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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 6 /plusminus put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 69 /E put dup 76 /L put dup 77 /M put dup 80 /P put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /mu put dup 62 /greater put dup 109 /m put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 4 /squaresolid put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1C87678CE98C24B934A76220 4DD9B2FF3A49786028E35DDE10AD2C926BD30AD47015FFE9469DE1F793D1C53A C8812CBCD402444EAEA7A50EC5FD93D6A04C2783B50EA48059E3E7407537CB8D 4C206846EF0764C05289733920E2399E58AD8F137C229F3CE3E34D2D1EAB2D53 20D44EFAC8EFA4D14A2EFE389D952527F98D0E49BD5BD2C8D58FF9CB9C78D974 75C2AB5467D73D2B5E277A3FDC35909938A9DF0EB91BD9159D3437BE22EE4544 3429AC8E2BFBE34AE54D3BA3AD04BDF3F4F43A2B43992DF88678681B3AB32CFD A23E2C98D1AF00AB206AC95B78BBE6316F7A0AB6BD3236C28C76288B3C25D1EB E9ABB3576C5EC15A71D26177F5883E9B48293D59015615E2EEAF2E9BA04151ED 5497B9A1C41CBA44BAFF13EA218F5EAC11952EE336AD1DBE6CE92F002EAA3B3D 3BE4C3792F3405763C4BD93EFC3B4FC34193439561841BA989DD8D9F9AEE7A7B 24AEB4654B35023C9720B8F31AA9452E29753FB7915CB29977E725611E37C0B7 784BCC26FACF8A7A0EB1E54290D27FFE52B2D87FAD080AD15EE1984C37E0EB30 122C3012D3A16B09C28903D138352AB5462674B6CFB63F1371768D094DDF288C 36FB9B58443F872D61F2CD8CED42FE0EFF3D7E9952A172BB1AFECB60BF79F2B6 04265FDE4F78BC9FD619AA733CD0412F1D9A7C13B271BF827DCBDC8ABAE24FF0 74D3C220621D7FF0EFE62D835A221D0A7C139E2E6681FC2BBA58FA3B80D416EC 3854C63BA040A4262B458340DAA18AA6AEA3BBAC61615CB85982B18664D3D3AF 340C65B969071CF2D0CABEB80E04623D0526F862ECA8280EEE236C535F70561A 854181132E677674AD5E14C6636F57541D3C821F0776D2CB9B8526D4B826791A 0B179B387D47B08982D338AE4D93711A9AFEC6B628B8EC464346666841657E34 0A8624A495F142A3D4BEDF75EA6AEB3F283B1B527748949E4767368AB7391F22 80B8DD8461C76DABE568B977E3CBE4B17F7A5D58CB025CAB581588CFE46CE7F8 7D54E7688CE550D5F283BAA71FECD03B45052F6C5467A3A93B1B1AF15B611A31 C49998ECB8988D5CD38B4DFB9E7F4B5A363E2D703396B0DE5934CE210331B2DC 5D0A41A7321E0B76A1DC8D3129CA0FE67228C0D9B4A56B3D6551D1B34ADBB2B9 19B3C9FAA8B33B7B1FAABE696F303F11E2A1039860905E19 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /Z put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 49 /infinity put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 33 /omega put dup 59 /comma put dup 77 /M put dup 78 /N put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (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 11 /ff put dup 12 /fi put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 59 /semicolon put dup 65 /A put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 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 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 15 /epsilon1 put dup 22 /mu put dup 23 /nu put dup 28 /tau put dup 33 /omega put dup 59 /comma put dup 61 /slash put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 84 /T put dup 88 /X put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 116 /t put dup 120 /x put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put dup 84 /T put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2C2822D3E73F25B81C424627D3D9A158EAB554233A25D3C6849ABA86F 1F25C1667CB57D2E79B7803083CB7CC0616467F68450D9A3FEAB534EB9721003 DBFEEFD050F3AC3492F5C74162A9A531ECEC0F47610B4940E946D21CAA771D30 A6C27ECBA11708CC46C62396BF9D1990D579D0C394899D24FE7A4382EA18E7E1 160E7283AF5BE17254790628E79FCC206F28B5566075B3A5697D5209062544FF D85FD89D6F43D6588B242AB2666B5D2861CD38A8CE676503EDFAE84D12A71E77 8405E468FE391F4F3F50D2C57ED55512036B0DB8E76A7EF413ED08673E56DE2C 16A3B65CD478433C0D2F9FEC4E662D54DAA43CFA6957D2A9AF8979BE06F70B68 ED4C8C493D6DAC4971A3F1D010A7726D084EC1074FECD7D12D72AE16C26194AF 21AF5774D9B860EEE8608D34F150092F09C19959BAA670022B9A9F263CD391E3 74DD1D1B4CD4D75273CAA4E37F68C631723E08FA35AD34C0AFB4621AE6689861 854D16CE1C375FD159A337E221A6FF1CFFB5693A0623E7EBB58C2969F590D081 AD92DD9E5322E26D6A15023664AC73A355998BCC48ADD0E7A4BC79790519606F A1FEF6075033BCD422EE8233B83D1E7C20043280D531223D5AD4D5B41669F884 95CE4D6DDE819B588742B930C579EDF743F2C74C95F717FAA6154FADC3FE2975 F59CFB1C1A29059487E75C48505BAEAD7145667D4E18E46E610C868A257173ED 0D30EAA4C090854DD8378E92D0A376226EA7DA63798F247BAC770FE26D70E72F 90CCFAADF118304646955DE0B9D25C4B419FBF62FB42ED17CD96B73438850949 4C538EEFBA097E8027AF80AF9107EF40CC1B780D5251766948179EA0AB479B77 6FDF0257A44FE2F4DF472A226FCC393FD7FE74350226134F431AD4E73507F26C 4CDD9C0691F210E86BDAB92FF517BF8CD5040E17D674AF9A0F0E03404BB83AD3 34538E73D2200CAD0CA80DAE206B04F180B378CF3445562A496638B1644F6C9F 3C184E65A1C0AF6E2F116E11BC4AE2071106AA6BE3837BAEEF0603AC732FF8F3 9BA0B2C9C36BE002B9FBBB7B9922347DEA4C62232CACB0B389078F55A84A42DF 03B8A28DB94000920D0CF53DE7AFA7D1AB6FD9A4402BACE3E5B93A0B6CF2F266 ADECF2B32DC94E20A4FFAAFB72FD80606CDC7D0A8FD072F490D9EDE10E180073 918CBD4AAAD2BF892500FBCDD7960DFA7182E4216D4099EF0494F2CB13BCBD47 4AD9E6BA8C03B346F7D11D755E084F40A172DE9F050B26D8649461D7F685FCCF 89CE96A3F1823C32F1E420551881C87D8EB84777E6C1A24A8D5B7DB08AF9A3D4 CB30701EB0601C3A98B3FE2A6F746CB4976A1D02EA5F2CCD8102BA39B99AE869 95B1A2D1FD5DDEF0C881F77D427A19898FF420DA116D4476B2AA58A783C1E2A2 BB2BA699502136E3187FE1E0F9C41BA75701267D851343A3D6AC0EA428AC36E5 6EE61EE445584B36F52CE503E2322C80E6A7B00A8D6E87E01F7E90150BFA509F EBD1CFD3810F32133D8D8B3ECE0C81C2733CE25CA38236D1ED442ADC0E823BB8 12F8A78259257758DD2FC52472E528511D22BB8A92748ECDA6AF3E5CD75D6682 856DE65902ED65F983BB0DB1FF2FFB8AF20335266FCFBE061215FF479EDC5BF1 865E9983668B9EC0F2E9D53D8834A2C6119D1B9D312B71FF2288A6AB68119FDA 4DFF5416E3A912D2247E99B07687C85F4E75D342E4E41A95120B046AA27F0886 E5547C4EC37A21DE32AFE0D539616B2ADF0EF89FED15B1F44DAE729FF8E33C4B E16F628E4A293B8CDA55BAE1EDF653EB75CA32A54AD5F3C9AA4A6DA0779D9E49 D5257DECF4959842839544B902628E48AFB4101A6ADA42CDFCFC8CF4E2BF2D07 C4D8832F9D1B20A0F041BB61CD1338F1F38E2B58535F441CE0E150B7243F4DFF CA2E2A20F7095AEA9D6CF507800AEEAD874A94E6F66574675DC7B4304AB2D444 77CEA0E476FA39E1E463F555E4B7427B3E77DE7E0BA7A4D25C4470543D18CA4D 91C34566465F88345A4886848FC369A814E2538996 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA1772CE422BB1D7283AD675B65 48A7EA0069A883EC1DAA3E1F9ECE7586D6CF0A128CD557C7E5D7AA3EA97EBAD3 9619D1BFCF4A6D64768741EDEA0A5B0EFBBF347CDCBE2E03D756967A16B613DB 0FC45FA2A3312E0C46A5FD0466AB097C58FFEEC40601B8395E52775D0AFCD7DB 8AB317333110531E5C44A4CB4B5ACD571A1A60960B15E450948A5EEA14DD330F EA209265DB8E1A1FC80DCD3860323FD26C113B041A88C88A21655878680A4466 FA10403D24BB97152A49B842C180E4D258C9D48F21D057782D90623116830BA3 9902B3C5F2F2DD01433B0D7099C07DBDE268D0FFED5169BCD03D48B2F058AD62 D8678C626DC7A3F352152C99BA963EF95F8AD11DB8B0D351210A17E4C2C55AD8 9EB64172935D3C20A398F3EEEEC31551966A7438EF3FEE422C6D4E05337620D5 ACC7B52BED984BFAAD36EF9D20748B05D07BE4414A63975125D272FAD83F76E6 10FFF8363014BE526D580873C5A42B70FA911EC7B86905F13AFE55EB0273F582 83158793B8CC296B8DE1DCCF1250FD57CB0E035C7EDA3B0092ED940D37A05493 2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA901C077A059F709F30 4384CB5FA748F2054FAD9A7A43D4EA427918BD414F766531136B60C3477C6632 BEFE3897B58C19276A301926C2AEF2756B367319772C9B201C49B4D935A8267B 041D6F1783B6AEA4DAC4F5B3507D7032AA640AAB12E343A4E9BDCF419C04A721 3888B25AF4E293AACED9A6BDC78E61DA1C424C6503CC1885F762BADE1E60F381 8ABB3D45547347BCA2454D6E5C5A1560CE38D9A926EEDC6FFA490ED1CD264BD0 C94DCAB5BB68785E3FD9D632A95C73E24B81DC57CEDCF18CF0AFE684D8FFC072 BC77C671698F2D7DA54F9B64C078F4AC2C901393180A9EB79381595E847BA1A3 DAB6627CA960A464C49A364058D884E3960D4E9070A3B90E4901BA7DE190680B 5676844E5AFE4C8B7DB211F8132397F78B49424DBA46346B39145BA5DD3599F9 548C23060E0945A2BBDBC7C43CDB2E2651B780D797D11026BB84D6ED76C23A00 E45E2A374C65C8F35DFE30B90E066582B142A4B3E6712136F12D7C9F3D63AE3F 3A991D97CA5D93731BDDCE7498423F5828F1563A1804B3CEC81D21E082665CD4 9B55AAEA6043B72B9236DA7981150121D86EDA08D0981BC19B518D96CFE9D7DD E9FA0B6F3C3B1E9F247C4000712084A6FE00478F425223016D14D58F34A0479D 4DC3B1E2A86B9A59D00ED0760581615D801EA912A650D50878E3E4269D207A19 7FCF41AFD2D076CA56CC27936D94FA7E04DEFA16596FE9933D1A46FB3F6DFDF7 B6CD62F0BCC4A59FF89EBE2AE4D38FD7FDBC11AA3F9868155BCF206BEFE23158 873A1299396E33EFFAB2C6C84CDF75A90A770316150BBD7F6A90004C7855033D 072B34A38447E774D13C415911180F323D538BC004BF25115835A7033A3317E9 C40184690B4F13801C7DC3AD94499CA44314985039883C7B143C34A8C48CCA65 D432DE74B86BDD5A509F47BE4FC09A25751A7AF7E60C7F1F342CC9B843ED3F29 F4650E505C63F98CDA16C5149A711EF5E1D08EC43774F44EEFFA352C154A1768 DC6C16FC6D923EB07E13368ABB60F0A35256EAAA374B56AEB6C9B0C2B8F78E39 51E0628BD64432395680B42ECF6A7C24D47E756612E650F14476C42C60849B3A AEAA51734CB342660ADB0D0F65163576E5CFD56135E0BBC01247846EB4AB2512 C66A20139E344C393FA68C2FAAE1F08A2C3ADE31F0D4A6D317D38EA2DC3EB396 507D3762530A213E69A9C7B5BC813358CDFD0ED4103059E7224BFD6196D8EF2E C3F366DABF982570FB9B32A8B3968F6CD980A7B31882598BE6638D07C237665D 5394DAC4420D1C000078F4E03E8A78E0C066AA97F06F5C20AA385BEAFB3A1350 88EB3C0FB8A5272867DD14B09ECFC617F7FEC1275D7C945C1F1509AC19DEF7A7 F6802BBAEA21A692E3E77313BCA1E49CF74BC5981DF8EABAA2DC6AF4BC98CA4B E4F177AA3880FC6422E873A629E7B7C7A8EBF2245B066796622FA775B550C312 6DFDFDA33501147C2312C5918AF7F05E620CAD2A18D5F744D72134B08D8A936B 10B3A64E17511D0AE7E46FCA6E066ADA91AD4E1046DE323A5ECB0CB2361E5C13 83905837ABF57FA51FC6E5B64B52B7C5472458A9825BEB514E3732D14F9007D7 84E3B817E117A6B905B58A3E0104D0E2A8A3B551595DFFFEBBE4E13E4AF30CAF E8E474E4EA107FE052544E39BB636FFAD35024CBC0AFA329CAEA8619F908D1BF 0F0452C9026E3856485A2C10FFA5E4DE8F2FB8733ED3FF4FECB7DA3CAF32F55D 687E05D86CAEAE7FE949B2D69F9AC80E9177BD2D9E202EE002854CD13B3E740F 343989E1DB5CCC1A2E3AEBEE4470BB610FB0D05A3B86487BE69FEC55D6107468 084A2A3F136AED4D15F17F328CB2B8D7B977E9410007E938524FA3A6CB91CAB7 A7170B71E1022EFD60FEE8EFD6B33115A4C6437B5B99CF7805AFDEB7B1594B31 F1FF160CA998F214D97C4A0CC1D725DF3EAAAAEF5CCCA58C86501BADC289411C FC95DA810796E940671807E4CD245B6D4B53477030A82BCC36F1E710092F1B3E 09343E6DD7DBCA36F78383B1647E4706A2F7FF661CE702F218326FEF5E8C703D 098766B1602EA73CE6807E9A814855FF03F0F552851C7F2A67FF16F6B97BAF4D 139D8E93CF48E7591FBCBD17B78822C3FD5018091EE837FB765D4BBCB447DD10 0791BC35297B461D9EA2EA64B9863428BF9FF7ABE1205396C77BE8E89CD892AD 3BA871DD1EE6E65DDFFFD0D4C36E3E9C6DF1B79AEC1E5D069FE01E80D1084478 69EBDAE58255063F3815DA196FB17AB2BE93E96E331133F601D674E8E8212564 E348CDED549DA8F2FBC56D6CBC6626C755ACFDB305C5D045E4109BF6227EC0C4 F83326FE8A520F6E4FFB627B4A9CF9AD66B97C1898C7108E7DCF8E21F35EFDFE 9F2119D9F3AEF602655E381321AB160B81245127E6737A81076C78358BFDA8F9 7460A10E2E93A8680FDD5C24E88690D31534521B86C96315DCA3BF492BB78D61 F20B605537492B2BD1D61C2EC76CF9F49148E1739D86 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 28 /tau put dup 30 /phi put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 62 /greater put dup 64 /partialdiff put dup 66 /B put dup 67 /C put dup 68 /D put dup 72 /H 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 83 /S put dup 84 /T put dup 86 /V put dup 88 /X put dup 89 /Y 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 109 /m put dup 110 /n put dup 112 /p put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec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%!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent 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 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 18 /grave put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 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 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 46 /period 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 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 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 97 /a put dup 101 /e put dup 104 /h put dup 108 /l put dup 109 /m put dup 111 /o put dup 114 /r put dup 121 /y put readonly def 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2039 y(+)g Fr(P)1631 1998 y Fn(!)1703 2039 y Fq(\001)g Fs(\()p Fr(!)j Fs(+)d Fr(\017)c Fs(_)-45 b Fr(y)2062 2054 y Fp(0)2102 2039 y Fs(\))22 b Fq(\000)g Fr(P)2338 1998 y Fn(!)2410 2039 y Fq(\001)g Fs(\()p Fr(!)k Fs(+)c Fr(\017)17 b Fs(_)-44 b Fr(y)2770 2054 y Fp(1)2809 2039 y Fs(\))p Fr(dt)27 b Fq(\025)1356 2277 y(\025)q Fr(\017)1490 2141 y Fk(Z)1590 2168 y Fn(T)1545 2367 y Fp(0)1661 2277 y Fr(V)22 b Fs(\()6 b(\026)-55 b Fr(x)1833 2292 y Fp(1)1895 2277 y Fs(+)22 b Fr(!)t(t)p Fs(\))f Fq(\000)i Fr(V)e Fs(\()6 b(\026)-55 b Fr(x)2423 2292 y Fp(0)2485 2277 y Fs(+)22 b Fr(!)t(t)p Fs(\))p Fr(dt)g Fq(\000)h Fr(O)s Fs(\()p Fr(\017)3084 2236 y Fp(2)3123 2277 y Fr(T)14 b Fs(\))3367 2503 y Fe(\004)555 2631 y Fs(As)37 b(it)g(is)g(reasonable)g(to)f(exp)s(ect,)j(for)d(small) h Fr(\017)p Fs(,)h(one)f(should)g(ha)m(v)m(e)p 3093 2551 89 4 v 38 w Fr(H)8 b Fs(\()p Fr(P)14 b Fs(\))34 b(=)466 2720 y Fp(1)p 466 2736 36 4 v 466 2793 a(2)511 2759 y Fq(j)p Fr(P)14 b Fq(j)644 2723 y Fp(2)706 2759 y Fs(+)24 b 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b(urthermor)i(e)456 4098 y Fs(\(9\))p 1497 4018 67 4 v 916 w Fr(L)q Fs(\()p Fr(!)t Fs(\))27 b(=)1845 4030 y(1)p 1845 4075 49 4 v 1845 4166 a(2)1904 4098 y Fq(j)p Fr(!)t Fq(j)2025 4056 y Fp(2)2085 4098 y Fs(+)22 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))p Fr(:)456 4310 y Fj(The)34 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))g Fj(term)h(c)-5 b(an)34 b(b)-5 b(e)35 b(estimate)-5 b(d)34 b(by)1731 4498 y Fr(C)7 b(\017)p Fq(k)p Fr(V)21 b Fq(k)2025 4513 y Fn(L)2073 4494 y Fg(1)2142 4498 y Fr(:)456 4699 y Ft(Pr)n(oof.)74 b Fs(F)-8 b(rom)23 b(theorem)h(1,)h(the)f(viscosit)m(y)h(solution)f Fr(u)p Fs(\()p Fr(x;)17 b(P)2764 4663 y Fn(!)2814 4699 y Fs(\))23 b(to)g(\(4\))g(is)h(semi-)456 4827 y(conca)m(v)m(e)34 b(in)g Fr(x)p Fs(,)f(and)h(therefore)f(di\013eren)m(tiable)i(at)e(its)g (minim)m(um)41 b(^)-55 b Fr(x)p Fs(;)34 b(therefore,)456 4955 y Fr(D)537 4970 y Fn(x)580 4955 y Fr(u)p Fs(\()6 b(^)-55 b Fr(x;)17 b(P)850 4919 y Fn(!)900 4955 y Fs(\))28 b(=)f(0.)43 b(Hence,)34 b(from)f(\(4\),)p 1424 5100 89 4 v 1424 5180 a Fr(H)7 b Fs(\()p Fr(P)1627 5139 y Fn(!)1677 5180 y Fs(\))28 b(=)1856 5113 y(1)p 1856 5158 49 4 v 1856 5249 a(2)1915 5180 y Fq(j)p Fr(P)2020 5139 y Fn(!)2069 5180 y Fq(j)2097 5139 y Fp(2)2159 5180 y Fs(+)22 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))p Fr(:)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 679 251 a Fl(LA)n(CK)33 b(OF)g(INTEGRABILITY)g (VIA)f(VISCOSITY)g(SOLUTION)g(METHODS)185 b(9)456 455 y Fs(T)-8 b(o)32 b(estimate)p 990 375 67 4 v 34 w Fr(L)p Fs(\()p Fr(!)t Fs(\))g(and)h(obtain)f(\(9\),)g(recall)i(that,)e(b)m(y)i (means)f(of)f(\(6\),)p 462 605 V 462 685 a Fr(L)q Fs(\()p Fr(!)t Fs(\))26 b(=)i(sup)846 766 y Fn(P)963 685 y Fq(\000)p Fr(P)14 b(!)26 b Fq(\000)p 1303 605 89 4 v 22 w Fr(H)8 b Fs(\()p Fr(P)14 b Fs(\))27 b(=)g(sup)1722 766 y Fn(P)1839 544 y Fk(\024)1891 685 y Fq(\000)p Fr(P)14 b(!)26 b Fq(\000)2241 617 y(j)p Fr(P)14 b Fq(j)2374 581 y Fp(2)p 2241 662 172 4 v 2303 753 a Fs(2)2423 544 y Fk(\025)2497 685 y Fs(+)22 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))28 b(=)2929 617 y Fq(j)p Fr(!)t Fq(j)3050 581 y Fp(2)p 2929 662 160 4 v 2984 753 a Fs(2)3120 685 y(+)22 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))p Fr(:)3367 905 y Fe(\004)555 1033 y Fs(As)33 b(a)g(corollary)f(to)h(the) g(previous)h(theorem)f(w)m(e)h(ha)m(v)m(e:)456 1227 y Fw(Corollary)39 b(1.)j Fj(F)-7 b(or)34 b(any)g Fr(!)1536 1405 y Fq(j)p Fr(P)1641 1364 y Fn(!)1713 1405 y Fs(+)22 b Fr(!)t Fq(j)27 b Fs(=)g Fr(O)s Fs(\()p Fr(\017)2189 1364 y Fp(1)p Fn(=)p Fp(2)2299 1405 y Fs(\))p Fr(:)456 1583 y Fj(The)34 b(term)h Fr(O)s Fs(\()p Fr(\017)1043 1547 y Fp(1)p Fn(=)p Fp(2)1152 1583 y Fs(\))g Fj(c)-5 b(an)34 b(b)-5 b(e)35 b(estimate)-5 b(d)34 b(by)1547 1761 y Fr(C)7 b(\017)1663 1720 y Fp(1)p Fn(=)p Fp(2)1790 1761 y Fs([1)22 b(+)g Fq(k)p Fr(V)g Fq(k)2165 1776 y Fn(L)2213 1757 y Fg(1)2282 1761 y Fs(])16 b Fr(:)456 1956 y Ft(Pr)n(oof.)87 b Fs(F)-8 b(or)32 b(an)m(y)h Fr(!)e Fq(2)d Fo(R)1503 1919 y Fn(N)1570 1956 y Fs(,)33 b(in)g(ligh)m(t)g(of)f (theorem)h(5,)f(w)m(e)i(ha)m(v)m(e)p 1346 2053 89 4 v 1346 2133 a Fr(H)7 b Fs(\()p 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Fp(2)2040 2881 y Fs(=)27 b Fr(O)s Fs(\()p Fr(\017)p Fs(\))p Fr(:)3367 3052 y Fe(\004)555 3180 y Fs(In)38 b(the)g(next)h(lemma,)h(w)m(e)f(consider)g(orbits)f(whose)h(rotation)e (n)m(um)m(b)s(ers)i(are)456 3308 y(close)e(and)g(ha)m(v)m(e)h(the)g (same)f(initial)g(p)s(oin)m(t,)h(and)f(estimate)h(the)f(di\013erence)i (b)s(e-)456 3436 y(t)m(w)m(een)47 b(their)f(actions.)84 b(F)-8 b(or)45 b(simplicit)m(y)-8 b(,)51 b(in)46 b(what)g(follo)m(ws)h (w)m(e)f(will)h(assume)456 3563 y Fr(T)41 b Fq(\025)28 b Fs(1.)456 3758 y Fw(Lemma)39 b(4.)j Fj(L)-5 b(et)35 b Fr(!)j Fj(and)c Fs(\012)i Fj(b)-5 b(e)34 b(given)g(r)-5 b(otation)35 b(numb)-5 b(ers.)45 b(Assume)35 b(that)g Fr(x)p Fs(\()p Fr(t)p Fs(\))456 3886 y Fj(and)29 b Fr(z)t Fs(\()p Fr(t)p Fs(\))i Fj(ar)-5 b(e,)31 b(r)-5 b(esp)g(e)g(ctively,)31 b(orbits)f(of)g(r)-5 b(otation)30 b(numb)-5 b(ers)30 b Fr(!)k Fj(and)c Fs(\012)p Fj(.)43 b(Supp)-5 b(ose)456 4014 y(that)37 b Fr(x)p Fs(\()p Fr(t)p Fs(\))g Fj(has)f(p)-5 b(erio)g(d)35 b Fr(T)51 b Fj(and)36 b(minimizes)f(the)h(action)g(among) g(al)5 b(l)36 b Fr(T)14 b Fj(-p)-5 b(erio)g(dic)456 4142 y(orbits)34 b(with)h(initial)f(c)-5 b(ondition)34 b Fr(x)p Fs(\(0\))p Fj(.)45 b(F)-7 b(urthermor)i(e)34 b(assume)g(that)1529 4320 y Fr(z)t Fs(\()p Fr(t)p Fs(\))29 b(=)e(\012)p Fr(t)c Fs(+)f Fr(f)11 b Fs(\(\012)p Fr(t;)17 b(\017)p Fs(\))456 4497 y Fj(satis\014es)34 b Fr(x)p Fs(\(0\))27 b(=)h Fr(z)t Fs(\(0\))p Fj(.)45 b(Then)1172 4675 y Fr(S)1232 4690 y Fn(x)1298 4675 y Fq(\000)22 b Fr(S)1457 4690 y Fn(z)1525 4675 y Fq(\024)28 b Fr(T)1717 4595 y Fk(\002)1759 4675 y Fr(C)1829 4690 y Fn(a)1870 4675 y Fr(T)j Fq(j)p Fr(!)25 b Fq(\000)d Fs(\012)p Fq(j)h Fs(+)f Fr(C)2460 4690 y Fn(b)2494 4675 y Fr(\017)2533 4634 y Fp(3)p Fn(=)p Fp(2)2643 4595 y Fk(\003)2701 4675 y Fr(;)456 4853 y Fj(the)34 b(c)-5 b(onstants)35 b(satisfy:)873 5031 y Fr(C)943 5046 y Fn(a)1068 5031 y Fq(\024)83 b Fr(C)7 b Fs(\(1)22 b(+)g Fq(k)p Fr(D)s(f)11 b Fq(k)1755 5046 y Fn(L)1803 5027 y Fg(1)1893 5031 y Fs(+)22 b Fq(k)p Fr(D)2125 4990 y Fp(2)2164 5031 y Fr(f)11 b Fq(k)2273 5046 y Fn(L)2321 5027 y Fg(1)2412 5031 y Fs(+)22 b Fq(k)p Fr(D)s(V)f Fq(k)2772 5046 y Fn(L)2820 5027 y Fg(1)2889 5031 y Fs(\))2927 4990 y Fp(2)2983 5031 y Fr(;)880 5191 y(C)950 5206 y Fn(b)1068 5191 y Fq(\024)83 b Fr(C)7 b Fs(\(1)22 b(+)g Fq(k)p Fr(V)f Fq(k)1690 5206 y Fn(L)1738 5187 y Fg(1)1807 5191 y Fs(\))c Fr(:)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 456 251 a Fl(10)666 b(DIOGO)24 b(A.)i(GOMES,)g(ENRICO)f(V)-9 b(ALDINOCI)456 450 y Ft(Pr)n(oof.)103 b Fs(Since)37 b(the)g(orbit)f Fr(x)p Fs(\()p Fr(t)p Fs(\))h(is)f (minimal,)i(the)f(orbit)42 b(~)-55 b Fr(x)35 b Fs(=)e Fr(!)t(t)25 b Fs(+)f Fr(f)11 b Fs(\()p Fr(!)t(t;)17 b(\017)p Fs(\))456 578 y(has)33 b(a)f(larger)g(action,)h(that)f(is:)791 805 y Fr(S)851 820 y Fn(x)895 805 y Fs(\()p Fr(T)14 b Fs(\))27 b Fq(\024)1163 669 y Fk(Z)1263 696 y Fn(T)1218 895 y Fp(0)1344 738 y Fs(1)p 1344 782 49 4 v 1344 873 a(2)1403 805 y Fq(j)p Fr(!)e Fs(+)d Fr(D)s(f)11 b Fs(\()p Fr(!)t(t;)17 b(\017)p 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1708 y Fp(2)2170 1749 y Fq(\000)23 b Fr(\017V)38 b Fs(\(\012)p Fr(t)23 b Fs(+)f Fr(f)11 b Fs(\(\012)p Fr(t;)17 b(\017)p Fs(\)\))g(+)1150 1967 y(+)22 b Fr(\017P)1364 1926 y Fp(\012)1442 1967 y Fq(\001)f Fs(\(\012)i(+)f Fr(D)s(f)11 b Fs(\(\012)p Fr(t;)17 b(\017)p Fs(\)\012\))22 b Fq(\000)p 2357 1887 67 4 v 23 w Fr(L)p Fs(\(\012\))p Fr(dt:)456 2151 y Fs(Then,)33 b(since)p 976 2071 V 34 w Fr(L)g Fs(is)g(con)m(v)m(ex)i(it)e(is)g(lo)s (cally)g(Lipsc)m(hitz,)h(and)f(so)1287 2242 y Fk(Z)1386 2268 y Fn(T)1342 2468 y Fp(0)p 1458 2298 V 1458 2378 a Fr(L)p Fs(\()p Fr(!)t Fs(\))22 b Fq(\000)p 1786 2298 V 22 w Fr(L)q Fs(\(\012\))28 b Fq(\024)g Fr(C)7 b Fq(j)p Fr(!)25 b Fq(\000)e Fs(\012)p Fq(j)p Fr(T)8 b(:)555 2590 y Fs(By)33 b(means)h(of)e(corollary)h(1,)746 2817 y Fr(\017)802 2681 y Fk(Z)902 2708 y Fn(T)858 2907 y Fp(0)974 2736 y Fk(\002)1015 2817 y Fr(P)1092 2776 y Fn(!)1164 2817 y Fq(\001)22 b Fs(\()p Fr(!)j Fs(+)d Fr(D)s(f)11 b Fs(\()p Fr(!)t(t;)17 b(\017)p Fs(\))p Fr(!)t Fs(\))k Fq(\000)h 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y Fq(j)p Fr(!)d Fq(\000)e Fs(\012)p Fq(j)17 b Fr(;)456 4409 y Fs(and)32 b(a)h(rough)f(estimate)i(on)e(the)h (constan)m(t)h(can)e(b)s(e)h(obtained)g(b)m(y)938 4582 y Fr(C)1008 4597 y Fp(2)1075 4582 y Fq(\024)28 b Fr(C)7 b Fs(\(1)22 b(+)g Fq(k)p Fr(D)s(f)11 b Fq(k)1707 4597 y Fn(L)1755 4578 y Fg(1)1845 4582 y Fs(+)22 b Fq(k)p Fr(D)2077 4541 y Fp(2)2116 4582 y Fr(f)11 b Fq(k)2225 4597 y Fn(L)2273 4578 y Fg(1)2364 4582 y Fs(+)22 b Fq(k)p Fr(D)s(V)f Fq(k)2724 4597 y Fn(L)2772 4578 y Fg(1)2841 4582 y Fs(\))2879 4541 y Fp(2)2935 4582 y Fr(:)3367 4755 y Fe(\004)456 4935 y Fw(Lemma)41 b(5.)i Fj(F)-7 b(or)36 b(any)h Fr(T)14 b Fj(-p)-5 b(erio)g(dic)35 b(curve)i Fr(x)p Fs(\()p Fr(t)p Fs(\))h Fj(with)e(r)-5 b(otation)37 b(numb)-5 b(er)37 b Fr(!)j Fj(we)456 5063 y(have)1720 5191 y Fr(S)1780 5206 y Fn(x)1824 5191 y Fs(\()p Fr(T)14 b Fs(\))28 b Fq(\025)g Fs(0)p Fr(:)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 679 251 a Fl(LA)n(CK)33 b(OF)g(INTEGRABILITY)g (VIA)f(VISCOSITY)g(SOLUTION)g(METHODS)147 b(11)456 450 y Ft(Pr)n(oof.)87 b Fs(Recall)33 b(that)986 698 y Fr(S)1046 713 y Fn(x)1090 698 y Fs(\()p Fr(T)14 b Fs(\))27 b(=)1368 563 y Fk(Z)1468 589 y Fn(T)1423 788 y Fp(0)1539 698 y Fr(L)p Fs(\()p Fr(x;)35 b Fs(_)-45 b Fr(x)q Fs(\))22 b(+)g Fr(P)2033 657 y Fn(!)2105 698 y Fq(\001)g Fs(\()17 b(_)-44 b Fr(x)22 b Fq(\000)h Fr(!)t Fs(\))f Fq(\000)p 2594 618 67 4 v 22 w Fr(L)q Fs(\()p Fr(!)t Fs(\))p Fr(dt;)456 951 y Fs(and)p 929 1119 V 929 1199 a Fr(L)p Fs(\()p Fr(!)t Fs(\))27 b Fq(\024)53 b Fs(lim)1268 1259 y Fn(n)p Fm(!1)1519 1132 y Fs(1)p 1479 1176 129 4 v 1479 1267 a Fr(nT)1634 1063 y Fk(Z)1734 1090 y Fn(nT)1690 1289 y Fp(0)1848 1199 y Fr(L)p Fs(\()p Fr(x;)35 b Fs(_)-45 b Fr(x)q Fs(\))22 b(+)g Fr(P)2342 1158 y Fn(!)2414 1199 y Fq(\001)g Fs(\()17 b(_)-44 b Fr(x)23 b Fq(\000)f Fr(!)t Fs(\))p Fr(dt)27 b Fs(=)1163 1484 y(=)1288 1417 y(1)p 1277 1461 71 4 v 1277 1552 a Fr(T)1374 1348 y Fk(Z)1474 1375 y Fn(T)1429 1574 y Fp(0)1545 1484 y Fr(L)p Fs(\()p Fr(x;)35 b Fs(_)-45 b Fr(x)q Fs(\))22 b(+)g Fr(P)2039 1443 y Fn(!)2111 1484 y Fq(\001)g Fs(\()17 b(_)-44 b Fr(x)22 b Fq(\000)h Fr(!)t Fs(\))p Fr(dt:)3367 1735 y Fe(\004)555 1863 y Fs(W)-8 b(e)31 b(sho)m(w)g(in)g(the)f(next)h(lemma)g(that)f(the)h(action)f Fr(S)36 b Fs(of)30 b(a)g(minimizing)i(curv)m(e)456 1990 y(is)h(almost)g(indep)s(enden)m(t)h(on)f(the)g(initial)g(p)s(oin)m(t.) 456 2205 y Fw(Lemma)h(6.)k Fj(Supp)-5 b(ose)31 b(that)g(the)g(system)g (is)f(smo)-5 b(othly)31 b(inte)-5 b(gr)g(able)30 b(at)h Fs(\012)h Fj(and)e(let)456 2333 y Fr(z)i Fs(=)c(\012)p Fr(t)22 b Fs(+)g Fr(f)11 b Fs(\(\012)p Fr(t;)17 b(\017)p Fs(\))p Fj(.)45 b(Then,)1302 2546 y Fq(j)p Fr(S)1390 2561 y Fn(z)1429 2546 y Fs(\()p Fr(T)14 b Fs(\))p Fq(j)27 b(\024)h Fr(C)7 b(\017)1852 2505 y Fp(1)p Fn(=)p Fp(2)1963 2546 y Fq(k)p Fr(z)t Fs(\()p Fr(T)14 b Fs(\))22 b Fq(\000)g Fr(z)t Fs(\(0\))p Fq(k)17 b Fr(;)456 2759 y Fj(in)45 b(which)f Fq(k)30 b(\001)g(k)45 b Fj(is)h(the)f(p)-5 b(erio)g(dic)45 b(distanc)-5 b(e)44 b(in)i(the)f(torus.)77 b(F)-7 b(urthermor)i(e,)48 b(if)456 2887 y Fr(!)31 b Fq(2)659 2848 y Fp(1)p 652 2864 51 4 v 652 2921 a Fn(T)712 2887 y Fo(Z)778 2851 y Fn(N)846 2887 y Fj(,)k(then)1401 3061 y Fq(j)p Fr(S)1489 3076 y Fn(z)1529 3061 y Fs(\()p Fr(T)14 b Fs(\))p Fq(j)27 b(\024)h Fr(C)1906 3076 y Fp(1)1945 3061 y Fr(\017)1984 3020 y Fp(1)p Fn(=)p Fp(2)2094 3061 y Fq(j)p Fr(!)e Fq(\000)c Fs(\012)p Fq(j)p Fr(T)8 b(;)456 3252 y Fj(and)34 b(the)h(c)-5 b(onstant)34 b Fr(C)1265 3267 y Fp(1)1332 3252 y Fq(\024)28 b Fr(C)7 b Fs(\(1)22 b(+)g Fq(k)p Fr(D)s(f)11 b Fq(k)1964 3267 y Fn(L)2012 3248 y Fg(1)2080 3252 y Fs(\)\(1)22 b(+)g Fq(k)p Fr(D)s(V)f Fq(k)2587 3267 y Fn(L)2635 3248 y Fg(1)2704 3252 y Fs(\))p Fj(.)456 3467 y Ft(Pr)n(oof.)107 b Fs(The)38 b(\014rst)f(estimate)i (follo)m(ws)f(from)f(the)g(existence)j(of)d(a)f(\()p Fr(C)3180 3430 y Fp(1)3220 3467 y Fs(\))h(vis-)456 3594 y(cosit)m(y)d(solution)g Fr(u)e Fs(corresp)s(onding)i(to)f(\012,)h (from)f Fw(\(A\))f Fs(at)g(page)h(2,)h(the)f(a-priori)456 3722 y(Lipsc)m(hitz)h(estimates)g(of)e(lemma)i(1,)e(and)1370 3935 y Fr(S)1430 3950 y Fn(z)1470 3935 y Fs(\()p Fr(T)14 b Fs(\))27 b(=)h Fr(u)p Fs(\()p Fr(z)t Fs(\(0\)\))22 b Fq(\000)g Fr(u)p Fs(\()p Fr(z)t Fs(\()p Fr(T)14 b Fs(\)\))p Fr(:)456 4148 y Fs(The)33 b(second)h(estimate)g(follo)m(ws)f(from)f (the)h(\014rst)g(one)g(and)g(the)g(h)m(yp)s(othesis.)76 b Fe(\004)555 4276 y Fs(By)46 b(com)m(bining)g(all)f(the)g(previous)h (lemmas,)k(one)45 b(can)g(pro)m(v)m(e)h(that)f(if)g(the)456 4404 y(Melnik)m(o)m(v)33 b(gap)e Fr(M)10 b Fs(,)32 b(as)f(de\014ned)i (in)e(\(7\),)g(is)g(to)s(o)g(large,)g(then)h(the)f(system)i(is)e(not) 456 4532 y(smo)s(othly)i(in)m(tegrable)g(at)g(\012.)456 4747 y Fw(Theorem)44 b(6.)g Fj(Supp)-5 b(ose)39 b(the)h(system)f(is)h (smo)-5 b(othly)39 b(inte)-5 b(gr)g(able)39 b(at)h Fs(\012)g Fj(and)f(as-)456 4875 y(sume)d(that)g(ther)-5 b(e)36 b(ar)-5 b(e)36 b(two)h(p)-5 b(erio)g(dic)35 b(orbits)h Fr(x)2199 4890 y Fp(0)2239 4875 y Fr(;)17 b(x)2338 4890 y Fp(1)2377 4875 y Fj(,)37 b(with)f(p)-5 b(erio)g(d)35 b Fr(T)14 b Fj(,)37 b(with)f(fr)-5 b(e-)456 5003 y(quency)34 b Fr(!)d Fq(2)983 4963 y Fp(1)p 975 4980 V 975 5037 a Fn(T)1036 5003 y Fo(Z)1102 4966 y Fn(N)1170 5003 y Fj(,)k(of)f(the)h (form)1449 5216 y Fr(x)1504 5231 y Fn(i)1532 5216 y Fs(\()p Fr(t)p Fs(\))28 b(=)34 b(\026)-55 b Fr(x)1830 5231 y Fn(i)1880 5216 y Fs(+)22 b Fr(!)t(t)g Fs(+)g Fr(\017y)2285 5231 y Fn(i)2313 5216 y Fs(\()p Fr(t)p Fs(\))p Fr(;)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 456 251 a Fl(12)666 b(DIOGO)24 b(A.)i(GOMES,)g(ENRICO)f(V)-9 b(ALDINOCI)456 450 y Fj(as)31 b(in)h(lemma)f(2.)43 b(L)-5 b(et)32 b(us)h(assume)e(that)h Fr(x)2007 465 y Fn(i)2068 450 y Fj(ar)-5 b(e)31 b(action)h(minimizing)e (among)h(al)5 b(l)456 578 y Fr(T)14 b Fj(-p)-5 b(erio)g(dic)33 b(orbits)i(with)g(initial)f(c)-5 b(ondition)34 b Fr(x)2178 593 y Fn(i)2206 578 y Fs(\(0\))p Fj(.)45 b(L)-5 b(et)1160 831 y Fr(M)38 b Fs(=)1396 695 y Fk(Z)1496 721 y Fn(T)1451 921 y Fp(0)1567 831 y Fr(V)22 b Fs(\()6 b(\026)-55 b Fr(x)1739 846 y Fp(1)1801 831 y Fs(+)22 b Fr(!)t(t)p Fs(\))f Fq(\000)i Fr(V)f Fs(\()6 b(\026)-55 b Fr(x)2330 846 y Fp(0)2392 831 y Fs(+)22 b Fr(!)t(t)p Fs(\))p Fr(dt:)456 1063 y Fj(Then,)456 1301 y Fs(\(10\))610 b Fr(M)38 b Fq(\024)1477 1161 y Fk(\024)1530 1301 y Fr(C)1600 1316 y Fp(1)1666 1234 y Fr(T)1737 1198 y Fp(2)p 1666 1279 111 4 v 1701 1370 a Fr(\017)1803 1301 y Fq(j)p Fr(!)25 b Fq(\000)d Fs(\012)p Fq(j)h Fs(+)f Fr(C)2305 1316 y Fp(2)2344 1301 y Fr(\017)2383 1260 y Fp(1)p Fn(=)p Fp(2)2493 1301 y Fr(T)2564 1161 y Fk(\025)2633 1301 y Fr(:)456 1548 y Fj(The)k(c)-5 b(onstant)26 b Fr(C)1097 1563 y Fp(1)1164 1548 y Fj(dep)-5 b(ends)25 b(p)-5 b(olynomial)5 b(ly)26 b(in)h Fq(k)p Fr(D)s(f)11 b Fq(k)2434 1563 y Fn(L)2482 1544 y Fg(1)2550 1548 y Fj(,)28 b Fq(k)p Fr(D)2742 1512 y Fp(2)2781 1548 y Fr(f)11 b Fq(k)2890 1563 y Fn(L)2938 1544 y Fg(1)3007 1548 y Fj(,)28 b Fq(k)p Fr(D)s(V)21 b Fq(k)3327 1563 y Fn(L)3375 1544 y Fg(1)456 1676 y Fj(and)k Fq(k)p Fr(V)c Fq(k)814 1691 y Fn(L)862 1672 y Fg(1)931 1676 y Fj(;)29 b(the)d(c)-5 b(onstant)26 b Fr(C)1593 1691 y Fp(2)1658 1676 y Fj(dep)-5 b(ends)25 b(p)-5 b(olynomial)5 b(ly)25 b(in)g Fq(k)p Fr(D)s(V)d Fq(k)2945 1691 y Fn(L)2993 1672 y Fg(1)3062 1676 y Fj(,)27 b Fq(k)p Fr(V)22 b Fq(k)3298 1691 y Fn(L)3346 1672 y Fg(1)3415 1676 y Fj(,)456 1804 y(in)34 b Fq(k)p Fr(y)673 1819 y Fn(i)701 1804 y Fq(k)751 1819 y Fn(L)799 1800 y Fg(1)868 1804 y Fj(,)g Fq(k)18 b Fs(_)-45 b Fr(y)1030 1819 y Fn(i)1058 1804 y Fq(k)1108 1819 y Fn(L)1156 1800 y Fg(1)1225 1804 y Fj(.)456 2007 y Ft(Pr)n(oof.)92 b Fs(Let)34 b Fr(z)1112 2022 y Fn(i)1174 2007 y Fs(b)s(e)f(a)h(minimal)g(orbit)g(with)g(frequency)i(\012)e(of)f (the)h(form)g(\(2\),)456 2135 y(with)e(initial)f(condition)38 b(\026)-55 b Fr(z)1429 2150 y Fn(i)1485 2135 y Fs(=)34 b(\026)-55 b Fr(x)1644 2150 y Fn(i)1673 2135 y Fs(.)43 b(Notice)32 b(that)f(the)h(p)s(ossibilit)m(y)h(of)e(this)h(c)m(hoice) 456 2263 y(dep)s(ends)j(on)g(assumption)g Fw(\(A\))p Fs(.)e(Assume)k Fr(S)2146 2278 y Fn(x)2186 2287 y Fi(0)2255 2263 y Fq(\024)31 b Fr(S)2423 2278 y Fn(x)2463 2287 y Fi(1)2501 2263 y Fs(.)49 b(Then)35 b(\(ev)-5 b(aluating)34 b(all)456 2390 y(actions)f(at)f(time)h Fr(T)14 b Fs(\))1219 2583 y Fr(S)1279 2598 y Fn(x)1319 2607 y Fi(1)1379 2583 y Fq(\000)23 b Fr(S)1539 2598 y Fn(x)1579 2607 y Fi(0)1645 2583 y Fq(\024)28 b Fr(S)1810 2598 y Fn(x)1850 2607 y Fi(1)1911 2583 y Fq(\000)23 b Fr(S)2071 2598 y Fn(z)2104 2607 y Fi(1)2164 2583 y Fs(+)f Fr(S)2322 2598 y Fn(z)2355 2607 y Fi(1)2416 2583 y Fq(\000)h Fr(S)2576 2598 y Fn(x)2616 2607 y Fi(0)2654 2583 y Fr(:)456 2776 y Fs(F)-8 b(rom)32 b(lemma)h(2,)f(w)m(e)i(ha)m(v)m(e)1424 2968 y Fr(\017M)g Fq(\000)22 b Fr(C)7 b(\017)1806 2927 y Fp(2)1846 2968 y Fr(T)42 b Fq(\024)28 b Fr(S)2110 2983 y Fn(x)2150 2992 y Fi(1)2210 2968 y Fq(\000)23 b Fr(S)2370 2983 y Fn(x)2410 2992 y Fi(0)2448 2968 y Fr(:)456 3161 y Fs(Lemma)33 b(4)f(yields)1139 3353 y Fr(S)1199 3368 y Fn(x)1239 3377 y Fi(1)1299 3353 y Fq(\000)23 b Fr(S)1459 3368 y Fn(z)1492 3377 y Fi(1)1558 3353 y Fq(\024)28 b Fr(T)1750 3273 y Fk(\002)1792 3353 y Fr(C)1862 3368 y Fn(a)1903 3353 y Fr(T)j Fq(j)p Fr(!)25 b Fq(\000)d Fs(\012)p Fq(j)h Fs(+)f Fr(C)2493 3368 y Fn(b)2527 3353 y Fr(\017)2566 3312 y Fp(3)p Fn(=)p Fp(2)2676 3273 y Fk(\003)2734 3353 y Fr(:)456 3546 y Fs(Lemma)33 b(6)f(implies)1459 3694 y Fq(j)p Fr(S)1547 3709 y Fn(z)1580 3718 y Fi(1)1618 3694 y Fq(j)27 b(\024)h Fr(C)1848 3709 y Fp(1)1888 3694 y Fr(\017)1927 3653 y Fp(1)p Fn(=)p Fp(2)2037 3694 y Fq(j)p Fr(!)d Fq(\000)e Fs(\012)p Fq(j)p Fr(T)8 b(:)456 3864 y Fs(Finally)-8 b(,)32 b(from)h(lemma)g(5)1776 4012 y Fr(S)1836 4027 y Fn(x)1876 4036 y Fi(0)1943 4012 y Fq(\025)28 b Fs(0)p Fr(;)456 4182 y Fs(yields)34 b(the)f(last)g (inequalit)m(y)h(necessary)h(to)d(the)h(estimate.)729 b Fe(\004)1038 4443 y Fs(4.)49 b Ft(Constr)n(uction)38 b(of)g(Periodic)g(Orbits)555 4629 y Fs(The)51 b(main)f(goal)g(of)f (this)i(section)g(is)f(to)g(use)h(a)e(w)m(ell)j(kno)m(wn)f(Liapuno)m (v-)456 4757 y(Sc)m(hmidt)32 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Fn(n)874 4847 y Fh(i)929 4812 y Fs(and)g Fr(!)1175 4776 y Fm(0)1171 4837 y Fn(n)1214 4847 y Fh(j)1275 4812 y Fs(are)g(non-parallel)g(for)g(eac)m(h)h Fr(i;)17 b(j)34 b Fs(=)27 b(1)p Fr(;)17 b(:)g(:)g(:)f(;)h(k)s Fs(.)40 b(Then,)28 b(there)456 4940 y(m)m(ust)40 b(b)s(e)f(an)f(index)i Fr(n)1311 4904 y Fm(\003)1389 4940 y Fr(>)f(n)1562 4955 y Fn(k)1643 4940 y Fs(so)g(that)g Fr(!)2052 4904 y Fm(0)2048 4965 y Fn(n)2091 4946 y Fg(\003)2169 4940 y Fs(is)h(parallel)f(to)f (none)i(of)e(the)h Fr(!)3348 4904 y Fm(0)3344 4965 y Fn(n)3387 4975 y Fh(i)3417 4940 y Fs(.)456 5068 y(Indeed,)k(if)d(not,)h (there)g(is)f(a)g(subsequence)j(whic)m(h)f(is)e(parallel)g(to)g(some)h Fr(!)3314 5032 y Fm(0)3310 5093 y Fn(n)3353 5103 y Fh(i)3375 5118 y Fi(0)3417 5068 y Fs(;)456 5199 y(since)36 b(suc)m(h)f (subsequence)k(con)m(v)m(erges)d(to)e(\012)2101 5163 y Fm(0)2160 5199 y Fs(and)g Fr(!)2416 5163 y Fm(0)2412 5224 y Fn(n)2455 5234 y Fh(i)2477 5249 y Fi(0)2554 5199 y Fs(is)h(rational,)g(w)m(e)g(w)m(ould)p eop end 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Fm(0)1068 887 y Fn(n)1143 862 y Fs(=)1282 823 y Fp(1)p 1258 839 84 4 v 1258 897 a Fn(T)1299 905 y Fh(n)1352 862 y Fs(\()p Fr(\027)1438 877 y Fn(n)p Fp(1)1520 862 y Fr(;)17 b(\027)1612 877 y Fn(n)p Fp(2)1694 862 y Fs(\),)34 b(with)f Fr(\027)2063 877 y Fn(n)p Fp(1)2146 862 y Fr(;)17 b(\027)2238 877 y Fn(n)p Fp(2)2349 862 y Fq(2)29 b Fo(Z)p Fs(.)46 b(Consider)35 b(a)e(sequence)456 995 y Fr(k)507 1010 y Fn(n)593 995 y Fs(=)40 b(\()p Fq(\000)p Fr(\027)872 1010 y Fn(n)p Fp(2)954 995 y Fr(;)17 b(\027)1046 1010 y Fn(n)p Fp(1)1129 995 y Fr(;)g Fs(0)p Fr(;)g(:)g(:)g(:)e(;)i Fs(0\))39 b Fq(2)h Fo(Z)1738 958 y Fn(N)1806 995 y Fs(.)64 b(Then,)43 b Fq(j)p Fr(k)2267 1010 y Fn(n)2313 995 y Fq(j)d(\024)56 b Fs(const)18 b Fr(T)2811 1010 y Fn(n)2858 995 y Fs(,)41 b Fr(!)2987 1010 y Fn(n)3061 995 y Fq(\001)27 b Fr(k)3167 1010 y Fn(n)3253 995 y Fs(=)40 b(0,)456 1122 y(and)32 b Fr(!)706 1137 y Fn(i)756 1122 y Fq(\001)22 b Fr(k)857 1137 y Fn(n)932 1122 y Fq(6)p Fs(=)27 b(0)32 b(if)h Fr(n)28 b Fq(6)p Fs(=)f Fr(i)p Fs(.)44 b(Therefore,)906 1226 y Fk(Z)1005 1253 y Fn(T)1046 1263 y Fh(j)961 1452 y Fp(0)1100 1362 y Fs(cos\(2)p Fr(\031)t(k)1427 1377 y Fn(n)1496 1362 y Fq(\001)22 b Fs(\()6 b(\026)-55 b Fr(x)22 b Fs(+)g Fr(!)1820 1377 y Fn(j)1856 1362 y Fr(t)p Fs(\)\))p Fr(dt)28 b Fs(=)g Fr(\016)2228 1377 y Fn(nj)2307 1362 y Fr(T)2364 1377 y Fn(n)2428 1362 y Fs(cos)q(\(2)p Fr(\031)t(k)2756 1377 y Fn(n)2824 1362 y Fq(\001)g Fs(\026)-55 b Fr(x)p Fs(\))p Fr(:)456 1585 y Fs(Let)1299 1769 y Fr(V)21 b Fs(\()p Fr(x)p Fs(\))28 b(=)1676 1644 y Fm(1)1640 1674 y Fk(X)1645 1883 y Fn(n)p Fp(=1)1800 1769 y Fr(e)1845 1728 y Fm(\000)p Fn(cT)1972 1736 y Fh(n)2035 1769 y Fs(cos)q(\(2)p Fr(\031)t(k)2363 1784 y Fn(n)2431 1769 y Fq(\001)22 b Fr(x)p Fs(\))p Fr(;)456 2005 y Fs(for)32 b(some)h Fr(c)28 b(>)f Fs(0)33 b(su\016cien)m(tly)i(large)d(to)h(mak)m(e)g Fr(V)54 b Fs(analytic.)555 2133 y(W)-8 b(e)48 b(will)h(sho)m(w)g(that)e (for)h(a)f(sequence)k Fr(\017)2141 2148 y Fn(n)2241 2133 y Fq(!)j Fs(0)47 b(the)h(inequalit)m(y)i(\(10\))d(in)456 2261 y(theorem)33 b(6)f(is)h(not)g(satis\014ed.)555 2389 y(Fix)g Fr(!)791 2404 y Fn(n)870 2389 y Fs(and)f(c)m(ho)s(ose)h Fr(\017)1407 2404 y Fn(n)1482 2389 y Fs(=)28 b Fr(e)1631 2353 y Fm(\000)p Fn(dT)1763 2361 y Fh(n)1810 2389 y Fs(,)k(for)g(some)h Fr(d)28 b(>)f Fs(0)32 b(to)g(b)s(e)h(determined.)45 b(By)456 2517 y(corollary)33 b(2)h(and)f(lemma)i(9,)e(w)m(e)i(obtain)e(t)m(w)m (o)h(p)s(erio)s(dic)g(orbits)g(of)f(the)h(system,)456 2645 y(whic)m(h)d(are)f(action)f(minimizing)j(among)d(tra)5 b(jectories)31 b(with)f(their)h(same)f(initial)456 2772 y(p)s(oin)m(t,)45 b(and)e(whose)h(Melnik)m(o)m(v)i(gap)c(is,)k(at)d (least,)j(of)c(the)h(order)g(of)g Fr(T)3152 2787 y Fn(n)3199 2772 y Fr(e)3244 2736 y Fm(\000)p Fn(cT)3371 2744 y Fh(n)3417 2772 y Fs(.)456 2900 y(Then,)33 b(b)m(y)h(means)g(of)e(\(3\),)g (inequalit)m(y)i(\(10\))e(reads)534 3135 y Fr(e)579 3094 y Fm(\000)p Fn(cT)706 3102 y Fh(n)780 3135 y Fq(\024)c Fr(K)968 3150 y Fp(1)1007 3135 y Fr(T)1078 3094 y Fn(K)1138 3103 y Fi(2)1064 3160 y Fn(n)1193 2994 y Fk(\022)1276 3068 y Fq(j)p Fs(\012)22 b Fq(\000)h Fr(!)1557 3083 y Fn(n)1604 3068 y Fq(j)p 1276 3112 356 4 v 1385 3213 a Fr(\017)1424 3169 y Fn(K)1484 3178 y Fi(3)1424 3223 y Fn(n)1664 3135 y Fs(+)1762 3066 y Fq(p)p 1845 3066 87 4 v 69 x Fr(\017)1884 3150 y Fn(n)1931 2994 y Fk(\023)2032 3135 y Fq(\024)28 b Fr(K)2220 3150 y Fp(1)2260 3135 y Fr(T)2331 3094 y Fn(K)2391 3103 y Fi(2)2317 3160 y Fn(n)2429 3135 y Fs(\()p Fr(e)2512 3094 y Fp(\()p Fn(dK)2635 3103 y Fi(3)2670 3094 y Fm(\000)p Fn(b)p Fp(\))p Fn(T)2823 3102 y Fh(n)2892 3135 y Fs(+)22 b Fr(e)3035 3094 y Fm(\000)p Fn(dT)3167 3102 y Fh(n)3210 3094 y Fn(=)p Fp(2)3285 3135 y Fs(\))17 b Fr(;)456 3364 y Fs(for)25 b(suitable)h(p)s(ositiv)m(e)h (constan)m(ts)g Fr(K)1816 3379 y Fn(i)1844 3364 y Fs(.)41 b(Therefore,)28 b(if)e Fr(d)h(>)g Fs(2)p Fr(c)f Fs(and)f Fr(b)j(>)g(c)8 b Fs(+)g Fr(K)3328 3379 y Fp(3)3367 3364 y Fr(d)p Fs(,)456 3492 y(this)33 b(inequalit)m(y)h(fails)f(as)g Fr(T)1479 3507 y Fn(n)1554 3492 y Fq(!)27 b(1)p Fs(.)1559 b Fe(\004)1660 3733 y Ft(References)456 3900 y Fv([A)n(CZE87])39 b(A.)c(Am)n(brosetti,)h(V.)f(Coti)f(Zelati,)h(and)f(I.)h(Ek)n(eland.)e (Symmetry)h(breaking)f(in)853 4010 y(Hamiltonian)28 b(systems.)f Fb(J.)j(Di\013er)l(ential)g(Equations)p Fv(,)e(67\(2\):165{184,)c (1987.)456 4120 y([BBV03])87 b(Massimiliano)29 b(Berti,)h(Luca)f (Biasco,)g(and)h(Enrico)e(V)-7 b(aldino)r(ci.)30 b(P)n(erio)r(dic)e (orbits)853 4229 y(close)19 b(to)f(elliptic)i(tori)e(and)h (applications)f(to)h(the)h(three-b)r(o)r(dy)e(problem.)h Fb(pr)l(eprint)p Fv(,)853 4339 y(2003.)456 4448 y([Bes00])138 b(Ugo)32 b(Bessi.)g(An)h(analytic)f(coun)n(terexample)g(to)g(the)h(KAM) g(theorem.)f Fb(Er)l(go)l(dic)853 4558 y(The)l(ory)g(Dynam.)e(Systems)p Fv(,)d(20\(2\):317{333,)d(2000.)456 4668 y([E99])210 b(W)-7 b(einan)38 b(E.)f(Aubry-Mather)f(theory)h(and)g(p)r(erio)r(dic)g (solutions)g(of)g(the)h(forced)853 4777 y(Burgers)26 b(equation.)h Fb(Comm.)k(Pur)l(e)f(Appl.)h(Math.)p Fv(,)e (52\(7\):811{828,)23 b(1999.)456 4887 y([EG01])145 b(L.)36 b(C.)g(Ev)-5 b(ans)34 b(and)i(D.)g(Gomes.)f(E\013ectiv)n(e)g (Hamiltonians)g(and)h(a)n(v)n(eraging)c(for)853 4996 y(Hamiltonian)24 b(dynamics.)f(I.)h Fb(A)n(r)l(ch.)i(R)l(ation.)h(Me)l (ch.)g(A)n(nal.)p Fv(,)e(157\(1\):1{33,)c(2001.)456 5106 y([F)-7 b(at97a])104 b(Alb)r(ert)29 b(F)-7 b(athi.)29 b(Solutions)f(KAM)g(faibles)h(conjugu)n(\023)-39 b(ees)26 b(et)j(barri)n(\022)-39 b(eres)25 b(de)k(Peierls.)853 5216 y Fb(C.)i(R.)f(A)l(c)l(ad.)g(Sci.)h(Paris)g(S)n(\023)-40 b(er.)30 b(I)f(Math.)p Fv(,)g(325\(6\):649{652,)23 b(1997.)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 456 251 a Fl(18)666 b(DIOGO)24 b(A.)i(GOMES,)g(ENRICO)f(V)-9 b(ALDINOCI)456 450 y Fv([F)i(at97b])100 b(Alb)r(ert)52 b(F)-7 b(athi.)52 b(Th)n(\023)-39 b(eor)n(\022)g(eme)48 b(KAM)j(faible)g(et)h(th)n(\023)-39 b(eorie)49 b(de)i(Mather)g(sur)g (les)853 560 y(syst)n(\022)-39 b(emes)24 b(lagrangiens.)f Fb(C.)28 b(R.)g(A)l(c)l(ad.)g(Sci.)g(Paris)h(S)n(\023)-40 b(er.)28 b(I)f(Math.)p Fv(,)g(324\(9\):1043{)853 669 y(1046,)f(1997.)456 779 y([F)-7 b(at98a])104 b(Alb)r(ert)37 b(F)-7 b(athi.)36 b(Orbite)g(h)n(\023)-39 b(et)n(\023)g(ero)r(clines)34 b(et)i(ensem)n(ble)g(de)g(Peierls.)f Fb(C.)j(R.)g(A)l(c)l(ad.)853 888 y(Sci.)31 b(Paris)g(S)n(\023)-40 b(er.)30 b(I)g(Math.)p Fv(,)f(326:1213{1216,)22 b(1998.)456 998 y([F)-7 b(at98b])100 b(Alb)r(ert)30 b(F)-7 b(athi.)29 b(Sur)f(la)h(con)n(v)n(ergence)d(du)j (semi-group)r(e)f(de)g(Lax-Oleinik.)g Fb(C.)j(R.)853 1108 y(A)l(c)l(ad.)g(Sci.)f(Paris)h(S)n(\023)-40 b(er.)30 b(I)g(Math.)p Fv(,)f(327:267{270,)23 b(1998.)456 1217 y([F)-7 b(or94])145 b(Gio)n(v)-5 b(anni)22 b(F)-7 b(orni.)22 b(Analytic)h(destruction)f(of)g(in)n(v)-5 b(arian)n(t)22 b(circles.)f Fb(Er)l(go)l(dic)27 b(The)l(ory)853 1327 y(Dynam.)k(Systems)p Fv(,)c(14\(2\):267{298,)c(1994.)456 1436 y([FS93])167 b(W)-7 b(endell)37 b(H.)f(Fleming)g(and)g(H.)h(Mete)f (Soner.)f Fb(Contr)l(ol)t(le)l(d)k(Markov)g(pr)l(o)l(c)l(esses)853 1546 y(and)31 b(visc)l(osity)g(solutions)p Fv(.)d(Springer-V)-7 b(erlag,)25 b(New)j(Y)-7 b(ork,)26 b(1993.)456 1656 y([Gom02])91 b(Diogo)26 b(Aguiar)g(Gomes.)g(Viscosit)n(y)g(solutions)g(of)g (Hamilton-Jacobi)f(equations,)853 1765 y(and)20 b(asymptotics)f(for)h (Hamiltonian)f(systems.)h Fb(Calc.)k(V)-6 b(ar.)23 b(Partial)h (Di\013er)l(ential)853 1875 y(Equations)p Fv(,)29 b(14\(3\):345{357,)23 b(2002.)456 1984 y([LPV88])96 b(P)-7 b(.)32 b(L.)h(Lions,)g(G.)f(P)n (apanicolao,)f(and)h(S.)h(R.)f(S.)h(V)-7 b(aradhan.)31 b(Homogeneization)853 2094 y(of)d(Hamilton-Jacobi)e(equations.)h Fb(Pr)l(eliminary)k(V)-6 b(ersion)p Fv(,)28 b(1988.)456 2204 y([Mat86])117 b(John)28 b(Mather.)h(A)g(criterion)e(for)h(the)h (nonexistence)f(of)h(in)n(v)-5 b(arian)n(t)27 b(circles.)h Fb(Inst.)853 2313 y(Hautes)1144 2292 y(\023)1132 2313 y(Etudes)h(Sci.)i(Publ.)f(Math.)p Fv(,)f(\(63\):153{204,)24 b(1986.)456 2423 y([Mat88])117 b(John)19 b(N.)g(Mather.)f(Destruction)h (of)g(in)n(v)-5 b(arian)n(t)18 b(circles.)g Fb(Er)l(go)l(dic)23 b(The)l(ory)g(Dynam.)853 2532 y(Systems)p Fv(,)28 b(8)1235 2502 y Fa(\003)1272 2532 y Fv(\(Charles)f(Conley)g(Memorial)g (Issue\):199{214,)d(1988.)1651 2860 y(Diogo)j(A.)h(Gomes)560 2970 y(Departamen)n(to)e(de)i(Matem\023)-42 b(atica,)27 b(Instituto)h(Sup)r(erior)f(T)n(\023)-39 b(ecnico,)26 b(Lisb)r(oa,)h(1049-001,)1794 3080 y(P)n(ortugal)1380 3189 y(e-mail:)36 b(dgomes@math.ist.utl.pt)1648 3416 y(Enrico)27 b(V)-7 b(aldino)r(ci)515 3526 y(Dipartimen)n(to)28 b(di)g(Matematica,)f(Univ)n(ersit\022)-42 b(a)26 b(di)i(Roma)f(T)-7 b(or)27 b(V)-7 b(ergata,)26 b(Roma,)h(I-00133,)1865 3635 y(Italy)1323 3745 y(e-mail:)36 b(v)-5 b(aldino)r(ci@mat.uniroma2.it)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF