 400.008 (eg-)s 156.6 y 54 (ner\047s)s 80.838 (argumen)s 121.93 (t,)s 133.615 (Kirsc)s 158.344 (h)s 168.665 (ga)s 179.311 (v)s 184.786 (e)s 193.891 (a)s 203.604 (nice,)s 229.889 (short)s 258.551 (pro)s 274.702 (of)s 287.761 (of)s 300.82 (the)s 320.266 (W)s 330.608 (egner)s 360.426 (estimate)s 404.875 (in)s 170.2 y 54 ([18)s 67.992 (],)s 79.07 (but)s 100.221 (obtained)s 146.314 (a)s 10 f 156.515 (j)s 2 f 159.556 (\244)s 10 f 167.161 (j)s 4 f 166.226 y 170.202 (2)s 2 f 170.2 y 174.952 (-dep)s 195.94 (endence.)s 244.793 (Recen)s 273.232 (tly)s 285.399 (,)s 293.436 (Stollmann)s 346.828 ([30)s 360.82 (])s 368.588 (presen)s 398.792 (ted)s 183.8 y 54 (a)s 63.64 (short,)s 95.4 (elemen)s 127.946 (tary)s 151.913 (pro)s 168.064 (of)s 181.05 (of)s 194.036 (the)s 213.41 (W)s 223.751 (egner)s 253.497 (estimate)s 297.873 (for)s 315.148 (Anderson-t)s 368.164 (yp)s 380.331 (e)s 389.362 (mo)s 404.267 (d-)s 197.4 y 54 (els)s 71.147 (with)s 97.358 (singular)s 140.085 (single-site)s 191.968 (probabilit)s 238.536 (y)s 249.235 (distributions)s 314.531 (that)s 339.526 (are)s 359.075 (assumed)s 404.267 (to)s 211 y 54 (b)s 60.388 (e)s 70.141 (simply)s 106.417 (H)s 114.63 (\304)s 114.63 (older)s 143.271 (con)s 159.392 (tin)s 172.471 (uous.)s 206.05 (He)s 224.015 (also)s 247.213 (obtains)s 286.835 (a)s 10 f 297.196 (j)s 2 f 300.238 (\244)s 10 f 307.842 (j)s 4 f 207.026 y 310.884 (2)s 2 f 211 y 315.634 (-dep)s 336.622 (endence.)s 385.956 (These)s 224.6 y 54 (pro)s 70.151 (ofs,)s 91.117 (and)s 113.316 (the)s 133.082 (pro)s 149.234 (of)s 162.612 (in)s 176.294 (this)s 198.554 (pap)s 216.5 (er,)s 233.482 (do)s 249.598 (not)s 269.972 (require)s 307.744 (sp)s 318.451 (ectral)s 349.805 (a)s 354.976 (v)s 360.451 (eraging.)s 405.788 (It)s 238.2 y 54 (is)s 65.335 (not)s 85.126 (clear,)s 114.762 (ho)s 126.016 (w)s 133.62 (ev)s 143.962 (er,)s 160.214 (ho)s 171.469 (w)s 183.351 (to)s 197.059 (extend)s 232.971 (the)s 252.154 (metho)s 282.266 (ds)s 296.643 (of)s 309.438 (this)s 331.115 (pap)s 349.061 (er)s 362.191 (in)s 375.29 (order)s 404.267 (to)s 251.8 y 54 (pro)s 69.543 (v)s 75.018 (e)s 83.658 (a)s 92.907 (W)s 103.248 (egner)s 132.602 (estimate)s 176.587 (for)s 193.47 (singular)s 235.051 (distributions)s 299.202 (with)s 324.267 (the)s 343.249 (correct)s 379.933 (v)s 385.408 (olume)s 265.4 y 54 (dep)s 71.338 (endence.)s 279 y 71 (In)s 84.038 (order)s 112.041 (to)s 124.775 (pro)s 140.318 (v)s 145.793 (e)s 153.66 (a)s 162.136 (lo)s 170.957 (calization)s 219.582 (result,)s 252.612 (w)s 260.216 (e)s 268.084 (need)s 292.984 (to)s 305.718 (assume)s 342.907 (that)s 365.983 (the)s 384.192 (family)s 292.6 y 54 (of)s 66.351 (op)s 78.214 (erators)s 10 f 114.716 (f)s 7 f 120.191 (H)s 8 f 288.626 y 130.183 (X)s 295.307 y 129.293 (!)s 10 f 292.6 y 141.34 (j)s 7 f 147.423 (!)s 10 f 157.673 (2)s 2 f 168.015 (\255)s 10 f 175.923 (g)s 2 f 184.929 (has)s 204.337 (a)s 213.342 (deterministic)s 279.014 (sp)s 289.721 (ectrum)s 326.74 (\247)s 334.648 (.)s 342.517 (F)s 348.752 (or)s 362.046 (the)s 380.785 (mo)s 395.689 (dels)s 306.2 y 54 (describ)s 87.854 (ed)s 101.575 (here)s 124.451 (this)s 144.924 (is)s 155.056 (insured)s 192.593 (if,)s 204.969 (for)s 220.849 (example,)s 266.075 (the)s 284.054 (single-site)s 333.788 (p)s 340.176 (oten)s 360.555 (tials)s 383.462 (satisfy)s 7 f 319.8 y 54 (u)s 8 f 321.584 y 60.268 (k)s 2 f 319.8 y 65.407 (\050)s 7 f 69.666 (x)s 2 f 75.924 (\051)s 83.224 (=)s 7 f 94.782 (u)s 2 f 101.051 (\050)s 7 f 105.309 (x)s 10 f 113.663 (\241)s 7 f 124.275 (k)s 2 f 130.32 (\051)s 134.579 (,)s 141.135 (for)s 157.726 (all)s 7 f 172.766 (k)s 10 f 181.853 (2)s 7 f 192.194 (Z)s 194.977 (Z)s 8 f 315.826 y 203.235 (d)s 2 f 319.8 y 208.109 (.)s 215.961 (Giv)s 233.071 (en)s 247.502 (the)s 266.191 (W)s 276.533 (egner)s 305.595 (estimate,)s 352.362 (the)s 371.052 (existence)s 333.4 y 54 (of)s 66.554 (lo)s 75.374 (calized)s 111.349 (states)s 142.578 (near)s 167.024 (the)s 185.965 (band)s 213.423 (edge)s 238.448 (for)s 255.29 (these)s 283.417 (mo)s 298.321 (dels)s 320.364 (follo)s 340.439 (ws)s 356.399 (pro)s 371.942 (vided)s 401.529 (w)s 409.133 (e)s 347 y 54 (mak)s 74.075 (e)s 82.592 (t)s 86.546 (w)s 94.15 (o)s 103.275 (other)s 131.897 (h)s 137.676 (yp)s 149.843 (otheses.)s 372.6 y 53.696 (\050H5\051)s 81.375 (The)s 104.209 (densit)s 132.557 (y)s 7 f 142.312 (h)s 4 f 374.243 y 148.621 (0)s 2 f 372.6 y 157.347 (deca)s 178.334 (ys)s 192.408 (su)s 202.81 (\261cien)s 230.49 (tly)s 247.544 (rapidly)s 285.313 (near)s 7 f 310.002 (m)s 2 f 323.592 (and)s 345.209 (near)s 7 f 369.899 (M)s 2 f 385.691 (in)s 398.792 (the)s 386.2 y 81.375 (follo)s 101.45 (wing)s 127.608 (sense:)s 410.8 y 173.037 (0)s 7 f 181.553 (\074)s 193.112 (I)s 195.499 (P)s 10 f 204.05 (fj)s 7 f 212.567 (\270)s 10 f 221.388 (\241)s 7 f 232.338 (m)s 10 f 241.952 (j)s 7 f 248.035 (\074)s 259.594 (\042)s 10 f 264.7 (g)s 273.216 (\267)s 7 f 284.775 (\042)s 4 f 406.279 y 289.881 (3)s 8 f 294.131 (d=)s 4 f 302.755 (2+)s 8 f 313.616 (\257)s 7 f 410.8 y 319.297 (;)s 2 f 453.5 y 171.936 (0)s 7 f 180.452 (\074)s 192.01 (I)s 194.398 (P)s 10 f 202.949 (fj)s 7 f 211.466 (\270)s 10 f 220.287 (\241)s 7 f 231.236 (M)s 10 f 243.053 (j)s 7 f 249.137 (\074)s 260.695 (\042)s 10 f 265.801 (g)s 274.318 (\267)s 7 f 285.876 (\042)s 4 f 448.979 y 290.982 (3)s 8 f 295.232 (d=)s 4 f 303.856 (2+)s 8 f 314.717 (\257)s 7 f 453.5 y 320.398 (;)s 2 f 473.6 y 81.375 (for)s 98.135 (some)s 7 f 125.571 (\257)s 135.384 (\076)s 2 f 146.942 (0)s 152.417 (.)s 499.2 y 53.696 (\050H6\051)s 81.375 (There)s 113.039 (exist)s 138.954 (constan)s 175.211 (ts)s 7 f 187.438 (B)s 11 f 495.227 y 196.293 (0)s 501.907 y 195.744 (\247)s 2 f 499.2 y 206.505 (satisfying)s 7 f 255.293 (B)s 11 f 500.843 y 263.599 (\241)s 7 f 499.2 y 273.752 (\074)s 285.31 (B)s 11 f 495.227 y 294.165 (0)s 501.907 y 293.616 (\241)s 7 f 499.2 y 303.769 (\074)s 315.327 (B)s 11 f 495.227 y 324.182 (0)s 4 f 501.907 y 323.633 (+)s 7 f 499.2 y 333.785 (\074)s 345.344 (B)s 4 f 500.843 y 353.649 (+)s 2 f 499.2 y 364.411 (suc)s 379.376 (h)s 389.109 (that)s 523.8 y 168.491 (\247)s 10 f 178.833 (\134)s 188.566 (f)s 2 f 194.041 (\050)s 7 f 198.3 (B)s 11 f 525.443 y 206.605 (\241)s 7 f 523.8 y 213.717 (;)s 218.583 (B)s 11 f 519.279 y 227.438 (0)s 526.507 y 226.889 (\241)s 2 f 523.8 y 234 (\051)s 10 f 240.692 ([)s 2 f 250.425 (\050)s 7 f 254.683 (B)s 11 f 519.279 y 263.538 (0)s 4 f 526.507 y 262.989 (+)s 7 f 523.8 y 270.1 (;)s 274.967 (B)s 4 f 525.443 y 283.273 (+)s 2 f 523.8 y 290.384 (\051)s 10 f 294.642 (g)s 303.159 (6)s 2 f 303.159 (=)s 10 f 314.717 (;)s 7 f 323.842 (:)s 2 f 552.9 y 71 (In)s 84.63 (ligh)s 101.967 (t)s 109.818 (of)s 122.231 (h)s 128.01 (yp)s 140.177 (othesis)s 176.132 (\050H6\051,)s 204.982 (w)s 212.586 (e)s 221.045 (de)s 231.995 (\257ne)s 252.621 (the)s 271.421 (band)s 298.739 (edges)s 327.942 (of)s 340.355 (the)s 359.156 (almost)s 394.442 (sure)s 566.5 y 54 (sp)s 64.707 (ectrum)s 101.845 (\247)s 113.404 (near)s 137.768 (the)s 156.626 (gap)s 7 f 177.309 (G)s 2 f 185.919 (,)s 192.61 (as)s 206.055 (follo)s 226.13 (ws:)s 588.332 y 167.424 (\176)s 7 f 591.1 y 164.822 (B)s 11 f 592.743 y 173.128 (\241)s 10 f 591.1 y 183.28 (\264)s 2 f 194.839 (sup)s 10 f 211.324 (f)s 7 f 216.799 (E)s 10 f 228.555 (\267)s 7 f 240.114 (B)s 11 f 586.579 y 248.969 (0)s 593.807 y 248.419 (\241)s 10 f 591.1 y 258.572 (j)s 7 f 264.656 (E)s 10 f 276.412 (2)s 2 f 286.753 (\247)s 10 f 294.661 (g)s 7 f 300.136 (;)s 2 f 621.8 y 231.263 (5)s do-end end endp showpage %%PageTrailer %%Page: 7 7 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 7 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f120 sf ( )S -993 -1000 :M f88 sf ( )S -989 -1000 :M f186 sf ( )S -981 -1000 :M f219 sf ( )S -973 -1000 :M f253 sf ( )S -961 -1000 :M f420 sf ( )S -948 -1000 :M f319 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 5 10.95 /CMBX10 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 13 10.95 /CMTI10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (and)s 85.832 y 167.911 (\176)s 7 f 88.6 y 165.309 (B)s 4 f 90.242 y 173.614 (+)s 10 f 88.6 y 183.767 (\264)s 2 f 195.325 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413.767 y 242.774 (=)s 7 f 256.614 (H)s 4 f 415.409 y 265.716 (0)s 2 f 413.767 y 273.812 (+)s 7 f 285.674 (V)s 4 f 415.462 y 292.062 (\244)s 7 f 413.767 y 298.456 (;)s 303.323 (H)s 4 f 415.409 y 312.425 (0)s 2 f 413.767 y 317.175 (\051)s 321.434 (,)s 329.836 (and)s 352.497 (to)s 367.249 (study)s 398.792 (the)s 427.367 y 54 (thermo)s 88.401 (dynamic)s 132.506 (limit)s 446.116 y 192.319 (lim)s 4 f 453.25 y 188.475 (\244)s 11 f 194.37 (!)s 202.87 (1)s 7 f 438.709 y 214.395 (\273)s 4 f 440.404 y 219.186 (\244)s 2 f 438.709 y 225.58 (\050)s 7 f 229.839 (\270)s 2 f 236.226 (\051)s 26.089 .4 214.395 443.579 r 10 f 453.628 y 220.596 (j)s 2 f 223.638 (\244)s 10 f 231.242 (j)s 446.116 y 244.726 (\264)s 7 f 256.284 (\273)s 2 f 261.579 (\050)s 7 f 265.837 (\270)s 2 f 272.225 (\051)s 7 f 276.483 (:)s 2 f 391.492 (\0501.8\051)s 469.862 y 54 (They)s 83.509 (pro)s 99.052 (v)s 104.527 (e)s 114.265 (that)s 139.212 (this)s 161.786 (limit)s 189.166 (\050prop)s 215.659 (ert)s 228.768 (y)s 239.419 (de)s 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/CMR10 findfont fdef 4 8 /CMR8 findfont fdef 5 10.95 /CMBX10 findfont fdef 6 6 /CMR6 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 16 14.4 /CMR12 findfont fdef 17 14.4 /CMBX12 findfont fdef 18 14.4 /CMMI12 findfont fdef 19 14.4 /CMSY10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (of)s 66.227 (the)s 84.841 (theory)s 118.997 (dev)s 135.423 (elop)s 155.193 (ed)s 169.549 (in)s 182.08 (section)s 218.396 (2)s 227.277 (to)s 240.416 (the)s 259.03 (single-site)s 309.399 (sp)s 320.106 (ectral)s 350.308 (shift)s 374.762 (function)s 88.6 y 54 (allo)s 70.729 (ws)s 86.447 (us)s 100.34 (to)s 113.564 (obtain)s 147.471 (the)s 166.17 (correct)s 202.571 (v)s 208.046 (olume)s 240.128 (dep)s 257.466 (endence.)s 303.038 (In)s 316.566 (section)s 352.967 (4,)s 365.006 (w)s 372.61 (e)s 380.967 (discuss)s 102.2 y 54 (the)s 72.823 (lo)s 81.644 (calization)s 130.883 (prop)s 153.118 (erties)s 182.373 (of)s 194.809 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(\270)s 2 f 246.2 (;)s 7 f 251.067 (H)s 260.45 (;)s 265.317 (H)s 4 f 544.506 y 274.419 (0)s 2 f 542.863 y 279.169 (\051)s 10 f 283.427 (j)s 7 f 289.511 (d)s 295.21 (\270)s 2 f 304.639 (=)s 7 f 316.197 (\271)s 2 f 322.795 (\050)s 7 f 327.054 (V)s 2 f 335.874 (\051)s 7 f 340.133 (;)s 2 f 391.492 (\0502.8\051)s 569.271 y 54 (and)s 75.292 (the)s 94.15 (SSF)s 117.115 (is)s 128.125 (b)s 134.513 (ounded,)s 10 f 591.8 y 192.816 (j)s 7 f 195.858 (\273)s 2 f 201.152 (\050)s 7 f 205.411 (\270)s 2 f 211.798 (;)s 7 f 216.665 (H)s 226.048 (;)s 230.915 (H)s 4 f 593.443 y 240.017 (0)s 2 f 591.8 y 244.767 (\051)s 10 f 249.026 (j)s 255.109 (\267)s 2 f 266.667 (1)s 7 f 272.142 (:)s 2 f 391.492 (\0502.9\051)s 621.8 y 231.263 (8)s do-end end endp showpage %%PageTrailer %%Page: 10 10 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 10 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( 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(\0502.16\051)s 621.8 y 231.263 (9)s do-end end endp showpage %%PageTrailer %%Page: 11 11 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 11 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f520 sf ( )S -958 -1000 :M f253 sf ( )S -946 -1000 :M f420 sf ( )S -933 -1000 :M f554 sf ( )S f353 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 9 6 /CMMI6 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 14 10.95 /LASY10 findfont fdef 17 14.4 /CMBX12 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (Since)s 82.592 (the)s 101.45 (series)s 130.803 (is)s 141.814 (con)s 157.935 (v)s 163.41 (ergen)s 188.686 (t,)s 199.636 (the)s 218.495 (di)s 227.62 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228.525 (10)s do-end end endp showpage %%PageTrailer %%Page: 12 12 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 12 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf -.709( )A f88 sf ( )S -980 -1000 :M f186 sf ( )S -972 -1000 :M f219 sf ( )S -964 -1000 :M f253 sf ( )S -952 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 5 10.95 /CMBX10 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 5 f 75 y 54 (Pro)s 74.44 (of)s 88.781 (of)s 103.123 (Theorem)s 156.595 (1.1.)s 2 f 95.827 y 54 (1.)s 71.802 (Let)s 7 f 92.894 (G)s 2 f 107 (=)s 121.014 (\050)s 7 f 125.272 (B)s 11 f 97.47 y 133.578 (\241)s 7 f 95.827 y 140.689 (;)s 145.556 (B)s 4 f 97.47 y 153.861 (+)s 2 f 95.827 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(\051)s 331.07 (\051)s 338.978 (and)s 360.27 (obtain)s 7 f 264.828 y 109.997 (I)s 112.385 (P)s 10 f 120.936 (f)s 2 f 129.453 (dist)s 150.197 (\050)s 7 f 154.455 (E)s 4 f 266.47 y 162.538 (0)s 7 f 264.828 y 167.288 (;)s 172.155 (\276)s 2 f 178.805 (\050)s 7 f 183.063 (H)s 4 f 266.523 y 192.165 (\244)s 2 f 264.828 y 198.56 (\051\051)s 7 f 210.118 (\074)s 221.676 (\264)s 10 f 227.506 (g)s 2 f 242.981 (=)s 7 f 261.498 (I)s 263.886 (P)s 10 f 272.437 (f)s 7 f 277.912 (T)s 285.831 (r)s 2 f 291.076 (\050)s 7 f 295.334 (E)s 4 f 266.523 y 303.417 (\244)s 2 f 264.828 y 309.812 (\050)s 7 f 314.07 (I)s 8 f 266.47 y 318.884 (\264)s 2 f 264.828 y 323.936 (\051)s 328.194 (\051)s 10 f 335.494 (\270)s 2 f 347.053 (1)s 10 f 352.528 (g)s 281.428 y 242.981 (\267)s 7 f 261.498 (I)s 263.886 (E)s 10 f 272.6 (f)s 7 f 278.075 (T)s 285.995 (r)s 2 f 291.239 (\050)s 7 f 295.498 (E)s 4 f 283.123 y 303.581 (\244)s 2 f 281.428 y 309.975 (\050)s 7 f 314.234 (I)s 8 f 283.07 y 319.047 (\264)s 2 f 281.428 y 324.099 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381.589 (so)s 393.925 (that)s 354.055 y 54 (inf)s 7 f 67.816 (\276)s 2 f 74.466 (\050)s 7 f 78.724 (H)s 4 f 355.75 y 87.826 (\244)s 2 f 354.055 y 94.221 (\051)s 7 f 101.521 (\076)s 113.079 (M)s 4 f 355.697 y 123.702 (0)s 2 f 354.055 y 128.452 (,)s 134.708 (uniformly)s 184.078 (in)s 196.309 (\244)s 203.913 (.)s 211.64 (Let)s 7 f 230.714 (\275)s 2 f 239.481 (b)s 245.869 (e)s 253.841 (a)s 262.422 (nonnegativ)s 314.739 (e,)s 325.862 (smo)s 345.085 (oth,)s 367.158 (monotone)s 367.655 y 54 (decreasing)s 107.89 (function)s 151.652 (suc)s 166.617 (h)s 177.224 (that)s 7 f 201.823 (\275)s 2 f 207.484 (\050)s 7 f 211.743 (x)s 2 f 218.001 (\051)s 226.757 (=)s 239.772 (1)s 245.247 (,)s 253.031 (for)s 7 f 270.665 (x)s 281.421 (\074)s 10 f 294.436 (\241)s 7 f 302.953 (\264)s 308.782 (=)s 2 f 314.257 (2)s 319.732 (,)s 327.517 (and)s 7 f 349.682 (\275)s 2 f 355.343 (\050)s 7 f 359.602 (x)s 2 f 365.86 (\051)s 374.617 (=)s 387.631 (0)s 393.106 (,)s 400.89 (for)s 7 f 381.255 y 54 (x)s 10 f 63.3 (\270)s 7 f 74.858 (\264)s 80.688 (=)s 2 f 86.163 (2)s 91.638 (.)s 99.331 (F)s 105.566 (urthermore,)s 165.365 (w)s 172.969 (e)s 180.839 (can)s 200.266 (assume)s 237.458 (that)s 7 f 260.536 (\275)s 2 f 269.2 (has)s 288.08 (compact)s 331.233 (supp)s 354.107 (ort:)s 375.714 (W)s 386.055 (e)s 393.925 (tak)s 409.133 (e)s 7 f 394.855 y 54 (\275)s 2 f 59.661 (\050)s 7 f 63.92 (x)s 2 f 70.178 (\051)s 77.478 (=)s 89.036 (0)s 98.161 (for)s 7 f 114.921 (x)s 124.221 (\074\074)s 144.296 (M)s 4 f 396.497 y 154.919 (0)s 2 f 394.855 y 159.669 (.)s 167.577 (By)s 184.762 (the)s 203.621 (functional)s 255.025 (calculus,)s 299.494 (w)s 307.098 (e)s 315.615 (ha)s 326.869 (v)s 332.344 (e)s 7 f 419.455 y 79.274 (\275)s 2 f 84.935 (\050)s 7 f 89.193 (H)s 4 f 421.15 y 98.296 (\244)s 10 f 419.455 y 107.123 (\241)s 7 f 118.073 (E)s 4 f 421.097 y 126.157 (0)s 10 f 419.455 y 133.34 (\241)s 2 f 144.29 (3)s 7 f 149.765 (\264)s 155.595 (=)s 2 f 161.07 (2\051)s 10 f 173.236 (\241)s 7 f 184.186 (\275)s 2 f 189.848 (\050)s 7 f 194.106 (H)s 4 f 421.15 y 203.208 (\244)s 10 f 419.455 y 212.036 (\241)s 7 f 222.986 (E)s 4 f 421.097 y 231.069 (0)s 2 f 419.455 y 238.253 (+)s 249.203 (3)s 7 f 254.678 (\264)s 260.508 (=)s 2 f 265.983 (2\051)s 436.055 y 89.274 (=)s 0 f 426.317 y 108.938 (X)s 8 f 448.451 y 107.79 (j)s 11 f 111.689 (2)s 8 f 117.356 (Z)s 118.206 (Z)s 10 f 436.055 y 124.531 (f)s 7 f 130.006 (\275)s 2 f 135.667 (\050)s 7 f 139.926 (E)s 8 f 437.697 y 148.009 (j)s 2 f 436.055 y 152.407 (\050)s 156.666 (\244)s 164.27 (\051)s 10 f 170.962 (\241)s 7 f 181.912 (E)s 4 f 437.697 y 189.995 (0)s 10 f 436.055 y 197.178 (\241)s 2 f 208.128 (3)s 7 f 213.603 (\264)s 219.433 (=)s 2 f 224.908 (2)s 230.383 (\051)s 10 f 237.075 (\241)s 7 f 248.025 (\275)s 2 f 253.686 (\050)s 7 f 257.944 (E)s 8 f 437.697 y 266.028 (j)s 2 f 436.055 y 270.426 (\050)s 274.684 (\244)s 282.289 (\051)s 10 f 288.98 (\241)s 7 f 299.93 (E)s 4 f 437.697 y 308.013 (0)s 2 f 436.055 y 315.197 (+)s 326.147 (3)s 7 f 331.622 (\264)s 337.452 (=)s 2 f 342.927 (2)s 348.402 (\051)s 10 f 352.66 (g)s 7 f 358.135 (P)s 8 f 437.697 y 365.165 (j)s 2 f 436.055 y 369.564 (\050)s 373.822 (\244)s 381.426 (\051)s 7 f 385.685 (;)s 2 f 391.492 (\0503.3\051)s 471.219 y 54 (where,)s 88.42 (due)s 108.746 (to)s 121.773 (the)s 140.274 (supp)s 163.147 (ort)s 180.462 (of)s 7 f 192.576 (\275)s 2 f 198.238 (,)s 204.644 (the)s 223.145 (sum)s 245.966 (is)s 256.619 (o)s 261.79 (v)s 267.265 (er)s 279.714 (the)s 298.215 (eigen)s 322.244 (v)s 327.415 (alues)s 7 f 354.494 (E)s 8 f 472.861 y 362.577 (j)s 2 f 471.219 y 366.976 (\050)s 371.234 (\244)s 378.838 (\051)s 386.39 (of)s 7 f 398.503 (H)s 4 f 472.914 y 407.606 (\244)s 2 f 484.819 y 54 (in)s 66.287 ([)s 7 f 69.328 (E)s 4 f 486.461 y 77.412 (0)s 10 f 484.819 y 83.618 (\241)s 2 f 93.592 (2)s 7 f 99.067 (\264)s 104.896 (;)s 109.763 (E)s 4 f 486.461 y 117.846 (0)s 2 f 484.819 y 124.053 (+)s 134.026 (2)s 7 f 139.501 (\264)s 2 f 145.331 (])s 148.373 (.)s 156.118 (The)s 178.138 (op)s 190.001 (erators)s 7 f 226.134 (P)s 8 f 486.461 y 233.164 (j)s 2 f 484.819 y 237.563 (\050)s 241.821 (\244)s 249.425 (\051)s 256.845 (are)s 274.637 (the)s 293.007 (pro)s 309.463 (jectors)s 344.045 (on)s 355.299 (to)s 368.194 (the)s 386.564 (corre-)s 498.419 y 54 (sp)s 64.707 (onding)s 101.314 (\257)s 107.397 (nite)s 130.012 (dimensional)s 191.013 (eigenspaces)s 249.642 (spanned)s 293.001 (b)s 298.781 (y)s 308.925 (normalized)s 365.637 (eigenfunc-)s 512.019 y 54 (tions)s 7 f 79.793 (\301)s 8 f 513.661 y 86.318 (j)s 2 f 512.019 y 90.716 (.)s 98.28 (Consequen)s 149.441 (tly)s 161.608 (,)s 167.472 (the)s 185.296 (di)s 194.421 (\256)s 200.809 (erence)s 233.263 (of)s 244.7 (the)s 262.524 (t)s 266.479 (w)s 274.083 (o)s 282.174 (op)s 294.036 (erators)s 329.624 (on)s 343.798 (the)s 361.622 (left)s 379.751 (in)s 391.492 (\0503.3\051)s 525.619 y 54 (is)s 64.049 (trace)s 90.492 (class.)s 120.102 (Note)s 145.602 (that)s 168.366 (this)s 188.756 (di)s 197.881 (\256)s 204.269 (erence)s 7 f 236.796 (\275)s 2 f 242.457 (\050)s 7 f 246.715 (H)s 4 f 527.314 y 255.817 (\244)s 10 f 525.619 y 262.722 (\241)s 7 f 271.748 (E)s 4 f 527.261 y 279.831 (0)s 10 f 525.619 y 285.091 (\241)s 2 f 294.117 (3)s 7 f 299.592 (\264)s 305.422 (=)s 2 f 310.897 (2)s 316.372 (\051)s 10 f 321.139 (\241)s 7 f 330.166 (\275)s 2 f 335.827 (\050)s 7 f 340.085 (H)s 4 f 527.314 y 349.188 (\244)s 10 f 525.619 y 356.092 (\241)s 7 f 365.118 (E)s 4 f 527.261 y 373.201 (0)s 2 f 525.619 y 378.461 (+)s 387.487 (3)s 7 f 392.962 (\264)s 398.792 (=)s 2 f 404.267 (2)s 409.742 (\051)s 539.219 y 54 (is,)s 68.988 (roughly)s 104.302 (,)s 111.93 (the)s 131.537 (n)s 137.316 (um)s 152.22 (b)s 158.608 (er)s 172.162 (of)s 185.382 (eigen)s 209.411 (v)s 214.582 (alues)s 242.766 (of)s 7 f 255.986 (H)s 4 f 540.914 y 265.088 (\244)s 2 f 539.219 y 275.882 (less)s 296.827 (than)s 7 f 323.126 (E)s 4 f 540.861 y 331.209 (0)s 2 f 539.219 y 338.892 (+)s 350.341 (2)s 7 f 355.816 (\264)s 2 f 366.045 (min)s 383.99 (us)s 398.792 (the)s 552.819 y 54 (n)s 59.779 (um)s 74.683 (b)s 81.071 (er)s 94.05 (of)s 106.694 (eigen)s 130.723 (v)s 135.894 (alues)s 163.503 (of)s 7 f 176.147 (H)s 4 f 554.514 y 185.249 (\244)s 2 f 552.819 y 195.467 (less)s 215.837 (than)s 7 f 241.56 (E)s 4 f 554.461 y 249.643 (0)s 10 f 552.819 y 256.942 (\241)s 2 f 268.008 (2)s 7 f 273.483 (\264)s 2 f 279.312 (.)s 287.741 (Ho)s 301.124 (w)s 308.728 (ev)s 319.07 (er,)s 335.133 (the)s 354.165 (op)s 366.027 (erator)s 7 f 398.503 (H)s 4 f 554.514 y 407.605 (\244)s 2 f 566.419 y 54 (ma)s 68.296 (y)s 78.455 (ha)s 89.709 (v)s 95.184 (e)s 104.431 (con)s 120.552 (tin)s 133.631 (uous)s 159.972 (sp)s 170.679 (ectrum)s 208.547 (to)s 222.661 (the)s 242.249 (left)s 262.142 (of)s 7 f 275.343 (E)s 4 f 568.061 y 283.426 (0)s 10 f 566.419 y 291.096 (\241)s 2 f 302.533 (2)s 7 f 308.008 (\264)s 2 f 313.838 (,)s 321.442 (so)s 335.616 (neither)s 373.485 (op)s 385.347 (erator)s 7 f 580.019 y 54 (\275)s 2 f 59.661 (\050)s 7 f 63.92 (H)s 4 f 581.714 y 73.022 (\244)s 10 f 580.019 y 82.034 (\241)s 7 f 93.169 (E)s 4 f 581.661 y 101.252 (0)s 10 f 580.019 y 108.62 (\241)s 2 f 119.754 (3)s 7 f 125.229 (\264)s 131.059 (=)s 2 f 136.534 (2)s 142.009 (\051)s 146.267 (,)s 153.305 (nor)s 7 f 173.079 (\275)s 2 f 178.74 (\050)s 7 f 182.999 (H)s 4 f 581.714 y 192.101 (\244)s 10 f 580.019 y 201.113 (\241)s 7 f 212.248 (E)s 4 f 581.661 y 220.331 (0)s 2 f 580.019 y 227.699 (+)s 238.833 (3)s 7 f 244.308 (\264)s 250.138 (=)s 2 f 255.613 (2)s 261.088 (\051)s 265.346 (,)s 272.384 (b)s 278.163 (y)s 287.869 (itself,)s 317.78 (is)s 329.068 (in)s 342.119 (the)s 361.254 (trace)s 388.937 (class.)s 621.8 y 228.525 (11)s do-end end endp showpage %%PageTrailer %%Page: 13 13 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 13 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f253 sf ( )S -955 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (The)s 76.281 (co)s 86.927 (e)s 91.794 (\261)s 100.919 (cien)s 119.473 (t)s 127.154 (of)s 7 f 139.397 (P)s 8 f 76.642 y 146.427 (j)s 2 f 75 y 150.826 (\050)s 155.084 (\244)s 162.689 (\051)s 170.37 (on)s 185.351 (the)s 203.982 (righ)s 222.566 (t)s 230.248 (side)s 251.981 (of)s 264.225 (\0503.3\051)s 290.156 (is)s 300.939 (alw)s 317.06 (a)s 322.231 (ys)s 335.752 (nonnegativ)s 388.069 (e)s 396.358 (and)s 88.6 y 54 (precisely)s 98.804 (equal)s 127.7 (to)s 141.083 (one)s 161.158 (for)s 7 f 177.918 (E)s 8 f 90.242 y 186.001 (j)s 2 f 88.6 y 190.399 (\050)s 194.658 (\244)s 202.262 (\051)s 10 f 209.562 (2)s 7 f 219.904 (I)s 8 f 90.242 y 224.717 (\264)s 2 f 88.6 y 229.769 (,)s 236.461 (so)s 249.905 (w)s 257.509 (e)s 266.026 (ha)s 277.28 (v)s 282.755 (e)s 7 f 109.799 y 77.593 (T)s 85.513 (r)s 2 f 90.757 (\050)s 7 f 95.015 (E)s 4 f 111.494 y 103.099 (\244)s 2 f 109.799 y 109.493 (\050)s 7 f 113.752 (I)s 8 f 111.442 y 118.565 (\264)s 2 f 109.799 y 123.617 (\051)s 127.876 (\051)s 10 f 135.176 (\267)s 7 f 146.734 (T)s 154.654 (r)s 2 f 159.898 (\050)s 7 f 164.156 (\275)s 2 f 169.818 (\050)s 7 f 174.076 (H)s 4 f 111.494 y 183.178 (\244)s 10 f 109.799 y 192.006 (\241)s 7 f 202.956 (E)s 4 f 111.442 y 211.039 (0)s 10 f 109.799 y 218.223 (\241)s 2 f 229.173 (3)s 7 f 234.648 (\264)s 240.478 (=)s 2 f 245.953 (2)s 251.428 (\051)s 10 f 258.119 (\241)s 7 f 269.069 (\275)s 2 f 274.73 (\050)s 7 f 278.989 (H)s 4 f 111.494 y 288.091 (\244)s 10 f 109.799 y 296.919 (\241)s 7 f 307.869 (E)s 4 f 111.442 y 315.952 (0)s 2 f 109.799 y 323.135 (+)s 334.085 (3)s 7 f 339.56 (\264)s 345.39 (=)s 2 f 350.865 (2)s 356.34 (\051)s 360.599 (\051)s 7 f 364.857 (:)s 2 f 391.492 (\0503.4\051)s 130.998 y 54 (Although)s 102.299 (the)s 121.094 (coun)s 143.299 (ting)s 165.744 (function)s 208.568 (for)s 225.264 (eigen)s 249.293 (v)s 254.464 (alues)s 281.837 (is)s 292.784 (not)s 312.188 (di)s 321.313 (\256eren)s 347.501 (tiable,)s 380.909 (w)s 388.513 (e)s 396.967 (will)s 144.598 y 54 (use)s 72.456 (the)s 90.852 (fact)s 111.985 (that)s 135.247 (this)s 156.137 (smo)s 175.36 (oth)s 194.364 (appro)s 221.465 (ximation)s 266.931 (is)s 277.479 (di)s 286.604 (\256eren)s 312.793 (tiable)s 342.747 (with)s 367.226 (resp)s 387.088 (ect)s 404.267 (to)s 158.198 y 54 (the)s 72.858 (energy)s 103.305 (.)s 179.025 y 54 (3.)s 67.881 (Returning)s 119.938 (to)s 133.487 (the)s 152.511 (exp)s 169.544 (ectation)s 211.685 (of)s 224.322 (the)s 243.346 (trace)s 270.917 (in)s 283.858 (\0503.4\051,)s 313.266 (w)s 320.87 (e)s 329.552 (can)s 349.793 (no)s 361.047 (w)s 372.772 (b)s 379.159 (ound)s 406.7 (it)s 192.625 y 54 (ab)s 65.863 (o)s 71.033 (v)s 76.508 (e)s 85.025 (b)s 90.804 (y)s 7 f 213.824 y 56.811 (I)s 59.199 (E)s 4 f 215.519 y 67.282 (\244)s 10 f 213.824 y 73.676 (f)s 7 f 79.151 (T)s 87.071 (r)s 2 f 92.315 (\050)s 7 f 96.574 (E)s 4 f 215.519 y 104.657 (\244)s 2 f 213.824 y 111.052 (\050)s 7 f 115.31 (I)s 8 f 215.467 y 120.123 (\264)s 2 f 213.824 y 125.176 (\051)s 129.434 (\051)s 10 f 133.692 (g)s 149.167 (\267)s 7 f 167.684 (I)s 170.072 (E)s 4 f 215.519 y 178.155 (\244)s 10 f 213.824 y 184.55 (f)s 7 f 190.025 (T)s 197.944 (r)s 2 f 203.189 ([)s 7 f 206.23 (\275)s 2 f 211.892 (\050)s 7 f 216.15 (H)s 4 f 215.519 y 225.252 (\244)s 10 f 213.824 y 234.08 (\241)s 7 f 245.03 (E)s 4 f 215.467 y 253.113 (0)s 10 f 213.824 y 260.297 (\241)s 2 f 271.247 (3)s 7 f 276.722 (\264)s 282.551 (=)s 2 f 288.026 (2)s 293.501 (\051)s 10 f 300.193 (\241)s 7 f 311.143 (\275)s 2 f 316.804 (\050)s 7 f 321.063 (H)s 4 f 215.519 y 330.165 (\244)s 10 f 213.824 y 338.993 (\241)s 7 f 349.943 (E)s 4 f 215.467 y 358.026 (0)s 2 f 213.824 y 365.209 (+)s 376.159 (3)s 7 f 381.634 (\264)s 387.464 (=)s 2 f 392.939 (2)s 398.414 (\051)s 402.672 (])s 10 f 405.714 (g)s 238.76 y 149.167 (\267)s 7 f 167.684 (I)s 170.072 (E)s 4 f 240.455 y 178.155 (\244)s 0 f 221.423 y 186.374 (\050)s 224.911 y 194.43 (Z)s 4 f 228.078 y 204.43 (3)s 8 f 208.68 (\264)s 213.233 (=)s 4 f 217.483 (2)s 11 f 247.634 y 199.986 (\241)s 4 f 206.597 (3)s 8 f 210.847 (\264)s 215.399 (=)s 4 f 219.649 (2)s 7 f 238.76 y 229.266 (T)s 237.186 (r)s 10 f 242.43 (f)s 247.905 (\241)s 7 f 256.422 (\275)s 11 f 234.239 y 262.083 (0)s 2 f 238.76 y 264.889 (\050)s 7 f 269.147 (H)s 4 f 240.455 y 278.249 (\244)s 10 f 238.76 y 287.077 (\241)s 7 f 298.027 (E)s 4 f 240.403 y 306.11 (0)s 10 f 238.76 y 313.294 (\241)s 7 f 324.244 (t)s 2 f 328.198 (\051)s 10 f 332.456 (g)s 7 f 340.364 (dt)s 0 f 221.423 y 350.018 (\051)s 7 f 238.76 y 359.898 (:)s 2 f 391.492 (\0503.5\051)s 268.04 y 54 (W)s 64.342 (e)s 72.966 (note)s 97.408 (that)s 121.241 (b)s 127.02 (y)s 136.557 (the)s 155.523 (sp)s 166.23 (ectral)s 196.785 (theorem,)s 242.576 (the)s 261.542 (supp)s 284.415 (ort)s 302.195 (of)s 7 f 314.774 (\275)s 11 f 264.066 y 320.436 (0)s 2 f 268.04 y 323.241 (\050)s 7 f 327.499 (x)s 2 f 333.758 (\051)s 341.774 (con)s 357.895 (tributing)s 404.267 (to)s 281.64 y 54 (the)s 73.729 (trace)s 102.005 (in)s 115.65 (\0503.5\051)s 142.679 (lies)s 162.469 (in)s 176.115 (the)s 195.843 (in)s 204.664 (terv)s 223.249 (al)s 236.286 ([)s 10 f 239.328 (\241)s 7 f 247.844 (\264)s 253.674 (=)s 2 f 259.149 (2)s 7 f 264.624 (;)s 269.491 (\264)s 275.321 (=)s 2 f 280.796 (2)s 286.271 (])s 289.313 (,)s 297.092 (and,)s 322.514 (b)s 328.293 (y)s 338.593 (c)s 343.155 (hoice)s 372.009 (of)s 7 f 385.35 (\275)s 2 f 391.012 (,)s 398.792 (the)s 295.24 y 54 (deriv)s 77.451 (ativ)s 95.701 (e)s 104.315 (is)s 115.424 (negativ)s 150.099 (e)s 158.713 (there.)s 191.277 (In)s 205.062 (order)s 233.811 (to)s 247.292 (ev)s 257.33 (aluate)s 290.277 (the)s 309.233 (trace,)s 339.802 (w)s 347.406 (e)s 356.02 (consider)s 398.792 (the)s 308.84 y 54 (op)s 65.863 (erator)s 7 f 99.313 (H)s 4 f 310.535 y 108.415 (\244)s 2 f 308.84 y 119.608 (as)s 134.2 (a)s 144.472 (function)s 188.508 (of)s 202.127 (the)s 222.133 (random)s 263.461 (coupling)s 308.409 (constan)s 344.666 (ts)s 358.041 (and)s 380.481 (rewrite)s 322.44 y 54 (di)s 63.125 (\256eren)s 89.314 (tiation)s 125.003 (with)s 150.35 (resp)s 170.212 (ect)s 188.259 (to)s 202.048 (the)s 221.311 (energy)s 7 f 256.726 (t)s 2 f 264.736 (in)s 277.916 (terms)s 308.83 (of)s 321.706 (di)s 330.831 (\256eren)s 357.02 (tiation)s 392.708 (with)s 336.04 y 54 (resp)s 73.862 (ect)s 91.605 (to)s 105.09 (the)s 124.05 (coupling)s 167.952 (constan)s 204.209 (ts)s 7 f 216.538 (\270)s 8 f 337.824 y 222.926 (k)s 7 f 336.04 y 228.065 (;)s 232.931 (k)s 10 f 242.188 (2)s 2 f 333.272 y 253.763 (\176)s 336.04 y 252.699 (\244)s 10 f 263.514 (\264)s 2 f 275.242 (\244)s 10 f 285.347 (\134)s 7 f 295.148 (Z)s 297.931 (Z)s 8 f 332.066 y 306.189 (d)s 2 f 336.04 y 311.063 (.)s 319.276 (F)s 325.512 (or)s 339.027 (this,)s 363.548 (w)s 371.152 (e)s 379.771 (use)s 398.792 (the)s 349.64 y 54 (Goh)s 73.847 (b)s 80.234 (erg-Krein)s 128.962 (form)s 150.892 (ula)s 169.142 (\050cf.)s 188.305 (Simon)s 221.763 ([27)s 235.755 (]\051)s 246.705 (giving)s 0 f 366.251 y 60.353 (X)s 8 f 390.305 y 59.475 (k)s 11 f 64.114 (2)s 4 f 388.283 y 70.603 (\176)s 390.305 y 69.781 (\244)s 7 f 375.988 y 77.785 (T)s 85.705 (r)s 0 f 361.651 y 92.774 (\275)s 7 f 368.581 y 107.237 (@)s 17.948 .4 101.474 373.451 r 383.5 y 101.474 (@)s 107.896 (\270)s 8 f 385.283 y 114.283 (k)s 7 f 375.988 y 120.622 (\275)s 2 f 126.284 (\050)s 7 f 130.542 (H)s 4 f 377.683 y 139.644 (\244)s 10 f 375.988 y 148.472 (\241)s 7 f 159.422 (E)s 4 f 377.631 y 167.505 (0)s 10 f 375.988 y 174.688 (\241)s 7 f 185.638 (t)s 2 f 189.593 (\051)s 0 f 361.651 y 193.851 (\276)s 2 f 375.988 y 204.393 (=)s 0 f 366.251 y 216.829 (X)s 8 f 390.305 y 215.951 (k)s 11 f 220.59 (2)s 4 f 388.283 y 227.079 (\176)s 390.305 y 226.257 (\244)s 7 f 375.988 y 234.261 (T)s 242.181 (r)s 0 f 361.651 y 249.25 (\275)s 7 f 375.988 y 256.75 (\275)s 11 f 371.467 y 262.411 (0)s 2 f 375.988 y 265.217 (\050)s 7 f 269.475 (H)s 4 f 377.683 y 278.577 (\244)s 10 f 375.988 y 287.405 (\241)s 7 f 298.355 (E)s 4 f 377.631 y 306.438 (0)s 10 f 375.988 y 313.622 (\241)s 7 f 324.572 (t)s 2 f 328.526 (\051)s 0 f 361.651 y 334.609 (\265)s 7 f 368.581 y 343.17 (@)s 349.592 (H)s 4 f 370.276 y 358.694 (\244)s 21.918 .4 343.17 373.451 r 7 f 383.5 y 345.156 (@)s 351.577 (\270)s 8 f 385.283 y 357.965 (k)s 0 f 361.651 y 366.289 (\266)s 373.65 (\276)s 7 f 375.988 y 382.975 (:)s 2 f 391.492 (\0503.6\051)s 408.621 y 54 (The)s 76.694 (pro)s 92.845 (of)s 105.501 (of)s 118.157 (this)s 139.695 (result)s 170.388 (is)s 181.584 (similar)s 217.752 (to)s 231.321 (the)s 250.364 (pro)s 266.515 (of)s 279.171 (in)s 292.132 ([27)s 306.123 (].)s 317.629 (It)s 329.677 (uses)s 353.1 (the)s 372.144 (fact)s 393.925 (that)s 422.221 y 54 (for)s 7 f 71.882 (g)s 10 f 82.411 (2)s 7 f 94.624 (C)s 11 f 418.248 y 103.233 (1)s 4 f 425.003 y 102.45 (0)s 2 f 422.221 y 112.233 (\050)s 7 f 116.492 (I)s 118.879 (R)s 2 f 127.278 (\051)s 131.537 (,)s 139.632 (w)s 147.236 (e)s 156.875 (ha)s 168.129 (v)s 173.604 (e)s 183.244 (that)s 208.092 (\050)s 7 f 212.35 (@)s 218.772 (H)s 4 f 423.916 y 227.874 (\244)s 7 f 422.221 y 234.268 (=)s 239.744 (@)s 246.165 (\270)s 8 f 424.005 y 252.553 (k)s 2 f 422.221 y 257.692 (\051)s 7 f 261.95 (g)s 2 f 267.566 (\050)s 7 f 271.824 (H)s 4 f 423.916 y 280.926 (\244)s 2 f 422.221 y 287.321 (\051)s 296.352 (is)s 308.485 (trace)s 337.014 (class,)s 367.131 (as)s 381.697 (follo)s 401.773 (ws)s 435.821 y 54 (from)s 80.453 (Prop)s 104.056 (osition)s 139.969 (5.1.)s 163.574 (W)s 173.916 (e)s 183.001 (use)s 202.488 (the)s 221.915 (expansion)s 273.34 (in)s 286.684 (\0503.3\051)s 313.41 (to)s 327.362 (ev)s 337.4 (aluate)s 370.818 (the)s 390.245 (trace)s 449.421 y 54 (on)s 69.208 (the)s 88.067 (righ)s 106.651 (t)s 114.56 (in)s 127.335 (\0503.6\051)s 153.493 (and)s 174.785 (write)s 7 f 475.77 y 59.766 (T)s 67.685 (r)s 0 f 461.432 y 74.755 (\275)s 7 f 475.77 y 82.255 (\275)s 11 f 471.249 y 87.916 (0)s 2 f 475.77 y 90.722 (\050)s 7 f 94.98 (H)s 4 f 477.465 y 104.082 (\244)s 10 f 475.77 y 112.91 (\241)s 7 f 123.86 (E)s 4 f 477.412 y 131.943 (0)s 10 f 475.77 y 139.127 (\241)s 7 f 150.077 (t)s 2 f 154.031 (\051)s 0 f 461.432 y 160.114 (\265)s 7 f 468.362 y 168.675 (@)s 175.097 (H)s 4 f 470.057 y 184.199 (\244)s 21.918 .4 168.675 473.232 r 7 f 483.281 y 170.66 (@)s 177.082 (\270)s 8 f 485.065 y 183.47 (k)s 0 f 461.432 y 191.794 (\266)s 199.155 (\276)s 2 f 475.77 y 209.696 (=)s 0 f 466.032 y 221.255 (X)s 8 f 487.988 y 226.528 (j)s 7 f 475.77 y 237.524 (\275)s 11 f 471.249 y 243.185 (0)s 2 f 475.77 y 245.991 (\050)s 7 f 250.249 (E)s 8 f 477.412 y 258.333 (j)s 2 f 475.77 y 262.731 (\050)s 266.99 (\244)s 274.594 (\051)s 10 f 281.285 (\241)s 7 f 292.235 (E)s 4 f 477.412 y 300.319 (0)s 10 f 475.77 y 307.502 (\241)s 7 f 318.452 (t)s 2 f 322.406 (\051)s 10 f 329.098 (h)s 7 f 333.356 (\301)s 8 f 477.412 y 339.88 (j)s 7 f 475.77 y 344.279 (;)s 0 f 461.432 y 349.146 (\265)s 7 f 468.362 y 357.707 (@)s 364.128 (H)s 4 f 470.057 y 373.231 (\244)s 21.918 .4 357.707 473.232 r 7 f 483.281 y 359.692 (@)s 366.114 (\270)s 8 f 485.065 y 372.501 (k)s 0 f 461.432 y 380.825 (\266)s 7 f 475.77 y 390.011 (\301)s 8 f 477.412 y 396.536 (j)s 10 f 475.77 y 400.934 (i)s 7 f 405.193 (;)s 2 f 499.756 y 391.492 (\0503.7\051)s 513.356 y 54 (where,)s 89.086 (as)s 102.835 (ab)s 114.698 (o)s 119.869 (v)s 125.344 (e,)s 137.283 (the)s 156.446 (the)s 175.609 (compactness)s 239.302 (of)s 252.078 (the)s 271.241 (supp)s 294.114 (ort)s 312.091 (of)s 7 f 324.866 (\275)s 11 f 509.382 y 330.528 (0)s 2 f 513.356 y 337.288 (implies)s 374.762 (that)s 398.792 (the)s 526.956 y 54 (sum)s 76.464 (is)s 86.762 (\257nite)s 114.032 (and)s 134.61 (o)s 139.781 (v)s 145.256 (er)s 157.348 (the)s 175.493 (eigen)s 199.522 (v)s 204.693 (alues)s 231.416 (of)s 7 f 243.173 (H)s 4 f 528.651 y 252.275 (\244)s 2 f 526.956 y 261.606 (in)s 273.668 (the)s 291.813 (in)s 300.634 (terv)s 319.219 (al)s 330.672 ([)s 7 f 333.714 (E)s 4 f 528.598 y 341.797 (0)s 10 f 526.956 y 347.554 (\241)s 2 f 357.077 (2)s 7 f 362.552 (\264)s 368.382 (;)s 373.248 (E)s 4 f 528.598 y 381.332 (0)s 2 f 526.956 y 387.088 (+)s 396.612 (2)s 7 f 402.087 (\264)s 2 f 407.917 (])s 410.958 (,)s 540.556 y 54 (including)s 102.33 (m)s 111.151 (ultiplicit)s 151.605 (y)s 156.472 (,)s 164.264 (with)s 190.085 (normalized)s 246.962 (eigenfunctions)s 7 f 319.383 (\301)s 8 f 542.198 y 325.907 (j)s 2 f 540.556 y 330.306 (.)s 340.854 (F)s 347.089 (or)s 361.383 (the)s 381.122 (case)s 405.179 (of)s 554.156 y 54 (additiv)s 87.458 (e)s 95.835 (p)s 102.222 (erturbations,)s 167.323 (the)s 186.041 (exp)s 203.074 (ectation)s 244.909 (of)s 257.239 (the)s 275.957 (deriv)s 299.409 (ativ)s 317.659 (e)s 326.035 (of)s 7 f 338.365 (H)s 4 f 555.851 y 347.467 (\244)s 2 f 554.156 y 357.371 (on)s 372.439 (the)s 391.157 (righ)s 409.742 (t)s 567.756 y 54 (side)s 75.961 (of)s 88.432 (\0503.7\051)s 114.59 (is)s 125.601 (equal)s 154.497 (to)s 10 f 586.505 y 195.789 (h)s 7 f 200.047 (\301)s 8 f 588.148 y 206.572 (j)s 7 f 586.505 y 210.97 (;)s 0 f 572.168 y 215.837 (\265)s 7 f 579.097 y 224.398 (@)s 230.82 (V)s 4 f 580.792 y 237.207 (\244)s 19.204 .4 224.398 583.968 r 7 f 594.016 y 225.026 (@)s 231.448 (\270)s 8 f 595.8 y 237.835 (k)s 0 f 572.168 y 244.802 (\266)s 7 f 586.505 y 253.988 (\301)s 8 f 588.148 y 260.512 (j)s 10 f 586.505 y 264.911 (i)s 7 f 269.169 (;)s 2 f 621.8 y 228.525 (12)s do-end end endp showpage %%PageTrailer %%Page: 14 14 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 14 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f253 sf ( )S -955 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (and)s 75.292 (for)s 92.051 (m)s 100.872 (ultiplicativ)s 152.581 (e)s 161.097 (p)s 167.485 (erturbations,)s 232.698 (it)s 243.648 (is)s 254.659 (equal)s 283.555 (to)s 10 f 102.844 y 170.03 (h)s 7 f 174.288 (\301)s 8 f 104.486 y 180.813 (j)s 7 f 102.844 y 185.211 (;)s 0 f 88.506 y 190.078 (\265)s 7 f 95.436 y 198.639 (@)s 205.061 (V)s 4 f 97.131 y 211.448 (\244)s 19.204 .4 198.639 100.306 r 7 f 110.355 y 199.267 (@)s 205.689 (\270)s 8 f 112.139 y 212.076 (k)s 0 f 88.506 y 219.043 (\266)s 2 f 102.844 y 228.229 (\050)s 232.487 (1)s 240.395 (+)s 7 f 251.345 (V)s 4 f 104.539 y 257.733 (\244)s 2 f 102.844 y 264.128 (\051)s 11 f 98.323 y 268.386 (\241)s 4 f 274.997 (1)s 7 f 102.844 y 279.747 (\301)s 8 f 104.486 y 286.272 (j)s 10 f 102.844 y 290.67 (i)s 7 f 294.928 (:)s 2 f 130.446 y 54 (W)s 64.342 (e)s 72.594 (recall)s 101.56 (that)s 125.02 (it)s 135.705 (follo)s 155.78 (ws)s 171.393 (from)s 197.013 (the)s 215.607 (h)s 221.386 (yp)s 233.553 (otheses)s 271.127 (in)s 283.637 (the)s 302.231 (m)s 311.052 (ultiplicativ)s 362.76 (e)s 371.012 (case)s 393.925 (that)s 144.046 y 54 (\050)s 58.258 (1)s 66.196 (+)s 7 f 77.175 (V)s 4 f 145.741 y 83.563 (\244)s 2 f 144.046 y 89.957 (\051)s 7 f 97.331 (\076)s 108.962 (C)s 4 f 145.688 y 116.788 (1)s 7 f 144.046 y 124.653 (\076)s 2 f 136.285 (0)s 141.76 (,)s 148.507 (for)s 165.31 (some)s 192.79 (constan)s 229.047 (t)s 7 f 236.999 (C)s 4 f 145.688 y 244.825 (1)s 2 f 144.046 y 249.575 (.)s 257.616 (Hence,)s 293.258 (in)s 306.077 (the)s 324.979 (next)s 349.661 (step,)s 375.935 (w)s 383.539 (e)s 392.1 (need)s 157.646 y 54 (to)s 67.383 (estimate)s 111.244 (the)s 130.103 (sum)s 0 f 163.92 y 188.871 (X)s 8 f 187.974 y 187.993 (k)s 11 f 192.632 (2)s 4 f 185.952 y 199.121 (\176)s 187.974 y 198.299 (\244)s 10 f 173.658 y 206.627 (h)s 7 f 210.885 (\301)s 8 f 175.3 y 217.409 (j)s 7 f 173.658 y 221.808 (;)s 0 f 159.32 y 226.675 (\265)s 7 f 166.25 y 235.236 (@)s 241.657 (V)s 4 f 167.945 y 248.045 (\244)s 19.204 .4 235.236 171.12 r 7 f 181.169 y 235.864 (@)s 242.285 (\270)s 8 f 182.953 y 248.673 (k)s 0 f 159.32 y 255.639 (\266)s 7 f 173.658 y 264.826 (\301)s 8 f 175.3 y 271.35 (j)s 10 f 173.658 y 275.749 (i)s 2 f 204.749 y 54 (from)s 79.641 (b)s 86.029 (elo)s 99.108 (w)s 110.423 (so)s 123.624 (w)s 131.228 (e)s 139.502 (can)s 159.333 (solv)s 177.644 (e)s 185.918 (\0503.7\051)s 211.833 (for)s 228.349 (an)s 243.314 (upp)s 261.868 (er)s 274.431 (b)s 280.818 (ound)s 307.95 (on)s 10 f 322.915 (\241)s 7 f 331.432 (T)s 339.352 (r)s 10 f 344.596 (f)s 7 f 350.071 (\275)s 11 f 200.775 y 355.732 (0)s 2 f 204.749 y 358.538 (\050)s 7 f 362.796 (H)s 4 f 206.444 y 371.898 (\244)s 10 f 204.749 y 380.24 (\241)s 7 f 390.703 (E)s 4 f 206.391 y 398.786 (0)s 10 f 204.749 y 405.483 (\241)s 7 f 218.349 y 54 (t)s 2 f 57.954 (\051)s 10 f 62.213 (g)s 73.237 (\270)s 2 f 87.303 (0)s 92.778 (.)s 105.201 (The)s 129.214 (Anderson-t)s 182.23 (yp)s 194.397 (e)s 204.418 (p)s 210.806 (oten)s 231.185 (tial)s 252.156 (dep)s 269.494 (ends)s 296.001 (linearly)s 336.774 (on)s 353.487 (the)s 373.85 (coupling)s 231.949 y 54 (constan)s 90.257 (ts)s 102.484 (so)s 115.928 (that)s 7 f 240.553 y 209.874 (@)s 216.295 (V)s 4 f 242.248 y 222.683 (\244)s 19.204 .4 209.874 245.423 r 7 f 255.472 y 210.501 (@)s 216.923 (\270)s 8 f 257.256 y 223.311 (k)s 2 f 247.961 y 233.319 (=)s 7 f 244.877 (u)s 8 f 249.745 y 251.146 (k)s 7 f 247.961 y 256.285 (:)s 2 f 391.492 (\0503.8\051)s 271.711 y 54 (F)s 60.235 (or)s 73.649 (the)s 92.508 (breather-t)s 140.323 (yp)s 152.489 (e)s 161.006 (mo)s 175.91 (del,)s 196.593 (the)s 215.452 (deriv)s 238.903 (ativ)s 257.153 (e)s 265.67 (is)s 7 f 292.147 y 149.269 (@)s 155.691 (V)s 4 f 293.842 y 162.078 (\244)s 19.204 .4 149.269 297.018 r 7 f 307.066 y 149.897 (@)s 156.319 (\270)s 8 f 308.85 y 162.706 (k)s 2 f 299.555 y 172.715 (=)s 184.273 (\050)s 7 f 188.531 (x)s 10 f 197.223 (\241)s 7 f 208.173 (k)s 2 f 214.218 (\051)s 10 f 220.91 (\242)s 226.385 (r)s 7 f 235.51 (u)s 8 f 301.339 y 241.778 (k)s 2 f 299.555 y 246.917 (\050)s 7 f 251.175 (\270)s 8 f 301.339 y 257.563 (k)s 2 f 299.555 y 262.702 (\050)s 7 f 266.96 (!)s 2 f 274.169 (\051)s 278.427 (\050)s 7 f 282.686 (x)s 10 f 291.377 (\241)s 7 f 302.327 (k)s 2 f 308.372 (\051)s 312.631 (\051)s 7 f 316.889 (:)s 2 f 391.492 (\0503.9\051)s 327.157 y 54 (It)s 64.792 (follo)s 84.867 (ws)s 99.674 (from)s 124.487 (this)s 144.769 (that)s 167.423 (for)s 183.112 (the)s 200.9 (Anderson-t)s 253.916 (yp)s 266.083 (e)s 273.529 (p)s 279.916 (oten)s 300.295 (tial,)s 321.947 (w)s 329.551 (e)s 336.997 (need)s 361.477 (to)s 373.789 (estimate)s 340.757 y 54 (from)s 79.885 (b)s 86.272 (elo)s 99.351 (w)s 110.91 (the)s 129.768 (sum)s 0 f 344.62 y 201.939 (X)s 8 f 368.674 y 201.061 (k)s 11 f 205.7 (2)s 4 f 366.652 y 212.189 (\176)s 368.674 y 211.366 (\244)s 10 f 354.357 y 217.261 (h)s 7 f 221.519 (\301)s 8 f 356 y 228.044 (j)s 7 f 354.357 y 232.442 (;)s 237.309 (u)s 8 f 356.141 y 243.577 (k)s 7 f 354.357 y 248.716 (\301)s 8 f 356 y 255.241 (j)s 10 f 354.357 y 259.639 (i)s 7 f 263.898 (;)s 2 f 386.017 (\0503.10\051)s 384.634 y 54 (and,)s 78.333 (for)s 95.093 (the)s 113.951 (breather-t)s 161.766 (yp)s 173.933 (e)s 182.45 (p)s 188.837 (oten)s 209.216 (tial,)s 231.725 (the)s 250.583 (sum)s 10 f 407.937 y 135.285 (\241)s 0 f 398.2 y 146.505 (X)s 8 f 422.254 y 145.627 (k)s 11 f 150.266 (2)s 4 f 420.231 y 156.755 (\176)s 422.254 y 155.933 (\244)s 10 f 407.937 y 161.827 (h)s 7 f 166.086 (\301)s 8 f 409.58 y 172.61 (j)s 7 f 407.937 y 177.009 (;)s 2 f 181.875 (\050)s 7 f 186.134 (x)s 10 f 194.825 (\241)s 7 f 205.775 (k)s 2 f 211.82 (\051)s 10 f 218.512 (\242)s 223.987 (r)s 7 f 233.112 (u)s 8 f 409.721 y 239.38 (k)s 2 f 407.937 y 244.519 (\050)s 7 f 248.778 (\270)s 8 f 409.721 y 255.165 (k)s 2 f 407.937 y 260.304 (\050)s 7 f 264.563 (!)s 2 f 271.771 (\051)s 276.03 (\050)s 7 f 280.288 (x)s 10 f 288.98 (\241)s 7 f 299.93 (k)s 2 f 305.975 (\051)s 310.233 (\051)s 7 f 314.492 (\301)s 8 f 409.58 y 321.016 (j)s 10 f 407.937 y 325.415 (i)s 7 f 329.673 (:)s 2 f 386.017 (\0503.11\051)s 444.542 y 54 (In)s 66.471 (ligh)s 83.808 (t)s 90.5 (of)s 101.754 (\0503.10\051)s 129.738 (\173\0503.11\051,)s 168.914 (w)s 176.518 (e)s 183.818 (de)s 194.768 (\257)s 200.852 (ne)s 214.235 (an)s 228.227 (auxiliary)s 272.666 (p)s 279.053 (oten)s 299.432 (tial)s 441.774 y 319.355 (\176)s 7 f 444.542 y 317.682 (V)s 4 f 446.237 y 324.07 (\244)s 2 f 444.542 y 332.898 (for)s 348.441 (the)s 366.082 (Anderson-)s 458.142 y 54 (t)s 57.954 (yp)s 70.121 (e)s 78.638 (mo)s 93.542 (del)s 111.183 (b)s 116.963 (y)s 473.516 y 146.754 (\176)s 7 f 476.283 y 145.081 (V)s 4 f 477.978 y 151.468 (\244)s 2 f 476.283 y 157.863 (\050)s 7 f 162.121 (x)s 2 f 168.379 (\051)s 10 f 175.679 (\264)s 0 f 466.546 y 188.116 (X)s 8 f 490.6 y 187.238 (k)s 11 f 191.877 (2)s 4 f 488.578 y 198.366 (\176)s 490.6 y 197.543 (\244)s 7 f 468.876 y 206.463 (@)s 212.885 (V)s 4 f 470.571 y 219.272 (\244)s 19.204 .4 206.463 473.746 r 7 f 483.795 y 207.091 (@)s 213.512 (\270)s 8 f 485.579 y 219.9 (k)s 2 f 476.283 y 226.867 (\050)s 7 f 231.125 (x)s 2 f 237.383 (\051)s 244.683 (=)s 0 f 466.546 y 257.119 (X)s 8 f 490.6 y 256.241 (k)s 11 f 260.88 (2)s 4 f 488.578 y 267.369 (\176)s 490.6 y 266.547 (\244)s 7 f 476.283 y 274.267 (u)s 8 f 478.067 y 280.535 (k)s 2 f 476.283 y 285.674 (\050)s 7 f 289.932 (x)s 10 f 298.624 (\241)s 7 f 309.574 (k)s 2 f 315.619 (\051)s 7 f 319.878 (;)s 2 f 386.017 (\0503.12\051)s 506.561 y 54 (and,)s 78.333 (for)s 95.093 (the)s 113.951 (breather-t)s 161.766 (yp)s 173.933 (e)s 182.45 (mo)s 197.354 (del,)s 527.095 y 138.665 (\176)s 7 f 529.863 y 136.993 (V)s 4 f 531.558 y 143.38 (\244)s 2 f 529.863 y 149.775 (\050)s 7 f 154.033 (x)s 2 f 160.291 (\051)s 10 f 167.591 (\264)s 0 f 520.126 y 180.027 (X)s 8 f 544.18 y 179.149 (k)s 11 f 183.788 (2)s 4 f 542.158 y 190.277 (\176)s 544.18 y 189.455 (\244)s 2 f 529.863 y 195.35 (\050)s 7 f 199.608 (x)s 10 f 208.299 (\241)s 7 f 219.249 (k)s 2 f 225.295 (\051)s 10 f 231.986 (\242)s 237.461 (r)s 7 f 246.586 (u)s 8 f 531.647 y 252.855 (k)s 2 f 529.863 y 257.994 (\050)s 7 f 262.252 (\270)s 8 f 531.647 y 268.64 (k)s 2 f 529.863 y 273.779 (\050)s 7 f 278.037 (!)s 2 f 285.246 (\051)s 289.504 (\050)s 7 f 293.762 (x)s 10 f 302.454 (\241)s 7 f 313.404 (k)s 2 f 319.449 (\051\051)s 7 f 327.966 (:)s 2 f 386.017 (\0503.13\051)s 564.6 y 54 (W)s 64.342 (e)s 73.348 (note)s 98.172 (that)s 122.387 (b)s 128.166 (y)s 138.085 (\050H3\051)s 164.429 (and)s 186.211 (\050H4\051)s 212.555 (there)s 241.059 (exists)s 271.783 (a)s 281.399 (\257nite)s 309.872 (constan)s 346.129 (t)s 7 f 354.527 (C)s 4 f 566.243 y 362.353 (1)s 7 f 564.6 y 370.962 (\076)s 2 f 383.337 (0)s 392.952 (suc)s 407.917 (h)s 578.2 y 54 (that)s 10 f 591.8 y 185.251 (j)s 7 f 188.292 (V)s 4 f 593.495 y 194.68 (\244)s 2 f 591.8 y 201.074 (\050)s 7 f 205.333 (x)s 2 f 211.591 (\051)s 10 f 215.849 (j)s 221.933 (\267)s 7 f 233.491 (C)s 4 f 593.443 y 241.317 (1)s 10 f 591.8 y 246.067 (j)s 2 f 589.032 y 250.782 (\176)s 7 f 591.8 y 249.109 (V)s 4 f 593.495 y 255.496 (\244)s 2 f 591.8 y 261.891 (\050)s 7 f 266.149 (x)s 2 f 272.408 (\051)s 10 f 276.666 (j)s 7 f 279.708 (;)s 2 f 386.017 (\0503.14\051)s 621.8 y 228.525 (13)s do-end end endp showpage %%PageTrailer %%Page: 15 15 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 15 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f253 sf ( )S -955 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (for)s 70.76 (an)s 82.014 (y)s 7 f 91.443 (x)s 10 f 100.743 (2)s 7 f 111.084 (I)s 113.472 (R)s 8 f 71.026 y 121.871 (d)s 2 f 75 y 126.745 (,)s 133.436 (and)s 154.728 (for)s 171.487 (an)s 182.742 (y)s 192.171 (subset)s 225.751 (\244)s 10 f 236.397 (\275)s 7 f 247.955 (I)s 250.343 (R)s 8 f 71.026 y 258.741 (d)s 2 f 75 y 263.615 (.)s 95.827 y 54 (4.)s 69.354 (W)s 79.696 (e)s 88.869 (estimate)s 133.387 (from)s 159.928 (b)s 166.316 (elo)s 179.395 (w)s 191.61 (the)s 211.126 (quan)s 234.242 (tit)s 245.496 (y)s 10 f 255.583 (h)s 7 f 259.841 (\301)s 8 f 97.47 y 266.365 (j)s 7 f 95.827 y 270.764 (;)s 2 f 93.06 y 277.303 (\176)s 7 f 95.827 y 275.631 (V)s 4 f 97.522 y 282.018 (\244)s 7 f 95.827 y 288.413 (\301)s 8 f 97.47 y 294.937 (j)s 10 f 95.827 y 299.336 (i)s 2 f 307.901 (using)s 337.21 (the)s 356.725 (Comparison)s 109.427 y 54 (Theorem)s 101.371 (of)s 114.949 (Kirsc)s 139.678 (h,)s 153.837 (Stollmann,)s 210.58 (and)s 232.979 (Stolz)s 261.461 (\050KSS\051)s 295.417 ([19)s 309.409 (])s 317.208 (pro)s 332.751 (v)s 338.226 (ed)s 353.933 (in)s 367.815 (section)s 405.483 (4.)s 123.027 y 54 (Referring)s 103.224 (to)s 117.864 (Theorem)s 165.384 (4.3,)s 187.638 (w)s 195.242 (e)s 205.015 (m)s 213.836 (ust)s 233.404 (construct)s 282.81 (a)s 293.191 (comparison)s 352.331 (p)s 358.718 (oten)s 379.097 (tial)s 7 f 399.821 (V)s 4 f 124.67 y 406.208 (0)s 2 f 123.027 y 410.958 (.)s 136.627 y 54 (W)s 64.342 (e)s 72.858 (do)s 88.067 (this)s 109.419 (as)s 122.863 (follo)s 142.938 (ws.)s 163.074 (W)s 173.416 (e)s 181.933 (c)s 186.495 (ho)s 198.358 (ose)s 216.668 (some)s 244.104 (0)s 7 f 252.621 (\074)s 264.179 (\262)s 4 f 138.27 y 268.624 (2)s 2 f 136.627 y 277.024 (so)s 290.468 (small)s 319.121 (that)s 161.227 y 137.496 ([)s 7 f 140.538 (E)s 4 f 162.87 y 148.621 (0)s 10 f 161.227 y 155.805 (\241)s 2 f 166.755 (2)s 7 f 172.23 (\264)s 178.059 (;)s 182.926 (E)s 4 f 162.87 y 191.009 (0)s 2 f 161.227 y 198.193 (+)s 209.143 (2)s 7 f 214.618 (\264)s 2 f 220.447 (])s 10 f 226.531 (\275)s 2 f 238.089 (\050)s 7 f 242.347 (B)s 11 f 162.87 y 250.653 (\241)s 2 f 161.227 y 260.198 (+)s 7 f 271.148 (\262)s 4 f 162.87 y 275.592 (2)s 7 f 161.227 y 280.342 (;)s 285.209 (B)s 4 f 162.87 y 293.515 (+)s 10 f 161.227 y 303.059 (\241)s 7 f 314.009 (\262)s 4 f 162.87 y 318.454 (2)s 2 f 161.227 y 323.204 (\051)s 7 f 327.462 (;)s 2 f 386.017 (\0503.15\051)s 185.827 y 54 (and)s 75.254 (so)s 88.661 (that,)s 115.398 (for)s 132.12 (the)s 150.941 (breather-t)s 198.756 (yp)s 210.923 (e)s 219.402 (mo)s 234.307 (del,)s 7 f 254.96 (\262)s 4 f 187.47 y 259.405 (2)s 7 f 185.827 y 264.155 (=)s 269.63 (C)s 4 f 187.47 y 277.456 (1)s 10 f 185.827 y 285.248 (\267)s 7 f 296.806 (\261)s 2 f 302.087 (,)s 308.749 (with)s 7 f 333.653 (\261)s 2 f 342.547 (as)s 355.954 (in)s 368.692 (\050H3\051.)s 398.792 (W)s 409.133 (e)s 199.427 y 54 (set)s 10 f 213.027 y 156.31 (D)s 2 f 168.102 (=)s 0 f 201.69 y 179.661 (n)s 7 f 213.027 y 186.327 (x)s 10 f 195.627 (2)s 7 f 205.969 (I)s 208.357 (R)s 8 f 208.506 y 216.755 (d)s 10 f 213.027 y 224.671 (j)s 2 f 210.26 y 232.427 (\176)s 7 f 213.027 y 230.754 (V)s 4 f 214.722 y 237.141 (\244)s 2 f 213.027 y 243.536 (\050)s 7 f 247.794 (x)s 2 f 254.053 (\051)s 10 f 261.352 (\270)s 7 f 272.911 (\262)s 4 f 214.67 y 277.355 (2)s 7 f 213.027 y 282.106 (=)s 287.581 (C)s 4 f 214.67 y 295.407 (1)s 0 f 201.69 y 300.157 (o)s 7 f 213.027 y 308.648 (;)s 2 f 386.017 (\0503.16\051)s 234.394 y 54 (and)s 75.292 (w)s 82.896 (e)s 91.413 (de)s 102.363 (\257ne)s 123.046 (the)s 141.904 (comparison)s 199.787 (p)s 206.175 (oten)s 226.554 (tial)s 7 f 246.021 (V)s 4 f 236.037 y 252.408 (0)s 2 f 234.394 y 260.808 (b)s 266.587 (y)s 7 f 258.994 y 167.124 (V)s 4 f 260.637 y 173.511 (0)s 2 f 258.994 y 178.261 (\050)s 7 f 182.519 (x)s 2 f 188.778 (\051)s 203.036 (=)s 7 f 221.553 (V)s 4 f 260.689 y 227.94 (\244)s 2 f 258.994 y 234.335 (\050)s 7 f 238.593 (x)s 2 f 244.851 (\051)s 252.151 (for)s 7 f 268.303 (x)s 10 f 277.602 (2)s 287.944 (D)s 8 f 254.473 y 296.695 (c)s 2 f 275.594 y 203.036 (=)s 221.553 (0)s 230.069 (for)s 7 f 246.221 (x)s 10 f 255.52 (2)s 265.862 (D)s 7 f 274.613 (:)s 2 f 386.017 (\0503.17\051)s 300.194 y 54 (W)s 64.342 (e)s 72.603 (then)s 97.29 (ha)s 108.544 (v)s 114.019 (e)s 122.281 (that)s 10 f 145.751 (j)s 7 f 148.793 (V)s 4 f 301.889 y 155.181 (\244)s 2 f 300.194 y 161.575 (\050)s 7 f 165.833 (x)s 2 f 172.092 (\051)s 10 f 176.35 (j)s 182.433 (\267)s 7 f 193.992 (\262)s 4 f 301.837 y 198.436 (2)s 2 f 300.194 y 203.186 (,)s 209.674 (and)s 230.711 (hence)s 260.873 ([)s 7 f 263.914 (E)s 4 f 301.837 y 271.998 (0)s 10 f 300.194 y 278.671 (\241)s 2 f 289.112 (2)s 7 f 294.587 (\264)s 300.416 (;)s 305.283 (E)s 4 f 301.837 y 313.366 (0)s 2 f 300.194 y 320.04 (+)s 330.48 (2)s 7 f 335.955 (\264)s 2 f 341.785 (])s 10 f 347.868 (\275)s 7 f 359.427 (\275)s 2 f 365.088 (\050)s 7 f 369.346 (H)s 4 f 301.837 y 378.449 (0)s 2 f 300.194 y 385.122 (+)s 7 f 395.562 (V)s 4 f 301.837 y 401.95 (0)s 2 f 300.194 y 406.7 (\051)s 410.958 (.)s 313.794 y 54 (Let)s 73.619 (0)s 7 f 82.135 (\074)s 93.694 (\262)s 4 f 315.437 y 98.138 (1)s 7 f 313.794 y 105.93 (\074)s 117.488 (\262)s 4 f 315.437 y 121.933 (2)s 7 f 313.794 y 126.683 (=)s 132.158 (C)s 4 f 315.437 y 139.984 (1)s 2 f 313.794 y 144.734 (,)s 151.426 (and)s 172.718 (w)s 180.322 (e)s 188.838 (set)s 7 f 340.269 y 165.43 (F)s 2 f 177.034 (=)s 0 f 328.932 y 188.592 (n)s 7 f 340.269 y 195.259 (x)s 10 f 204.559 (2)s 7 f 214.9 (I)s 217.288 (R)s 8 f 335.748 y 225.687 (d)s 10 f 340.269 y 233.602 (j)s 2 f 337.501 y 241.358 (\176)s 7 f 340.269 y 239.685 (V)s 4 f 341.964 y 246.073 (\244)s 2 f 340.269 y 252.467 (\050)s 7 f 256.726 (x)s 2 f 262.984 (\051)s 10 f 270.284 (\267)s 7 f 281.842 (\262)s 4 f 341.912 y 286.287 (1)s 0 f 328.932 y 291.037 (o)s 7 f 340.269 y 299.528 (:)s 2 f 386.017 (\0503.18\051)s 366.744 y 54 (By)s 70.939 (the)s 89.551 (equicon)s 125.443 (tin)s 138.522 (uit)s 151.601 (y)s 160.784 (assumption)s 218.451 (\050H3\051,)s 247.15 (there)s 274.917 (exists)s 304.905 (a)s 313.783 (\257nite)s 341.52 (constan)s 377.777 (t)s 7 f 385.439 (\265)s 393.925 (\076)s 2 f 405.483 (0)s 410.958 (,)s 380.344 y 54 (indep)s 80.463 (enden)s 108.142 (t)s 116.05 (of)s 128.521 (\244)s 136.125 (,)s 142.817 (so)s 156.261 (that)s 404.944 y 188.22 (dist)s 205.922 (\050)s 10 f 210.181 (D)s 7 f 218.932 (;)s 223.798 (F)s 2 f 232.361 (\051)s 10 f 239.661 (\270)s 7 f 251.219 (\265)s 259.705 (\076)s 2 f 271.263 (0)s 7 f 276.738 (:)s 2 f 386.017 (\0503.19\051)s 429.544 y 54 (Theorem)s 100.264 (4.3)s 117.905 (then)s 142.847 (implies)s 180.016 (that)s 10 f 454.144 y 152.881 (h)s 7 f 157.139 (\301)s 8 f 455.787 y 163.664 (j)s 7 f 454.144 y 168.062 (;)s 2 f 451.377 y 174.602 (\176)s 7 f 454.144 y 172.929 (V)s 4 f 455.839 y 179.316 (\244)s 7 f 454.144 y 185.711 (\301)s 8 f 455.787 y 192.235 (j)s 10 f 454.144 y 196.634 (i)s 210.892 (\270)s 7 f 229.409 (\262)s 4 f 455.787 y 233.854 (1)s 10 f 454.144 y 238.604 (h)s 7 f 242.862 (\301)s 8 f 455.787 y 249.386 (j)s 7 f 454.144 y 253.785 (;)s 2 f 258.652 (\050)s 262.91 (1)s 10 f 270.818 (\241)s 7 f 281.768 (\302)s 8 f 455.839 y 288.62 (F)s 2 f 454.144 y 295.679 (\051)s 7 f 299.938 (\301)s 8 f 455.787 y 306.462 (j)s 10 f 454.144 y 310.861 (i)s 470.744 y 210.892 (\270)s 2 f 229.409 (\050)s 7 f 233.667 (\262)s 4 f 472.387 y 238.112 (1)s 7 f 470.744 y 242.862 (=)s 248.337 (C)s 4 f 472.387 y 256.163 (2)s 2 f 470.744 y 260.913 (\051)s 10 f 265.172 (k)s 7 f 270.647 (\301)s 8 f 472.387 y 277.171 (j)s 10 f 470.744 y 281.57 (k)s 4 f 466.223 y 287.045 (2)s 7 f 470.744 y 291.795 (;)s 2 f 386.017 (\0503.20\051)s 495.344 y 54 (for)s 71.486 (a)s 81.338 (\257nite)s 110.049 (constan)s 146.305 (t)s 7 f 154.94 (C)s 4 f 496.987 y 162.767 (2)s 7 f 495.344 y 171.77 (\076)s 2 f 184.539 (0)s 194.391 (that)s 218.843 (is)s 230.581 (indep)s 257.043 (enden)s 284.723 (t)s 293.358 (of)s 306.556 (\244)s 318.537 (and)s 7 f 340.555 (j)s 2 f 345.691 (,)s 353.291 (and)s 375.31 (dep)s 392.648 (ends)s 508.944 y 54 (only)s 78.029 (on)s 7 f 93.238 (\264)s 99.067 (;)s 103.934 (\265)s 109.379 (;)s 2 f 116.07 (and)s 7 f 137.362 (H)s 4 f 510.587 y 146.464 (0)s 2 f 508.944 y 151.214 (.)s 529.772 y 54 (5.)s 67.383 (Returning)s 119.274 (to)s 132.658 (\0503.6\051)s 155.166 (\173\0503.7\051,)s 189.841 (w)s 197.445 (e)s 205.962 (ha)s 217.216 (v)s 222.691 (e)s 231.208 (the)s 250.066 (lo)s 258.279 (w)s 265.883 (er)s 278.688 (b)s 285.076 (ound,)s 0 f 549.784 y 174.979 (X)s 8 f 573.838 y 174.101 (k)s 11 f 178.74 (2)s 4 f 571.816 y 185.229 (\176)s 573.838 y 184.407 (\244)s 10 f 559.521 y 190.301 (h)s 7 f 194.559 (\301)s 8 f 561.164 y 201.084 (j)s 7 f 559.521 y 205.482 (;)s 0 f 545.184 y 210.349 (\265)s 7 f 552.114 y 218.91 (@)s 225.332 (V)s 4 f 553.809 y 231.719 (\244)s 19.204 .4 218.91 556.984 r 7 f 567.032 y 219.538 (@)s 225.96 (\270)s 8 f 568.816 y 232.347 (k)s 0 f 545.184 y 239.314 (\266)s 7 f 559.521 y 248.5 (\301)s 8 f 561.164 y 255.024 (j)s 10 f 559.521 y 259.423 (i)s 266.723 (\270)s 7 f 278.281 (C)s 4 f 561.164 y 286.107 (0)s 7 f 559.521 y 290.858 (;)s 2 f 386.017 (\0503.21\051)s 621.8 y 228.525 (14)s do-end end endp showpage %%PageTrailer %%Page: 16 16 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 16 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f253 sf ( )S -955 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (uniformly)s 103.914 (in)s 7 f 116.689 (j)s 2 f 121.825 (,)s 128.517 (so)s 141.961 (w)s 149.565 (e)s 158.082 (obtain)s 192.148 (from)s 218.033 (\0503.6\051)s 240.541 (\173\0503.7\051,)s 10 f 99.6 y 88.229 (\241)s 7 f 96.746 (T)s 104.665 (r)s 10 f 109.91 (f)s 7 f 115.385 (\275)s 11 f 95.079 y 121.046 (0)s 2 f 99.6 y 123.852 (\050)s 7 f 128.11 (H)s 4 f 101.295 y 137.212 (\244)s 10 f 99.6 y 146.04 (\241)s 7 f 156.99 (E)s 4 f 101.242 y 165.073 (0)s 10 f 99.6 y 172.257 (\241)s 7 f 183.207 (t)s 2 f 187.161 (\051)s 10 f 191.419 (g)s 121.349 y 98.229 (\267)s 113.942 y 117.946 (\241)s 2 f 126.462 (1)s 13.992 .4 117.946 118.812 r 7 f 128.861 y 118.653 (C)s 4 f 130.503 y 126.48 (0)s 0 f 111.612 y 135.84 (X)s 8 f 135.666 y 134.962 (k)s 11 f 139.601 (2)s 4 f 133.644 y 146.09 (\176)s 135.666 y 145.268 (\244)s 7 f 121.349 y 155.421 (T)s 163.341 (r)s 0 f 107.012 y 170.41 (\275)s 7 f 113.942 y 182.042 (@)s 188.464 (\275)s 17.948 .4 179.11 118.812 r 128.861 y 179.11 (@)s 185.532 (\270)s 8 f 130.644 y 191.919 (k)s 2 f 121.349 y 198.258 (\050)s 7 f 202.516 (H)s 4 f 123.044 y 211.619 (\244)s 10 f 121.349 y 220.446 (\241)s 7 f 231.396 (E)s 4 f 122.992 y 239.48 (0)s 10 f 121.349 y 246.663 (\241)s 7 f 257.613 (t)s 2 f 261.567 (\051)s 0 f 107.012 y 265.825 (\276)s 10 f 156.183 y 98.229 (\267)s 148.775 y 117.946 (\241)s 2 f 126.462 (1)s 13.992 .4 117.946 153.645 r 7 f 163.694 y 118.653 (C)s 4 f 165.336 y 126.48 (0)s 0 f 146.445 y 135.84 (X)s 8 f 170.499 y 134.962 (k)s 11 f 139.601 (2)s 4 f 168.477 y 146.09 (\176)s 170.499 y 145.268 (\244)s 7 f 156.183 y 155.421 (T)s 163.341 (r)s 0 f 141.845 y 170.41 (\275)s 7 f 148.775 y 184.873 (@)s 17.948 .4 179.11 153.645 r 163.694 y 179.11 (@)s 185.532 (\270)s 8 f 165.478 y 191.919 (k)s 10 f 156.183 y 198.258 (f)s 7 f 203.733 (\275)s 2 f 209.394 (\050)s 7 f 213.653 (H)s 4 f 157.878 y 222.755 (\244)s 10 f 156.183 y 231.583 (\241)s 7 f 242.533 (E)s 4 f 157.825 y 250.616 (0)s 10 f 156.183 y 257.799 (\241)s 7 f 268.749 (t)s 2 f 272.703 (\051)s 10 f 279.395 (\241)s 7 f 290.345 (\275)s 2 f 296.006 (\050)s 7 f 300.265 (H)s 4 f 157.825 y 309.367 (0)s 10 f 156.183 y 316.55 (\241)s 7 f 327.5 (E)s 4 f 157.825 y 335.583 (0)s 10 f 156.183 y 342.767 (\241)s 7 f 353.717 (t)s 2 f 357.671 (\051)s 10 f 361.929 (g)s 0 f 141.845 y 367.404 (\276)s 7 f 156.183 y 376.729 (:)s 2 f 386.017 (\0503.22\051)s 192.217 y 54 (W)s 64.342 (e)s 74.195 (remark)s 113.005 (that)s 138.067 (the)s 158.262 (op)s 170.125 (erator)s 10 f 192.217 y 203.764 (f)s 7 f 192.217 y 209.239 (\275)s 2 f 214.9 (\050)s 7 f 219.159 (H)s 4 f 193.912 y 228.261 (\244)s 10 f 192.217 y 237.089 (\241)s 7 f 248.039 (E)s 4 f 193.859 y 256.122 (0)s 10 f 192.217 y 263.305 (\241)s 7 f 274.255 (t)s 2 f 278.209 (\051)s 10 f 284.901 (\241)s 7 f 295.851 (\275)s 2 f 301.512 (\050)s 7 f 305.771 (H)s 4 f 193.859 y 314.873 (0)s 10 f 192.217 y 322.056 (\241)s 7 f 333.006 (E)s 4 f 193.859 y 341.089 (0)s 10 f 192.217 y 348.273 (\241)s 7 f 359.223 (t)s 2 f 363.177 (\051)s 10 f 192.217 y 367.435 (g)s 2 f 192.217 y 377.897 (is)s 390.245 (trace)s 205.817 y 54 (class)s 80.422 (since)s 108 (the)s 127.609 (di)s 136.734 (\256erence)s 7 f 177.36 (H)s 4 f 207.512 y 186.462 (\244)s 10 f 205.817 y 195.79 (\241)s 7 f 207.241 (H)s 4 f 207.459 y 216.343 (0)s 2 f 205.817 y 225.385 (=)s 7 f 238.194 (V)s 4 f 207.512 y 244.582 (\244)s 2 f 205.817 y 255.376 (has)s 275.654 (compact)s 320.205 (supp)s 343.078 (ort.)s 367.26 (With)s 396.297 (this)s 219.417 y 54 (estimate,)s 100.903 (the)s 119.761 (righ)s 138.346 (t)s 146.254 (side)s 168.215 (of)s 180.686 (\0503.5\051)s 206.844 (can)s 226.919 (b)s 233.306 (e)s 241.823 (b)s 248.211 (ounded)s 286.536 (ab)s 298.398 (o)s 303.569 (v)s 309.044 (e)s 317.561 (b)s 323.34 (y)s 10 f 243.429 y 71.938 (\241)s 2 f 80.454 (1)s 13.992 .4 71.938 248.299 r 7 f 258.348 y 72.645 (C)s 4 f 259.99 y 80.471 (0)s 0 f 241.099 y 92.874 (X)s 8 f 265.153 y 91.996 (k)s 11 f 96.635 (2)s 4 f 263.131 y 103.124 (\176)s 265.153 y 102.301 (\244)s 0 f 236.988 y 113.063 (Z)s 4 f 240.154 y 123.063 (3)s 8 f 127.313 (\264)s 131.865 (=)s 4 f 136.115 (2)s 11 f 259.71 y 118.618 (\241)s 4 f 125.229 (3)s 8 f 129.479 (\264)s 134.032 (=)s 4 f 138.282 (2)s 7 f 250.836 y 147.29 (dt)s 159.377 (I)s 161.765 (E)s 0 f 236.499 y 172.304 (\275)s 7 f 243.429 y 186.767 (@)s 17.948 .4 181.004 248.299 r 258.348 y 181.004 (@)s 187.426 (\270)s 8 f 260.131 y 193.813 (k)s 7 f 250.836 y 202.585 (T)s 210.505 (r)s 10 f 215.75 (f)s 7 f 221.225 (\275)s 2 f 226.886 (\050)s 7 f 231.144 (H)s 4 f 252.531 y 240.246 (\244)s 10 f 250.836 y 249.074 (\241)s 7 f 260.024 (E)s 4 f 252.479 y 268.107 (0)s 10 f 250.836 y 275.291 (\241)s 7 f 286.241 (t)s 2 f 290.195 (\051)s 10 f 296.887 (\241)s 7 f 307.837 (\275)s 2 f 313.498 (\050)s 7 f 317.756 (H)s 4 f 252.479 y 326.858 (0)s 10 f 250.836 y 334.042 (\241)s 7 f 344.992 (E)s 4 f 252.479 y 353.075 (0)s 10 f 250.836 y 360.258 (\241)s 7 f 371.208 (t)s 2 f 375.162 (\051)s 10 f 379.421 (g)s 0 f 236.499 y 384.896 (\276)s 7 f 250.836 y 394.221 (:)s 2 f 275.87 y 386.017 (\0503.23\051)s 289.47 y 54 (In)s 67.139 (order)s 95.242 (to)s 108.077 (ev)s 118.114 (aluate)s 150.415 (the)s 168.725 (exp)s 185.758 (ectation,)s 230.336 (w)s 237.94 (e)s 245.907 (select)s 275.228 (one)s 294.754 (random)s 334.385 (v)s 339.556 (ariable)s 7 f 374.929 (\270)s 8 f 291.254 y 381.317 (k)s 2 f 289.47 y 386.456 (,)s 392.708 (with)s 7 f 303.07 y 54 (k)s 10 f 63.087 (2)s 2 f 300.303 y 74.493 (\176)s 303.07 y 73.429 (\244)s 81.033 (,)s 87.005 (and)s 107.398 (\257rst)s 129.099 (in)s 137.92 (tegrate)s 174.16 (with)s 198.203 (resp)s 218.065 (ect)s 234.808 (to)s 247.292 (this)s 267.746 (v)s 272.917 (ariable)s 307.94 (using)s 335.694 (h)s 341.473 (yp)s 353.64 (othesis)s 388.754 (\050H4\051.)s 316.67 y 54 (Because)s 95.884 (of)s 108.355 (the)s 127.213 (p)s 133.6 (ositivit)s 166.511 (y)s 175.941 (of)s 10 f 188.411 (\241)s 7 f 196.928 (\275)s 11 f 312.697 y 202.589 (0)s 2 f 316.67 y 205.395 (,)s 212.087 (and)s 233.378 (of)s 245.849 (the)s 264.708 (densit)s 293.056 (y)s 7 f 302.485 (h)s 4 f 318.313 y 308.794 (0)s 2 f 316.67 y 313.544 (,)s 320.236 (w)s 327.84 (e)s 336.357 (obtain)s 10 f 345.812 y 94.934 (\241)s 0 f 331.963 y 105.275 (Z)s 7 f 345.812 y 117.1 (d\270)s 8 f 347.595 y 129.187 (k)s 7 f 345.812 y 137.368 (h)s 4 f 347.454 y 143.677 (0)s 2 f 345.812 y 148.427 (\050)s 7 f 152.685 (\270)s 8 f 347.595 y 159.072 (k)s 2 f 345.812 y 164.211 (\051)s 7 f 338.404 y 175.433 (@)s 17.948 .4 169.67 343.274 r 353.323 y 169.67 (@)s 176.091 (\270)s 8 f 355.107 y 182.479 (k)s 7 f 345.812 y 191.251 (T)s 199.171 (r)s 10 f 204.415 (f)s 7 f 209.89 (\275)s 2 f 215.552 (\050)s 7 f 219.81 (H)s 4 f 347.507 y 228.912 (\244)s 10 f 345.812 y 237.74 (\241)s 7 f 248.69 (E)s 4 f 347.454 y 256.773 (0)s 10 f 345.812 y 263.957 (\241)s 7 f 274.907 (t)s 2 f 278.861 (\051)s 10 f 285.552 (\241)s 7 f 296.502 (\275)s 2 f 302.164 (\050)s 7 f 306.422 (H)s 4 f 347.454 y 315.524 (0)s 10 f 345.812 y 322.708 (\241)s 7 f 333.658 (E)s 4 f 347.454 y 341.741 (0)s 10 f 345.812 y 348.924 (\241)s 7 f 359.874 (t)s 2 f 363.828 (\051)s 10 f 368.087 (g)s 369.989 y 104.934 (\267)s 116.492 (k)s 7 f 121.967 (h)s 4 f 371.632 y 128.276 (0)s 10 f 369.989 y 133.026 (k)s 11 f 371.632 y 138.501 (1)s 10 f 369.989 y 150.543 (f)s 7 f 156.018 (T)s 163.937 (r)s 10 f 169.182 (f)s 7 f 174.657 (\275)s 2 f 180.318 (\050)s 7 f 184.576 (H)s 8 f 364.662 y 194.568 (m;k)s 4 f 373.284 y 193.679 (\244)s 10 f 369.989 y 212.02 (\241)s 7 f 222.97 (E)s 4 f 371.632 y 231.053 (0)s 10 f 369.989 y 238.237 (\241)s 7 f 249.187 (t)s 2 f 253.141 (\051)s 10 f 259.833 (\241)s 7 f 270.783 (\275)s 2 f 276.444 (\050)s 7 f 280.702 (H)s 8 f 364.662 y 290.694 (M)s 299.237 (;k)s 4 f 373.284 y 289.804 (\244)s 10 f 369.989 y 309.171 (\241)s 7 f 320.121 (E)s 4 f 371.632 y 328.204 (0)s 10 f 369.989 y 335.387 (\241)s 7 f 346.337 (t)s 2 f 350.291 (\051)s 10 f 354.55 (g)s 7 f 360.025 (;)s 2 f 386.017 (\0503.24\051)s 396.167 y 54 (where)s 7 f 86.009 (H)s 8 f 390.84 y 96.001 (M)s 104.544 (;k)s 4 f 399.462 y 95.111 (\244)s 2 f 396.167 y 116.039 (is)s 127.396 (the)s 146.599 (lo)s 155.42 (cal)s 172.799 (Hamiltonian)s 7 f 236.107 (H)s 4 f 397.862 y 245.209 (\244)s 2 f 396.167 y 255.599 (with)s 280.886 (the)s 300.089 (coupling)s 344.235 (constan)s 380.491 (t)s 7 f 388.745 (\270)s 8 f 397.951 y 395.132 (k)s 2 f 396.167 y 404.267 (at)s 409.767 y 54 (the)s 7 f 74.266 (k)s 8 f 405.793 y 80.312 (th)s 2 f 409.767 y 88.779 (-site)s 113.973 (\257xed)s 141.844 (at)s 156.635 (its)s 173.313 (maxim)s 205.554 (um)s 225.821 (v)s 230.992 (alue.)s 262.591 (Similarly)s 304.596 (,)s 313.048 (the)s 333.315 (small)s 7 f 363.375 (m)s 2 f 378.048 (denotes)s 423.367 y 54 (the)s 73.149 (minim)s 103.261 (um)s 122.41 (v)s 127.581 (alue)s 150.988 (of)s 163.749 (the)s 182.897 (coupling)s 226.988 (constan)s 263.244 (t.)s 276.282 (W)s 286.623 (e)s 295.43 (note)s 320.054 (once)s 345.286 (again)s 374.776 (that)s 398.792 (the)s 436.967 y 54 (di)s 63.125 (\256erence)s 10 f 102.253 (f)s 7 f 107.728 (\275)s 2 f 113.389 (\050)s 7 f 117.648 (H)s 8 f 431.64 y 127.639 (m;k)s 4 f 440.262 y 126.75 (\244)s 10 f 436.967 y 143.595 (\241)s 7 f 153.048 (E)s 4 f 438.61 y 161.131 (0)s 10 f 436.967 y 166.818 (\241)s 7 f 176.271 (t)s 2 f 180.225 (\051)s 10 f 185.42 (\241)s 7 f 194.874 (\275)s 2 f 200.535 (\050)s 7 f 204.793 (H)s 8 f 431.64 y 214.785 (M)s 223.328 (;k)s 4 f 440.262 y 213.896 (\244)s 10 f 436.967 y 231.765 (\241)s 7 f 241.218 (E)s 4 f 438.61 y 249.302 (0)s 10 f 436.967 y 254.988 (\241)s 7 f 264.442 (t)s 2 f 268.396 (\051)s 10 f 272.654 (g)s 2 f 281.031 (is)s 291.293 (trace)s 317.95 (class.)s 347.631 (Consequen)s 398.792 (tly)s 410.958 (,)s 450.567 y 54 (w)s 61.604 (e)s 70.121 (are)s 88.401 (left)s 107.564 (with)s 132.505 (the)s 151.364 (task)s 174.846 (of)s 187.316 (estimating)s 10 f 473.971 y 55.2 (k)s 7 f 60.675 (h)s 4 f 475.613 y 66.984 (0)s 10 f 473.971 y 71.734 (k)s 11 f 475.613 y 77.209 (1)s 31.009 .4 55.2 478.841 r 7 f 488.889 y 64.416 (C)s 4 f 490.532 y 72.243 (0)s 0 f 471.641 y 93.154 (X)s 8 f 495.695 y 92.276 (k)s 11 f 96.915 (2)s 4 f 493.673 y 103.404 (\176)s 495.695 y 102.581 (\244)s 0 f 467.53 y 110.301 (Z)s 4 f 470.696 y 120.301 (3)s 8 f 124.551 (\264)s 129.103 (=)s 4 f 133.353 (2)s 11 f 490.252 y 115.856 (\241)s 4 f 122.468 (3)s 8 f 126.718 (\264)s 131.27 (=)s 4 f 135.52 (2)s 7 f 481.378 y 142.095 (dt)s 0 f 467.53 y 156.615 (Z)s 471.641 y 168.992 (Y)s 8 f 493.863 y 168.44 (l)s 11 f 171.072 (6)s 4 f 171.072 (=)s 8 f 177.683 (k)s 7 f 481.378 y 187.189 (h)s 4 f 483.021 y 193.498 (0)s 2 f 481.378 y 198.248 (\050)s 7 f 202.506 (\270)s 8 f 483.162 y 208.894 (l)s 2 f 481.378 y 212.026 (\051)s 7 f 219.326 (d)s 225.025 (\270)s 8 f 483.162 y 231.413 (l)s 7 f 481.378 y 237.586 (T)s 245.506 (r)s 10 f 250.75 (f)s 7 f 256.225 (\275)s 2 f 261.887 (\050)s 7 f 266.145 (H)s 8 f 476.051 y 276.137 (m;k)s 4 f 484.673 y 275.247 (\244)s 10 f 481.378 y 291.155 (\241)s 7 f 299.672 (E)s 4 f 483.021 y 307.755 (0)s 10 f 481.378 y 312.505 (\241)s 7 f 321.022 (t)s 2 f 324.976 (\051)s 10 f 329.235 (\241)s 7 f 337.751 (\275)s 2 f 343.413 (\050)s 7 f 347.671 (H)s 8 f 476.051 y 357.663 (M)s 366.206 (;k)s 4 f 484.673 y 356.773 (\244)s 10 f 481.378 y 373.706 (\241)s 7 f 382.223 (E)s 4 f 483.021 y 390.306 (0)s 10 f 481.378 y 395.056 (\241)s 7 f 403.573 (t)s 2 f 407.527 (\051)s 10 f 411.785 (g)s 7 f 417.26 (:)s 2 f 506.412 y 386.017 (\0503.25\051)s 527.24 y 54 (6.)s 69.629 (The)s 92.886 (expression)s 146.408 (in)s 155.229 (v)s 160.704 (olving)s 193.999 (the)s 213.606 (trace)s 241.76 (in)s 255.283 (\0503.25\051)s 287.666 (is)s 299.425 (basically)s 344.947 (the)s 364.554 (n)s 370.333 (um)s 385.238 (b)s 391.625 (er)s 405.179 (of)s 540.84 y 54 (eigen)s 78.029 (v)s 83.2 (alues)s 110.572 (created)s 148.864 (in)s 161.575 (the)s 180.369 (in)s 189.19 (terv)s 207.775 (al)s 219.878 ([)s 7 f 222.919 (E)s 4 f 542.482 y 231.002 (0)s 10 f 540.84 y 238.058 (\241)s 2 f 248.88 (2)s 7 f 254.355 (\264)s 260.185 (;)s 265.052 (E)s 4 f 542.482 y 273.135 (0)s 2 f 540.84 y 280.191 (+)s 291.013 (2)s 7 f 296.488 (\264)s 2 f 302.318 (])s 308.946 (b)s 314.725 (y)s 324.09 (decreasing)s 377.043 (the)s 7 f 395.837 (k)s 8 f 536.866 y 401.882 (th)s 2 f 540.84 y 410.35 (-)s 554.44 y 54 (coupling)s 97.928 (constan)s 134.184 (t)s 142.22 (from)s 168.232 (the)s 187.218 (maxim)s 219.46 (um)s 238.446 (v)s 243.617 (alue)s 7 f 266.861 (\270)s 8 f 550.466 y 273.249 (M)s 557.622 y 273.249 (k)s 2 f 554.44 y 286.542 (to)s 300.053 (the)s 319.039 (minim)s 349.151 (um)s 368.137 (v)s 373.308 (alue)s 7 f 396.552 (\270)s 8 f 550.466 y 402.94 (m)s 557.622 y 402.94 (k)s 2 f 554.44 y 410.958 (.)s 568.04 y 54 (This)s 79.21 (trace)s 106.823 (can)s 127.105 (b)s 133.492 (e)s 142.216 (rewritten)s 189.935 (in)s 202.917 (terms)s 233.632 (of)s 246.31 (a)s 255.643 (sp)s 266.349 (ectral)s 297.004 (shift)s 321.91 (function)s 365.004 (as)s 378.656 (follo)s 398.731 (ws.)s 581.64 y 54 (W)s 64.342 (e)s 74.138 (consider)s 118.091 (explicitly)s 166.821 (the)s 186.958 (Anderson-t)s 239.974 (yp)s 252.141 (e)s 261.937 (additiv)s 295.395 (e)s 305.191 (case.)s 336.465 (The)s 360.252 (other)s 390.153 (cases)s 621.8 y 228.525 (15)s do-end end endp showpage %%PageTrailer %%Page: 17 17 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 17 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf ( )S f186 sf ( )S -976 -1000 :M f219 sf ( )S -967 -1000 :M f520 sf ( )S -958 -1000 :M f253 sf ( )S -946 -1000 :M f420 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 9 6 /CMMI6 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (are)s 72.349 (treated)s 110.165 (similarly)s 150.406 (.)s 158.521 (W)s 168.863 (e)s 177.448 (let)s 7 f 193.334 (H)s 4 f 76.642 y 202.436 (1)s 10 f 75 y 210.342 (\264)s 7 f 222.015 (H)s 8 f 69.673 y 232.007 (M)s 240.55 (;k)s 4 f 78.295 y 231.117 (\244)s 2 f 75 y 251.769 (b)s 258.157 (e)s 266.742 (the)s 285.669 (unp)s 304.223 (erturb)s 334.397 (ed)s 349.066 (op)s 360.928 (erator,)s 396.358 (and)s 88.6 y 54 (write,)s 7 f 102.2 y 142.832 (H)s 8 f 96.873 y 152.824 (m;k)s 4 f 105.495 y 151.935 (\244)s 2 f 102.2 y 170.885 (=)s 7 f 182.443 (H)s 4 f 103.843 y 191.545 (1)s 2 f 102.2 y 198.728 (+)s 209.678 (\050)s 7 f 213.937 (\270)s 8 f 97.679 y 220.324 (m)s 104.907 y 220.324 (k)s 10 f 102.2 y 230.776 (\241)s 7 f 241.726 (\270)s 8 f 97.679 y 248.114 (M)s 104.907 y 248.114 (k)s 2 f 102.2 y 257.629 (\051)s 7 f 261.887 (u)s 8 f 103.984 y 268.156 (k)s 2 f 102.2 y 276.336 (=)s 7 f 287.895 (H)s 4 f 103.843 y 296.997 (1)s 2 f 102.2 y 304.18 (+)s 7 f 315.13 (V)s 322.126 (:)s 2 f 386.017 (\0503.26\051)s 119.339 y 54 (Although)s 102.369 (the)s 121.234 (di)s 130.359 (\256erence)s 7 f 170.242 (V)s 2 f 182.719 (is)s 193.736 (not)s 213.209 (trace)s 240.621 (class,)s 269.343 (it)s 280.299 (do)s 292.162 (es)s 305.004 (ha)s 316.258 (v)s 321.733 (e)s 330.256 (compact)s 374.063 (supp)s 396.936 (ort.)s 132.939 y 54 (W)s 64.342 (e)s 73.314 (sho)s 88.887 (w)s 100.901 (in)s 114.131 (section)s 151.147 (5)s 160.728 (that)s 184.908 (the)s 204.222 (di)s 213.347 (\256erence)s 253.678 (of)s 266.604 (su)s 277.007 (\261cien)s 304.686 (tly)s 321.871 (large)s 349.123 (p)s 355.511 (o)s 360.681 (w)s 368.286 (ers)s 385.866 (of)s 398.792 (the)s 146.539 y 54 (resolv)s 81.466 (en)s 92.112 (ts)s 103.537 (of)s 7 f 115.206 (H)s 4 f 148.181 y 124.308 (1)s 2 f 146.539 y 131.906 (and)s 7 f 152.395 (H)s 4 f 148.181 y 161.498 (1)s 2 f 146.539 y 167.077 (+)s 7 f 176.422 (V)s 2 f 188.091 (is)s 198.299 (not)s 216.964 (only)s 240.191 (in)s 252.163 (the)s 270.22 (trace)s 296.823 (class,)s 324.894 (but)s 344.167 (is)s 354.376 (in)s 366.349 (the)s 384.405 (sup)s 401.195 (er-)s 160.139 y 54 (trace)s 80.97 (class)s 10 f 106.207 (I)s 4 f 162.367 y 112.169 (1)s 8 f 116.419 (=p)s 2 f 160.139 y 125.448 (,)s 131.792 (for)s 148.116 (all)s 7 f 162.889 (p)s 10 f 171.44 (\270)s 2 f 182.998 (1)s 188.473 (.)s 196.237 (Sp)s 208.708 (eci)s 221.483 (\257cally)s 248.858 (,)s 255.201 (our)s 274.263 (assumptions)s 336.061 (imply)s 366.346 (that)s 389.636 (there)s 173.739 y 54 (exists)s 83.809 (a)s 92.509 (\257nite)s 120.067 (constan)s 156.324 (t)s 7 f 163.807 (M)s 4 f 175.381 y 174.43 (0)s 2 f 173.739 y 182.405 (suc)s 197.37 (h)s 206.678 (that)s 229.978 (\050)s 7 f 234.236 (H)s 4 f 175.381 y 243.339 (1)s 2 f 173.739 y 249.672 (+)s 7 f 259.771 (M)s 4 f 175.381 y 270.394 (0)s 2 f 173.739 y 275.144 (\051)s 11 f 169.765 y 279.403 (\241)s 4 f 286.014 (1)s 2 f 173.739 y 293.989 (and)s 314.855 (\050)s 7 f 319.114 (H)s 4 f 175.381 y 328.216 (1)s 2 f 173.739 y 334.549 (+)s 7 f 344.649 (V)s 2 f 355.052 (+)s 7 f 365.152 (M)s 4 f 175.381 y 375.775 (0)s 2 f 173.739 y 380.525 (\051)s 11 f 169.765 y 384.783 (\241)s 4 f 391.395 (1)s 2 f 173.739 y 399.37 (are)s 187.339 y 54 (b)s 60.388 (ounded.)s 103.254 (Let)s 122.967 (us)s 137.113 (de)s 148.063 (\257ne)s 168.841 (the)s 187.794 (function)s 7 f 230.775 (g)s 2 f 236.391 (\050)s 7 f 240.649 (\270)s 2 f 247.037 (\051)s 254.494 (=)s 266.209 (\050)s 7 f 270.468 (\270)s 2 f 279.351 (+)s 7 f 290.364 (M)s 4 f 188.981 y 300.987 (0)s 2 f 187.339 y 305.737 (\051)s 11 f 183.365 y 309.996 (\241)s 8 f 316.607 (k)s 2 f 187.339 y 321.746 (,)s 328.555 (for)s 7 f 345.409 (\270)s 354.995 (\076\076)s 375.227 (M)s 4 f 188.981 y 385.85 (0)s 2 f 187.339 y 390.601 (.)s 398.792 (W)s 409.133 (e)s 200.939 y 54 (pro)s 69.543 (v)s 75.018 (e)s 83.535 (that)s 107.26 (for)s 7 f 124.019 (k)s 133.106 (\076)s 144.664 (pd)s 155.873 (=)s 2 f 161.348 (2)s 170.473 (+)s 182.64 (2,)s 194.806 (and)s 7 f 216.098 (p)s 224.649 (\076)s 2 f 236.207 (1)s 241.682 (,)s 7 f 219.616 y 170.389 (g)s 2 f 176.004 (\050)s 7 f 180.263 (H)s 4 f 221.258 y 189.365 (1)s 2 f 219.616 y 196.548 (+)s 7 f 207.498 (V)s 2 f 216.319 (\051)s 10 f 223.011 (\241)s 7 f 233.961 (g)s 2 f 239.576 (\050)s 7 f 243.835 (H)s 4 f 221.258 y 252.937 (1)s 2 f 219.616 y 257.687 (\051)s 10 f 264.987 (2)s 275.328 (I)s 4 f 221.844 y 281.291 (1)s 8 f 285.541 (=p)s 7 f 219.616 y 294.57 (:)s 2 f 386.017 (\0503.27\051)s 238.293 y 54 (Sp)s 66.471 (ectral)s 96.601 (shift)s 120.983 (function)s 7 f 163.553 (\273)s 2 f 168.848 (\050)s 7 f 173.106 (\270)s 2 f 182.535 (;)s 7 f 187.402 (H)s 4 f 239.936 y 196.504 (1)s 2 f 238.293 y 203.053 (+)s 7 f 213.37 (V)s 220.366 (;)s 225.232 (H)s 4 f 239.936 y 234.334 (1)s 2 f 238.293 y 239.084 (\051)s 246.676 (is)s 257.37 (de)s 268.32 (\257ned)s 294.77 (for)s 311.212 (the)s 329.754 (pair)s 351.976 (\050)s 7 f 356.234 (H)s 4 f 239.936 y 365.336 (1)s 7 f 238.293 y 370.086 (;)s 374.953 (H)s 4 f 239.936 y 384.055 (1)s 2 f 238.293 y 390.605 (+)s 7 f 400.921 (V)s 2 f 409.742 (\051)s 251.893 y 54 (b)s 59.779 (y)s 7 f 270.57 y 81.917 (\273)s 2 f 87.211 (\050)s 7 f 91.47 (\270)s 2 f 100.899 (;)s 7 f 105.766 (H)s 4 f 272.213 y 114.868 (1)s 2 f 270.57 y 122.051 (+)s 7 f 133.001 (V)s 139.997 (;)s 144.864 (H)s 4 f 272.213 y 153.966 (1)s 2 f 270.57 y 158.716 (\051)s 166.016 (=)s 7 f 177.574 (sg)s 188.322 (n)s 2 f 194.895 (\050)s 7 f 199.153 (g)s 11 f 266.049 y 204.769 (0)s 2 f 270.57 y 207.575 (\050)s 7 f 211.833 (\270)s 2 f 218.22 (\051\051)s 7 f 229.779 (\273)s 2 f 235.073 (\050)s 7 f 239.332 (g)s 2 f 244.947 (\050)s 7 f 249.206 (\270)s 2 f 255.593 (\051)s 262.893 (;)s 7 f 267.76 (g)s 2 f 273.375 (\050)s 7 f 277.634 (H)s 4 f 272.213 y 286.736 (1)s 2 f 270.57 y 293.919 (+)s 7 f 304.869 (V)s 2 f 313.69 (\051)s 7 f 317.948 (;)s 322.815 (g)s 2 f 328.431 (\050)s 7 f 332.689 (H)s 4 f 272.213 y 341.791 (1)s 2 f 270.57 y 346.541 (\051)s 350.8 (\051)s 7 f 355.058 (:)s 2 f 386.017 (\0503.28\051)s 289.248 y 54 (Because)s 94.838 (the)s 112.65 (function)s 7 f 154.492 (\275)s 11 f 285.274 y 160.153 (0)s 2 f 289.248 y 165.563 (has)s 184.045 (compact)s 226.799 (supp)s 249.672 (ort,)s 269.549 (and)s 289.795 (the)s 307.607 (fact)s 328.157 (that)s 350.836 (the)s 368.649 (di)s 377.774 (\256erence)s 10 f 302.848 y 54 (f)s 7 f 59.475 (g)s 2 f 65.091 (\050)s 7 f 69.349 (H)s 4 f 304.49 y 78.451 (1)s 2 f 302.848 y 85.985 (+)s 7 f 97.285 (V)s 2 f 106.106 (\051)s 10 f 113.148 (\241)s 7 f 124.448 (g)s 2 f 130.063 (\050)s 7 f 134.322 (H)s 4 f 304.49 y 143.424 (1)s 2 f 302.848 y 148.174 (\051)s 10 f 152.432 (g)s 2 f 162.083 (is)s 173.619 (sup)s 190.409 (er-trace)s 231.145 (class,)s 260.515 (w)s 268.119 (e)s 277.161 (can)s 297.761 (apply)s 328.399 (the)s 347.783 (Birman-Krein)s 316.448 y 54 (iden)s 73.771 (tit)s 85.025 (y)s 94.454 ([3)s 102.971 (])s 109.663 (to)s 123.046 (the)s 141.904 (trace)s 169.31 (in)s 182.085 (\0503.25\051.)s 217.976 (This)s 242.979 (giv)s 256.971 (es)s 7 f 336.145 y 101.908 (T)s 109.828 (r)s 10 f 115.072 (f)s 7 f 120.547 (\275)s 2 f 126.208 (\050)s 7 f 130.467 (H)s 8 f 330.818 y 140.459 (m;k)s 4 f 339.44 y 139.569 (\244)s 10 f 336.145 y 157.911 (\241)s 7 f 168.861 (E)s 4 f 337.788 y 176.944 (0)s 10 f 336.145 y 184.127 (\241)s 7 f 195.077 (t)s 2 f 199.031 (\051)s 10 f 205.723 (\241)s 7 f 216.673 (\275)s 2 f 222.334 (\050)s 7 f 226.593 (H)s 8 f 330.818 y 236.585 (M)s 245.128 (;k)s 4 f 339.44 y 235.695 (\244)s 10 f 336.145 y 255.061 (\241)s 7 f 266.011 (E)s 4 f 337.788 y 274.094 (0)s 10 f 336.145 y 281.278 (\241)s 7 f 292.228 (t)s 2 f 296.182 (\051)s 10 f 300.44 (g)s 2 f 358.452 y 111.908 (=)s 10 f 130.425 (\241)s 0 f 344.603 y 140.766 (Z)s 8 f 367.326 y 146.322 (I)s 147.347 (R)s 7 f 351.044 y 160.517 (d)s 12.087 .4 157.323 355.915 r 365.963 y 157.323 (d\270)s 358.452 y 170.61 (\275)s 2 f 176.271 (\050)s 7 f 180.53 (\270)s 10 f 189.35 (\241)s 7 f 200.3 (E)s 4 f 360.095 y 208.384 (0)s 10 f 358.452 y 215.567 (\241)s 7 f 226.517 (t)s 2 f 230.471 (\051)s 7 f 237.771 (\273)s 2 f 243.066 (\050)s 7 f 247.324 (\270)s 2 f 253.711 (;)s 7 f 258.578 (H)s 4 f 360.095 y 267.68 (1)s 2 f 358.452 y 274.864 (+)s 7 f 285.814 (V)s 292.809 (;)s 297.676 (H)s 4 f 360.095 y 306.778 (1)s 2 f 358.452 y 311.528 (\051)s 7 f 318.828 (d)s 324.528 (\270)s 2 f 386.338 y 111.908 (=)s 10 f 130.425 (\241)s 0 f 372.489 y 140.766 (Z)s 8 f 395.211 y 146.322 (I)s 147.347 (R)s 7 f 378.93 y 160.517 (d)s 12.087 .4 157.323 383.8 r 393.849 y 157.323 (d\270)s 386.338 y 170.61 (\275)s 2 f 176.271 (\050)s 7 f 180.53 (\270)s 10 f 189.35 (\241)s 7 f 200.3 (E)s 4 f 387.98 y 208.384 (0)s 10 f 386.338 y 215.567 (\241)s 7 f 226.517 (t)s 2 f 230.471 (\051)s 7 f 237.771 (\273)s 2 f 243.066 (\050)s 7 f 247.324 (g)s 2 f 252.94 (\050)s 7 f 257.198 (\270)s 2 f 263.585 (\051;)s 7 f 275.752 (g)s 2 f 281.368 (\050)s 7 f 285.626 (H)s 4 f 387.98 y 294.728 (1)s 2 f 386.338 y 301.912 (+)s 7 f 312.862 (V)s 2 f 321.682 (\051)s 7 f 325.941 (;)s 330.807 (g)s 2 f 336.423 (\050)s 7 f 340.681 (H)s 4 f 387.98 y 349.784 (1)s 2 f 386.338 y 354.534 (\051)s 358.792 (\051)s 7 f 363.05 (:)s 2 f 386.017 (\0503.29\051)s 408.893 y 54 (W)s 64.342 (e)s 73.346 (estimate)s 117.695 (the)s 137.042 (in)s 145.863 (tegral)s 177.406 (using)s 206.547 (the)s 225.893 (H)s 234.105 (\304)s 234.105 (older)s 261.999 (inequalit)s 303.366 (y)s 313.283 (and)s 335.063 (the)s 7 f 354.409 (L)s 8 f 404.919 y 361.861 (p)s 2 f 408.893 y 366.64 (-theory)s 405.179 (of)s 422.493 y 54 (section)s 90.044 (2.)s 103.255 (Let)s 419.603 y 123.483 (\176)s 7 f 422.493 y 122.357 (\273)s 2 f 127.651 (\050)s 7 f 131.91 (\270)s 2 f 138.297 (\051)s 145.597 (=)s 7 f 157.155 (\273)s 2 f 162.45 (\050)s 7 f 166.708 (g)s 2 f 172.324 (\050)s 7 f 176.582 (\270)s 2 f 182.97 (\051;)s 7 f 195.136 (g)s 2 f 200.752 (\050)s 7 f 205.01 (H)s 4 f 424.135 y 214.112 (1)s 2 f 422.493 y 220.262 (+)s 7 f 230.178 (V)s 2 f 238.999 (\051)s 7 f 243.257 (;)s 248.124 (g)s 2 f 253.74 (\050)s 7 f 257.998 (H)s 4 f 424.135 y 267.1 (1)s 2 f 422.493 y 271.85 (\051)s 276.109 (\051)s 280.367 (,)s 286.645 (for)s 302.888 (notational)s 354.687 (con)s 370.808 (v)s 376.283 (enience.)s 436.093 y 54 (Let)s 7 f 74.096 (\302)s 2 f 85.075 (b)s 91.462 (e)s 100.456 (the)s 119.792 (c)s 124.355 (haracteristic)s 187.612 (function)s 230.977 (for)s 248.214 (the)s 267.55 (in)s 276.37 (terv)s 294.955 (al)s 307.599 ([)s 10 f 310.641 (\241)s 7 f 319.157 (\264)s 324.987 (;)s 329.854 (\264)s 2 f 335.684 (])s 342.853 (so)s 356.774 (that)s 380.977 (w)s 388.581 (e)s 397.575 (can)s 449.693 y 54 (replace)s 7 f 91.241 (\275)s 11 f 445.719 y 96.903 (0)s 2 f 449.693 y 103.461 (in)s 116.339 (\0503.29\051)s 148.075 (b)s 153.854 (y)s 7 f 163.386 (\302)s 170.237 (\275)s 11 f 445.719 y 175.898 (0)s 2 f 449.693 y 178.704 (.)s 186.92 (W)s 197.262 (e)s 205.881 (write)s 235.294 (\176)s 7 f 233.997 (\302)s 2 f 240.849 (\050)s 7 f 245.107 (\270)s 2 f 251.494 (\051)s 10 f 258.965 (\264)s 7 f 270.695 (\302)s 2 f 277.546 (\050)s 7 f 281.805 (\270)s 10 f 290.694 (\241)s 7 f 301.712 (E)s 4 f 451.335 y 309.795 (0)s 10 f 449.693 y 317.047 (\241)s 7 f 328.066 (t)s 2 f 332.02 (\051)s 336.278 (.)s 344.494 (F)s 350.73 (or)s 364.246 (an)s 375.5 (y)s 7 f 385.032 (p)s 393.754 (\076)s 2 f 405.483 (1)s 410.958 (,)s 463.293 y 54 (and)s 7 f 74.965 (q)s 2 f 83.569 (suc)s 98.534 (h)s 107.941 (that)s 4 f 458.982 y 132.554 (1)s 4.279 .4 132.539 460.755 r 8 f 467.069 y 132.539 (p)s 2 f 463.293 y 139.798 (+)s 4 f 458.982 y 151.294 (1)s 4.25 .4 151.294 460.755 r 8 f 467.069 y 151.378 (q)s 2 f 463.293 y 159.786 (=)s 171.344 (1)s 176.819 (,)s 183.249 (the)s 201.781 (righ)s 220.366 (t)s 227.947 (side)s 249.581 (of)s 261.725 (\0503.29\051)s 293.032 (can)s 312.78 (b)s 319.168 (e)s 327.358 (b)s 333.745 (ounded)s 371.743 (ab)s 383.606 (o)s 388.777 (v)s 394.252 (e)s 402.442 (b)s 408.221 (y)s 0 f 477.935 y 75.02 (\050)s 481.424 y 83.075 (Z)s 2 f 504.146 y 88.631 (supp)s 8 f 113.089 (\302)s 10 f 495.273 y 120.692 (j)s 7 f 123.733 (\275)s 11 f 490.752 y 129.395 (0)s 10 f 495.273 y 132.2 (j)s 8 f 490.752 y 135.242 (q)s 0 f 477.935 y 139.824 (\051)s 4 f 480.702 y 147.879 (1)s 8 f 152.13 (=q)s 0 f 480.935 y 165.828 (\275)s 481.424 y 173.328 (Z)s 10 f 495.273 y 185.153 (j)s 2 f 492.383 y 189.321 (\176)s 7 f 495.273 y 188.195 (\273)s 2 f 193.489 (\050)s 7 f 197.748 (\270)s 2 f 204.135 (\051)s 212.732 (\176)s 7 f 211.435 (\302)s 2 f 218.286 (\050)s 7 f 222.545 (\270)s 2 f 228.932 (\051)s 10 f 233.191 (j)s 8 f 490.752 y 236.232 (p)s 0 f 480.935 y 241.011 (\276)s 4 f 483.702 y 248.511 (1)s 8 f 252.761 (=p)s 10 f 495.273 y 264.832 (\267)s 7 f 276.39 (C)s 4 f 496.915 y 284.216 (0)s 7 f 495.273 y 288.966 (\264)s 4 f 490.752 y 294.796 (\0501)s 11 f 302.352 (\241)s 8 f 308.963 (q)s 4 f 313.045 (\051)s 8 f 316.35 (=q)s 10 f 495.273 y 328.224 (k)s 2 f 492.383 y 334.826 (\176)s 7 f 495.273 y 333.699 (\273)s 2 f 340.29 (\176)s 7 f 338.994 (\302)s 10 f 345.845 (k)s 8 f 496.968 y 351.32 (L)s 9 f 494.69 y 357.1 (p)s 7 f 495.273 y 361.955 (;)s 2 f 386.017 (\0503.30\051)s 522.031 y 54 (Here,)s 84.609 (w)s 92.213 (e)s 102.076 (in)s 110.897 (tegrated)s 155.465 (one)s 176.886 (p)s 183.273 (o)s 188.444 (w)s 196.048 (er)s 210.2 (of)s 7 f 224.017 (\275)s 11 f 518.057 y 229.678 (0)s 2 f 522.031 y 237.48 (using)s 267.478 (the)s 287.683 (fact)s 310.625 (that)s 10 f 335.696 (\241)s 7 f 344.212 (\275)s 11 f 518.057 y 349.874 (0)s 7 f 522.031 y 357.964 (\076)s 2 f 371.766 (0)s 382.237 (on)s 398.792 (the)s 535.631 y 54 (supp)s 76.873 (ort)s 94.545 (of)s 7 f 107.016 (\302)s 2 f 113.868 (,)s 120.559 (and)s 141.851 (w)s 149.455 (e)s 157.972 (used)s 182.974 (the)s 201.833 (fact)s 223.429 (that)s 10 f 247.154 (j)s 7 f 250.195 (\275)s 11 f 531.657 y 255.857 (0)s 10 f 535.631 y 258.662 (j)s 2 f 264.745 (=)s 10 f 276.304 (O)s 2 f 285.325 (\050)s 7 f 289.584 (\264)s 11 f 531.657 y 295.414 (\241)s 4 f 302.025 (1)s 2 f 535.631 y 306.775 (\051)s 311.033 (,)s 317.725 (to)s 331.108 (obtain)s 0 f 547.679 y 98.42 (\050)s 551.168 y 106.475 (Z)s 2 f 573.89 y 112.031 (supp)s 8 f 136.489 (\302)s 10 f 565.016 y 144.092 (j)s 7 f 147.134 (\275)s 11 f 560.495 y 152.795 (0)s 10 f 565.016 y 155.6 (j)s 8 f 560.495 y 158.642 (q)s 11 f 162.724 (\241)s 4 f 169.335 (1)s 10 f 565.016 y 177.127 (j)s 7 f 180.169 (\275)s 11 f 560.495 y 185.83 (0)s 10 f 565.016 y 188.636 (j)s 0 f 547.679 y 191.677 (\051)s 4 f 550.445 y 199.733 (1)s 8 f 203.983 (=q)s 10 f 565.016 y 222.815 (\267)s 7 f 241.332 (\264)s 4 f 560.495 y 247.162 (\0501)s 11 f 254.717 (\241)s 8 f 261.328 (q)s 4 f 265.41 (\051)s 8 f 268.716 (=q)s 0 f 547.679 y 282.415 (\303)s 10 f 565.016 y 290.331 (\241)s 0 f 551.168 y 300.673 (Z)s 2 f 573.89 y 306.229 (supp)s 8 f 330.687 (\302)s 7 f 565.016 y 338.289 (\275)s 11 f 560.495 y 343.951 (0)s 0 f 547.679 y 346.756 (!)s 4 f 550.445 y 354.673 (1)s 8 f 358.923 (=q)s 10 f 591.8 y 222.815 (\267)s 7 f 241.332 (C)s 4 f 593.443 y 249.158 (0)s 7 f 591.8 y 253.908 (\264)s 4 f 587.279 y 259.738 (\0501)s 11 f 267.293 (\241)s 8 f 273.905 (q)s 4 f 277.987 (\051)s 8 f 281.292 (=q)s 7 f 591.8 y 290.124 (:)s 2 f 386.017 (\0503.31\051)s 621.8 y 228.525 (16)s do-end end endp showpage %%PageTrailer %%Page: 18 18 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 18 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f387 sf ( )S -991 -1000 :M f54 sf ( )S -987 -1000 :M f120 sf -.709( )A f88 sf ( )S -980 -1000 :M f152 sf ( )S f186 sf ( )S -968 -1000 :M f219 sf ( )S -959 -1000 :M f253 sf ( )S -947 -1000 :M f420 sf ( )S f587 sf ( )S -920 -1000 :M f319 sf ( )S -917 -1000 :M f554 sf ( )S f353 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 5 10.95 /CMBX10 findfont fdef 6 6 /CMR6 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 12 6 /CMSY6 findfont fdef 13 10.95 /CMTI10 findfont fdef 14 10.95 /LASY10 findfont fdef 17 14.4 /CMBX12 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (By)s 71.185 (a)s 80.31 (simple)s 114.438 (c)s 119 (hange)s 150.634 (of)s 163.105 (v)s 168.276 (ariables,)s 211.558 (w)s 219.163 (e)s 227.679 (\257nd)s 10 f 105.523 y 75.03 (k)s 2 f 102.633 y 81.631 (\176)s 7 f 105.523 y 80.505 (\273)s 2 f 87.095 (\176)s 7 f 85.799 (\302)s 10 f 92.65 (k)s 8 f 107.165 y 98.125 (p)s 2 f 105.523 y 112.904 (=)s 0 f 91.185 y 131.421 (\275)s 91.674 y 138.921 (Z)s 10 f 105.523 y 150.746 (j)s 7 f 153.787 (\273)s 2 f 159.082 (\050)s 7 f 163.34 (g)s 2 f 168.956 (\050)s 7 f 173.214 (\270)s 2 f 179.602 (\051)s 183.86 (;)s 7 f 191.768 (g)s 2 f 197.384 (\050)s 7 f 201.642 (H)s 4 f 107.165 y 210.744 (1)s 2 f 105.523 y 217.928 (+)s 7 f 228.878 (V)s 2 f 237.699 (\051)s 7 f 241.957 (;)s 246.824 (g)s 2 f 252.439 (\050)s 7 f 256.698 (H)s 4 f 107.165 y 265.8 (1)s 2 f 105.523 y 270.55 (\051)s 274.808 (\051)s 10 f 279.067 (j)s 8 f 101.002 y 282.108 (p)s 7 f 105.523 y 289.929 (\302)s 2 f 296.78 (\050)s 7 f 301.038 (\270)s 10 f 309.859 (\241)s 7 f 320.809 (E)s 4 f 107.165 y 328.892 (0)s 10 f 105.523 y 336.076 (\241)s 7 f 347.026 (t)s 2 f 350.98 (\051)s 7 f 358.28 (d)s 363.979 (\270)s 0 f 91.185 y 370.367 (\276)s 4 f 93.952 y 377.867 (1)s 8 f 382.117 (=p)s 10 f 136.356 y 112.904 (\267)s 7 f 131.421 (C)s 4 f 137.999 y 139.247 (1)s 0 f 122.019 y 145.822 (\275)s 122.508 y 153.322 (Z)s 8 f 145.23 y 158.878 (I)s 159.902 (R)s 10 f 136.356 y 168.679 (j)s 7 f 171.72 (\273)s 2 f 177.015 (\050)s 7 f 181.273 (\270)s 2 f 187.661 (;)s 7 f 192.527 (g)s 2 f 198.143 (\050)s 7 f 202.401 (H)s 4 f 137.999 y 211.503 (1)s 2 f 136.356 y 218.687 (+)s 7 f 229.637 (V)s 2 f 238.458 (\051)s 7 f 242.716 (;)s 247.583 (g)s 2 f 253.198 (\050)s 7 f 257.457 (H)s 4 f 137.999 y 266.559 (1)s 2 f 136.356 y 271.309 (\051)s 275.567 (\051)s 10 f 279.826 (j)s 8 f 131.835 y 282.867 (p)s 7 f 136.356 y 290.688 (d)s 296.387 (\270)s 0 f 122.019 y 302.774 (\276)s 4 f 124.785 y 310.274 (1)s 8 f 314.525 (=p)s 10 f 161.391 y 112.904 (\267)s 7 f 131.421 (C)s 4 f 163.033 y 139.247 (1)s 10 f 161.391 y 147.039 (k)s 7 f 152.514 (g)s 2 f 158.129 (\050)s 7 f 162.388 (H)s 4 f 163.033 y 171.49 (1)s 2 f 161.391 y 178.673 (+)s 7 f 189.623 (V)s 2 f 198.444 (\051)s 10 f 205.136 (\241)s 7 f 216.086 (g)s 2 f 221.701 (\050)s 7 f 225.96 (H)s 4 f 163.033 y 235.062 (1)s 2 f 161.391 y 239.812 (\051)s 10 f 244.07 (k)s 4 f 155.619 y 249.545 (1)s 8 f 253.795 (=p)s 4 f 165.219 y 249.545 (1)s 8 f 253.795 (=p)s 7 f 161.391 y 262.824 (:)s 2 f 386.017 (\0503.32\051)s 187.482 y 54 (W)s 64.342 (e)s 72.927 (recall)s 102.226 (that)s 7 f 126.019 (V)s 2 f 137.996 (=)s 149.669 (\050)s 7 f 153.927 (\270)s 8 f 183.508 y 160.314 (m)s 190.664 y 160.314 (k)s 10 f 187.482 y 170.812 (\241)s 7 f 181.808 (\270)s 8 f 183.508 y 188.195 (M)s 190.664 y 188.195 (k)s 2 f 187.482 y 197.711 (\051)s 7 f 201.969 (u)s 8 f 189.266 y 208.237 (k)s 2 f 187.482 y 213.376 (.)s 221.49 (In)s 235.246 (particular,)s 288.926 (the)s 307.853 (v)s 313.328 (olume)s 345.638 (of)s 358.178 (the)s 377.104 (supp)s 399.978 (ort)s 201.082 y 54 (of)s 7 f 65.781 (V)s 2 f 77.561 (has)s 96.399 (order)s 124.361 (one,)s 146.925 (and)s 167.527 (is)s 177.848 (indep)s 204.31 (enden)s 231.989 (t)s 239.208 (of)s 10 f 250.988 (j)s 2 f 254.03 (\244)s 10 f 261.634 (j)s 2 f 264.676 (.)s 272.354 (W)s 282.696 (e)s 290.522 (pro)s 306.065 (v)s 311.54 (e)s 319.367 (in)s 331.451 (section)s 367.322 (5)s 375.757 (that)s 398.792 (the)s 216.591 y 54 (constan)s 90.257 (t)s 10 f 97.207 (k)s 7 f 102.682 (g)s 2 f 108.297 (\050)s 7 f 112.556 (H)s 4 f 218.234 y 121.658 (1)s 2 f 216.591 y 126.925 (+)s 7 f 135.958 (V)s 2 f 144.779 (\051)s 10 f 149.554 (\241)s 7 f 158.588 (g)s 2 f 164.203 (\050)s 7 f 168.462 (H)s 4 f 218.234 y 177.564 (1)s 2 f 216.591 y 182.314 (\051)s 10 f 186.572 (k)s 4 f 210.819 y 192.047 (1)s 8 f 196.297 (=p)s 4 f 220.419 y 192.047 (1)s 8 f 196.297 (=p)s 2 f 216.591 y 208.018 (dep)s 225.355 (ends)s 249.4 (only)s 272.471 (on)s 286.721 (the)s 304.621 (single-site)s 354.276 (p)s 360.663 (oten)s 381.043 (tial)s 7 f 399.551 (u)s 8 f 218.375 y 405.819 (k)s 2 f 216.591 y 410.958 (,)s 231.632 y 54 (and)s 75.119 (is)s 85.956 (indep)s 112.419 (enden)s 140.098 (t)s 147.833 (of)s 10 f 160.131 (j)s 2 f 163.172 (\244)s 10 f 170.777 (j)s 2 f 173.818 (.)s 181.669 (Consequen)s 232.83 (tly)s 244.996 (,)s 251.549 (the)s 270.235 (righ)s 288.819 (t)s 296.554 (side)s 318.342 (of)s 330.64 (\0503.32\051)s 362.1 (is)s 372.938 (b)s 379.325 (ounded)s 245.232 y 54 (ab)s 65.863 (o)s 71.033 (v)s 76.508 (e)s 86.177 (b)s 91.956 (y)s 7 f 102.537 (C)s 4 f 246.874 y 110.363 (0)s 7 f 245.232 y 115.113 (\264)s 4 f 241.258 y 120.943 (\0501)s 11 f 128.499 (\241)s 8 f 135.11 (q)s 4 f 139.192 (\051)s 8 f 142.498 (=q)s 2 f 245.232 y 151.33 (,)s 159.461 (indep)s 185.923 (enden)s 213.603 (t)s 222.663 (of)s 10 f 236.285 (j)s 2 f 239.327 (\244)s 10 f 246.931 (j)s 2 f 249.973 (.)s 261.337 (This)s 287.491 (estimate,)s 335.833 (equations)s 386.017 (\0503.25\051)s 258.832 y 54 (and)s 75.292 (\0503.5\051,)s 104.492 (lead)s 127.608 (us)s 141.661 (to)s 155.044 (the)s 173.903 (result)s 7 f 282.255 y 127.362 (I)s 129.75 (P)s 10 f 138.301 (f)s 2 f 143.776 (dist)s 164.52 (\050)s 7 f 168.778 (E)s 4 f 283.897 y 176.861 (0)s 7 f 282.255 y 181.612 (;)s 186.478 (\276)s 2 f 193.128 (\050)s 7 f 197.386 (H)s 4 f 283.95 y 206.489 (\244)s 2 f 282.255 y 212.883 (\051)s 217.141 (\051)s 7 f 224.441 (\074)s 236 (\264)s 10 f 241.83 (g)s 250.346 (\267)s 7 f 261.904 (C)s 8 f 283.95 y 269.731 (W)s 7 f 282.255 y 279.431 (\264)s 4 f 277.733 y 285.261 (1)s 8 f 289.511 (=)s 293.761 (q)s 10 f 282.255 y 298.343 (k)s 7 f 303.818 (g)s 10 f 309.433 (k)s 11 f 283.897 y 314.908 (1)s 10 f 282.255 y 323.909 (j)s 2 f 326.95 (\244)s 10 f 334.554 (j)s 7 f 337.596 (;)s 2 f 386.017 (\0503.33\051)s 305.677 y 54 (for)s 70.76 (an)s 82.014 (y)s 7 f 91.443 (q)s 99.766 (\076)s 2 f 111.324 (1)s 116.799 (.)s 14 f 124.707 (2)s 17 f 339.993 y 54 (4)s 78.3 (Lo)s 96.583 (calization)s 169.033 (Estimates)s 243.713 (on)s 266.213 (Eigenfunctions)s 2 f 364.437 y 54 (The)s 77.944 (lo)s 86.765 (calization)s 137.476 (prop)s 159.71 (erties)s 190.437 (of)s 204.344 (the)s 224.638 (eigenfunctions)s 297.614 (of)s 311.52 (the)s 331.814 (lo)s 340.635 (cally-p)s 372.877 (erturb)s 403.05 (ed)s 378.037 y 54 (Hamiltonians)s 7 f 121.984 (H)s 4 f 379.732 y 131.087 (\244)s 2 f 378.037 y 141.834 (are)s 160.817 (essen)s 184.968 (tial)s 205.137 (for)s 222.6 (the)s 242.161 (pro)s 258.312 (of)s 271.485 (of)s 284.659 (the)s 304.22 (W)s 314.562 (egner)s 344.495 (estimate)s 389.058 (giv)s 403.05 (en)s 391.637 y 54 (in)s 66.771 (section)s 103.328 (3.)s 116.71 (W)s 127.051 (e)s 135.564 (presen)s 165.768 (t)s 173.672 (t)s 177.626 (w)s 185.23 (o)s 194.351 (results)s 229.174 (concerning)s 283.95 (these)s 311.991 (eigenfunctions)s 383.527 (in)s 396.297 (this)s 405.237 y 54 (section.)s 96.396 (The)s 119.43 (results)s 154.782 (here)s 179.063 (apply)s 209.701 (to)s 223.61 (an)s 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(erator)s 194.773 (at)s 208.645 (an)s 224.341 (energy)s 7 f 259.838 (E)s 10 f 272.407 (2)s 7 f 283.562 (G)s 2 f 292.171 (.)s 301.543 (This)s 327.034 (is)s 338.533 (a)s 348.145 (v)s 353.62 (ersion)s 385.833 (of)s 398.792 (the)s 459.637 y 54 (Com)s 76.204 (b)s 82.592 (es-Thomas)s 137.463 (result)s 167.971 ([10)s 181.963 (])s 188.655 (pro)s 204.198 (v)s 209.673 (ed)s 224.273 (in)s 237.048 ([1)s 245.564 (].)s 5 f 480.464 y 54 (Prop)s 81.436 (osition)s 123.325 (4.1.)s 13 f 151.026 (L)s 157.334 (et)s 7 f 170.922 (H)s 4 f 482.107 y 180.024 (0)s 13 f 480.464 y 189.688 (satisfy)s 224.822 (hyp)s 240.773 (othesis)s 277.866 (\050H1a\051,)s 314.674 (and)s 336.936 (let)s 7 f 353.322 (E)s 10 f 366.881 (2)s 7 f 379.026 (G)s 13 f 387.636 (.)s 399.017 (L)s 405.325 (et)s 7 f 494.064 y 54 (d)s 11 f 495.707 y 59.699 (\247)s 2 f 494.064 y 69.852 (=)s 7 f 84.452 (dist)s 2 f 103.011 (\050)s 7 f 107.269 (B)s 11 f 495.707 y 115.575 (\247)s 7 f 494.064 y 122.686 (;)s 127.553 (E)s 2 f 136.267 (\051)s 13 f 140.525 (.)s 148.92 (Ther)s 171.447 (e)s 180.401 (exists)s 210.386 (a)s 219.9 (c)s 224.377 (onstant,)s 266.912 (dep)s 282.582 (ending)s 317.841 (on)s 7 f 333.512 (d)s 11 f 495.707 y 339.211 (\247)s 13 f 494.064 y 346.322 (,)s 353.598 (so)s 367.589 (that)s 10 f 520.35 y 157.081 (j)s 7 f 160.122 (G)s 4 f 521.992 y 168.732 (0)s 2 f 520.35 y 173.482 (\050)s 7 f 177.74 (x)s 183.998 (;)s 188.865 (y)s 2 f 194.626 (;)s 7 f 199.493 (E)s 2 f 208.207 (\051)s 10 f 212.466 (j)s 221.591 (\267)s 7 f 236.191 (C)s 244.8 (e)s 11 f 515.829 y 249.899 (\241)s 10 f 508.501 y 256.51 (p)s 21.136 .438 265.635 508.501 r 8 f 515.829 y 265.635 (d)s 12 f 516.907 y 270.009 (\241)s 8 f 515.829 y 276.286 (d)s 6 f 516.907 y 280.66 (+)s 11 f 515.829 y 286.771 (j)s 8 f 289.132 (x)s 11 f 293.917 (\241)s 8 f 300.528 (y)s 11 f 305.017 (j)s 7 f 520.35 y 307.878 (;)s 2 f 391.492 (\0504.1\051)s 13 f 543.773 y 54 (for)s 71.489 (al)s 80.444 (l)s 7 f 87.16 (x)s 93.418 (;)s 98.285 (y)s 10 f 107.088 (2)s 7 f 117.43 (I)s 119.744 (R)s 8 f 539.799 y 128.143 (d)s 13 f 543.773 y 136.934 (su)s 147.288 (\261ciently)s 192.201 (sep)s 206.752 (ar)s 216.406 (ate)s 230.118 (d.)s 2 f 564.6 y 71 (W)s 81.342 (e)s 90.123 (\257rst)s 112.987 (presen)s 143.191 (t)s 151.364 (a)s 160.754 (simple)s 195.146 (result)s 225.918 (indicating)s 277.283 (the)s 296.406 (exp)s 313.439 (onen)s 335.644 (tial)s 355.375 (deca)s 376.362 (y)s 386.056 (of)s 398.792 (the)s 578.2 y 54 (eigenfunctions)s 126.17 (of)s 7 f 139.271 (H)s 4 f 579.895 y 148.373 (\244)s 2 f 578.2 y 159.048 (a)s 164.219 (w)s 171.823 (a)s 176.994 (y)s 187.053 (from)s 213.568 (the)s 233.057 (supp)s 255.93 (ort)s 274.232 (of)s 287.333 (the)s 306.822 (lo)s 315.643 (cal)s 333.306 (p)s 339.694 (erturbation)s 7 f 398.176 (V)s 4 f 579.895 y 404.564 (\244)s 2 f 578.2 y 410.958 (.)s 591.8 y 54 (Let)s 7 f 73.619 (H)s 4 f 593.443 y 82.721 (0)s 2 f 591.8 y 91.121 (b)s 97.508 (e)s 106.025 (a)s 115.15 (bac)s 131.271 (kground)s 174.188 (Hamiltonian)s 237.151 (whic)s 258.747 (h)s 268.48 (is)s 279.491 (p)s 285.878 (erturb)s 316.052 (ed)s 330.652 (b)s 336.431 (y)s 345.86 (a)s 354.985 (p)s 361.372 (oten)s 381.751 (tial)s 7 f 401.218 (V)s 4 f 593.495 y 407.605 (\244)s 2 f 621.8 y 228.525 (17)s do-end end endp showpage %%PageTrailer %%Page: 19 19 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 19 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f120 sf ( )S -993 -1000 :M f88 sf ( )S -989 -1000 :M f186 sf ( )S -981 -1000 :M f219 sf ( )S -973 -1000 :M f520 sf ( )S -963 -1000 :M f253 sf ( )S -951 -1000 :M f420 sf ( )S f319 sf ( )S -936 -1000 :M f554 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 4 8 /CMR8 findfont fdef 5 10.95 /CMBX10 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 9 6 /CMMI6 findfont fdef 10 10.95 /CMSY10 findfont fdef 11 8 /CMSY8 findfont fdef 13 10.95 /CMTI10 findfont fdef 14 10.95 /LASY10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 54 (supp)s 76.873 (orted)s 105.246 (in)s 117.771 (a)s 126.646 (b)s 133.034 (ounded)s 171.109 (region)s 203.74 (\244)s 214.744 (so)s 227.938 (that)s 7 f 251.414 (H)s 4 f 76.695 y 260.516 (\244)s 2 f 75 y 269.952 (=)s 7 f 281.51 (H)s 4 f 76.642 y 290.612 (0)s 2 f 75 y 297.296 (+)s 7 f 307.747 (V)s 4 f 76.695 y 314.134 (\244)s 2 f 75 y 320.529 (,)s 327.02 (acting)s 359.621 (on)s 7 f 374.579 (L)s 4 f 71.026 y 382.031 (2)s 2 f 75 y 386.781 (\050)s 7 f 391.04 (I)s 393.427 (R)s 8 f 71.026 y 401.826 (d)s 2 f 75 y 406.7 (\051)s 410.958 (.)s 88.6 y 54 (F)s 60.235 (or)s 73.601 (an)s 84.855 (y)s 94.236 (region)s 10 f 127.069 (O)s 139.132 (\275)s 7 f 150.69 (I)s 153.078 (R)s 8 f 84.626 y 161.477 (d)s 2 f 88.6 y 166.35 (,)s 173.004 (let)s 7 f 188.772 (\302)s 11 f 90.295 y 195.624 (O)s 2 f 88.6 y 206.694 (b)s 213.082 (e)s 221.551 (the)s 240.361 (c)s 244.923 (haracteristic)s 307.655 (function)s 350.495 (of)s 362.918 (the)s 381.728 (region.)s 102.2 y 54 (Similar)s 91.747 (results)s 126.574 (hold)s 150.908 (for)s 167.667 (m)s 176.488 (ultiplicativ)s 228.196 (e)s 236.713 (p)s 243.101 (erturbations.)s 5 f 123.027 y 54 (Prop)s 81.436 (osition)s 123.008 (4.2.)s 13 f 149.882 (L)s 156.19 (et)s 7 f 169.524 (\301)s 13 f 180.708 (b)s 185.185 (e)s 194.882 (an)s 7 f 211.294 (L)s 4 f 119.054 y 218.746 (2)s 13 f 123.027 y 223.496 (-eigenfunction)s 295.875 (of)s 7 f 309.488 (H)s 4 f 124.722 y 318.591 (\244)s 13 f 123.027 y 329.645 (satisfying)s 7 f 379.077 (H)s 4 f 124.722 y 388.179 (\244)s 7 f 123.027 y 394.574 (\301)s 2 f 405.483 (=)s 7 f 136.627 y 54 (E)s 62.714 (\301)s 13 f 69.239 (,)s 77.78 (with)s 7 f 102.578 (E)s 10 f 116.168 (2)s 7 f 128.344 (G)s 13 f 136.953 (,)s 145.495 (the)s 164.696 (sp)s 174.21 (e)s 178.688 (ctr)s 191.42 (al)s 204.745 (gap)s 225.905 (of)s 7 f 239.79 (H)s 4 f 138.27 y 248.892 (0)s 13 f 136.627 y 258.572 (as)s 273.576 (in)s 288.021 (\050H1b\051.)s 327.181 (L)s 333.489 (et)s 10 f 347.094 (O)s 13 f 361.046 (b)s 365.523 (e)s 375.49 (an)s 392.173 (op)s 402.807 (en)s 150.227 y 54 (subset)s 86.388 (of)s 10 f 99.189 (f)s 13 f 104.664 (supp)s 7 f 128.488 (V)s 4 f 151.922 y 134.875 (\244)s 10 f 150.227 y 141.27 (g)s 8 f 146.254 y 146.745 (c)s 10 f 150.227 y 153.968 (\275)s 7 f 165.526 (I)s 167.841 (R)s 8 f 146.254 y 176.24 (d)s 13 f 150.227 y 184.959 (such)s 209.792 (that)s 232.107 (dist)s 2 f 251.453 (\050)s 10 f 255.712 (O)s 7 f 264.733 (;)s 13 f 269.6 (supp)s 7 f 293.424 (V)s 4 f 151.922 y 299.811 (\244)s 2 f 150.227 y 306.206 (\051)s 7 f 313.506 (\076)s 325.064 (\261)s 333.387 (\076)s 2 f 344.945 (0)s 13 f 350.42 (.)s 358.791 (Then,)s 390.634 (ther)s 408.963 (e)s 163.827 y 54 (exist)s 79.507 (c)s 83.985 (onstants)s 7 f 127.638 (A)s 8 f 165.522 y 135.851 (E)s 7 f 163.827 y 146.07 (\076)s 2 f 157.629 (0)s 13 f 167.021 (and)s 7 f 188.288 (C)s 8 f 165.522 y 196.115 (E)s 7 f 163.827 y 206.334 (\076)s 2 f 217.892 (0)s 13 f 227.285 (such)s 252.19 (that)s 10 f 187.365 y 187.312 (k)s 7 f 192.787 (\302)s 11 f 189.06 y 199.639 (O)s 7 f 187.365 y 207.108 (\301)s 10 f 213.632 (k)s 222.149 (\267)s 7 f 233.707 (A)s 8 f 189.06 y 241.92 (E)s 7 f 187.365 y 249.097 (e)s 11 f 182.844 y 254.196 (\241)s 8 f 260.807 (C)s 9 f 184.189 y 266.865 (E)s 8 f 182.844 y 273.085 (\261)s 7 f 187.365 y 277.646 (:)s 2 f 391.492 (\0504.2\051)s 5 f 218.131 y 54 (Pro)s 74.44 (of.)s 2 f 92.948 (W)s 103.29 (e)s 111.807 (b)s 118.194 (egin)s 141.311 (b)s 147.09 (y)s 156.519 (rewriting)s 203.422 (the)s 222.28 (eigen)s 246.309 (v)s 251.48 (alue)s 274.597 (equation)s 319.309 (as)s 241.669 y 185.772 (\050)s 7 f 190.031 (H)s 4 f 243.311 y 199.133 (0)s 10 f 241.669 y 206.316 (\241)s 7 f 217.266 (E)s 2 f 225.98 (\051)s 7 f 230.239 (\301)s 2 f 239.805 (=)s 10 f 251.363 (\241)s 7 f 259.88 (V)s 4 f 243.364 y 266.267 (\244)s 7 f 241.669 y 272.662 (\301)s 279.186 (:)s 2 f 391.492 (\0504.3\051)s 265.207 y 54 (Since)s 82.592 (the)s 101.45 (energy)s 7 f 136.46 (E)s 10 f 148.216 (2)s 7 f 158.557 (\275)s 2 f 164.219 (\050)s 7 f 168.477 (H)s 4 f 266.849 y 177.579 (0)s 2 f 265.207 y 182.329 (\051)s 186.588 (,)s 193.279 (w)s 200.883 (e)s 209.4 (ha)s 220.654 (v)s 226.129 (e)s 7 f 288.745 y 192.858 (\301)s 2 f 202.424 (=)s 10 f 213.982 (\241)s 7 f 222.499 (R)s 4 f 290.387 y 230.813 (0)s 2 f 288.745 y 235.563 (\050)s 7 f 239.821 (E)s 2 f 248.536 (\051)s 7 f 252.794 (V)s 4 f 290.44 y 259.182 (\244)s 7 f 288.745 y 265.576 (\301)s 272.101 (:)s 2 f 391.492 (\0504.4\051)s 312.283 y 54 (W)s 64.342 (e)s 72.858 (no)s 84.112 (w)s 95.671 (m)s 104.492 (ultiply)s 139.471 (on)s 154.679 (the)s 173.538 (left)s 192.7 (b)s 198.479 (y)s 207.908 (the)s 226.767 (c)s 231.329 (haracteristic)s 294.109 (function)s 336.997 (of)s 10 f 349.468 (O)s 2 f 362.139 (to)s 375.523 (obtain,)s 10 f 335.821 y 171.846 (k)s 7 f 177.321 (\302)s 11 f 337.516 y 184.172 (O)s 7 f 335.821 y 191.641 (\301)s 10 f 198.166 (k)s 2 f 206.682 (=)s 10 f 218.24 (k)s 7 f 223.715 (\302)s 11 f 337.516 y 230.567 (O)s 7 f 335.821 y 238.036 (R)s 4 f 337.463 y 246.35 (0)s 2 f 335.821 y 251.1 (\050)s 7 f 255.358 (E)s 2 f 264.073 (\051)s 7 f 268.331 (V)s 4 f 337.516 y 274.719 (\244)s 7 f 335.821 y 281.113 (\301)s 10 f 287.638 (k)s 7 f 293.113 (:)s 2 f 391.492 (\0504.5\051)s 359.359 y 54 (W)s 64.342 (e)s 73.624 (no)s 84.879 (w)s 97.203 (use)s 116.888 (the)s 136.513 (estimate)s 181.14 (on)s 197.114 (the)s 216.738 (deca)s 237.726 (y)s 247.921 (of)s 261.158 (the)s 280.782 (resolv)s 308.249 (en)s 318.895 (t)s 327.569 (of)s 7 f 340.806 (R)s 4 f 361.001 y 349.12 (0)s 2 f 359.359 y 353.87 (\050)s 7 f 358.129 (E)s 2 f 366.843 (\051)s 375.517 (giv)s 389.509 (en)s 404.875 (in)s 372.959 y 54 (Prop)s 77.603 (osition)s 112.948 (4.1)s 130.589 (to)s 143.973 (obtain)s 178.039 (the)s 196.898 (estimate.)s 14 f 245.017 (2)s 2 f 386.559 y 71 (Kirsc)s 95.729 (h,)s 109.302 (Stollmann,)s 165.459 (and)s 187.389 (Stolz)s 215.403 ([19)s 229.394 (])s 236.725 (presen)s 266.928 (t)s 275.475 (a)s 285.239 (nice)s 308.386 (result,)s 342.734 (called)s 374.398 (here)s 398.792 (the)s 400.159 y 54 (KSS)s 78.599 (Comparison)s 139.79 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98.027 (f)s 7 f 103.502 (x)s 10 f 112.802 (j)s 7 f 118.886 (V)s 4 f 548.242 y 125.273 (\244)s 2 f 546.547 y 131.668 (\050)s 7 f 135.926 (x)s 2 f 142.184 (\051)s 10 f 149.484 (6)s 2 f 149.484 (=)s 7 f 161.042 (V)s 4 f 548.19 y 167.43 (0)s 2 f 546.547 y 172.18 (\050)s 7 f 176.438 (x)s 2 f 182.697 (\051)s 10 f 186.955 (g)s 2 f 192.43 (\051)s 7 f 199.73 (\076)s 211.288 (\265)s 219.774 (\076)s 2 f 231.333 (0)s 13 f 236.808 (.)s 568.262 y 54 (We)s 73.892 (then)s 98.238 (have,)s 10 f 591.8 y 131.617 (k)s 7 f 137.092 (\301)s 10 f 143.617 (k)s 152.133 (\267)s 2 f 163.692 (\050)s 167.95 (1)s 175.858 (+)s 10 f 186.808 (k)s 2 f 192.283 (\050)s 7 f 196.542 (H)s 4 f 587.279 y 206.533 (0)s 594.507 y 205.644 (\244)s 10 f 591.8 y 214.472 (\241)s 7 f 225.422 (E)s 2 f 234.136 (\051)s 11 f 587.279 y 238.394 (\241)s 4 f 245.005 (1)s 7 f 591.8 y 249.756 (W)s 4 f 593.443 y 260.097 (1)s 10 f 591.8 y 264.847 (k)s 2 f 270.322 (\051)s 10 f 274.581 (k)s 2 f 280.056 (\050)s 284.314 (1)s 10 f 292.222 (\241)s 7 f 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190.982 (\241)s 4 f 197.594 (1)s 10 f 167.6 y 202.344 (k)s 11 f 169.295 y 207.819 (I)s 6 f 170.406 y 212.503 (2)s 9 f 216.169 (q)s 10 f 167.6 y 226.892 (\267)s 2 f 241.492 (2)s 10 f 246.967 (k)s 7 f 252.442 (J)s 8 f 169.384 y 258.514 (\256)s 263.973 (;)s 266.334 (\257)s 2 f 167.6 y 272.015 (\050)s 10 f 276.273 (\241)s 2 f 284.79 (\242)s 296.348 (+)s 307.298 (1)s 312.773 (\051)s 11 f 163.079 y 317.032 (\241)s 4 f 323.643 (1)s 10 f 167.6 y 328.393 (k)s 11 f 169.295 y 333.868 (I)s 6 f 170.406 y 338.552 (2)s 9 f 342.218 (q)s 7 f 167.6 y 346.858 (:)s 2 f 391.492 (\0505.8\051)s 192.2 y 54 (Com)s 76.204 (bining)s 109.706 (this)s 131.102 (observ)s 161.306 (ation)s 189.333 (with)s 214.318 (\0505.7\051)s 240.52 (and)s 261.855 (\0505.8\051,)s 291.109 (w)s 298.713 (e)s 307.274 (\257nd)s 329.217 (that)s 7 f 352.986 (V)s 8 f 193.984 y 359.373 (ef)s 368.281 (f)s 10 f 192.2 y 376.861 (2)s 387.275 (I)s 4 f 194.428 y 393.237 (2)s 8 f 397.487 (q)s 401.569 (=)s 405.819 (k)s 2 f 192.2 y 410.958 (.)s 205.8 y 54 (W)s 64.342 (e)s 72.697 (c)s 77.259 (ho)s 89.122 (ose)s 7 f 107.271 (k)s 2 f 116.805 (so)s 130.088 (large)s 156.723 (that)s 180.287 (2)s 7 f 185.762 (q)s 191.043 (=)s 2 f 196.518 (\050)s 7 f 200.776 (k)s 10 f 208.932 (\241)s 2 f 219.559 (2\051)s 10 f 232.334 (\267)s 2 f 243.892 (1)s 7 f 249.367 (=p)s 2 f 260.351 (,)s 266.914 (i.)s 276.486 (e.)s 287.882 (w)s 295.487 (e)s 303.842 (can)s 323.755 (tak)s 338.964 (e)s 7 f 347.319 (k)s 356.406 (\076)s 2 f 367.964 (2)s 7 f 373.439 (pq)s 2 f 386.34 (+)s 396.967 (2)s 7 f 405.483 (\076)s 219.4 y 54 (dp=)s 2 f 70.684 (2)s 78.592 (+)s 89.542 (2)s 95.017 (.)s 102.925 (This)s 127.928 (pro)s 143.471 (v)s 148.946 (es)s 161.781 (the)s 180.64 (theorem.)s 14 f 227.512 (2)s 2 f 621.8 y 228.525 (21)s do-end end endp showpage %%PageTrailer %%Page: 23 23 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 23 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f88 sf ( )S -993 -1000 :M f186 sf ( )S -985 -1000 :M f319 sf ( )S -982 -1000 :M f353 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 5 10.95 /CMBX10 findfont fdef 7 10.95 /CMMI10 findfont fdef 13 10.95 /CMTI10 findfont fdef 20 24.88 /CMBX12 findfont fdef 66 66 translate 72 72.27 div dup scale 20 f 155 y 54 (Bibliograph)s 196.124 (y)s 2 f 208.6 y 72.402 ([1])s 89.435 (J.-M.)s 117.86 (Barbaroux,)s 174.758 (J.)s 186.454 (M.)s 202.56 (Com)s 224.764 (b)s 231.152 (es,)s 246.531 (and)s 267.2 (P)s 273.739 (.)s 279.808 (D.)s 294.241 (Hislop:)s 332.011 (Lo)s 344.634 (calization)s 393.286 (near)s 222.2 y 89.435 (band)s 116.806 (edges)s 146.063 (for)s 162.819 (random)s 202.995 (Sc)s 213.641 (hr)s 224.013 (\304)s 224.013 (odinger)s 262.973 (op)s 274.835 (erators,)s 13 f 314.495 (Helv.)s 342.779 (Phys.)s 372.869 (A)s 380.449 (cta)s 5 f 398.366 (70)s 2 f 410.958 (,)s 235.8 y 89.435 (16)s 100.385 (\17343)s 120.46 (\0501997\051.)s 257.514 y 72.402 ([2])s 89.435 (M.)s 106.163 (S.)s 118.937 (Birman,)s 161.398 (M.)s 178.126 (Z.)s 191.508 (Solomjak:)s 243.215 (Sp)s 255.686 (ectral)s 286.132 (theory)s 320.532 (of)s 333.002 (self-adjoin)s 381.425 (t)s 389.332 (op)s 401.195 (er-)s 271.114 y 89.435 (ators)s 116.902 (in)s 129.677 (Hilb)s 150.36 (ert)s 167.424 (space,)s 199.726 (Dordrec)s 237.656 (h)s 243.435 (t:)s 255.602 (D.)s 270.658 (Reidel)s 304.269 (Publishing)s 358.623 (Co.)s 378.698 (1987.)s 292.829 y 72.402 ([3])s 89.435 (M.)s 105.147 (S.)s 116.904 (Birman,)s 158.552 (D.)s 172.59 (R.)s 186.324 (Y)s 193.624 (afaev:)s 225.965 (The)s 247.456 (sp)s 258.163 (ectral)s 287.592 (shift)s 311.272 (function:)s 357.909 (The)s 379.4 (w)s 387.004 (ork)s 405.179 (of)s 306.429 y 89.435 (M.)s 105.017 (G.)s 119.155 (Krein)s 148.455 (and)s 168.599 (its)s 182.721 (further)s 218.439 (dev)s 234.864 (elopmen)s 274.102 (t,)s 13 f 284.134 (St.)s 300.148 (Petersbur)s 345.353 (g)s 353.252 (Mathematics)s 320.029 y 89.435 (Journal)s 5 f 129.476 (4)s 2 f 135.772 (,)s 142.464 (833)s 158.889 (\173870)s 184.439 (\0501992\051.)s 341.743 y 72.402 ([4])s 89.435 (D.)s 104.451 (Busc)s 127.172 (hmann,)s 166.68 (G.)s 181.924 (Stolz:)s 213.536 (Tw)s 229.049 (o-parameter)s 290.51 (sp)s 301.217 (ectral)s 331.623 (a)s 336.794 (v)s 342.269 (eraging)s 380.583 (and)s 401.833 (lo-)s 355.343 y 89.435 (calization)s 138.931 (for)s 155.91 (non-monotonic)s 230.955 (random)s 271.356 (Sc)s 282.002 (hr)s 292.374 (\304)s 292.374 (odinger)s 331.558 (op)s 343.42 (erators,)s 13 f 383.358 (T)s 390.354 (r)s 394.412 (ans.)s 368.943 y 89.435 (A)s 97.295 (mer.)s 123.179 (Math.)s 155.105 (So)s 166.298 (c.)s 5 f 178.343 (353)s 2 f 197.231 (,)s 203.923 (635)s 220.348 (\173653)s 245.898 (\0502001\051.)s 390.657 y 72.402 ([5])s 89.435 (J.)s 102.134 (M.)s 119.244 (Com)s 141.448 (b)s 147.835 (es,)s 164.188 (P)s 170.728 (.)s 177.8 (D.)s 193.236 (Hislop:)s 232.078 (Lo)s 244.701 (calization)s 294.356 (for)s 311.496 (some)s 339.312 (con)s 355.433 (tin)s 368.512 (uous)s 394.503 (ran-)s 404.257 y 89.435 (dom)s 114.391 (Hamiltonians)s 182.296 (in)s 7 f 195.693 (d)s 2 f 201.393 (-dimensions,)s 13 f 264.951 (J.)s 278.548 (F)s 284.856 (unct.)s 313.412 (A)s 321.272 (nal.)s 2 f 343.672 (,)s 5 f 351.141 (124)s 2 f 370.03 (,)s 377.5 (149-180)s 417.857 y 89.435 (\0501994\051.)s 439.572 y 72.402 ([6])s 89.435 (J.)s 101.439 (M.)s 117.853 (Com)s 140.057 (b)s 146.445 (es,)s 162.07 (P)s 168.609 (.)s 174.986 (D.)s 189.727 (Hislop:)s 227.651 (Landau)s 267.029 (Hamiltonians)s 333.996 (with)s 358.622 (random)s 398.487 (p)s 404.875 (o-)s 453.172 y 89.435 (ten)s 104.34 (tials:)s 132.867 (Lo)s 145.49 (calization)s 195.007 (and)s 216.54 (densit)s 244.889 (y)s 254.56 (of)s 267.272 (states,)s 13 f 301.763 (Commun.)s 352.634 (Math.)s 384.782 (Phys.)s 2 f 410.958 (,)s 5 f 466.772 y 89.435 (177)s 2 f 108.324 (,)s 115.016 (603)s 131.441 (\173629)s 156.991 (\0501996\051.)s 488.486 y 72.402 ([7])s 89.435 (J.)s 101.756 (M.)s 118.487 (Com)s 140.691 (b)s 147.078 (es,)s 162.958 (P)s 169.497 (.)s 176.191 (D.)s 191.248 (Hislop,)s 228.115 (E.)s 242.261 (Mourre:)s 285.212 (Sp)s 297.683 (ectral)s 328.132 (a)s 333.303 (v)s 338.778 (eraging,)s 380.177 (p)s 386.564 (ertur-)s 502.086 y 89.435 (bation)s 122.685 (of)s 134.339 (singular)s 174.98 (sp)s 185.687 (ectra,)s 215.48 (and)s 235.955 (lo)s 244.775 (calization,)s 13 f 296.439 (T)s 303.434 (r)s 307.492 (ans.)s 330.246 (A)s 338.106 (mer.)s 363.238 (Math.)s 394.412 (So)s 405.605 (c.)s 5 f 515.686 y 89.435 (348)s 2 f 108.324 (,)s 115.016 (4883)s 136.916 (\1734894)s 167.941 (\0501996\051.)s 537.4 y 72.402 ([8])s 89.435 (J.)s 103.689 (M.)s 122.354 (Com)s 144.558 (b)s 150.945 (es,)s 169.242 (P)s 175.781 (.)s 184.408 (D.)s 201.399 (Hislop,)s 240.683 (E.)s 256.762 (Mourre:)s 303.58 (Correlated)s 359.718 (W)s 370.06 (egner)s 401.225 (in-)s 551 y 89.435 (equalities)s 139.677 (for)s 158.255 (random)s 200.254 (Sc)s 210.9 (hr)s 221.272 (\304)s 221.272 (odinger)s 262.054 (op)s 273.917 (erators,)s 315.853 (in)s 13 f 330.446 (A)s 338.026 (dvanc)s 364.89 (es)s 379.995 (in)s 395.099 (Dif-)s 564.6 y 89.435 (fer)s 101.888 (ential)s 133.829 (Equations)s 186.349 (and)s 209.055 (Mathematic)s 264.766 (al)s 278.518 (Physics:)s 325.481 (Pr)s 336.967 (o)s 342.004 (c)s 346.481 (e)s 350.958 (e)s 355.435 (dings)s 385.417 (of)s 399.729 (the)s 578.2 y 89.435 (International)s 156.531 (Confer)s 188.571 (enc)s 204.242 (e)s 213.807 (on)s 230.089 (Di)s 241.714 (\256)s 248.43 (er)s 257.524 (ential)s 288.637 (Equations)s 340.329 (and)s 362.207 (Mathemat-)s 591.8 y 89.435 (ic)s 97.271 (al)s 110.541 (Physics)s 151.107 (1997)s 2 f 173.494 (,)s 181.487 (Con)s 200.649 (temp)s 225.287 (orary)s 255.285 (Mathematics)s 5 f 321.783 (217)s 2 f 340.671 (,)s 348.664 (E.)s 363.849 (Carlen,)s 403.506 (E.)s 621.8 y 228.525 (22)s do-end end endp showpage %%PageTrailer %%Page: 24 24 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 24 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f88 sf ( )S -993 -1000 :M f186 sf ( )S -985 -1000 :M f219 sf ( )S -977 -1000 :M f319 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 5 10.95 /CMBX10 findfont fdef 7 10.95 /CMMI10 findfont fdef 8 8 /CMMI8 findfont fdef 13 10.95 /CMTI10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 89.435 (M.)s 105.855 (Harrell,)s 145.513 (M.)s 161.932 (Loss,)s 189.333 (eds.,)s 214.088 (191)s 230.513 (\173204,)s 258.856 (American)s 308.156 (Mathematical)s 377.5 (So)s 389.362 (ciet)s 406.092 (y)s 410.958 (,)s 88.6 y 89.435 (1998.)s 110.133 y 72.402 ([9])s 89.435 (J.)s 101.526 (M.)s 118.026 (Com)s 140.231 (b)s 146.618 (es,)s 162.313 (P)s 168.852 (.)s 175.315 (D.)s 190.143 (Hislop,)s 226.825 (A.)s 241.501 (Tip:)s 266.329 (Band)s 295.148 (edge)s 319.861 (lo)s 328.682 (calization)s 377.729 (and)s 398.792 (the)s 123.733 y 89.435 (densit)s 117.784 (y)s 127.678 (of)s 140.614 (states)s 172.226 (for)s 189.45 (acoustic)s 231.951 (and)s 253.708 (electromagnetic)s 332.679 (w)s 340.283 (a)s 345.454 (v)s 350.929 (es)s 364.229 (in)s 377.47 (random)s 137.333 y 89.435 (media,)s 13 f 124.719 (A)s 132.578 (nn.)s 152.167 (Inst.)s 177.935 (H.)s 193.351 (Poinc)s 220.366 (ar)s 230.3 (\266)s 230.58 (e)s 5 f 239.267 (70)s 2 f 251.86 (,)s 258.551 (381)s 274.976 (\173428)s 300.526 (\0501999\051.)s 158.867 y 66.927 ([10])s 89.435 (J.)s 102.516 (M.)s 120.007 (Com)s 142.211 (b)s 148.598 (es,)s 165.428 (L.)s 179.725 (Thomas:)s 227.542 (Asymptotic)s 287.373 (b)s 293.76 (eha)s 309.881 (vior)s 332.878 (of)s 346.11 (eigenfunctions)s 172.467 y 89.435 (for)s 106.681 (m)s 115.502 (ultiparticle)s 171.985 (Sc)s 182.63 (hr)s 193.003 (\304)s 193.003 (odinger)s 232.452 (op)s 244.315 (erators,)s 13 f 284.585 (Commun.)s 335.682 (Math.)s 368.054 (Phys.)s 5 f 398.366 (34)s 2 f 410.958 (,)s 186.067 y 89.435 (251)s 105.86 (\173270)s 131.411 (\0501973\051.)s 207.6 y 66.927 ([11])s 89.435 (W.)s 108.205 (F)s 114.44 (aris:)s 141.121 (A)s 153.806 (lo)s 162.627 (calization)s 212.725 (principle)s 258.596 (for)s 276.18 (m)s 285 (ultiplicativ)s 336.709 (e)s 346.049 (p)s 352.437 (erturbations,)s 13 f 221.2 y 89.435 (J.)s 102.46 (F)s 108.768 (unct.)s 136.751 (A)s 144.611 (nal.)s 5 f 166.17 (67)s 2 f 178.762 (,)s 185.454 (105)s 201.879 (\173114)s 227.429 (\0501986\051.)s 242.733 y 66.927 ([12])s 89.435 (A.)s 103.825 (Figotin,)s 144.628 (A.)s 159.017 (Klein:)s 192.218 (Lo)s 204.841 (calization)s 253.601 (of)s 265.557 (classical)s 307.139 (w)s 314.743 (a)s 319.914 (v)s 325.389 (es)s 337.71 (I:)s 347.841 (acoustic)s 389.363 (mo)s 404.267 (d-)s 256.333 y 89.435 (els,)s 13 f 108.355 (Commun.)s 159.004 (Math.)s 190.929 (Phys.)s 5 f 220.756 (180)s 2 f 239.644 (,)s 246.336 (439)s 262.761 (\173482)s 288.311 (\0501996\051.)s 277.867 y 66.927 ([13])s 89.435 (A.)s 104.558 (Figotin,)s 146.046 (A.)s 161.168 (Klein:)s 195.064 (Lo)s 207.687 (calization)s 257.18 (of)s 269.869 (classical)s 312.184 (w)s 319.789 (a)s 324.959 (v)s 330.434 (es)s 343.489 (I)s 347.747 (I:)s 358.611 (electromag-)s 291.467 y 89.435 (netic)s 116.202 (w)s 123.806 (a)s 128.977 (v)s 134.452 (es,)s 13 f 150.33 (Commun.)s 200.979 (Math.)s 232.904 (Phys.)s 5 f 262.731 (184)s 2 f 281.619 (,)s 288.311 (411)s 304.736 (\173441)s 330.286 (\0501997\051.)s 313 y 66.927 ([14])s 89.435 (P)s 95.975 (.)s 103.909 (D.)s 120.208 (Hislop,)s 158.627 (F.)s 173.709 (Klopp:)s 213.302 (The)s 237.053 (W)s 247.395 (egner)s 277.868 (estimate)s 322.972 (and)s 345.506 (the)s 365.607 (in)s 374.428 (tegrated)s 326.6 y 89.435 (densit)s 117.784 (y)s 127.904 (of)s 141.067 (states)s 172.905 (for)s 190.356 (some)s 218.483 (random)s 259.355 (op)s 271.218 (erators)s 308.531 (with)s 334.164 (non-sign)s 378.717 (de)s 389.667 (\257nite)s 340.2 y 89.435 (p)s 95.823 (oten)s 116.202 (tials,)s 143.03 (in)s 155.805 (preparation.)s 361.734 y 66.927 ([15])s 89.435 (D.)s 103.391 (Hundertmark,)s 173.747 (B.)s 187.094 (Simon:)s 224.26 (An)s 241.106 (optimal)s 7 f 280.155 (L)s 8 f 357.76 y 287.607 (p)s 2 f 361.734 y 292.386 (-b)s 302.423 (ound)s 328.698 (on)s 342.806 (the)s 360.563 (Krein)s 389.91 (sp)s 400.617 (ec-)s 375.334 y 89.435 (tral)s 110.149 (shift)s 134.848 (function,)s 180.777 (preprin)s 215.209 (t)s 223.117 (2000,)s 251.709 (to)s 265.092 (app)s 283.038 (ear)s 301.318 (in)s 13 f 314.093 (J.)s 327.118 (d\047A)s 343.932 (nalyse)s 377.232 (Math.)s 2 f 405.239 (.)s 396.867 y 66.927 ([16])s 89.435 (F.)s 102.921 (Klopp:)s 139.852 (Lo)s 152.475 (calization)s 201.395 (for)s 217.8 (some)s 244.882 (con)s 261.003 (tin)s 274.082 (uous)s 299.338 (random)s 339.164 (Sc)s 349.81 (hr)s 360.182 (\304)s 360.182 (odinger)s 398.792 (op-)s 410.467 y 89.435 (erators,)s 13 f 129.099 (Commun.)s 179.748 (Math.)s 211.673 (Phys.)s 5 f 241.5 (167)s 2 f 260.388 (,)s 267.08 (553)s 283.505 (\173569)s 309.055 (\0501995\051.)s 432 y 66.927 ([17])s 89.435 (W.)s 107.045 (Kirsc)s 131.774 (h,)s 144.281 (Random)s 187.897 (Sc)s 198.543 (hr)s 208.915 (\304)s 208.915 (odinger)s 247.543 (op)s 259.405 (erators:)s 300.117 (a)s 308.907 (course,)s 345.229 (in)s 357.668 (Sc)s 368.314 (hr)s 378.686 (\304)s 378.686 (odinger)s 445.6 y 89.435 (Op)s 104.34 (erators,)s 143.816 (Sonderb)s 183.084 (org)s 201.738 (DK)s 222.035 (1988,)s 250.439 (ed.)s 267.847 (H.)s 282.517 (Holden)s 319.695 (and)s 340.752 (A.)s 355.422 (Jensen,)s 393.773 (Lec-)s 459.2 y 89.435 (ture)s 112.583 (Notes)s 143.364 (in)s 156.139 (Ph)s 169.371 (ysics)s 5 f 195.346 (345)s 2 f 214.235 (,)s 220.927 (Berlin:)s 257.913 (Springer,)s 304.816 (1989.)s 480.734 y 66.927 ([18])s 89.435 (W.)s 107.657 (Kirsc)s 132.386 (h:)s 146.929 (W)s 157.271 (egner)s 186.777 (estimates)s 235.233 (and)s 256.8 (lo)s 265.621 (calization)s 315.172 (for)s 332.207 (allo)s 348.937 (y-t)s 362.32 (yp)s 374.487 (e)s 383.279 (p)s 389.667 (oten-)s 494.334 y 89.435 (tials,)s 13 f 116.263 (Math.)s 148.188 (Zeit.)s 5 f 173.945 (221)s 2 f 192.833 (,)s 199.525 (507)s 215.95 (\173512)s 241.5 (\0501996\051.)s 515.867 y 66.927 ([19])s 89.435 (W.)s 109.013 (Kirsc)s 133.741 (h,)s 148.555 (P)s 155.095 (.)s 163.418 (Stollmann,)s 220.815 (and)s 243.738 (G.)s 260.654 (Stolz:)s 295.55 (Lo)s 308.172 (calization)s 359.079 (for)s 377.47 (random)s 529.467 y 89.435 (p)s 95.823 (erturbations)s 158.047 (of)s 170.57 (p)s 176.958 (erio)s 194.934 (dic)s 212.628 (Sc)s 223.274 (hr)s 233.646 (\304)s 233.646 (odinger)s 272.662 (op)s 284.525 (erators,)s 13 f 324.254 (R)s 331.681 (andom)s 367.548 (Op)s 380.98 (er)s 390.074 (ators)s 543.067 y 89.435 (and)s 110.703 (Sto)s 125.534 (chastic)s 162.192 (Equations)s 5 f 213.005 (6)s 2 f 219.302 (,)s 225.993 (241)s 246.068 (\173)s 255.193 (268)s 275.268 (\0501998\051.)s 564.6 y 66.927 ([20])s 89.435 (W.)s 106.537 (Kirsc)s 131.266 (h,)s 143.365 (P)s 149.905 (.)s 155.752 (Stollmann,)s 210.434 (G.)s 224.874 (Stolz:)s 256.085 (Anderson)s 304.303 (lo)s 313.124 (calization)s 361.554 (for)s 377.47 (random)s 578.2 y 89.435 (Sc)s 100.081 (hr\304)s 110.453 (odinger)s 148.895 (op)s 160.757 (erators)s 196.857 (with)s 221.276 (long)s 244.479 (range)s 273.796 (in)s 282.617 (teractions,)s 13 f 335.823 (Commun.)s 385.993 (Math.)s 591.8 y 89.435 (Phys.)s 5 f 119.262 (195)s 2 f 138.15 (,)s 144.842 (495)s 161.267 (\173507)s 186.817 (\0501998\051.)s 621.8 y 228.525 (23)s do-end end endp showpage %%PageTrailer %%Page: 25 25 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 25 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f88 sf ( )S -993 -1000 :M f319 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 5 10.95 /CMBX10 findfont fdef 13 10.95 /CMTI10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 66.927 ([21])s 89.435 (V.)s 105.118 (Kostrykin,)s 160.323 (R.)s 175.853 (Sc)s 186.499 (hrader:)s 227.049 (Scattering)s 280.175 (theory)s 315.354 (approac)s 352.797 (h)s 363.308 (to)s 377.47 (random)s 88.6 y 89.435 (Sc)s 100.081 (hr)s 110.453 (\304)s 110.453 (odinger)s 149.504 (op)s 161.367 (erators)s 198.075 (in)s 210.937 (one-dimension,)s 13 f 285.932 (R)s 293.359 (ev.)s 310.789 (Math.)s 342.794 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(estimates)s 246.421 (and)s 267.548 (lo)s 276.369 (calization)s 325.481 (for)s 342.076 (con)s 358.197 (tin)s 371.276 (uum)s 396.054 (An-)s 468.8 y 89.435 (derson)s 124.745 (mo)s 139.649 (dels)s 162.153 (with)s 187.638 (some)s 215.616 (singular)s 257.617 (distributions,)s 13 f 325.365 (A)s 333.225 (r)s 337.282 (chiv)s 360.728 (der)s 380.396 (Mathe-)s 482.4 y 89.435 (matik)s 5 f 119.669 (75)s 2 f 132.262 (,)s 138.954 (307)s 155.379 (\173311)s 180.929 (\0502000\051.)s 505 y 66.927 ([31])s 89.435 (H.)s 105.282 (v)s 110.757 (on)s 126.908 (Dreifus,)s 169.088 (A.)s 184.935 (Klein:)s 220.279 (A)s 233.083 (new)s 256.534 (pro)s 272.685 (of)s 286.099 (of)s 299.512 (lo)s 308.333 (calization)s 358.551 (for)s 376.253 (the)s 396.054 (An-)s 518.6 y 89.435 (derson)s 125.823 (tigh)s 144.377 (t-binding)s 193.449 (mo)s 208.353 (del,)s 13 f 231.063 (Commun.)s 283.204 (Math.)s 316.62 (Phys.)s 5 f 348.068 (124)s 2 f 366.957 (,)s 375.675 (245)s 392.1 (\173299)s 532.2 y 89.435 (\0501989\051.)s 554.8 y 66.927 ([32])s 89.435 (F.)s 103.435 (W)s 113.776 (egner:)s 147.584 (The)s 170.252 (densit)s 198.601 (y)s 208.19 (of)s 220.82 (states)s 252.126 (for)s 269.046 (disordered)s 322.252 (systems,)s 13 f 366.13 (Zeit.)s 392.301 (Phy.)s 568.4 y 89.435 (B)s 5 f 100.793 (44)s 2 f 113.385 (,)s 120.077 (9)s 125.552 (\17315)s 145.627 (\0501981\051.)s 621.8 y 228.525 (24)s do-end end endp showpage %%PageTrailer %%Page: 26 26 %%BeginPageSetup %RBIIncludePageSlotInvocation mTSsetup pmSVsetup initializepage (Shu Nakamura; ページ: 26 / 26)setjob %%EndPageSetup gS 0 0 584 829 rC -1000 -1000 :M f54 sf ( )S -997 -1000 :M f88 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10.95 /CMR10 findfont fdef 5 10.95 /CMBX10 findfont fdef 66 66 translate 72 72.27 div dup scale 2 f 75 y 66.927 ([33])s 89.435 (D.)s 105.925 (R.)s 122.11 (Y)s 129.41 (afaev:)s 165.127 (Mathematical)s 236.215 (Scattering)s 289.995 (Theory:)s 335.171 (General)s 377.47 (Theory)s 410.958 (,)s 88.6 y 89.435 (T)s 96.431 (ranslations)s 154.659 (of)s 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