%!PS-Adobe-3.0 %%Title: (Consor2001_1.tex) %%Creator: (Textures\250: LaserWriter 8 8.5.1) %%CreationDate: (11:12 AM Thursday, August 23, 2001) %%For: (drahotova) %%Routing: (mailto:\000drahotov@seis.karlov.mff.cuni.cz) %%Pages: 26 %%DocumentFonts: CMR10 CMR12 CMBX12 CMR8 CMMI12 CMMI8 CMSY10 CMEX10 CMSY8 CMTI12 CMMI6 CMSY6 CMMI10 CMR6 %%DocumentNeededFonts: %%DocumentSuppliedFonts: CMR10 CMR12 CMBX12 CMR8 CMMI12 CMMI8 CMSY10 CMEX10 CMSY8 CMTI12 CMMI6 CMSY6 CMMI10 CMR6 %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: Default 595 842 0 () () %ADO_ImageableArea: 14 14 582 819 %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults userdict/dscInfo 5 dict dup begin /Title(Consor2001_1.tex)def /Creator(Textures\250: LaserWriter 8 8.5.1)def /CreationDate(11:12 AM Thursday, August 23, 2001)def /For(drahotova)def /Pages 26 def end put /md 233 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: lw8_basic-2.3 %%Copyright: Copyright 1990-1997 Adobe Systems Incorporated and Apple Computer Incorporated. 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F def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace T }{ currentcmykcolor F }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { 2state? $o $t $p $s $cs ps }bd /popstatic { /ps xs /$cs xs /$s xs /$p xs /$t xs /$o xs /2state? xs }bd /pushgstate { currentpoint pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { errordict/nocurrentpoint{pop 0 0}put 2state? { pushgstate gR }if pushgstate gR pushgstate pushstatic pm restore mTS setmatrix }bd /bn { /pm save store popstatic popgstate gS popgstate 2state? 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All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont /f133/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 /f147 f133 12 scf fc %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 cleartomark %%EndFont /f170/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 /f184 f170 12 scf fc %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont /f208/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 /f222 f208 12 scf fc %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 165 /Xi put dup 166 /Pi put dup 167 /Sigma put dup 168 /Upsilon put dup 169 /Phi put dup 170 /Psi put dup 173 /Omega put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 185 /macron put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 190 /oe put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 194 /Oslash put dup 195 /suppress put dup 196 /dieresis put dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 4 /Xi put dup 5 /Pi put dup 6 /Sigma put dup 7 /Upsilon put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 15 /ffl put dup 16 /dotlessi put dup 17 /dotlessj put dup 18 /grave put dup 19 /acute put dup 20 /caron put dup 21 /breve put dup 22 /macron put dup 23 /ring put dup 24 /cedilla put dup 25 /germandbls put dup 26 /ae put dup 27 /oe put dup 28 /oslash put dup 29 /AE put dup 30 /OE put dup 31 /Oslash put dup 32 /suppress put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 36 /dollar put dup 37 /percent put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486858B2A4B5A0CC2E1BF4E2A4A0E748483C3BCF5DE47CC5260A3A967C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont /f245/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 /f258 f245 12 scf fc %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.0 %%CreationDate: 1991 Aug 18 17:49:36 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5000786 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31FA4BDCF3EB512 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cleartomark %%EndFont /f282/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 /f296 f282 12 scf fc %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.0 %%CreationDate: 1991 Aug 18 17:51:11 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5000783 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31FA4BDCF3EB512 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cleartomark %%EndFont /f319/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 /f333 f319 12 scf fc %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 165 /divide put dup 166 /diamondmath put dup 167 /plusminus put dup 168 /minusplus put dup 169 /circleplus put dup 170 /circleminus put dup 173 /circlemultiply put dup 174 /circledivide put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 178 /bullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 185 /precedesequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 189 /propersubset put dup 190 /propersuperset put dup 191 /lessmuch put dup 192 /greatermuch put dup 193 /precedes put dup 194 /follows put dup 195 /arrowleft put dup 196 /spade put dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 4 /divide put dup 5 /diamondmath put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 9 /circleminus put dup 10 /circlemultiply put dup 11 /circledivide put dup 12 /circledot put dup 13 /circlecopyrt put dup 14 /openbullet put dup 15 /bullet put dup 16 /equivasymptotic put dup 17 /equivalence put dup 18 /reflexsubset put dup 19 /reflexsuperset put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 23 /followsequal put dup 24 /similar put dup 25 /approxequal put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 30 /precedes put dup 31 /follows put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 36 /arrowboth put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 42 /arrowdblup put dup 43 /arrowdbldown put dup 44 /arrowdblboth put dup 45 /arrownorthwest put dup 46 /arrowsouthwest put dup 47 /proportional put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 52 /triangle put dup 53 /triangleinv put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 58 /logicalnot put dup 59 /emptyset put dup 60 /Rfractur put dup 61 /Ifractur put dup 62 /latticetop put dup 63 /perpendicular put dup 64 /aleph put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 93 /unionmulti put dup 94 /logicaland put dup 95 /logicalor put dup 96 /turnstileleft put dup 97 /turnstileright put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 108 /arrowbothv put dup 109 /arrowdblbothv put dup 110 /backslash put dup 111 /wreathproduct put dup 112 /radical put dup 113 /coproduct put dup 114 /nabla put dup 115 /integral put dup 116 /unionsq put dup 117 /intersectionsq put dup 118 /subsetsqequal put dup 119 /supersetsqequal put dup 120 /section put dup 121 /dagger put dup 122 /daggerdbl put dup 123 /paragraph put dup 124 /club put dup 125 /diamond put dup 126 /heart put dup 127 /spade put dup 128 /arrowleft put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def 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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 /f371 f357 12 scf fc %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) 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 %%EndFont /f395/CMEX10 :bsr 32/space pd :esr /f409 f395 12 scf fc %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 5000818 def 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%%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31DC36E555668D9 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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 /f484 f470 12 scf fc %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.0 %%CreationDate: 1991 Aug 18 17:50:24 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 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/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 readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5000781 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACEE583A5C939393E012707B47E0C1FA47D284A1EDC9D01A497D772BCA8C543388E6DC0D1E2C4944740470E0914F65EFB0737B0851B2BA713A9A00B36D07DA6BCB52920B9B59EFE587734027A3C5E6566AAD332FE6FBCCED1417802822A3B81D6187875263D6BBDA04BBCF6E4870FEEAD60F104BB3C5A766610DD11AEA64A6B107B0B04439FA2888B8CC39232BB83F7695ABA81F0260CD5248B9E649CD803271DC8BB1656323089E9E2BB50F2B9508887D31FA4BDCF3EB512 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont /f507/CMMI6 :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 /f521 f507 12 scf fc %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 5000816 def 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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 /f558 f544 12 scf fc %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.0 %%CreationDate: 1991 Aug 18 17:49:13 % Copyright (C) 1988 Blue Sky Research. 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Knuth) 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 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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 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/f582/CMMI10 :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 /f596 f582 12 scf fc %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1988 Blue Sky Research. All rights reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def /FullName (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 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/eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /exclamdown put dup 61 /equal put dup 62 /questiondown put dup 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put dup 128 /suppress put dup 160 /space put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec 9B9C1569015F2C1D2BF560F4C0D52257BACDD6500ABDA5ED9835F6A016CFC8F00B6C052ED76A87856B50F4D80DFAEB508C97F8281F3F88B17E4D3B90C0F65EC379791AACDC162A66CBBC5BE2F53AAD8DE72DD113B55A022FBFEE658CB95F5BB32BA0357B5E050FDDF264A07470BEF1C52119B6FBD5C77EBED964AC5A2BBEC9D8B3E48AE5BB003A63D545774B922B9D5FF6B0066ECE43645A131879B032137D6D823385FE55F3402D557FD3B4486858B2A4B5A0CC2E1BF4E2A4A0E748483C3BCF5DE47CC5260A3A967C 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219.096 (k)s 9 f 363.959 y 224.235 (=)s 3 f 230.11 (d)s 9 f 236.638 (\277)s 3 f 243.081 (\051)s 253.608 (=)s 7 f 359.234 y 269.906 (1)s 4.25 .4 269.906 361.159 r 368.097 y 269.906 (2)s 3 f 363.959 y 275.356 ([)s 12 f 278.62 (L)s 3 f 286.896 (\050)s 9 f 291.466 (x)s 10 f 359.604 y 298.143 (k)s 9 f 363.959 y 303.282 (;)s 3 f 308.546 (d)s 9 f 315.073 (x)s 10 f 359.604 y 321.75 (k)s 9 f 363.959 y 326.889 (=)s 3 f 332.764 (d)s 9 f 339.292 (\277)s 3 f 345.735 (\051])s 7 f 359.604 y 353.568 (2)s 3 f 363.959 y 358.318 (.)s 371.431 (The)s 397.126 (mo)s 413.119 (di\257ed)s 446.647 (La-)s 378.459 y 8.536 (grangian)s 12 f 57.234 (L)s 10 f 374.104 y 65.51 (M)s 3 f 378.459 y 75.026 (\050)s 9 f 79.595 (x)s 10 f 374.104 y 86.272 (k)s 9 f 378.459 y 91.411 (;)s 3 f 96.675 (d)s 9 f 103.203 (x)s 10 f 374.104 y 109.88 (k)s 9 f 378.459 y 115.019 (=)s 3 f 120.894 (d)s 9 f 127.421 (\277)s 3 f 133.864 (\051)s 142.743 (yields)s 176.166 (the)s 196.795 (same)s 226.627 (Euler-Lagrange)s 309.591 (equations)s 362.597 (as)s 377.416 (the)s 398.045 (standard)s 447.461 (pa-)s 392.959 y 8.536 (rameteric)s 59.763 (Lagrangian)s 12 f 120.29 (L)s 3 f 128.566 (\050)s 9 f 133.136 (x)s 10 f 388.604 y 139.813 (k)s 9 f 392.959 y 144.952 (;)s 3 f 150.215 (d)s 9 f 156.743 (x)s 10 f 388.604 y 163.42 (k)s 9 f 392.959 y 168.559 (=)s 3 f 174.434 (d)s 9 f 180.962 (u)s 3 f 187.649 (\051,)s 198.603 (but)s 219.15 (represen)s 261.319 (ts)s 273.445 (a)s 282.242 (homogeneous)s 353.117 (function)s 398.142 (of)s 410.529 (the)s 429.771 (second)s 407.459 y 8.536 (order)s 39.332 (in)s 53.157 (d)s 9 f 59.684 (x)s 10 f 403.104 y 66.362 (k)s 9 f 407.459 y 71.5 (=)s 3 f 77.375 (d)s 9 f 83.903 (\277)s 3 f 94.379 (\050not)s 119.953 (of)s 133.451 (the)s 153.803 (\257rst)s 178.137 (order\051.)s 218.305 (Consequen)s 273.203 (tly)s 286.259 (,)s 293.584 (the)s 313.937 (relev)s 337.763 (an)s 349.839 (t)s 358.441 (Hessian)s 401.44 (determinan)s 459.211 (t)s 421.959 y 8.536 (do)s 21.265 (es)s 35.687 (not)s 57.225 (v)s 62.773 (anish)s 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98.989 (x)s 7 f 446.604 y 105.666 (2)s 9 f 450.959 y 110.416 (=)s 3 f 116.291 (d)s 9 f 122.819 (x)s 7 f 446.604 y 129.496 (3)s 3 f 450.959 y 134.246 (\051)s 143.568 (is)s 156.219 (referred)s 200.465 (to)s 215.662 (as)s 230.924 (the)s 251.996 (reduced)s 296.568 (Lagrangian.)s 365.167 (Again,)s 403.742 (the)s 424.814 (Hessian)s 465.459 y 8.536 (determinan)s 66.306 (t)s 75.219 (do)s 87.948 (es)s 102.148 (not)s 123.463 (iden)s 144.678 (tically)s 180.68 (v)s 186.229 (anish)s 217.401 (in)s 231.535 (this)s 254.874 (case.)s 285.593 (In)s 300.703 (b)s 307.557 (oth)s 328.872 (cases,)s 362.174 (the)s 382.836 (Legendre)s 433.687 (trans-)s 479.959 y 8.536 (form)s 38.124 (can)s 61.511 (b)s 68.365 (e)s 79.35 (used)s 108.024 (to)s 124.231 (compute)s 173.729 (the)s 195.81 (Hamiltonian)s 265.213 (from)s 294.802 (the)s 316.883 (Lagrangian,)s 383.976 (and)s 408.668 (vice)s 434.34 (v)s 440.215 (ersa,)s 494.459 y 8.536 (and)s 31.698 (the)s 52.25 (Hamiltonian)s 120.123 (canonical)s 172.007 (equations)s 224.936 (can)s 246.793 (b)s 253.647 (e)s 263.101 (deriv)s 288.559 (ed)s 304.541 (from)s 332.599 (the)s 353.15 (Euler-Lagrange)s 436.037 (equa-)s 508.959 y 8.536 (tions.)s 45.64 (The)s 71.041 (relations)s 120.008 (b)s 126.862 (et)s 136.327 (w)s 144.487 (een)s 166.625 (mo)s 182.618 (di\257ed)s 215.852 (Hamiltonians)s 289.294 (and)s 313.39 (Lagrangians)s 380.795 (are)s 401.627 (discussed)s 453.988 (in)s 523.459 y 8.536 (detail.)s 47.312 (It)s 60.56 (is)s 72.898 (sho)s 89.609 (wn)s 109.062 (that)s 135.043 (the)s 155.802 (standard)s 205.348 (form)s 233.613 (of)s 247.518 (the)s 268.277 (Hamiltonian,)s 339.752 (deriv)s 365.21 (ed)s 381.399 (from)s 409.665 (the)s 430.423 (elasto-)s 537.959 y 8.536 (dynamic)s 55.674 (equation)s 103.465 (and)s 126.124 (represen)s 168.293 (ting)s 192.257 (the)s 212.305 (eik)s 226.666 (onal)s 251.936 (equation,)s 303.028 (whic)s 326.202 (h)s 336.458 (has)s 357.224 (b)s 364.078 (een)s 384.779 (broadly)s 427.347 (used)s 453.988 (in)s 552.459 y 8.536 (the)s 28.821 (seismic)s 68.819 (ra)s 78.937 (y)s 89.104 (metho)s 121.416 (d,)s 135.186 (corresp)s 172.133 (onds)s 199.663 (to)s 214.073 (the)s 234.358 (mo)s 250.351 (di\257ed)s 282.386 (Lagrangian)s 12 f 343.956 (L)s 10 f 548.104 y 352.233 (M)s 3 f 552.459 y 361.748 (\050)s 9 f 366.318 (x)s 10 f 548.104 y 372.995 (k)s 9 f 552.459 y 378.134 (;)s 3 f 383.398 (d)s 9 f 389.925 (x)s 10 f 548.104 y 396.602 (k)s 9 f 552.459 y 401.741 (=)s 3 f 407.616 (d)s 9 f 414.144 (\277)s 3 f 420.587 (\051,)s 432.398 (not)s 453.336 (to)s 566.959 y 8.536 (the)s 29.247 (standard)s 78.746 (parameteric)s 143.846 (Lagrangian)s 12 f 205.843 (L)s 3 f 214.12 (\050)s 9 f 218.689 (x)s 10 f 562.604 y 225.366 (k)s 9 f 566.959 y 230.505 (;)s 3 f 235.769 (d)s 9 f 242.297 (x)s 10 f 562.604 y 248.974 (k)s 9 f 566.959 y 254.113 (=)s 3 f 259.988 (d)s 9 f 266.515 (u)s 3 f 273.203 (\051.)s 287.685 (It)s 300.886 (is)s 313.176 (also)s 337.217 (sho)s 353.928 (wn)s 373.334 (that)s 399.268 (the)s 419.979 (relations)s 12 f 581.459 y 8.536 (L)s 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384.929 (anisotropic)s 444.85 (me-)s 653.959 y 8.536 (dia)s 28.119 (are)s 47.702 (brie\260)s 73.813 (y)s 83.931 (discussed)s 135.043 (as)s 149.469 (sp)s 160.958 (ecial)s 187.722 (cases.)s 182.095 .4 8.536 665.859 r 1 f 683.939 y 8.536 (Seismic)s 44.147 (W)s 53.592 (a)s 58.314 (v)s 63.314 (es)s 75.036 (in)s 86.703 (Complex)s 128.647 (3-D)s 147.953 (Structures,)s 199.175 (Rep)s 216.814 (ort)s 232.953 (11,)s 698.439 y 8.536 (Departmen)s 57.036 (t)s 64.258 (of)s 75.647 (Geoph)s 103.772 (ysics,)s 130.272 (Charles)s 166.467 (Univ)s 187.3 (ersit)s 205.995 (y)s 210.439 (,)s 216.55 (Praha)s 246.161 (2001)s 3 f 266.161 (.)s 735.628 y 227.346 (211)s do-end end endp showpage %%Page: 2 2 %%BeginPageSetup initializepage (drahotova; page: 2 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f184 sf -.651( )A f258 sf ( )S -993 -1000 :M f296 sf ( )S f333 sf ( )S -977 -1000 :M f371 sf ( )S -965 -1000 :M f222 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 15 17.28 /CMBX12 findfont fdef 58 49 translate 72 72.27 div dup scale 15 f 3.464 y 8.536 (1)s 37.696 (In)s 55.196 (tro)s 80.956 (duction)s 3 f 38.383 y 8.536 (The)s 33.071 (problem)s 79.147 (of)s 92.911 (F)s 99.6 (ermat\047s)s 141.825 (v)s 147.373 (ariational)s 200.63 (principle)s 249.317 (in)s 263.408 (an)s 280.109 (anisotropic)s 340.611 (inhomogeneous)s 422.655 (medium)s 52.883 y 8.536 (is)s 21.577 (mostly)s 61.055 (of)s 75.662 (academic)s 127.804 (in)s 137.269 (terest)s 171.199 (only)s 192.087 (.)s 204.25 (Practically)s 264.713 (ev)s 275.81 (erything)s 323.709 (that)s 350.392 (follo)s 371.934 (ws)s 390.197 (from)s 419.165 (F)s 425.854 (ermat\047s)s 67.383 y 8.536 (v)s 14.084 (ariational)s 66.835 (principle)s 115.016 (can)s 136.434 (also)s 159.875 (b)s 166.729 (e)s 175.744 (deriv)s 201.202 (ed)s 216.745 (b)s 222.946 (y)s 232.94 (applying)s 280.795 (high-frequency)s 359.983 (asymptotic)s 420.305 (metho)s 452.618 (ds)s 81.883 y 8.536 (to)s 23.72 (the)s 44.778 (elasto)s 74.545 (dynamic)s 122.694 (equation,)s 174.965 (and)s 198.635 (from)s 227.2 (the)s 248.259 (consequen)s 299.893 (t)s 309.202 (eik)s 323.563 (onal)s 349.844 (equation.)s 404.861 (The)s 429.836 (author)s 96.383 y 8.536 (w)s 16.696 (an)s 28.772 (ts)s 41.305 (to)s 55.079 (emphasize)s 110.695 (that)s 135.566 (he)s 150.645 (do)s 163.374 (es)s 176.56 (not)s 196.861 (exp)s 215.139 (ect)s 233.482 (an)s 245.558 (y)s 255.088 (practical)s 302.806 (consequences)s 373.175 (to)s 386.949 (follo)s 408.49 (w)s 420.305 (from)s 447.461 (the)s 110.883 y 8.536 (presen)s 40.913 (ted)s 60.836 (treatmen)s 106.857 (t.)s 119.808 (The)s 143.648 (eik)s 158.009 (onal)s 183.154 (equation,)s 234.146 (follo)s 255.688 (wing)s 283.444 (from)s 310.874 (the)s 330.797 (anisotropic)s 390.604 (elasto)s 420.371 (dynamic)s 125.383 y 8.536 (equation)s 56.515 (using)s 87.26 (the)s 107.496 (asymptotic)s 167.943 (metho)s 200.255 (ds,)s 218.598 (reads,)s 9 f 150.826 y 198.466 (G)s 3 f 207.734 (\050)s 9 f 212.304 (x)s 10 f 145.871 y 218.981 (k)s 9 f 150.826 y 224.12 (;)s 229.384 (p)s 10 f 152.626 y 235.281 (k)s 3 f 150.826 y 240.42 (\051)s 248.322 (=)s 260.794 (1)s 9 f 270.586 (;)s 3 f 448.766 (\0501\051)s 176.269 y 8.536 (where)s 9 f 43.852 (G)s 3 f 53.12 (\050)s 9 f 57.69 (x)s 10 f 171.914 y 64.367 (k)s 9 f 176.269 y 69.506 (;)s 74.769 (p)s 10 f 178.069 y 80.667 (k)s 3 f 176.269 y 85.806 (\051)s 95.664 (is)s 108.851 (the)s 130.459 (eigen)s 156.243 (v)s 161.792 (alue)s 187.969 (of)s 202.723 (the)s 224.331 (Christo\256el)s 282.886 (matrix)s 322.445 (\241)s 10 f 178.069 y 329.786 (ik)s 3 f 176.269 y 343.488 (=)s 9 f 358.295 (a)s 10 f 170.58 y 364.463 (j)s 368.362 (l)s 179.291 y 364.463 (ik)s 9 f 176.269 y 372.496 (p)s 10 f 178.069 y 378.393 (j)s 9 f 176.269 y 382.792 (p)s 10 f 178.069 y 388.689 (l)s 3 f 176.269 y 391.821 (.)s 404.423 (Here)s 9 f 433.534 (p)s 10 f 178.069 y 439.431 (i)s 3 f 176.269 y 448.114 (are)s 190.769 y 8.536 (co)s 19.307 (v)s 24.855 (arian)s 50.64 (t)s 59.408 (comp)s 87.151 (onen)s 110.977 (ts)s 124.38 (of)s 138.044 (the)s 158.562 (slo)s 172.01 (wness)s 205.714 (v)s 211.589 (ector,)s 9 f 244.58 (x)s 10 f 186.414 y 251.257 (i)s 3 f 190.769 y 258.85 (the)s 279.368 (general)s 320.123 (curvilinear)s 378.828 (co)s 390.251 (ordinates,)s 444.85 (and)s 9 f 205.269 y 8.536 (a)s 10 f 199.58 y 14.704 (j)s 18.602 (l)s 208.291 y 14.704 (ik)s 3 f 205.269 y 27.248 (the)s 48.078 (densit)s 78.497 (y)s 89.21 (normalized)s 149.859 (elastic)s 186.421 (mo)s 202.414 (duli.)s 232.266 (The)s 257.013 (eik)s 271.374 (onal)s 297.426 (equation)s 345.999 (\0501\051)s 365.524 (corresp)s 402.471 (onds)s 430.547 (to)s 445.502 (an)s 457.579 (y)s 219.769 y 8.536 (of)s 23.874 (the)s 46.066 (three)s 78.049 (elemen)s 112.973 (tary)s 140.06 (w)s 148.22 (a)s 153.769 (v)s 159.643 (es)s 175.373 (\050qP)s 193.159 (,)s 202.296 (qS1)s 226.772 (or)s 243.089 (qS2\051)s 272.135 (whic)s 295.309 (h)s 307.709 (ma)s 323.049 (y)s 335.123 (propagate)s 391.912 (in)s 407.576 (anisotropic)s 234.269 y 8.536 (inhomogeneous)s 89.994 (medium.)s 139.536 (Eik)s 156.67 (onal)s 181.924 (equation)s 229.699 (\0501\051)s 248.425 (ma)s 263.765 (y)s 273.68 (b)s 280.534 (e)s 289.469 (used)s 316.094 (to)s 330.251 (write)s 360.075 (the)s 380.107 (Hamiltonian)s 447.461 (ra)s 457.579 (y)s 248.769 y 8.536 (tracing)s 48.355 (equations:)s 261.746 y 153.094 (d)s 9 f 159.621 (x)s 10 f 257.391 y 166.298 (i)s 16.599 .4 153.094 267.064 r 3 f 278.095 y 154.908 (d)s 9 f 161.435 (\277)s 3 f 269.864 y 174.226 (=)s 261.746 y 187.898 (1)s 5.875 .4 187.898 267.064 r 278.095 y 187.898 (2)s 9 f 261.746 y 200.101 (@)s 206.956 (G)s 16.147 .4 200.089 267.064 r 278.095 y 200.089 (@)s 206.945 (p)s 10 f 279.895 y 212.842 (i)s 9 f 269.864 y 221.352 (;)s 3 f 261.746 y 239.566 (d)s 9 f 246.094 (p)s 10 f 263.546 y 251.991 (i)s 15.819 .4 239.566 267.064 r 3 f 278.095 y 240.99 (d)s 9 f 247.518 (\277)s 3 f 269.864 y 259.918 (=)s 12 f 272.39 (\241)s 3 f 261.746 y 282.924 (1)s 5.875 .4 282.924 267.064 r 278.095 y 282.924 (2)s 9 f 261.746 y 295.517 (@)s 302.372 (G)s 16.926 .4 295.115 267.064 r 278.095 y 295.115 (@)s 301.971 (x)s 10 f 274.629 y 308.648 (i)s 9 f 269.864 y 317.158 (;)s 3 f 448.766 (\0502\051)s 298.051 y 8.536 (see)s 295.017 y 27.582 (\267)s 298.051 y 26.276 (Cerv)s 50.428 (en)s 62.342 (\266)s 62.178 (y)s 71.041 (\0502001a\051.)s 117.622 (Here)s 9 f 144.105 (\277)s 3 f 153.209 (denotes)s 194.449 (a)s 202.985 (parameter)s 257.867 (along)s 287.945 (the)s 306.925 (ra)s 317.043 (y)s 322.265 (,)s 328.441 (corresp)s 365.388 (onding)s 402.646 (to)s 415.751 (the)s 434.732 (tra)s 449.419 (v)s 455.294 (el)s 312.551 y 8.536 (time.)s 41.607 (It)s 54.911 (is)s 67.305 (not)s 88.773 (di\261cult)s 132.435 (to)s 147.375 (pro)s 164.021 (v)s 169.896 (e)s 179.614 (that)s 9 f 205.651 (G)s 3 f 214.92 (\050)s 9 f 219.489 (x)s 10 f 308.196 y 226.166 (i)s 9 f 312.551 y 229.56 (;)s 234.824 (p)s 10 f 314.351 y 240.721 (i)s 3 f 312.551 y 244.115 (\051)s 253.18 (is)s 265.575 (a)s 275.946 (homogeneous)s 348.395 (function)s 394.994 (of)s 408.956 (the)s 429.771 (second)s 327.051 y 8.536 (degree)s 45.161 (in)s 9 f 58.938 (p)s 10 f 328.851 y 64.835 (i)s 3 f 327.051 y 68.229 (.)s 76.924 (By)s 95.432 (a)s 105.293 (homogeneous)s 177.232 (function)s 9 f 223.322 (f)s 3 f 230.395 (\050)s 9 f 234.964 (p)s 10 f 328.851 y 240.862 (i)s 3 f 327.051 y 244.256 (\051)s 252.811 (of)s 266.262 (the)s 9 f 286.568 (k)s 3 f 293.081 (-th)s 312.081 (degree)s 348.706 (in)s 9 f 362.483 (p)s 10 f 328.851 y 368.381 (i)s 3 f 327.051 y 371.775 (,)s 379.042 (w)s 387.202 (e)s 396.41 (understand)s 457.905 (a)s 341.551 y 8.536 (function)s 9 f 54.556 (f)s 3 f 61.629 (\050)s 9 f 66.199 (p)s 10 f 343.351 y 72.096 (i)s 3 f 341.551 y 75.49 (\051)s 83.976 (whic)s 107.149 (h)s 117.593 (satis\257es)s 160.872 (the)s 181.108 (relation)s 9 f 366.994 y 190.425 (f)s 3 f 197.498 (\050)s 9 f 202.067 (ap)s 10 f 368.794 y 214.132 (i)s 3 f 366.994 y 217.526 (\051)s 225.429 (=)s 9 f 237.901 (a)s 10 f 362.039 y 244.069 (k)s 9 f 366.994 y 249.208 (f)s 3 f 256.281 (\050)s 9 f 260.85 (p)s 10 f 368.794 y 266.747 (i)s 3 f 366.994 y 270.141 (\051)s 9 f 278.627 (;)s 3 f 448.766 (\0503\051)s 392.437 y 8.536 (for)s 27.868 (an)s 39.944 (y)s 51.442 (non)s 70.046 (v)s 75.595 (anishing)s 123.387 (constan)s 162.292 (t)s 9 f 172.159 (a)s 3 f 178.327 (.)s 190.954 (The)s 216.487 (homogeneous)s 289.738 (function)s 9 f 337.138 (f)s 3 f 344.211 (\050)s 9 f 348.781 (p)s 10 f 394.237 y 354.678 (i)s 3 f 392.437 y 358.072 (\051)s 367.938 (of)s 382.7 (the)s 9 f 404.317 (k)s 3 f 410.831 (-th)s 431.141 (degree)s 406.937 y 8.536 (satis\257es)s 51.815 (the)s 72.051 (Euler\047s)s 111.443 (theorem)s 9 f 432.38 y 175.817 (p)s 10 f 434.18 y 181.714 (j)s 9 f 432.38 y 186.112 (@)s 192.968 (f)s 3 f 200.041 (\050)s 9 f 204.61 (p)s 10 f 434.18 y 210.507 (i)s 3 f 432.38 y 213.901 (\051)s 9 f 218.471 (=@)s 231.201 (p)s 10 f 434.18 y 237.098 (j)s 3 f 432.38 y 244.83 (=)s 9 f 257.302 (k)s 263.816 (f)s 3 f 270.889 (\050)s 9 f 275.458 (p)s 10 f 434.18 y 281.355 (i)s 3 f 432.38 y 284.749 (\051)s 9 f 293.235 (:)s 3 f 448.766 (\0504\051)s 457.823 y 8.536 (The)s 32.341 (ra)s 42.459 (y)s 52.229 (tracing)s 91.7 (equations)s 143.966 (\0502\051)s 162.549 (tak)s 178.868 (e)s 187.659 (the)s 207.547 (standard)s 256.223 (form)s 283.618 (of)s 296.652 (Hamiltonian)s 363.862 (canonical)s 415.083 (equations)s 482.41 y 164.716 (d)s 9 f 171.244 (x)s 10 f 478.055 y 177.921 (i)s 16.599 .4 164.716 487.728 r 3 f 498.759 y 166.53 (d)s 9 f 173.058 (\277)s 3 f 490.528 y 185.848 (=)s 9 f 482.41 y 199.52 (@)s 12 f 206.376 (H)s 17.106 .4 199.52 487.728 r 9 f 498.759 y 200 (@)s 206.855 (p)s 10 f 500.559 y 212.752 (i)s 9 f 490.528 y 221.742 (;)s 3 f 482.41 y 239.956 (d)s 9 f 246.484 (p)s 10 f 484.21 y 252.381 (i)s 15.819 .4 239.956 487.728 r 3 f 498.759 y 241.38 (d)s 9 f 247.908 (\277)s 3 f 490.528 y 260.308 (=)s 12 f 272.78 (\241)s 9 f 482.41 y 283.314 (@)s 12 f 290.169 (H)s 17.106 .4 283.314 487.728 r 9 f 498.759 y 283.403 (@)s 290.259 (x)s 10 f 495.292 y 296.936 (i)s 9 f 490.528 y 305.536 (;)s 3 f 448.766 (\0505\051)s 522.946 y 8.536 (if)s 19.307 (w)s 27.466 (e)s 36.605 (in)s 46.07 (tro)s 61.41 (duce)s 88.827 (Hamiltonian)s 12 f 156.384 (H)s 3 f 166.634 (\050)s 9 f 171.204 (x)s 10 f 518.591 y 177.881 (k)s 9 f 522.946 y 183.02 (;)s 188.284 (p)s 10 f 524.746 y 194.181 (k)s 3 f 522.946 y 199.32 (\051)s 207.806 (b)s 214.007 (y)s 224.125 (the)s 244.361 (relation)s 12 f 548.389 y 174.326 (H)s 3 f 184.576 (\050)s 9 f 189.146 (x)s 10 f 543.434 y 195.823 (k)s 9 f 548.389 y 200.962 (;)s 206.225 (p)s 10 f 550.189 y 212.123 (k)s 3 f 548.389 y 217.262 (\051)s 225.164 (=)s 7 f 543.664 y 238.836 (1)s 4.25 .4 238.836 545.589 r 552.527 y 238.836 (2)s 9 f 548.389 y 244.286 (G)s 3 f 253.555 (\050)s 9 f 258.124 (x)s 10 f 543.434 y 264.801 (k)s 9 f 548.389 y 269.94 (;)s 275.204 (p)s 10 f 550.189 y 281.101 (k)s 3 f 548.389 y 286.24 (\051)s 9 f 294.726 (:)s 3 f 448.766 (\0506\051)s 573.832 y 8.536 (Hamiltonian)s 12 f 76.266 (H)s 3 f 86.516 (\050)s 9 f 91.085 (x)s 10 f 569.477 y 97.763 (k)s 9 f 573.832 y 102.901 (;)s 108.165 (p)s 10 f 575.632 y 114.062 (k)s 3 f 573.832 y 119.201 (\051)s 127.86 (is)s 139.848 (again)s 171.353 (a)s 181.317 (homogeneous)s 253.36 (function)s 299.553 (of)s 313.107 (the)s 333.515 (second)s 371.614 (degree)s 408.341 (in)s 9 f 422.222 (p)s 10 f 575.632 y 428.119 (i)s 3 f 573.832 y 431.513 (,)s 438.909 (simi-)s 588.332 y 8.536 (larly)s 35.626 (as)s 9 f 50.052 (G)s 3 f 59.32 (\050)s 9 f 63.89 (x)s 10 f 583.977 y 70.567 (k)s 9 f 588.332 y 75.706 (;)s 80.97 (p)s 10 f 590.132 y 86.867 (k)s 3 f 588.332 y 92.006 (\051.)s 105.061 (The)s 129.214 (relation)s 12 f 602.832 y 201.178 (H)s 3 f 211.428 (\050)s 9 f 215.997 (x)s 10 f 597.877 y 222.674 (k)s 9 f 602.832 y 227.813 (;)s 233.077 (p)s 10 f 604.632 y 238.974 (k)s 3 f 602.832 y 244.113 (\051)s 252.016 (=)s 7 f 598.107 y 265.688 (1)s 4.25 .4 265.688 600.032 r 606.97 y 265.688 (2)s 3 f 602.832 y 448.766 (\0507\051)s 623.379 y 8.536 (is)s 21.726 (satis\257ed)s 68.273 (along)s 100.981 (the)s 122.592 (whole)s 157.258 (ra)s 167.376 (y)s 172.598 (.)s 185.209 (It)s 199.309 (is)s 212.499 (w)s 220.659 (ell)s 237.7 (kno)s 255.978 (wn)s 276.283 (that)s 303.116 (relations)s 352.209 (\0501\051)s 372.514 (and)s 396.736 (\0507\051)s 417.042 (represen)s 459.211 (t)s 637.879 y 8.536 (alternativ)s 58.147 (ely)s 76.75 (the)s 96.986 (slo)s 110.433 (wness)s 143.855 (surface)s 183.413 (in)s 197.121 (a)s 206.913 (phase)s 239.617 (space)s 271.015 (sp)s 282.504 (eci\257ed)s 318.406 (b)s 324.608 (y)s 334.726 (co)s 346.149 (ordinates)s 9 f 397.13 (p)s 10 f 639.679 y 403.028 (i)s 3 f 637.879 y 406.422 (.)s 660.915 y 26.161 (Note)s 54.553 (that)s 80.012 (the)s 100.249 (same)s 129.69 (Hamiltonian)s 197.249 (ra)s 207.367 (y)s 217.486 (equations)s 270.1 (\0505\051)s 289.031 (are)s 308.615 (obtained)s 356.922 (also)s 380.488 (if)s 391.259 (w)s 399.419 (e)s 408.559 (use)s 428.861 (Hamil-)s 675.415 y 8.536 (tonian)s 12 f 46.235 (H)s 3 f 56.485 (\050)s 9 f 61.054 (x)s 10 f 671.06 y 67.731 (k)s 9 f 675.415 y 72.87 (;)s 78.134 (p)s 10 f 677.215 y 84.031 (k)s 3 f 675.415 y 89.17 (\051)s 99.019 (=)s 7 f 670.69 y 114.637 (1)s 4.25 .4 114.637 672.615 r 679.553 y 114.637 (2)s 3 f 675.415 y 120.087 (\050)s 9 f 124.657 (G)s 3 f 133.925 (\050)s 9 f 138.494 (x)s 10 f 671.06 y 145.171 (k)s 9 f 675.415 y 150.31 (;)s 155.574 (p)s 10 f 677.215 y 161.471 (k)s 3 f 675.415 y 166.61 (\051)s 12 f 174.625 (\241)s 3 f 187.403 (1\051.)s 209.764 (Then)s 12 f 241.587 (H)s 3 f 251.837 (\050)s 9 f 256.407 (x)s 10 f 671.06 y 263.084 (k)s 9 f 675.415 y 268.223 (;)s 273.487 (p)s 10 f 677.215 y 279.384 (k)s 3 f 675.415 y 284.523 (\051)s 294.152 (equals)s 330.937 (zero)s 356.886 (along)s 389.362 (the)s 410.741 (whole)s 445.176 (ra)s 455.294 (y)s 460.516 (.)s 691.128 y 8.536 (This)s 34.918 (form)s 62.213 (is)s 73.582 (also)s 96.7 (common)s 143.252 (in)s 156.513 (the)s 176.302 (seismological)s 245.832 (literature,)s 300.307 (see)s 688.095 y 320.161 (\267)s 691.128 y 318.856 (Cerv)s 343.008 (en)s 354.921 (\266)s 354.758 (y)s 364.429 (\0502001a,)s 405.196 (Eq.\0503.6.3\051\051.)s 705.628 y 8.536 (Here,)s 39.538 (ho)s 51.615 (w)s 59.774 (ev)s 70.871 (er,)s 87.843 (w)s 96.003 (e)s 105.142 (shall)s 132.624 (use)s 152.925 (the)s 173.161 (Hamiltonian)s 240.718 (giv)s 255.732 (en)s 271.398 (b)s 277.6 (y)s 287.718 (\0506\051)s 306.648 (consisten)s 352.799 (tly)s 365.854 (.)s 735.628 y 227.346 (212)s do-end end endp showpage %%Page: 3 3 %%BeginPageSetup initializepage (drahotova; page: 3 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f222 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 15 17.28 /CMBX12 findfont fdef 58 49 translate 72 72.27 div 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(ev)s 271.718 (er,)s 290.294 (some)s 321.018 (restrictions)s 383.141 (are)s 404.008 (imp)s 423.917 (osed)s 451.377 (on)s 210.82 y 8.536 (this)s 32.349 (transform.)s 93.54 (F)s 100.229 (or)s 115.491 (this)s 139.304 (reason,)s 180.315 (w)s 188.474 (e)s 198.514 (shall)s 226.897 (brie\260)s 253.008 (y)s 264.027 (recapitulate)s 329.552 (it)s 342.203 (here.)s 374.933 (F)s 381.622 (or)s 396.884 (more)s 427.16 (details,)s 225.32 y 8.536 (see)s 27.237 (Babic)s 56.12 (h)s 66.269 (and)s 88.821 (Buldyrev)s 139.278 (\0501972\051,)s 178.861 (Brdi)s 201.216 (\267)s 201.542 (ck)s 212.313 (a)s 221.81 (and)s 244.362 (Hlad)s 267.531 (\266)s 268.837 (\263k)s 281.924 (\0501987\051,)s 321.507 (Goldstein)s 374.232 (\0501980\051,)s 413.816 (Kline)s 444.85 (and)s 239.82 y 8.536 (Ka)s 23.219 (y)s 33.337 (\0501965\051,)s 73.156 (etc.)s 262.856 y 26.161 (W)s 37.254 (e)s 46.392 (in)s 55.858 (tro)s 71.198 (duce)s 98.614 (\134momen)s 141.371 (ta\042)s 9 f 161.607 (p)s 10 f 264.656 y 167.504 (i)s 3 f 262.856 y 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3 f 330.356 y 162.516 (\050)s 9 f 167.086 (i)s 3 f 174.427 (=)s 186.9 (1)s 9 f 192.774 (;)s 3 f 198.038 (2)s 9 f 203.913 (;)s 3 f 209.177 (3\051,)s 226.483 (using)s 256.83 (\05024\051.)s 286.072 (This)s 312.502 (is)s 323.919 (p)s 330.773 (ossible)s 367.713 (only)s 393.099 (if)s 403.471 (the)s 423.308 (relev)s 447.134 (an)s 459.211 (t)s 344.856 y 8.536 (Hessian)s 51.419 (determinan)s 109.189 (t)s 117.675 (is)s 129.49 (di\256eren)s 167.351 (t)s 175.837 (from)s 203.58 (zero,)s 377.818 y 184.772 (det)s 0 f 363.218 y 201.092 (\265)s 9 f 369.7 y 219.946 (@)s 7 f 365.345 y 226.802 (2)s 12 f 369.7 y 231.552 (L)s 40.469 .4 209.653 375.018 r 9 f 386.049 y 209.653 (@)s 216.508 (x)s 10 f 382.583 y 223.185 (i)s 13 f 226.579 (0)s 9 f 386.049 y 229.385 (@)s 236.24 (x)s 10 f 382.583 y 242.917 (j)s 13 f 247.316 (0)s 0 f 363.218 y 251.322 (\266)s 12 f 377.818 y 262.016 (6)s 3 f 262.016 (=)s 274.488 (0)s 9 f 284.28 (:)s 3 f 442.891 (\05025\051)s 409.728 y 8.536 (If)s 20.479 (\05025\051)s 45.482 (is)s 57.494 (satis\257ed,)s 106.176 (w)s 114.336 (e)s 123.672 (can)s 145.411 (solv)s 165.059 (e)s 174.396 (\05024\051)s 199.398 (for)s 9 f 217.547 (x)s 10 f 405.374 y 224.224 (i)s 13 f 227.618 (0)s 3 f 409.728 y 234.537 (and)s 257.582 (determine)s 9 f 312.612 (x)s 10 f 405.374 y 319.289 (i)s 13 f 322.683 (0)s 3 f 409.728 y 329.158 (=)s 9 f 341.966 (f)s 10 f 405.374 y 349.038 (i)s 3 f 409.728 y 352.432 (\050)s 9 f 357.002 (x)s 10 f 405.374 y 363.679 (k)s 9 f 409.728 y 368.818 (;)s 374.082 (p)s 10 f 411.528 y 379.979 (k)s 3 f 409.728 y 385.118 (\051.)s 398.765 (W)s 409.858 (e)s 419.194 (can)s 440.933 (then)s 424.228 y 8.536 (determine)s 63.369 (the)s 83.605 (Hamiltonian)s 12 f 151.162 (H)s 3 f 161.412 (\050)s 9 f 165.982 (x)s 10 f 419.874 y 172.659 (k)s 9 f 424.228 y 177.798 (;)s 183.061 (p)s 10 f 426.028 y 188.959 (k)s 3 f 424.228 y 194.098 (\051)s 202.584 (b)s 208.785 (y)s 218.903 (relation)s 12 f 450.728 y 128.114 (H)s 3 f 138.364 (\050)s 9 f 142.933 (x)s 10 f 445.774 y 149.61 (k)s 9 f 450.728 y 154.749 (;)s 160.013 (p)s 10 f 452.528 y 165.91 (k)s 3 f 450.728 y 171.049 (\051)s 178.952 (=)s 191.424 ([)s 9 f 194.688 (x)s 10 f 445.774 y 201.365 (i)s 13 f 204.759 (0)s 9 f 450.728 y 207.564 (p)s 10 f 452.528 y 213.461 (i)s 12 f 450.728 y 219.522 (\241)s 231.522 (L)s 3 f 239.799 (\050)s 9 f 244.368 (x)s 10 f 445.774 y 251.045 (k)s 9 f 450.728 y 256.184 (;)s 261.448 (x)s 10 f 445.774 y 268.125 (k)s 13 f 273.264 (0)s 3 f 450.728 y 276.069 (\051])s 10 f 453.039 y 283.902 (x)s 11 f 450.762 y 288.687 (i)s 14 f 291.861 (0)s 7 f 453.039 y 294.555 (=)s 10 f 301.167 (f)s 11 f 450.762 y 306.132 (i)s 7 f 453.039 y 309.305 (\050)s 10 f 312.611 (x)s 11 f 450.762 y 317.396 (k)s 10 f 453.039 y 321.986 (;p)s 11 f 454.451 y 328.626 (k)s 7 f 453.039 y 333.216 (\051)s 9 f 450.728 y 340.938 (:)s 3 f 442.891 (\05026\051)s 477.228 y 8.536 (Di\256eren)s 48.842 (tial)s 69.731 (d)s 12 f 76.259 (L)s 3 f 88.452 (can)s 109.994 (b)s 116.848 (e)s 125.986 (expressed)s 178.665 (in)s 192.373 (t)s 196.616 (w)s 204.776 (o)s 214.567 (alternativ)s 264.178 (e)s 273.317 (w)s 281.477 (a)s 287.025 (ys:)s 509.013 y 61.845 (d)s 12 f 68.373 (L)s 3 f 86.649 (=)s 9 f 500.895 y 107.885 (@)s 12 f 114.741 (L)s 16.926 .4 106.988 506.213 r 9 f 517.244 y 106.988 (@)s 113.844 (x)s 10 f 513.778 y 120.521 (i)s 3 f 509.013 y 127.115 (d)s 9 f 133.642 (x)s 10 f 504.058 y 140.319 (i)s 3 f 509.013 y 146.38 (+)s 9 f 500.895 y 161.685 (@)s 12 f 168.541 (L)s 19.732 .4 159.385 506.213 r 9 f 517.244 y 159.385 (@)s 166.241 (x)s 10 f 513.778 y 172.918 (i)s 13 f 176.312 (0)s 3 f 509.013 y 182.317 (d)s 9 f 188.845 (x)s 10 f 504.058 y 195.522 (i)s 13 f 198.916 (0)s 3 f 509.013 y 205.055 (=)s 12 f 217.527 (\241)s 9 f 500.895 y 228.06 (@)s 12 f 234.916 (H)s 17.106 .4 228.06 506.213 r 9 f 517.244 y 228.15 (@)s 235.005 (x)s 10 f 513.778 y 241.682 (i)s 3 f 509.013 y 248.366 (d)s 9 f 254.894 (x)s 10 f 504.058 y 261.571 (i)s 12 f 509.013 y 267.631 (\241)s 9 f 500.895 y 280.831 (@)s 12 f 287.687 (H)s 17.106 .4 280.831 506.213 r 9 f 517.244 y 281.311 (@)s 288.166 (p)s 10 f 519.044 y 294.063 (i)s 3 f 509.013 y 301.137 (d)s 9 f 307.664 (p)s 10 f 510.813 y 313.562 (i)s 3 f 509.013 y 319.622 (+)s 9 f 331.428 (x)s 10 f 504.058 y 338.105 (i)s 13 f 341.499 (0)s 3 f 509.013 y 344.304 (d)s 9 f 350.832 (p)s 10 f 510.813 y 356.729 (i)s 3 f 509.013 y 362.79 (+)s 9 f 374.595 (p)s 10 f 510.813 y 380.492 (i)s 3 f 509.013 y 383.886 (d)s 9 f 390.414 (x)s 10 f 504.058 y 397.091 (i)s 13 f 400.485 (0)s 9 f 509.013 y 407.207 (:)s 3 f 442.891 (\05027\051)s 542.488 y 8.536 (In)s 23.366 (the)s 43.749 (second)s 81.823 (relation)s 125.053 (of)s 138.582 (\05027\051,)s 166.835 (w)s 174.995 (e)s 184.281 (ha)s 196.357 (v)s 202.232 (e)s 211.518 (used)s 12 f 238.494 (L)s 3 f 250.355 (=)s 9 f 263.078 (x)s 10 f 538.133 y 269.755 (i)s 13 f 273.149 (0)s 9 f 542.488 y 275.954 (p)s 10 f 544.288 y 281.851 (i)s 12 f 542.488 y 288.012 (\241)s 300.112 (H)s 3 f 310.362 (\050)s 9 f 314.932 (x)s 10 f 538.133 y 321.609 (k)s 9 f 542.488 y 326.748 (;)s 332.012 (p)s 10 f 544.288 y 337.909 (k)s 3 f 542.488 y 343.048 (\051.)s 356.545 (Then)s 387.372 (\05027\051)s 412.325 (yields)s 445.502 (t)s 449.745 (w)s 457.905 (o)s 556.988 y 8.536 (imp)s 28.445 (ortan)s 55.535 (t)s 64.021 (relations)s 9 f 568.655 y 168.121 (@)s 12 f 174.976 (L)s 16.926 .4 167.223 573.973 r 9 f 585.004 y 167.223 (@)s 174.079 (x)s 10 f 581.537 y 180.756 (i)s 3 f 576.773 y 188.683 (=)s 12 f 201.155 (\241)s 9 f 568.655 y 211.689 (@)s 12 f 218.544 (H)s 17.106 .4 211.689 573.973 r 9 f 585.004 y 211.778 (@)s 218.634 (x)s 10 f 581.537 y 225.311 (i)s 9 f 576.773 y 233.911 (;)s 250.925 (x)s 10 f 571.818 y 257.602 (i)s 13 f 260.995 (0)s 3 f 576.773 y 267.134 (=)s 9 f 568.655 y 280.806 (@)s 12 f 287.662 (H)s 17.106 .4 280.806 573.973 r 9 f 585.004 y 281.286 (@)s 288.141 (p)s 10 f 586.804 y 294.039 (i)s 9 f 576.773 y 303.029 (:)s 3 f 442.891 (\05028\051)s 603.837 y 8.536 (Equations)s 63.484 (\05023\051,)s 91.204 (\05024\051)s 115.572 (and)s 137.982 (\05028\051)s 162.351 (then)s 188.677 (yield)s 216.636 (the)s 236.435 (\257nal)s 262.109 (Hamiltonian)s 329.229 (canonical)s 380.361 (system)s 418.895 (of)s 431.839 (six)s 449.419 (or-)s 618.337 y 8.536 (dinary)s 44.548 (di\256eren)s 82.408 (tial)s 102.427 (equations)s 154.171 (of)s 166.683 (the)s 186.049 (\257rst)s 209.397 (order,)s 242.645 (alternativ)s 292.256 (e)s 300.525 (to)s 314.016 (the)s 333.382 (Euler-Lagrange)s 415.083 (equations)s 632.837 y 8.536 (\05023\051,)s 646.481 y 162.758 (d)s 9 f 169.286 (x)s 10 f 642.126 y 175.963 (i)s 16.599 .4 162.758 651.799 r 3 f 662.83 y 164.45 (d)s 9 f 170.977 (u)s 3 f 654.599 y 183.89 (=)s 9 f 646.481 y 197.562 (@)s 12 f 204.417 (H)s 17.106 .4 197.562 651.799 r 9 f 662.83 y 198.041 (@)s 204.897 (p)s 10 f 664.63 y 210.794 (i)s 9 f 654.599 y 219.784 (;)s 3 f 646.481 y 241.914 (d)s 9 f 248.442 (p)s 10 f 648.281 y 254.339 (i)s 15.819 .4 241.914 651.799 r 3 f 662.83 y 243.216 (d)s 9 f 249.744 (u)s 3 f 654.599 y 262.267 (=)s 12 f 274.739 (\241)s 9 f 646.481 y 285.272 (@)s 12 f 292.127 (H)s 17.106 .4 285.272 651.799 r 9 f 662.83 y 285.362 (@)s 292.217 (x)s 10 f 659.364 y 298.894 (i)s 9 f 654.599 y 307.494 (:)s 3 f 442.891 (\05029\051)s 681.664 y 8.536 (The)s 32.994 (system)s 72.271 (of)s 85.958 (equations)s 138.878 (\05029\051)s 163.989 (represen)s 206.158 (ts)s 219.584 (the)s 240.126 (ra)s 250.244 (y)s 260.668 (tracing)s 300.793 (system)s 340.069 (in)s 354.083 (Hamiltonian)s 421.947 (form,)s 453.336 (or)s 696.164 y 8.536 (the)s 28.772 (Hamiltonian)s 96.329 (ra)s 106.447 (y)s 116.565 (equations.)s 735.628 y 227.346 (216)s do-end end endp showpage %%Page: 7 7 %%BeginPageSetup initializepage (drahotova; page: 7 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 26.161 (Th)s 40.848 (us,)s 59.853 (if)s 71.153 (Hessian)s 114.566 (\05025\051)s 139.901 (is)s 152.245 (di\256eren)s 190.106 (t)s 199.122 (from)s 227.394 (zero,)s 256.125 (w)s 264.285 (e)s 273.953 (can)s 296.024 (construct)s 348.188 (Hamiltonian)s 12 f 416.275 (H)s 3 f 426.525 (\050)s 9 f 431.095 (x)s 10 f -.891 y 437.772 (k)s 9 f 3.464 y 442.911 (;)s 448.174 (p)s 10 f 5.264 y 454.072 (k)s 3 f 3.464 y 459.211 (\051)s 17.964 y 8.536 (from)s 37.561 (Lagrangian)s 12 f 100.365 (L)s 3 f 108.642 (\050)s 9 f 113.211 (x)s 10 f 13.609 y 119.888 (k)s 9 f 17.964 y 125.027 (;)s 130.291 (x)s 10 f 13.609 y 136.968 (k)s 13 f 142.107 (0)s 3 f 17.964 y 144.912 (\051,)s 158.265 (and)s 182.395 (vice)s 207.503 (v)s 213.378 (ersa.)s 246.012 (Condition)s 302.128 (\05025\051,)s 331.8 (ho)s 343.876 (w)s 352.036 (ev)s 363.133 (er,)s 381.708 (often)s 412.691 (causes)s 450.007 (se-)s 32.464 y 8.536 (rious)s 38.1 (di\261culties.)s 101.202 (W)s 112.295 (e)s 122.21 (shall)s 150.469 (no)s 162.545 (w)s 175.724 (explain)s 217.299 (the)s 238.311 (main)s 268.462 (problem,)s 318.391 (connected)s 374 (with)s 401.54 (Lagrangians)s 46.964 y 8.536 (represen)s 50.705 (ted)s 70.941 (b)s 77.142 (y)s 87.26 (homogeneous)s 159.13 (functions)s 209.785 (of)s 223.167 (the)s 243.403 (\257rst)s 267.621 (degree)s 304.176 (in)s 9 f 317.884 (x)s 10 f 42.609 y 324.561 (i)s 13 f 327.955 (0)s 3 f 46.964 y 330.761 (.)s 70 y 26.161 (In)s 41.351 (seismology)s 95.009 (,)s 102.823 (F)s 109.512 (ermat\047s)s 151.861 (principle)s 200.674 (has)s 222.134 (mostly)s 260.894 (b)s 267.748 (een)s 289.144 (used)s 316.48 (in)s 330.695 (parameteric)s 395.826 (form)s 424.076 (\05022\051.)s 454.972 (It)s 84.5 y 8.536 (is)s 22.167 (required)s 70.002 (that)s 97.276 (the)s 119.327 (Euler-Lagrange)s 203.714 (equations)s 258.143 (\05023\051)s 284.764 (hold)s 312.69 (for)s 332.457 (an)s 344.533 (y)s 356.466 (parameter)s 9 f 414.42 (u)s 3 f 421.107 (.)s 435.04 (F)s 441.729 (or)s 457.905 (a)s 99 y 8.536 (parameter)s 9 f 64.674 (\276)s 3 f 71.783 (,)s 78.964 (di\256eren)s 116.824 (t)s 125.31 (from)s 9 f 153.053 (u)s 3 f 159.741 (,)s 166.921 (\05022\051)s 191.726 (reads)s 9 f 131.411 y 111.551 (\261)s 12 f 117.205 (I)s 3 f 124.625 (\050)s 9 f 129.194 (l)s 3 f 132.958 (\051)s 140.861 (=)s 9 f 153.333 (\261)s 0 f 117.3 y 160.987 (Z)s 10 f 120.466 y 170.987 (R)s 140.022 y 166.542 (S)s 12 f 131.411 y 179.938 (L)s 3 f 188.215 (\050)s 9 f 192.784 (x)s 10 f 126.456 y 199.461 (k)s 9 f 131.411 y 204.6 (;)s 209.864 (x)s 10 f 126.456 y 216.541 (k)s 13 f 221.68 (0)s 3 f 131.411 y 224.486 (\051d)s 9 f 235.583 (\276)s 3 f 246.025 (=)s 258.497 (0)s 9 f 268.289 (;)s 285.302 (x)s 10 f 126.456 y 291.98 (k)s 13 f 297.118 (0)s 3 f 131.411 y 303.257 (=)s 315.729 (d)s 9 f 322.257 (x)s 10 f 126.456 y 328.934 (k)s 9 f 131.411 y 334.073 (=)s 3 f 339.948 (d)s 9 f 346.476 (\276)s 357.501 (:)s 3 f 162.022 y 8.536 (Substituting)s 75.837 (d)s 9 f 82.364 (u)s 3 f 92.385 (=)s 104.857 (\050d)s 9 f 115.954 (u=)s 3 f 128.517 (d)s 9 f 135.044 (\276)s 3 f 142.153 (\051d)s 9 f 153.25 (\276)s 3 f 164.276 (in)s 173.741 (to)s 188.102 (\05022\051)s 212.907 (yields)s 9 f 194.433 y 67.81 (\261)s 12 f 73.465 (I)s 3 f 80.885 (\050)s 9 f 85.454 (l)s 3 f 89.218 (\051)s 97.121 (=)s 9 f 109.593 (\261)s 0 f 180.322 y 117.247 (Z)s 10 f 183.489 y 127.247 (R)s 203.044 y 122.802 (S)s 12 f 194.433 y 138.198 (L)s 3 f 146.475 (\050)s 9 f 151.044 (x)s 10 f 189.479 y 157.721 (k)s 9 f 194.433 y 162.86 (;)s 168.124 (a)s 13 f 189.479 y 174.292 (\241)s 7 f 180.903 (1)s 9 f 194.433 y 185.653 (x)s 10 f 189.479 y 192.33 (k)s 13 f 197.469 (0)s 3 f 194.433 y 200.275 (\051)s 9 f 204.844 (a)s 3 f 211.012 (d)s 9 f 217.54 (\276)s 228.565 (;)s 249.496 (a)s 3 f 258.997 (=)s 271.469 (d)s 9 f 277.997 (u=)s 3 f 290.559 (d)s 9 f 297.087 (\276)s 308.112 (;)s 329.043 (x)s 10 f 189.479 y 335.72 (k)s 13 f 340.859 (0)s 3 f 194.433 y 346.998 (=)s 359.47 (d)s 9 f 365.997 (x)s 10 f 189.479 y 372.674 (k)s 9 f 194.433 y 377.813 (=)s 3 f 383.688 (d)s 9 f 390.216 (\276)s 401.242 (:)s 3 f 225.955 y 8.536 (Both)s 37.02 (expressions)s 97.525 (for)s 9 f 114.751 (\261)s 12 f 120.405 (I)s 3 f 127.825 (\050)s 9 f 132.395 (l)s 3 f 136.159 (\051)s 143.92 (are)s 162.778 (the)s 182.288 (same)s 211.003 (if)s 9 f 221.049 (a)s 12 f 227.217 (L)s 3 f 235.494 (\050)s 9 f 240.063 (x)s 10 f 221.6 y 246.74 (k)s 9 f 225.955 y 251.879 (;)s 257.143 (a)s 13 f 221.6 y 263.311 (\241)s 7 f 269.922 (1)s 9 f 225.955 y 274.672 (x)s 10 f 221.6 y 281.349 (k)s 13 f 286.488 (0)s 3 f 225.955 y 289.294 (\051)s 297.196 (=)s 12 f 309.668 (L)s 3 f 317.945 (\050)s 9 f 322.514 (x)s 10 f 221.6 y 329.191 (k)s 9 f 225.955 y 334.33 (;)s 339.594 (x)s 10 f 221.6 y 346.271 (k)s 13 f 351.41 (0)s 3 f 225.955 y 354.216 (\051,)s 365.386 (that)s 390.119 (is,)s 404.618 (if)s 12 f 414.663 (L)s 3 f 422.94 (\050)s 9 f 427.509 (x)s 10 f 221.6 y 434.186 (k)s 9 f 225.955 y 439.325 (;)s 444.589 (x)s 10 f 221.6 y 451.266 (k)s 13 f 456.405 (0)s 3 f 225.955 y 459.211 (\051)s 240.455 y 8.536 (is)s 20.443 (a)s 30.327 (homogeneous)s 102.289 (function)s 148.401 (of)s 161.875 (the)s 182.202 (\257rst)s 206.512 (degree)s 243.159 (in)s 9 f 256.959 (x)s 10 f 236.1 y 263.637 (i)s 13 f 267.03 (0)s 3 f 240.455 y 269.836 (.)s 278.598 (Th)s 293.285 (us)s 308.456 (\05022\051)s 333.353 (and)s 356.292 (\05023\051)s 381.19 (ma)s 396.53 (y)s 406.74 (b)s 413.594 (e)s 422.825 (used)s 449.745 (for)s 254.955 y 8.536 (arbitrarily)s 65.88 (c)s 70.776 (hosen)s 104.359 (parameter)s 9 f 161.377 (u)s 3 f 172.86 (only)s 199.524 (if)s 12 f 211.174 (L)s 3 f 219.451 (\050)s 9 f 224.02 (x)s 10 f 250.6 y 230.697 (k)s 9 f 254.955 y 235.836 (;)s 241.1 (x)s 10 f 250.6 y 247.777 (k)s 13 f 252.916 (0)s 3 f 254.955 y 255.722 (\051)s 265.087 (is)s 277.782 (a)s 288.453 (homogeneous)s 361.202 (function)s 408.102 (of)s 422.363 (the)s 443.479 (\257rst)s 269.455 y 8.536 (degree)s 45.091 (in)s 9 f 58.799 (x)s 10 f 265.1 y 65.476 (k)s 13 f 70.615 (0)s 3 f 269.455 y 73.421 (.)s 292.491 y 26.161 (It)s 38.251 (is,)s 52.822 (ho)s 64.898 (w)s 73.057 (ev)s 84.155 (er,)s 100.619 (p)s 107.473 (ossible)s 144.176 (to)s 157.902 (pro)s 174.548 (v)s 180.423 (e)s 188.926 (that)s 213.749 (the)s 233.35 (Hessian)s 275.598 (determinan)s 333.368 (t)s 341.219 (\05025\051)s 365.39 (v)s 370.938 (anishes)s 410.905 (iden)s 432.121 (tically)s 306.991 y 8.536 (if)s 12 f 18.821 (L)s 3 f 27.098 (\050)s 9 f 31.667 (x)s 10 f 302.636 y 38.344 (k)s 9 f 306.991 y 43.483 (;)s 48.747 (x)s 10 f 302.636 y 55.424 (k)s 13 f 60.563 (0)s 3 f 306.991 y 63.368 (\051)s 71.369 (is)s 82.698 (a)s 92.004 (homogeneous)s 163.389 (function)s 208.924 (of)s 221.82 (the)s 241.57 (\257rst)s 265.302 (degree)s 301.372 (in)s 9 f 314.595 (x)s 10 f 302.636 y 321.272 (i)s 13 f 324.666 (0)s 3 f 306.991 y 327.471 (.)s 335.795 (F)s 342.484 (unction)s 9 f 384.429 (@)s 12 f 391.284 (L)s 9 f 399.561 (=@)s 412.291 (x)s 10 f 302.636 y 418.968 (j)s 13 f 423.367 (0)s 3 f 306.991 y 429.603 (is)s 440.933 (then)s 321.491 y 8.536 (a)s 18.327 (homogeneous)s 90.198 (function)s 136.218 (of)s 149.6 (the)s 169.836 (zeroth)s 205.738 (degree)s 242.293 (in)s 9 f 256.001 (x)s 10 f 317.136 y 262.678 (j)s 13 f 267.077 (0)s 3 f 321.491 y 269.883 (,)s 277.063 (and)s 299.91 (the)s 320.146 (Euler)s 351.64 (theorem)s 397.334 (yields)s 9 f 354.852 y 117.816 (x)s 10 f 349.898 y 124.493 (i)s 13 f 127.887 (0)s 9 f 346.734 y 133.892 (@)s 7 f 342.38 y 140.748 (2)s 12 f 346.734 y 145.498 (L)s 3 f 153.774 (\050)s 9 f 158.344 (x)s 10 f 342.38 y 165.021 (k)s 9 f 346.734 y 170.16 (;)s 175.424 (x)s 10 f 342.38 y 182.101 (k)s 13 f 187.24 (0)s 3 f 346.734 y 190.045 (\051)s 60.722 .4 133.892 352.052 r 9 f 363.084 y 144.019 (@)s 150.874 (x)s 10 f 359.617 y 157.551 (i)s 13 f 160.945 (0)s 9 f 363.084 y 163.751 (@)s 170.606 (x)s 10 f 359.617 y 177.283 (j)s 13 f 181.682 (0)s 3 f 354.852 y 199.148 (=)s 9 f 211.62 (x)s 10 f 349.898 y 218.297 (i)s 13 f 221.691 (0)s 9 f 346.734 y 234.135 (@)s 19.732 .4 227.696 352.052 r 363.084 y 227.696 (@)s 234.552 (x)s 10 f 359.617 y 241.229 (i)s 13 f 244.623 (0)s 0 f 340.252 y 252.545 (\265)s 9 f 346.734 y 261.106 (@)s 12 f 267.962 (L)s 3 f 276.238 (\050)s 9 f 280.808 (x)s 10 f 342.38 y 287.485 (k)s 9 f 346.734 y 292.624 (;)s 297.887 (x)s 10 f 342.38 y 304.564 (k)s 13 f 309.703 (0)s 3 f 346.734 y 312.509 (\051)s 55.972 .4 261.106 352.052 r 9 f 363.084 y 278.724 (@)s 285.579 (x)s 10 f 359.617 y 292.256 (j)s 13 f 296.655 (0)s 0 f 340.252 y 318.278 (\266)s 3 f 354.852 y 328.973 (=)s 341.445 (0)s 9 f 351.236 (:)s 3 f 386.496 y 8.536 (Th)s 23.223 (us,)s 43.316 (for)s 62.667 (an)s 74.744 (y)s 86.261 (\257xed)s 9 f 116.057 (j)s 3 f 121.593 (,)s 130.524 (v)s 136.398 (ector)s 9 f 167.173 (@)s 7 f 382.141 y 174.029 (2)s 12 f 386.496 y 178.779 (L)s 9 f 187.055 (=@)s 199.786 (x)s 10 f 382.141 y 206.463 (i)s 13 f 209.857 (0)s 9 f 386.496 y 212.662 (@)s 219.518 (x)s 10 f 382.141 y 226.195 (j)s 13 f 230.593 (0)s 3 f 386.496 y 238.716 (is)s 251.931 (p)s 258.785 (erp)s 275.43 (endicular)s 327.747 (to)s 343.507 (v)s 349.382 (ector)s 9 f 380.157 (x)s 10 f 382.141 y 386.834 (i)s 13 f 390.228 (0)s 3 f 386.496 y 393.034 (.)s 405.719 (This)s 433.948 (sho)s 450.659 (ws)s 400.996 y 8.536 (that)s 35.44 (all)s 53.205 (the)s 74.887 (three)s 106.36 (column)s 148.93 (v)s 154.805 (ectors)s 190.26 (in)s 205.415 (the)s 227.096 (Hessian)s 271.425 (determinan)s 329.195 (t)s 339.127 (are)s 360.156 (situated)s 406.708 (in)s 421.862 (a)s 433.1 (plane.)s 415.496 y 8.536 (Consequen)s 63.434 (tly)s 76.489 (,)s 83.67 (they)s 110.107 (are)s 129.69 (linearly)s 171.794 (dep)s 190.398 (enden)s 220.099 (t)s 228.585 (and)s 251.432 (the)s 271.668 (Hessian)s 314.551 (determinan)s 372.321 (t)s 380.807 (v)s 386.356 (anishes.)s 438.532 y 26.161 (The)s 50.401 (\257nal)s 76.6 (result)s 109.392 (is)s 121.296 (that)s 146.842 (the)s 167.166 (dual)s 193.365 (Legendre)s 243.878 (transformation)s 323.995 (cannot)s 362.597 (b)s 369.451 (e)s 378.678 (used)s 405.595 (to)s 420.044 (compute)s 453.032 y 8.536 (the)s 28.196 (Hamiltonian)s 95.178 (from)s 122.344 (the)s 142.004 (Lagrangian,)s 206.329 (if)s 216.524 (Lagrangian)s 12 f 277.47 (L)s 3 f 285.746 (\050)s 9 f 290.316 (x)s 10 f 448.677 y 296.993 (k)s 9 f 453.032 y 302.132 (;)s 307.396 (x)s 10 f 448.677 y 314.073 (k)s 13 f 319.212 (0)s 3 f 453.032 y 322.017 (\051)s 329.927 (is)s 341.166 (a)s 350.382 (homogeneous)s 421.676 (function)s 467.532 y 8.536 (of)s 21.885 (the)s 42.087 (\257rst)s 66.272 (degree)s 102.794 (in)s 9 f 116.469 (x)s 10 f 463.177 y 123.146 (i)s 13 f 126.54 (0)s 3 f 467.532 y 129.345 (.)s 137.82 (Consequen)s 192.718 (tly)s 205.774 (,)s 212.928 (the)s 233.13 (Hamiltonian)s 300.655 (ra)s 310.773 (y)s 320.857 (tracing)s 360.643 (equations)s 413.223 (cannot)s 451.704 (b)s 458.558 (e)s 482.032 y 8.536 (obtained)s 57.573 (from)s 86.048 (the)s 107.015 (Lagrangian)s 169.269 (ra)s 179.387 (y)s 190.237 (tracing)s 230.788 (equations)s 284.133 (b)s 290.334 (y)s 301.184 (the)s 322.152 (application)s 383.592 (of)s 397.706 (the)s 418.673 (standard)s 496.532 y 8.536 (dual)s 34.647 (Legendre)s 85.071 (transform.)s 519.568 y 26.161 (W)s 37.254 (e)s 46.728 (shall)s 74.545 (sho)s 91.255 (w)s 103.993 (a)s 114.12 (simple)s 151.076 (consequence)s 217.732 (of)s 231.449 (the)s 252.021 (Lagragian)s 307.35 (b)s 314.204 (eing)s 339.344 (a)s 349.471 (homogeneous)s 421.676 (function)s 534.068 y 8.536 (of)s 21.7 (the)s 41.718 (\257rst)s 65.718 (degree)s 102.056 (in)s 9 f 115.546 (x)s 10 f 529.713 y 122.223 (i)s 13 f 125.617 (0)s 3 f 534.068 y 128.423 (.)s 136.836 (In)s 151.301 (this)s 173.996 (case,)s 201.956 (w)s 210.116 (e)s 219.037 (obtain)s 9 f 255.374 (x)s 10 f 529.713 y 262.051 (i)s 13 f 265.445 (0)s 9 f 534.068 y 268.251 (p)s 10 f 535.868 y 274.148 (i)s 3 f 534.068 y 280.875 (=)s 9 f 293.347 (x)s 10 f 529.713 y 300.024 (i)s 13 f 303.418 (0)s 3 f 534.068 y 306.224 (\050)s 9 f 310.793 (@)s 12 f 317.649 (L)s 9 f 325.925 (=@)s 338.656 (x)s 10 f 529.713 y 345.333 (i)s 13 f 348.727 (0)s 3 f 534.068 y 351.532 (\051)s 359.435 (=)s 12 f 371.907 (L)s 3 f 380.184 (\050)s 9 f 384.753 (x)s 10 f 529.713 y 391.43 (k)s 9 f 534.068 y 396.569 (;)s 401.833 (x)s 10 f 529.713 y 408.51 (k)s 13 f 413.649 (0)s 3 f 534.068 y 416.454 (\051,)s 428.03 (so)s 442.239 (that)s 9 f 560.568 y 114.399 (x)s 10 f 555.613 y 121.076 (i)s 13 f 124.47 (0)s 9 f 560.568 y 127.276 (p)s 10 f 562.368 y 133.173 (i)s 12 f 560.568 y 139.233 (\241)s 151.233 (L)s 3 f 159.51 (\050)s 9 f 164.08 (x)s 10 f 555.613 y 170.757 (k)s 9 f 560.568 y 175.896 (;)s 181.159 (x)s 10 f 555.613 y 187.836 (k)s 13 f 192.975 (0)s 3 f 560.568 y 195.781 (\051)s 203.684 (=)s 12 f 216.156 (L)s 3 f 224.432 (\050)s 9 f 229.002 (x)s 10 f 555.613 y 235.679 (k)s 9 f 560.568 y 240.818 (;)s 246.082 (x)s 10 f 555.613 y 252.759 (k)s 13 f 257.898 (0)s 3 f 560.568 y 260.703 (\051)s 12 f 267.939 (\241)s 279.939 (L)s 3 f 288.216 (\050)s 9 f 292.785 (x)s 10 f 555.613 y 299.462 (k)s 9 f 560.568 y 304.601 (;)s 309.865 (x)s 10 f 555.613 y 316.542 (k)s 13 f 321.681 (0)s 3 f 560.568 y 324.487 (\051)s 332.389 (=)s 344.861 (0)s 9 f 354.653 (:)s 3 f 587.068 y 8.536 (Equation)s 59.287 (\05026\051)s 84.092 (then)s 110.856 (yields)s 12 f 601.568 y 197.975 (H)s 3 f 208.225 (\050)s 9 f 212.795 (x)s 10 f 596.613 y 219.472 (k)s 9 f 601.568 y 224.611 (;)s 229.874 (p)s 10 f 603.368 y 235.772 (k)s 3 f 601.568 y 240.911 (\051)s 248.813 (=)s 261.285 (0)s 9 f 271.077 (:)s 3 f 442.891 (\05030\051)s 622.568 y 8.536 (Th)s 23.223 (us,)s 42.082 (w)s 50.242 (e)s 59.794 (ha)s 71.87 (v)s 77.745 (e)s 87.296 (obtained)s 136.014 (the)s 156.663 (in)s 166.128 (teresting)s 214.912 (result)s 248.028 (that)s 12 f 273.899 (H)s 3 f 284.149 (\050)s 9 f 288.719 (x)s 10 f 618.213 y 295.396 (k)s 9 f 622.568 y 300.535 (;)s 305.798 (p)s 10 f 624.368 y 311.696 (k)s 3 f 622.568 y 316.835 (\051)s 325.44 (=)s 338.615 (0)s 348.819 (for)s 367.183 (Lagrangians)s 433.753 (repre-)s 637.068 y 8.536 (sen)s 24.594 (ted)s 45.273 (b)s 51.475 (y)s 62.036 (homogeneous)s 134.349 (function)s 180.813 (of)s 194.638 (the)s 215.317 (\257rst)s 239.978 (degree)s 276.976 (in)s 9 f 291.128 (x)s 10 f 632.713 y 297.805 (i)s 13 f 301.199 (0)s 3 f 637.068 y 304.004 (.)s 313.82 (W)s 324.913 (e)s 334.495 (are,)s 357.896 (ho)s 369.972 (w)s 378.132 (ev)s 389.229 (er,)s 406.755 (not)s 428.087 (able)s 453.336 (to)s 651.568 y 8.536 (deriv)s 33.994 (e)s 43.133 (the)s 63.369 (actual)s 98.618 (form)s 126.361 (of)s 12 f 139.743 (H)s 3 f 149.993 (\050)s 9 f 154.562 (x)s 10 f 647.213 y 161.239 (k)s 9 f 651.568 y 166.378 (;)s 171.642 (p)s 10 f 653.368 y 177.539 (k)s 3 f 651.568 y 182.678 (\051.)s 674.604 y 26.161 (Nev)s 46.066 (ertheless,)s 97.685 (it)s 109.892 (is)s 122.165 (p)s 129.019 (ossible)s 166.815 (to)s 181.633 (mo)s 197.626 (dify)s 221.583 (the)s 242.277 (Lagrangian)s 304.256 (in)s 313.721 (to)s 328.539 (a)s 338.788 (new)s 363.398 (form,)s 394.977 (for)s 413.385 (whic)s 436.559 (h)s 447.461 (the)s 689.104 y 8.536 (Euler-Lagrange)s 90.909 (equations)s 143.324 (are)s 162.708 (still)s 185.422 (satis\257ed,)s 233.699 (but)s 255.042 (the)s 275.079 (Hessian)s 317.763 (determinan)s 375.533 (t)s 383.821 (do)s 396.55 (es)s 410.125 (not)s 430.815 (iden)s 452.03 (ti-)s 703.604 y 8.536 (cally)s 36.279 (v)s 41.827 (anish.)s 77.142 (In)s 91.825 (this)s 114.738 (con)s 132.036 (tribution,)s 184.91 (w)s 193.07 (e)s 202.209 (shall)s 229.691 (describ)s 265.985 (e)s 275.123 (t)s 279.366 (w)s 287.526 (o)s 297.318 (suc)s 313.376 (h)s 323.82 (p)s 330.674 (ossibilities.)s 735.628 y 227.346 (217)s do-end end endp showpage %%Page: 8 8 %%BeginPageSetup initializepage (drahotova; page: 8 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S -943 -1000 :M f222 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 15 17.28 /CMBX12 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 26.161 (1\051)s 42.164 (W)s 53.257 (e)s 64.038 (can)s 87.221 (use)s 109.164 (the)s 131.042 (v)s 136.591 (ariable)s 9 f 176.747 (u)s 3 f 189.562 (=)s 9 f 204.83 (\277)s 3 f 216.831 (along)s 249.806 (the)s 271.684 (curv)s 293.879 (e,)s 308.334 (where)s 9 f 343.92 (\277)s 3 f 355.922 (represen)s 398.091 (ts)s 412.854 (the)s 434.732 (tra)s 449.419 (v)s 455.294 (el)s 17.964 y 8.536 (time)s 35.148 (along)s 66.33 (the)s 86.414 (curv)s 108.608 (e.)s 122.266 (W)s 133.359 (e)s 142.347 (can)s 163.737 (then)s 190.349 (in)s 199.814 (tro)s 215.154 (duce)s 242.419 (the)s 262.504 (mo)s 278.496 (di\257ed)s 310.331 (Lagrangian)s 12 f 371.701 (L)s 10 f 13.609 y 379.978 (M)s 3 f 17.964 y 389.493 (\050)s 9 f 394.062 (x)s 10 f 13.609 y 400.74 (k)s 9 f 17.964 y 405.878 (;)s 3 f 413.175 (\137)s 9 f 411.142 (x)s 10 f 13.609 y 417.819 (k)s 3 f 17.964 y 422.958 (\051)s 431.293 (b)s 437.494 (y)s 447.461 (the)s 32.464 y 8.536 (relation)s 12 f 46.964 y 119.173 (L)s 10 f 42.009 y 127.45 (M)s 3 f 46.964 y 136.965 (\050)s 9 f 141.535 (x)s 10 f 42.009 y 148.212 (k)s 9 f 46.964 y 153.351 (;)s 3 f 160.648 (\137)s 9 f 158.615 (x)s 10 f 42.009 y 165.292 (k)s 3 f 46.964 y 170.431 (\051)s 178.333 (=)s 7 f 42.239 y 192.005 (1)s 4.25 .4 192.005 44.164 r 51.102 y 192.005 (2)s 3 f 46.964 y 197.455 ([)s 12 f 200.719 (L)s 7 f 42.009 y 208.996 (2)s 3 f 46.964 y 213.746 (\050)s 9 f 218.315 (x)s 10 f 42.009 y 224.992 (k)s 9 f 46.964 y 230.131 (;)s 3 f 237.428 (\137)s 9 f 235.395 (x)s 10 f 42.009 y 242.072 (k)s 3 f 46.964 y 247.211 (\051])s 7 f 42.009 y 255.044 (2)s 9 f 46.964 y 263.711 (;)s 3 f 286.674 (\137)s 9 f 284.641 (x)s 10 f 42.009 y 291.318 (i)s 3 f 46.964 y 298.046 (=)s 310.518 (d)s 9 f 317.045 (x)s 10 f 42.009 y 323.723 (i)s 9 f 46.964 y 327.116 (=)s 3 f 332.991 (d)s 9 f 339.519 (\277)s 349.879 (:)s 3 f 67.964 y 8.536 (W)s 19.629 (e)s 28.747 (emphasize)s 84.931 (that)s 112.401 (\137)s 9 f 110.368 (x)s 10 f 63.609 y 117.045 (i)s 3 f 67.964 y 124.336 (is)s 136.131 (used)s 162.939 (to)s 177.28 (denote)s 215.12 (d)s 9 f 221.648 (x)s 10 f 63.609 y 228.325 (i)s 9 f 67.964 y 231.719 (=)s 3 f 237.594 (d)s 9 f 244.122 (\277)s 3 f 254.461 (to)s 268.802 (distinguish)s 328.314 (it)s 340.044 (from)s 9 f 367.766 (x)s 10 f 63.609 y 374.443 (i)s 13 f 377.837 (0)s 3 f 67.964 y 383.976 (=)s 396.448 (d)s 9 f 402.976 (x)s 10 f 63.609 y 409.653 (i)s 9 f 67.964 y 413.047 (=)s 3 f 418.922 (d)s 9 f 425.449 (u)s 3 f 432.137 (,)s 439.301 (v)s 444.85 (alid)s 82.464 y 8.536 (for)s 26.487 (an)s 38.563 (y)s 48.681 (parameter)s 9 f 104.82 (u)s 3 f 111.507 (.)s 119.993 (F)s 126.682 (or)s 141.043 (a)s 150.834 (detailed)s 195.223 (treatmen)s 241.243 (t,)s 252.993 (see)s 271.989 (Section)s 313.113 (3.)s 105.5 y 26.161 (2\051)s 39.477 (As)s 55.792 (the)s 74.983 (v)s 80.532 (ariable)s 9 f 118.001 (u)s 3 f 127.56 (along)s 157.849 (the)s 177.04 (ra)s 187.158 (y)s 192.38 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26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f596 sf ( )S -983 -1000 :M f184 sf ( )S -979 -1000 :M f222 sf -.751( )A f258 sf ( )S -972 -1000 :M f296 sf ( )S -964 -1000 :M f333 sf ( )S -956 -1000 :M f521 sf ( )S -946 -1000 :M f371 sf ( )S -934 -1000 :M ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 2 10 /CMMI10 findfont fdef 3 12 /CMR12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 11 6 /CMMI6 findfont fdef 12 12 /CMSY10 findfont fdef 17 14.4 /CMSY10 findfont fdef 58 49 translate 72 72.27 div dup scale 6 f 3.523 y 8.536 (3.1)s 45.436 (Mo)s 69.353 (di\257ed)s 113.644 (Lagrangian)s 17 f 197.719 (L)s 2 f -1.703 y 207.651 (M)s 6 f 3.523 y 218.943 (.)s 230.643 (Deriv)s 269.218 (ation)s 310.393 (of)s 328.843 (Hamiltonian)s 21.523 y 45.436 (canonical)s 116.086 (equations)s 3 f 52.309 y 8.536 (W)s 19.629 (e)s 28.768 (no)s 40.844 (w)s 53.247 (in)s 62.712 (tro)s 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f 178.029 y 39.71 (,)s 9 f 199.391 y 164.272 (g)s 10 f 201.191 y 169.899 (ij)s 3 f 199.391 y 177.191 (\050)s 9 f 181.76 (x)s 10 f 194.436 y 188.438 (k)s 9 f 199.391 y 193.576 (;)s 3 f 200.873 (\137)s 9 f 198.84 (x)s 10 f 194.436 y 205.517 (k)s 3 f 199.391 y 210.656 (\051)s 218.559 (=)s 9 f 191.273 y 232.231 (@)s 7 f 186.918 y 239.086 (2)s 12 f 191.273 y 243.837 (L)s 10 f 186.918 y 252.113 (M)s 3 f 191.273 y 261.629 (\050)s 9 f 266.198 (x)s 10 f 186.918 y 272.875 (k)s 9 f 191.273 y 278.014 (;)s 3 f 285.311 (\137)s 9 f 283.278 (x)s 10 f 186.918 y 289.955 (k)s 3 f 191.273 y 295.094 (\051)s 67.432 .4 232.231 196.591 r 9 f 207.622 y 248.518 (@)s 3 f 257.407 (\137)s 9 f 255.374 (x)s 10 f 204.156 y 262.051 (i)s 9 f 207.622 y 265.445 (@)s 3 f 274.333 (\137)s 9 f 272.3 (x)s 10 f 204.156 y 278.977 (j)s 9 f 199.391 y 304.78 (;)s 3 f 442.891 (\05037\051)s 222.461 y 8.536 (and)s 31.383 (the)s 51.619 (relation)s 94.702 (of)s 9 f 108.083 (g)s 10 f 224.261 y 113.71 (ij)s 3 f 222.461 y 124.919 (to)s 139.28 (the)s 159.516 (Hessian)s 202.399 (determinan)s 260.169 (t:)s 254.437 y 170.327 (det)s 0 f 239.837 y 188.646 (\265)s 9 f 246.319 y 199.937 (@)s 7 f 241.964 y 206.793 (2)s 12 f 246.319 y 211.543 (L)s 10 f 241.964 y 219.82 (M)s 34.858 .4 197.207 251.637 r 9 f 262.668 y 197.207 (@)s 3 f 206.096 (\137)s 9 f 204.063 (x)s 10 f 259.201 y 210.74 (i)s 9 f 262.668 y 214.134 (@)s 3 f 223.022 (\137)s 9 f 220.989 (x)s 10 f 259.201 y 227.666 (j)s 0 f 239.837 y 233.265 (\266)s 3 f 254.437 y 243.959 (=)s 256.431 (det)s 272.751 (\050)s 9 f 277.32 (g)s 10 f 256.237 y 282.946 (ij)s 3 f 254.437 y 290.239 (\051)s 9 f 298.725 (:)s 3 f 442.891 (\05038\051)s 284.397 y 8.536 (W)s 19.629 (e)s 28.768 (shall)s 56.249 (no)s 68.326 (w)s 80.728 (ev)s 91.499 (aluate)s 7 f 279.673 y 130.297 (d)s 9.418 .4 127.949 281.597 r 288.535 y 127.949 (d)s 10 f 132.671 (\277)s 3 f 284.397 y 138.567 (\050)s 9 f 143.136 (@)s 12 f 149.992 (L)s 10 f 280.043 y 158.268 (M)s 9 f 284.397 y 167.784 (=@)s 3 f 182.547 (\137)s 9 f 180.514 (x)s 10 f 280.043 y 187.191 (i)s 3 f 284.397 y 190.585 (\051)s 12 f 197.821 (\241)s 9 f 209.821 (@)s 12 f 216.677 (L)s 10 f 280.043 y 224.953 (M)s 9 f 284.397 y 234.469 (=@)s 247.199 (x)s 10 f 280.043 y 253.876 (i)s 3 f 284.397 y 257.27 (.)s 265.756 (W)s 276.849 (e)s 285.988 (obtain)s 309.098 y 44.019 (d)s 12.971 .4 40.797 314.416 r 325.447 y 40.797 (d)s 9 f 47.325 (\277)s 0 f 299.616 y 56.968 (\303)s 9 f 309.098 y 66.085 (@)s 12 f 72.94 (L)s 10 f 304.743 y 81.217 (M)s 24.648 .4 66.085 314.416 r 9 f 325.447 y 69.945 (@)s 3 f 78.834 (\137)s 9 f 76.801 (x)s 10 f 321.98 y 83.478 (i)s 0 f 299.616 y 91.932 (!)s 12 f 317.216 y 102.516 (\241)s 9 f 309.098 y 115.716 (@)s 12 f 122.571 (L)s 10 f 304.743 y 130.848 (M)s 24.648 .4 115.716 314.416 r 9 f 325.447 y 119.576 (@)s 126.432 (x)s 10 f 321.98 y 133.109 (i)s 3 f 317.216 y 144.896 (=)s 157.369 (2)s 0 f 299.616 y 165.243 (\042)s 3 f 309.098 y 175.498 (d)s 12.971 .4 172.277 314.416 r 325.447 y 172.277 (d)s 9 f 178.805 (\277)s 0 f 299.616 y 188.448 (\303)s 12 f 317.216 y 196.364 (L)s 9 f 309.098 y 206.738 (@)s 12 f 213.594 (L)s 16.926 .4 205.841 314.416 r 9 f 325.447 y 205.841 (@)s 3 f 214.729 (\137)s 9 f 212.696 (x)s 10 f 321.98 y 219.373 (i)s 0 f 299.616 y 223.967 (!)s 12 f 317.216 y 234.551 (\241)s 246.551 (L)s 9 f 309.098 y 258.924 (@)s 12 f 265.78 (L)s 16.926 .4 258.027 314.416 r 9 f 325.447 y 258.027 (@)s 264.883 (x)s 10 f 321.98 y 271.56 (i)s 0 f 299.616 y 276.154 (#)s 3 f 317.216 y 285.32 (=)s 297.792 (2)s 0 f 299.616 y 305.667 (\042)s 3 f 309.098 y 315.922 (d)s 12.971 .4 312.701 314.416 r 325.447 y 312.701 (d)s 9 f 319.228 (\277)s 0 f 299.616 y 328.871 (\303)s 9 f 309.098 y 338.885 (@)s 12 f 345.741 (L)s 16.926 .4 337.988 314.416 r 9 f 325.447 y 337.988 (@)s 3 f 346.877 (\137)s 9 f 344.844 (x)s 10 f 321.98 y 351.521 (i)s 0 f 299.616 y 356.115 (!)s 12 f 317.216 y 366.698 (\241)s 9 f 309.098 y 380.795 (@)s 12 f 387.65 (L)s 16.926 .4 379.898 314.416 r 9 f 325.447 y 379.898 (@)s 386.753 (x)s 10 f 321.98 y 393.43 (i)s 0 f 299.616 y 398.024 (#)s 3 f 317.216 y 407.191 (=)s 419.663 (0)s 9 f 429.455 (;)s 3 f 349.806 y 8.536 (as)s 12 f 25.193 (L)s 3 f 33.47 (\050)s 9 f 38.039 (x)s 10 f 345.452 y 44.716 (k)s 9 f 349.806 y 49.855 (;)s 3 f 57.152 (\137)s 9 f 55.119 (x)s 10 f 345.452 y 61.796 (k)s 3 f 349.806 y 66.935 (\051)s 78.636 (=)s 94.905 (1)s 106.928 (along)s 140.492 (the)s 162.96 (ra)s 173.077 (y)s 178.3 (,)s 188.269 (see)s 209.496 (\05034\051)s 236.532 (and)s 261.611 (\05032\051.)s 297.679 (Th)s 312.366 (us,)s 333.498 (the)s 355.965 (mo)s 371.958 (di\257ed)s 406.175 (Lagrangian)s 12 f 364.306 y 8.536 (L)s 10 f 359.952 y 16.813 (M)s 3 f 364.306 y 26.328 (\050)s 9 f 30.897 (x)s 10 f 359.952 y 37.574 (k)s 9 f 364.306 y 42.713 (;)s 3 f 50.01 (\137)s 9 f 47.977 (x)s 10 f 359.952 y 54.654 (k)s 3 f 364.306 y 59.793 (\051)s 68.279 (satis\257es)s 111.558 (the)s 131.794 (Euler-Lagrange)s 214.365 (equations,)s 387.808 y 176.722 (d)s 12.971 .4 173.5 393.126 r 404.157 y 173.5 (d)s 9 f 180.028 (\277)s 0 f 381.326 y 187.671 (\265)s 9 f 387.808 y 196.232 (@)s 12 f 203.088 (L)s 10 f 383.453 y 211.364 (M)s 24.648 .4 196.232 393.126 r 9 f 404.157 y 200.093 (@)s 3 f 208.981 (\137)s 9 f 206.948 (x)s 10 f 400.691 y 213.625 (i)s 0 f 381.326 y 222.08 (\266)s 12 f 395.926 y 232.107 (\241)s 9 f 387.808 y 245.307 (@)s 12 f 252.163 (L)s 10 f 383.453 y 260.44 (M)s 24.648 .4 245.307 393.126 r 9 f 404.157 y 249.168 (@)s 256.023 (x)s 10 f 400.691 y 262.7 (i)s 3 f 395.926 y 274.488 (=)s 286.96 (0)s 9 f 296.752 (;)s 3 f 442.891 (\05039\051)s 423.94 y 8.536 (corresp)s 45.483 (onding)s 83.996 (to)s 98.357 (the)s 118.593 (functional)s 12 f 453.364 y 108.778 (I)s 3 f 116.198 (\050)s 9 f 120.767 (l)s 3 f 124.531 (\051)s 132.434 (=)s 144.906 (2)s 0 f 439.253 y 150.781 (Z)s 10 f 442.42 y 160.781 (R)s 461.976 y 156.337 (S)s 12 f 453.364 y 167.732 (L)s 10 f 448.41 y 176.009 (M)s 3 f 453.364 y 185.525 (\050)s 9 f 190.094 (x)s 10 f 448.41 y 196.771 (k)s 9 f 453.364 y 201.91 (;)s 3 f 209.207 (\137)s 9 f 207.174 (x)s 10 f 448.41 y 213.851 (k)s 3 f 453.364 y 218.99 (\051d)s 9 f 230.087 (\277)s 3 f 239.863 (=)s 0 f 439.253 y 252.335 (Z)s 10 f 442.42 y 262.335 (R)s 461.976 y 257.891 (S)s 9 f 453.364 y 271.287 (g)s 10 f 455.164 y 276.913 (ij)s 3 f 453.364 y 284.206 (\050)s 9 f 288.775 (x)s 10 f 448.41 y 295.452 (k)s 9 f 453.364 y 300.591 (;)s 3 f 307.888 (\137)s 9 f 305.855 (x)s 10 f 448.41 y 312.532 (k)s 3 f 453.364 y 317.671 (\051)s 324.273 (\137)s 9 f 322.24 (x)s 10 f 448.41 y 328.917 (i)s 3 f 453.364 y 334.344 (\137)s 9 f 332.311 (x)s 10 f 448.41 y 338.988 (j)s 3 f 453.364 y 343.387 (d)s 9 f 349.914 (\277)s 360.274 (:)s 3 f 442.891 (\05040\051)s 480.989 y 8.536 (W)s 19.629 (e)s 28.421 (ha)s 40.497 (v)s 46.372 (e)s 55.164 (in)s 64.629 (tro)s 79.97 (duced)s 113.567 (the)s 133.456 (factor)s 166.727 (2)s 176.172 (b)s 183.026 (efore)s 211.075 (the)s 230.964 (in)s 240.429 (tegral,)s 276.707 (as)s 290.787 (w)s 298.947 (e)s 307.739 (wish)s 334.221 (to)s 348.235 (k)s 354.11 (eep)s 374.652 (the)s 394.541 (same)s 423.635 (v)s 429.183 (ariable)s 9 f 495.489 y 8.536 (\277)s 3 f 20.238 (in)s 35.288 (\05040\051)s 61.435 (as)s 77.203 (in)s 92.253 (\05031\051,)s 122 (corresp)s 158.947 (onding)s 198.802 (to)s 214.505 (the)s 236.083 (tra)s 250.77 (v)s 256.645 (el)s 270.39 (time,)s 302.095 (see)s 322.432 (\05036\051.)s 355.833 (This)s 384.004 (factor)s 418.964 (do)s 431.693 (es)s 446.808 (not)s 509.989 y 8.536 (in\260)s 24.855 (uence)s 57.738 (F)s 64.426 (ermat\047s)s 106.513 (v)s 112.061 (ariational)s 165.18 (principle)s 213.729 (and)s 236.819 (the)s 257.299 (consequen)s 308.933 (t)s 317.663 (Euler-Lagrange)s 400.479 (equations)s 453.336 (at)s 524.489 y 8.536 (all.)s 29.425 (Consequen)s 84.323 (tly)s 97.378 (,)s 104.559 (v)s 110.107 (ariational)s 162.982 (principle)s 9 f 553.914 y 113.938 (\261)s 0 f 539.803 y 119.592 (Z)s 10 f 542.969 y 129.592 (R)s 562.525 y 125.148 (S)s 3 f 553.914 y 136.544 (2)s 12 f 142.419 (L)s 10 f 548.959 y 150.695 (M)s 3 f 553.914 y 160.211 (\050)s 9 f 164.78 (x)s 10 f 548.959 y 171.457 (k)s 9 f 553.914 y 176.596 (;)s 3 f 183.893 (\137)s 9 f 181.86 (x)s 10 f 548.959 y 188.537 (k)s 3 f 553.914 y 193.676 (\051d)s 9 f 204.773 (\277)s 3 f 214.549 (=)s 9 f 227.021 (\261)s 0 f 539.803 y 232.675 (Z)s 10 f 542.969 y 242.675 (R)s 562.525 y 238.231 (S)s 9 f 553.914 y 251.627 (g)s 10 f 555.714 y 257.253 (ij)s 3 f 553.914 y 264.546 (\050)s 9 f 269.115 (x)s 10 f 548.959 y 275.792 (k)s 9 f 553.914 y 280.931 (;)s 3 f 288.228 (\137)s 9 f 286.195 (x)s 10 f 548.959 y 292.872 (k)s 3 f 553.914 y 298.011 (\051)s 304.613 (\137)s 9 f 302.58 (x)s 10 f 548.959 y 309.257 (i)s 3 f 553.914 y 314.684 (\137)s 9 f 312.651 (x)s 10 f 548.959 y 319.328 (j)s 3 f 553.914 y 323.727 (d)s 9 f 330.255 (\277)s 3 f 340.031 (=)s 352.503 (0)s 442.891 (\05041\051)s 582.205 y 8.536 (yields)s 41.566 (the)s 61.802 (same)s 91.242 (extremals)s 144.508 (as)s 158.934 (F)s 165.623 (ermat\047s)s 207.466 (v)s 213.014 (ariational)s 265.889 (principle)s 314.194 (\05031\051.)s 605.241 y 26.161 (The)s 49.76 (mo)s 65.753 (di\257ed)s 97.186 (Lagrangian)s 12 f 158.154 (L)s 10 f 600.886 y 166.431 (M)s 3 f 605.241 y 175.946 (\050)s 9 f 180.516 (x)s 10 f 600.886 y 187.193 (k)s 9 f 605.241 y 192.332 (;)s 3 f 199.629 (\137)s 9 f 197.596 (x)s 10 f 600.886 y 204.273 (k)s 3 f 605.241 y 209.412 (\051)s 217.345 (is)s 228.607 (not)s 248.942 (a)s 258.181 (homogeneous)s 329.498 (function)s 374.965 (of)s 387.794 (the)s 407.477 (\257rst)s 431.141 (degree)s 619.741 y 8.536 (in)s 23.524 (\137)s 9 f 21.491 (x)s 10 f 615.386 y 28.168 (i)s 3 f 619.741 y 34.725 (as)s 12 f 48.397 (L)s 3 f 56.674 (\050)s 9 f 61.243 (x)s 10 f 615.386 y 67.92 (k)s 9 f 619.741 y 73.059 (;)s 3 f 80.356 (\137)s 9 f 78.323 (x)s 10 f 615.386 y 85 (k)s 3 f 619.741 y 90.139 (\051,)s 101.286 (but)s 122.074 (a)s 131.112 (homogeneous)s 202.229 (function)s 247.496 (of)s 260.124 (the)s 279.606 (second)s 316.779 (degree)s 352.58 (in)s 367.568 (\137)s 9 f 365.535 (x)s 10 f 615.386 y 372.212 (i)s 3 f 619.741 y 375.606 (.)s 383.841 (In)s 397.77 (this)s 419.929 (case,)s 447.461 (the)s 634.241 y 8.536 (Hessian)s 52.212 (determinan)s 109.982 (t)s 119.261 (\05038\051)s 144.859 (do)s 157.588 (es)s 172.154 (not)s 193.835 (v)s 199.384 (anish)s 230.922 (iden)s 252.137 (tically)s 282.817 (,)s 290.989 (and)s 314.628 (the)s 335.657 (Legendre)s 386.874 (dual)s 413.778 (transform)s 648.741 y 8.536 (ma)s 23.876 (y)s 33.994 (b)s 40.848 (e)s 49.987 (used)s 76.816 (to)s 91.177 (construct)s 142.811 (the)s 163.047 (Hamiltonian.)s 235.174 (See)s 256.063 (also)s 279.628 (\05016\051.)s 671.777 y 26.161 (W)s 37.254 (e)s 46.392 (in)s 55.858 (tro)s 71.198 (duce)s 98.614 (momen)s 135.496 (ta)s 9 f 149.857 (p)s 10 f 673.577 y 155.754 (i)s 3 f 671.777 y 163.064 (and)s 185.911 (Hamiltonian)s 12 f 253.469 (H)s 10 f 667.422 y 263.719 (M)s 3 f 671.777 y 273.234 (\050)s 9 f 277.804 (x)s 10 f 667.422 y 284.481 (k)s 9 f 671.777 y 289.62 (;)s 294.884 (p)s 10 f 673.577 y 300.781 (k)s 3 f 671.777 y 305.92 (\051)s 314.406 (b)s 320.607 (y)s 330.725 (relations)s 9 f 703.397 y 86.214 (p)s 10 f 705.197 y 92.111 (i)s 3 f 703.397 y 98.838 (=)s 9 f 695.279 y 112.51 (@)s 12 f 119.366 (L)s 10 f 690.924 y 127.642 (M)s 24.648 .4 112.51 700.597 r 9 f 711.628 y 116.371 (@)s 3 f 125.259 (\137)s 9 f 123.226 (x)s 10 f 708.161 y 129.903 (i)s 9 f 703.397 y 142.274 (;)s 12 f 159.288 (H)s 10 f 698.442 y 169.538 (M)s 3 f 703.397 y 179.054 (\050)s 9 f 183.623 (x)s 10 f 698.442 y 190.3 (k)s 9 f 703.397 y 195.439 (;)s 200.703 (p)s 10 f 705.197 y 206.6 (k)s 3 f 703.397 y 211.739 (\051)s 219.642 (=)s 232.114 ([)s 237.41 (\137)s 9 f 235.378 (x)s 10 f 698.442 y 242.055 (i)s 9 f 703.397 y 245.448 (p)s 10 f 705.197 y 251.346 (i)s 12 f 703.397 y 257.406 (\241)s 269.406 (L)s 10 f 698.442 y 277.683 (M)s 3 f 703.397 y 287.198 (\050)s 9 f 291.768 (x)s 10 f 698.442 y 298.445 (k)s 9 f 703.397 y 303.584 (;)s 3 f 310.88 (\137)s 9 f 308.847 (x)s 10 f 698.442 y 315.525 (k)s 3 f 703.397 y 320.663 (\051])s 7 f 705.708 y 329.945 (\137)s 10 f 328.497 (x)s 11 f 703.43 y 333.281 (i)s 7 f 705.708 y 336.455 (=)s 10 f 343.066 (f)s 11 f 703.43 y 348.032 (i)s 7 f 705.708 y 351.205 (\050)s 10 f 354.511 (x)s 11 f 703.43 y 359.296 (k)s 10 f 705.708 y 363.886 (;p)s 11 f 707.119 y 370.526 (k)s 7 f 705.708 y 375.116 (\051)s 9 f 703.397 y 382.838 (:)s 3 f 442.891 (\05042\051)s 735.628 y 227.346 (219)s do-end end endp showpage %%Page: 10 10 %%BeginPageSetup initializepage (drahotova; page: 10 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f596 sf ( )S -992 -1000 :M f184 sf -.651( )A f222 sf ( )S -985 -1000 :M f258 sf ( )S f296 sf ( )S -974 -1000 :M f333 sf ( )S -966 -1000 :M f371 sf ( )S -954 -1000 :M f446 sf ( )S -941 -1000 :M f484 sf ( )S f371 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 10 /CMMI10 findfont fdef 3 12 /CMR12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 16 12 /CMTI12 findfont fdef 17 14.4 /CMSY10 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (As)s 27.054 (the)s 48.448 (Hessian)s 92.489 (determinan)s 150.259 (t)s 159.903 (for)s 12 f 179.013 (L)s 10 f -.891 y 187.29 (M)s 3 f 3.464 y 201.88 (do)s 214.609 (es)s 229.541 (not)s 251.588 (v)s 257.136 (anish,)s 292.593 (the)s 313.987 (\257rst)s 339.363 (equation)s 388.5 (of)s 403.04 (\05042\051)s 429.004 (can)s 451.704 (b)s 458.558 (e)s 17.964 y 8.536 (in)s 18.001 (v)s 23.876 (erted)s 54.94 (to)s 70.337 (yield)s 101.802 (\137)s 9 f 99.769 (x)s 10 f 13.609 y 106.446 (i)s 3 f 17.964 y 114.937 (=)s 9 f 129.172 (f)s 10 f 13.609 y 136.245 (i)s 3 f 17.964 y 139.639 (\050)s 9 f 144.209 (x)s 10 f 13.609 y 150.886 (k)s 9 f 17.964 y 156.024 (;)s 161.288 (p)s 10 f 19.764 y 167.185 (k)s 3 f 17.964 y 172.324 (\051.)s 188.488 (In)s 204.208 (the)s 225.48 (follo)s 247.021 (wing,)s 279.65 (w)s 287.809 (e)s 297.984 (shall)s 326.502 (refer)s 354.628 (to)s 12 f 370.025 (H)s 10 f 13.609 y 380.275 (M)s 3 f 17.964 y 389.791 (\050)s 9 f 394.36 (x)s 10 f 13.609 y 401.037 (k)s 9 f 17.964 y 406.176 (;)s 411.44 (p)s 10 f 19.764 y 417.337 (k)s 3 f 17.964 y 422.476 (\051)s 431.998 (as)s 447.461 (the)s 16 f 32.464 y 8.536 (mo)s 23.536 (di\257e)s 44.536 (d)s 54.736 (Hamiltonian)s 3 f 118.359 (.)s 126.845 (Using)s 159.871 (also)s 183.436 (\05028\051,)s 9 f 58.285 y 155.25 (@)s 12 f 162.106 (L)s 10 f 53.93 y 170.383 (M)s 24.648 .4 155.25 63.603 r 9 f 74.635 y 159.111 (@)s 165.966 (x)s 10 f 71.168 y 172.643 (i)s 3 f 66.403 y 184.431 (=)s 12 f 196.903 (\241)s 9 f 58.285 y 207.437 (@)s 12 f 214.292 (H)s 10 f 53.93 y 224.542 (M)s 26.621 .4 207.437 63.603 r 9 f 74.635 y 212.284 (@)s 219.139 (x)s 10 f 71.168 y 225.816 (i)s 9 f 66.403 y 239.174 (;)s 3 f 258.221 (\137)s 9 f 256.188 (x)s 10 f 61.448 y 262.865 (i)s 3 f 66.403 y 269.592 (=)s 9 f 58.285 y 283.264 (@)s 12 f 290.12 (H)s 10 f 53.93 y 300.37 (M)s 26.621 .4 283.264 63.603 r 9 f 74.635 y 288.501 (@)s 295.357 (p)s 10 f 76.435 y 301.254 (i)s 9 f 66.403 y 315.002 (;)s 3 f 442.891 (\05043\051)s 98.301 y 8.536 (w)s 16.696 (e)s 25.834 (arriv)s 49.987 (e)s 59.126 (at)s 73.487 (the)s 93.723 (Hamiltonian)s 161.28 (ra)s 171.398 (y)s 181.516 (equations)s 234.129 (in)s 247.838 (the)s 268.073 (follo)s 289.615 (wing)s 317.684 (form,)s 123.456 y 155.201 (d)s 9 f 161.729 (x)s 10 f 119.101 y 168.406 (i)s 16.599 .4 155.201 128.774 r 3 f 139.805 y 157.015 (d)s 9 f 163.543 (\277)s 3 f 131.574 y 176.333 (=)s 9 f 123.456 y 190.005 (@)s 12 f 196.86 (H)s 10 f 119.101 y 207.11 (M)s 26.621 .4 190.005 128.774 r 9 f 139.805 y 195.242 (@)s 202.098 (p)s 10 f 141.605 y 207.995 (i)s 9 f 131.574 y 221.742 (;)s 3 f 123.456 y 239.956 (d)s 9 f 246.484 (p)s 10 f 125.256 y 252.381 (i)s 15.819 .4 239.956 128.774 r 3 f 139.805 y 241.38 (d)s 9 f 247.908 (\277)s 3 f 131.574 y 260.308 (=)s 12 f 272.78 (\241)s 9 f 123.456 y 283.314 (@)s 12 f 290.169 (H)s 10 f 119.101 y 300.419 (M)s 26.621 .4 283.314 128.774 r 9 f 139.805 y 288.161 (@)s 295.016 (x)s 10 f 136.339 y 301.693 (i)s 9 f 131.574 y 315.051 (:)s 3 f 442.891 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227.739 (;)s 252.586 (G)s 3 f 261.854 (\050)s 9 f 266.423 (x)s 10 f 451.081 y 273.1 (k)s 9 f 456.035 y 278.239 (;)s 283.503 (p)s 10 f 457.835 y 289.4 (k)s 3 f 456.035 y 294.539 (\051)s 302.442 (=)s 314.914 (1)s 9 f 324.706 (:)s 3 f 442.891 (\05052\051)s 482.535 y 8.536 (Th)s 23.223 (us,)s 42.494 (function)s 9 f 89.257 (G)s 3 f 98.525 (\050)s 9 f 103.094 (x)s 10 f 478.181 y 109.771 (k)s 9 f 482.535 y 114.91 (;)s 120.174 (p)s 10 f 484.335 y 126.071 (k)s 3 f 482.535 y 131.21 (\051)s 140.438 (represen)s 182.607 (ts)s 196.47 (the)s 217.449 (eigen)s 243.233 (v)s 248.782 (alue)s 274.329 (of)s 288.453 (the)s 309.431 (Christo\256el)s 367.356 (matrix)s 406.286 (\241)s 10 f 484.335 y 413.627 (ij)s 3 f 482.535 y 420.92 (,)s 429.028 (see)s 448.766 (\0501\051)s 497.035 y 8.536 (and)s 31.821 (\0506\051.)s 56.636 (Ho)s 70.993 (w)s 79.152 (ev)s 90.25 (er,)s 107.769 (to)s 122.569 (obtain)s 159.562 (the)s 180.236 (actual)s 215.924 (form)s 244.106 (of)s 257.926 (slo)s 271.373 (wness)s 305.233 (surface)s 9 f 345.229 (G)s 3 f 354.497 (\050)s 9 f 359.067 (x)s 10 f 492.681 y 365.744 (k)s 9 f 497.035 y 370.883 (;)s 376.147 (p)s 10 f 498.835 y 382.044 (k)s 3 f 497.035 y 387.183 (\051)s 395.832 (=)s 409.05 (1)s 419.28 (from)s 447.461 (the)s 511.535 y 8.536 (kno)s 26.813 (wn)s 46.772 (group)s 81.091 (v)s 86.966 (elo)s 101.654 (cit)s 114.383 (y)s 125.529 (surface)s 12 f 166.115 (L)s 10 f 507.181 y 174.391 (M)s 3 f 511.535 y 183.907 (\050)s 9 f 188.476 (x)s 10 f 507.181 y 195.153 (k)s 9 f 511.535 y 200.292 (;)s 3 f 207.589 (\137)s 9 f 205.556 (x)s 10 f 507.181 y 212.233 (k)s 3 f 511.535 y 217.372 (\051)s 227.025 (=)s 7 f 506.811 y 242.447 (1)s 4.25 .4 242.447 508.735 r 515.674 y 242.447 (2)s 3 f 511.535 y 247.897 (,)s 256.362 (it)s 269.14 (w)s 277.3 (ould)s 304.439 (b)s 311.293 (e)s 321.46 (necessary)s 374.514 (to)s 389.903 (solv)s 409.551 (e)s 419.718 (equation)s 9 f 526.035 y 8.536 (p)s 10 f 527.835 y 14.433 (i)s 3 f 526.035 y 21.921 (=)s 9 f 35.153 (@)s 12 f 42.009 (L)s 10 f 521.681 y 50.285 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683.919 y 240.081 (@)s 7 f 679.564 y 246.936 (2)s 9 f 683.919 y 251.686 (G)s 36.918 .4 232.059 689.237 r 700.269 y 232.059 (@)s 238.914 (p)s 10 f 702.069 y 244.811 (m)s 9 f 700.269 y 252.83 (@)s 259.685 (p)s 10 f 702.069 y 265.583 (i)s 3 f 692.037 y 273.51 (=)s 9 f 285.982 (p)s 10 f 693.837 y 291.879 (m)s 6.057 .4 299.898 685.671 r 9 f 692.037 y 299.898 (g)s 10 f 687.083 y 307.371 (mi)s 3 f 692.037 y 318.284 (\050)s 9 f 322.853 (x)s 10 f 687.083 y 329.53 (k)s 9 f 692.037 y 334.669 (;)s 339.933 (p)s 10 f 693.837 y 345.83 (k)s 3 f 692.037 y 350.969 (\051)s 9 f 359.455 (:)s 3 f 442.891 (\05054\051)s 735.628 y 227.346 (221)s do-end end endp showpage %%Page: 12 12 %%BeginPageSetup initializepage (drahotova; page: 12 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f184 sf -.651( )A f258 sf ( )S -993 -1000 :M f296 sf ( )S f333 sf ( )S -977 -1000 :M f371 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (The)s 31.537 (con)s 48.836 (tra)s 63.523 (v)s 69.072 (arian)s 94.856 (t)s 102.191 (comp)s 129.933 (onen)s 153.76 (ts)s 165.729 (of)s 177.96 (metric)s 213.364 (tensor)s 6.057 .4 247.527 -2.903 r 9 f 3.464 y 247.527 (g)s 10 f -.891 y 255.001 (mi)s 3 f 3.464 y 268.679 (are)s 287.111 (related)s 325.126 (to)s 338.335 (its)s 353.569 (co)s 364.339 (v)s 369.888 (arian)s 395.672 (t)s 403.007 (comp)s 430.75 (onen)s 454.576 (ts)s 6.057 .4 8.536 11.597 r 9 f 17.964 y 8.536 (g)s 10 f 20.797 y 14.593 (ij)s 3 f 17.964 y 25.802 (as)s 6.057 .4 205.066 27.964 r 9 f 34.33 y 205.066 (g)s 10 f 37.163 y 211.122 (ik)s 6.057 .4 219.155 27.964 r 9 f 34.33 y 219.155 (g)s 10 f 29.375 y 226.629 (ij)s 3 f 34.33 y 237.255 (=)s 9 f 249.727 (\261)s 10 f 28.641 y 255.381 (j)s 37.352 y 254.931 (k)s 9 f 34.33 y 263.986 (;)s 3 f 442.891 (\05055\051)s 54.791 y 8.536 (where)s 9 f 41.733 (\261)s 10 f 49.102 y 47.387 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9 f 94.534 y 283.492 (:)s 3 f 442.891 (\05056\051)s 119.776 y 8.536 (W)s 19.629 (e)s 28.768 (shall)s 56.249 (no)s 68.326 (w)s 80.728 (use)s 101.029 (the)s 121.265 (relation)s 9 f 149.458 y 63.536 (p)s 10 f 151.258 y 69.433 (i)s 9 f 149.458 y 72.827 (p)s 10 f 151.258 y 78.724 (m)s 9 f 141.34 y 90.716 (@)s 7 f 136.986 y 97.572 (2)s 12 f 141.34 y 102.322 (H)s 10 f 136.986 y 112.572 (M)s 36.918 .4 87.943 146.658 r 9 f 157.69 y 87.943 (@)s 94.798 (p)s 10 f 159.49 y 100.695 (i)s 9 f 157.69 y 104.089 (@)s 110.945 (p)s 10 f 159.49 y 116.842 (m)s 3 f 149.458 y 129.394 (=)s 9 f 141.866 (p)s 10 f 151.258 y 147.763 (i)s 9 f 149.458 y 151.157 (p)s 10 f 151.258 y 157.054 (m)s 6.057 .4 165.073 143.092 r 9 f 149.458 y 165.073 (g)s 10 f 144.504 y 172.546 (im)s 3 f 149.458 y 183.459 (\050)s 9 f 188.028 (x)s 10 f 144.504 y 194.705 (k)s 9 f 149.458 y 199.844 (;)s 205.108 (p)s 10 f 151.258 y 211.005 (k)s 3 f 149.458 y 216.144 (\051)s 224.047 (=)s 6.057 .4 236.519 143.092 r 9 f 149.458 y 236.519 (g)s 10 f 152.292 y 242.576 (ik)s 3 f 149.458 y 252.642 (\137)s 9 f 250.609 (x)s 10 f 144.504 y 257.286 (k)s 6.057 .4 262.425 143.092 r 9 f 149.458 y 262.425 (g)s 10 f 152.292 y 268.482 (ml)s 3 f 149.458 y 281.165 (\137)s 9 f 279.132 (x)s 10 f 144.504 y 285.809 (l)s 6.057 .4 288.941 143.092 r 9 f 149.458 y 288.941 (g)s 10 f 144.504 y 296.415 (im)s 3 f 149.458 y 310.661 (=)s 325.166 (\137)s 9 f 323.133 (x)s 10 f 144.504 y 329.81 (m)s 3 f 149.458 y 339.861 (\137)s 9 f 337.828 (x)s 10 f 144.504 y 344.505 (l)s 6.057 .4 347.637 143.092 r 9 f 149.458 y 347.637 (g)s 10 f 152.292 y 353.694 (ml)s 3 f 149.458 y 364.345 (\050)s 9 f 368.914 (x)s 10 f 144.504 y 375.591 (k)s 9 f 149.458 y 380.73 (;)s 385.994 (p)s 10 f 151.258 y 391.891 (k)s 3 f 149.458 y 397.03 (\051)s 9 f 405.516 (;)s 3 f 180.099 y 8.536 (and)s 31.383 (obtain)s 9 f 194.599 y 135.168 (p)s 10 f 196.399 y 141.065 (i)s 9 f 194.599 y 144.459 (p)s 10 f 196.399 y 150.356 (m)s 6.057 .4 158.375 188.233 r 9 f 194.599 y 158.375 (g)s 10 f 189.644 y 165.848 (im)s 3 f 194.599 y 176.761 (\050)s 9 f 181.33 (x)s 10 f 189.644 y 188.007 (k)s 9 f 194.599 y 193.146 (;)s 198.41 (p)s 10 f 196.399 y 204.307 (k)s 3 f 194.599 y 209.446 (\051)s 217.349 (=)s 231.854 (\137)s 9 f 229.821 (x)s 10 f 189.644 y 236.498 (m)s 3 f 194.599 y 246.549 (\137)s 9 f 244.516 (x)s 10 f 189.644 y 251.193 (l)s 6.057 .4 254.325 188.233 r 9 f 194.599 y 254.325 (g)s 10 f 197.432 y 260.382 (ml)s 3 f 194.599 y 271.033 (\050)s 9 f 275.602 (x)s 10 f 189.644 y 282.279 (k)s 9 f 194.599 y 287.418 (;)s 292.682 (p)s 10 f 196.399 y 298.579 (k)s 3 f 194.599 y 303.718 (\051)s 311.621 (=)s 324.093 (1)s 9 f 333.884 (:)s 3 f 442.891 (\05057\051)s 215.06 y 8.536 (Relation)s 56.007 (\05057\051)s 81.123 (is)s 93.249 (satis\257ed)s 138.731 (along)s 170.375 (the)s 190.921 (ra)s 201.039 (y)s 206.261 (.)s 215.679 (Th)s 230.366 (us,)s 6.057 .4 249.098 208.694 r 9 f 215.06 y 249.098 (g)s 10 f 217.894 y 255.154 (ml)s 3 f 215.06 y 265.805 (\050)s 9 f 270.374 (x)s 10 f 210.706 y 277.051 (k)s 9 f 215.06 y 282.19 (;)s 287.454 (p)s 10 f 216.86 y 293.351 (k)s 3 f 215.06 y 298.49 (\051)s 307.287 (is)s 319.413 (the)s 9 f 339.959 (p)s 10 f 216.86 y 345.856 (i)s 3 f 215.06 y 349.25 (-domain)s 395.255 (alternativ)s 444.865 (e)s 454.315 (of)s 229.56 y 8.536 (the)s 28.772 (w)s 36.931 (a)s 42.48 (v)s 48.355 (e)s 57.494 (propagation)s 122.771 (metric)s 159.326 (tensor)s 9 f 194.641 (g)s 10 f 231.36 y 200.267 (ml)s 3 f 229.56 y 210.918 (\050)s 9 f 215.487 (x)s 10 f 225.206 y 222.164 (k)s 9 f 229.56 y 227.303 (;)s 3 f 234.6 (\137)s 9 f 232.567 (x)s 10 f 225.206 y 239.244 (k)s 3 f 229.56 y 244.383 (\051,)s 256.133 (giv)s 271.147 (en)s 286.813 (in)s 300.521 (\0509\051.)s 252.596 y 26.161 (A)s 38.411 (similar)s 76.516 (expression)s 132.637 (for)s 150.114 (the)s 169.875 (con)s 187.174 (tra)s 201.861 (v)s 207.41 (arian)s 233.194 (t)s 241.206 (comp)s 268.949 (onen)s 292.775 (ts)s 305.421 (of)s 318.329 (the)s 338.091 (w)s 346.25 (a)s 351.799 (v)s 357.674 (e)s 366.338 (propagation)s 431.141 (metric)s 267.096 y 8.536 (tensor)s 44.928 (w)s 53.087 (as)s 68.59 (deriv)s 94.049 (ed)s 110.792 (earlier)s 147.771 (b)s 153.973 (y)s 165.167 (Han)s 186.052 (yga,)s 212.53 (Lenarto)s 252.183 (wicz)s 279.371 (and)s 303.295 (P)s 310.963 (a)s 317.491 (jc)s 325.977 (hel)s 345.984 (\0501984\051,)s 387.149 (and)s 411.073 (b)s 417.274 (y)s 428.469 (Klime)s 458.525 (\267)s 459.145 (s)s 281.596 y 8.536 (\0501994\051.)s 51.745 (Han)s 72.63 (yga,)s 98.63 (Lenarto)s 138.283 (wicz)s 165.089 (and)s 188.631 (P)s 196.299 (a)s 202.827 (jc)s 211.313 (hel)s 230.938 (\0501984\051)s 268.188 (ev)s 279.285 (en)s 295.646 (refer)s 323.431 (to)s 338.487 (an)s 355.501 (older)s 385.571 (reference)s 435.55 (Rund)s 296.096 y 8.536 (\0501966\051.)s 51.155 (W)s 62.248 (a)s 67.796 (v)s 73.671 (e)s 83.308 (propagation)s 149.083 (metric)s 186.136 (tensor)s 6.057 .4 221.949 289.73 r 9 f 296.096 y 221.949 (g)s 10 f 291.741 y 228.006 (mn)s 3 f 296.096 y 245.597 (is)s 257.91 (also)s 281.973 (closely)s 320.071 (related)s 359.735 (to)s 374.595 (the)s 395.328 (metric)s 432.382 (tensor)s 310.596 y 8.536 (of)s 21.918 (the)s 42.154 (general)s 82.625 (theory)s 119.507 (of)s 132.889 (relativit)s 173.361 (y)s 178.583 (.)s 333.632 y 26.161 (6\051)s 40.522 (The)s 64.674 (\257rst)s 88.892 (equation)s 136.871 (of)s 150.252 (\05042\051)s 175.058 (can)s 196.599 (also)s 220.164 (b)s 227.018 (e)s 236.157 (expressed)s 288.836 (as)s 303.262 (follo)s 324.803 (ws,)s 345.105 (see)s 364.1 (\05037\051,)s 9 f 366.314 y 135.509 (p)s 10 f 368.114 y 141.406 (i)s 3 f 366.314 y 148.134 (=)s 9 f 358.196 y 161.806 (@)s 12 f 168.661 (L)s 10 f 353.841 y 176.938 (M)s 24.648 .4 161.806 363.514 r 9 f 374.545 y 165.666 (@)s 3 f 174.555 (\137)s 9 f 172.522 (x)s 10 f 371.079 y 179.199 (i)s 3 f 366.314 y 190.987 (=)s 205.492 (\137)s 9 f 203.459 (x)s 10 f 361.359 y 210.136 (j)s 9 f 358.196 y 218.464 (@)s 7 f 353.841 y 225.32 (2)s 12 f 358.196 y 230.07 (L)s 10 f 353.841 y 238.346 (M)s 34.858 .4 215.734 363.514 r 9 f 374.545 y 215.734 (@)s 3 f 224.623 (\137)s 9 f 222.59 (x)s 10 f 371.079 y 229.267 (i)s 9 f 374.545 y 232.661 (@)s 3 f 241.549 (\137)s 9 f 239.516 (x)s 10 f 371.079 y 246.193 (j)s 3 f 366.314 y 255.125 (=)s 9 f 267.597 (g)s 10 f 368.114 y 273.223 (ij)s 3 f 366.314 y 280.516 (\050)s 9 f 285.085 (x)s 10 f 361.359 y 291.762 (k)s 9 f 366.314 y 296.901 (;)s 3 f 304.198 (\137)s 9 f 302.165 (x)s 10 f 361.359 y 308.842 (k)s 3 f 366.314 y 313.981 (\051)s 320.584 (\137)s 9 f 318.551 (x)s 10 f 361.359 y 325.228 (j)s 9 f 366.314 y 333.543 (;)s 3 f 442.891 (\05058\051)s 12 f 396.198 y 8.536 (L)s 10 f 391.844 y 16.813 (M)s 3 f 396.198 y 26.328 (\050)s 9 f 30.897 (x)s 10 f 391.844 y 37.574 (k)s 9 f 396.198 y 42.713 (;)s 3 f 50.01 (\137)s 9 f 47.977 (x)s 10 f 391.844 y 54.654 (k)s 3 f 396.198 y 59.793 (\051)s 68.279 (b)s 75.133 (eing)s 99.939 (a)s 109.73 (homogeneous)s 181.6 (function)s 227.621 (of)s 241.002 (the)s 261.238 (second)s 299.164 (degree)s 335.719 (in)s 351.461 (\137)s 9 f 349.428 (x)s 10 f 391.844 y 356.105 (i)s 3 f 396.198 y 359.499 (.)s 367.985 (This)s 394.814 (also)s 418.379 (yields)s 421.441 y 190.823 (\137)s 9 f 188.79 (x)s 10 f 416.486 y 195.467 (i)s 3 f 421.441 y 202.194 (=)s 9 f 214.666 (g)s 10 f 416.486 y 220.723 (ij)s 3 f 421.441 y 228.015 (\050)s 9 f 232.585 (x)s 10 f 416.486 y 239.262 (k)s 9 f 421.441 y 244.401 (;)s 3 f 251.698 (\137)s 9 f 249.665 (x)s 10 f 416.486 y 256.342 (k)s 3 f 421.441 y 261.481 (\051)s 9 f 266.05 (p)s 10 f 423.241 y 271.947 (j)s 9 f 421.441 y 280.262 (:)s 3 f 442.891 (\05059\051)s 446.684 y 8.536 (Here)s 9 f 36.007 (g)s 10 f 442.329 y 42.064 (ij)s 3 f 446.684 y 49.356 (\050)s 9 f 53.926 (x)s 10 f 442.329 y 60.603 (k)s 9 f 446.684 y 65.742 (;)s 3 f 73.039 (\137)s 9 f 71.006 (x)s 10 f 442.329 y 77.683 (k)s 3 f 446.684 y 82.822 (\051)s 91.04 (are)s 110.356 (the)s 130.324 (con)s 147.623 (tra)s 162.31 (v)s 167.858 (arian)s 193.643 (t)s 201.861 (comp)s 229.604 (onen)s 253.43 (ts)s 266.283 (of)s 279.398 (the)s 299.366 (w)s 307.526 (a)s 313.074 (v)s 318.949 (e)s 327.821 (propagation)s 392.83 (metric)s 429.118 (tensor,)s 461.184 y 8.536 (and)s 31.383 (can)s 52.924 (b)s 59.778 (e)s 68.917 (determined)s 130.278 (b)s 136.479 (y)s 146.597 (in)s 156.062 (v)s 161.937 (erting)s 9 f 195.881 (g)s 10 f 462.984 y 201.508 (ij)s 3 f 461.184 y 208.8 (\050)s 9 f 213.369 (x)s 10 f 456.829 y 220.046 (k)s 9 f 461.184 y 225.185 (;)s 3 f 232.482 (\137)s 9 f 230.449 (x)s 10 f 456.829 y 237.126 (k)s 3 f 461.184 y 242.265 (\051.)s 484.219 y 26.161 (W)s 37.254 (e)s 46.732 (no)s 58.808 (w)s 71.549 (tak)s 87.869 (e)s 97.347 (in)s 106.812 (to)s 121.512 (accoun)s 156.435 (t)s 165.26 (the)s 185.835 (transformation)s 266.204 (relations)s 314.26 (b)s 321.115 (et)s 330.58 (w)s 338.739 (een)s 359.967 (the)s 380.542 (co)s 391.313 (v)s 396.861 (arian)s 422.646 (t)s 9 f 431.471 (y)s 10 f 486.019 y 437.2 (i)s 3 f 484.219 y 444.85 (and)s 498.719 y 8.536 (con)s 25.834 (tra)s 40.522 (v)s 46.07 (arian)s 71.855 (t)s 9 f 79.991 (y)s 10 f 494.365 y 86.151 (i)s 3 f 498.719 y 93.112 (comp)s 120.855 (onen)s 144.681 (ts)s 157.452 (of)s 170.485 (v)s 176.36 (ector)s 9 f 205.257 (\176)s 205.385 (y)s 3 f 211.545 (,)s 218.446 (in)s 231.804 (co)s 243.228 (ordinates)s 293.86 (sp)s 305.349 (eci\257ed)s 340.902 (b)s 347.103 (y)s 356.872 (the)s 376.758 (Finslerian)s 431.141 (metric)s 513.219 y 8.536 (tensor)s 9 f 43.851 (g)s 10 f 515.019 y 49.477 (ij)s 3 f 513.219 y 56.77 (\050)s 9 f 61.339 (x)s 10 f 515.019 y 68.016 (k)s 9 f 513.219 y 73.155 (;)s 3 f 80.452 (\137)s 9 f 78.419 (x)s 10 f 515.019 y 85.096 (k)s 3 f 513.219 y 90.235 (\051,)s 9 f 527.719 y 167.607 (y)s 10 f 529.519 y 173.336 (i)s 3 f 527.719 y 180.063 (=)s 9 f 192.535 (g)s 10 f 529.519 y 198.162 (ij)s 9 f 527.719 y 205.454 (y)s 10 f 522.765 y 211.614 (j)s 9 f 527.719 y 219.929 (;)s 248.693 (y)s 10 f 522.765 y 254.852 (i)s 3 f 527.719 y 261.579 (=)s 9 f 274.052 (g)s 10 f 522.765 y 280.108 (ij)s 9 f 527.719 y 287.401 (y)s 10 f 529.519 y 293.13 (j)s 9 f 527.719 y 301.445 (:)s 3 f 548.181 y 8.536 (Equations)s 64.344 (\05058\051)s 89.573 (and)s 112.842 (\05059\051)s 138.071 (then)s 165.257 (indicate)s 210.069 (that)s 235.95 (the)s 256.608 (co)s 267.379 (v)s 272.928 (arian)s 298.712 (t)s 307.621 (comp)s 335.364 (onen)s 359.19 (ts)s 9 f 372.734 (p)s 10 f 549.981 y 378.631 (i)s 3 f 548.181 y 386.364 (of)s 400.169 (the)s 420.828 (slo)s 434.275 (wness)s 562.681 y 8.536 (v)s 14.411 (ector)s 44.943 (and)s 68.947 (the)s 90.34 (con)s 107.639 (tra)s 122.326 (v)s 127.875 (arian)s 153.659 (t)s 163.302 (comp)s 191.045 (onen)s 214.871 (ts)s 231.182 (\137)s 9 f 229.149 (x)s 10 f 558.326 y 235.826 (i)s 3 f 562.681 y 244.294 (of)s 258.833 (the)s 280.226 (group)s 314.675 (v)s 320.55 (elo)s 335.237 (cit)s 347.966 (y)s 359.241 (v)s 365.116 (ector)s 395.648 (represen)s 437.817 (t)s 447.461 (the)s 577.181 y 8.536 (comp)s 36.279 (onen)s 60.105 (ts)s 73.226 (of)s 86.607 (the)s 106.843 (same)s 136.283 (v)s 142.158 (ector)s 171.533 (in)s 185.241 (the)s 205.477 (Finslerian)s 260.21 (space.)s 600.216 y 26.161 (7\051)s 40.522 (The)s 64.674 (comparison)s 126.753 (of)s 140.135 (Equation)s 190.885 (\05054\051)s 215.691 (with)s 242.454 (\05059\051)s 267.26 (and)s 290.107 (of)s 303.488 (\05056\051)s 328.294 (with)s 355.057 (\05058\051)s 379.863 (sho)s 396.574 (ws)s 413.611 (that)s 6.057 .4 164.13 619.092 r 9 f 625.459 y 164.13 (g)s 10 f 628.292 y 170.187 (mn)s 3 f 625.459 y 186.696 (=)s 9 f 199.168 (g)s 10 f 627.259 y 204.795 (mn)s 9 f 625.459 y 221.887 (;)s 6.057 .4 246.734 619.092 r 625.459 y 246.734 (g)s 10 f 620.504 y 252.791 (mn)s 3 f 625.459 y 269.3 (=)s 9 f 281.773 (g)s 10 f 620.504 y 287.829 (mn)s 9 f 625.459 y 304.922 (:)s 3 f 442.891 (\05060\051)s 650.702 y 8.536 (The)s 32.483 (only)s 58.062 (di\256erence)s 110.405 (is)s 122.015 (that)s 6.057 .4 147.268 644.335 r 9 f 650.702 y 147.268 (g)s 10 f 653.535 y 153.325 (mn)s 3 f 650.702 y 170.212 (and)s 6.057 .4 192.854 644.335 r 9 f 650.702 y 192.854 (g)s 10 f 646.347 y 200.328 (mn)s 3 f 650.702 y 217.215 (are)s 236.593 (expressed)s 289.067 (in)s 302.57 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227.346 (222)s do-end end endp showpage %%Page: 13 13 %%BeginPageSetup initializepage (drahotova; page: 13 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S -943 -1000 :M f558 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 14 6 /CMSY6 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (Using)s 42.031 (\05033\051,)s 70.686 (\05035\051)s 95.96 (and)s 119.276 (\05057\051,)s 147.931 (w)s 156.09 (e)s 165.698 (can)s 187.708 (also)s 211.742 (express)s 253.139 (Lagrangians)s 12 f 319.764 (L)s 3 f 328.041 (\050)s 9 f 332.61 (x)s 10 f -.891 y 339.287 (k)s 9 f 3.464 y 344.426 (;)s 3 f 351.723 (\137)s 9 f 349.69 (x)s 10 f -.891 y 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335.684 (;)s 345.177 (x)s 7 f 505.247 y 351.854 (2)s 3 f 509.602 y 360.47 (=)s 9 f 373.475 (x)s 7 f 511.402 y 380.152 (2)s 9 f 509.602 y 384.902 (;)s 394.395 (x)s 7 f 505.247 y 401.072 (3)s 3 f 509.602 y 409.688 (=)s 9 f 422.693 (x)s 7 f 511.402 y 429.37 (3)s 3 f 509.602 y 434.12 (.)s 443.544 (The)s 524.102 y 8.536 (co)s 19.307 (v)s 24.855 (arian)s 50.64 (t)s 59.789 (comp)s 87.532 (onen)s 111.358 (ts)s 125.143 (of)s 139.188 (the)s 160.088 (w)s 168.248 (a)s 173.796 (v)s 179.671 (e)s 189.474 (propagation)s 255.415 (metric)s 292.634 (tensor)s 328.612 (are)s 348.859 (then)s 376.287 (giv)s 391.3 (en)s 407.631 (b)s 413.832 (y)s 424.614 (relation)s 538.602 y 8.536 (\05018\051,)s 9 f 553.102 y 191.069 (g)s 10 f 554.902 y 196.695 (ij)s 3 f 553.102 y 207.321 (=)s 9 f 219.793 (V)s 13 f 548.147 y 229.254 (\241)s 7 f 235.865 (2)s 3 f 553.102 y 240.615 (\050)s 9 f 245.185 (x)s 10 f 554.902 y 251.862 (k)s 3 f 553.102 y 257.001 (\051)s 9 f 261.57 (\261)s 10 f 554.902 y 266.774 (ij)s 9 f 553.102 y 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245.32 (di\257ed)s 277.593 (Lagrangian.)s 344.545 (W)s 355.638 (e)s 365.064 (use)s 9 f 385.653 (u)s 3 f 396.162 (=)s 9 f 409.123 (\277)s 3 f 415.566 (,)s 423.106 (where)s 9 f 457.337 (\277)s 3 f 266.933 y 8.536 (is)s 20.351 (the)s 40.587 (tra)s 55.274 (v)s 61.149 (el)s 73.552 (time)s 100.316 (along)s 131.649 (the)s 151.884 (curv)s 174.079 (es,)s 191.116 (and)s 213.963 (use)s 234.264 (\05035\051)s 12 f 293.433 y 116.772 (L)s 10 f 288.479 y 125.049 (M)s 3 f 293.433 y 134.564 (\050)s 9 f 139.134 (x)s 10 f 295.233 y 145.811 (k)s 9 f 293.433 y 150.95 (;)s 3 f 158.247 (\137)s 9 f 156.214 (x)s 10 f 295.233 y 162.891 (k)s 3 f 293.433 y 168.03 (\051)s 175.932 (=)s 7 f 288.708 y 189.604 (1)s 4.25 .4 189.604 290.633 r 297.571 y 189.604 (2)s 9 f 293.433 y 195.054 (V)s 13 f 288.479 y 204.515 (\241)s 7 f 211.127 (2)s 3 f 293.433 y 215.877 (\050)s 9 f 220.446 (x)s 10 f 295.233 y 227.123 (k)s 3 f 293.433 y 232.262 (\051\050)s 243.434 (\137)s 9 f 241.401 (x)s 10 f 295.233 y 248.078 (i)s 3 f 293.433 y 253.505 (\137)s 9 f 251.472 (x)s 10 f 295.233 y 258.149 (i)s 3 f 293.433 y 261.543 (\051)s 9 f 270.029 (;)s 3 f 289.075 (\137)s 9 f 287.042 (x)s 10 f 295.233 y 293.72 (i)s 3 f 293.433 y 300.447 (=)s 312.919 (d)s 9 f 319.447 (x)s 10 f 295.233 y 326.124 (i)s 9 f 293.433 y 329.518 (=)s 3 f 335.392 (d)s 9 f 341.92 (\277)s 352.28 (:)s 3 f 442.891 (\05075\051)s 319.933 y 8.536 (Mo)s 25.504 (di\257ed)s 57.49 (F)s 64.178 (ermat\047s)s 106.021 (v)s 111.57 (ariational)s 164.444 (principle)s 212.749 (\05041\051)s 237.554 (then)s 264.318 (reads)s 9 f 352.344 y 166.411 (\261)s 0 f 338.233 y 174.065 (Z)s 10 f 341.4 y 184.065 (R)s 360.956 y 179.62 (S)s 9 f 352.344 y 193.016 (V)s 13 f 347.39 y 202.477 (\241)s 7 f 209.088 (2)s 3 f 352.344 y 213.838 (\050)s 9 f 218.408 (x)s 10 f 354.144 y 225.085 (k)s 3 f 352.344 y 230.224 (\051\050)s 241.395 (\137)s 9 f 239.362 (x)s 10 f 354.144 y 246.04 (i)s 3 f 352.344 y 251.466 (\137)s 9 f 249.433 (x)s 10 f 354.144 y 256.111 (i)s 3 f 352.344 y 259.504 (\051d)s 9 f 270.602 (\277)s 3 f 280.378 (=)s 292.85 (0)s 9 f 302.641 (:)s 3 f 442.891 (\05076\051)s 382.289 y 8.536 (The)s 32.688 (corresp)s 69.635 (onding)s 108.149 (Euler-Lagrange)s 190.72 (equations)s 243.333 (are)s 405.956 y 129.503 (d)s 12.971 .4 126.282 411.274 r 422.305 y 126.282 (d)s 9 f 132.809 (\277)s 0 f 399.474 y 140.452 (\265)s 3 f 405.956 y 163.659 (2)s 35.166 .4 149.014 411.274 r 9 f 422.305 y 149.014 (V)s 7 f 418.838 y 158.475 (2)s 3 f 422.305 y 163.225 (\050)s 9 f 167.794 (x)s 10 f 424.105 y 174.471 (k)s 3 f 422.305 y 179.61 (\051)s 414.074 y 187.412 (\137)s 9 f 185.379 (x)s 10 f 415.874 y 192.056 (i)s 0 f 399.474 y 195.45 (\266)s 12 f 414.074 y 205.478 (\241)s 3 f 217.478 (\050)s 224.08 (\137)s 9 f 222.048 (x)s 10 f 415.874 y 228.725 (i)s 3 f 414.074 y 234.151 (\137)s 9 f 232.118 (x)s 10 f 415.874 y 238.796 (i)s 3 f 414.074 y 242.189 (\051)s 9 f 405.956 y 252.994 (@)s 16.926 .4 247.959 411.274 r 422.305 y 247.959 (@)s 254.814 (x)s 10 f 424.105 y 261.491 (i)s 0 f 399.474 y 266.085 (\265)s 3 f 405.956 y 289.292 (1)s 35.166 .4 274.646 411.274 r 9 f 422.305 y 274.646 (V)s 7 f 418.838 y 284.107 (2)s 3 f 422.305 y 288.858 (\050)s 9 f 293.427 (x)s 10 f 424.105 y 300.104 (k)s 3 f 422.305 y 305.243 (\051)s 0 f 399.474 y 311.012 (\266)s 3 f 414.074 y 321.707 (=)s 334.179 (0)s 9 f 343.97 (:)s 3 f 442.891 (\05077\051)s 447.815 y 8.536 (If)s 22.167 (w)s 30.326 (e)s 41.35 (tak)s 57.669 (e)s 68.693 (in)s 78.159 (to)s 94.405 (accoun)s 129.328 (t)s 141.732 (\137)s 9 f 139.699 (x)s 10 f 449.615 y 146.376 (i)s 3 f 447.815 y 151.803 (\137)s 9 f 149.77 (x)s 10 f 449.615 y 156.447 (i)s 3 f 447.815 y 166.383 (=)s 9 f 182.063 (V)s 7 f 443.461 y 191.524 (2)s 3 f 447.815 y 196.275 (,)s 205.811 (w)s 213.971 (e)s 224.995 (can)s 248.421 (see)s 269.302 (that)s 296.645 (\05077\051)s 323.336 (is)s 337.036 (fully)s 365.684 (equiv)s 392.448 (alen)s 413.01 (t)s 423.381 (to)s 439.628 (\05073\051.)s 462.315 y 8.536 (Th)s 23.223 (us,)s 41.055 (F)s 47.744 (ermat\047s)s 88.948 (v)s 94.497 (ariational)s 146.733 (principles)s 199.034 (\05071\051)s 223.201 (and)s 245.41 (\05076\051)s 269.577 (yield)s 297.334 (the)s 316.932 (same)s 345.733 (extremals,)s 401.752 (ev)s 412.85 (en)s 427.878 (though)s 476.815 y 8.536 (F)s 15.225 (ermat\047s)s 57.067 (v)s 62.616 (ariational)s 115.49 (principle)s 163.795 (in)s 177.504 (\05076\051)s 202.309 (is)s 214.124 (not)s 235.013 (constructed)s 298.397 (in)s 312.105 (the)s 332.341 (standard)s 381.364 (w)s 389.524 (a)s 395.072 (y)s 405.19 (of)s 418.572 (\05071\051.)s 499.851 y 26.161 (It)s 38.873 (is)s 50.676 (simple)s 87.283 (to)s 101.632 (determine)s 156.452 (the)s 176.675 (Hessian)s 219.545 (determinan)s 277.316 (t)s 285.789 (for)s 303.728 (Lagrangian)s 12 f 365.237 (L)s 10 f 495.497 y 373.513 (M)s 3 f 499.851 y 383.029 (.)s 391.51 (F)s 398.199 (rom)s 422.339 (\05075\051,)s 450.398 (w)s 458.558 (e)s 514.351 y 8.536 (obtain)s 9 f 525.173 y 163.812 (@)s 7 f 520.818 y 170.668 (2)s 12 f 525.173 y 175.418 (L)s 10 f 520.818 y 183.694 (M)s 3 f 525.173 y 193.21 (\050)s 9 f 197.779 (x)s 10 f 526.973 y 204.456 (k)s 9 f 525.173 y 209.595 (;)s 3 f 216.892 (\137)s 9 f 214.859 (x)s 10 f 526.973 y 221.536 (k)s 3 f 525.173 y 226.675 (\051)s 67.432 .4 163.812 530.491 r 9 f 541.522 y 180.099 (@)s 3 f 188.988 (\137)s 9 f 186.955 (x)s 10 f 543.322 y 193.632 (i)s 9 f 541.522 y 197.026 (@)s 3 f 205.914 (\137)s 9 f 203.881 (x)s 10 f 543.322 y 210.558 (j)s 3 f 533.291 y 235.778 (=)s 9 f 248.25 (V)s 13 f 528.336 y 257.711 (\241)s 7 f 264.322 (2)s 3 f 533.291 y 269.072 (\050)s 9 f 273.641 (x)s 10 f 535.091 y 280.318 (k)s 3 f 533.291 y 285.457 (\051)s 9 f 290.027 (\261)s 10 f 535.091 y 295.231 (ij)s 9 f 533.291 y 306.44 (;)s 3 f 560.711 y 8.536 (so)s 22.962 (that)s 579.651 y 152.977 (det)s 0 f 565.05 y 169.296 (\265)s 9 f 571.532 y 177.857 (@)s 7 f 567.178 y 184.713 (2)s 12 f 571.532 y 189.463 (L)s 10 f 567.178 y 197.74 (M)s 3 f 571.532 y 207.255 (\050)s 9 f 211.824 (x)s 10 f 573.332 y 218.501 (k)s 9 f 571.532 y 223.64 (;)s 3 f 230.937 (\137)s 9 f 228.904 (x)s 10 f 573.332 y 235.581 (k)s 3 f 571.532 y 240.72 (\051)s 67.432 .4 177.857 576.85 r 9 f 587.882 y 194.145 (@)s 3 f 203.033 (\137)s 9 f 201 (x)s 10 f 589.682 y 207.677 (i)s 9 f 587.882 y 211.071 (@)s 3 f 219.96 (\137)s 9 f 217.927 (x)s 10 f 589.682 y 224.604 (j)s 0 f 565.05 y 246.489 (\266)s 3 f 579.651 y 257.184 (=)s 9 f 269.656 (V)s 13 f 574.696 y 279.117 (\241)s 7 f 285.728 (6)s 12 f 579.651 y 293.812 (6)s 3 f 293.812 (=)s 306.284 (0)s 9 f 316.075 (:)s 3 f 442.891 (\05078\051)s 607.071 y 8.536 (Th)s 23.223 (us,)s 41.418 (the)s 61.468 (dual)s 87.393 (Legendre)s 137.632 (transform)s 191.366 (can)s 212.722 (b)s 219.576 (e)s 228.529 (used)s 255.172 (to)s 269.348 (compute)s 316.814 (the)s 336.865 (relev)s 360.691 (an)s 372.767 (t)s 381.068 (mo)s 397.061 (di\257ed)s 428.861 (Hamil-)s 621.571 y 8.536 (tonian)s 46.01 (and)s 69.775 (\257nd)s 94.194 (the)s 115.348 (Hamiltonian)s 183.825 (canonical)s 236.312 (equations.)s 296.251 (Before)s 333.886 (w)s 342.046 (e)s 352.103 (do)s 369.341 (this,)s 396.666 (w)s 404.825 (e)s 414.883 (only)s 441.586 (note)s 636.071 y 8.536 (that)s 33.994 (the)s 54.23 (mo)s 70.223 (di\257ed)s 102.209 (Lagrangian)s 163.73 (\05075\051)s 188.535 (is)s 200.351 (constan)s 239.256 (t)s 247.742 (along)s 279.075 (the)s 299.311 (whole)s 332.602 (extremal)s 381.233 (and)s 404.08 (equals)s 7 f 631.346 y 440.922 (1)s 4.25 .4 440.922 633.271 r 640.209 y 440.922 (2)s 3 f 636.071 y 446.372 (,)s 12 f 663.63 y 193.427 (L)s 10 f 658.676 y 201.703 (M)s 3 f 663.63 y 211.219 (\050)s 9 f 215.788 (x)s 10 f 665.43 y 222.465 (k)s 9 f 663.63 y 227.604 (;)s 3 f 234.901 (\137)s 9 f 232.868 (x)s 10 f 665.43 y 239.545 (k)s 3 f 663.63 y 244.684 (\051)s 252.587 (=)s 7 f 658.905 y 266.259 (1)s 4.25 .4 266.259 660.83 r 667.768 y 266.259 (2)s 9 f 663.63 y 275.625 (;)s 3 f 442.891 (\05079\051)s 690.13 y 8.536 (see)s 27.192 (\05036\051.)s 56.453 (This)s 82.942 (also)s 106.167 (immediately)s 172.737 (follo)s 194.278 (ws)s 210.976 (from)s 238.379 (\05075\051,)s 266.176 (if)s 276.607 (w)s 284.766 (e)s 293.565 (tak)s 309.885 (e)s 318.684 (in)s 328.149 (to)s 342.17 (accoun)s 377.093 (t)s 385.239 (that)s 412.391 (\137)s 9 f 410.358 (x)s 10 f 691.93 y 417.035 (i)s 3 f 690.13 y 422.462 (\137)s 9 f 420.429 (x)s 10 f 691.93 y 427.106 (i)s 3 f 690.13 y 433.833 (=)s 9 f 446.305 (V)s 7 f 685.776 y 455.766 (2)s 3 f 690.13 y 460.516 (.)s 735.628 y 227.346 (225)s do-end end endp showpage %%Page: 16 16 %%BeginPageSetup initializepage (drahotova; page: 16 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f184 sf -.651( )A f258 sf ( )S -993 -1000 :M f632 sf ( )S f296 sf ( )S -981 -1000 :M f333 sf ( )S -973 -1000 :M f521 sf ( )S -963 -1000 :M f371 sf ( )S -951 -1000 :M f446 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 8 6 /CMR6 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 11 6 /CMMI6 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 26.161 (Using)s 59.187 (\05042\051,)s 87.256 (w)s 95.416 (e)s 104.554 (obtain)s 9 f 25.403 y 183.146 (p)s 10 f 27.203 y 189.044 (i)s 3 f 25.403 y 195.771 (=)s 9 f 17.285 y 209.443 (@)s 12 f 216.298 (L)s 10 f 12.93 y 224.575 (M)s 24.648 .4 209.443 22.603 r 9 f 33.635 y 213.303 (@)s 3 f 222.192 (\137)s 9 f 220.159 (x)s 10 f 35.435 y 226.836 (i)s 3 f 25.403 y 238.624 (=)s 9 f 251.096 (V)s 13 f 20.448 y 260.557 (\241)s 7 f 267.168 (2)s 3 f 25.403 y 273.951 (\137)s 9 f 271.918 (x)s 10 f 27.203 y 278.595 (i)s 9 f 25.403 y 285.906 (:)s 3 f 442.891 (\05080\051)s 51.268 y 8.536 (This)s 35.365 (can)s 56.906 (b)s 63.76 (e)s 72.899 (simply)s 110.499 (in)s 119.964 (v)s 125.839 (erted)s 155.866 (to)s 170.227 (yield)s 77.768 y 209.911 (\137)s 9 f 207.878 (x)s 10 f 79.568 y 214.555 (i)s 3 f 77.768 y 221.283 (=)s 9 f 233.755 (V)s 7 f 72.813 y 243.216 (2)s 9 f 77.768 y 247.966 (p)s 10 f 79.568 y 253.863 (i)s 9 f 77.768 y 261.174 (:)s 3 f 442.891 (\05081\051)s 104.268 y 8.536 (The)s 32.688 (mo)s 48.681 (di\257ed)s 80.667 (Hamiltonian)s 12 f 148.225 (H)s 10 f 99.913 y 158.475 (M)s 3 f 104.268 y 167.99 (\050)s 9 f 172.56 (x)s 10 f 106.068 y 179.237 (k)s 9 f 104.268 y 184.376 (;)s 189.639 (p)s 10 f 106.068 y 195.537 (k)s 3 f 104.268 y 200.675 (\051)s 209.162 (is)s 220.977 (then)s 247.74 (giv)s 262.754 (en)s 278.421 (b)s 284.622 (y)s 294.74 (relation)s 337.823 (\05042\051)s 12 f 130.768 y 79.845 (H)s 10 f 125.813 y 90.095 (M)s 3 f 130.768 y 99.611 (\050)s 9 f 104.18 (x)s 10 f 132.568 y 110.857 (k)s 9 f 130.768 y 115.996 (;)s 121.26 (p)s 10 f 132.568 y 127.157 (k)s 3 f 130.768 y 132.296 (\051)s 140.199 (=)s 152.671 ([)s 157.968 (\137)s 9 f 155.935 (x)s 10 f 132.568 y 162.612 (i)s 9 f 130.768 y 166.006 (p)s 10 f 132.568 y 171.903 (i)s 12 f 130.768 y 177.963 (\241)s 189.963 (L)s 10 f 125.813 y 198.24 (M)s 3 f 130.768 y 207.755 (\050)s 9 f 212.325 (x)s 10 f 132.568 y 219.002 (k)s 9 f 130.768 y 224.141 (;)s 3 f 231.438 (\137)s 9 f 229.405 (x)s 10 f 132.568 y 236.082 (k)s 3 f 130.768 y 241.221 (\051])s 7 f 132.779 y 250.502 (\137)s 10 f 249.054 (x)s 11 f 133.999 y 253.839 (i)s 7 f 132.779 y 257.012 (=)s 10 f 263.623 (V)s 8 f 130.501 y 270.462 (2)s 10 f 132.779 y 274.629 (p)s 11 f 133.999 y 278.908 (i)s 3 f 130.768 y 285.915 (=)s 9 f 298.387 (V)s 7 f 125.813 y 307.848 (2)s 9 f 130.768 y 312.598 (p)s 10 f 132.568 y 318.495 (i)s 9 f 130.768 y 321.889 (p)s 10 f 132.568 y 327.786 (i)s 12 f 130.768 y 333.847 (\241)s 7 f 126.043 y 347.047 (1)s 4.25 .4 347.047 127.968 r 134.906 y 347.047 (2)s 9 f 130.768 y 352.497 (V)s 7 f 125.813 y 361.958 (2)s 9 f 130.768 y 366.708 (p)s 10 f 132.568 y 372.605 (i)s 9 f 130.768 y 375.999 (p)s 10 f 132.568 y 381.896 (i)s 9 f 130.768 y 389.207 (:)s 3 f 157.268 y 8.536 (Th)s 23.223 (us,)s 12 f 171.768 y 165.956 (H)s 10 f 166.813 y 176.206 (M)s 3 f 171.768 y 185.721 (\050)s 9 f 190.291 (x)s 10 f 173.568 y 196.968 (k)s 9 f 171.768 y 202.107 (;)s 207.371 (p)s 10 f 173.568 y 213.268 (k)s 3 f 171.768 y 218.407 (\051)s 226.309 (=)s 7 f 167.043 y 239.981 (1)s 4.25 .4 239.981 168.968 r 175.906 y 239.981 (2)s 9 f 171.768 y 245.431 (V)s 7 f 166.813 y 254.892 (2)s 3 f 171.768 y 259.643 (\050)s 9 f 264.212 (x)s 10 f 173.568 y 270.889 (k)s 3 f 171.768 y 276.028 (\051)s 9 f 280.597 (p)s 10 f 173.568 y 286.494 (i)s 9 f 171.768 y 289.888 (p)s 10 f 173.568 y 295.786 (i)s 9 f 171.768 y 303.096 (:)s 3 f 442.891 (\05082\051)s 192.768 y 8.536 (The)s 32.688 (mo)s 48.681 (di\257ed)s 80.667 (Hamiltonian)s 148.225 (is)s 160.04 (constan)s 198.945 (t)s 207.431 (along)s 238.764 (the)s 259 (whole)s 292.291 (extremal,)s 12 f 219.268 y 192.83 (H)s 10 f 214.313 y 203.08 (M)s 3 f 219.268 y 212.595 (\050)s 9 f 217.165 (x)s 10 f 221.068 y 223.842 (k)s 9 f 219.268 y 228.981 (;)s 234.245 (p)s 10 f 221.068 y 240.142 (k)s 3 f 219.268 y 245.281 (\051)s 253.183 (=)s 7 f 214.543 y 266.855 (1)s 4.25 .4 266.855 216.468 r 223.406 y 266.855 (2)s 9 f 219.268 y 276.222 (;)s 3 f 245.768 y 8.536 (see)s 28.79 (\05052\051.)s 61.94 (As)s 80.558 (w)s 88.718 (e)s 99.115 (kno)s 117.393 (w,)s 9 f 134.632 (V)s 7 f 241.413 y 144.093 (2)s 3 f 245.768 y 148.843 (\050)s 9 f 153.413 (x)s 10 f 247.568 y 160.09 (k)s 3 f 245.768 y 165.229 (\051)s 9 f 169.798 (p)s 10 f 247.568 y 175.695 (i)s 9 f 245.768 y 179.089 (p)s 10 f 247.568 y 184.986 (i)s 3 f 245.768 y 193.555 (is)s 206.629 (eigen)s 232.414 (v)s 237.962 (alue)s 9 f 264.026 (G)s 3 f 273.294 (\050)s 9 f 277.864 (x)s 10 f 247.568 y 284.541 (k)s 9 f 245.768 y 289.68 (;)s 294.943 (p)s 10 f 247.568 y 300.841 (k)s 3 f 245.768 y 305.979 (\051)s 315.724 (of)s 330.364 (the)s 351.859 (Christo\256el)s 410.3 (matrix)s 449.745 (for)s 260.268 y 8.536 (isotropic)s 56.253 (media,)s 9 f 94.114 (G)s 3 f 103.382 (\050)s 9 f 107.952 (x)s 10 f 262.068 y 114.629 (k)s 9 f 260.268 y 119.768 (;)s 125.032 (p)s 10 f 262.068 y 130.929 (k)s 3 f 260.268 y 136.068 (\051)s 143.97 (=)s 9 f 156.443 (V)s 7 f 255.913 y 165.904 (2)s 3 f 260.268 y 170.654 (\050)s 9 f 175.223 (x)s 10 f 262.068 y 181.9 (k)s 3 f 260.268 y 187.039 (\051)s 9 f 191.608 (p)s 10 f 262.068 y 197.506 (i)s 9 f 260.268 y 200.899 (p)s 10 f 262.068 y 206.797 (i)s 3 f 260.268 y 210.191 (.)s 218.677 (Consequen)s 273.575 (tly)s 286.63 (,)s 9 f 286.768 y 174.167 (G)s 3 f 183.435 (\050)s 9 f 188.004 (x)s 10 f 288.568 y 194.681 (k)s 9 f 286.768 y 199.82 (;)s 205.084 (p)s 10 f 288.568 y 210.981 (k)s 3 f 286.768 y 216.12 (\051)s 224.023 (=)s 9 f 236.495 (V)s 7 f 281.813 y 245.956 (2)s 9 f 286.768 y 250.706 (p)s 10 f 288.568 y 256.603 (i)s 9 f 286.768 y 259.997 (p)s 10 f 288.568 y 265.894 (i)s 3 f 286.768 y 272.622 (=)s 285.094 (1)s 9 f 294.885 (:)s 3 f 442.891 (\05083\051)s 313.268 y 8.536 (along)s 39.869 (the)s 60.105 (whole)s 93.396 (extremal.)s 146.597 (This)s 173.426 (represen)s 215.595 (ts)s 228.716 (the)s 248.951 (eik)s 263.312 (onal)s 288.77 (equation)s 336.749 (for)s 354.7 (isotropic)s 402.418 (media.)s 336.304 y 26.161 (The)s 50.011 (Hamiltonian)s 117.267 (ra)s 127.385 (y)s 137.2 (tracing)s 176.717 (system)s 215.386 (\05044\051)s 239.889 (for)s 257.538 (isotropic)s 304.953 (media)s 339.248 (in)s 352.654 (Cartesian)s 405.292 (co)s 416.715 (ordinates)s 350.804 y 8.536 (then)s 35.3 (reads)s 361.314 y 146.376 (d)s 9 f 152.904 (x)s 10 f 363.114 y 159.581 (i)s 16.599 .4 146.376 366.632 r 3 f 377.664 y 148.19 (d)s 9 f 154.718 (\277)s 3 f 369.432 y 167.508 (=)s 9 f 179.98 (V)s 7 f 364.477 y 189.441 (2)s 9 f 369.432 y 194.191 (p)s 10 f 371.232 y 200.089 (i)s 9 f 369.432 y 207.399 (;)s 3 f 361.314 y 225.613 (d)s 9 f 232.141 (p)s 10 f 363.114 y 238.038 (i)s 15.819 .4 225.613 366.632 r 3 f 377.664 y 227.037 (d)s 9 f 233.565 (\277)s 3 f 369.432 y 245.965 (=)s 12 f 258.437 (\241)s 7 f 364.707 y 268.97 (1)s 4.25 .4 268.97 366.632 r 373.57 y 268.97 (2)s 9 f 369.432 y 274.42 (p)s 10 f 371.232 y 280.318 (k)s 9 f 369.432 y 285.457 (p)s 10 f 371.232 y 291.354 (k)s 9 f 361.314 y 297.693 (@)s 304.548 (V)s 7 f 356.959 y 314.009 (2)s 21.067 .4 297.693 366.632 r 9 f 377.664 y 299.763 (@)s 306.618 (x)s 10 f 379.463 y 313.295 (i)s 9 f 369.432 y 323.876 (:)s 3 f 396.474 y 8.536 (Using)s 41.562 (\05083\051,)s 69.631 (w)s 77.791 (e)s 86.93 (obtain)s 9 f 123.485 (p)s 10 f 398.274 y 129.382 (k)s 9 f 396.474 y 134.521 (p)s 10 f 398.274 y 140.418 (k)s 3 f 396.474 y 148.89 (=)s 161.362 (1)s 9 f 167.237 (=V)s 7 f 392.119 y 182.573 (2)s 3 f 396.474 y 187.323 (,)s 194.504 (so)s 208.93 (that)s 420.807 y 156.258 (d)s 9 f 162.786 (x)s 10 f 422.607 y 169.463 (i)s 16.599 .4 156.258 426.125 r 3 f 437.157 y 158.072 (d)s 9 f 164.6 (\277)s 3 f 428.925 y 177.39 (=)s 9 f 189.862 (V)s 7 f 423.97 y 199.323 (2)s 9 f 428.925 y 204.073 (p)s 10 f 430.725 y 209.971 (i)s 9 f 428.925 y 217.281 (;)s 3 f 420.807 y 239.412 (d)s 9 f 245.939 (p)s 10 f 422.607 y 251.836 (i)s 15.819 .4 239.412 426.125 r 3 f 437.157 y 240.836 (d)s 9 f 247.363 (\277)s 3 f 428.925 y 259.764 (=)s 12 f 272.236 (\241)s 9 f 420.807 y 282.769 (@)s 3 f 289.625 (ln)s 9 f 299.416 (V)s 26.108 .4 282.769 426.125 r 437.157 y 287.36 (@)s 294.215 (x)s 10 f 438.957 y 300.892 (i)s 9 f 428.925 y 313.994 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f 693.699 y 277.346 (ij)s 3 f 691.899 y 284.639 (\050)s 9 f 289.208 (x)s 10 f 686.944 y 295.885 (k)s 3 f 691.899 y 301.024 (\051)s 9 f 309.51 (:)s 3 f 442.891 (\05085\051)s 735.628 y 227.346 (226)s do-end end endp showpage %%Page: 17 17 %%BeginPageSetup initializepage (drahotova; page: 17 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (All)s 27.718 (relations)s 75.364 (deriv)s 100.822 (ed)s 116.418 (in)s 130.056 (Section)s 171.109 (3.1)s 189.969 (simplify)s 234.352 (in)s 247.989 (this)s 270.831 (case.)s 300.247 (The)s 324.329 (mo)s 340.322 (di\257ed)s 372.236 (Lagrangian)s 433.687 (reads,)s 17.964 y 8.536 (see)s 27.532 (\05035\051:)s 12 f 32.464 y 143.207 (L)s 10 f 27.509 y 151.484 (M)s 3 f 32.464 y 160.999 (\050)s 9 f 165.569 (x)s 10 f 27.509 y 172.246 (k)s 9 f 32.464 y 177.385 (;)s 3 f 184.681 (\137)s 9 f 182.648 (x)s 10 f 27.509 y 189.325 (k)s 3 f 32.464 y 194.464 (\051)s 202.367 (=)s 7 f 27.739 y 216.039 (1)s 4.25 .4 216.039 29.664 r 36.602 y 216.039 (2)s 9 f 32.464 y 221.489 (V)s 13 f 27.509 y 230.95 (\241)s 7 f 237.561 (2)s 3 f 32.464 y 242.311 (\050)s 9 f 246.881 (x)s 10 f 27.509 y 253.558 (k)s 3 f 32.464 y 258.697 (\051)s 9 f 263.266 (G)s 10 f 34.264 y 272.534 (ij)s 3 f 32.464 y 279.827 (\050)s 9 f 284.396 (x)s 10 f 27.509 y 291.073 (k)s 3 f 32.464 y 296.212 (\051)s 302.815 (\137)s 9 f 300.782 (x)s 10 f 27.509 y 307.459 (i)s 3 f 32.464 y 312.886 (\137)s 9 f 310.853 (x)s 10 f 27.509 y 317.53 (j)s 9 f 32.464 y 325.845 (:)s 3 f 442.891 (\05086\051)s 53.36 y 8.536 (The)s 32.688 (relev)s 56.515 (an)s 68.591 (t)s 77.077 (Euler-Lagrange)s 159.648 (equations)s 212.262 (\05039\051)s 237.067 (are)s 256.65 (as)s 271.076 (follo)s 292.618 (ws:)s 77.451 y 135.031 (d)s 12.971 .4 131.809 82.769 r 93.8 y 131.809 (d)s 9 f 138.337 (\277)s 3 f 85.569 y 145.98 (\050)s 9 f 150.549 (V)s 13 f 80.614 y 160.01 (\241)s 7 f 166.622 (2)s 9 f 85.569 y 171.372 (G)s 10 f 87.369 y 180.64 (ij)s 3 f 85.569 y 189.965 (\137)s 9 f 187.932 (x)s 10 f 80.614 y 194.61 (j)s 3 f 85.569 y 199.008 (\051)s 12 f 206.244 (\241)s 7 f 80.844 y 219.444 (1)s 4.25 .4 219.444 82.769 r 89.707 y 219.444 (2)s 3 f 85.569 y 226.927 (\137)s 9 f 224.894 (x)s 10 f 80.614 y 231.571 (k)s 3 f 85.569 y 238.743 (\137)s 9 f 236.71 (x)s 10 f 80.614 y 243.387 (l)s 9 f 77.451 y 252.755 (@)s 16.926 .4 247.719 82.769 r 93.8 y 247.719 (@)s 254.575 (x)s 10 f 90.334 y 261.252 (i)s 3 f 85.569 y 265.846 (\050)s 9 f 270.415 (V)s 13 f 80.614 y 279.876 (\241)s 7 f 286.487 (2)s 9 f 85.569 y 291.237 (G)s 10 f 87.369 y 300.506 (k)s 305.144 (l)s 3 f 85.569 y 308.276 (\051)s 316.179 (=)s 328.651 (0)s 9 f 338.443 (:)s 3 f 442.891 (\05087\051)s 115.558 y 8.536 (F)s 15.225 (or)s 9 f 29.586 (p)s 10 f 117.358 y 35.483 (i)s 3 f 115.558 y 38.877 (,)s 46.057 (w)s 54.217 (e)s 63.356 (can)s 84.897 (use)s 105.198 (\05042\051)s 130.004 (to)s 144.365 (obtain)s 9 f 149.255 y 153.409 (p)s 10 f 151.055 y 159.306 (i)s 3 f 149.255 y 166.033 (=)s 9 f 141.137 y 179.705 (@)s 12 f 186.561 (L)s 10 f 136.783 y 194.838 (M)s 24.648 .4 179.705 146.455 r 9 f 157.487 y 183.566 (@)s 3 f 192.454 (\137)s 9 f 190.421 (x)s 10 f 154.02 y 197.098 (i)s 3 f 149.255 y 208.886 (=)s 9 f 221.358 (V)s 13 f 144.301 y 230.819 (\241)s 7 f 237.43 (2)s 3 f 149.255 y 242.181 (\050)s 9 f 246.75 (x)s 10 f 144.301 y 253.427 (k)s 3 f 149.255 y 258.566 (\051)s 9 f 263.135 (G)s 10 f 151.055 y 272.404 (ij)s 3 f 149.255 y 279.696 (\050)s 9 f 284.266 (x)s 10 f 144.301 y 290.943 (k)s 3 f 149.255 y 296.082 (\051)s 302.684 (\137)s 9 f 300.651 (x)s 10 f 144.301 y 307.328 (j)s 9 f 149.255 y 315.643 (:)s 3 f 442.891 (\05088\051)s 180.155 y 8.536 (This)s 34.908 (can)s 55.993 (b)s 62.847 (e)s 71.53 (simply)s 108.673 (in)s 118.138 (v)s 124.013 (erted)s 153.584 (for)s 173.112 (\137)s 9 f 171.079 (x)s 10 f 175.8 y 177.756 (j)s 3 f 180.155 y 182.154 (.)s 190.488 (W)s 201.581 (e)s 210.263 (tak)s 226.583 (e)s 235.265 (in)s 244.73 (to)s 258.635 (accoun)s 293.558 (t)s 301.587 (that)s 9 f 326.589 (G)s 10 f 181.955 y 335.857 (ij)s 9 f 180.155 y 343.15 (G)s 10 f 175.8 y 352.418 (ik)s 3 f 180.155 y 363.784 (=)s 9 f 376.256 (\261)s 10 f 175.8 y 381.91 (k)s 183.121 y 381.46 (j)s 3 f 180.155 y 387.049 (,)s 393.865 (where)s 9 f 427.352 (G)s 10 f 175.8 y 436.62 (ik)s 3 f 180.155 y 448.113 (are)s 194.655 y 8.536 (the)s 28.772 (con)s 46.07 (tra)s 60.758 (v)s 66.306 (arian)s 92.091 (t)s 100.577 (comp)s 128.319 (onen)s 152.146 (ts)s 165.266 (of)s 178.648 (the)s 198.884 (metric)s 235.439 (tensor.)s 275.323 (Then)s 220.913 y 180.174 (\137)s 9 f 178.141 (x)s 10 f 215.958 y 184.818 (j)s 3 f 220.913 y 192.55 (=)s 9 f 205.022 (V)s 7 f 215.958 y 214.483 (2)s 3 f 220.913 y 219.233 (\050)s 9 f 223.802 (x)s 10 f 215.958 y 230.479 (k)s 3 f 220.913 y 235.618 (\051)s 9 f 240.188 (G)s 10 f 215.958 y 249.456 (j)s 253.355 (i)s 3 f 220.913 y 256.749 (\050)s 9 f 261.318 (x)s 10 f 215.958 y 267.995 (k)s 3 f 220.913 y 273.134 (\051)s 9 f 277.703 (p)s 10 f 222.713 y 283.601 (i)s 9 f 220.913 y 290.911 (:)s 3 f 442.891 (\05089\051)s 247.17 y 8.536 (The)s 32.688 (mo)s 48.681 (di\257ed)s 80.667 (Lagrangian)s 12 f 142.189 (L)s 10 f 242.816 y 150.465 (M)s 3 f 247.17 y 163.897 (can)s 185.439 (then)s 212.202 (b)s 219.057 (e)s 228.195 (expressed)s 280.874 (in)s 294.582 (terms)s 327.286 (of)s 9 f 340.668 (p)s 10 f 248.97 y 346.565 (k)s 3 f 247.17 y 351.704 (,)s 358.884 (see)s 377.88 (\05086\051)s 402.685 (and)s 425.532 (\05089\051:)s 12 f 273.428 y 185.52 (L)s 10 f 268.473 y 193.796 (M)s 3 f 273.428 y 206.645 (=)s 7 f 268.703 y 220.317 (1)s 4.25 .4 220.317 270.628 r 277.566 y 220.317 (2)s 9 f 273.428 y 225.767 (V)s 7 f 268.473 y 235.228 (2)s 9 f 273.428 y 239.978 (p)s 10 f 275.228 y 245.875 (j)s 9 f 273.428 y 250.274 (p)s 10 f 275.228 y 256.171 (k)s 9 f 273.428 y 261.31 (G)s 10 f 268.473 y 270.578 (j)s 274.477 (k)s 9 f 273.428 y 283.532 (:)s 3 f 442.891 (\05090\051)s 299.686 y 8.536 (The)s 32.688 (reduced)s 76.424 (Hamiltonian)s 12 f 143.982 (H)s 10 f 295.331 y 154.232 (M)s 3 f 299.686 y 163.747 (\050)s 9 f 168.317 (x)s 10 f 295.331 y 174.994 (k)s 9 f 299.686 y 180.133 (;)s 185.396 (p)s 10 f 301.486 y 191.294 (k)s 3 f 299.686 y 196.432 (\051)s 204.918 (is)s 216.734 (obtained)s 265.039 (from)s 292.781 (\05042\051,)s 320.851 (\05089\051)s 345.656 (and)s 368.503 (\05090\051,)s 12 f 325.944 y 146.696 (H)s 10 f 320.989 y 156.946 (M)s 3 f 325.944 y 166.461 (\050)s 9 f 171.031 (x)s 10 f 320.989 y 177.708 (k)s 9 f 325.944 y 182.847 (;)s 188.11 (p)s 10 f 327.744 y 194.008 (k)s 3 f 325.944 y 199.147 (\051)s 207.049 (=)s 7 f 321.219 y 220.721 (1)s 4.25 .4 220.721 323.144 r 330.082 y 220.721 (2)s 9 f 325.944 y 226.171 (V)s 7 f 320.989 y 235.632 (2)s 3 f 325.944 y 240.382 (\050)s 9 f 244.952 (x)s 10 f 320.989 y 251.629 (k)s 3 f 325.944 y 256.768 (\051)s 9 f 261.337 (G)s 10 f 320.989 y 270.605 (ij)s 3 f 325.944 y 277.898 (\050)s 9 f 282.467 (x)s 10 f 320.989 y 289.144 (k)s 3 f 325.944 y 294.283 (\051)s 9 f 298.853 (p)s 10 f 327.744 y 304.75 (i)s 9 f 325.944 y 308.144 (p)s 10 f 327.744 y 314.041 (j)s 9 f 325.944 y 322.356 (;)s 3 f 442.891 (\05091\051)s 352.201 y 8.536 (see)s 27.799 (also)s 51.632 (\05063\051.)s 81.81 (W)s 92.903 (e)s 102.309 (remind)s 142.396 (the)s 162.9 (reader)s 199.07 (that)s 12 f 224.796 (L)s 10 f 347.847 y 233.073 (M)s 3 f 352.201 y 242.588 (\050)s 9 f 247.157 (x)s 10 f 347.847 y 253.834 (k)s 9 f 352.201 y 258.973 (;)s 3 f 266.27 (\137)s 9 f 264.237 (x)s 10 f 347.847 y 270.914 (k)s 3 f 352.201 y 276.053 (\051)s 284.412 (=)s 7 f 347.477 y 298.539 (1)s 4.25 .4 298.539 349.401 r 356.339 y 298.539 (2)s 3 f 352.201 y 308.174 (and)s 12 f 331.289 (H)s 10 f 347.847 y 341.539 (M)s 3 f 352.201 y 351.054 (\050)s 9 f 355.623 (x)s 10 f 347.847 y 362.3 (k)s 9 f 352.201 y 367.439 (;)s 372.703 (p)s 10 f 354.001 y 378.6 (k)s 3 f 352.201 y 383.739 (\051)s 392.098 (=)s 7 f 347.477 y 406.225 (1)s 4.25 .4 406.225 349.401 r 356.339 y 406.225 (2)s 3 f 352.201 y 415.86 (along)s 447.461 (the)s 366.701 y 8.536 (whole)s 41.827 (ra)s 51.945 (y)s 57.167 (,)s 64.348 (see)s 83.343 (\05036\051)s 108.149 (and)s 130.996 (\05052\051.)s 160.37 (This)s 187.199 (yields,)s 223.493 (along)s 254.826 (the)s 275.062 (whole)s 308.354 (ra)s 318.472 (y)s 323.694 (,)s 9 f 392.959 y 109.943 (G)s 10 f 394.759 y 119.212 (ij)s 3 f 392.959 y 126.504 (\050)s 9 f 131.074 (x)s 10 f 388.004 y 137.751 (k)s 3 f 392.959 y 142.89 (\051)s 149.492 (\137)s 9 f 147.459 (x)s 10 f 388.004 y 154.136 (i)s 3 f 392.959 y 159.563 (\137)s 9 f 157.53 (x)s 10 f 388.004 y 164.207 (j)s 3 f 392.959 y 171.939 (=)s 9 f 184.411 (V)s 7 f 388.004 y 193.872 (2)s 3 f 392.959 y 198.622 (\050)s 9 f 203.191 (x)s 10 f 388.004 y 209.868 (k)s 3 f 392.959 y 215.007 (\051)s 9 f 223.493 (;)s 240.507 (G)s 10 f 388.004 y 249.775 (ij)s 3 f 392.959 y 257.068 (\050)s 9 f 261.637 (x)s 10 f 388.004 y 268.314 (k)s 3 f 392.959 y 273.453 (\051)s 9 f 278.023 (p)s 10 f 394.759 y 283.92 (i)s 9 f 392.959 y 287.314 (p)s 10 f 394.759 y 293.211 (j)s 3 f 392.959 y 300.943 (=)s 9 f 313.415 (V)s 13 f 388.004 y 322.876 (\241)s 7 f 329.487 (2)s 3 f 392.959 y 334.237 (\050)s 9 f 338.807 (x)s 10 f 388.004 y 345.484 (k)s 3 f 392.959 y 350.623 (\051)s 9 f 359.109 (:)s 3 f 442.891 (\05092\051)s 419.217 y 8.536 (Finally)s 43.62 (,)s 50.801 (the)s 71.037 (Hamiltonian)s 138.594 (ra)s 148.712 (y)s 158.83 (tracing)s 198.649 (system)s 237.62 (is)s 249.435 (as)s 263.861 (follo)s 285.402 (ws:)s 444.129 y 100.865 (d)s 9 f 107.393 (x)s 10 f 439.775 y 114.07 (i)s 16.599 .4 100.865 449.447 r 3 f 460.479 y 102.679 (d)s 9 f 109.207 (\277)s 3 f 452.247 y 128.664 (=)s 9 f 444.129 y 149.002 (@)s 12 f 155.858 (H)s 10 f 439.775 y 166.108 (M)s 26.621 .4 149.002 449.447 r 9 f 460.479 y 154.24 (@)s 161.095 (p)s 10 f 462.279 y 166.992 (i)s 3 f 452.247 y 180.157 (=)s 9 f 192.629 (V)s 7 f 447.293 y 202.09 (2)s 9 f 452.247 y 206.84 (G)s 10 f 447.293 y 216.108 (ik)s 9 f 452.247 y 224.141 (p)s 10 f 454.047 y 230.038 (k)s 9 f 452.247 y 239.094 (;)s 3 f 476.722 y 101.645 (d)s 9 f 108.172 (p)s 10 f 478.522 y 114.07 (i)s 15.819 .4 101.645 482.04 r 3 f 493.072 y 103.069 (d)s 9 f 109.597 (\277)s 3 f 484.84 y 128.664 (=)s 12 f 147.802 (\241)s 9 f 476.722 y 158.336 (@)s 12 f 165.191 (H)s 10 f 472.368 y 175.441 (M)s 26.621 .4 158.336 482.04 r 9 f 493.072 y 163.183 (@)s 170.038 (x)s 10 f 489.605 y 176.715 (i)s 3 f 484.84 y 189.49 (=)s 12 f 201.962 (\241)s 7 f 480.116 y 212.495 (1)s 4.25 .4 212.495 482.04 r 488.978 y 212.495 (2)s 9 f 484.84 y 217.945 (G)s 10 f 479.886 y 227.214 (j)s 231.112 (k)s 9 f 484.84 y 236.251 (p)s 10 f 486.64 y 242.148 (j)s 9 f 484.84 y 246.547 (p)s 10 f 486.64 y 252.444 (k)s 9 f 476.722 y 258.783 (@)s 265.639 (V)s 7 f 472.368 y 275.1 (2)s 21.067 .4 258.783 482.04 r 9 f 493.072 y 260.853 (@)s 267.709 (x)s 10 f 489.605 y 274.386 (i)s 12 f 484.84 y 283.716 (\241)s 7 f 480.116 y 296.916 (1)s 4.25 .4 296.916 482.04 r 488.978 y 296.916 (2)s 9 f 484.84 y 302.366 (V)s 7 f 479.886 y 311.827 (2)s 9 f 484.84 y 316.577 (p)s 10 f 486.64 y 322.475 (j)s 9 f 484.84 y 326.873 (p)s 10 f 486.64 y 332.77 (k)s 9 f 476.722 y 339.109 (@)s 345.965 (G)s 10 f 472.368 y 355.233 (j)s 359.132 (k)s 25.161 .4 339.109 482.04 r 9 f 493.072 y 343.227 (@)s 350.082 (x)s 10 f 489.605 y 356.759 (i)s 9 f 484.84 y 369.387 (:)s 3 f 515.74 y 8.536 (As)s 9 f 25.895 (G)s 10 f 511.385 y 35.164 (j)s 39.062 (k)s 9 f 515.74 y 44.201 (p)s 10 f 517.54 y 50.098 (j)s 9 f 515.74 y 54.497 (p)s 10 f 517.54 y 60.394 (k)s 9 f 515.74 y 65.533 (@)s 72.389 (V)s 7 f 511.385 y 81.85 (2)s 9 f 515.74 y 86.6 (=@)s 99.33 (x)s 10 f 511.385 y 106.007 (i)s 3 f 515.74 y 112.734 (=)s 9 f 125.206 (V)s 13 f 511.385 y 134.667 (\241)s 7 f 141.279 (2)s 3 f 515.74 y 146.029 (\050)s 9 f 150.598 (x)s 10 f 511.385 y 157.275 (k)s 3 f 515.74 y 162.414 (\051)s 9 f 166.983 (@)s 173.839 (V)s 7 f 511.385 y 183.3 (2)s 9 f 515.74 y 188.05 (=@)s 200.78 (x)s 10 f 511.385 y 207.457 (i)s 3 f 515.74 y 214.185 (=)s 226.657 (2)s 9 f 232.532 (@)s 3 f 239.387 (ln)s 9 f 249.179 (V)s 257.334 (=@)s 270.065 (x)s 10 f 511.385 y 276.742 (i)s 3 f 515.74 y 280.136 (,)s 287.316 (w)s 295.476 (e)s 304.615 (obtain)s 541.763 y 106.483 (d)s 9 f 113.011 (x)s 10 f 537.409 y 119.688 (i)s 16.599 .4 106.483 547.081 r 3 f 558.113 y 108.297 (d)s 9 f 114.825 (\277)s 3 f 549.881 y 127.615 (=)s 9 f 140.087 (V)s 7 f 544.927 y 149.548 (2)s 9 f 549.881 y 154.298 (G)s 10 f 544.927 y 163.567 (ik)s 9 f 549.881 y 171.599 (p)s 10 f 551.681 y 177.497 (k)s 9 f 549.881 y 186.552 (;)s 3 f 541.763 y 204.766 (d)s 9 f 211.294 (p)s 10 f 543.563 y 217.191 (i)s 15.819 .4 204.766 547.081 r 3 f 558.113 y 206.19 (d)s 9 f 212.718 (\277)s 3 f 549.881 y 225.118 (=)s 12 f 237.59 (\241)s 9 f 541.763 y 248.123 (@)s 3 f 254.979 (ln)s 9 f 264.77 (V)s 26.108 .4 248.123 547.081 r 558.113 y 252.714 (@)s 259.57 (x)s 10 f 554.646 y 266.247 (i)s 12 f 549.881 y 278.098 (\241)s 7 f 545.157 y 291.298 (1)s 4.25 .4 291.298 547.081 r 554.02 y 291.298 (2)s 9 f 549.881 y 296.748 (V)s 7 f 544.927 y 306.209 (2)s 9 f 549.881 y 310.959 (p)s 10 f 551.681 y 316.856 (j)s 9 f 549.881 y 321.255 (p)s 10 f 551.681 y 327.152 (k)s 9 f 541.763 y 333.491 (@)s 340.347 (G)s 10 f 537.409 y 349.615 (j)s 353.513 (k)s 25.161 .4 333.491 547.081 r 9 f 558.113 y 337.608 (@)s 344.464 (x)s 10 f 554.646 y 351.141 (i)s 9 f 549.881 y 363.769 (:)s 3 f 442.891 (\05093\051)s 581.446 y 8.536 (This)s 35.61 (corresp)s 72.557 (onds)s 100.284 (fully)s 127.293 (to)s 141.899 (the)s 162.38 (Hamiltonian)s 230.183 (ra)s 240.301 (y)s 250.664 (equations)s 303.523 (\0503.5.54\051)s 346.851 (in)s 578.412 y 362.11 (\267)s 581.446 y 360.804 (Cerv)s 384.957 (en)s 396.87 (\266)s 396.707 (y)s 407.07 (\0502001a\051)s 449.745 (for)s 9 f 595.946 y 8.536 (n)s 3 f 18.883 (=)s 31.355 (0,)s 44.41 (if)s 55.181 (w)s 63.341 (e)s 72.48 (tak)s 88.799 (e)s 97.938 (in)s 107.403 (to)s 121.764 (accoun)s 156.687 (t)s 165.173 (that)s 629.037 y 154.891 (lim)s 10 f 635.859 y 154.097 (n)s 13 f 159.254 (!)s 7 f 167.754 (0)s 0 f 611.437 y 174.004 (\303)s 9 f 629.037 y 181.921 (n)s 13 f 624.082 y 188.935 (\241)s 7 f 195.546 (1)s 9 f 620.919 y 205.413 (@)s 3 f 212.268 (\0501)s 9 f 222.712 (=V)s 3 f 238.048 (\051)s 10 f 616.564 y 242.618 (n)s 42.863 .4 205.413 626.237 r 9 f 637.268 y 218.381 (@)s 225.236 (x)s 10 f 633.802 y 231.913 (i)s 0 f 611.437 y 249.475 (!)s 3 f 629.037 y 260.725 (=)s 12 f 273.197 (\241)s 9 f 620.919 y 283.731 (@)s 3 f 290.586 (ln)s 9 f 300.378 (V)s 26.108 .4 283.731 626.237 r 637.268 y 288.322 (@)s 295.177 (x)s 10 f 633.802 y 301.854 (i)s 9 f 629.037 y 314.955 (:)s 3 f 662.128 y 8.536 (Note)s 37.75 (that)s 64.031 (the)s 85.089 (mo)s 101.082 (di\257ed)s 133.89 (Lagrangian)s 196.235 (for)s 215.008 (isotropic)s 263.549 (media)s 298.968 (and)s 322.638 (curvilinear)s 381.883 (co)s 393.307 (ordinates)s 445.111 (w)s 453.27 (as)s 676.628 y 8.536 (also)s 31.108 (used)s 56.944 (b)s 63.145 (y)s 72.271 (Babic)s 101.154 (h)s 110.605 (and)s 132.459 (Buldyrev)s 182.217 (\0501972\051.)s 223.011 (The)s 246.17 (authors)s 287.673 (apply)s 318.992 (the)s 338.235 (Legendre)s 387.667 (transformation)s 691.128 y 8.536 (to)s 22.932 (it)s 34.717 (to)s 49.113 (deriv)s 74.571 (e)s 83.745 (the)s 104.016 (relev)s 127.843 (an)s 139.919 (t)s 148.44 (mo)s 164.433 (di\257ed)s 196.454 (Hamiltonian)s 264.047 (\050ev)s 279.713 (en)s 295.415 (though)s 335.269 (they)s 361.742 (do)s 378.096 (not)s 399.02 (use)s 419.356 (the)s 439.628 (term)s 705.628 y 8.536 (\134mo)s 30.404 (di\257ed\042\051.)s 735.628 y 227.346 (227)s do-end end endp showpage %%Page: 18 18 %%BeginPageSetup initializepage (drahotova; page: 18 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f222 sf ( )S -983 -1000 :M f258 sf ( )S f296 sf ( )S -972 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278.261 (.)s 173.285 y 26.161 (W)s 37.254 (e)s 46.392 (assume)s 86.995 (that)s 112.453 (the)s 132.689 (mo)s 148.682 (di\257ed)s 180.667 (Hamiltonian)s 12 f 248.225 (H)s 10 f 168.931 y 258.475 (M)s 3 f 173.285 y 267.991 (\050)s 9 f 272.56 (x)s 10 f 175.085 y 279.237 (k)s 9 f 173.285 y 284.376 (;)s 289.64 (p)s 10 f 175.085 y 295.537 (k)s 3 f 173.285 y 300.676 (\051)s 309.162 (is)s 320.977 (giv)s 335.991 (en)s 351.657 (b)s 357.859 (y)s 367.977 (the)s 388.212 (relation)s 12 f 199.669 y 34.69 (H)s 10 f 194.714 y 44.941 (M)s 3 f 199.669 y 54.456 (\050)s 9 f 59.025 (x)s 10 f 201.469 y 65.702 (k)s 9 f 199.669 y 70.841 (;)s 76.105 (p)s 10 f 201.469 y 82.002 (k)s 3 f 199.669 y 87.141 (\051)s 95.044 (=)s 7 f 194.944 y 108.716 (1)s 4.25 .4 108.716 196.869 r 203.807 y 108.716 (2)s 9 f 199.669 y 114.166 (G)s 3 f 123.434 (\050)s 9 f 128.004 (x)s 10 f 201.469 y 134.681 (k)s 9 f 199.669 y 139.82 (;)s 145.083 (p)s 10 f 201.469 y 150.981 (k)s 3 f 199.669 y 156.12 (\051)s 9 f 164.606 (;)s 181.619 (G)s 3 f 190.888 (\050)s 9 f 195.457 (x)s 10 f 201.469 y 202.134 (k)s 9 f 199.669 y 207.273 (;)s 212.537 (p)s 10 f 201.469 y 218.434 (k)s 3 f 199.669 y 223.573 (\051)s 231.476 (=)s 9 f 243.948 (A)s 7 f 194.714 y 252.756 (2)s 3 f 199.669 y 257.506 (\050)s 9 f 262.075 (x)s 10 f 201.469 y 268.752 (k)s 3 f 199.669 y 273.891 (\051)s 9 f 278.461 (p)s 7 f 194.714 y 284.358 (2)s 202.635 y 284.358 (1)s 3 f 199.669 y 291.775 (+)s 9 f 303.58 (B)s 7 f 194.714 y 313.112 (2)s 3 f 199.669 y 317.862 (\050)s 9 f 322.431 (x)s 10 f 201.469 y 329.108 (k)s 3 f 199.669 y 334.247 (\051)s 9 f 338.817 (p)s 7 f 194.714 y 344.714 (2)s 202.635 y 344.714 (2)s 3 f 199.669 y 352.131 (+)s 9 f 363.936 (C)s 7 f 194.714 y 373.204 (2)s 3 f 199.669 y 377.954 (\050)s 9 f 382.524 (x)s 10 f 201.469 y 389.201 (k)s 3 f 199.669 y 394.34 (\051)s 9 f 398.909 (p)s 7 f 194.714 y 404.806 (2)s 202.635 y 404.806 (3)s 9 f 199.669 y 413.473 (:)s 3 f 442.891 (\05094\051)s 226.052 y 8.536 (As)s 25.895 (w)s 34.055 (e)s 43.194 (immediately)s 110.103 (see,)s 132.362 (slo)s 145.809 (wness)s 179.231 (surface)s 12 f 218.789 (H)s 10 f 221.697 y 229.039 (M)s 3 f 226.052 y 238.555 (\050)s 9 f 243.124 (x)s 10 f 227.852 y 249.801 (k)s 9 f 226.052 y 254.94 (;)s 260.204 (p)s 10 f 227.852 y 266.101 (k)s 3 f 226.052 y 271.24 (\051)s 279.143 (=)s 7 f 221.327 y 292.815 (1)s 4.25 .4 292.815 223.252 r 230.19 y 292.815 (2)s 3 f 226.052 y 302.181 (is)s 313.997 (an)s 330.316 (ellipsoid,)s 9 f 252.435 y 138.923 (A)s 7 f 247.48 y 147.731 (2)s 3 f 252.435 y 152.482 (\050)s 9 f 157.051 (x)s 10 f 254.235 y 163.728 (k)s 3 f 252.435 y 168.867 (\051)s 9 f 173.436 (p)s 7 f 247.48 y 179.333 (2)s 255.401 y 179.333 (1)s 3 f 252.435 y 186.75 (+)s 9 f 198.556 (B)s 7 f 247.48 y 208.087 (2)s 3 f 252.435 y 212.838 (\050)s 9 f 217.407 (x)s 10 f 254.235 y 224.084 (k)s 3 f 252.435 y 229.223 (\051)s 9 f 233.792 (p)s 7 f 247.48 y 239.689 (2)s 255.401 y 239.689 (2)s 3 f 252.435 y 247.106 (+)s 9 f 258.912 (C)s 7 f 247.48 y 268.18 (2)s 3 f 252.435 y 272.93 (\050)s 9 f 277.499 (x)s 10 f 254.235 y 284.176 (k)s 3 f 252.435 y 289.315 (\051)s 9 f 293.885 (p)s 7 f 247.48 y 299.782 (2)s 255.401 y 299.782 (3)s 3 f 252.435 y 307.865 (=)s 320.337 (1)s 9 f 330.129 (;)s 3 f 442.891 (\05095\051)s 278.818 y 8.536 (with)s 36.305 (half-axes)s 86.334 (1)s 9 f 92.208 (=)s 97.431 (A)s 3 f 106.239 (,)s 114.676 (1)s 9 f 120.551 (=B)s 3 f 140.88 (and)s 164.732 (1)s 9 f 170.607 (=C)s 3 f 185.751 (.)s 197.253 (Actually)s 240.005 (,)s 248.443 (it)s 261.198 (w)s 269.358 (ould)s 296.474 (b)s 303.328 (e)s 313.472 (more)s 343.852 (general)s 385.33 (to)s 400.696 (consider)s 447.461 (the)s 293.318 y 8.536 (generally)s 59.798 (orien)s 84.93 (ted)s 106.491 (ellipsoid)s 9 f 153.576 (G)s 3 f 162.844 (\050)s 9 f 167.413 (x)s 10 f 295.118 y 174.09 (k)s 9 f 293.318 y 179.229 (;)s 184.493 (p)s 10 f 295.118 y 190.39 (k)s 3 f 293.318 y 195.529 (\051)s 205.688 (=)s 9 f 220.416 (g)s 10 f 288.963 y 226.473 (ij)s 3 f 293.318 y 233.765 (\050)s 9 f 238.335 (x)s 10 f 295.118 y 245.012 (k)s 3 f 293.318 y 250.151 (\051)s 9 f 254.72 (p)s 10 f 295.118 y 260.617 (i)s 9 f 293.318 y 264.011 (p)s 10 f 295.118 y 269.908 (j)s 3 f 293.318 y 274.307 (,)s 283.144 (and)s 307.317 (ev)s 318.414 (en)s 335.406 (the)s 356.967 (follo)s 378.508 (wing)s 407.903 (deriv)s 433.034 (ations)s 307.818 y 8.536 (w)s 16.696 (ould)s 41.528 (b)s 48.382 (e)s 56.242 (more)s 84.337 (concise)s 122.943 (due)s 143.858 (to)s 156.94 (Einstein)s 201.582 (summation)s 261.076 (con)s 278.374 (v)s 284.249 (en)s 295.673 (tion.)s 323.968 (The)s 346.842 (diagonalized)s 412.799 (ellipsoidal)s 322.318 y 8.536 (form)s 35.314 (\05095\051)s 59.155 (is,)s 73.463 (ho)s 85.539 (w)s 93.699 (ev)s 104.796 (er,)s 120.996 (more)s 149.407 (transparen)s 203.979 (t.)s 216.712 (W)s 227.805 (e)s 235.98 (denote)s 9 f 272.876 (p)s 10 f 324.118 y 278.773 (i)s 3 f 322.318 y 285.501 (=)s 12 f 297.973 (j)s 9 f 301.373 (\176)s 301.306 (p)s 12 f 307.203 (j)s 9 f 310.537 (N)s 10 f 324.118 y 319.946 (i)s 3 f 322.318 y 323.34 (,)s 329.749 (where)s 9 f 362.728 (N)s 10 f 324.118 y 372.137 (i)s 3 f 322.318 y 378.484 (is)s 389.334 (the)s 408.606 (unit)s 432.447 (v)s 438.322 (ector)s 336.818 y 8.536 (along)s 9 f 39.936 (\176)s 39.869 (p)s 3 f 49.683 (\050p)s 61.106 (erp)s 77.752 (endicular)s 128.668 (to)s 143.029 (the)s 163.265 (w)s 171.425 (a)s 176.973 (v)s 182.848 (efron)s 208.306 (t\051.)s 225.931 (This)s 252.76 (yields)s 12 f 363.201 y 115.236 (j)s 9 f 118.637 (\176)s 118.57 (p)s 12 f 124.467 (j)s 3 f 131.133 (=)s 143.606 ([)s 9 f 146.869 (A)s 7 f 358.246 y 155.678 (2)s 3 f 363.201 y 160.428 (\050)s 9 f 164.997 (x)s 10 f 365.001 y 171.674 (k)s 3 f 363.201 y 176.813 (\051)s 9 f 181.382 (N)s 7 f 358.246 y 192.045 (2)s 366.168 y 190.791 (1)s 3 f 363.201 y 199.462 (+)s 9 f 211.267 (B)s 7 f 358.246 y 220.799 (2)s 3 f 363.201 y 225.549 (\050)s 9 f 230.118 (x)s 10 f 365.001 y 236.795 (k)s 3 f 363.201 y 241.934 (\051)s 9 f 246.504 (N)s 7 f 358.246 y 257.166 (2)s 366.168 y 255.913 (2)s 3 f 363.201 y 264.583 (+)s 9 f 276.388 (C)s 7 f 358.246 y 285.657 (2)s 3 f 363.201 y 290.407 (\050)s 9 f 294.976 (x)s 10 f 365.001 y 301.653 (k)s 3 f 363.201 y 306.792 (\051)s 9 f 311.361 (N)s 7 f 358.246 y 322.024 (2)s 366.168 y 320.77 (3)s 3 f 363.201 y 326.774 (])s 13 f 358.246 y 330.038 (\241)s 7 f 336.649 (1)s 10 f 340.899 (=)s 7 f 345.149 (2)s 9 f 363.201 y 353.816 (:)s 3 f 442.891 (\05096\051)s 389.584 y 8.536 (As)s 25.895 (phase)s 58.599 (v)s 64.474 (elo)s 79.162 (cit)s 91.891 (y)s 12 f 102.009 (C)s 3 f 112.944 (equals)s 148.585 (1)s 9 f 154.46 (=)s 12 f 160.335 (j)s 9 f 163.735 (\176)s 163.668 (p)s 12 f 169.565 (j)s 3 f 172.899 (,)s 12 f 415.967 y 121.315 (C)s 3 f 131.666 (=)s 144.138 ([)s 9 f 147.402 (A)s 7 f 411.012 y 156.21 (2)s 3 f 415.967 y 160.961 (\050)s 9 f 165.53 (x)s 10 f 417.767 y 172.207 (k)s 3 f 415.967 y 177.346 (\051)s 9 f 181.915 (N)s 7 f 411.012 y 192.578 (2)s 418.934 y 191.324 (1)s 3 f 415.967 y 199.994 (+)s 9 f 211.8 (B)s 7 f 411.012 y 221.332 (2)s 3 f 415.967 y 226.082 (\050)s 9 f 230.651 (x)s 10 f 417.767 y 237.328 (k)s 3 f 415.967 y 242.467 (\051)s 9 f 247.037 (N)s 7 f 411.012 y 257.699 (2)s 418.934 y 256.446 (2)s 3 f 415.967 y 265.116 (+)s 9 f 276.921 (C)s 7 f 411.012 y 286.189 (2)s 3 f 415.967 y 290.939 (\050)s 9 f 295.509 (x)s 10 f 417.767 y 302.186 (k)s 3 f 415.967 y 307.325 (\051)s 9 f 311.894 (N)s 7 f 411.012 y 322.557 (2)s 418.934 y 321.303 (3)s 3 f 415.967 y 327.307 (])s 7 f 411.012 y 330.571 (1)s 10 f 334.821 (=)s 7 f 339.071 (2)s 9 f 415.967 y 347.737 (:)s 3 f 442.891 (\05097\051)s 442.35 y 8.536 (Hamiltonian)s 76.094 (ra)s 86.211 (y)s 96.329 (tracing)s 136.148 (system)s 175.119 (\05044\051)s 199.924 (is)s 211.739 (easily)s 244.117 (obtained)s 292.422 (from)s 320.165 (\05094\051,)s 467.744 y 80.267 (d)s 9 f 86.794 (x)s 7 f 469.544 y 93.471 (1)s 17.955 .4 80.267 473.062 r 3 f 484.093 y 82.759 (d)s 9 f 89.286 (\277)s 3 f 475.862 y 102.755 (=)s 9 f 115.227 (A)s 7 f 470.907 y 124.035 (2)s 9 f 475.862 y 128.785 (p)s 7 f 477.662 y 134.682 (1)s 9 f 475.862 y 143.349 (;)s 3 f 467.744 y 169.396 (d)s 9 f 175.924 (p)s 7 f 469.544 y 181.821 (1)s 17.175 .4 169.396 473.062 r 3 f 484.093 y 171.498 (d)s 9 f 178.026 (\277)s 3 f 475.862 y 191.104 (=)s 12 f 203.576 (\241)s 7 f 471.137 y 214.109 (1)s 4.25 .4 214.109 473.062 r 480 y 214.109 (2)s 0 f 461.261 y 219.56 (\265)s 9 f 467.744 y 228.121 (@)s 234.976 (A)s 7 f 463.389 y 243.784 (2)s 20.414 .4 228.121 473.062 r 9 f 484.093 y 229.186 (@)s 236.042 (x)s 7 f 485.893 y 242.719 (1)s 9 f 475.862 y 249.734 (p)s 7 f 470.907 y 255.632 (2)s 478.828 y 255.632 (1)s 3 f 475.862 y 263.048 (+)s 9 f 467.744 y 276.054 (@)s 282.909 (B)s 7 f 463.389 y 292.441 (2)s 21.137 .4 276.054 473.062 r 9 f 484.093 y 277.481 (@)s 284.337 (x)s 7 f 485.893 y 291.014 (1)s 9 f 475.862 y 298.391 (p)s 7 f 470.907 y 304.288 (2)s 478.828 y 304.288 (2)s 3 f 475.862 y 311.705 (+)s 9 f 467.744 y 324.71 (@)s 331.566 (C)s 7 f 463.389 y 340.834 (2)s 20.874 .4 324.71 473.062 r 9 f 484.093 y 326.006 (@)s 332.861 (x)s 7 f 485.893 y 339.538 (1)s 9 f 475.862 y 346.784 (p)s 7 f 470.907 y 352.681 (2)s 478.828 y 352.681 (3)s 0 f 461.261 y 357.431 (\266)s 9 f 475.862 y 368.709 (;)s 3 f 499.403 y 79.543 (d)s 9 f 86.071 (x)s 7 f 501.203 y 92.748 (2)s 17.955 .4 79.543 504.721 r 3 f 515.753 y 82.035 (d)s 9 f 88.563 (\277)s 3 f 507.521 y 102.031 (=)s 9 f 114.503 (B)s 7 f 502.567 y 124.035 (2)s 9 f 507.521 y 128.785 (p)s 7 f 509.321 y 134.682 (2)s 9 f 507.521 y 143.349 (;)s 3 f 499.403 y 169.396 (d)s 9 f 175.924 (p)s 7 f 501.203 y 181.821 (2)s 17.175 .4 169.396 504.721 r 3 f 515.753 y 171.498 (d)s 9 f 178.026 (\277)s 3 f 507.521 y 191.104 (=)s 12 f 203.576 (\241)s 7 f 502.797 y 214.109 (1)s 4.25 .4 214.109 504.721 r 511.659 y 214.109 (2)s 0 f 492.921 y 219.56 (\265)s 9 f 499.403 y 228.121 (@)s 234.976 (A)s 7 f 495.049 y 243.784 (2)s 20.414 .4 228.121 504.721 r 9 f 515.753 y 229.186 (@)s 236.042 (x)s 7 f 517.553 y 242.719 (2)s 9 f 507.521 y 249.734 (p)s 7 f 502.567 y 255.632 (2)s 510.488 y 255.632 (1)s 3 f 507.521 y 263.048 (+)s 9 f 499.403 y 276.054 (@)s 282.909 (B)s 7 f 495.049 y 292.441 (2)s 21.137 .4 276.054 504.721 r 9 f 515.753 y 277.481 (@)s 284.337 (x)s 7 f 517.553 y 291.014 (2)s 9 f 507.521 y 298.391 (p)s 7 f 502.567 y 304.288 (2)s 510.488 y 304.288 (2)s 3 f 507.521 y 311.705 (+)s 9 f 499.403 y 324.71 (@)s 331.566 (C)s 7 f 495.049 y 340.834 (2)s 20.874 .4 324.71 504.721 r 9 f 515.753 y 326.006 (@)s 332.861 (x)s 7 f 517.553 y 339.538 (2)s 9 f 507.521 y 346.784 (p)s 7 f 502.567 y 352.681 (2)s 510.488 y 352.681 (3)s 0 f 492.921 y 357.431 (\266)s 9 f 507.521 y 368.709 (;)s 3 f 442.891 (\05098\051)s 531.063 y 81.807 (d)s 9 f 88.334 (x)s 7 f 532.863 y 95.011 (3)s 17.955 .4 81.807 536.381 r 3 f 547.413 y 84.299 (d)s 9 f 90.826 (\277)s 3 f 539.181 y 104.295 (=)s 9 f 116.767 (C)s 7 f 534.226 y 126.035 (2)s 9 f 539.181 y 130.785 (p)s 7 f 540.981 y 136.682 (3)s 9 f 539.181 y 145.349 (;)s 3 f 531.063 y 171.396 (d)s 9 f 177.923 (p)s 7 f 532.863 y 183.821 (3)s 17.175 .4 171.396 536.381 r 3 f 547.413 y 173.498 (d)s 9 f 180.026 (\277)s 3 f 539.181 y 193.104 (=)s 12 f 205.576 (\241)s 7 f 534.456 y 216.109 (1)s 4.25 .4 216.109 536.381 r 543.319 y 216.109 (2)s 0 f 524.581 y 221.559 (\265)s 9 f 531.063 y 230.121 (@)s 236.976 (A)s 7 f 526.708 y 245.784 (2)s 20.414 .4 230.121 536.381 r 9 f 547.413 y 231.186 (@)s 238.042 (x)s 7 f 549.213 y 244.719 (3)s 9 f 539.181 y 251.734 (p)s 7 f 534.226 y 257.632 (2)s 542.148 y 257.632 (1)s 3 f 539.181 y 265.048 (+)s 9 f 531.063 y 278.054 (@)s 284.909 (B)s 7 f 526.708 y 294.441 (2)s 21.137 .4 278.054 536.381 r 9 f 547.413 y 279.481 (@)s 286.337 (x)s 7 f 549.213 y 293.014 (3)s 9 f 539.181 y 300.391 (p)s 7 f 534.226 y 306.288 (2)s 542.148 y 306.288 (2)s 3 f 539.181 y 313.705 (+)s 9 f 531.063 y 326.71 (@)s 333.566 (C)s 7 f 526.708 y 342.834 (2)s 20.874 .4 326.71 536.381 r 9 f 547.413 y 328.006 (@)s 334.861 (x)s 7 f 549.213 y 341.538 (3)s 9 f 539.181 y 348.784 (p)s 7 f 534.226 y 354.681 (2)s 542.148 y 354.681 (3)s 0 f 524.581 y 359.431 (\266)s 9 f 539.181 y 370.709 (:)s 3 f 571.096 y 8.536 (Th)s 23.223 (us,)s 41.566 (group)s 74.857 (v)s 80.732 (elo)s 95.42 (cit)s 108.149 (y)s 118.267 (comp)s 146.009 (onen)s 169.836 (ts)s 12 f 182.956 (U)s 10 f 572.896 y 190.466 (i)s 3 f 571.096 y 197.194 (=)s 211.699 (\137)s 9 f 209.666 (x)s 10 f 572.896 y 216.343 (i)s 3 f 571.096 y 223.07 (=)s 9 f 235.542 (@)s 12 f 242.397 (H)s 9 f 252.647 (=@)s 265.378 (p)s 10 f 572.896 y 271.275 (i)s 3 f 571.096 y 278.586 (are)s 298.169 (giv)s 313.182 (en)s 328.849 (b)s 335.05 (y)s 345.168 (relations)s 12 f 597.479 y 128.723 (U)s 7 f 599.279 y 136.233 (1)s 3 f 597.479 y 144.316 (=)s 9 f 156.788 (A)s 7 f 592.524 y 165.596 (2)s 9 f 597.479 y 170.346 (p)s 7 f 599.279 y 176.243 (1)s 9 f 597.479 y 184.91 (;)s 12 f 205.84 (U)s 7 f 599.279 y 213.35 (2)s 3 f 597.479 y 221.434 (=)s 9 f 233.906 (B)s 7 f 592.524 y 243.438 (2)s 9 f 597.479 y 248.188 (p)s 7 f 599.279 y 254.085 (2)s 9 f 597.479 y 262.752 (;)s 12 f 283.682 (U)s 7 f 599.279 y 291.192 (3)s 3 f 597.479 y 299.275 (=)s 9 f 311.747 (C)s 7 f 592.524 y 321.016 (2)s 9 f 597.479 y 325.766 (p)s 7 f 599.279 y 331.663 (3)s 9 f 597.479 y 340.33 (:)s 3 f 442.891 (\05099\051)s 623.862 y 8.536 (The)s 32.688 (in)s 42.154 (v)s 48.029 (ersion)s 82.038 (for)s 9 f 99.989 (p)s 10 f 625.662 y 105.886 (i)s 3 f 623.862 y 113.197 (is)s 125.012 (simple)s 9 f 650.245 y 118.806 (p)s 7 f 652.045 y 124.703 (1)s 3 f 650.245 y 132.786 (=)s 9 f 145.258 (A)s 13 f 645.29 y 154.067 (\241)s 7 f 160.678 (2)s 12 f 650.245 y 165.428 (U)s 7 f 652.045 y 172.938 (1)s 9 f 650.245 y 181.605 (;)s 202.535 (p)s 7 f 652.045 y 208.432 (2)s 3 f 650.245 y 216.515 (=)s 9 f 228.987 (B)s 13 f 645.29 y 238.519 (\241)s 7 f 245.13 (2)s 12 f 650.245 y 249.881 (U)s 7 f 652.045 y 257.391 (2)s 9 f 650.245 y 266.057 (;)s 286.988 (p)s 7 f 652.045 y 292.885 (3)s 3 f 650.245 y 300.968 (=)s 9 f 313.44 (C)s 13 f 645.29 y 322.708 (\241)s 7 f 329.32 (2)s 12 f 650.245 y 334.07 (U)s 7 f 652.045 y 341.58 (3)s 9 f 650.245 y 350.246 (:)s 3 f 437.016 (\050100\051)s 676.628 y 8.536 (Equation)s 58.725 (\05042\051)s 82.969 (can)s 103.949 (b)s 110.803 (e)s 119.38 (used)s 145.647 (to)s 159.446 (compute)s 206.537 (the)s 226.211 (mo)s 242.204 (di\257ed)s 273.628 (Lagrangian)s 334.588 (from)s 361.77 (the)s 381.444 (mo)s 397.437 (di\257ed)s 428.861 (Hamil-)s 691.128 y 8.536 (tonian,)s 12 f 705.628 y 151.227 (L)s 10 f 700.673 y 159.504 (M)s 3 f 705.628 y 169.019 (\050)s 9 f 173.589 (x)s 10 f 707.428 y 180.266 (k)s 9 f 705.628 y 185.405 (;)s 3 f 192.702 (\137)s 9 f 190.669 (x)s 10 f 707.428 y 197.346 (k)s 3 f 705.628 y 202.485 (\051)s 210.387 (=)s 224.892 (\137)s 9 f 222.859 (x)s 10 f 707.428 y 229.536 (i)s 9 f 705.628 y 232.93 (p)s 10 f 707.428 y 238.827 (i)s 12 f 705.628 y 244.888 (\241)s 256.888 (H)s 10 f 700.673 y 267.138 (M)s 3 f 705.628 y 276.653 (\050)s 9 f 281.223 (x)s 10 f 707.428 y 287.9 (k)s 9 f 705.628 y 293.039 (;)s 298.303 (p)s 10 f 707.428 y 304.2 (k)s 3 f 705.628 y 309.339 (\051)s 9 f 317.825 (;)s 3 f 735.628 y 227.346 (228)s do-end end endp showpage %%Page: 19 19 %%BeginPageSetup initializepage (drahotova; page: 19 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (where)s 9 f 42.48 (p)s 10 f 5.264 y 48.377 (i)s 3 f 3.464 y 55.688 (are)s 75.271 (expressed)s 127.949 (in)s 141.658 (terms)s 174.362 (of)s 12 f 187.743 (U)s 10 f 5.264 y 195.253 (i)s 3 f 3.464 y 201.981 (=)s 216.486 (\137)s 9 f 214.453 (x)s 10 f 5.264 y 221.13 (i)s 3 f 3.464 y 228.44 (using)s 259.186 (\050100\051.)s 294.435 (Using)s 327.461 (also)s 351.026 (\05094\051,)s 379.096 (w)s 387.255 (e)s 396.394 (obtain)s 12 f 29.964 y 49.94 (L)s 10 f 25.009 y 58.216 (M)s 3 f 29.964 y 67.732 (\050)s 9 f 72.301 (x)s 10 f 31.764 y 78.978 (k)s 9 f 29.964 y 84.117 (;)s 3 f 91.414 (\137)s 9 f 89.381 (x)s 10 f 31.764 y 96.058 (k)s 3 f 29.964 y 101.197 (\051)s 115.766 (=)s 136.938 (\137)s 9 f 134.905 (x)s 7 f 31.764 y 141.582 (1)s 9 f 29.964 y 146.332 (p)s 7 f 31.764 y 152.229 (1)s 3 f 29.964 y 159.646 (+)s 173.485 (\137)s 9 f 171.452 (x)s 7 f 31.764 y 178.129 (2)s 9 f 29.964 y 182.879 (p)s 7 f 31.764 y 188.776 (2)s 3 f 29.964 y 196.193 (+)s 210.031 (\137)s 9 f 207.998 (x)s 7 f 31.764 y 214.675 (3)s 9 f 29.964 y 219.425 (p)s 7 f 31.764 y 225.322 (3)s 12 f 29.964 y 232.739 (\241)s 7 f 25.239 y 245.939 (1)s 4.25 .4 245.939 27.164 r 34.102 y 245.939 (2)s 3 f 29.964 y 251.389 (\050)s 9 f 255.958 (A)s 7 f 25.009 y 264.767 (2)s 9 f 29.964 y 269.517 (p)s 7 f 25.009 y 275.414 (2)s 32.93 y 275.414 (1)s 3 f 29.964 y 282.83 (+)s 9 f 294.636 (B)s 7 f 25.009 y 304.168 (2)s 9 f 29.964 y 308.918 (p)s 7 f 25.009 y 314.815 (2)s 32.93 y 314.815 (2)s 3 f 29.964 y 322.232 (+)s 9 f 334.037 (C)s 7 f 25.009 y 343.305 (2)s 9 f 29.964 y 348.055 (p)s 7 f 25.009 y 353.953 (2)s 32.93 y 353.953 (3)s 3 f 29.964 y 358.703 (\051)s 47.464 y 115.766 (=)s 136.938 (\137)s 9 f 134.905 (x)s 7 f 42.509 y 141.582 (2)s 50.43 y 141.582 (1)s 9 f 47.464 y 146.332 (A)s 13 f 42.509 y 155.141 (\241)s 7 f 161.752 (2)s 3 f 47.464 y 169.168 (+)s 183.007 (\137)s 9 f 180.974 (x)s 7 f 42.509 y 187.651 (2)s 50.43 y 187.651 (2)s 9 f 47.464 y 192.401 (B)s 13 f 42.509 y 201.933 (\241)s 7 f 208.544 (2)s 3 f 47.464 y 215.961 (+)s 229.799 (\137)s 9 f 227.766 (x)s 7 f 42.509 y 234.443 (2)s 50.43 y 234.443 (3)s 9 f 47.464 y 239.193 (C)s 13 f 42.509 y 248.461 (\241)s 7 f 255.073 (2)s 12 f 47.464 y 262.489 (\241)s 7 f 42.739 y 275.689 (1)s 4.25 .4 275.689 44.664 r 51.602 y 275.689 (2)s 3 f 47.464 y 281.139 (\050)s 287.742 (\137)s 9 f 285.709 (x)s 7 f 42.509 y 292.386 (2)s 50.43 y 292.386 (1)s 9 f 47.464 y 297.136 (A)s 13 f 42.509 y 305.944 (\241)s 7 f 312.555 (2)s 3 f 47.464 y 319.972 (+)s 333.81 (\137)s 9 f 331.777 (x)s 7 f 42.509 y 338.454 (2)s 50.43 y 338.454 (2)s 9 f 47.464 y 343.205 (B)s 13 f 42.509 y 352.736 (\241)s 7 f 359.348 (2)s 3 f 47.464 y 366.764 (+)s 380.603 (\137)s 9 f 378.57 (x)s 7 f 42.509 y 385.247 (2)s 50.43 y 385.247 (3)s 9 f 47.464 y 389.997 (C)s 13 f 42.509 y 399.265 (\241)s 7 f 405.876 (2)s 3 f 47.464 y 410.626 (\051)s 9 f 419.112 (:)s 3 f 73.964 y 8.536 (This)s 35.365 (yields,)s 12 f 88.464 y 126.399 (L)s 10 f 83.509 y 134.675 (M)s 3 f 88.464 y 144.191 (\050)s 9 f 148.76 (x)s 10 f 90.264 y 155.437 (k)s 9 f 88.464 y 160.576 (;)s 3 f 167.873 (\137)s 9 f 165.84 (x)s 10 f 90.264 y 172.517 (k)s 3 f 88.464 y 177.656 (\051)s 185.558 (=)s 7 f 83.739 y 199.231 (1)s 4.25 .4 199.231 85.664 r 92.602 y 199.231 (2)s 3 f 88.464 y 204.681 (\050)s 9 f 209.25 (A)s 13 f 83.509 y 218.058 (\241)s 7 f 224.669 (2)s 3 f 88.464 y 231.452 (\137)s 9 f 229.419 (x)s 7 f 83.509 y 236.097 (2)s 91.43 y 236.097 (1)s 3 f 88.464 y 243.513 (+)s 9 f 255.319 (B)s 13 f 83.509 y 264.85 (\241)s 7 f 271.462 (2)s 3 f 88.464 y 278.245 (\137)s 9 f 276.212 (x)s 7 f 83.509 y 282.889 (2)s 91.43 y 282.889 (2)s 3 f 88.464 y 290.305 (+)s 9 f 302.111 (C)s 13 f 83.509 y 311.379 (\241)s 7 f 317.99 (2)s 3 f 88.464 y 324.773 (\137)s 9 f 322.74 (x)s 7 f 83.509 y 329.417 (2)s 91.43 y 329.417 (3)s 3 f 88.464 y 334.167 (\051)s 9 f 342.654 (:)s 3 f 437.016 (\050101\051)s 109.464 y 8.536 (Th)s 23.223 (us,)s 41.566 (group)s 74.857 (v)s 80.732 (elo)s 95.42 (cit)s 108.149 (y)s 118.267 (surface)s 12 f 157.825 (L)s 10 f 105.109 y 166.101 (M)s 3 f 109.464 y 175.617 (\050)s 9 f 180.186 (x)s 10 f 111.264 y 186.863 (k)s 9 f 109.464 y 192.002 (;)s 12 f 197.266 (U)s 10 f 111.264 y 204.776 (k)s 3 f 109.464 y 209.915 (\051)s 217.818 (=)s 7 f 104.739 y 231.49 (1)s 4.25 .4 231.49 106.664 r 113.602 y 231.49 (2)s 3 f 109.464 y 240.856 (is)s 252.671 (again)s 284.004 (ellipsoidal)s 9 f 135.964 y 156.232 (A)s 13 f 131.009 y 165.04 (\241)s 7 f 171.651 (2)s 12 f 135.964 y 176.401 (U)s 7 f 131.009 y 185.103 (2)s 138.93 y 183.911 (1)s 3 f 135.964 y 192.52 (+)s 9 f 204.325 (B)s 13 f 131.009 y 213.857 (\241)s 7 f 220.468 (2)s 12 f 135.964 y 225.218 (U)s 7 f 131.009 y 233.92 (2)s 138.93 y 232.728 (2)s 3 f 135.964 y 241.337 (+)s 9 f 253.142 (C)s 13 f 131.009 y 262.41 (\241)s 7 f 269.021 (2)s 12 f 135.964 y 273.772 (U)s 7 f 131.009 y 282.473 (2)s 138.93 y 281.282 (3)s 3 f 135.964 y 290.557 (=)s 303.029 (1)s 9 f 312.82 (:)s 3 f 437.016 (\050102\051)s 162.464 y 8.536 (The)s 32.72 (half-axes)s 81.775 (of)s 95.189 (the)s 115.457 (group)s 148.78 (v)s 154.655 (elo)s 169.343 (cit)s 182.072 (y)s 192.222 (ellipsoid)s 238.013 (are)s 9 f 257.628 (A;)s 271.7 (B)s 3 f 281.232 (,)s 288.452 (and)s 9 f 311.331 (C)s 3 f 320.599 (.)s 329.181 (They)s 359.567 (are)s 379.182 (recipro)s 414.758 (cal)s 433.068 (to)s 447.461 (the)s 176.964 y 8.536 (half-axes)s 57.559 (of)s 70.941 (the)s 91.177 (slo)s 104.624 (wness)s 138.046 (ellipsoid.)s 200 y 26.161 (Using)s 12 f 59.174 (U)s 10 f 201.8 y 66.684 (i)s 3 f 200 y 73.412 (=)s 12 f 85.884 (U)s 9 f 94.585 (t)s 10 f 201.8 y 98.828 (i)s 3 f 200 y 102.222 (,)s 109.393 (where)s 9 f 143.324 (t)s 10 f 201.8 y 147.567 (i)s 3 f 200 y 154.866 (is)s 166.668 (the)s 186.892 (unit)s 211.685 (v)s 217.559 (ector)s 246.922 (along)s 278.242 (the)s 298.466 (ra)s 308.584 (y)s 313.806 (,)s 9 f 320.976 (t)s 10 f 201.8 y 325.219 (i)s 3 f 200 y 331.947 (=)s 344.419 (d)s 9 f 350.946 (x)s 10 f 201.8 y 357.623 (i)s 9 f 200 y 361.017 (=)s 3 f 366.892 (d)s 9 f 373.42 (s)s 3 f 378.955 (,)s 386.125 (w)s 394.285 (e)s 403.411 (obtain)s 439.954 (from)s 214.5 y 8.536 (\050102\051)s 12 f 229 y 151.625 (U)s 7 f 224.045 y 160.326 (2)s 3 f 229 y 165.076 (\050)s 9 f 169.646 (A)s 13 f 224.045 y 178.454 (\241)s 7 f 185.065 (2)s 9 f 229 y 189.815 (t)s 7 f 224.045 y 194.058 (2)s 231.966 y 194.058 (1)s 3 f 229 y 201.475 (+)s 9 f 213.28 (B)s 13 f 224.045 y 222.812 (\241)s 7 f 229.423 (2)s 9 f 229 y 234.173 (t)s 7 f 224.045 y 238.416 (2)s 231.966 y 238.416 (2)s 3 f 229 y 245.833 (+)s 9 f 257.639 (C)s 13 f 224.045 y 266.907 (\241)s 7 f 273.518 (2)s 9 f 229 y 278.268 (t)s 7 f 224.045 y 282.511 (2)s 231.966 y 282.511 (3)s 3 f 229 y 287.261 (\051)s 295.164 (=)s 307.636 (1)s 9 f 317.427 (:)s 3 f 250 y 8.536 (This)s 35.365 (yields)s 12 f 264.5 y 147.006 (U)s 3 f 159.041 (=)s 171.513 (\050)s 9 f 176.083 (A)s 13 f 259.545 y 184.891 (\241)s 7 f 191.502 (2)s 9 f 264.5 y 196.252 (t)s 7 f 259.545 y 200.495 (2)s 267.466 y 200.495 (1)s 3 f 264.5 y 207.912 (+)s 9 f 219.717 (B)s 13 f 259.545 y 229.249 (\241)s 7 f 235.86 (2)s 9 f 264.5 y 240.611 (t)s 7 f 259.545 y 244.854 (2)s 267.466 y 244.854 (2)s 3 f 264.5 y 252.27 (+)s 9 f 264.076 (C)s 13 f 259.545 y 273.344 (\241)s 7 f 279.955 (2)s 9 f 264.5 y 284.705 (t)s 7 f 259.545 y 288.948 (2)s 267.466 y 288.948 (3)s 3 f 264.5 y 293.698 (\051)s 13 f 259.545 y 298.268 (\241)s 7 f 304.879 (1)s 10 f 309.129 (=)s 7 f 313.379 (2)s 9 f 264.5 y 322.046 (:)s 3 f 437.016 (\050103\051)s 294.035 y 26.161 (The)s 50.541 (Euler-Lagrange)s 133.339 (equations)s 186.18 (\05039\051)s 211.213 (corresp)s 248.159 (onding)s 286.9 (to)s 301.488 (mo)s 317.481 (di\257ed)s 349.694 (Lagrangian)s 12 f 411.443 (L)s 10 f 289.681 y 419.72 (M)s 3 f 294.035 y 429.235 (\050)s 9 f 433.805 (x)s 10 f 295.835 y 440.482 (i)s 9 f 294.035 y 443.876 (;)s 3 f 451.173 (\137)s 9 f 449.14 (x)s 10 f 295.835 y 455.817 (i)s 3 f 294.035 y 459.211 (\051)s 308.535 y 8.536 (giv)s 23.55 (en)s 39.216 (b)s 45.417 (y)s 55.535 (\050101\051)s 86.216 (read:)s 334.046 y 96.43 (d)s 12.971 .4 93.208 339.364 r 350.395 y 93.208 (d)s 9 f 99.736 (\277)s 3 f 342.164 y 107.379 (\050)s 9 f 111.948 (A)s 13 f 337.209 y 120.757 (\241)s 7 f 127.368 (2)s 3 f 342.164 y 134.151 (\137)s 9 f 132.118 (x)s 7 f 343.964 y 138.795 (1)s 3 f 342.164 y 143.545 (\051)s 12 f 150.781 (\241)s 7 f 337.439 y 163.981 (1)s 4.25 .4 163.981 339.364 r 346.302 y 163.981 (2)s 0 f 327.564 y 169.431 (\265)s 9 f 334.046 y 177.992 (@)s 184.848 (A)s 13 f 329.691 y 193.656 (\241)s 7 f 200.267 (2)s 27.025 .4 177.992 339.364 r 9 f 350.395 y 182.363 (@)s 189.219 (x)s 7 f 352.195 y 195.896 (1)s 3 f 342.164 y 208.25 (\137)s 9 f 206.217 (x)s 7 f 337.209 y 212.894 (2)s 345.13 y 212.894 (1)s 3 f 342.164 y 220.311 (+)s 9 f 334.046 y 233.316 (@)s 240.172 (B)s 13 f 329.691 y 249.704 (\241)s 7 f 256.315 (2)s 27.749 .4 233.316 339.364 r 9 f 350.395 y 238.049 (@)s 244.905 (x)s 7 f 352.195 y 251.582 (1)s 3 f 342.164 y 264.298 (\137)s 9 f 262.265 (x)s 7 f 337.209 y 268.942 (2)s 345.13 y 268.942 (2)s 3 f 342.164 y 276.359 (+)s 9 f 334.046 y 289.364 (@)s 296.219 (C)s 13 f 329.691 y 305.488 (\241)s 7 f 312.099 (2)s 27.485 .4 289.364 339.364 r 9 f 350.395 y 293.965 (@)s 300.821 (x)s 7 f 352.195 y 307.498 (1)s 3 f 342.164 y 320.082 (\137)s 9 f 318.049 (x)s 7 f 337.209 y 324.726 (2)s 345.13 y 324.726 (3)s 0 f 327.564 y 329.476 (\266)s 3 f 342.164 y 346.837 (=)s 365.976 (0)s 9 f 375.768 (;)s 3 f 365.706 y 95.706 (d)s 12.971 .4 92.485 371.024 r 382.055 y 92.485 (d)s 9 f 99.012 (\277)s 3 f 373.824 y 106.655 (\050)s 9 f 111.225 (B)s 13 f 368.869 y 120.757 (\241)s 7 f 127.368 (2)s 3 f 373.824 y 134.151 (\137)s 9 f 132.118 (x)s 7 f 375.624 y 138.795 (2)s 3 f 373.824 y 143.545 (\051)s 12 f 150.781 (\241)s 7 f 369.099 y 163.981 (1)s 4.25 .4 163.981 371.024 r 377.962 y 163.981 (2)s 0 f 359.223 y 169.431 (\265)s 9 f 365.706 y 177.992 (@)s 184.848 (A)s 13 f 361.351 y 193.656 (\241)s 7 f 200.267 (2)s 27.025 .4 177.992 371.024 r 9 f 382.055 y 182.363 (@)s 189.219 (x)s 7 f 383.855 y 195.896 (2)s 3 f 373.824 y 208.25 (\137)s 9 f 206.217 (x)s 7 f 368.869 y 212.894 (2)s 376.79 y 212.894 (1)s 3 f 373.824 y 220.311 (+)s 9 f 365.706 y 233.316 (@)s 240.172 (B)s 13 f 361.351 y 249.704 (\241)s 7 f 256.315 (2)s 27.749 .4 233.316 371.024 r 9 f 382.055 y 238.049 (@)s 244.905 (x)s 7 f 383.855 y 251.582 (2)s 3 f 373.824 y 264.298 (\137)s 9 f 262.265 (x)s 7 f 368.869 y 268.942 (2)s 376.79 y 268.942 (2)s 3 f 373.824 y 276.359 (+)s 9 f 365.706 y 289.364 (@)s 296.219 (C)s 13 f 361.351 y 305.488 (\241)s 7 f 312.099 (2)s 27.485 .4 289.364 371.024 r 9 f 382.055 y 293.965 (@)s 300.821 (x)s 7 f 383.855 y 307.498 (2)s 3 f 373.824 y 320.082 (\137)s 9 f 318.049 (x)s 7 f 368.869 y 324.726 (2)s 376.79 y 324.726 (3)s 0 f 359.223 y 329.476 (\266)s 3 f 373.824 y 346.837 (=)s 365.976 (0)s 9 f 375.768 (;)s 3 f 437.016 (\050104\051)s 397.365 y 95.97 (d)s 12.971 .4 92.748 402.683 r 413.715 y 92.748 (d)s 9 f 99.276 (\277)s 3 f 405.483 y 106.919 (\050)s 9 f 111.488 (C)s 13 f 400.529 y 120.757 (\241)s 7 f 127.368 (2)s 3 f 405.483 y 134.151 (\137)s 9 f 132.118 (x)s 7 f 407.283 y 138.795 (3)s 3 f 405.483 y 143.545 (\051)s 12 f 150.781 (\241)s 7 f 400.759 y 163.981 (1)s 4.25 .4 163.981 402.683 r 409.621 y 163.981 (2)s 0 f 390.883 y 169.431 (\265)s 9 f 397.365 y 177.992 (@)s 184.848 (A)s 13 f 393.011 y 193.656 (\241)s 7 f 200.267 (2)s 27.025 .4 177.992 402.683 r 9 f 413.715 y 182.363 (@)s 189.219 (x)s 7 f 415.515 y 195.896 (3)s 3 f 405.483 y 208.25 (\137)s 9 f 206.217 (x)s 7 f 400.529 y 212.894 (2)s 408.45 y 212.894 (1)s 3 f 405.483 y 220.311 (+)s 9 f 397.365 y 233.316 (@)s 240.172 (B)s 13 f 393.011 y 249.704 (\241)s 7 f 256.315 (2)s 27.749 .4 233.316 402.683 r 9 f 413.715 y 238.049 (@)s 244.905 (x)s 7 f 415.515 y 251.582 (3)s 3 f 405.483 y 264.298 (\137)s 9 f 262.265 (x)s 7 f 400.529 y 268.942 (2)s 408.45 y 268.942 (2)s 3 f 405.483 y 276.359 (+)s 9 f 397.365 y 289.364 (@)s 296.219 (C)s 13 f 393.011 y 305.488 (\241)s 7 f 312.099 (2)s 27.485 .4 289.364 402.683 r 9 f 413.715 y 293.965 (@)s 300.821 (x)s 7 f 415.515 y 307.498 (3)s 3 f 405.483 y 320.082 (\137)s 9 f 318.049 (x)s 7 f 400.529 y 324.726 (2)s 408.45 y 324.726 (3)s 0 f 390.883 y 329.476 (\266)s 3 f 405.483 y 346.837 (=)s 365.976 (0)s 9 f 375.768 (:)s 3 f 437.515 y 8.536 (W)s 19.629 (e)s 28.751 (can)s 50.276 (see)s 69.255 (that)s 94.696 (Lagrangian)s 156.201 (ra)s 166.319 (y)s 176.42 (tracing)s 216.223 (system)s 255.177 (\050104\051)s 285.84 (also)s 309.389 (follo)s 330.93 (ws)s 347.951 (directly)s 390.691 (from)s 418.417 (Hamilto-)s 452.015 y 8.536 (nian)s 34.647 (ra)s 44.765 (y)s 54.883 (tracing)s 94.702 (system)s 133.672 (\05098\051,)s 161.741 (if)s 172.512 (w)s 180.672 (e)s 189.81 (use)s 210.112 (\050100\051.)s 475.051 y 26.161 (Note)s 54.081 (that)s 79.069 (mo)s 95.062 (di\257ed)s 126.577 (Lagrangian)s 187.628 (\050101\051)s 217.837 (can)s 238.908 (also)s 262.002 (b)s 268.856 (e)s 277.525 (obtained)s 325.359 (from)s 352.631 (mo)s 368.624 (di\257ed)s 400.139 (Hamiltonian)s 489.551 y 8.536 (\05094\051)s 32.535 (in)s 45.436 (a)s 54.421 (more)s 82.99 (straigh)s 117.978 (tforw)s 144.742 (ard)s 164.824 (w)s 172.984 (a)s 178.532 (y)s 183.754 (,)s 190.289 (using)s 220.228 (the)s 239.658 (w)s 247.818 (a)s 253.366 (v)s 259.241 (e)s 267.573 (propagation)s 332.044 (metric)s 367.793 (tensor.)s 407.408 (Using)s 439.628 (\05053\051,)s 504.051 y 8.536 (w)s 16.696 (e)s 25.834 (obtain)s 62.39 (from)s 90.132 (\05094\051)s 114.938 (for)s 9 f 132.889 (g)s 10 f 499.696 y 138.946 (ij)s 3 f 504.051 y 149.571 (=)s 6.057 .4 162.044 497.684 r 9 f 504.051 y 162.044 (g)s 10 f 499.696 y 169.517 (ij)s 3 f 504.051 y 176.81 (,)s 9 f 544.801 y 162.311 (g)s 10 f 539.846 y 168.368 (ij)s 3 f 544.801 y 178.994 (=)s 0 f 521.2 y 191.466 (0)s 538.801 y 191.466 (B)s 545.201 y 191.466 (@)s 9 f 530.201 y 205.216 (A)s 7 f 525.846 y 214.024 (2)s 3 f 530.201 y 228.774 (0)s 253.056 (0)s 544.701 y 205.216 (0)s 9 f 228.774 (B)s 7 f 540.346 y 238.306 (2)s 3 f 544.701 y 253.056 (0)s 559.201 y 205.216 (0)s 228.774 (0)s 9 f 253.056 (C)s 7 f 554.846 y 262.324 (2)s 0 f 521.2 y 272.074 (1)s 538.801 y 272.074 (C)s 545.201 y 272.074 (A)s 9 f 544.801 y 286.741 (:)s 3 f 585.551 y 8.536 (This)s 35.365 (yields,)s 71.659 (see)s 90.654 (\05055\051,)s 9 f 626.301 y 152.61 (g)s 10 f 628.101 y 158.236 (ij)s 3 f 626.301 y 168.862 (=)s 0 f 602.7 y 181.334 (0)s 620.301 y 181.334 (B)s 626.701 y 181.334 (@)s 9 f 611.701 y 195.084 (A)s 13 f 607.346 y 203.892 (\241)s 7 f 210.503 (2)s 3 f 611.701 y 225.253 (0)s 256.146 (0)s 626.201 y 195.084 (0)s 9 f 225.253 (B)s 13 f 621.846 y 234.785 (\241)s 7 f 241.396 (2)s 3 f 626.201 y 256.146 (0)s 640.701 y 195.084 (0)s 225.253 (0)s 9 f 256.146 (C)s 13 f 636.346 y 265.415 (\241)s 7 f 272.026 (2)s 0 f 602.7 y 281.776 (1)s 620.301 y 281.776 (C)s 626.701 y 281.776 (A)s 9 f 626.301 y 296.443 (:)s 3 f 667.051 y 8.536 (The)s 32.688 (mo)s 48.681 (di\257ed)s 80.667 (Lagrangian)s 142.189 (is)s 154.004 (then)s 180.767 (giv)s 195.781 (en)s 211.448 (b)s 217.649 (y)s 227.767 (\05035\051)s 252.572 (and)s 275.419 (yields)s 308.449 (\050101\051.)s 735.628 y 227.346 (229)s do-end end endp showpage %%Page: 20 20 %%BeginPageSetup initializepage (drahotova; page: 20 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f222 sf ( )S -983 -1000 :M f258 sf ( )S f296 sf ( )S -972 -1000 :M f333 sf ( )S -964 -1000 :M f371 sf ( )S -952 -1000 :M f446 sf ( )S -939 -1000 :M f222 sf ( )S -935 -1000 :M f484 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 15 17.28 /CMBX12 findfont fdef 16 12 /CMTI12 findfont fdef 58 49 translate 72 72.27 div dup scale 15 f 3.464 y 8.536 (4)s 37.696 (Reduced)s 117.456 (Lagrangians)s 226.014 (and)s 263.544 (Hamiltonians)s 3 f 38.383 y 8.536 (The)s 33.092 (next)s 59.934 (p)s 66.788 (ossibilit)s 105.758 (y)s 116.28 (of)s 130.066 (o)s 135.615 (v)s 141.49 (ercoming)s 192.157 (the)s 212.797 (di\261culties)s 269.405 (connected)s 324.641 (with)s 351.809 (the)s 372.449 (v)s 377.998 (anishing)s 424.814 (Hessian)s 52.883 y 8.536 (determinan)s 66.306 (t)s 74.802 (consists)s 118.09 (in)s 131.808 (in)s 141.273 (tro)s 156.613 (ducing)s 194.484 (reduced)s 238.229 (Lagrangians)s 304.395 (and)s 327.251 (Hamiltonians.)s 404.042 (They)s 434.405 (corre-)s 67.383 y 8.536 (sp)s 20.025 (ond)s 42.872 (to)s 57.233 (the)s 77.469 (sp)s 88.957 (ecial)s 115.721 (c)s 120.617 (hoice)s 150.644 (of)s 164.026 (parameter)s 9 f 220.164 (u)s 3 f 226.852 (,)s 234.032 (namely)s 9 f 274.83 (u)s 3 f 284.851 (=)s 9 f 297.323 (x)s 7 f 63.028 y 304 (1)s 3 f 67.383 y 308.75 (,)s 9 f 315.931 (u)s 3 f 325.951 (=)s 9 f 338.423 (x)s 7 f 63.028 y 345.101 (2)s 3 f 67.383 y 353.767 (or)s 9 f 368.128 (u)s 3 f 378.149 (=)s 9 f 390.621 (x)s 7 f 63.028 y 397.298 (3)s 3 f 67.383 y 402.048 (.)s 90.419 y 26.161 (Consider)s 75.184 (\257rst)s 99.402 (the)s 119.638 (general)s 160.109 (parameteric)s 224.734 (F)s 231.422 (ermat\047s)s 273.265 (v)s 278.814 (ariational)s 331.688 (principle)s 379.993 (\05022\051,)s 9 f 119.492 y 128.947 (\261)s 0 f 105.381 y 136.601 (Z)s 10 f 108.548 y 146.601 (R)s 128.103 y 142.156 (S)s 12 f 119.492 y 155.552 (L)s 3 f 163.829 (\050)s 9 f 168.398 (x)s 10 f 114.537 y 175.075 (k)s 9 f 119.492 y 180.214 (;)s 185.478 (x)s 10 f 114.537 y 192.155 (k)s 13 f 197.294 (0)s 3 f 119.492 y 200.1 (\051d)s 9 f 211.197 (u)s 3 f 221.217 (=)s 233.69 (0)s 9 f 243.481 (;)s 268.328 (x)s 10 f 114.537 y 275.005 (k)s 13 f 280.144 (0)s 3 f 119.492 y 286.283 (=)s 298.755 (d)s 9 f 305.283 (x)s 10 f 114.537 y 311.96 (k)s 9 f 119.492 y 317.099 (=)s 3 f 322.974 (d)s 9 f 329.501 (u)s 340.105 (:)s 3 f 437.016 (\050105\051)s 147.276 y 8.536 (This)s 36.385 (principle)s 85.711 (can)s 108.273 (b)s 115.127 (e)s 125.286 (used)s 153.135 (for)s 172.107 (an)s 184.183 (y)s 195.322 (parameter)s 9 f 252.48 (u)s 3 f 259.168 (,)s 267.624 (including)s 9 f 319.56 (u)s 3 f 331.318 (=)s 9 f 345.527 (x)s 7 f 142.921 y 352.204 (1)s 3 f 147.276 y 356.954 (,)s 9 f 365.41 (u)s 3 f 377.168 (=)s 9 f 391.377 (x)s 7 f 142.921 y 398.054 (2)s 3 f 147.276 y 407.741 (or)s 9 f 423.122 (u)s 3 f 434.88 (=)s 9 f 449.089 (x)s 7 f 142.921 y 455.766 (3)s 3 f 147.276 y 460.516 (.)s 161.776 y 8.536 (The)s 32.583 (Euler-Lagrange)s 115.05 (equations)s 167.558 (corresp)s 204.505 (onding)s 242.913 (to)s 257.169 (\050105\051)s 287.744 (are)s 307.222 (giv)s 322.236 (en)s 337.798 (b)s 343.999 (y)s 354.012 (\05023\051.)s 383.351 (It)s 395.971 (w)s 404.131 (as)s 418.452 (sho)s 435.163 (wn)s 453.988 (in)s 176.276 y 8.536 (Section)s 49.859 (2)s 59.849 (that,)s 88.819 (in)s 102.726 (this)s 125.837 (case,)s 154.22 (Lagrangian)s 12 f 215.94 (L)s 3 f 224.217 (\050)s 9 f 228.786 (x)s 10 f 171.921 y 235.463 (k)s 9 f 176.276 y 240.602 (;)s 245.866 (x)s 10 f 171.921 y 252.543 (k)s 13 f 257.682 (0)s 3 f 176.276 y 260.488 (\051)s 269.172 (is)s 281.186 (a)s 291.176 (homogeneous)s 363.245 (function)s 409.464 (of)s 423.044 (the)s 443.479 (\257rst)s 190.776 y 8.536 (degree)s 45.336 (in)s 9 f 59.289 (x)s 10 f 186.421 y 65.966 (i)s 13 f 69.36 (0)s 3 f 190.776 y 76.327 (and)s 99.419 (that)s 125.122 (the)s 145.603 (corresp)s 182.549 (onding)s 221.308 (Hamiltonian)s 12 f 289.11 (H)s 3 f 299.36 (\050)s 9 f 303.93 (x)s 10 f 186.421 y 310.607 (k)s 9 f 190.776 y 315.746 (;)s 321.01 (p)s 10 f 192.576 y 326.907 (k)s 3 f 190.776 y 332.046 (\051)s 340.777 (v)s 346.325 (anishes,)s 12 f 390.497 (H)s 3 f 400.748 (\050)s 9 f 405.317 (x)s 10 f 186.421 y 411.994 (k)s 9 f 190.776 y 417.133 (;)s 422.397 (p)s 10 f 192.576 y 428.294 (k)s 3 f 190.776 y 433.433 (\051)s 441.752 (=)s 454.641 (0,)s 205.276 y 8.536 (see)s 27.532 (\05030\051.)s 56.906 (W)s 67.999 (e)s 77.138 (also)s 100.703 (ha)s 112.779 (v)s 118.654 (e)s 9 f 234.389 y 89.299 (p)s 10 f 236.189 y 95.196 (i)s 3 f 234.389 y 101.923 (=)s 9 f 226.271 y 117.895 (@)s 12 f 124.751 (L)s 19.732 .4 115.595 231.589 r 9 f 242.621 y 115.595 (@)s 122.451 (x)s 10 f 239.154 y 129.128 (i)s 13 f 132.522 (0)s 9 f 234.389 y 140.444 (;)s 157.458 (x)s 10 f 229.434 y 164.135 (i)s 13 f 167.529 (0)s 3 f 234.389 y 173.667 (=)s 9 f 226.271 y 187.34 (@)s 12 f 194.195 (H)s 17.106 .4 187.34 231.589 r 9 f 242.621 y 187.819 (@)s 194.674 (p)s 10 f 244.421 y 200.572 (i)s 9 f 234.389 y 209.562 (;)s 12 f 226.575 (H)s 3 f 236.825 (\050)s 9 f 241.395 (x)s 10 f 229.434 y 248.072 (k)s 9 f 234.389 y 253.211 (;)s 258.475 (p)s 10 f 236.189 y 264.372 (k)s 3 f 234.389 y 269.511 (\051)s 277.413 (=)s 9 f 289.886 (x)s 10 f 229.434 y 296.563 (i)s 13 f 299.956 (0)s 9 f 234.389 y 302.762 (p)s 10 f 236.189 y 308.659 (i)s 12 f 234.389 y 314.72 (\241)s 326.72 (L)s 3 f 334.996 (\050)s 9 f 339.566 (x)s 10 f 229.434 y 346.243 (k)s 9 f 234.389 y 351.382 (;)s 356.646 (x)s 10 f 229.434 y 363.323 (k)s 13 f 368.462 (0)s 3 f 234.389 y 371.267 (\051)s 9 f 379.753 (:)s 3 f 437.016 (\050106\051)s 6 f 280.789 y 8.536 (4.1)s 45.436 (Legendre)s 115.461 (transform)s 190.209 (for)s 215.276 (reduced)s 276.276 (Lagrangians)s 298.789 y 45.436 (and)s 76.711 (Hamiltonians)s 3 f 329.575 y 8.536 (Assume)s 53.139 (no)s 65.215 (w)s 78.685 (that)s 9 f 105.21 (u)s 3 f 117.048 (=)s 9 f 131.336 (x)s 7 f 325.22 y 138.013 (3)s 3 f 329.575 y 142.764 (.)s 154.451 (Then)s 12 f 186.199 (L)s 3 f 194.476 (\050)s 9 f 199.045 (x)s 10 f 325.22 y 205.722 (k)s 9 f 329.575 y 210.861 (;)s 216.125 (x)s 10 f 325.22 y 222.802 (k)s 13 f 227.941 (0)s 3 f 329.575 y 230.746 (\051)s 240.466 (=)s 12 f 254.754 (L)s 10 f 325.22 y 263.031 (R)s 3 f 329.575 y 269.983 (\050)s 9 f 274.552 (x)s 10 f 325.22 y 281.229 (k)s 9 f 329.575 y 286.368 (;)s 291.632 (x)s 10 f 325.22 y 298.309 (K)s 13 f 306.542 (0)s 3 f 329.575 y 309.348 (\051,)s 322.432 (where)s 9 f 357.443 (x)s 10 f 325.22 y 364.12 (K)s 13 f 372.354 (0)s 3 f 329.575 y 380.309 (=)s 394.598 (d)s 9 f 401.126 (x)s 10 f 325.22 y 407.803 (K)s 9 f 329.575 y 416.036 (=)s 3 f 421.911 (d)s 9 f 428.439 (x)s 7 f 325.22 y 435.116 (3)s 3 f 329.575 y 444.85 (and)s 9 f 344.075 y 8.536 (K)s 3 f 22.927 (=)s 35.598 (1)s 9 f 41.473 (;)s 3 f 46.736 (2.)s 61.448 (Lagrangian)s 12 f 123.087 (L)s 10 f 339.72 y 131.364 (R)s 3 f 344.075 y 142.349 (is)s 154.281 (no)s 170.717 (longer)s 206.084 (a)s 215.992 (homogeneous)s 287.979 (function)s 334.116 (of)s 347.615 (the)s 367.968 (\257rst)s 392.303 (degree)s 428.975 (in)s 9 f 442.8 (x)s 10 f 339.72 y 449.477 (K)s 13 f 457.711 (0)s 3 f 344.075 y 460.516 (.)s 358.575 y 8.536 (The)s 32.688 (Euler-Lagrange)s 115.26 (equations)s 167.873 (for)s 185.824 (the)s 206.06 (Lagrangian)s 12 f 267.582 (L)s 10 f 354.22 y 275.859 (R)s 3 f 358.575 y 282.81 (\050)s 9 f 287.379 (x)s 10 f 354.22 y 294.056 (k)s 9 f 358.575 y 299.195 (;)s 304.459 (x)s 10 f 354.22 y 311.136 (K)s 13 f 319.37 (0)s 3 f 358.575 y 322.175 (\051)s 330.661 (are)s 350.244 (as)s 364.671 (follo)s 386.212 (ws:)s 381.058 y 145.431 (d)s 17.955 .4 139.718 386.376 r 397.408 y 139.718 (d)s 9 f 146.246 (x)s 7 f 393.941 y 152.923 (3)s 0 f 374.576 y 158.873 (\265)s 9 f 381.058 y 167.434 (@)s 12 f 174.289 (L)s 10 f 376.703 y 182.566 (R)s 22.084 .4 167.434 386.376 r 9 f 397.408 y 167.902 (@)s 174.757 (x)s 10 f 393.941 y 181.434 (I)s 13 f 186.244 (0)s 0 f 374.576 y 190.718 (\266)s 12 f 389.176 y 200.745 (\241)s 9 f 381.058 y 213.945 (@)s 12 f 220.801 (L)s 10 f 376.703 y 229.077 (R)s 22.084 .4 213.945 386.376 r 9 f 397.408 y 215.816 (@)s 222.671 (x)s 10 f 393.941 y 229.348 (I)s 3 f 389.176 y 240.562 (=)s 253.034 (0)s 9 f 262.826 (;)s 287.673 (I)s 3 f 297.132 (=)s 309.604 (1)s 9 f 315.479 (;)s 3 f 320.743 (2)s 9 f 330.534 (:)s 3 f 437.016 (\050107\051)s 416.838 y 8.536 (Th)s 23.223 (us,)s 40.867 (\050107\051)s 70.674 (consists)s 113.079 (of)s 125.588 (t)s 129.831 (w)s 137.99 (o)s 146.909 (ordinary)s 193.361 (di\256eren)s 231.222 (tial)s 251.237 (equations)s 302.977 (of)s 315.485 (the)s 334.848 (second)s 371.9 (order,)s 405.146 (not)s 425.161 (of)s 437.669 (three)s 431.338 y 8.536 (as)s 22.962 (\05023\051.)s 454.374 y 26.161 (Using,)s 62.451 (\050106\051,)s 96.395 (w)s 104.554 (e)s 113.693 (also)s 137.258 (obtain)s 9 f 173.813 (x)s 7 f 450.02 y 180.49 (3)s 13 f 185.24 (0)s 3 f 454.374 y 191.379 (=)s 9 f 203.851 (@)s 12 f 210.707 (H)s 9 f 220.957 (=@)s 233.687 (p)s 7 f 456.174 y 239.584 (3)s 3 f 454.374 y 247.668 (=)s 260.14 (1,)s 273.195 (as)s 9 f 287.622 (x)s 7 f 450.02 y 294.299 (3)s 13 f 299.049 (0)s 3 f 454.374 y 305.187 (=)s 317.66 (d)s 9 f 324.187 (x)s 7 f 450.02 y 330.864 (3)s 9 f 454.374 y 335.614 (=)s 3 f 341.489 (d)s 9 f 348.017 (x)s 7 f 450.02 y 354.694 (3)s 3 f 454.374 y 359.444 (.)s 367.93 (This)s 394.759 (yields,)s 12 f 477.536 y 148.738 (H)s 3 f 158.988 (\050)s 9 f 163.557 (x)s 10 f 472.582 y 170.234 (k)s 9 f 477.536 y 175.373 (;)s 180.637 (p)s 10 f 479.336 y 186.534 (k)s 3 f 477.536 y 191.673 (\051)s 199.576 (=)s 9 f 212.048 (p)s 7 f 479.336 y 217.945 (3)s 3 f 477.536 y 225.361 (+)s 12 f 237.167 (H)s 10 f 472.582 y 247.417 (R)s 3 f 477.536 y 254.368 (\050)s 9 f 258.938 (x)s 10 f 472.582 y 265.615 (k)s 9 f 477.536 y 270.754 (;)s 276.018 (p)s 10 f 479.336 y 281.915 (K)s 3 f 477.536 y 290.148 (\051)s 298.051 (=)s 310.523 (0)s 9 f 320.315 (:)s 3 f 437.016 (\050108\051)s 500.698 y 8.536 (W)s 19.629 (e)s 29.864 (shall)s 58.442 (call)s 12 f 81.08 (H)s 10 f 496.344 y 91.331 (R)s 3 f 500.698 y 98.282 (\050)s 9 f 102.851 (x)s 10 f 496.344 y 109.528 (k)s 9 f 500.698 y 114.667 (;)s 119.931 (p)s 10 f 502.498 y 125.828 (K)s 3 f 500.698 y 134.062 (\051)s 143.644 (the)s 16 f 164.977 (r)s 169.327 (e)s 174.127 (duc)s 191.227 (e)s 196.027 (d)s 207.235 (Hamiltonian)s 3 f 270.858 (.)s 282.634 (Using)s 316.756 (\050108\051,)s 9 f 352.071 (p)s 7 f 502.498 y 357.968 (3)s 3 f 500.698 y 367.732 (is)s 380.643 (obtained)s 430.045 (b)s 436.246 (y)s 447.461 (the)s 515.198 y 8.536 (equation)s 9 f 529.698 y 185.899 (p)s 7 f 531.498 y 191.797 (3)s 3 f 529.698 y 199.88 (=)s 12 f 212.352 (\241H)s 10 f 524.744 y 231.935 (R)s 3 f 529.698 y 238.887 (\050)s 9 f 243.456 (x)s 10 f 524.744 y 250.133 (k)s 9 f 529.698 y 255.272 (;)s 260.536 (p)s 10 f 531.498 y 266.433 (K)s 3 f 529.698 y 274.667 (\051)s 9 f 283.153 (:)s 3 f 437.016 (\050109\051)s 549.268 y 8.536 (This)s 34.657 (equation)s 81.928 (represen)s 124.097 (ts)s 136.509 (an)s 152.121 (explicit)s 192.864 (equation)s 240.134 (of)s 252.808 (the)s 272.336 (slo)s 285.783 (wness)s 318.497 (surface.)s 362.389 (The)s 385.833 (reduced)s 428.861 (Hamil-)s 563.768 y 8.536 (tonian)s 46.967 (is)s 60.659 (obtained)s 110.84 (from)s 140.459 (equation)s 12 f 190.314 (H)s 3 f 200.564 (\050)s 9 f 205.133 (x)s 10 f 565.568 y 211.81 (k)s 9 f 563.768 y 216.949 (;)s 222.213 (p)s 10 f 565.568 y 228.11 (k)s 3 f 563.768 y 233.249 (\051)s 244.345 (=)s 7 f 559.043 y 261.211 (1)s 4.25 .4 261.211 560.968 r 567.906 y 261.211 (2)s 3 f 563.768 y 272.454 (b)s 278.655 (y)s 290.649 (solving)s 332.084 (it)s 345.71 (for)s 9 f 365.537 (p)s 7 f 565.568 y 371.434 (3)s 3 f 563.768 y 376.184 (.)s 390.299 (In)s 406.858 (seismology)s 460.516 (,)s 578.268 y 8.536 (this)s 32.998 (is)s 46.363 (a)s 57.705 (w)s 65.864 (ell-kno)s 99.808 (wn)s 120.289 (pro)s 137.587 (cedure,)s 179.996 (ev)s 191.093 (en)s 208.31 (in)s 223.568 (anisotropic)s 285.238 (media,)s 325.036 (as)s 341.012 (it)s 354.312 (is)s 367.677 (used)s 396.056 (in)s 411.314 (the)s 433.1 (re\260)s 449.419 (ec-)s 592.768 y 8.536 (tion/transmission)s 102.731 (problem)s 148.425 (and)s 171.272 (in)s 184.98 (one-w)s 214.681 (a)s 220.23 (y)s 230.347 (propagation.)s 300.194 (See)s 589.735 y 322.388 (\267)s 592.768 y 321.083 (Cerv)s 345.235 (en)s 357.148 (\266)s 356.985 (y)s 367.103 (\0502001a\051.)s 615.804 y 26.161 (As)s 9 f 43.869 (p)s 10 f 617.604 y 49.766 (i)s 3 f 615.804 y 57.088 (=)s 9 f 70.154 (@)s 77.009 (T)s 85.201 (=@)s 97.932 (x)s 10 f 611.449 y 104.609 (i)s 3 f 615.804 y 108.003 (,)s 115.619 (Equation)s 166.719 (\050109\051)s 197.748 (represen)s 239.917 (ts)s 253.387 (a)s 263.528 (partial)s 301.737 (di\256eren)s 339.598 (tial)s 360.836 (equation)s 409.163 (of)s 422.894 (the)s 443.479 (\257rst)s 630.304 y 8.536 (order)s 39.216 (for)s 9 f 57.167 (T)s 3 f 69.019 (=)s 9 f 81.491 (T)s 3 f 90.01 (\050)s 9 f 94.579 (x)s 10 f 625.949 y 101.256 (i)s 3 f 630.304 y 104.65 (\051,)s 9 f 653.466 y 91.459 (@)s 98.314 (T)s 106.506 (=@)s 119.237 (x)s 7 f 648.511 y 125.914 (3)s 3 f 653.466 y 133.997 (=)s 12 f 146.469 (\241H)s 10 f 648.511 y 166.053 (R)s 3 f 653.466 y 173.004 (\050)s 9 f 177.574 (x)s 10 f 648.511 y 184.251 (k)s 9 f 653.466 y 189.39 (;)s 3 f 194.653 (d)s 9 f 201.181 (T)s 209.373 (=@)s 222.104 (x)s 10 f 648.511 y 228.781 (K)s 3 f 653.466 y 237.014 (\051)s 9 f 245.5 (;)s 262.514 (K)s 3 f 276.706 (=)s 289.178 (1)s 9 f 295.053 (;)s 3 f 300.316 (2)s 9 f 310.108 (;)s 323.205 (k)s 3 f 333.052 (=)s 345.524 (1)s 9 f 351.399 (;)s 3 f 356.663 (2)s 9 f 362.538 (;)s 3 f 367.802 (3)s 9 f 377.593 (:)s 3 f 676.628 y 8.536 (This)s 34.616 (equation)s 81.845 (is)s 92.911 (usually)s 132.372 (called)s 164.914 (the)s 184.401 (ev)s 195.172 (alution)s 234.241 (Hamilton-Jacobi)s 322.099 (equation.)s 374.398 (Actually)s 417.15 (,)s 423.731 (the)s 443.218 (ev)s 453.988 (a-)s 691.128 y 8.536 (lution)s 42.968 (Hamilton-Jacobi)s 132.062 (equation)s 180.529 (is)s 192.831 (obtained)s 241.624 (from)s 269.854 (the)s 290.578 (stationary)s 346.942 (Hamilton-Jacobi)s 436.037 (equa-)s 705.628 y 8.536 (tion)s 12 f 32.688 (H)s 3 f 42.938 (\050)s 9 f 47.508 (x)s 10 f 701.273 y 54.185 (k)s 9 f 705.628 y 59.324 (;)s 64.588 (p)s 10 f 707.428 y 70.485 (k)s 3 f 705.628 y 75.624 (\051)s 83.526 (=)s 7 f 700.903 y 97.199 (1)s 4.25 .4 97.199 702.828 r 709.766 y 97.199 (2)s 3 f 705.628 y 106.565 (as)s 120.991 (its)s 137.376 (one-w)s 167.077 (a)s 172.626 (y)s 182.744 (alternativ)s 232.354 (e;)s 244.757 (sp)s 256.246 (ecifying)s 9 f 299.329 (u)s 3 f 309.349 (=)s 9 f 321.821 (x)s 7 f 701.273 y 328.498 (3)s 3 f 705.628 y 337.165 (and)s 360.012 (solving)s 399.57 (it)s 411.32 (for)s 9 f 429.271 (p)s 7 f 707.428 y 435.168 (3)s 3 f 705.628 y 439.918 (.)s 735.628 y 227.346 (230)s do-end end endp showpage %%Page: 21 21 %%BeginPageSetup initializepage (drahotova; page: 21 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f184 sf -.651( )A f222 sf ( )S -993 -1000 :M ( )S -989 -1000 :M f258 sf ( )S f296 sf ( )S -978 -1000 :M f333 sf ( )S -970 -1000 :M f371 sf ( )S -958 -1000 :M f446 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 12 /CMR12 findfont fdef 4 12 /CMBX12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 26.161 (Equations)s 81.546 (\050106\051)s 112.227 (simplify)s 156.68 (for)s 9 f 174.631 (u)s 3 f 184.652 (=)s 9 f 197.124 (x)s 7 f 5.264 y 203.801 (3)s 3 f 3.464 y 212.468 (as)s 226.894 (follo)s 248.436 (ws:)s 9 f 37.403 y 75.686 (p)s 10 f 39.203 y 81.584 (I)s 3 f 37.403 y 89.727 (=)s 9 f 29.285 y 103.399 (@)s 12 f 110.254 (L)s 10 f 24.93 y 118.531 (R)s 22.084 .4 103.399 34.603 r 9 f 45.635 y 103.867 (@)s 110.722 (x)s 10 f 42.168 y 117.399 (I)s 13 f 122.209 (0)s 9 f 37.403 y 130.599 (;)s 143.696 (x)s 10 f 32.448 y 150.373 (I)s 13 f 155.183 (0)s 3 f 37.403 y 161.322 (=)s 9 f 29.285 y 174.994 (@)s 12 f 181.849 (H)s 10 f 24.93 y 192.099 (R)s 24.057 .4 174.994 34.603 r 9 f 45.635 y 178.241 (@)s 185.096 (p)s 10 f 47.435 y 190.994 (I)s 9 f 37.403 y 204.167 (;)s 12 f 217.264 (H)s 10 f 32.448 y 227.514 (R)s 3 f 37.403 y 234.466 (\050)s 9 f 239.035 (x)s 10 f 32.448 y 245.712 (k)s 9 f 37.403 y 250.851 (;)s 256.115 (p)s 10 f 39.203 y 262.012 (K)s 3 f 37.403 y 270.246 (\051)s 278.148 (=)s 9 f 290.62 (x)s 10 f 32.448 y 297.297 (I)s 13 f 302.107 (0)s 9 f 37.403 y 304.913 (p)s 10 f 39.203 y 310.81 (I)s 12 f 37.403 y 318.286 (\241)s 330.286 (L)s 10 f 32.448 y 338.563 (R)s 3 f 37.403 y 345.514 (\050)s 9 f 350.084 (x)s 10 f 32.448 y 356.761 (k)s 9 f 37.403 y 361.9 (;)s 367.164 (x)s 10 f 32.448 y 373.841 (K)s 13 f 382.074 (0)s 3 f 37.403 y 384.88 (\051)s 9 f 393.366 (:)s 3 f 437.016 (\050110\051)s 69.301 y 8.536 (Th)s 23.223 (us,)s 41.566 (the)s 61.802 (problem)s 107.496 (reduces)s 149.339 (from)s 177.081 (three)s 207.109 (dimensions)s 267.294 (to)s 281.655 (t)s 285.898 (w)s 294.058 (o)s 303.85 (dimensions.)s 92.337 y 26.161 (As)s 44.43 (the)s 65.576 (reduced)s 110.222 (Lagrangian)s 12 f 172.653 (L)s 10 f 87.982 y 180.93 (R)s 3 f 92.337 y 187.882 (\050)s 9 f 192.451 (x)s 10 f 87.982 y 199.128 (k)s 9 f 92.337 y 204.267 (;)s 209.531 (x)s 10 f 87.982 y 216.208 (K)s 13 f 224.441 (0)s 3 f 92.337 y 227.247 (\051)s 236.643 (is)s 249.368 (no)s 266.597 (longer)s 302.757 (a)s 313.458 (homogeneous)s 386.239 (function)s 433.169 (of)s 447.461 (the)s 106.837 y 8.536 (\257rst)s 32.507 (degree)s 68.816 (in)s 9 f 82.278 (x)s 10 f 102.482 y 88.955 (I)s 13 f 93.765 (0)s 3 f 106.837 y 96.57 (,)s 103.554 (the)s 123.543 (Hessian)s 166.18 (determinan)s 223.95 (t)s 232.19 (is)s 243.758 (not)s 264.401 (iden)s 285.616 (tically)s 320.945 (zero,)s 348.818 (and)s 371.418 (the)s 391.408 (dual)s 417.272 (Legendre)s 121.337 y 8.536 (transform)s 61.57 (\050110\051)s 91.366 (can)s 112.023 (b)s 118.877 (e)s 127.132 (applied)s 167.372 (to)s 180.848 (compute)s 12 f 227.616 (H)s 10 f 116.982 y 237.866 (R)s 3 f 121.337 y 244.818 (\050)s 9 f 249.387 (x)s 10 f 116.982 y 256.064 (k)s 9 f 121.337 y 261.203 (;)s 266.467 (p)s 10 f 123.137 y 272.364 (K)s 3 f 121.337 y 280.598 (\051.)s 293.358 (The)s 316.626 (\257nal)s 341.853 (Hamiltonian)s 408.526 (ra)s 418.644 (y)s 427.878 (tracing)s 135.837 y 8.536 (system)s 47.506 (consists)s 90.785 (of)s 104.167 (four)s 128.646 (ordinary)s 175.972 (di\256eren)s 213.832 (tial)s 234.721 (equations)s 287.334 (of)s 300.716 (the)s 320.952 (\257rst)s 345.17 (order,)s 160.992 y 154.031 (d)s 9 f 160.558 (x)s 10 f 156.637 y 167.235 (I)s 18.015 .4 154.031 166.31 r 3 f 177.341 y 154.06 (d)s 9 f 160.588 (x)s 7 f 173.875 y 167.265 (3)s 3 f 169.11 y 176.578 (=)s 9 f 160.992 y 190.25 (@)s 12 f 197.106 (H)s 10 f 156.637 y 207.356 (R)s 24.057 .4 190.25 166.31 r 9 f 177.341 y 193.498 (@)s 200.353 (p)s 10 f 179.141 y 206.25 (I)s 9 f 169.11 y 219.424 (;)s 3 f 160.992 y 241.914 (d)s 9 f 248.442 (p)s 10 f 162.792 y 254.339 (I)s 17.955 .4 241.554 166.31 r 3 f 177.341 y 241.554 (d)s 9 f 248.082 (x)s 7 f 173.875 y 254.759 (3)s 3 f 169.11 y 264.042 (=)s 12 f 276.515 (\241)s 9 f 160.992 y 287.048 (@)s 12 f 293.903 (H)s 10 f 156.637 y 304.153 (R)s 24.057 .4 287.048 166.31 r 9 f 177.341 y 289.905 (@)s 296.761 (x)s 10 f 173.875 y 303.438 (I)s 9 f 169.11 y 316.221 (:)s 3 f 437.016 (\050111\051)s 201.675 y 8.536 (T)s 16.043 (o)s 25.834 (complete)s 75.445 (the)s 95.681 (solution,)s 143.398 (\050109\051)s 174.079 (for)s 9 f 192.03 (p)s 7 f 203.475 y 197.927 (3)s 3 f 201.675 y 206.594 (m)s 216.059 (ust)s 235.707 (b)s 242.561 (e)s 251.7 (added.)s 224.71 y 26.161 (The)s 51.978 (most)s 82.429 (di\261cult)s 127.176 (step)s 153.711 (in)s 169.083 (computing)s 228.844 (the)s 250.745 (reduced)s 296.144 (Hamiltonian)s 12 f 365.366 (H)s 10 f 220.356 y 375.616 (R)s 3 f 224.71 y 382.568 (\050)s 9 f 387.137 (x)s 10 f 220.356 y 393.814 (k)s 9 f 224.71 y 398.953 (;)s 404.217 (p)s 10 f 226.51 y 410.114 (K)s 3 f 224.71 y 418.348 (\051)s 428.498 (from)s 457.905 (a)s 239.21 y 8.536 (kno)s 26.813 (wn)s 44.438 (reduced)s 86.868 (Lagrangian)s 12 f 147.084 (L)s 10 f 234.856 y 155.361 (R)s 3 f 239.21 y 162.313 (\050)s 9 f 166.882 (x)s 10 f 234.856 y 173.559 (k)s 9 f 239.21 y 178.698 (;)s 183.962 (x)s 10 f 234.856 y 190.639 (K)s 13 f 198.872 (0)s 3 f 239.21 y 201.678 (\051)s 208.858 (consists)s 250.832 (in)s 263.234 (the)s 282.165 (solution)s 325.313 (of)s 337.389 (equations)s 9 f 388.697 (p)s 10 f 241.01 y 394.594 (I)s 3 f 239.21 y 402.737 (=)s 9 f 415.209 (@)s 12 f 422.065 (L)s 10 f 234.856 y 430.341 (R)s 9 f 239.21 y 437.293 (=@)s 450.023 (x)s 10 f 234.856 y 456.7 (I)s 13 f 461.51 (0)s 3 f 253.71 y 8.536 (\050)s 9 f 13.105 (I)s 3 f 23.39 (=)s 36.689 (1)s 9 f 42.564 (;)s 3 f 47.828 (2\051)s 62.674 (for)s 9 f 81.111 (x)s 10 f 249.356 y 87.788 (I)s 13 f 92.597 (0)s 3 f 253.71 y 99.562 (=)s 9 f 112.861 (x)s 10 f 249.356 y 119.538 (I)s 13 f 124.348 (0)s 3 f 253.71 y 127.153 (\050)s 9 f 131.722 (x)s 10 f 249.356 y 138.4 (k)s 9 f 253.71 y 143.538 (;)s 148.802 (p)s 10 f 255.51 y 154.699 (K)s 3 f 253.71 y 162.933 (\051.)s 177.445 (The)s 202.082 (same)s 232.008 (applies)s 271.725 (to)s 286.571 (the)s 307.292 (solution)s 352.232 (of)s 9 f 366.099 (x)s 10 f 249.356 y 372.776 (I)s 13 f 377.586 (0)s 3 f 253.71 y 384.551 (=)s 9 f 397.849 (@)s 12 f 404.704 (H)s 10 f 249.356 y 414.955 (R)s 9 f 253.71 y 421.906 (=@)s 434.636 (p)s 10 f 255.51 y 440.534 (I)s 3 f 253.71 y 449.745 (for)s 9 f 268.21 y 8.536 (p)s 7 f 270.01 y 14.433 (1)s 9 f 268.21 y 19.183 (;)s 24.447 (p)s 7 f 270.01 y 30.344 (2)s 3 f 268.21 y 35.094 (,)s 43.213 (if)s 54.734 (w)s 62.894 (e)s 72.783 (wish)s 100.363 (to)s 115.475 (determine)s 171.058 (the)s 192.045 (reduced)s 236.531 (Lagrangian)s 12 f 298.803 (L)s 10 f 263.856 y 307.08 (R)s 3 f 268.21 y 314.031 (\050)s 9 f 318.601 (x)s 10 f 263.856 y 325.278 (k)s 9 f 268.21 y 330.417 (;)s 335.681 (x)s 10 f 263.856 y 342.358 (K)s 13 f 350.591 (0)s 3 f 268.21 y 353.397 (\051)s 362.633 (from)s 391.127 (the)s 412.113 (kno)s 430.391 (wn)s 450.072 (re-)s 282.71 y 8.536 (duced)s 42.48 (Hamiltonian.)s 305.746 y 26.161 (The)s 50.163 (disadv)s 82.54 (an)s 94.616 (tage)s 119.924 (of)s 133.155 (the)s 153.24 (approac)s 193.386 (h)s 203.679 (based)s 236.233 (on)s 252.401 (the)s 272.487 (reduced)s 316.072 (Lagrangian)s 377.443 (and)s 400.139 (Hamiltonian)s 320.246 y 8.536 (is)s 19.538 (that)s 44.183 (it)s 55.12 (is)s 66.122 (applicable)s 120.794 (only)s 145.765 (to)s 159.313 (one-w)s 189.014 (a)s 194.563 (y)s 203.868 (propagation,)s 271.758 (along)s 302.278 (or)s 315.826 (against)s 355.55 (the)s 9 f 374.973 (x)s 7 f 315.892 y 381.65 (3)s 3 f 320.246 y 389.503 (axis.)s 417.693 (It)s 429.605 (fails)s 453.336 (at)s 334.746 y 8.536 (turning)s 49.704 (p)s 56.558 (oin)s 71.899 (ts,)s 87.796 (where)s 121.131 (the)s 140.758 (ra)s 150.876 (ys)s 165.02 (c)s 169.916 (hange)s 203.251 (their)s 230.711 (direction)s 279.06 (with)s 305.215 (resp)s 326.495 (ect)s 344.817 (to)s 358.569 (the)s 9 f 378.196 (x)s 7 f 336.546 y 384.873 (3)s 3 f 334.746 y 389.623 (-axis.)s 421.798 (F)s 428.486 (or)s 442.239 (one-)s 349.246 y 8.536 (w)s 16.696 (a)s 22.244 (y)s 32.634 (propagation)s 98.183 (without)s 142.19 (turning)s 184.239 (p)s 191.093 (oin)s 206.433 (ts,)s 223.157 (ho)s 235.234 (w)s 243.393 (ev)s 254.49 (er,)s 271.802 (it)s 283.823 (is)s 295.91 (fully)s 322.946 (alternativ)s 372.556 (e)s 381.967 (to)s 396.599 (the)s 417.107 (approac)s 457.252 (h)s 363.746 y 8.536 (based)s 41.111 (on)s 57.301 (the)s 77.407 (mo)s 93.4 (di\257ed)s 125.257 (Lagrangian)s 186.649 (and)s 209.367 (Hamiltonian,)s 280.085 (only)s 305.74 (the)s 325.847 (computational)s 403.397 (sc)s 412.928 (hemes)s 448.113 (are)s 378.246 y 8.536 (di\256eren)s 46.397 (t.)s 59.452 (See)s 80.341 (the)s 100.577 (example)s 146.597 (for)s 164.548 (ellipsoidal)s 219.446 (anisotrop)s 266.837 (y)s 276.955 (in)s 290.664 (Section)s 331.788 (4.4.)s 401.282 y 26.161 (In)s 40.829 (general,)s 84.553 (the)s 104.775 (ra)s 114.893 (y)s 124.996 (tracing)s 164.801 (equations)s 217.399 (based)s 250.089 (on)s 266.394 (the)s 286.615 (mo)s 302.608 (di\257ed)s 334.579 (Hamiltonian)s 402.122 (\050or)s 421.038 (on)s 437.343 (mo)s 453.336 (d-)s 415.782 y 8.536 (i\257ed)s 35.391 (Lagrangian\051)s 102.879 (are)s 123.859 (preferable,)s 183.375 (as)s 199.199 (they)s 227.033 (do)s 244.749 (not)s 267.035 (p)s 273.889 (ose)s 294.934 (an)s 307.01 (y)s 318.525 (di\261culties)s 376.126 (with)s 404.286 (the)s 425.919 (turning)s 430.282 y 8.536 (p)s 15.39 (oin)s 30.73 (ts)s 43.851 (of)s 57.233 (the)s 77.469 (ra)s 87.586 (y)s 92.809 (.)s 6 f 473.61 y 8.536 (4.2)s 45.436 (Reduced)s 111.902 (Hamiltonian)s 205.119 (ra)s 219.161 (y)s 233.111 (tracing)s 288.102 (in)s 307.002 (general)s 363.277 (anisotropic)s 491.61 y 45.436 (media)s 3 f 522.396 y 8.536 (The)s 33.757 (reduced)s 78.561 (Hamiltonian)s 147.188 (ra)s 157.306 (y)s 168.492 (tracing)s 209.38 (system)s 249.419 (\050111\051)s 281.168 (is)s 294.052 (applicable)s 350.606 (to)s 366.036 (general)s 407.576 (anisotropic)s 536.896 y 8.536 (inhomogeneous)s 90.143 (media)s 124.685 (and)s 147.477 (to)s 161.784 (arbitrary)s 211.666 (curvilinear)s 270.034 (co)s 281.458 (ordinates)s 9 f 332.385 (x)s 10 f 532.541 y 339.062 (I)s 3 f 536.896 y 343.871 (,)s 9 f 351.008 (I)s 3 f 360.467 (=)s 372.939 (1)s 9 f 378.814 (;)s 3 f 384.078 (2.)s 398.421 (It)s 411.091 (consists)s 454.315 (of)s 551.396 y 8.536 (four)s 31.942 (equations)s 83.483 (only)s 104.371 (.)s 112.5 (It)s 124.152 (is,)s 138.373 (ho)s 150.449 (w)s 158.609 (ev)s 169.706 (er,)s 185.82 (not)s 205.636 (simple)s 241.184 (to)s 254.472 (calculate)s 9 f 302.357 (@)s 309.213 (p)s 7 f 553.196 y 315.11 (3)s 9 f 551.396 y 319.86 (=@)s 332.59 (p)s 10 f 553.196 y 338.487 (I)s 3 f 551.396 y 346.141 (and)s 9 f 367.915 (@)s 374.771 (p)s 7 f 553.196 y 380.668 (3)s 9 f 551.396 y 385.418 (=@)s 398.149 (x)s 10 f 547.041 y 404.826 (I)s 3 f 551.396 y 409.635 (.)s 417.764 (Actually)s 460.516 (,)s 9 f 565.896 y 8.536 (p)s 7 f 567.696 y 14.433 (3)s 3 f 565.896 y 23.1 (is)s 34.915 (a)s 44.706 (solution)s 89.16 (of)s 102.542 (an)s 118.861 (algebraic)s 168.472 (equation)s 216.451 (of)s 229.832 (the)s 250.068 (sixth)s 279.182 (order.)s 588.932 y 26.161 (It)s 39.922 (is,)s 56.295 (ho)s 68.372 (w)s 76.531 (ev)s 87.628 (er,)s 105.895 (kno)s 124.173 (wn)s 144.139 (from)s 172.918 (the)s 194.19 (seismic)s 235.175 (ra)s 245.293 (y)s 256.447 (theory)s 294.365 (that)s 9 f 320.859 (p)s 7 f 590.732 y 326.756 (3)s 3 f 588.932 y 336.458 (is)s 349.309 (an)s 366.665 (eigen)s 392.449 (v)s 397.998 (alue)s 423.839 (of)s 438.257 (some)s 603.432 y 8.536 (6)s 12 f 15.379 (\243)s 3 f 25.681 (6)s 34.641 (matrix)s 4 f 71.997 (A)s 3 f 82.191 (.)s 90.4 (See)s 600.398 y 111.763 (\267)s 603.432 y 110.457 (Cerv)s 134.61 (en)s 146.523 (\266)s 146.359 (y)s 155.646 (\0502001a\051,)s 200.675 (Equations)s 255.229 (\0505.4.124\051)s 303.355 (and)s 325.371 (\0505.4.135\051,)s 376.927 (and)s 398.943 (also)s 600.398 y 422.982 (\267)s 603.432 y 421.676 (Cerv)s 445.829 (en)s 457.742 (\266)s 457.579 (y)s 617.932 y 8.536 (\0502001b\051,)s 54.79 (where)s 88.617 (other)s 119.181 (references)s 172.984 (can)s 194.409 (b)s 201.263 (e)s 210.285 (found.)s 247.781 (If)s 259.41 (w)s 267.569 (e)s 276.592 (denote)s 314.336 (the)s 334.456 (eigen)s 360.24 (v)s 365.789 (alue)s 390.478 (of)s 4 f 403.743 (A)s 3 f 417.738 (b)s 423.939 (y)s 9 f 433.94 (\276)s 3 f 444.85 (and)s 632.432 y 8.536 (the)s 28.772 (relev)s 52.598 (an)s 64.674 (t)s 73.16 (6)s 12 f 81.702 (\243)s 3 f 93.702 (1)s 103.493 (eigen)s 129.278 (v)s 135.153 (ector)s 164.527 (b)s 170.729 (y)s 4 f 180.847 (W)s 3 f 194.979 (,)s 202.159 (the)s 222.395 (eigen)s 248.179 (v)s 253.728 (alue)s 278.533 (system)s 317.504 (reads)s 4 f 658.932 y 202.631 (A)s 211.326 (W)s 3 f 228.791 (=)s 4 f 241.263 (W)s 9 f 255.395 (\276)s 266.421 (:)s 3 f 437.016 (\050112\051)s 685.432 y 8.536 (It)s 21.987 (should)s 59.986 (b)s 66.84 (e)s 76.705 (noted)s 110.07 (that)s 136.254 (the)s 157.216 (6)s 12 f 166.252 (\243)s 3 f 178.747 (6)s 189.265 (matrix)s 4 f 228.178 (A)s 3 f 243.015 (is)s 255.556 (not)s 277.171 (symmetrical,)s 347.664 (and,)s 374.683 (consequen)s 426.317 (tly)s 439.372 (,)s 447.461 (the)s 699.932 y 8.536 (6)s 12 f 17.665 (\243)s 3 f 30.253 (1)s 40.908 (eigen)s 66.692 (v)s 72.567 (ectors)s 4 f 107.44 (W)s 3 f 126.351 (are)s 146.798 (not)s 168.549 (orthogonal.)s 234.458 (Matrix)s 4 f 274.483 (A)s 3 f 284.677 (,)s 292.937 (ho)s 305.013 (w)s 313.173 (ev)s 324.27 (er,)s 342.321 (can)s 364.726 (b)s 371.58 (e)s 381.582 (symmetrized)s 451.377 (b)s 457.579 (y)s 735.628 y 227.346 (231)s do-end end endp showpage %%Page: 22 22 %%BeginPageSetup initializepage (drahotova; page: 22 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f222 sf ( )S -983 -1000 :M -.751( )A f258 sf ( )S -976 -1000 :M f296 sf ( )S f333 sf ( )S -960 -1000 :M f371 sf ( )S -948 -1000 :M f446 sf ( )S -935 -1000 :M f558 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 4 12 /CMBX12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 14 6 /CMSY6 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (m)s 18.001 (ultiplying)s 71.202 (it)s 82.952 (b)s 89.153 (y)s 99.271 (the)s 119.507 (6)s 12 f 128.049 (\243)s 3 f 140.049 (6)s 149.84 (matrix)s 4 f 188.027 (I)s 7 f 5.264 y 193.055 (1)s 3 f 3.464 y 201.722 (from)s 229.464 (the)s 249.7 (left,)s 273.526 (where)s 4 f 307.471 (I)s 7 f 5.264 y 312.498 (1)s 3 f 3.464 y 321.165 (is)s 332.98 (giv)s 347.994 (en)s 363.66 (b)s 369.862 (y)s 379.98 (the)s 400.216 (relation)s 4 f 37.547 y 194.109 (I)s 7 f 39.347 y 199.137 (1)s 3 f 37.547 y 207.221 (=)s 0 f 19.947 y 219.693 (\303)s 3 f 27.63 y 233.047 (\136)s 4 f 30.197 y 232.609 (0)s 3 f 27.13 y 248.936 (\136)s 4 f 30.197 y 249.359 (I)s 3 f 42.88 y 232.186 (\136)s 4 f 45.947 y 232.609 (I)s 3 f 43.38 y 249.797 (\136)s 4 f 45.947 y 249.359 (0)s 0 f 19.947 y 261.109 (!)s 9 f 37.547 y 274.943 (:)s 3 f 437.016 (\050113\051)s 74.697 y 8.536 (Here)s 72.13 y 36.217 (\136)s 4 f 74.697 y 35.779 (0)s 3 f 45.951 (and)s 71.63 y 67.879 (\136)s 4 f 74.697 y 68.303 (I)s 3 f 76.752 (are)s 95.84 (3)s 12 f 103.37 (\243)s 3 f 114.358 (3)s 123.655 (n)s 129.856 (ull)s 146.333 (and)s 168.685 (iden)s 189.9 (tit)s 201.976 (y)s 211.599 (matrices,)s 261.531 (resp)s 282.812 (ectiv)s 306.964 (ely)s 320.672 (.)s 328.993 (As)s 345.858 (w)s 354.017 (e)s 362.661 (can)s 383.707 (see,)s 4 f 405.571 (I)s 7 f 76.497 y 410.598 (1)s 3 f 74.697 y 418.77 (is)s 430.09 (a)s 439.386 (6)s 12 f 446.916 (\243)s 3 f 457.905 (6)s 89.197 y 8.536 (analogue)s 57.494 (of)s 70.876 (the)s 91.111 (w)s 99.271 (ell-kno)s 133.215 (wn)s 152.146 (2)s 12 f 160.687 (\243)s 3 f 172.687 (2)s 182.479 (P)s 190.147 (auli)s 212.994 (matrix.)s 112.233 y 26.161 (W)s 37.254 (e)s 46.621 (shall)s 74.332 (no)s 86.408 (w)s 99.039 (express)s 140.197 (eigen)s 165.981 (v)s 171.53 (alue)s 9 f 196.564 (\276)s 3 f 207.818 (in)s 221.755 (term)s 250.053 (of)s 4 f 263.664 (A)s 3 f 278.004 (and)s 4 f 301.08 (W)s 3 f 315.212 (.)s 324.384 (Multiplying)s 388.58 (\050112\051)s 419.489 (from)s 447.461 (the)s 126.733 y 8.536 (left)s 29.098 (b)s 35.3 (y)s 4 f 45.417 (W)s 10 f 122.378 y 59.549 (T)s 4 f 126.733 y 66.179 (I)s 7 f 128.533 y 71.206 (1)s 3 f 126.733 y 75.957 (,)s 83.137 (w)s 91.297 (e)s 100.435 (obtain)s 9 f 141.233 y 169.155 (\276)s 3 f 179.597 (=)s 4 f 192.069 (W)s 10 f 136.278 y 206.201 (T)s 4 f 141.233 y 212.83 (I)s 7 f 143.033 y 217.858 (1)s 4 f 141.233 y 222.608 (A)s 231.303 (W)s 9 f 245.435 (=)s 4 f 251.31 (W)s 10 f 136.278 y 265.442 (T)s 4 f 141.233 y 272.071 (I)s 7 f 143.033 y 277.099 (1)s 4 f 141.233 y 281.849 (W)s 9 f 299.897 (:)s 3 f 437.016 (\050114\051)s 162.233 y 8.536 (Denoting)s 60.599 (the)s 82.148 (partial)s 121.321 (deriv)s 146.453 (ativ)s 166.036 (e)s 176.487 (of)s 9 f 191.182 (\276)s 3 f 203.52 (with)s 231.596 (resp)s 252.877 (ect)s 273.12 (to)s 288.793 (an)s 300.869 (y)s 312.3 (quan)s 337.105 (tit)s 349.182 (y)s 360.612 (b)s 366.813 (y)s 378.244 (a)s 389.348 (prime,)s 427.544 (w)s 435.704 (e)s 446.155 (can)s 176.733 y 8.536 (simply)s 46.136 (determine)s 9 f 100.968 (\276)s 14 f 169.555 y 108.077 (0)s 3 f 176.733 y 115.188 (from)s 142.931 (\050114\051,)s 176.875 (in)s 190.583 (terms)s 223.287 (of)s 4 f 236.669 (A)s 14 f 169.555 y 246.863 (0)s 3 f 176.733 y 250.058 (.)s 258.544 (W)s 269.637 (e)s 278.776 (obtain,)s 318.595 (see)s 173.7 y 338.896 (\267)s 176.733 y 337.59 (Cerv)s 361.743 (en)s 373.656 (\266)s 373.493 (y)s 383.611 (\0502001b\051,)s 9 f 203.233 y 165.21 (\276)s 14 f 195.455 y 172.319 (0)s 3 f 203.233 y 178.847 (=)s 4 f 191.319 (W)s 10 f 198.278 y 205.451 (T)s 4 f 203.233 y 212.08 (I)s 7 f 205.033 y 217.108 (1)s 4 f 203.233 y 221.858 (A)s 14 f 195.455 y 232.053 (0)s 4 f 203.233 y 235.247 (W)s 9 f 249.379 (=)s 4 f 255.254 (W)s 10 f 198.278 y 269.386 (T)s 4 f 203.233 y 276.015 (I)s 7 f 205.033 y 281.043 (1)s 4 f 203.233 y 285.793 (W)s 9 f 303.842 (:)s 3 f 437.016 (\050115\051)s 229.733 y 8.536 (Th)s 23.223 (us,)s 41.566 (the)s 61.802 (Hamiltonian)s 129.36 (ra)s 139.478 (y)s 149.596 (tracing)s 189.415 (system)s 228.385 (\050111\051)s 259.065 (reads)s 255.554 y 64.918 (d)s 9 f 71.446 (x)s 10 f 251.2 y 78.123 (I)s 18.015 .4 64.918 260.872 r 3 f 271.904 y 64.948 (d)s 9 f 71.476 (x)s 7 f 268.437 y 78.153 (3)s 3 f 263.672 y 87.466 (=)s 12 f 99.938 (\241)s 4 f 109.272 (W)s 10 f 258.718 y 123.403 (T)s 4 f 263.672 y 130.033 (I)s 7 f 265.472 y 135.061 (1)s 9 f 255.554 y 141.267 (@)s 4 f 148.122 (A)s 17.562 .4 141.011 260.872 r 9 f 271.904 y 141.011 (@)s 147.866 (p)s 10 f 273.704 y 153.763 (I)s 4 f 263.672 y 159.773 (W)s 9 f 173.905 (=)s 4 f 179.78 (W)s 10 f 258.718 y 193.912 (T)s 4 f 263.672 y 200.541 (I)s 7 f 265.472 y 205.569 (1)s 4 f 263.672 y 210.319 (W)s 9 f 228.367 (;)s 3 f 255.554 y 250.858 (d)s 9 f 257.386 (p)s 10 f 257.354 y 263.283 (I)s 17.955 .4 250.498 260.872 r 3 f 271.904 y 250.498 (d)s 9 f 257.026 (x)s 7 f 268.437 y 263.703 (3)s 3 f 263.672 y 272.986 (=)s 4 f 285.458 (W)s 10 f 258.718 y 299.59 (T)s 4 f 263.672 y 306.219 (I)s 7 f 265.472 y 311.247 (1)s 9 f 255.554 y 317.843 (@)s 4 f 324.699 (A)s 18.342 .4 317.197 260.872 r 9 f 271.904 y 317.197 (@)s 324.052 (x)s 10 f 268.437 y 330.729 (I)s 4 f 263.672 y 336.739 (W)s 9 f 350.871 (=)s 4 f 356.746 (W)s 10 f 258.718 y 370.878 (T)s 4 f 263.672 y 377.507 (I)s 7 f 265.472 y 382.535 (1)s 4 f 263.672 y 387.285 (W)s 9 f 405.334 (:)s 3 f 437.016 (\050116\051)s 297.812 y 8.536 (F)s 15.225 (or)s 29.777 (more)s 59.342 (details)s 96.807 (and)s 119.845 (detailed)s 164.424 (expressions)s 225.845 (for)s 4 f 243.987 (A)s 3 f 258.289 (and)s 4 f 281.327 (W)s 3 f 299.567 (refer)s 326.848 (to)s 294.779 y 342.705 (\267)s 297.812 y 341.4 (Cerv)s 365.552 (en)s 377.465 (\266)s 377.302 (y)s 387.611 (\0502001b\051)s 430.885 (in)s 444.784 (this)s 312.312 y 8.536 (v)s 14.411 (olume.)s 53.577 (Some)s 84.91 (simple)s 121.531 (analytical)s 175.384 (examples)s 226.039 (are)s 245.622 (also)s 269.187 (discussed)s 320.299 (there.)s 6 f 355.64 y 8.536 (4.3)s 45.436 (Isotropic)s 113.076 (media,)s 165.242 (Cartesian)s 238.291 (co)s 254.041 (ordinates)s 3 f 386.426 y 8.536 (W)s 19.629 (e)s 29.656 (shall)s 58.025 (again)s 90.246 (consider)s 136.894 (an)s 154.101 (isotropic)s 202.706 (medium)s 248.636 (and)s 272.371 (Cartesian)s 326.198 (co)s 337.622 (ordinates)s 9 f 389.491 (x)s 7 f 388.226 y 396.168 (1)s 9 f 386.426 y 400.918 (;)s 406.182 (x)s 7 f 388.226 y 412.859 (2)s 9 f 386.426 y 417.609 (;)s 422.873 (x)s 7 f 388.226 y 429.55 (3)s 3 f 386.426 y 434.3 (,)s 442.591 (as)s 457.905 (a)s 400.926 y 8.536 (simple)s 44.774 (example)s 90.411 (of)s 103.41 (the)s 123.264 (general)s 163.353 (pro)s 180.651 (cedure)s 217.476 (based)s 249.797 (on)s 265.734 (the)s 285.587 (reduced)s 328.94 (Lagrangian.)s 394.904 (The)s 418.673 (standard)s 415.426 y 8.536 (Lagrangian,)s 73.321 (in)s 87.03 (parameteric)s 151.654 (form,)s 182.66 (then)s 209.424 (reads)s 12 f 441.926 y 77.038 (L)s 3 f 85.315 (\050)s 9 f 89.884 (x)s 10 f 443.726 y 96.561 (k)s 9 f 441.926 y 101.7 (;)s 106.964 (x)s 14 f 434.148 y 113.641 (0)s 10 f 444.892 y 113.641 (k)s 3 f 441.926 y 118.78 (\051)s 126.683 (=)s 9 f 139.155 (V)s 13 f 436.971 y 148.616 (\241)s 7 f 155.227 (1)s 3 f 441.926 y 159.977 (\050)s 9 f 164.547 (x)s 10 f 443.726 y 171.224 (k)s 3 f 441.926 y 176.363 (\051[\050)s 9 f 188.765 (x)s 14 f 434.148 y 195.442 (0)s 7 f 444.892 y 195.442 (1)s 3 f 441.926 y 200.192 (\051)s 7 f 436.971 y 204.762 (2)s 3 f 441.926 y 212.178 (+)s 223.984 (\050)s 9 f 228.553 (x)s 14 f 434.148 y 235.23 (0)s 7 f 444.892 y 235.23 (2)s 3 f 441.926 y 239.98 (\051)s 7 f 436.971 y 244.55 (2)s 3 f 441.926 y 251.966 (+)s 263.772 (\050)s 9 f 268.341 (x)s 14 f 434.148 y 275.018 (0)s 7 f 444.892 y 275.018 (3)s 3 f 441.926 y 279.768 (\051)s 7 f 436.971 y 284.338 (2)s 3 f 441.926 y 289.088 (])s 7 f 436.971 y 292.352 (1)s 10 f 296.602 (=)s 7 f 300.852 (2)s 9 f 441.926 y 309.518 (;)s 326.532 (x)s 14 f 434.148 y 333.209 (0)s 10 f 444.892 y 333.209 (i)s 3 f 441.926 y 339.936 (=)s 352.408 (d)s 9 f 358.936 (x)s 10 f 443.726 y 365.613 (i)s 9 f 441.926 y 369.007 (=)s 3 f 374.882 (d)s 9 f 381.41 (u)s 392.014 (:)s 3 f 468.426 y 8.536 (If)s 22.412 (w)s 30.572 (e)s 41.842 (c)s 46.737 (ho)s 59.466 (ose)s 81.246 (the)s 103.612 (parameter)s 161.881 (along)s 195.345 (curv)s 217.539 (e)s 9 f 228.809 (u)s 3 f 242.457 (=)s 9 f 258.556 (x)s 7 f 470.226 y 265.233 (3)s 3 f 468.426 y 269.983 (,)s 279.827 (w)s 287.986 (e)s 299.256 (obtain)s 337.942 (the)s 360.309 (reduced)s 406.175 (Lagrangian)s 12 f 482.926 y 8.536 (L)s 10 f 478.571 y 16.813 (R)s 3 f 482.926 y 23.764 (\050)s 9 f 28.333 (x)s 10 f 484.726 y 35.01 (k)s 9 f 482.926 y 40.149 (;)s 45.413 (x)s 14 f 475.748 y 52.09 (0)s 10 f 485.892 y 52.09 (K)s 3 f 482.926 y 60.324 (\051,)s 12 f 509.426 y 74.526 (L)s 10 f 504.471 y 82.803 (R)s 3 f 509.426 y 89.755 (\050)s 9 f 94.324 (x)s 10 f 511.226 y 101.001 (k)s 9 f 509.426 y 106.14 (;)s 111.404 (x)s 14 f 501.648 y 118.081 (0)s 10 f 512.392 y 118.081 (K)s 3 f 509.426 y 126.314 (\051)s 134.217 (=)s 9 f 146.689 (V)s 13 f 504.471 y 156.15 (\241)s 7 f 162.761 (1)s 3 f 509.426 y 167.511 (\050)s 9 f 172.081 (x)s 10 f 511.226 y 178.758 (k)s 3 f 509.426 y 183.897 (\051[\050)s 9 f 196.299 (x)s 14 f 501.648 y 202.976 (0)s 7 f 512.392 y 202.976 (1)s 3 f 509.426 y 207.726 (\051)s 7 f 504.471 y 212.296 (2)s 3 f 509.426 y 219.713 (+)s 231.518 (\050)s 9 f 236.087 (x)s 14 f 501.648 y 242.764 (0)s 7 f 512.392 y 242.764 (2)s 3 f 509.426 y 247.514 (\051)s 7 f 504.471 y 252.084 (2)s 3 f 509.426 y 259.501 (+)s 271.306 (1])s 7 f 504.471 y 280.445 (1)s 10 f 284.695 (=)s 7 f 288.945 (2)s 9 f 509.426 y 297.612 (;)s 314.625 (x)s 14 f 501.648 y 321.302 (0)s 10 f 512.392 y 321.302 (K)s 3 f 509.426 y 332.869 (=)s 345.341 (d)s 9 f 351.869 (x)s 10 f 511.226 y 358.546 (K)s 9 f 509.426 y 366.779 (=)s 3 f 372.654 (d)s 9 f 379.182 (x)s 7 f 511.226 y 385.859 (3)s 9 f 509.426 y 394.526 (:)s 3 f 437.016 (\050117\051)s 535.926 y 8.536 (Here)s 9 f 36.275 (K)s 3 f 50.466 (=)s 62.938 (1)s 9 f 68.813 (;)s 3 f 74.077 (2.)s 88.438 (F)s 95.127 (ermat\047s)s 136.969 (v)s 142.518 (ariational)s 195.392 (principle)s 243.697 (then)s 270.461 (reads)s 9 f 567.67 y 127.944 (\261)s 0 f 553.559 y 133.599 (Z)s 10 f 556.726 y 143.599 (R)s 576.281 y 139.154 (S)s 9 f 567.67 y 150.55 (V)s 13 f 562.715 y 160.011 (\241)s 7 f 166.622 (1)s 3 f 567.67 y 171.372 (\050)s 9 f 175.942 (x)s 10 f 569.47 y 182.619 (k)s 3 f 567.67 y 187.758 (\051[\050)s 9 f 200.16 (x)s 14 f 559.892 y 206.837 (0)s 7 f 570.637 y 206.837 (1)s 3 f 567.67 y 211.587 (\051)s 7 f 562.715 y 216.157 (2)s 3 f 567.67 y 223.573 (+)s 235.379 (\050)s 9 f 239.948 (x)s 14 f 559.892 y 246.625 (0)s 7 f 570.637 y 246.625 (2)s 3 f 567.67 y 251.375 (\051)s 7 f 562.715 y 255.945 (2)s 3 f 567.67 y 263.361 (+)s 275.167 (1])s 7 f 562.715 y 284.306 (1)s 10 f 288.556 (=)s 7 f 292.806 (2)s 3 f 567.67 y 297.556 (d)s 9 f 304.084 (x)s 7 f 569.47 y 310.761 (3)s 3 f 567.67 y 318.844 (=)s 331.316 (0)s 9 f 341.108 (:)s 3 f 437.016 (\050118\051)s 597.615 y 8.536 (The)s 32.688 (relev)s 56.515 (an)s 68.591 (t)s 77.077 (Euler-Lagrange)s 159.648 (equations)s 212.262 (are)s 231.845 (as)s 246.271 (follo)s 267.812 (ws:)s 623.459 y 48.613 (d)s 17.955 .4 42.9 628.777 r 639.809 y 42.9 (d)s 9 f 49.427 (x)s 7 f 641.609 y 56.105 (3)s 0 f 616.977 y 62.055 (\275)s 9 f 623.459 y 131.961 (x)s 14 f 616.281 y 138.638 (0)s 10 f 626.426 y 138.638 (I)s 133.9 .4 70.755 628.777 r 9 f 639.809 y 70.755 (V)s 3 f 80.216 (\050)s 9 f 84.785 (x)s 10 f 641.609 y 91.462 (i)s 3 f 639.809 y 94.856 (\051[1)s 111.231 (+)s 123.036 (\050)s 9 f 127.606 (x)s 14 f 633.398 y 134.283 (0)s 7 f 642.431 y 134.283 (1)s 3 f 639.809 y 139.033 (\051)s 7 f 636.342 y 143.602 (2)s 3 f 639.809 y 151.019 (+)s 162.824 (\050)s 9 f 167.394 (x)s 14 f 633.398 y 174.071 (0)s 7 f 642.431 y 174.071 (2)s 3 f 639.809 y 178.821 (\051)s 7 f 636.342 y 183.39 (2)s 3 f 639.809 y 188.14 (])s 7 f 636.342 y 191.404 (1)s 10 f 195.654 (=)s 7 f 199.904 (2)s 0 f 616.977 y 205.854 (\276)s 12 f 631.577 y 216.021 (\241)s 3 f 228.021 ([1)s 239.826 (+)s 251.632 (\050)s 9 f 256.201 (x)s 14 f 623.799 y 262.878 (0)s 7 f 634.544 y 262.878 (1)s 3 f 631.577 y 267.628 (\051)s 7 f 626.623 y 272.198 (2)s 3 f 631.577 y 279.614 (+)s 291.42 (\050)s 9 f 295.989 (x)s 14 f 623.799 y 302.666 (0)s 7 f 634.544 y 302.666 (2)s 3 f 631.577 y 307.416 (\051)s 7 f 626.623 y 311.986 (2)s 3 f 631.577 y 316.736 (])s 7 f 626.623 y 319.999 (1)s 10 f 324.25 (=)s 7 f 328.5 (2)s 9 f 623.459 y 340.193 (@)s 18.342 .4 334.45 628.777 r 639.809 y 334.45 (@)s 341.305 (x)s 10 f 641.609 y 347.982 (I)s 3 f 631.577 y 353.992 (\050)s 623.459 y 361.554 (1)s 9.461 .4 359.761 628.777 r 9 f 639.809 y 359.761 (V)s 3 f 631.577 y 370.422 (\051)s 378.325 (=)s 390.797 (0)s 9 f 400.589 (:)s 3 f 437.016 (\050119\051)s 664.809 y 8.536 (T)s 16.043 (o)s 25.834 (compute)s 9 f 73.487 (p)s 10 f 666.609 y 79.384 (I)s 3 f 664.809 y 84.194 (,)s 91.374 (w)s 99.534 (e)s 108.672 (use)s 128.974 (\050110\051:)s 9 f 691.309 y 92.295 (p)s 10 f 693.109 y 98.192 (I)s 3 f 691.309 y 106.335 (=)s 9 f 118.807 (@)s 12 f 125.663 (L)s 10 f 686.354 y 133.94 (R)s 9 f 691.309 y 140.891 (=@)s 153.621 (x)s 14 f 683.531 y 160.299 (0)s 10 f 694.275 y 160.299 (I)s 3 f 691.309 y 168.442 (=)s 9 f 180.914 (x)s 14 f 683.531 y 187.591 (0)s 10 f 694.275 y 187.591 (I)s 9 f 691.309 y 192.4 (=V)s 3 f 207.736 ([1)s 219.542 (+)s 231.347 (\050)s 9 f 235.917 (x)s 14 f 683.531 y 242.594 (0)s 7 f 694.275 y 242.594 (1)s 3 f 691.309 y 247.344 (\051)s 7 f 686.354 y 251.913 (2)s 3 f 691.309 y 259.33 (+)s 271.135 (\050)s 9 f 275.705 (x)s 14 f 683.531 y 282.382 (0)s 7 f 694.275 y 282.382 (2)s 3 f 691.309 y 287.132 (\051)s 7 f 686.354 y 291.701 (2)s 3 f 691.309 y 296.451 (])s 7 f 686.354 y 299.715 (1)s 10 f 303.965 (=)s 7 f 308.215 (2)s 9 f 691.309 y 316.882 (;)s 333.896 (I)s 3 f 343.354 (=)s 355.827 (1)s 9 f 361.701 (;)s 3 f 366.965 (2)s 9 f 376.757 (:)s 3 f 437.016 (\050120\051)s 735.628 y 227.346 (232)s do-end end endp showpage %%Page: 23 23 %%BeginPageSetup initializepage (drahotova; page: 23 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f222 sf ( )S -983 -1000 :M f258 sf ( )S f296 sf ( )S -972 -1000 :M f333 sf ( )S -964 -1000 :M f371 sf ( )S -952 -1000 :M f446 sf ( )S -939 -1000 :M f558 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 6 14.4 /CMBX12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 14 6 /CMSY6 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (The)s 32.688 (t)s 36.931 (w)s 45.091 (o)s 54.883 (equations)s 107.496 (\050120\051)s 138.176 (can)s 159.718 (b)s 166.572 (e)s 175.711 (solv)s 195.359 (ed)s 211.025 (for)s 9 f 228.977 (x)s 14 f -3.714 y 235.654 (0)s 10 f 6.43 y 235.654 (I)s 3 f 3.464 y 244.38 (to)s 258.741 (yield)s 9 f 27.385 y 155.814 (x)s 14 f 19.607 y 162.491 (0)s 10 f 30.352 y 162.491 (I)s 3 f 27.385 y 170.634 (=)s 9 f 183.106 (p)s 10 f 29.185 y 189.003 (I)s 9 f 27.385 y 193.813 (V)s 3 f 203.274 ([1)s 12 f 215.08 (\241)s 9 f 227.08 (V)s 7 f 22.43 y 236.541 (2)s 3 f 27.385 y 241.291 (\050)s 9 f 245.86 (p)s 7 f 22.43 y 251.757 (2)s 30.352 y 251.757 (1)s 3 f 27.385 y 259.174 (+)s 9 f 270.979 (p)s 7 f 22.43 y 276.877 (2)s 30.352 y 276.877 (2)s 3 f 27.385 y 281.627 (\051])s 13 f 22.43 y 289.46 (\241)s 7 f 296.071 (1)s 10 f 300.321 (=)s 7 f 304.571 (2)s 9 f 27.385 y 313.238 (:)s 3 f 437.016 (\050121\051)s 51.306 y 8.536 (Using)s 40.882 (\050121\051,)s 74.283 (the)s 93.839 (reduced)s 136.895 (Lagrangian)s 12 f 197.737 (L)s 10 f 46.952 y 206.014 (R)s 3 f 51.306 y 212.966 (\050)s 9 f 217.535 (x)s 10 f 53.106 y 224.212 (i)s 9 f 51.306 y 227.606 (;)s 232.87 (x)s 14 f 44.128 y 239.547 (0)s 10 f 54.273 y 239.547 (I)s 3 f 51.306 y 244.357 (\051)s 252.163 (can)s 273.025 (b)s 279.879 (e)s 288.338 (expressed)s 340.337 (in)s 353.366 (terms)s 385.39 (of)s 9 f 398.093 (p)s 10 f 53.106 y 403.99 (I)s 3 f 51.306 y 408.8 (,)s 415.436 (see)s 433.753 (\050117\051:)s 12 f 75.228 y 153.616 (L)s 10 f 70.273 y 161.893 (R)s 3 f 75.228 y 172.178 (=)s 9 f 184.65 (V)s 13 f 70.273 y 194.111 (\241)s 7 f 200.722 (1)s 3 f 75.228 y 205.472 ([1)s 12 f 217.278 (\241)s 9 f 229.277 (V)s 7 f 70.273 y 238.739 (2)s 3 f 75.228 y 243.489 (\050)s 9 f 248.058 (p)s 7 f 70.273 y 253.955 (2)s 78.194 y 253.955 (1)s 3 f 75.228 y 261.372 (+)s 9 f 273.177 (p)s 7 f 70.273 y 279.074 (2)s 78.194 y 279.074 (2)s 3 f 75.228 y 283.824 (\051])s 13 f 70.273 y 291.658 (\241)s 7 f 298.269 (1)s 10 f 302.519 (=)s 7 f 306.769 (2)s 9 f 75.228 y 315.436 (:)s 3 f 437.016 (\050122\051)s 99.149 y 8.536 (The)s 33.636 (\257nal)s 60.694 (equation)s 109.62 (for)s 128.519 (the)s 149.702 (reduced)s 194.386 (Hamiltonian)s 12 f 262.891 (H)s 10 f 94.795 y 273.141 (R)s 3 f 99.149 y 280.092 (\050)s 9 f 284.662 (x)s 10 f 100.949 y 291.339 (i)s 9 f 99.149 y 294.733 (;)s 299.996 (p)s 10 f 100.949 y 305.894 (i)s 3 f 99.149 y 309.288 (\051)s 318.721 (is)s 331.484 (giv)s 346.497 (en)s 363.111 (b)s 369.313 (y)s 380.378 (\050110\051,)s 415.507 (where)s 450.398 (w)s 458.558 (e)s 113.649 y 8.536 (insert)s 41.24 (\050121\051)s 71.92 (and)s 94.767 (\050122\051:)s 12 f 137.571 y 120.617 (H)s 10 f 132.616 y 130.867 (R)s 3 f 137.571 y 137.818 (\050)s 9 f 142.387 (x)s 10 f 139.371 y 149.065 (k)s 9 f 137.571 y 154.203 (;)s 159.467 (p)s 10 f 139.371 y 165.364 (K)s 3 f 137.571 y 173.598 (\051)s 181.501 (=)s 12 f 193.973 (\241)s 9 f 203.306 (V)s 13 f 132.616 y 212.767 (\241)s 7 f 219.378 (1)s 3 f 137.571 y 224.128 (\050)s 9 f 228.698 (x)s 10 f 139.371 y 235.375 (k)s 3 f 137.571 y 240.514 (\051[1)s 12 f 256.888 (\241)s 9 f 268.888 (V)s 7 f 132.616 y 278.349 (2)s 3 f 137.571 y 283.1 (\050)s 9 f 287.669 (p)s 7 f 132.616 y 293.566 (2)s 140.537 y 293.566 (1)s 3 f 137.571 y 300.983 (+)s 9 f 312.788 (p)s 7 f 132.616 y 318.685 (2)s 140.537 y 318.685 (2)s 3 f 137.571 y 323.435 (\051])s 7 f 132.616 y 331.269 (1)s 10 f 335.519 (=)s 7 f 339.769 (2)s 9 f 137.571 y 348.435 (:)s 3 f 437.016 (\050123\051)s 161.492 y 8.536 (The)s 32.688 (relev)s 56.515 (an)s 68.591 (t)s 77.077 (Hamiltonian)s 144.634 (ra)s 154.752 (y)s 164.87 (tracing)s 204.689 (system)s 243.66 (\050111\051)s 274.34 (then)s 301.104 (reads)s 183.247 y 63.572 (d)s 9 f 70.1 (x)s 10 f 185.047 y 76.777 (I)s 18.015 .4 63.572 188.565 r 3 f 199.596 y 63.602 (d)s 9 f 70.13 (x)s 7 f 201.396 y 76.807 (3)s 3 f 191.365 y 86.12 (=)s 9 f 183.247 y 139.426 (V)s 148.887 (p)s 10 f 185.047 y 154.784 (I)s 99.436 .4 99.792 188.565 r 3 f 199.596 y 99.792 ([1)s 12 f 111.598 (\241)s 9 f 123.598 (V)s 7 f 196.13 y 133.059 (2)s 3 f 199.596 y 137.809 (\050)s 9 f 142.378 (p)s 7 f 195.463 y 148.275 (2)s 202.218 y 148.275 (1)s 3 f 199.596 y 155.692 (+)s 9 f 167.497 (p)s 7 f 195.463 y 173.394 (2)s 202.218 y 173.394 (2)s 3 f 199.596 y 178.145 (\051])s 7 f 196.13 y 185.978 (1)s 10 f 190.228 (=)s 7 f 194.478 (2)s 9 f 191.365 y 204.345 (;)s 3 f 183.247 y 219.002 (d)s 9 f 225.529 (p)s 10 f 185.047 y 231.427 (I)s 17.955 .4 218.642 188.565 r 3 f 199.596 y 218.642 (d)s 9 f 225.169 (x)s 7 f 201.396 y 231.846 (3)s 3 f 191.365 y 241.13 (=)s 183.247 y 301.582 (1)s 99.436 .4 254.802 188.565 r 199.596 y 254.802 ([1)s 12 f 266.607 (\241)s 9 f 278.607 (V)s 7 f 196.13 y 288.068 (2)s 3 f 199.596 y 292.818 (\050)s 9 f 297.388 (p)s 7 f 195.463 y 303.285 (2)s 202.218 y 303.285 (1)s 3 f 199.596 y 310.702 (+)s 9 f 322.507 (p)s 7 f 195.463 y 328.404 (2)s 202.218 y 328.404 (2)s 3 f 199.596 y 333.154 (\051])s 7 f 196.13 y 340.987 (1)s 10 f 345.237 (=)s 7 f 349.488 (2)s 9 f 183.247 y 362.381 (@)s 18.342 .4 356.638 188.565 r 199.596 y 356.638 (@)s 363.493 (x)s 10 f 201.396 y 370.17 (I)s 0 f 176.765 y 376.18 (\265)s 3 f 183.247 y 386.534 (1)s 9.461 .4 384.741 188.565 r 9 f 199.596 y 384.741 (V)s 0 f 176.765 y 395.402 (\266)s 9 f 191.365 y 406.68 (:)s 3 f 437.016 (\050124\051)s 222.018 y 8.536 (T)s 16.043 (o)s 25.834 (complete)s 75.445 (the)s 95.681 (solution,)s 143.398 (w)s 151.558 (e)s 160.697 (m)s 170.162 (ust)s 189.81 (add)s 212.657 (\050109\051:)s 9 f 245.939 y 107.39 (p)s 7 f 247.739 y 113.287 (3)s 3 f 245.939 y 121.371 (=)s 12 f 133.843 (\241H)s 10 f 240.984 y 153.426 (R)s 3 f 245.939 y 160.378 (\050)s 9 f 164.947 (x)s 10 f 247.739 y 171.624 (k)s 9 f 245.939 y 176.763 (;)s 182.027 (p)s 10 f 247.739 y 187.924 (K)s 3 f 245.939 y 196.158 (\051)s 204.06 (=)s 9 f 216.532 (V)s 13 f 240.984 y 225.993 (\241)s 7 f 232.604 (1)s 3 f 245.939 y 237.355 (\050)s 9 f 241.924 (x)s 10 f 247.739 y 248.601 (k)s 3 f 245.939 y 253.74 (\051[1)s 12 f 270.115 (\241)s 9 f 282.115 (V)s 7 f 240.984 y 291.576 (2)s 3 f 245.939 y 296.326 (\050)s 9 f 300.895 (p)s 7 f 240.984 y 306.792 (2)s 248.906 y 306.792 (1)s 3 f 245.939 y 314.209 (+)s 9 f 326.014 (p)s 7 f 240.984 y 331.912 (2)s 248.906 y 331.912 (2)s 3 f 245.939 y 336.662 (\051])s 7 f 240.984 y 344.495 (1)s 10 f 348.745 (=)s 7 f 352.995 (2)s 9 f 245.939 y 361.662 (:)s 3 f 437.016 (\050125\051)s 269.861 y 8.536 (The)s 32.275 (c)s 37.171 (hoice)s 66.785 (of)s 79.754 (sign)s 103.558 (in)s 116.853 (\050125\051)s 147.12 (corresp)s 184.067 (onds)s 211.135 (to)s 225.083 (the)s 244.905 (propagation)s 309.769 (in)s 323.064 (the)s 342.886 (p)s 349.741 (ositiv)s 377.222 (e)s 385.948 (direction)s 434.492 (of)s 447.461 (the)s 9 f 284.361 y 8.536 (x)s 7 f 286.16 y 15.213 (3)s 3 f 284.361 y 23.88 (axis.)s 307.396 y 26.161 (The)s 49.109 (reduced)s 91.641 (Hamiltonian)s 157.995 (deriv)s 183.453 (ed)s 197.916 (here)s 222.17 (from)s 248.709 (the)s 267.741 (reduced)s 310.273 (Lagrangian)s 370.591 (using)s 400.133 (the)s 419.165 (F)s 425.854 (ermat\047s)s 321.896 y 8.536 (v)s 14.084 (ariational)s 68.213 (principle)s 117.772 (corresp)s 154.719 (onds)s 183.454 (exactly)s 225.18 (to)s 240.795 (the)s 262.284 (reduced)s 307.274 (Hamiltonian)s 376.086 (deriv)s 401.544 (ed)s 418.464 (from)s 447.461 (the)s 336.396 y 8.536 (eik)s 22.897 (onal)s 49.631 (equation)s 9 f 98.886 (V)s 7 f 332.042 y 108.347 (2)s 9 f 336.396 y 113.097 (p)s 10 f 338.196 y 118.994 (i)s 9 f 336.396 y 122.388 (p)s 10 f 338.196 y 128.286 (i)s 3 f 336.396 y 137.185 (=)s 151.83 (1)s 162.898 (\050whic)s 190.64 (h)s 202.361 (further)s 243.13 (follo)s 264.671 (ws)s 282.985 (from)s 312.004 (the)s 333.516 (elasto)s 363.283 (dynamic)s 411.885 (equation\051.)s 350.896 y 8.536 (Compare)s 60.459 (Equation)s 112.869 (\050123\051)s 145.208 (giv)s 160.222 (en)s 177.548 (here)s 204.665 (with)s 233.088 (the)s 254.984 (expression)s 313.238 (for)s 332.849 (the)s 354.744 (reduced)s 400.139 (Hamiltonian)s 365.396 y 8.536 (used)s 35.367 (in)s 362.363 y 50.383 (\267)s 365.396 y 49.078 (Cerv)s 73.23 (en)s 85.143 (\266)s 84.98 (y)s 95.1 (\0502001a\051,)s 140.797 (Eq.\0503.1.28\051.)s 205.916 (One)s 230.723 (sees)s 254.356 (that,)s 283.081 (ev)s 294.178 (en)s 309.847 (the)s 330.085 (ra)s 340.203 (y)s 350.323 (tracing)s 390.145 (systems,)s 437.016 (giv)s 452.03 (en)s 379.896 y 8.536 (here)s 33.994 (b)s 40.195 (y)s 50.313 (\050124\051,)s 84.257 (and)s 107.104 (the)s 127.34 (ra)s 137.458 (y)s 147.576 (tracing)s 187.395 (systems)s 231 (\0503.1.29\051)s 274.083 (in)s 376.863 y 289.097 (\267)s 379.896 y 287.791 (Cerv)s 311.944 (en)s 323.857 (\266)s 323.694 (y)s 333.812 (\0502001a\051,)s 379.506 (are)s 399.089 (the)s 419.325 (same.)s 402.932 y 26.161 (The)s 51.771 (w)s 59.931 (ell-kno)s 93.875 (wn)s 114.263 (disadv)s 146.641 (an)s 158.717 (tage)s 185.633 (of)s 200.473 (ra)s 210.591 (y)s 222.167 (tracing)s 263.444 (system)s 303.872 (\050124\051)s 336.01 (consists)s 380.747 (in)s 395.913 (the)s 417.607 (fact)s 442.239 (that)s 417.432 y 8.536 (parameter)s 9 f 65.147 (x)s 7 f 419.232 y 71.824 (3)s 3 f 417.432 y 80.964 (along)s 112.77 (the)s 133.479 (ra)s 143.597 (y)s 154.188 (is)s 166.477 (not)s 187.838 (necessarily)s 246.865 (monotonic)s 304.782 (along)s 336.588 (the)s 357.297 (ra)s 367.415 (y)s 372.637 (.)s 382.543 (The)s 407.169 (ra)s 417.286 (y)s 427.878 (tracing)s 431.932 y 8.536 (system)s 47.599 (\050124\051)s 78.371 (fails)s 103.008 (at)s 117.461 (ra)s 127.579 (y)s 137.789 (turning)s 179.659 (p)s 186.513 (oin)s 201.853 (ts,)s 218.353 (at)s 232.806 (whic)s 255.979 (h)s 266.516 (the)s 286.844 (ra)s 296.962 (y)s 307.172 (is)s 319.08 (p)s 325.934 (erp)s 342.579 (endicular)s 393.588 (to)s 408.041 (the)s 9 f 428.369 (x)s 7 f 433.732 y 435.046 (3)s 3 f 431.932 y 443.805 (axis)s 446.432 y 8.536 (\050the)s 33.341 (minim)s 65.653 (um)s 85.889 (with)s 112.653 (resp)s 133.933 (ect)s 152.864 (to)s 9 f 167.225 (x)s 7 f 448.232 y 173.902 (3)s 3 f 446.432 y 178.652 (,)s 185.832 (for)s 203.783 (example\051.)s 6 f 489.379 y 8.536 (4.4)s 45.436 (Ellipsoidal)s 124.334 (anisotrop)s 189.766 (y)s 196.966 (,)s 206.866 (Cartesian)s 279.914 (co)s 295.664 (ordinates)s 3 f 520.165 y 8.536 (W)s 19.629 (e)s 28.404 (shall)s 55.521 (start)s 83.292 (from)s 110.67 (F)s 117.359 (ermat\047s)s 158.838 (v)s 164.386 (ariational)s 216.897 (principle)s 264.838 (in)s 278.182 (parameteric)s 342.442 (form)s 369.821 (\05022\051,)s 397.599 (and)s 420.082 (from)s 447.461 (the)s 534.665 y 8.536 (homogeneous)s 80.406 (ellipsoidal)s 135.304 (Lagrangian:)s 12 f 558.587 y 67.081 (L)s 3 f 75.357 (\050)s 9 f 79.927 (x)s 10 f 560.387 y 86.604 (k)s 9 f 558.587 y 91.743 (;)s 97.007 (x)s 14 f 550.809 y 103.684 (0)s 10 f 561.553 y 103.684 (k)s 3 f 558.587 y 108.823 (\051)s 116.725 (=)s 129.197 ([\050)s 9 f 137.031 (x)s 14 f 550.809 y 143.708 (0)s 7 f 561.553 y 143.708 (1)s 3 f 558.587 y 148.458 (\051)s 7 f 553.632 y 153.027 (2)s 9 f 558.587 y 157.777 (A)s 13 f 553.632 y 166.585 (\241)s 7 f 173.197 (2)s 3 f 558.587 y 180.613 (+)s 192.419 (\050)s 9 f 196.988 (x)s 14 f 550.809 y 203.665 (0)s 7 f 561.553 y 203.665 (2)s 3 f 558.587 y 208.415 (\051)s 7 f 553.632 y 212.985 (2)s 9 f 558.587 y 217.735 (B)s 13 f 553.632 y 227.266 (\241)s 7 f 233.878 (2)s 3 f 558.587 y 241.294 (+)s 253.1 (\050)s 9 f 257.669 (x)s 14 f 550.809 y 264.346 (0)s 7 f 561.553 y 264.346 (3)s 3 f 558.587 y 269.096 (\051)s 7 f 553.632 y 273.666 (2)s 9 f 558.587 y 278.416 (C)s 13 f 553.632 y 287.684 (\241)s 7 f 294.295 (2)s 3 f 558.587 y 299.045 (])s 7 f 553.632 y 302.309 (1)s 10 f 306.559 (=)s 7 f 310.809 (2)s 9 f 558.587 y 319.476 (;)s 336.49 (x)s 14 f 550.809 y 343.167 (0)s 10 f 561.553 y 343.167 (i)s 3 f 558.587 y 349.894 (=)s 362.366 (d)s 9 f 368.894 (x)s 10 f 560.387 y 375.571 (i)s 9 f 558.587 y 378.965 (=)s 3 f 384.84 (d)s 9 f 391.367 (u)s 401.971 (:)s 3 f 437.016 (\050126\051)s 582.508 y 8.536 (Here)s 9 f 36.207 (A;)s 50.279 (B)s 59.811 (;)s 65.074 (C)s 3 f 78.191 (are)s 97.707 (smo)s 118.334 (oth)s 139.155 (functions)s 189.742 (of)s 203.056 (Cartesian)s 255.928 (co)s 267.352 (ordinates)s 9 f 318.265 (x)s 10 f 584.308 y 324.942 (i)s 3 f 582.508 y 328.336 (.)s 336.8 (As)s 354.091 (Lagrangian)s 415.545 (\050126\051)s 446.158 (is)s 457.905 (a)s 597.008 y 8.536 (homogeneous)s 79.934 (function)s 125.481 (of)s 138.391 (the)s 158.154 (\257rst)s 181.9 (degree)s 217.982 (in)s 9 f 231.218 (x)s 14 f 589.83 y 237.895 (0)s 10 f 599.975 y 237.895 (i)s 3 f 597.008 y 241.289 (,)s 248.092 (the)s 267.855 (Hessian)s 310.266 (determinan)s 368.036 (t)s 376.049 (v)s 381.598 (anishes,)s 425.086 (and)s 447.461 (the)s 611.508 y 8.536 (dual)s 35.444 (Legendre)s 86.665 (transform)s 141.381 (cannot)s 180.691 (b)s 187.545 (e)s 197.48 (used)s 225.106 (to)s 240.264 (deriv)s 265.722 (e)s 275.658 (the)s 296.69 (corresp)s 333.637 (onding)s 372.947 (Hamiltonian.)s 447.465 (W)s 458.558 (e)s 626.008 y 8.536 (can,)s 33.341 (ho)s 45.417 (w)s 53.577 (ev)s 64.674 (er,)s 81.646 (in)s 91.111 (tro)s 106.452 (duce)s 133.868 (parameter)s 9 f 190.006 (u)s 3 f 200.027 (=)s 9 f 212.499 (x)s 7 f 627.808 y 219.176 (3)s 3 f 626.008 y 227.843 (and)s 250.69 (reduced)s 294.425 (Lagrangian)s 12 f 355.947 (L)s 10 f 621.653 y 364.224 (R)s 3 f 626.008 y 371.175 (\050)s 9 f 375.745 (x)s 10 f 627.808 y 382.422 (i)s 9 f 626.008 y 385.816 (;)s 391.079 (x)s 14 f 618.83 y 397.756 (0)s 10 f 628.975 y 397.756 (I)s 3 f 626.008 y 402.566 (\051:)s 12 f 649.929 y 115.963 (L)s 10 f 644.975 y 124.24 (R)s 3 f 649.929 y 131.192 (\050)s 9 f 135.761 (x)s 10 f 651.729 y 142.438 (k)s 9 f 649.929 y 147.577 (;)s 152.841 (x)s 14 f 642.151 y 159.518 (0)s 10 f 652.896 y 159.518 (K)s 3 f 649.929 y 167.751 (\051)s 175.654 (=)s 188.126 ([\050)s 9 f 195.959 (x)s 14 f 642.151 y 202.636 (0)s 7 f 652.896 y 202.636 (1)s 3 f 649.929 y 207.386 (\051)s 7 f 644.975 y 211.956 (2)s 9 f 649.929 y 216.706 (A)s 13 f 644.975 y 225.514 (\241)s 7 f 232.125 (2)s 3 f 649.929 y 239.542 (+)s 251.347 (\050)s 9 f 255.917 (x)s 14 f 642.151 y 262.594 (0)s 7 f 652.896 y 262.594 (2)s 3 f 649.929 y 267.344 (\051)s 7 f 644.975 y 271.913 (2)s 9 f 649.929 y 276.663 (B)s 13 f 644.975 y 286.195 (\241)s 7 f 292.806 (2)s 3 f 649.929 y 300.223 (+)s 9 f 312.028 (C)s 13 f 644.975 y 321.297 (\241)s 7 f 327.908 (2)s 3 f 649.929 y 332.658 (])s 7 f 644.975 y 335.922 (1)s 10 f 340.172 (=)s 7 f 344.422 (2)s 9 f 649.929 y 353.089 (:)s 3 f 437.016 (\050127\051)s 673.851 y 8.536 (F)s 15.225 (ermat\047s)s 57.067 (v)s 62.616 (ariational)s 115.49 (principle)s 163.795 (then)s 190.559 (reads)s 9 f 703.017 y 120.924 (\261)s 0 f 688.905 y 126.578 (Z)s 10 f 692.072 y 136.578 (R)s 711.628 y 132.134 (S)s 3 f 703.017 y 143.53 ([\050)s 9 f 151.363 (x)s 14 f 695.239 y 158.04 (0)s 7 f 705.983 y 158.04 (1)s 3 f 703.017 y 162.79 (\051)s 7 f 698.062 y 167.36 (2)s 9 f 703.017 y 172.11 (A)s 13 f 698.062 y 180.918 (\241)s 7 f 187.529 (2)s 3 f 703.017 y 194.946 (+)s 206.751 (\050)s 9 f 211.321 (x)s 14 f 695.239 y 217.998 (0)s 7 f 705.983 y 217.998 (2)s 3 f 703.017 y 222.748 (\051)s 7 f 698.062 y 227.317 (2)s 9 f 703.017 y 232.067 (B)s 13 f 698.062 y 241.599 (\241)s 7 f 248.21 (2)s 3 f 703.017 y 255.627 (+)s 9 f 267.432 (C)s 13 f 698.062 y 276.701 (\241)s 7 f 283.312 (2)s 3 f 703.017 y 288.062 (])s 7 f 698.062 y 291.326 (1)s 10 f 295.576 (=)s 7 f 299.826 (2)s 3 f 703.017 y 304.576 (d)s 9 f 311.104 (x)s 7 f 704.817 y 317.781 (3)s 3 f 703.017 y 325.864 (=)s 338.336 (0)s 9 f 348.128 (;)s 3 f 735.628 y 227.346 (233)s do-end end endp showpage %%Page: 24 24 %%BeginPageSetup initializepage (drahotova; page: 24 of 26)setjob %%EndPageSetup gS 0 0 568 805 rC -1000 -1000 :M f409 sf ( )S -991 -1000 :M f184 sf ( )S -987 -1000 :M f258 sf ( )S f296 sf ( )S -976 -1000 :M f333 sf ( )S -968 -1000 :M f371 sf ( )S -956 -1000 :M f446 sf ( )S -943 -1000 :M f558 sf ( )S 0 0 :M initclip TeXdict begin do-bop 0 10 /CMEX10 findfont fdef 3 12 /CMR12 findfont fdef 7 8 /CMR8 findfont fdef 9 12 /CMMI12 findfont fdef 10 8 /CMMI8 findfont fdef 12 12 /CMSY10 findfont fdef 13 8 /CMSY8 findfont fdef 14 6 /CMSY6 findfont fdef 58 49 translate 72 72.27 div dup scale 3 f 3.464 y 8.536 (and)s 31.383 (the)s 51.619 (relev)s 75.445 (an)s 87.521 (t)s 96.007 (Euler-Lagrange)s 178.579 (equations)s 231.192 (are)s 250.775 (as)s 265.201 (follo)s 286.743 (ws:)s 25.253 y 77.839 (d)s 17.955 .4 72.126 30.571 r 41.602 y 72.126 (d)s 9 f 78.653 (x)s 7 f 43.402 y 85.33 (3)s 0 f 18.77 y 91.28 (\265)s 9 f 25.253 y 99.841 (@)s 106.697 (D)s 16.938 .4 99.841 30.571 r 41.602 y 102.567 (x)s 14 f 35.191 y 109.244 (0)s 10 f 44.535 y 109.244 (I)s 0 f 18.77 y 117.979 (\266)s 12 f 33.371 y 128.007 (\241)s 9 f 25.253 y 141.909 (@)s 148.765 (D)s 18.342 .4 141.207 30.571 r 41.602 y 141.207 (@)s 148.062 (x)s 10 f 43.402 y 154.739 (I)s 3 f 33.371 y 164.082 (=)s 176.554 (0)s 9 f 186.346 (;)s 207.276 (D)s 3 f 220.692 (=)s 233.164 ([\050)s 9 f 240.997 (x)s 14 f 25.593 y 247.674 (0)s 7 f 36.337 y 247.674 (1)s 3 f 33.371 y 252.424 (\051)s 7 f 28.416 y 256.994 (2)s 9 f 33.371 y 261.744 (A)s 13 f 28.416 y 270.552 (\241)s 7 f 277.163 (2)s 3 f 33.371 y 284.58 (+)s 296.385 (\050)s 9 f 300.955 (x)s 14 f 25.593 y 307.632 (0)s 7 f 36.337 y 307.632 (2)s 3 f 33.371 y 312.382 (\051)s 7 f 28.416 y 316.951 (2)s 9 f 33.371 y 321.701 (B)s 13 f 28.416 y 331.233 (\241)s 7 f 337.844 (2)s 3 f 33.371 y 345.261 (+)s 9 f 357.066 (C)s 13 f 28.416 y 366.335 (\241)s 7 f 372.946 (2)s 3 f 33.371 y 377.696 (])s 7 f 28.416 y 380.96 (1)s 10 f 385.21 (=)s 7 f 389.46 (2)s 9 f 33.371 y 398.126 (:)s 3 f 437.016 (\050128\051)s 64.658 y 8.536 (T)s 16.043 (o)s 25.834 (compute)s 9 f 73.487 (p)s 10 f 66.458 y 79.384 (I)s 3 f 64.658 y 84.194 (,)s 91.374 (w)s 99.534 (e)s 108.672 (use)s 128.974 (\050110\051,)s 9 f 89.28 y 140.29 (p)s 7 f 91.08 y 146.187 (1)s 3 f 89.28 y 154.27 (=)s 9 f 166.742 (x)s 14 f 81.502 y 173.419 (0)s 7 f 92.246 y 173.419 (1)s 9 f 89.28 y 178.17 (A)s 13 f 84.325 y 186.978 (\241)s 7 f 193.589 (2)s 9 f 89.28 y 198.339 (D)s 13 f 84.325 y 208.421 (\241)s 7 f 215.032 (1)s 9 f 89.28 y 223.699 (;)s 244.629 (p)s 7 f 91.08 y 250.527 (2)s 3 f 89.28 y 258.61 (=)s 9 f 271.082 (x)s 14 f 81.502 y 277.759 (0)s 7 f 92.246 y 277.759 (2)s 9 f 89.28 y 282.509 (B)s 13 f 84.325 y 292.041 (\241)s 7 f 298.652 (2)s 9 f 89.28 y 303.402 (D)s 13 f 84.325 y 313.484 (\241)s 7 f 320.096 (1)s 9 f 89.28 y 328.762 (;)s 3 f 437.016 (\050129\051)s 113.902 y 8.536 (whic)s 31.709 (h)s 42.154 (can)s 63.695 (b)s 70.549 (e)s 79.688 (solv)s 99.336 (ed)s 115.003 (for)s 9 f 132.954 (x)s 14 f 106.724 y 139.631 (0)s 10 f 116.869 y 139.631 (I)s 3 f 113.902 y 148.357 (to)s 162.718 (yield)s 9 f 145.619 y 88.349 (x)s 14 f 137.841 y 95.026 (0)s 7 f 148.586 y 95.026 (1)s 3 f 145.619 y 103.11 (=)s 9 f 137.501 y 146.425 (C)s 13 f 133.146 y 155.693 (\241)s 7 f 162.304 (1)s 9 f 137.501 y 167.054 (A)s 7 f 133.146 y 175.862 (2)s 9 f 137.501 y 180.612 (p)s 7 f 139.301 y 186.51 (1)s 104.121 .4 116.782 142.819 r 3 f 153.851 y 116.782 ([1)s 12 f 128.587 (\241)s 9 f 140.587 (A)s 7 f 150.384 y 149.395 (2)s 9 f 153.851 y 1