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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 112 /p put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM5 %!PS-AdobeFont-1.1: MSBM5 2.1 %%CreationDate: 1992 Oct 17 08:36:07 % 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 (MSBM5) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM5 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 readonly def /FontBBox{0 -574 3027 1074}readonly def /UniqueID 5032013 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put dup 101 /e put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 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 3 /square put dup 22 /harpoonupright put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 44 /comma put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 58 /colon put dup 65 /A put dup 67 /C put dup 70 /F put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W 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 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 readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % 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 (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 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 19 /acute put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 58 /colon 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 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 87 /W put dup 92 /quotedblleft 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 127 /dieresis put readonly def /FontBBox{-35 -250 1190 750}readonly def /UniqueID 5000826 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSL10 %!PS-AdobeFont-1.1: CMSL10 1.0 %%CreationDate: 1991 Aug 20 16:40:20 % 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 (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 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 34 /quotedblright put dup 35 /numbersign 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 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 84 /T put dup 90 /Z put dup 92 /quotedblleft 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 119 /w put dup 121 /y put readonly def /FontBBox{-62 -250 1123 750}readonly def /UniqueID 5000798 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % 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 (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 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 6 /plusminus put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 20 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash 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 dup 114 /nabla put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 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%!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 76 /L put dup 77 /M put dup 78 /N put dup 106 /j put dup 107 /k put dup 108 /l put dup 114 /r put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA06DA87FC7163A5A2A756A598FAB07633 89DE8BB201D5DB4627484A80A431B6AFDBBBF23D4157D4AFE17E6B1C853DD417 25F84CD55402AB88AB7EEFDEDBF2C2C731BD25567C53B474CCF739188A930039 098A197F9C4BE7594D79442B2C8A67447DE44698321145D7689B91EF235EA80E B600AA8E238064F154284096C4C2554EFE8DDF13AFF8D3CE30E0999375C0FEE6 F992DEA5FC3897E2CC8B7A90238E61E41622DE80F438DD994C73275CC52249D9 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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 (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 67 /C put dup 82 /R put 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: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle 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 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 62 /braceex put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 101 /tildewide put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 112 /radicalbig put dup 113 /radicalBig put dup 115 /radicalBigg 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 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 27 /sigma put dup 30 /phi put dup 31 /chi put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 64 /partialdiff put dup 72 /H put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 83 /S put dup 87 /W put dup 97 /a put dup 99 /c put dup 100 /d 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 126 /vector put readonly def /FontBBox{0 -250 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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 67 /C put dup 73 /I put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 7 /Upsilon put dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put 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 61 /equal put dup 65 /A put dup 66 /B put dup 68 /D put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O 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 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 108 /l put dup 111 /o put dup 112 /p put dup 115 /s put dup 117 /u put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 13 /circlecopyrt put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 25 /approxequal put dup 26 /propersubset put dup 33 /arrowright put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 59 /emptyset put dup 68 /D put dup 82 /R put dup 91 /union put dup 92 /intersection put dup 94 /logicaland 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 110 /backslash put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H 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 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 90 /Z 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /vector put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 7 /Upsilon 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 34 /quotedblright put dup 39 /quoteright 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 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 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 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 91 /bracketleft put dup 92 /quotedblleft 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 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 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. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 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 19 /acute put dup 34 /quotedblright 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 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight 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 88 /X put dup 89 /Y put dup 92 /quotedblleft 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 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 127 /dieresis put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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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 76 /L put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 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 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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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 11 /ff put dup 12 /fi 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 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 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 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 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 127 /dieresis 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 2EC54E09B984FCA4AB7D2EA182BCF1263AA244B07EC0EA912A2BCC6CA6105B29 044005DDBEAF88E0F05541BBD233977A447B469F013D8535A9D7023CC0FB7B49 A95CD2B6F18935C37F49E9A73E97A8602C5C26EE13D7A04A188336FCAB4CDEE0 23DE9D803FD6E8D846B3F729BD36137E834E016242CD2F7BF048959DD45AD413 19B985D05E5D422F3D0968375EA6A90FBEBF8B42B15F15280469D69629C08A42 1C298CC027CC288B9C984239ABB96B6A891C1360D08F9ECC22202861E4CE9B39 8BF32A838963396432F41A007E3779ECB087F30BD088C2D2B28AF6D526BD8913 631CA26B40841CF47BCDDFC27E0A635805C211F2C3F06EF5076A70F74C7B94DB 4889AA0CC4E8FF85AC122B664ECFFAFE297099ADCB690FA2C981147B65082817 8A35A2A71B03228887FB8A61C14A5BA3C868ADC4C13240B403AEF8F5A6685EEB AFCCDDD13BD8E4618B9832B9FFD750E89CDD6D73FA5AD527348BC06F090BC121 FC542AB11E0D2D48FEAC90DEC57315D0AEBE4DB05AD7CEC091E5861B6A808980 005CF003B3968D308F252D51D817D48B43743643101C5FE631912BB5D93911E3 E8BA1ECFEF56DE67245BAF9457A6B4C88327D91323BF1F05F21622771A2BA081 65FE453B7498A8370F728B25EBF111C1D2FE171337AC7EEB4BFEA6BA6DA4F49B 54E9EAB9C8E4B61580A2CAB28EFC5EBF8CAD1C98C69DEDA4A874119204BC5E91 525B5EC287527615048AB7A43B190D78F87D9EDBD09538AB3D25D6279CE8DB20 7F1FE544270258B74775F5506323E1606FED984BBE66B1C7FCA057C62416807A 47C9E0836D65EB6B70C56C248C5632F2DC228B011292AB28220F8719BC206ECF 6FEC66B62FEA9E7587FE2F3116F034412DF9A4D5BD0238B1DC9AFE39F4A3149B 0920D63FDEE7BE500F367C64F705385BAF09E879A5BC3AD18EFAC7D1AD83A1A3 8A0CA507D9D99DE12E02E8A220E5EEF3C35366DE28CE7E3BC703712A4EA27FB7 2A10D479E9208342A567D6EC7D67B6799351318AAA743F73AA703D605F24E987 6ACE02357543D0005B63212785115443D88C3FF60AEDDB71634A7EE5BE606BA7 AD9F55E2D2A1CA834A9A49CA3AA4710BE7FAE2CAE3C1AF9D61142844E7486230 16CCDCBFC9CE8B524947CF64624739F4E4DA4751DB2573A894CC58909D88103C 6579DFFB1CC9A53461A92CD0BEC8D19BC8E50DB610CB6383E7357FF57D579196 1CBFD48EBCE7640F4E25B83199F8FCF25A91EEFBEDDF42DC5FD6BD900951E235 1EBEDAD93001ADAD834496A34D5F631E48EC1DD990E8577EE68A56AA94C58296 088EE3E205AD26EFCE8DAF6BF28FCB3A291CB05049E5FEFDF74BF5FE6A783B79 E0AADCD83BC16B5BAD11C292603E88300B62DB079C73D2EAF88ECD3ECD2CC997 FF502BDB209FC267772034BF820DCABC993DDB3AE78709369193A5AD87C07462 A4BA2AF10AE3310E0A65D0CE921046A6B62D4BA595D6BF5B6ED0883CD2F68786 5ECC6C749EB688D2D45DE93E3439D5F106563C7F82ED929A6F37C0D5B129CCB6 7ABBAA5184BEF445722FA9ECD29510C5777CEC01D9DED1A56A4599B074533B9E 54609E9F6722CBD0569EE0B401A9D8FD8ABA6C766CE0FA27D0AD762857B8ACEA 23E36431A02291D23712AF8CC020D06041EDFEA0321879461DA5EF840EAD5349 DE70C45FCD5E85AAE3232C08FD2F20DA607C089F7CA3250D7FA03568F46F5E50 342A4B4BC8420EFF3C84FFFA251B66B50F6415ED1D208D6F5BD50E77B16B71C5 7ED8C56FD278D2635290D56E959847F7BD3E98F9C9CA24C75A86068E862A6DED 8F8E8FF95F215808B426D748E6442B8936DEA04889753178733941AC0791DC63 6EBB666D1AB1EE4DD1C137BB6209CECE3DAD4ABF0A56AC5F5C8A055D936FF45A 458F06C15665D3BAE1F75675E5FB3D77782D4EF72E6ED7BDE131B3FEFD7A1F41 7841151224B9BFA77A28737831C305614BEFCE2C16CBAA11F3346DA51DCCA4B0 A3F807F64AE2DCEFF1CFD6F13ECB1B43F6246D72939912B50BF2032C2166FE99 1489F35BD351844C01CCF991084FD609B61C1D6831D7F859F20072615C8ECD8A E9DE860FF467D722A51B03FA456497076DDECAF5E1EC68025DF5DF75E3E2045B 6E14026131E09F1323A629103357784FB88C85379C9C493E422C4C524AD9A6CC CAE9A0386DF47EAEC349447C6974C7E0D71F20F78214E1C2744908AD5E32A54D 9EAC4EB0721415272BF6D8E32B9807FFF2D60BC452B39877892A2D4A4D45C8DC A4F6518BD1D7ADF5DA2614FFAD8BDD7CFB0EBAB6299A8D3BD5E2BA1DF4F37388 A1D95A96A4D7602D14032CD18878B1BACF96F4AF259D0D44E8555BFE154FCF3F FB8CF81E1510741D3B750DA183BF3B6D5D3307B0E20BB0E85A9AFF17C9DC26EB 61C6389AC8FF77B306E36AC9FDDB3E816C99289DBEA600F858B1F82B17660391 F41CE0B2CE7522AACF76A391E24749EE22C28883B56CDFF229C5D73724876BE2 F70EC02F20EDE7F2A617A27724AD6F45B4033BE8EA092C81214D364E2BF4606C 1393F053A65B0A88AFC7F34A1EAB6E86239F889205308ACCD1DCC55565264A6A 220D8EEE02B340967A08BA740B48F1100309F2EC983AAAD1A7CA46983B7D07A4 56C525040EC11765DB69EE8A3AC988D29A537066459E889BC646FE82ACA3134B EBF966DF903F8239BA30BB9AD529C8EBA74189E2CF295F737817BF8686A3DCDC 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 65 /A 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 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 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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Fq(2)1569 2789 y Fs(dx)g Fr(\025)1781 2733 y Ft(\()p Fs(N)j Fr(\000)18 b Ft(2\))2064 2703 y Fq(2)p 1781 2770 321 4 v 1920 2846 a Ft(4)2125 2676 y Fn(Z)2171 2864 y Fm(R)2213 2848 y Fl(N)2294 2733 y Fr(j)p Fs(u)p Fr(j)2388 2703 y Fq(2)p 2294 2770 131 4 v 2294 2846 a Fr(j)p Fs(x)p Fr(j)2387 2822 y Fq(2)2458 2789 y Fs(dx)24 b(;)101 2985 y Ft(and)34 b(it)g(is)g(w)n(ell)g(kno)n(wn)f(that)h(the)g(constan)n(t)f (\()p Fs(N)f Fr(\000)22 b Ft(2\))1860 2955 y Fq(2)1897 2985 y Fs(=)p Ft(4)33 b(is)h(optimal.)56 b(With)34 b(t)n(w)n(o)g (singularities)e(lo)r(cated)i(at)101 3085 y Fr(\006)p Fs(y)26 b Fr(2)d Fp(R)371 3054 y Fo(N)434 3085 y Ft(,)28 b(from)f(the)h(ab)r(o)n(v)n(e)e(inequalit)n(y)h(w)n(e)g(get)h(without)g (e\013ort)f(that)177 3180 y Fn(R)216 3277 y Fm(R)258 3260 y Fl(N)330 3247 y Fr(jr)p Fs(u)p Fr(j)493 3217 y Fq(2)553 3247 y Fs(dx)19 b Fr(\000)755 3207 y Fq(\()p Fo(N)6 b Fk(\000)p Fq(2\))951 3182 y Fj(2)p 755 3228 229 4 v 852 3276 a Fq(8)1007 3180 y Fn(R)1046 3277 y Fm(R)1088 3260 y Fl(N)1159 3155 y Fn(\020)1301 3214 y Fq(1)p 1219 3228 198 4 v 1219 3276 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)r Fk(j)1385 3259 y Fj(2)1444 3247 y Ft(+)1619 3214 y Fq(1)p 1537 3228 197 4 v 1537 3276 a Fk(j)p Fo(x)p Fq(+)p Fo(y)r Fk(j)1702 3259 y Fj(2)1744 3155 y Fn(\021)1821 3247 y Fr(j)p Fs(u)p Fr(j)1915 3217 y Fq(2)1975 3247 y Fs(dx)24 b Ft(=)2186 3214 y Fq(1)p 2186 3228 34 4 v 2186 3276 a(2)2243 3185 y Fn(P)2331 3272 y Fk(\006)2401 3180 y Fn(R)2440 3277 y Fm(R)2482 3260 y Fl(N)2553 3247 y Fr(jr)p Fs(u)2693 3259 y Fk(\006)2749 3247 y Fr(j)2772 3217 y Fq(2)2828 3247 y Fr(\000)2921 3207 y Fq(\()p Fo(N)6 b Fk(\000)p Fq(2\))3117 3182 y Fj(2)p 2921 3228 229 4 v 3018 3276 a Fq(4)3169 3206 y Fk(j)p Fo(u)3228 3214 y Fi(\006)3277 3206 y Fk(j)3297 3181 y Fj(2)p 3169 3228 161 4 v 3194 3276 a Fk(j)p Fo(x)p Fk(j)3272 3259 y Fj(2)3362 3247 y Fs(dx)24 b Fr(\025)e Ft(0)101 3414 y(where)31 b Fs(u)393 3426 y Fk(\006)449 3414 y Ft(\()p Fr(\001)p Ft(\))f(=)g Fs(u)p Ft(\()p Fr(\001)21 b(\006)f Fs(y)s Ft(\).)49 b(F)-7 b(or)31 b(a)h(giv)n(en)f(function)h Fs(u)f Ft(with)h(compact)f(supp)r(ort)h(and)f Fs(d)f Ft(:=)g Fr(j)p Fs(y)s Fr(j)h Ft(large)f(enough,)101 3514 y(it)f(is)f(ho)n(w)n(ev)n(er)e(clear)i(that)g(the)h(constan)n(t)f(\()p Fs(N)g Fr(\000)18 b Ft(2\))1732 3484 y Fq(2)1769 3514 y Fs(=)p Ft(8)28 b(can)g(b)r(e)g(replaced)g(b)n(y)g(\()p Fs(N)g Fr(\000)18 b Ft(2\))2876 3484 y Fq(2)2913 3514 y Fs(=)p Ft(4.)39 b(T)-7 b(o)28 b(impro)n(v)n(e)e(up)r(on)101 3613 y(\()p Fs(N)j Fr(\000)19 b Ft(2\))387 3583 y Fq(2)424 3613 y Fs(=)p Ft(8)29 b(for)g(general)f(functions)i(and)f(in)h (presence)e(of)i(t)n(w)n(o)e(singularities,)h(one)g(has)g(to)g(break)g (the)h(scaling)101 3713 y(in)n(v)-5 b(ariance)26 b(b)n(y)i(in)n(tro)r (ducing)e(a)i(new)f(scale.)36 b(This)28 b(can)f(b)r(e)h(done)f(b)n(y)g (adding)g(a)g(lo)n(w)n(er)f(order)g(term.)37 b(One)27 b(of)g(the)101 3813 y(goals)32 b(in)i(this)f(pap)r(er)g(is)g(to)h (obtain)f(estimates)g(for)g(the)g(b)r(est)h(constan)n(t)f Fs(\025)g Ft(=)f Fs(\025)p Ft(\()p 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4269 y Fq(2)968 4299 y Fs(=)p Ft(4])27 b(and)g(an)n(y)g Fs(y)f Fr(2)d Fp(R)1625 4269 y Fo(N)1716 4299 y Ft(with)28 b Fs(d)23 b Ft(:=)g Fr(j)p Fs(y)s Fr(j)g Fs(>)f Ft(0.)201 4441 y(The)39 b(ab)r(o)n(v)n(e)e(result)i(can)f(of)h(course)f(b)r(e)h (rein)n(terpreted)f(as)g(a)h(lo)n(w)n(er)e(estimate)i(on)f(the)h(sp)r (ectrum)g(of)g(the)101 4541 y(Sc)n(hr\177)-42 b(odinger)26 b(op)r(erator)1334 4693 y Fr(\000)p Ft(\001)18 b Fr(\000)g Fs(\026)1633 4576 y Fn(\022)1821 4637 y Ft(1)p 1704 4674 V 1704 4750 a Fr(j)p Fs(x)h Fr(\000)f Fs(y)s Fr(j)1943 4726 y Fq(2)2008 4693 y Ft(+)2218 4637 y(1)p 2101 4674 V 2101 4750 a Fr(j)p Fs(x)h Ft(+)f Fs(y)s Fr(j)2340 4726 y Fq(2)2387 4576 y Fn(\023)101 4873 y Ft(since)30 b(for)g(a)g(\014xed)g Fs(\026)d Fr(2)h Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)29 b Fr(\000)19 b Ft(2\))1269 4843 y Fq(2)1306 4873 y Fs(=)p Ft(4\),)30 b Fr(\000)p Fs(\025)h Ft(is)f(the)g(b)r(ottom)h(of)f(the)g (sp)r(ectrum)h(of)f(this)g(op)r(erator.)43 b(Suc)n(h)30 b(an)101 4973 y(op)r(erator)21 b(is)h(indeed)h(semi-b)r(ounded)g(from)f (b)r(elo)n(w,)h(as)f(w)n(e)g(shall)g(see)g(b)r(elo)n(w.)35 b(By)22 b(a)g(simple)h(rescaling)e(argumen)n(t,)101 5073 y(it)31 b(is)g(easy)f(to)h(see)f(that)h Fs(\025)p Ft(\()p Fs(\026;)14 b(d)p Ft(\))p Fs(=d)1212 5042 y Fq(2)1281 5073 y Ft(is)31 b(indep)r(enden)n(t)g(of)g Fs(d)p Ft(.)47 b(A)31 b(similar)f(fact)h(also)e(holds)i(in)g(the)g(case)f(of)h(more) 101 5172 y(than)37 b(t)n(w)n(o)e(singularities.)61 b(In)37 b(suc)n(h)f(a)f(case,)j(after)e(division)f(b)n(y)h(the)h(correct)e (scaling)g(parameter,)i(the)f(b)r(est)101 5272 y(constan)n(t)27 b(do)r(es)g(not)h(dep)r(end)g(on)f(the)h(distances)f(b)r(et)n(w)n(een)g (the)h(singularities)e(an)n(ymore,)g(but)i(still)g(dep)r(ends)g(on)101 5371 y(the)g(relativ)n(e)f(p)r(osition)g(of)h(eac)n(h)e(of)i(them,)g Fh(i.e.,)g Ft(on)f(the)h(geometric)f(pattern)g(of)h(the)g(singularit)n (y)e(p)r(oin)n(ts.)p 101 5466 499 4 v 201 5560 a Fg(Date)5 b Fy(:)23 b(No)n(v)n(em)n(b)r(er)h(10,)g(2006.)201 5643 y(2000)j Fg(Mathematics)e(Subje)l(ct)h(Classi\014c)l(ation.)36 b Fy(26D10,)24 b(35J10,)h(46E35;)f(35P15,)g(35Q40,)h(46N50,)f(47N50,)g (81V45,)g(81V55.)201 5723 y Fg(Key)g(wor)l(ds)j(and)e(phr)l(ases.)37 b Fy(Hardy)23 b(inequalities;)g(w)n(eigh)n(ted)i(norms;)d(optimal)h (inequalities;)g(Sc)n(hr\177)-35 b(odinger)24 b(op)r(erator;)f (singular)101 5806 y(p)r(oten)n(tials;)i(Dirac-Coulom)n(b)e (Hamiltonian.)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 101 -103 a Fq(2)1028 b(R.)22 b(BOSI,)g(J.)g (DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)201 96 y Ft(It)h(is)f(certainly)f(out)i(of)f(the)g(scop)r(e)g(of)h(this)f(in)n (tro)r(duction)g(to)g(presen)n(t)g(all)g(v)-5 b(arious)21 b(forms)h(of)g(Hardy's)f(inequal-)101 195 y(it)n(y)-7 b(.)51 b(One)32 b(can)g(for)f(instance)h(refer)g(to)g([45)o(])g(for)g (an)g(up-to-date)g(in)n(tro)r(duction.)50 b(Multip)r(olar)32 b(p)r(oten)n(tials)g(ha)n(v)n(e)101 295 y(recen)n(tly)24 b(b)r(een)g(studied)g(in)h([28)o(],)g(in)f(a)f(di\013eren)n(t)i(con)n (text.)35 b(Huge)24 b(e\013orts)f(ha)n(v)n(e)g(b)r(een)h(done)g(o)n(v)n (er)e(the)j(past)e(y)n(ears)101 395 y(to)g(impro)n(v)n(e)f(on)h (Hardy's)g(inequalit)n(y)-7 b(,)23 b(but)h(mostly)f(in)h(the)f(case)g (of)g(a)g(single)g(singularit)n(y:)33 b(see)23 b([22)o(,)g(3,)g(4,)g (15)o(,)g(23)o(].)101 494 y(Also)35 b(see)f([21)o(,)h(20)o(,)g(19)o(])g (and)f(references)g(therein)h(for)f(some)g(existence)g(results)h(of)f (ground)g(states)g(for)g(linear)101 594 y(and)24 b(nonlinear)f(Sc)n (hr\177)-42 b(odinger)22 b(equations)h(with)i(m)n(ultip)r(olar)e(in)n (v)n(erse)g(square)f(singular)h(p)r(oten)n(tials,)h(and)g([19)o(])g (for)101 694 y(questions)h(related)g(to)h(the)g(self-adjoin)n(tness)e (of)i(the)g(op)r(erators.)34 b(Among)25 b(other)g(results,)g(it)h(is)g (pro)n(v)n(ed)e(in)i(these)101 799 y(pap)r(ers)34 b(that)i(the)f(op)r (erator)e Fr(\000)p Ft(\001)23 b Fr(\000)1299 737 y Fn(P)1386 758 y Fo(M)1386 824 y(k)q Fq(=1)1525 799 y Fs(\026)1575 811 y Fo(k)1630 799 y Fr(j)p Fs(x)h Fr(\000)f Fs(y)1853 811 y Fo(k)1893 799 y Fr(j)1916 769 y Fk(\000)p Fq(2)2040 799 y Ft(is)35 b(p)r(ositiv)n(e)f(if)2529 737 y Fn(P)2616 758 y Fo(M)2616 824 y(k)q Fq(=1)2755 799 y Fs(\026)2805 764 y Fq(+)2805 824 y Fo(k)2895 799 y Fs(<)h Ft(\()p Fs(N)d Fr(\000)23 b Ft(2\))3288 769 y Fq(2)3325 799 y Fs(=)p Ft(4,)36 b(where)101 914 y Fr(f)p Fs(y)184 926 y Fo(k)267 914 y Ft(:)43 b Fs(k)31 b Ft(=)e(1)p Fs(;)e Ft(2)14 b Fs(;)g(:)g(:)g(:)27 b(M)9 b Fr(g)30 b Ft(is)h(an)n(y)f(set)h (of)g(disjoin)n(t)g(p)r(oles.)47 b(Recipro)r(cally)-7 b(,)31 b(if)2579 852 y Fn(P)2667 872 y Fo(M)2667 939 y(k)q Fq(=1)2805 914 y Fs(\026)2855 879 y Fq(+)2855 939 y Fo(k)2939 914 y Fs(>)e Ft(\()p Fs(N)g Fr(\000)21 b Ft(2\))3321 884 y Fq(2)3358 914 y Fs(=)p Ft(4,)31 b(there)101 1029 y(exists)d(a)f(con\014guration)f(of)i(p)r(oles)f(suc)n(h)h(that)g Fr(\000)p Ft(\001)18 b Fr(\000)1811 967 y Fn(P)1899 987 y Fo(M)1899 1054 y(k)q Fq(=1)2038 1029 y Fs(\026)2088 1041 y Fo(k)2143 1029 y Fr(j)p Fs(x)h Fr(\000)f Fs(y)2356 1041 y Fo(k)2396 1029 y Fr(j)2419 999 y Fk(\000)p Fq(2)2536 1029 y Ft(is)28 b(not)g(p)r(ositiv)n(e.)37 b(Moreo)n(v)n(er,)25 b(there)101 1134 y(exists)33 b(a)f(con\014guration)f(of)i(p)r(oles)g (suc)n(h)f(that)h(this)h(op)r(erator)d(is)h(p)r(ositiv)n(e)h(if)g(and)g (only)f(if)i Fs(\026)3087 1098 y Fq(+)3087 1159 y Fo(k)3174 1134 y Fs(<)d Ft(\()p Fs(N)g Fr(\000)22 b Ft(2\))3561 1104 y Fq(2)3598 1134 y Fs(=)p Ft(4)101 1249 y(for)31 b(all)g Fs(k)j Ft(and)593 1186 y Fn(P)681 1207 y Fo(M)681 1273 y(k)q Fq(=1)819 1249 y Fs(\026)869 1213 y Fq(+)869 1274 y Fo(k)954 1249 y Fs(<)28 b Ft(\()p Fs(N)i Fr(\000)20 b Ft(2\))1335 1218 y Fq(2)1373 1249 y Fs(=)p Ft(4.)46 b(F)-7 b(elli,)33 b(Marc)n(hini)d(and)h(T)-7 b(erracini)30 b(also)g(consider)g(in)i([21)o(])f(mo)r(di\014ed)101 1348 y(p)r(oten)n(tials)21 b(whic)n(h)h(are)e(sums)i(of)f(in)n(v)n (erse)f(square)g(p)r(oten)n(tials)h(restricted)g(to)g(compact)g(supp)r (orts)g(around)f(a)i(giv)n(en)101 1448 y(n)n(um)n(b)r(er)27 b(of)g(singularities.)35 b(In)27 b(this)h(case,)e(they)h(discuss)g (again)e(the)j(p)r(ositivit)n(y)f(of)g(the)g(op)r(erator)e(and,)i(in)g (some)101 1547 y(cases,)g(also)f(giv)n(e)h(estimates)g(for)g(the)h(lo)n (w)n(est)f(eigen)n(v)-5 b(alue)27 b(of)g(the)h(corresp)r(onding)e(Sc)n (h\177)-42 b(odinger)26 b(op)r(erator.)201 1647 y(Our)i(purp)r(ose)h (in)g(the)h(case)e(of)h(the)h(Sc)n(hr\177)-42 b(odinger)27 b(op)r(erators)g(is)i(to)g(giv)n(e)g(an)f(as)h(go)r(o)r(d)f(as)h(p)r (ossible)g(estimate)101 1753 y(for)22 b(the)h(lo)n(w)n(er)d(b)r(ound)j (of)f(the)h(sp)r(ectrum)f(of)h(the)f(op)r(erator)f Fr(\000)p Ft(\001)8 b Fr(\000)2179 1691 y Fn(P)2265 1711 y Fo(M)2265 1778 y(k)q Fq(=1)2509 1716 y Fo(\026)p 2414 1734 232 4 v 2414 1782 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)2558 1791 y Fl(k)2593 1782 y Fk(j)2613 1765 y Fj(2)2655 1753 y Ft(,)24 b Fs(\026)f Fr(2)g Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)j Fr(\000)8 b Ft(2\))3227 1723 y Fq(2)3263 1753 y Fs(=)p Ft(4],)23 b Fs(M)31 b Fr(\025)23 b Ft(2,)101 1874 y Fs(y)142 1886 y Fq(1)193 1874 y Fs(;)14 b(:)g(:)g(:)27 b(y)395 1886 y Fo(M)492 1874 y Fr(2)d Fp(R)631 1844 y Fo(N)694 1874 y Ft(.)38 b(W)-7 b(e)28 b(will)g(use)g(t)n(w)n(o)f (di\013eren)n(t)h(metho)r(ds,)g(the)h(so-called)d(IMS)i(metho)r(d,)h (see)e(Section)h(1,)g(and)101 1974 y(the)g(\\expansion)e(of)i(the)g (squares")d(metho)r(d,)j(see)g(Section)f(2,)g(whic)n(h)h(has)f(already) f(b)r(een)i(in)n(tro)r(duced)f(ab)r(o)n(v)n(e)f(in)101 2073 y(the)i(case)f(of)h(a)f(single)g(singularit)n(y)-7 b(.)201 2229 y(F)g(rom)35 b(a)g(mathematical)g(p)r(oin)n(t)h(of)g (view,)h(in)n(v)n(erse)d(square)g(p)r(oten)n(tials)i(are)e(in)n (teresting)h(b)r(ecause)g(of)h(their)101 2328 y(criticalit)n(y)-7 b(.)36 b(There)25 b(are)f(v)-5 b(arious)25 b(motiv)-5 b(ations)25 b(for)g(applications)g(in)h(ph)n(ysics,)f(see)g(for)g (instance)g(a)h(list)f(of)h(topics)101 2428 y(in)f([21)o(,)g(19)o(],)h (and)f(related)f(nonlinear)g(problems)g(in)h(PDEs.)35 b(On)24 b(the)i(other)e(hand,)h(the)g(1)p Fs(=)p Fr(j)p Fs(x)p Fr(j)3049 2398 y Fq(2)3111 2428 y Ft(term)g(app)r(ears)e(in)101 2528 y(the)31 b(linearization)e(of)h(critical)f(nonlinear)g(PDEs,)h (see)g(for)g(instance)f([5,)h(43)o(,)h(7)o(],)g(and)f(pla)n(ys)f(a)h (crucial)f(role)g(for)101 2627 y(understanding)e(the)h(asymptotic)f(b)r (eha)n(vior)g(of)g(branc)n(hes)f(of)i(solutions)f(in)h(some)f (bifurcation)g(problems.)201 2838 y(The)k(second)g(topic)h(of)f(this)h (pap)r(er)f(is)g(concerned)f(with)i(Hardy)f(inequalities)g(for)g(Dirac) g(equations)g(in)g(the)101 2938 y(framew)n(ork)d(of)i(relativistic)f (quan)n(tum)g(mec)n(hanics.)42 b(In)30 b(suc)n(h)g(a)f(setting,)h(the)g (Coulom)n(b)f(p)r(oten)n(tial)h(is)f(critical.)101 3037 y(Hardy)38 b(inequalities)g(ha)n(v)n(e)g(b)r(een)h(studied)g(long)e (ago)g(for)h(simpli\014ed)h(relativistic)f(equations)g(coupled)g(with) 101 3137 y(m)n(ultip)r(olar)25 b(p)r(oten)n(tials)f(of)h(quan)n(tum)g (c)n(hemistry)f(for)g(instance)g(in)h([9,)g(34)o(],)h(motiv)-5 b(ated)24 b(b)n(y)h(the)g(question)g(of)f(the)101 3236 y(stabilit)n(y)i(of)h(matter.)36 b(A)27 b(k)n(ey)f(estimate)g(in)h(suc) n(h)f(a)g(case)g(is)g(a)g(Hardy)g(inequalit)n(y)g(whic)n(h)g(w)n(as)g (deriv)n(ed)g(b)n(y)g(Kato)101 3336 y(in)i([30)o(]:)1491 3495 y(\()p Fr(\000)p Ft(\001)18 b(+)g(1\))1832 3461 y Fq(1)p Fo(=)p Fq(2)1960 3495 y Fr(\025)2062 3439 y Ft(2)p 2057 3476 51 4 v 2057 3552 a Fs(\031)2167 3439 y Ft(1)p 2141 3476 94 4 v 2141 3552 a Fr(j)p Fs(x)p Fr(j)2268 3495 y Fs(;)101 3677 y Ft(in)41 b(dimension)f Fs(N)53 b Ft(=)44 b(3.)75 b(A)41 b(re\014ned)f(relativistic)g(op)r(erator)e(w)n (as)i(in)n(tro)r(duced)g(b)n(y)g(Bro)n(wn)f(and)h(Ra)n(v)n(enhall)101 3777 y(and)g(optimal)g(corresp)r(onding)e(inequalities)h(ha)n(v)n(e)g (b)r(een)h(deriv)n(ed)f(in)i([6)o(,)f(24)o(].)74 b(Also)40 b(see)f([26)o(,)h(2])g(for)f(some)101 3876 y(consequences.)71 b(In)40 b(the)g(case)e(of)i(the)g(Dirac)f(op)r(erator)e(coupled)j(to)f (Coulom)n(b)f(in)n(teractions,)k(Hardy)c(t)n(yp)r(e)101 3976 y(inequalities)31 b(are)f(m)n(uc)n(h)h(more)f(recen)n(t,)h(see)g ([13)o(,)g(12)o(].)47 b(F)-7 b(or)31 b(a)f(pure)h(Coulom)n(b)f (singularit)n(y)g(these)h(inequalities)101 4081 y(read)c(as)g(follo)n (ws.)36 b(F)-7 b(or)27 b(all)g Fs(\027)h Fr(2)c Ft(\(0)p Fs(;)14 b Ft(1],)27 b(for)g(all)g Fs(\036)d Fr(2)f Fs(L)1781 4051 y Fq(2)1818 4081 y Ft(\()p Fp(R)1910 4051 y Fq(3)1947 4081 y Fs(;)14 b Fp(C)2044 4051 y Fq(2)2082 4081 y Ft(\),)28 b(with)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))23 b(:=)2654 4012 y Fr(p)p 2723 4012 227 4 v 69 x Ft(1)18 b Fr(\000)g Fs(\027)2912 4057 y Fq(2)2950 4081 y Ft(,)738 4176 y Fn(Z)784 4365 y Fm(R)826 4348 y Fj(3)978 4233 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)1266 4203 y Fq(2)p 887 4270 509 4 v 887 4346 a Ft(1)k(+)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))19 b(+)1328 4314 y Fo(\027)p 1308 4328 78 4 v 1308 4375 a Fk(j)p Fo(x)p Fk(j)1428 4289 y Fs(dx)g Ft(+)1620 4222 y Fn(\002)1654 4289 y Ft(1)f Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1963 4222 y Fn(\003)2012 4176 y(Z)2059 4365 y Fm(R)2101 4348 y Fj(3)2151 4289 y Fr(j)p Fs(\036)p Fr(j)2246 4255 y Fq(2)2284 4289 y Fs(dx)23 b Fr(\025)2485 4176 y Fn(Z)2531 4365 y Fm(R)2573 4348 y Fj(3)2657 4233 y Fs(\027)p 2634 4270 94 4 v 2634 4346 a Fr(j)p Fs(x)p Fr(j)2751 4289 y(j)p Fs(\036)p Fr(j)2846 4255 y Fq(2)2907 4289 y Fs(dx)h(:)101 4511 y Ft(Here)38 b(some)g(of)g(the)h(terms)f(can)g(b)r(e)h(in\014nite) g(and)f(the)h(matrices)f Fs(\033)2324 4523 y Fo(i)2352 4511 y Fs(;)55 b(i)40 b Ft(=)h(1)p Fs(;)14 b Ft(2)p Fs(;)g Ft(3)37 b(are)g(the)i(so-called)e(P)n(auli)101 4611 y(matrices.)69 b(See)39 b(Section)g(3)f(for)g(more)g(precisions)f(and)h(explanations)g (on)g(these)h(matrices)f(and)g(the)h(ab)r(o)n(v)n(e)101 4710 y(inequalit)n(y)-7 b(.)35 b(In)24 b(particular,)e(exactly)h(as)g (in)g(the)h(case)e(of)h(the)h(Sc)n(hr\177)-42 b(odinger)21 b(op)r(erator,)h(the)i(constan)n(t)e Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))24 b(is)f(the)101 4810 y(smallest)30 b(eigen)n(v)-5 b(alue)30 b(of)h Fs(H)c Fr(\000)20 b Fs(\027)5 b(=)p Fr(j)p Fs(x)p Fr(j)p Ft(,)32 b(where)e Fs(H)37 b Ft(is)30 b(the)h(Dirac)g(op)r(erator)d(and)j Fs(\027)i Fr(2)28 b Ft(\(0)p Fs(;)14 b Ft(1\).)46 b(W)-7 b(e)31 b(p)r(ostp)r(one)f(the)101 4909 y(precise)24 b(explanation)g(of)h(the)g (relation)e(of)i(the)g(optimal)g(v)-5 b(alue)24 b(of)h Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))25 b(and)g(the)g(sp)r(ectrum)g(of)f Fs(H)32 b Ft(to)24 b(Section)h(3,)101 5009 y(as)32 b(w)n(ell)g(as)g (some)g(commen)n(ts)g(on)h(the)g(self-adjoin)n(tness)e(of)i(the)g(op)r (erators.)49 b(F)-7 b(or)32 b(a)g(general)g(in)n(tro)r(duction)g(to)101 5109 y(the)c(Dirac)f(equation)g(w)n(e)h(refer)e(to)i([44)o(].)201 5208 y(Scaling)39 b(prop)r(erties)g(explain)g(wh)n(y)h(in)n(v)n(erse)e (square)h(p)r(oten)n(tials)g(and)h(Coulom)n(b)f(p)r(oten)n(tials)h(are) e(critical)101 5308 y(resp)r(ectiv)n(ely)23 b(for)g(the)g(Sc)n(hr\177) -42 b(odinger)22 b(and)h(the)h(Dirac)f(op)r(erators.)33 b(It)24 b(is)f(clear)f(that)i(1)p Fs(=)p Fr(j)p Fs(x)p Fr(j)2889 5278 y Fq(2)2949 5308 y Ft(has)f(the)h(same)f(scaling)101 5408 y(la)n(w)h(as)g Fr(\000)p Ft(\001.)36 b(As)24 b(for)g(Dirac's)g (op)r(erator,)g(the)g(principal)h(part)f(of)g Fs(H)31 b Ft(scales)24 b(lik)n(e)g(1)p Fs(=)p Fr(j)p Fs(x)p Fr(j)p Ft(,)h(whic)n(h)f(can)h(also)e(b)r(e)i(seen)101 5507 y(in)k(the)f(ab)r(o)n(v)n(e)f(inequalit)n(y)h(at)g(the)h(lev)n(el)f(of) g(the)h(op)r(erator)d Fs(\036)f Fr(7!)f(\000)p Ft(\()n Fs(~)-40 b(\033)22 b Fr(\001)d(r)p Ft(\)\()p Fr(j)p Fs(x)p Fr(j)12 b Fs(~)-40 b(\033)24 b Fr(\001)19 b(r)14 b Fs(\036)p Ft(\).)40 b(Some)28 b(further)g(details)101 5607 y(will)i(b)r(e)h(giv)n (en)e(at)g(the)i(b)r(eginning)f(of)f(Section)h(3.)44 b(More)29 b(strikingly)-7 b(,)29 b(one)h(can)f(also)g(pro)n(v)n(e)f (that)i(the)h(standard)101 5706 y(Hardy)26 b(inequalit)n(y)h(for)f(the) h(Sc)n(hr\177)-42 b(odinger)25 b(op)r(erator)g(is)i(a)f(consequence)g (of)g(the)i(Hardy-lik)n(e)d(inequalit)n(y)h(for)g(the)101 5806 y(Dirac)c(op)r(erator)f(coupled)h(to)g(one)g(Coulom)n(b)g (singularit)n(y)-7 b(.)33 b(F)-7 b(or)22 b(the)h(con)n(v)n(enience)e (of)h(the)h(reader,)f(w)n(e)g(repro)r(duce)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 956 -103 a Fq(HARD)n(Y)30 b(INEQUALITIES)e(WITH)h (SEVERAL)g(SINGULARITIES)822 b(3)101 96 y Ft(here)27 b(some)g(computations)g(whic)n(h)h(already)e(app)r(eared)h(in)h([12)o (].)37 b(By)27 b(taking)g(the)h(limit)g(as)f Fs(\027)i Fr(!)23 b Ft(1,)k(w)n(e)g(get)716 175 y Fn(Z)762 363 y Fm(R)804 347 y Fj(3)865 231 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)1153 201 y Fq(2)p 865 269 327 4 v 908 349 a Ft(1)k(+)1083 316 y Fq(1)p 1061 330 78 4 v 1061 377 a Fk(j)p Fo(x)p Fk(j)1224 288 y Fs(dx)h Ft(+)1416 175 y Fn(Z)1462 363 y Fm(R)1504 347 y Fj(3)1555 288 y Fr(j)p Fs(\036)p Fr(j)1650 253 y Fq(2)1710 288 y Fs(dx)24 b Fr(\025)1912 175 y Fn(Z)1958 363 y Fm(R)2000 347 y Fj(3)2060 231 y Fr(j)p Fs(\036)p Fr(j)2155 201 y Fq(2)p 2060 269 133 4 v 2080 345 a Fr(j)p Fs(x)p Fr(j)2226 288 y Fs(dx)84 b Fr(8)14 b Fs(\036)23 b Fr(2)h Fs(H)2687 253 y Fq(1)2724 288 y Ft(\()p Fp(R)2816 253 y Fq(3)2853 288 y Fs(;)14 b Fp(C)2950 253 y Fq(2)2987 288 y Ft(\))24 b Fs(:)101 507 y Ft(If)k(w)n(e)g(replace)e Fs(\036)p Ft(\()p Fr(\001)p Ft(\))j(b)n(y)e Fs(")907 477 y Fk(\000)p Fq(1)996 507 y Fs(\036)p Ft(\()p Fs(")1116 477 y Fk(\000)p Fq(1)1206 507 y Fr(\001)p Ft(\))h(and)f(tak)n(e)g(the)h(limit)g(as)f Fs(")c Fr(!)g Ft(0,)k(w)n(e)h(obtain)1267 586 y Fn(Z)1313 774 y Fm(R)1355 758 y Fj(3)1406 699 y Fr(j)p Fs(x)p Fr(j)14 b(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)1801 664 y Fq(2)1862 699 y Fs(dx)24 b Fr(\025)2064 586 y Fn(Z)2110 774 y Fm(R)2152 758 y Fj(3)2212 642 y Fr(j)p Fs(\036)p Fr(j)2307 612 y Fq(2)p 2212 679 V 2232 756 a Fr(j)p Fs(x)p Fr(j)2378 699 y Fs(dx)g(:)101 886 y Ft(By)k(taking)f Fs(\036)c Ft(=)g(\()p Fs(f)t(;)14 b Ft(0\))27 b(with)h Fs(f)37 b Ft(purely)27 b(real,)g(w)n(e)g(end)h(up)g(with)1352 965 y Fn(Z)1398 1153 y Fm(R)1440 1137 y Fj(3)1491 1078 y Fr(j)p Fs(x)p Fr(j)14 b(jr)p Fs(f)9 b Fr(j)1763 1043 y Fq(2)1823 1078 y Fs(dx)24 b Fr(\025)2025 965 y Fn(Z)2071 1153 y Fm(R)2113 1137 y Fj(3)2173 1022 y Fr(j)p Fs(f)9 b Fr(j)2269 991 y Fq(2)p 2173 1059 V 2193 1135 a Fr(j)p Fs(x)p Fr(j)2339 1078 y Fs(dx)101 1270 y Ft(for)27 b(all)h Fs(f)j Fr(2)24 b Fs(H)571 1240 y Fq(1)608 1270 y Ft(\()p Fp(R)700 1240 y Fq(3)737 1270 y Fs(;)14 b Fp(C)p Ft(\),)28 b(whic)n(h)g(is)f(itself)h(equiv)-5 b(alen)n(t)28 b(to)1011 1349 y Fn(Z)1057 1538 y Fm(R)1099 1521 y Fj(3)1149 1462 y Fr(jr)p Fs(u)p Fr(j)1312 1428 y Fq(2)1372 1462 y Fs(dx)c Fr(\025)1584 1406 y Ft(1)p 1584 1443 42 4 v 1584 1519 a(4)1649 1349 y Fn(Z)1695 1538 y Fm(R)1737 1521 y Fj(3)1798 1406 y Fr(j)p Fs(u)p Fr(j)1892 1376 y Fq(2)p 1798 1443 131 4 v 1798 1519 a Fr(j)p Fs(x)p Fr(j)1891 1495 y Fq(2)1961 1462 y Fs(dx)84 b Fr(8)23 b Fs(u)g Fr(2)g Fs(H)2429 1428 y Fq(1)2466 1462 y Ft(\()p Fp(R)2558 1428 y Fq(3)2596 1462 y Fs(;)14 b Fp(C)p Ft(\))23 b Fs(;)101 1665 y Ft(as)35 b(sho)n(wn)f(b)n(y)h(considering)f Fs(u)h Ft(=)1218 1594 y Fn(p)p 1301 1594 94 4 v 71 x Fr(j)p Fs(x)p Fr(j)15 b Fs(f)9 b Ft(.)59 b(W)-7 b(e)36 b(observ)n(e)d(that)j(\()p Fs(N)c Fr(\000)23 b Ft(2\))2476 1635 y Fq(2)2513 1665 y Fs(=)p Ft(4)35 b(=)g(1)p Fs(=)p Ft(4)f(if)i Fs(N)44 b Ft(=)35 b(3,)i(so)e(that)g(w)n(e)101 1765 y(reco)n(v)n(er)27 b(the)i(optimal)f(constan)n(t,)h(and)f(ev)n(en)h(correctiv)n(e)e(terms) h(at)h(all)f(orders.)39 b(See)29 b([22)o(,)g(12)o(])g(for)f(more)g (details)101 1864 y(and)g(further)f(references.)201 2003 y(A)34 b(ma)5 b(jor)32 b(di\013erence)h(b)r(et)n(w)n(een)g(Dirac)g(and) g(Sc)n(hr\177)-42 b(odinger)31 b(op)r(erators)h(coupled)h(resp)r(ectiv) n(ely)f(to)h(Coulom)n(b)101 2102 y(t)n(yp)r(e)40 b(in)n(teractions)f (and)h(to)f(m)n(ultiple)i(in)n(v)n(erse)d(square)g(singular)h(p)r(oten) n(tials)g(lies)h(in)g(the)g(structure)g(of)f(the)101 2202 y(con)n(tin)n(uous)23 b(sp)r(ectrum.)36 b(While)24 b(the)g(Sc)n(hr\177)-42 b(odinger)21 b(op)r(erators)h(are)h(semi-b)r (ounded)g(from)g(b)r(elo)n(w,)h(th)n(us)g(allo)n(wing)101 2302 y(only)i(for)g(some)g(p)r(ositiv)n(e)g(con)n(tin)n(uous)f(sp)r (ectrum,)i(Dirac)f(op)r(erators)e(ha)n(v)n(e)i(con)n(tin)n(uous)f(sp)r (ectrum)i(ev)n(erywhere)101 2401 y(except)d(in)g(a)f(gap.)34 b(There)23 b(is)h(therefore)e(a)i(natural)e(limitation)i(of)g(the)f (coupling)g(constan)n(t,)h(called)f(the)h Fh(coupling)101 2501 y(constan)n(t)29 b(threshold,)g Ft(whic)n(h)g(has)g(b)r(een)h (studied)f(in)h([32)o(])f(for)g(smo)r(oth)g(p)r(oten)n(tials)g(and)g (in)h([11)o(])f(in)h(the)f(case)g(of)101 2601 y(one)e(Coulom)n(b)g (singularit)n(y)g(and)g(a)g(constan)n(t)g(magnetic)g(\014eld.)201 2700 y(Our)j(purp)r(ose)h(in)g(the)h(case)e(of)h(Dirac)f(op)r(erators)g (is)h(to)g(giv)n(e)f(estimates)g(of)i(the)f(lo)n(w)n(est)f(energy)g (lev)n(el)h(for)f(a)101 2800 y(Dirac-Coulom)n(b)d(op)r(erator)f(in)j (terms)f(of)g(the)g(in)n(terdistance)g(b)r(et)n(w)n(een)g(the)h Fs(M)37 b Ft(singularities,)27 b(or)g(equiv)-5 b(alen)n(tly)101 2899 y(to)29 b(determine)g(estimates)f(of)h(the)g(coupling)f (threshold.)40 b(Suc)n(h)29 b(a)f(coupling)h(threshold)f(can)g(b)r(e)i (seen)e(from)g(t)n(w)n(o)101 2999 y(p)r(oin)n(ts)g(of)f(view:)261 3118 y(\(i\))42 b(Either)37 b(w)n(e)g(\014x)g(the)h(con\014guration)e (of)i(the)f(singularities)g(and)g(lo)r(ok)g(for)g(estimates)g(of)g(the) h(largest)390 3218 y(coupling)32 b(constan)n(t)g Fs(\027)37 b Ft(for)32 b(whic)n(h)h(the)g(lo)n(w)n(est)e(eigen)n(v)-5 b(alue)31 b(is)i(ab)r(o)n(v)n(e)e Fr(\000)p Ft(1,)i(the)f(upp)r(er)h(b) r(ound)g(of)f(the)390 3317 y(negativ)n(e)26 b(con)n(tin)n(uous)h(sp)r (ectrum.)238 3417 y(\(ii\))42 b(Or)27 b(w)n(e)h(\014x)g(the)g(coupling) g(constan)n(t)f Fs(\027)33 b Ft(to)28 b(some)f(v)-5 b(alue)28 b(in)g(\(0)p Fs(;)14 b Ft(1\))28 b(and)g(lo)r(ok)f(for)g(estimates)h (that)g(guar-)390 3517 y(an)n(tee)k(that)g(the)g(lo)n(w)n(est)f(eigen)n (v)-5 b(alue)31 b(of)h(the)h(op)r(erator)d(is)i(ab)r(o)n(v)n(e)f Fr(\000)p Ft(1.)49 b(This)32 b(determines)g(a)f(minimal)390 3616 y(distance)c(b)r(et)n(w)n(een)h(singularities)e(if)i Fs(\027)5 b(M)32 b(>)23 b Ft(1.)101 3736 y(Both)j(approac)n(hes)d(are)i (equiv)-5 b(alen)n(t)25 b(and)h(amoun)n(t)f(to)h(\014nding)f(estimates) h(for)f(the)h(optimal)f(constan)n(t)g(in)h(Hardy)101 3835 y(t)n(yp)r(e)i(inequalities)f(for)g(Dirac)h(op)r(erators)d(with)j (m)n(ultiple)g(Coulom)n(b)f(singularities.)201 3935 y(In)35 b(the)h(Sc)n(hr\177)-42 b(odinger)33 b(and)j(in)f(the)h(Dirac)f(case,)h (w)n(e)f(in)n(v)n(estigate)f(the)h(asymptotics)g Fs(d)h Fr(!)g Ft(+)p Fr(1)f Ft(when)g(the)101 4034 y(singularities)h(are)g (asymptotically)f(far)h(from)h(eac)n(h)f(other,)i(and)f(also)e(the)i (limit)h Fs(d)g Fr(!)h Ft(0)d(corresp)r(onding)f(to)101 4134 y(all)h(singularities)e(merged)h(in)h(a)f(single)g(p)r(oin)n(t)h (\(further)f(assumptions)g(are)g(ho)n(w)n(ev)n(er)e(needed)j(for)f(the) h(Dirac)101 4234 y(op)r(erator\).)201 4372 y(F)-7 b(rom)36 b(a)g(ph)n(ysical)g(p)r(oin)n(t)h(of)f(view,)j(the)e(m)n(ultip)r(olar)f (Dirac-Coulom)n(b)f(op)r(erator)f(describ)r(es)i(the)h(state)g(of)101 4472 y(one)30 b(c)n(harged)f(particle)g(in)i(a)f(molecule)g(with)g Fs(M)39 b Ft(\014xed)31 b(n)n(uclei,)g(in)f(the)h(Born-Opp)r(enheimer)e (appro)n(ximation.)101 4572 y(In)i(atomic)f(units,)i Fs(\027)i Ft(=)27 b Fs(\013)15 b(Z)6 b Ft(,)31 b Fs(Z)36 b Ft(is)31 b(the)g(n)n(uclear)e(c)n(harge)g(n)n(um)n(b)r(er)i(and)f Fs(\013)h Ft(is)g(the)g(Sommerfeld)f(\014ne-structure)101 4671 y(constan)n(t,)35 b(whose)e(v)-5 b(alue)34 b(is)g(1)p Fs(=)p Ft(137)p Fs(:)p Ft(037)14 b Fs(:)g(:)g(:)30 b Ft(Hence)k(the)h(condition)e Fs(\027)39 b(<)34 b Ft(1)f(means)h(that)g (the)h(n)n(uclear)d(c)n(harge)101 4771 y(cannot)20 b(b)r(e)i(larger)c (than)j(1)p Fs(=\013)p Ft(.)34 b(Finding)21 b(the)g(lo)n(w)n(est)f (energy)g(lev)n(el)g(in)h(the)g(gap)f(of)g(the)h(Dirac-Coulom)n(b)e(op) r(erator)101 4870 y(is)28 b(a)f(basic)g(question)g(for)g(studying)h (stabilit)n(y)-7 b(,)27 b(computing)h(energy)e(lev)n(els)h(and)h (getting)f(estimates)g(for)g(related)101 4970 y(nonlinear)g(mo)r(dels.) 201 5109 y(T)-7 b(o)29 b(our)f(kno)n(wledge,)h(when)g(there)g(is)h (more)e(than)h(one)g(singularit)n(y)-7 b(,)29 b(no)g(explicit)g (estimates)g(for)g(the)h(lo)n(w)n(est)101 5208 y(eigen)n(v)-5 b(alue)33 b(of)g(Dirac)g(op)r(erators)f(ha)n(v)n(e)g(b)r(een)i(deriv)n (ed)f(y)n(et.)54 b(In)34 b(the)f(case)g(of)g(a)g(crystal,)h(whic)n(h)g (is)f(a)g(sligh)n(tly)101 5308 y(di\013eren)n(t)41 b(setting,)j(Hardy)c (inequalities)g(for)h(Dirac)f(t)n(yp)r(e)h(op)r(erators)d(are)i(curren) n(tly)g(under)g(in)n(v)n(estigation,)101 5408 y(see)28 b([8].)40 b(Estimates)28 b(could)g(b)r(e)h(deduced)g(from)f(Kato's)f (inequalit)n(y)h(or)g(from)g(the)h(inequalit)n(y)f(stated)h(in)f([6,)h (24)o(])101 5507 y(for)g(the)g(Bro)n(wn-Ra)n(v)n(enhall)d(Hamiltonian)j (and)g(their)g(extensions)f(to)h(the)g(m)n(ultip)r(olar)g(case,)f(but)i (they)f(w)n(ould)101 5607 y(an)n(yw)n(a)n(y)d(not)h(co)n(v)n(er)f(the)i (whole)f(range)g(of)g(the)h(coupling)f(constan)n(t,)g(as)g(w)n(e)g(do)h (here.)201 5706 y(In)35 b([31)o(],)j(Klaus)c(studied)i(conditions)f (under)g(whic)n(h)g(the)h(Dirac)e(op)r(erator)g(coupled)h(to)g(a)g(p)r (oten)n(tial)g(with)101 5806 y(sev)n(eral)28 b(Coulom)n(b)g (singularities)g(is)h(self-adjoin)n(t.)41 b(The)29 b(case)g(of)g(t)n(w) n(o)f(singularities)g(when)h(they)h(are)e(far)h(apart)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 101 -103 a Fq(4)1028 b(R.)22 b(BOSI,)g(J.)g (DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)101 96 y Ft(from)29 b(eac)n(h)f(other)h(has)f(b)r(een)i(studied)f(in)h([25)o (].)41 b(Also)29 b(see)f([10])h(for)f(a)h(more)f(general)g(approac)n(h) f(of)i(double)g(w)n(ell)101 195 y(Hamiltonians,)e(and)h([46)o(])g(for)f (a)g(semi-classical)f(analysis)g(in)i(the)g(case)f(of)g(p)r(oten)n (tials)g(with)h(m)n(ultiple)h(w)n(ells.)201 378 y(The)21 b(pap)r(er)g(is)h(organized)d(as)i(follo)n(ws.)34 b(In)22 b(Section)f(1)g(w)n(e)g(use)h(the)g(w)n(ell-kno)n(wn)e(IMS)h(metho)r(d) h(to)g(deriv)n(e)e(some)101 484 y(lo)n(w)n(er)29 b(estimates)h(on)g (the)h(lo)n(w)n(est)e(eigen)n(v)-5 b(alue)30 b(of)g(the)h(op)r(erator)d Fr(\000)p Ft(\001)20 b Fr(\000)2424 421 y Fn(P)2512 442 y Fo(M)2512 509 y(k)q Fq(=1)2756 447 y Fo(\026)p 2660 465 232 4 v 2660 512 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)2804 521 y Fl(k)2840 512 y Fk(j)2860 496 y Fj(2)2902 484 y Ft(,)31 b Fs(\026)d Fr(2)g Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)29 b Fr(\000)19 b Ft(2\))3514 453 y Fq(2)3551 484 y Fs(=)p Ft(4],)101 605 y Fs(M)43 b Fr(\025)33 b Ft(2)h(and)g Fs(y)608 617 y Fq(1)659 605 y Fs(;)14 b(:)g(:)g(:)27 b(y)861 617 y Fo(M)968 605 y Fr(2)35 b Fp(R)1118 575 y Fo(N)1181 605 y Ft(.)56 b(This)34 b(metho)r(d)h(consists)e(in)i(lo)r (calizing)e(the)h(w)n(a)n(v)n(e)f(functions)h(around)f(the)101 705 y(singularities)d(b)n(y)h(using)g(a)g(w)n(ell)g(c)n(hosen)f (partition)h(of)g Fp(R)1929 674 y Fo(N)1992 705 y Ft(.)48 b(In)32 b(some)e(cases)h(the)g(geometric)f(pattern)h(de\014ned)101 804 y(b)n(y)d(the)g(singularit)n(y)e(cen)n(ters)g(allo)n(ws)h(for)g(b)r (etter)h(estimates)f(than)h(the)g(general)e(ones.)201 904 y(In)37 b(Section)g(2)f(w)n(e)g(expand)h(some)f(w)n(ell)g(c)n (hosen)g(squared)g(quan)n(tities)g(and)h(in)n(tegrate)e(b)n(y)i(parts)f (to)g(pro)n(v)n(e)101 1003 y(another)31 b(t)n(yp)r(e)g(of)g(estimates,) h(whic)n(h)g(in)f(some)g(cases)f(impro)n(v)n(e)g(those)h(obtained)g(b)n (y)g(the)h(IMS)f(metho)r(d.)49 b(The)101 1109 y(idea)25 b(here)g(is)f(to)h(sho)n(w)f(that)i(for)e(some)h(function)g Fs(Q)p Ft(\()p Fs(x;)14 b(y)1887 1121 y Fq(1)1925 1109 y Fs(;)g(:)g(:)g(:)f(y)2113 1121 y Fo(M)2187 1109 y Ft(\),)26 b(the)f(op)r(erator)e Fr(\000)p Ft(\001)13 b Fr(\000)2965 1047 y Fn(P)3053 1068 y Fo(M)3053 1134 y(k)q Fq(=1)3297 1072 y Fo(\026)p 3202 1090 V 3202 1138 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)3346 1147 y Fl(k)3381 1138 y Fk(j)3401 1121 y Fj(2)3456 1109 y Ft(+)g Fs(Q)25 b Ft(is)101 1218 y(nonnegativ)n(e.)35 b(The)26 b(constan)n(t)e Fs(\025)i Ft(is)f(then)h(de\014ned)g(as)f(the)h(in\014m)n(um)g(of)f Fs(Q)p Ft(.)36 b(Of)25 b(course,)g(this)h(pro)r(cedure)e(cannot)101 1318 y(pro)n(vide)j(the)h(b)r(est)g(constan)n(t)f Fs(\025)p Ft(,)h(since)f(it)h(is)g(based)f(on)g(a)g(p)r(oin)n(t)n(wise)g (estimate)h(of)f Fs(Q)p Ft(.)201 1418 y(Section)e(3)g(deals)g(with)h (Hardy-t)n(yp)r(e)f(inequalities)g(for)g(Dirac)g(op)r(erator)f(with)i (Coulom)n(b)e(singularities.)35 b(Due)101 1517 y(to)20 b(the)g(non)g(homogeneit)n(y)f(of)g(the)i(Dirac)e(op)r(erator,)h(the)g (b)r(est)g(constan)n(t)f(hea)n(vily)g(dep)r(ends)i(on)e(the)h(in)n (terdistance)101 1617 y(b)r(et)n(w)n(een)29 b(the)h(singularities,)e (and)h(not)g(only)f(on)h(the)g(geometric)f(pattern)h(de\014ned)g(b)n(y) g(them.)42 b(In)29 b(this)g(case)f(w)n(e)101 1717 y(are)d(only)g(able)g (to)g(use)g(the)h(IMS)g(metho)r(d,)g(whic)n(h)f(giv)n(es)g(go)r(o)r(d)f (results)h(only)g(for)g(large)f(in)n(terdistances,)h(that)h(is,)101 1816 y(for)31 b(v)n(ery)e(distan)n(t)i(singularities.)45 b(F)-7 b(or)31 b(nearb)n(y)e(singularities,)i(w)n(e)f(in)n(tro)r(duce)h (a)f(sligh)n(tly)g(mo)r(di\014ed)h(v)n(ersion)f(of)101 1916 y(the)e(Hardy)f(inequalit)n(y)-7 b(.)201 2057 y(When)29 b(dealing)f(with)h(the)f(Sc)n(hr\177)-42 b(odinger)27 b(op)r(erator,)g(w)n(e)h(alw)n(a)n(ys)e(consider)i(dimensions)g Fs(N)33 b Fr(\025)24 b Ft(3.)39 b(The)28 b(Dirac)101 2156 y(case)c(is)g(studied)g(only)g(in)g(the)h(ph)n(ysical)e(space)g (with)i Fs(N)32 b Ft(=)22 b(3.)36 b(Also)23 b(note)h(that)h(in)f(the)h (case)e(of)h(Dirac)g(op)r(erators,)101 2256 y(the)j(essen)n(tial)f(sp)r (ectrum)g(is)h(not)f(b)r(ounded)h(from)f(b)r(elo)n(w,)h(and)f(so,)g (when)h(w)n(e)f(sp)r(eak)g(of)g(the)h(lo)n(w)n(est)f(eigen)n(v)-5 b(alue,)101 2356 y(w)n(e)39 b(alw)n(a)n(ys)e(mean)i(the)g(lo)n(w)n(est) f(eigen)n(v)-5 b(alue)39 b(in)g(the)g(gap)g(of)g(the)g(essen)n(tial)f (sp)r(ectrum.)72 b(All)39 b(estimates)g(can)101 2455 y(b)r(e)c(w)n(ork)n(ed)d(out)j(for)e(complex)h(v)-5 b(alued)34 b(functions)h(and)f(spinors,)h(but)f(since)g(w)n(e)g(do)g(not)g (consider)g(ev)n(olution)101 2555 y(equations,)g(results)e(will)h(b)r (e)h(stated)e(for)h(real)f(v)-5 b(alued)33 b(functions)g(whenev)n(er)f (p)r(ossible,)i(and)e(without)i(further)101 2655 y(notice.)45 b(F)-7 b(or)30 b(simplicit)n(y)-7 b(,)31 b(w)n(e)f(ha)n(v)n(e)f (assumed)g(that)i(coupling)e(constan)n(ts)h(are)f(the)i(same)e(for)h (all)g(singularities.)101 2754 y(The)f(extension)g(to)g(the)g(case)f (when)i(they)f(di\013er)g(can)g(b)r(e)g(w)n(ork)n(ed)e(out)i(b)n(y)g (the)g(same)g(metho)r(ds,)h(but)f(is)g(left)h(to)101 2854 y(the)e(reader.)313 3042 y(1.)41 b Fu(Hard)n(y)31 b(inequalities)h(f)n(or)f(the)h(Schr)1813 3035 y(\177)1810 3042 y(odinger)f(opera)-6 b(tor)32 b(and)f(the)h(IMS)f(method)201 3191 y Ft(The)g(results)g(of)g(this)h(section)e(rely)h(on)g(the)g (so-called)f(\\IMS")h(\(for)g(Ismagilo)n(v,)f(Morgan,)h(Morgan-Simon,) 101 3291 y(Sigal,)e(see)f([35)o(,)h(41)o(]\))g(truncation)f(metho)r(d.) 40 b(Our)28 b(goal)f(is)i(to)f(obtain)g(estimates)h(for)f(the)h(lo)n(w) n(est)e(eigen)n(v)-5 b(alue)28 b(of)101 3401 y Fr(\000)p Ft(\001)20 b Fr(\000)f Fs(\026)14 b(V)451 3413 y Fo(M)525 3401 y Ft(\()p Fs(x)p Ft(\),)31 b(where)e Fs(V)980 3413 y Fo(M)1054 3401 y Ft(\()p Fs(x)p Ft(\))e(=)1283 3339 y Fn(P)1371 3359 y Fo(M)1371 3426 y(k)q Fq(=1)1619 3369 y(1)p 1519 3383 V 1519 3430 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)1663 3439 y Fl(k)1699 3430 y Fk(j)1719 3413 y Fj(2)1761 3401 y Ft(,)j Fs(M)35 b Fr(\025)25 b Ft(2)k(and)h Fs(y)2296 3413 y Fq(1)2346 3401 y Fs(;)14 b(:)g(:)g(:)28 b(y)2549 3413 y Fo(M)2652 3401 y Ft(are)g Fs(M)38 b Ft(p)r(oin)n(ts)30 b(of)f Fp(R)3319 3371 y Fo(N)3382 3401 y Ft(.)43 b(Notice)101 3520 y(that)29 b(the)f(Hamiltonian)g(is)f(essen)n(tially)g(self-adjoin) n(t)h(if)g Fs(\026)c Fr(\024)f Ft(\()p Fs(N)28 b Fr(\000)18 b Ft(2\))2334 3490 y Fq(2)2371 3520 y Fs(=)p Ft(4)g Fr(\000)g Ft(1,)28 b(otherwise)f(one)g(has)h(to)g(use)f(the)101 3620 y(corresp)r(onding)f(F)-7 b(riedric)n(hs)27 b(extension.)36 b(See)28 b([29)o(,)f(19)o(])h(for)f(more)g(details.)37 b(De\014ne)28 b Fs(d)g Ft(b)n(y)1421 3761 y Fs(d)23 b Ft(:=)116 b(min)1598 3815 y Fq(1)p Fk(\024)p Fo(j)s Fk(6)p Fq(=)p Fo(k)q Fk(\024)p Fo(M)1936 3761 y Fr(j)p Fs(y)2000 3773 y Fo(k)2059 3761 y Fr(\000)19 b Fs(y)2184 3773 y Fo(j)2218 3761 y Fr(j)p Fs(=)p Ft(2)14 b Fs(:)101 3964 y Fz(Theorem)44 b(1.)j Ff(Consider)41 b Fs(\026)g Fr(2)h Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)34 b Fr(\000)25 b Ft(2\))1600 3934 y Fq(2)1637 3964 y Fs(=)p Ft(4])p Ff(.)68 b(F)-6 b(or)39 b(any)h Fs(M)50 b Fr(\025)41 b Ft(2)p Ff(,)h(ther)l(e)d(is)h(a) g(nonne)l(gative)g(c)l(onstant)101 4064 y Fs(K)172 4076 y Fo(M)269 4064 y Fs(<)22 b(\031)406 4034 y Fq(2)473 4064 y Ff(such)30 b(that,)g(for)h(any)f Fs(u)23 b Fr(2)g Fs(H)1374 4034 y Fq(1)1411 4064 y Ft(\()p Fp(R)1503 4034 y Fo(N)1566 4064 y Ft(\))p Ff(,)631 4140 y Fn(Z)677 4328 y Fm(R)719 4312 y Fl(N)791 4253 y Fr(jr)p Fs(u)p Fr(j)954 4218 y Fq(2)1014 4253 y Fs(dx)c Ft(+)1216 4196 y Fs(K)1287 4208 y Fo(M)1378 4196 y Ft(+)g(\()p Fs(M)27 b Ft(+)18 b(1\))c Fs(\026)p 1216 4233 607 4 v 1479 4309 a(d)1522 4285 y Fq(2)1860 4140 y Fn(Z)1906 4328 y Fm(R)1948 4312 y Fl(N)2020 4253 y Fr(j)p Fs(u)p Fr(j)2114 4218 y Fq(2)2174 4253 y Fs(dx)23 b Fr(\025)g Fs(\026)2453 4140 y Fn(Z)2499 4328 y Fm(R)2541 4312 y Fl(N)2612 4253 y Fs(V)2660 4265 y Fo(M)2734 4253 y Ft(\()p Fs(x)p Ft(\))14 b Fr(j)p Fs(u)p Fr(j)2953 4218 y Fq(2)3014 4253 y Fs(dx)24 b(:)201 4507 y Ft(A)h Fh(partition)f(of)h(unit)n(y)32 b Ft(in)25 b Fp(R)1098 4476 y Fo(N)1185 4507 y Ft(is)g(a)f(\014nite)h(set)g Fr(f)p Fs(J)1756 4519 y Fo(k)1797 4507 y Fr(g)1839 4471 y Fo(M)6 b Fq(+1)1839 4532 y Fo(k)q Fq(=1)2021 4507 y Ft(of)24 b(real)g(v)-5 b(alued)25 b(functions)g Fs(J)2930 4519 y Fo(k)2994 4507 y Fr(2)e Fs(W)3162 4476 y Fq(1)p Fo(;)p Fk(1)3285 4507 y Ft(\()p Fp(R)3377 4476 y Fo(N)3440 4507 y Ft(\),)j(suc)n(h)101 4621 y(that)281 4559 y Fn(P)369 4580 y Fo(M)6 b Fq(+1)369 4646 y Fo(k)q Fq(=1)540 4621 y Fs(J)594 4591 y Fq(2)586 4645 y Fo(k)655 4621 y Ft(=)22 b(1.)37 b(Under)27 b(these)h(conditions,)f(w)n(e)g(ha)n(v)n(e:)240 4757 y(\()p Fs(a)p Ft(\))390 4694 y Fn(P)478 4715 y Fo(M)6 b Fq(+1)478 4782 y Fo(k)q Fq(=1)649 4757 y Fs(J)695 4769 y Fo(k)750 4757 y Fs(@)794 4769 y Fo(a)834 4757 y Fs(J)880 4769 y Fo(k)944 4757 y Ft(=)23 b(0)k(for)g(an)n(y)g Fs(a)c Ft(=)f(1)14 b Fs(;)g(:)g(:)g(:)27 b(N)9 b Ft(,)248 4900 y(\()p Fs(b)p Ft(\))42 b Fs(J)436 4912 y Fo(M)6 b Fq(+1)617 4900 y Ft(:=)728 4797 y Fn(q)p 811 4797 461 4 v 103 x Ft(1)18 b Fr(\000)954 4838 y Fn(P)1041 4858 y Fo(M)1041 4925 y(k)q Fq(=1)1180 4900 y Fs(J)1234 4871 y Fq(2)1226 4925 y Fo(k)1271 4900 y Ft(,)248 5032 y(\()p Fs(c)p Ft(\))390 4970 y Fn(P)478 4991 y Fo(M)6 b Fq(+1)478 5057 y Fo(k)q Fq(=1)649 5032 y Fr(jr)p Fs(J)787 5044 y Fo(k)828 5032 y Fr(j)851 5002 y Fq(2)912 5032 y Fr(2)23 b Fs(L)1047 5002 y Fk(1)1117 5032 y Ft(\()p Fp(R)1209 5002 y Fo(N)1272 5032 y Ft(\).)101 5153 y(If)28 b(w)n(e)g(additionally)e(require)h(that) 101 5294 y(\(1\))871 b(\012)1138 5306 y Fo(k)1197 5294 y Fr(\\)19 b Ft(\012)1331 5306 y Fo(l)1379 5294 y Ft(=)k Fr(;)82 b Ft(for)27 b(an)n(y)g Fs(k)s(;)h(l)c Ft(=)f(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)t(;)41 b(k)26 b Fr(6)p Ft(=)d Fs(l)h(;)101 5435 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Fr(jr)p Fs(J)2501 5687 y Fo(k)2543 5675 y Fr(j)2566 5645 y Fq(2)p 2363 5712 240 4 v 2366 5788 a Ft(1)g Fr(\000)g Fs(J)2563 5760 y Fq(2)2555 5813 y Fo(k)2636 5731 y Fs(;)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 956 -103 a Fq(HARD)n(Y)30 b(INEQUALITIES)e(WITH)h (SEVERAL)g(SINGULARITIES)822 b(5)101 96 y Ft(where)27 b(w)n(e)h(ha)n(v)n(e)e(computed)132 219 y Fo(N)101 244 y Fn(X)101 419 y Fo(a)p Fq(=1)235 322 y Fr(j)p Fs(J)304 334 y Fo(M)6 b Fq(+1)485 322 y Fs(@)529 334 y Fo(a)569 322 y Fs(J)615 334 y Fo(M)g Fq(+1)773 322 y Fr(j)796 288 y Fq(2)856 322 y Ft(=)975 219 y Fo(N)944 244 y Fn(X)944 419 y Fo(a)p Fq(=1)1078 227 y Fn(\014)1078 277 y(\014)1078 327 y(\014)1145 219 y Fo(M)1120 244 y Fn(X)1120 422 y Fo(k)q Fq(=1)1254 322 y Fs(J)1300 334 y Fo(k)1355 322 y Fs(@)1399 334 y Fo(a)1439 322 y Fs(J)1485 334 y Fo(k)1526 227 y Fn(\014)1526 277 y(\014)1526 327 y(\014)1554 248 y Fq(2)1614 322 y Ft(=)1732 219 y Fo(N)1702 244 y Fn(X)1702 419 y Fo(a)p Fq(=1)1861 219 y Fo(M)1836 244 y Fn(X)1836 422 y Fo(k)q Fq(=1)1970 322 y Fr(j)p Fs(J)2039 334 y Fo(k)2094 322 y Fs(@)2138 334 y Fo(a)2178 322 y Fs(J)2224 334 y Fo(k)2265 322 y Fr(j)2288 288 y Fq(2)2371 322 y Ft(=)-14 b Fr(\))46 b(jr)p Fs(J)2689 334 y Fo(M)6 b Fq(+1)2847 322 y Fr(j)2870 288 y Fq(2)2931 322 y Ft(=)3044 219 y Fo(M)3019 244 y Fn(X)3018 422 y Fo(k)q Fq(=1)3234 266 y Fs(J)3288 236 y Fq(2)3280 290 y Fo(k)p 3163 303 235 4 v 3163 379 a Ft(1)18 b Fr(\000)g Fs(J)3360 351 y Fq(2)3352 404 y Fo(k)3421 322 y Fr(jr)p Fs(J)3559 334 y Fo(k)3600 322 y Fr(j)3623 288 y Fq(2)3660 322 y Fs(:)101 552 y Ft(In)28 b(the)g(sequel)f(w)n(e)g(will)h(alw)n(a)n(ys)e(use)h (partitions)g(of)h(unit)n(y)g(that)g(satisfy)g(\(1\).)201 651 y(Note)23 b(that)g(to)g(a)n(v)n(oid)e(a)h(singularit)n(y)g(for)g (the)i(gradien)n(t)d(of)i Fs(J)2071 663 y Fo(M)6 b Fq(+1)2252 651 y Ft(at)22 b(the)i(p)r(oin)n(ts)f(where)f(1)9 b Fr(\000)g Fs(J)3146 621 y Fq(2)3138 675 y Fo(k)3205 651 y Ft(=)23 b(0,)g(from)g(\()p Fs(d)p Ft(\))101 751 y(w)n(e)34 b(shall)f(assume)g (that)g(the)h(additional)g(constrain)n(t)e Fr(jr)p Fs(J)1990 763 y Fo(k)2031 751 y Fr(j)2054 721 y Fq(2)2124 751 y Ft(=)h Fs(F)12 b Ft(\()p Fs(x)p Ft(\)\(1)23 b Fr(\000)f Fs(J)2636 721 y Fq(2)2628 774 y Fo(k)2674 751 y Ft(\),)35 b(for)e Fs(k)j Ft(=)d(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)42 b Ft(and)33 b(for)101 853 y(some)27 b Fs(F)35 b Fr(2)24 b Fs(L)533 822 y Fk(1)603 853 y Ft(\()p Fp(R)695 822 y Fo(N)758 853 y Ft(\).)37 b(The)28 b(functions)g(sin)n(us)f(and)g (cosin)n(us,)g(for)g(example,)g(satisfy)g(this)h(last)f(requiremen)n (t.)201 1003 y(P)n(artitions)h(of)h(unit)n(y)h(can)g(b)r(e)g(used)f(to) h(lo)r(calize)f(the)h(Sc)n(hr\177)-42 b(odinger)27 b(op)r(erator.)42 b(Here)29 b(is)g(a)h(statemen)n(t)f(tak)n(en)101 1102 y(from)f([41)o(],)f(with)i(its)e(pro)r(of.)101 1265 y Fz(Lemma)43 b(2.)k Ff(L)l(et)38 b Ft(\()p Fs(J)803 1277 y Fo(k)844 1265 y Ft(\))876 1230 y Fo(M)6 b Fq(+1)876 1290 y Fo(k)q Fq(=1)1073 1265 y Ff(b)l(e)39 b(a)g(p)l(artition)h(of)g (unity)e(satisfying)48 b Ft(\(1\))p Ff(.)65 b(F)-6 b(or)40 b(any)f Fs(u)g Fr(2)h Fs(H)3118 1235 y Fq(1)3155 1265 y Ft(\()p Fp(R)3247 1235 y Fo(N)3310 1265 y Ft(\))f Ff(and)g(any)101 1369 y Fs(V)j Fr(2)24 b Fs(L)327 1338 y Fq(1)327 1392 y(lo)r(c)413 1369 y Ft(\()p Fp(R)505 1338 y Fo(N)569 1369 y Ft(\))p Ff(,)175 1490 y Fn(Z)221 1678 y Fm(R)263 1662 y Fl(N)334 1510 y Fn(\020)384 1603 y Fr(jr)p Fs(u)p Fr(j)547 1568 y Fq(2)602 1603 y Fr(\000)18 b Fs(V)33 b Fr(j)p Fs(u)p Fr(j)860 1568 y Fq(2)897 1510 y Fn(\021)969 1603 y Fs(dx)24 b Ft(=)1171 1499 y Fo(M)6 b Fq(+1)1188 1524 y Fn(X)1187 1702 y Fo(k)q Fq(=1)1338 1490 y Fn(Z)1384 1678 y Fm(R)1426 1662 y Fl(N)1498 1510 y Fn(\020)1547 1603 y Fr(jr)p Ft(\()p Fs(J)1717 1615 y Fo(k)1772 1603 y Fs(u)p Ft(\))p Fr(j)1875 1568 y Fq(2)1931 1603 y Fr(\000)18 b Fs(V)33 b Fr(j)p Fs(J)2164 1615 y Fo(k)2219 1603 y Fs(u)p Fr(j)2290 1568 y Fq(2)2326 1510 y Fn(\021)2399 1603 y Fs(dx)19 b Fr(\000)2591 1490 y Fn(Z)2637 1678 y Fm(R)2679 1662 y Fl(N)2751 1461 y Fn( )2816 1499 y Fo(M)6 b Fq(+1)2833 1524 y Fn(X)2833 1702 y Fo(k)q Fq(=1)2998 1603 y Fr(jr)p Fs(J)3136 1615 y Fo(k)3177 1603 y Fr(j)3200 1568 y Fq(2)3237 1461 y Fn(!)3317 1603 y Fr(j)p Fs(u)p Fr(j)3411 1568 y Fq(2)3471 1603 y Fs(dx)23 b(:)101 1835 y Ff(Pr)l(o)l(of.)43 b Ft(On)28 b(the)g(one)f(hand,)554 1949 y Fn(Z)600 2138 y Fm(R)642 2121 y Fl(N)714 2062 y Fs(V)808 1920 y Fn( )874 1958 y Fo(M)6 b Fq(+1)891 1983 y Fn(X)890 2162 y Fo(k)q Fq(=1)1055 2062 y Fr(j)p Fs(J)1124 2074 y Fo(k)1179 2062 y Fs(u)p Fr(j)1250 2028 y Fq(2)1287 1920 y Fn(!)1376 2062 y Fs(dx)23 b Ft(=)1577 1949 y Fn(Z)1623 2138 y Fm(R)1665 2121 y Fl(N)1736 2062 y Fs(V)1831 1920 y Fn( )1897 1958 y Fo(M)6 b Fq(+1)1913 1983 y Fn(X)1913 2162 y Fo(k)q Fq(=1)2078 2062 y Fr(j)p Fs(J)2147 2074 y Fo(k)2188 2062 y Fr(j)2211 2028 y Fq(2)2248 1920 y Fn(!)2342 2062 y Fr(j)p Fs(u)p Fr(j)2436 2028 y Fq(2)2495 2062 y Fs(dx)24 b Ft(=)2697 1949 y Fn(Z)2743 2138 y Fm(R)2785 2121 y Fl(N)2856 2062 y Fs(V)33 b Fr(j)p Fs(u)p Fr(j)3031 2028 y Fq(2)3091 2062 y Fs(dx)24 b(:)101 2287 y Ft(On)k(the)g(other)f(hand,)558 2410 y Fo(M)6 b Fq(+1)575 2435 y Fn(X)575 2613 y Fo(k)q Fq(=1)740 2513 y Fr(jr)p Ft(\()p Fs(J)910 2525 y Fo(k)965 2513 y Fs(u)p Ft(\))p Fr(j)1068 2479 y Fq(2)1128 2513 y Ft(=)23 b Fr(jr)p Fs(u)p Fr(j)1379 2479 y Fq(2)1434 2513 y Ft(+)1517 2371 y Fn( )1583 2410 y Fo(M)6 b Fq(+1)1600 2435 y Fn(X)1599 2613 y Fo(k)q Fq(=1)1764 2513 y Fr(jr)p Fs(J)1902 2525 y Fo(k)1943 2513 y Fr(j)1966 2479 y Fq(2)2004 2371 y Fn(!)2083 2513 y Fr(j)p Fs(u)p Fr(j)2177 2479 y Fq(2)2233 2513 y Ft(+)2316 2371 y Fn( )2381 2410 y Fo(M)g Fq(+1)2398 2435 y Fn(X)2398 2613 y Fo(k)q Fq(=1)2563 2513 y Fs(J)2609 2525 y Fo(k)2663 2513 y Fr(r)p Fs(J)2778 2525 y Fo(k)2819 2371 y Fn(!)2913 2513 y Fr(r)p Ft(\()p Fr(j)p Fs(u)p Fr(j)3108 2479 y Fq(2)3145 2513 y Ft(\))24 b Fs(:)101 2743 y Ft(Com)n(bined)k(with)g(Prop)r(ert)n(y)e(\()p Fs(a)p Ft(\),)i(this)g(pro)n(v)n(es)d(the)j(result.)1634 b Fe(\003)201 2913 y Ft(Thanks)27 b(to)g(Lemma)h(2)f(and)g(Prop)r(ert)n (y)f(\()p Fs(d)p 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3476 y Fo(M)6 b Fq(+1)2378 3501 y Fn(X)2378 3679 y Fo(k)q Fq(=1)2529 3467 y Fn(Z)2575 3655 y Fm(R)2617 3639 y Fl(N)2688 3580 y Fr(jr)p Fs(J)2826 3592 y Fo(k)2867 3580 y Fr(j)2890 3545 y Fq(2)2941 3580 y Fr(j)p Fs(u)p Fr(j)3035 3545 y Fq(2)3095 3580 y Fs(dx)420 3873 y Ft(=)568 3760 y Fn(Z)614 3948 y Fm(R)656 3932 y Fl(N)727 3873 y Fr(jr)p Ft(\()p Fs(J)897 3885 y Fo(M)g Fq(+1)1069 3873 y Fs(u)p Ft(\))p Fr(j)1172 3838 y Fq(2)1232 3873 y Fs(dx)19 b Fr(\000)f Fs(\026)1488 3760 y Fn(Z)1534 3948 y Fm(R)1576 3932 y Fl(N)1648 3873 y Fs(V)1696 3885 y Fo(M)1798 3781 y Fn(\020)1847 3873 y Ft(1)g Fr(\000)1990 3810 y Fn(P)2078 3831 y Fo(M)2078 3898 y(k)q Fq(=1)2216 3873 y Fs(J)2270 3843 y Fq(2)2262 3896 y Fo(k)2308 3781 y Fn(\021)2385 3873 y Fr(j)p Fs(u)p Fr(j)2479 3838 y Fq(2)2539 3873 y Fs(dx)h Fr(\000)2757 3769 y Fo(M)2731 3794 y Fn(X)2731 3973 y Fo(k)q Fq(=1)2866 3760 y Fn(Z)2912 3948 y Fm(R)2954 3932 y Fl(N)3035 3817 y Fr(jr)p Fs(J)3173 3829 y Fo(k)3214 3817 y Fr(j)3237 3786 y Fq(2)p 3035 3854 240 4 v 3038 3930 a Ft(1)f Fr(\000)g Fs(J)3235 3901 y Fq(2)3227 3955 y Fo(k)3298 3873 y Fr(j)p Fs(u)p Fr(j)3392 3838 y Fq(2)3452 3873 y Fs(dx)24 b(;)642 4207 y Fr(R)712 4219 y Fo(M)809 4207 y Fr(\025)f(\000)1001 4103 y Fo(M)976 4128 y Fn(X)976 4307 y Fo(k)q Fq(=1)1110 4094 y Fn(Z)1156 4283 y Fm(R)1198 4266 y Fl(N)1279 4151 y Fr(jr)p Fs(J)1417 4163 y Fo(k)1458 4151 y Fr(j)1481 4121 y Fq(2)p 1279 4188 V 1282 4264 a Ft(1)18 b Fr(\000)g Fs(J)1479 4235 y Fq(2)1471 4289 y Fo(k)1542 4207 y Fr(j)p Fs(u)p Fr(j)1636 4173 y Fq(2)1696 4207 y Fs(dx)i Fr(\000)e Fs(\026)1953 4094 y Fn(Z)1999 4283 y Fm(R)2041 4266 y Fl(N)2112 4207 y Fs(V)2160 4219 y Fo(M)2262 4115 y Fn(\020)2311 4207 y Ft(1)g Fr(\000)2454 4145 y Fn(P)2542 4165 y Fo(M)2542 4232 y(k)q Fq(=1)2681 4207 y Fs(J)2735 4177 y Fq(2)2727 4231 y Fo(k)2772 4115 y Fn(\021)2849 4207 y Fr(j)p Fs(u)p Fr(j)2943 4173 y Fq(2)3003 4207 y Fs(dx)24 b(:)101 4424 y Ft(Here)41 b(w)n(e)g(successiv)n(ely)e(used)i(Prop)r(erties)f(\()p Fs(b)p Ft(\))h(and)g(\()p Fs(d)p Ft(\))h(and)f Fr(jr)p Ft(\()p Fs(J)2339 4436 y Fo(M)6 b Fq(+1)2511 4424 y Fs(u)p Ft(\))p Fr(j)2614 4394 y Fq(2)2696 4424 y Fr(\025)45 b Ft(0.)77 b(Using)41 b(the)g(fact)g(that)101 4524 y(\012)161 4536 y Fo(j)215 4524 y Fr(\\)18 b Ft(\012)348 4536 y Fo(k)412 4524 y Ft(=)23 b Fr(;)k Ft(for)g(an)n(y)g Fs(j)5 b Ft(,)28 b Fs(k)e Ft(=)c(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)-5 b Ft(,)28 b Fs(j)g Fr(6)p Ft(=)22 b Fs(k)s Ft(,)28 b(then)g(the)g(ab)r(o)n(v)n(e)e(inequalit)n(y)h(can)g(b)r(e)h (rewritten)g(as)524 4758 y Fr(R)594 4770 y Fo(M)691 4758 y Fr(\025)23 b(\000)883 4654 y Fo(M)858 4679 y Fn(X)858 4858 y Fo(k)q Fq(=1)992 4645 y Fn(Z)1038 4834 y Fq(\012)1085 4843 y Fl(k)1140 4641 y Fn(\024)1193 4702 y Fr(jr)p Fs(J)1331 4714 y Fo(k)1372 4702 y Fr(j)1395 4672 y Fq(2)p 1193 4739 V 1196 4815 a Ft(1)18 b Fr(\000)g Fs(J)1393 4786 y Fq(2)1385 4840 y Fo(k)1461 4758 y Ft(+)g Fs(\026)c Ft(\(1)k Fr(\000)g Fs(J)1837 4724 y Fq(2)1829 4779 y Fo(k)1875 4758 y Ft(\))c Fs(V)1969 4770 y Fo(M)2043 4758 y Ft(\()p Fs(x)p Ft(\))2154 4641 y Fn(\025)2213 4758 y Fr(j)p Fs(u)p Fr(j)2307 4724 y Fq(2)2357 4758 y Fs(dx)19 b Fr(\000)2549 4645 y Fn(Z)2596 4834 y Fq(\007)2664 4758 y Fs(\026)14 b(V)2776 4770 y Fo(M)2850 4758 y Ft(\()p Fs(x)p Ft(\))g Fr(j)p Fs(u)p Fr(j)3069 4724 y Fq(2)3121 4758 y Fs(dx)24 b(;)101 4998 y Ft(with)39 b(\007)i(:=)g Fp(R)596 4968 y Fo(N)685 4998 y Fr(n)26 b([)808 4968 y Fo(M)808 5022 y(k)q Fq(=1)p 933 4932 60 4 v 933 4998 a Ft(\012)993 5010 y Fo(k)1034 4998 y Ft(.)70 b(Consider)37 b(no)n(w)h(the)h(case)f Fs(M)50 b Ft(=)41 b(2,)g Fs(y)2393 5010 y Fq(1)2471 4998 y Ft(=)g Fs(y)s Ft(,)h Fs(y)2727 5010 y Fq(2)2805 4998 y Ft(=)f Fr(\000)p Fs(y)g Ft(and)d(assume)g(that) 101 5098 y(0)23 b Fs(<)f(d)i Fr(\024)e(j)p Fs(y)s Fr(j)p Ft(.)101 5256 y Fz(Lemma)34 b(3.)42 b Ff(Ther)l(e)33 b(is)f(a)g(p)l(artition)g(of)h(unity)e Fr(f)p Fs(J)1711 5268 y Fo(k)1751 5256 y Fr(g)1793 5226 y Fq(3)1793 5280 y Fo(k)q Fq(=1)1949 5256 y Ff(satisfying)41 b Ft(\(1\))31 b Ff(with)i Fs(J)2694 5268 y Fq(1)2757 5256 y Fr(\021)26 b Ft(1)32 b Ff(on)f Fs(B)t Ft(\()p Fs(y)s(;)14 b(d=)p Ft(2\))p Ff(,)32 b Fs(J)3484 5268 y Fq(1)3548 5256 y Fr(\021)26 b Ft(0)101 5358 y Ff(on)31 b Fs(B)t Ft(\()p Fs(y)s(;)14 b(d)p Ft(\))476 5328 y Fo(c)511 5358 y Ff(,)31 b Fs(J)613 5370 y Fq(2)651 5358 y Ft(\()p Fs(x)p Ft(\))26 b(=)f Fs(J)924 5370 y Fq(1)961 5358 y Ft(\()p Fr(\000)p Fs(x)p Ft(\))32 b Ff(for)f(any)h Fs(x)25 b Fr(2)h Fp(R)1676 5328 y Fo(N)1739 5358 y Ff(,)32 b Ft(0)25 b Fs(<)f(d)i Fr(\024)f(j)p Fs(y)s Fr(j)p Ff(,)31 b(such)g(that,)h(for)g(any)f Fs(\026)25 b(>)g Ft(0)p Ff(,)32 b(ther)l(e)f(exists)f(a)101 5458 y(c)l(onstant)f Fs(K)503 5470 y Fq(2)563 5458 y Fr(2)23 b Ft([0)p Fs(;)14 b(\031)793 5427 y Fq(2)830 5458 y Ft(\))30 b Ff(for)h(which,)h(almost)e(everywher)l(e)h(for)g(al)t (l)g Fs(x)23 b Fr(2)h Ft(\012)f(:=)g(supp\()p Fs(J)2817 5470 y Fq(1)2854 5458 y Ft(\))c Fr([)g Ft(supp\()p Fs(J)3228 5470 y Fq(2)3265 5458 y Ft(\))p Ff(,)31 b(we)f(have)746 5583 y Fq(3)703 5608 y Fn(X)702 5787 y Fo(k)q Fq(=1)851 5687 y Fr(jr)p Fs(J)989 5699 y Fo(k)1030 5687 y Fr(j)1053 5652 y Fq(2)1108 5687 y Ft(+)19 b Fs(\026)14 b(J)1310 5652 y Fq(2)1302 5707 y(3)1360 5687 y Fs(V)1408 5699 y Fq(2)1446 5687 y Ft(\()p Fs(x)p Ft(\))24 b(=)1696 5608 y Fn(X)1669 5787 y Fo(k)q Fq(=1)p Fo(;)p Fq(2)1880 5630 y Fr(jr)p Fs(J)2018 5642 y Fo(k)2059 5630 y Fr(j)2082 5600 y Fq(2)p 1880 5668 240 4 v 1883 5744 a Ft(1)18 b Fr(\000)g Fs(J)2080 5715 y Fq(2)2072 5769 y Fo(k)2148 5687 y Ft(+)g Fs(\026)c(J)2349 5652 y Fq(2)2341 5707 y(3)2400 5687 y Fs(V)2448 5699 y Fq(2)2486 5687 y Ft(\()p Fs(x)p Ft(\))24 b Fr(\024)2718 5630 y Fs(K)2789 5642 y Fq(2)2844 5630 y Ft(+)18 b(2)c Fs(\026)p 2718 5668 315 4 v 2835 5744 a(d)2878 5720 y Fq(2)3057 5687 y Fs(:)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 101 -103 a Fq(6)1028 b(R.)22 b(BOSI,)g(J.)g (DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)201 96 y Ft(In)28 b(the)g(pro)r(of)f(of)g(this)h(result,)f(w)n(e)h(use)f (\014rst)h(a)f(partition)g(of)g(unit)n(y)h(de\014ned)g(as)f(follo)n (ws.)36 b(Let)101 363 y(\(2\))998 b Fs(J)8 b Ft(\()p Fs(r)r Ft(\))25 b(:=)1498 168 y Fn(8)1498 243 y(>)1498 268 y(<)1498 417 y(>)1498 442 y(:)1613 238 y Ft(1)311 b(if)84 b Fs(r)26 b Fr(\024)c Ft(1)p Fs(=)p Ft(2)1613 362 y(sin\()p Fs(\031)17 b(r)r Ft(\))84 b(if)g(1)p Fs(=)p Ft(2)21 b Fr(\024)i Fs(r)j Fr(\024)c Ft(1)1613 487 y(0)311 b(if)84 b Fs(r)26 b Fr(\025)c Ft(1)101 652 y(and)28 b(de\014ne)g Fs(J)549 664 y Fq(1)586 652 y Ft(\()p Fs(x)p Ft(\))c(:=)f Fs(J)8 b Ft(\()p Fr(j)p Fs(x)19 b Fr(\000)f Fs(y)s Fr(j)p Fs(=d)p Ft(\),)27 b Fs(J)1370 664 y Fq(2)1408 652 y Ft(\()p Fs(x)p Ft(\))d(:=)e Fs(J)8 b Ft(\()p Fr(j)p Fs(x)20 b Ft(+)e Fs(y)s Fr(j)p Fs(=d)p Ft(\),)27 b(and)h Fs(J)2354 664 y Fq(3)2414 652 y Ft(:=)2525 580 y Fn(p)p 2608 580 427 4 v 72 x Ft(1)18 b Fr(\000)g Fs(J)2805 623 y Fq(2)2797 674 y(1)2860 652 y Fr(\000)g Fs(J)2997 623 y Fq(2)2989 674 y(2)3035 652 y Ft(.)101 820 y Ff(Pr)l(o)l(of.)43 b Ft(The)30 b(lo)n(w)n(er)e(b)r(ound)i Fs(K)1082 832 y Fq(2)1146 820 y Fr(\025)c Ft(0)j(immediately)h(follo)n(ws)e(b)n(y)i (ev)-5 b(aluating)29 b(the)h(l.h.s.)43 b(at)30 b Fs(x)d Ft(=)f(0.)42 b(As)30 b(for)f(the)101 919 y(upp)r(er)24 b(b)r(ound,)h(consider)d(the)i(ab)r(o)n(v)n(e)e(partition)h(of)g(unit)n (y)-7 b(.)36 b(Th)n(us)23 b(de\014ned,)i Fr(f)p Fs(J)2573 931 y Fq(1)2609 919 y Fs(;)14 b(J)2692 931 y Fq(2)2730 919 y Fs(;)g(J)2813 931 y Fq(3)2850 919 y Fr(g)23 b Ft(is)g(a)g (partition)g(of)h(unit)n(y)101 1019 y(of)k Fp(R)256 989 y Fo(N)347 1019 y Ft(satisfying)g(\(1\).)38 b(Let)28 b Fs(\022)e Ft(:=)d Fr(j)p Fs(y)s Fr(j)p Fs(=d)g Fr(\025)g Ft(1)k(and)h(\012)1787 1031 y Fq(+)1865 1019 y Ft(:=)23 b Fr(f)p Fs(x)h Fr(2)g Ft(\012)14 b Fs(;)37 b(x)19 b Fr(\001)g Fs(y)26 b(>)d Ft(0)p Fr(g)p Ft(.)36 b(By)28 b(Prop)r(ert)n(y)e(\()p Fs(d)p Ft(\),)j(using)e(the)101 1119 y(symmetry)g(with)i(resp)r(ect)e(to)g(the)h(h)n(yp)r(erplane)f Fr(f)p Fs(x)c Fr(2)h Fp(R)1885 1088 y Fo(N)1984 1119 y Ft(:)37 b Fs(x)19 b Fr(\001)g Fs(y)26 b Ft(=)c(0)p Fr(g)p Ft(,)27 b(w)n(e)g(get)248 1345 y(sup)287 1415 y Fq(\012)387 1203 y Fn(")479 1241 y Fq(3)436 1266 y Fn(X)435 1445 y Fo(k)q Fq(=1)584 1345 y Fr(jr)p Fs(J)722 1357 y Fo(k)763 1345 y Fr(j)786 1311 y Fq(2)842 1345 y Ft(+)18 b Fs(\026)c(J)1043 1311 y Fq(2)1035 1365 y(3)1094 1345 y Fs(V)1142 1357 y Fq(2)1179 1203 y Fn(#)1251 1345 y Ft(=)22 b(sup)1354 1415 y Fq(\012)1401 1423 y Fj(+)1477 1228 y Fn(\024)1531 1289 y Fr(jr)p Fs(J)1669 1301 y Fq(1)1706 1289 y Fr(j)1729 1259 y Fq(2)p 1531 1326 236 4 v 1532 1402 a Ft(1)c Fr(\000)g Fs(J)1729 1373 y Fq(2)1721 1424 y(1)1795 1345 y Ft(+)g Fs(\026)1942 1278 y Fn(\000)1980 1345 y Ft(1)g Fr(\000)g Fs(J)2177 1311 y Fq(2)2169 1365 y(1)2214 1278 y Fn(\001)2266 1345 y Fs(V)2314 1357 y Fq(2)2352 1228 y Fn(\025)573 1632 y Ft(=)750 1575 y(1)p 730 1613 81 4 v 730 1689 a Fs(d)773 1665 y Fq(2)909 1632 y Ft(sup)835 1705 y Fo(t)p Fk(2)p Fq(\(1)p Fo(=)p Fq(2)p Fo(;)p Fq(1\))1123 1490 y Fn(")1241 1575 y Fr(j)p Fs(J)1318 1545 y Fk(0)1342 1575 y Ft(\()p Fs(t)p Ft(\))p Fr(j)1459 1545 y Fq(2)p 1182 1613 375 4 v 1182 1689 a Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)1519 1665 y Fq(2)1585 1632 y Ft(+)18 b Fs(\026)1718 1564 y Fn(\000)1756 1632 y Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)2093 1597 y Fq(2)2131 1564 y Fn(\001)2183 1515 y(\022)2375 1575 y Ft(1)p 2254 1613 284 4 v 2254 1689 a(\()p Fs(s)19 b Ft(+)f Fs(\022)r Ft(\))2500 1665 y Fq(2)2566 1632 y Ft(+)2780 1575 y(1)p 2659 1613 V 2659 1689 a(\()p Fs(s)g Fr(\000)g Fs(\022)r Ft(\))2904 1665 y Fq(2)2952 1515 y Fn(\023)3013 1715 y Fk(j)p Fo(s)p Fq(=)p Fo(\022)r Fk(\000)p Fo(t)3230 1490 y Fn(#)573 1892 y Ft(=)750 1836 y(1)p 730 1873 81 4 v 730 1949 a Fs(d)773 1925 y Fq(2)909 1892 y Ft(sup)835 1966 y Fo(t)p Fk(2)p Fq(\(1)p Fo(=)p Fq(2)p Fo(;)p Fq(1\))1123 1775 y Fn(\024)1237 1836 y Fr(j)p Fs(J)1314 1806 y Fk(0)1337 1836 y Ft(\()p Fs(t)p Ft(\))p Fr(j)1454 1806 y Fq(2)p 1177 1873 375 4 v 1177 1949 a Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)1514 1925 y Fq(2)1580 1892 y Ft(+)18 b Fs(\026)1713 1825 y Fn(\000)1751 1892 y Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)2088 1858 y Fq(2)2126 1825 y Fn(\001)2178 1775 y(\022)2387 1836 y Ft(1)p 2249 1873 317 4 v 2249 1949 a(\(2)p Fs(\022)21 b Fr(\000)d Fs(t)p Ft(\))2528 1925 y Fq(2)2594 1892 y Ft(+)2700 1836 y(1)p 2687 1873 68 4 v 2687 1949 a Fs(t)2717 1925 y Fq(2)2764 1775 y Fn(\023\025)803 2146 y Fr(\024)944 2090 y Ft(1)p 924 2127 81 4 v 924 2203 a Fs(d)967 2179 y Fq(2)1103 2146 y Ft(sup)1028 2219 y Fo(t)p Fk(2)p Fq(\(1)p Fo(=)p Fq(2)p Fo(;)p Fq(1\))1317 2029 y Fn(\024)1430 2090 y Fr(j)p Fs(J)1507 2059 y Fk(0)1531 2090 y Ft(\()p Fs(t)p Ft(\))p Fr(j)1648 2059 y Fq(2)p 1371 2127 375 4 v 1371 2203 a Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)1708 2179 y Fq(2)1774 2146 y Ft(+)18 b Fs(\026)1907 2078 y Fn(\000)1945 2146 y Ft(1)g Fr(\000)g(j)p Fs(J)8 b Ft(\()p Fs(t)p Ft(\))p Fr(j)2282 2111 y Fq(2)2320 2078 y Fn(\001)2372 2029 y(\022)2560 2090 y Ft(1)p 2443 2127 275 4 v 2443 2203 a(\(2)18 b Fr(\000)g Fs(t)p 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2870 y Fs(J)8 b Ft(\()p Fs(r)r Ft(\))25 b(:=)1559 2675 y Fn(8)1559 2749 y(>)1559 2774 y(<)1559 2924 y(>)1559 2949 y(:)1675 2744 y Ft(1)188 b(if)83 b Fs(r)26 b Fr(\024)c Ft(1)p Fs(=)p Ft(2)1675 2869 y Fs(g)s Ft(\()p Fs(r)r Ft(\))84 b(if)f(1)p Fs(=)p Ft(2)22 b Fr(\024)g Fs(r)k Fr(\024)d Ft(1)1675 2993 y(0)188 b(if)83 b Fs(r)26 b Fr(\025)c Ft(1)14 b Fs(;)101 3137 y Ft(and)28 b Fs(g)i Ft(as)d(the)h(solution)f (to)g(the)h(ODE)1073 3277 y Fr(j)p Fs(g)1139 3247 y Fk(0)1162 3277 y Ft(\()p Fs(t)p Ft(\))p Fr(j)1279 3247 y Fq(2)p 1036 3314 318 4 v 1036 3390 a Ft(1)18 b Fr(\000)g Fs(g)1222 3366 y Fq(2)1259 3390 y Ft(\()p Fs(t)p Ft(\))1386 3333 y(=)23 b Fs(A)c Fr(\000)f Fs(\026)1702 3266 y Fn(\000)1740 3333 y Ft(1)g Fr(\000)g Fs(g)1926 3299 y Fq(2)1963 3333 y Ft(\()p Fs(t)p Ft(\))2057 3266 y Fn(\001)2109 3216 y(\022)2317 3277 y Ft(1)p 2180 3314 317 4 v 2180 3390 a(\(2)p Fs(\022)j Fr(\000)d Fs(t)p Ft(\))2459 3366 y Fq(2)2525 3333 y Ft(+)2630 3277 y(1)p 2617 3314 68 4 v 2617 3390 a Fs(t)2647 3366 y 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y Fs(\026)14 b Ft(\()p Fs(M)27 b Fr(\000)18 b Ft(1\))p 2735 5701 362 4 v 2875 5777 a Fs(d)2918 5753 y Fq(2)3106 5607 y Fn(Z)3152 5796 y Fq(\012)3199 5805 y Fl(k)3229 5720 y Fr(j)p Fs(J)3298 5732 y Fo(k)3352 5720 y Fs(u)p Fr(j)3423 5686 y Fq(2)3483 5720 y Fs(dx)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 956 -103 a Fq(HARD)n(Y)30 b(INEQUALITIES)e(WITH)h (SEVERAL)g(SINGULARITIES)822 b(7)101 96 y Ft(and)28 b(th)n(us)f(pro)n (vide)g(a)g(lo)n(w)n(er)f(b)r(ound)i(for)f Fs(Q)p Ft([)p Fs(J)1545 108 y Fo(k)1599 96 y Fs(u)p Ft(]:)1219 323 y Fs(Q)p Ft([)p Fs(J)1354 335 y Fo(k)1408 323 y Fs(u)p Ft(])c Fr(\025)f(\000)1678 267 y Fs(\026)14 b Ft(\()p Fs(M)27 b Fr(\000)18 b Ft(1\))p 1678 304 362 4 v 1818 380 a Fs(d)1861 356 y Fq(2)2049 210 y Fn(Z)2095 399 y Fq(\012)2142 408 y Fl(k)2172 323 y Fr(j)p Fs(J)2241 335 y Fo(k)2295 323 y Fs(u)p Fr(j)2366 289 y Fq(2)2426 323 y Fs(dx)24 b(:)101 563 y Ft(No)n(w,)33 b(observ)n(e)d(that)i Fs(V)851 575 y Fo(M)956 563 y Fr(\024)e Fs(M)t(=d)1221 533 y Fq(2)1290 563 y Ft(on)h(\007.)50 b(F)-7 b(or)31 b(ev)n(ery)g Fs(k)i Ft(=)d(1,)j(2)14 b Fs(;)g(:)g(:)g(:)o Ft(,)33 b Fs(M)-5 b Ft(,)33 b(w)n(e)f(can)f(apply)h(Lemma)g(3)f(on)h (\012)3640 575 y Fo(k)101 663 y Ft(with)d(\()p Fs(y)364 675 y Fo(k)405 663 y Fs(;)14 b(y)483 675 y Fo(l)508 663 y Ft(\))25 b(=)f(\()p Fr(\000)p Fs(y)s(;)14 b(y)s Ft(\))28 b(up)h(to)g(a)f(c)n(hange)f(of)i(co)r(ordinates,)e(for)h(some)g Fs(y)2444 675 y Fo(l)2494 663 y Fr(6)p Ft(=)c Fs(y)2624 675 y Fo(k)2665 663 y Ft(,)29 b(and)f(for)g(all)g Fs(j)i Fr(6)p Ft(=)24 b Fs(k)s Ft(,)29 b Fs(l)r Ft(,)f(b)r(ound)101 762 y Fr(j)p Fs(x)19 b Fr(\000)f Fs(y)314 774 y Fo(j)349 762 y Fr(j)372 732 y Fk(\000)p Fq(2)489 762 y Ft(b)n(y)27 b(1)p Fs(=d)731 732 y Fq(2)768 762 y Ft(.)37 b(Hence)27 b(w)n(e)h(get)560 1026 y Fr(R)630 1038 y Fo(M)727 1026 y Fr(\025)22 b(\000)918 922 y Fo(M)893 947 y Fn(X)893 1126 y Fo(k)q Fq(=1)1027 913 y Fn(Z)1073 1102 y Fq(\012)1120 1111 y Fl(k)1175 909 y Fn(\024)1229 970 y Fs(K)1300 982 y Fq(2)1355 970 y Ft(+)c(2)c 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b(1\),)27 b(w)n(e)101 1389 y(obtain)598 1491 y Fo(M)573 1515 y Fn(X)573 1694 y Fo(k)q Fq(=1)707 1594 y Fs(Q)p Ft([)p Fs(J)842 1606 y Fo(k)897 1594 y Fs(u)p Ft(])18 b(+)g Fr(R)1139 1606 y Fo(M)1236 1594 y Fr(\025)23 b(\000)1399 1538 y Fs(K)1470 1550 y Fq(2)1524 1538 y Ft(+)18 b Fs(\026)c Ft(\()p Fs(M)28 b Ft(+)18 b(1\))p 1399 1575 571 4 v 1643 1651 a Fs(d)1686 1627 y Fq(2)2032 1491 y Fo(M)2006 1515 y Fn(X)2006 1694 y Fo(k)q Fq(=1)2141 1481 y Fn(Z)2187 1670 y Fq(\012)2234 1679 y Fl(k)2288 1594 y Fr(j)p Fs(u)p Fr(j)2382 1560 y Fq(2)2433 1594 y Fs(dx)h Fr(\000)2635 1538 y Fs(\026)14 b(M)p 2635 1575 154 4 v 2672 1651 a(d)2715 1627 y Fq(2)2812 1481 y Fn(Z)2859 1670 y Fq(\007)2928 1594 y Fr(j)p Fs(u)p Fr(j)3022 1560 y Fq(2)3072 1594 y Fs(dx)24 b(;)101 1831 y Ft(from)k(whic)n(h)f(the)h(result)f(follo)n (ws.)2438 b Fe(\003)101 2001 y Fz(Remarks.)61 b Ft(There)35 b(are)g(man)n(y)g(p)r(ossibilities)h(for)f(impro)n(ving)f(the)i(result) g(of)g(Theorem)e(1)i(for)f Fs(M)45 b Fr(\025)37 b Ft(2)e(and)101 2101 y Fs(\026)23 b(<)g Ft(\()p Fs(N)k Fr(\000)19 b Ft(2\))546 2071 y Fq(2)583 2101 y Fs(=)p Ft(4.)242 2240 y(\(1\))42 b(One)27 b(can)g(notice)h(that)g(when)g(applying)f(the)h(Hardy)e (inequalit)n(y)i(for)f(one)g(singularit)n(y)-7 b(,)26 b(w)n(e)h(can)h(write)494 2360 y Fn(Z)540 2549 y Fm(R)582 2532 y Fl(N)628 2473 y Fr(jr)p Ft(\()p Fs(J)798 2485 y Fo(k)853 2473 y Fs(u)p Ft(\))p Fr(j)956 2439 y Fq(2)1017 2473 y Fs(dx)42 b Fr(\000)f Fs(\026)1319 2360 y Fn(Z)1365 2549 y Fm(R)1407 2532 y Fl(N)1529 2417 y Fr(j)p Fs(J)1598 2429 y Fo(k)1653 2417 y Fs(u)p Fr(j)1724 2387 y Fq(2)p 1488 2454 314 4 v 1488 2530 a Fr(j)p Fs(x)19 b Fr(\000)f Fs(y)1701 2542 y Fo(k)1742 2530 y Fr(j)1765 2506 y Fq(2)1835 2473 y Fs(dx)24 b Fr(\025)2036 2406 y Fn(\000)2074 2473 y Ft(\()p Fs(N)k Fr(\000)18 b Ft(2\))2358 2439 y Fq(2)2395 2473 y Fs(=)p Ft(4)f Fr(\000)h Fs(\026)2629 2406 y Fn(\001)2681 2360 y(Z)2727 2549 y Fm(R)2769 2532 y Fl(N)2892 2417 y Fr(j)p Fs(J)2961 2429 y Fo(k)3016 2417 y Fs(u)p 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2807 y Fn(\025)2772 2811 y(Z)2818 3000 y Fm(R)2860 2983 y Fl(N)2931 2924 y Fr(j)p Fs(J)3000 2936 y Fo(k)3055 2924 y Fs(u)p Fr(j)3126 2890 y Fq(2)3186 2924 y Fs(dx)1792 3348 y Fr(\025)1909 3292 y Ft(1)p 1890 3329 81 4 v 1890 3405 a Fs(d)1933 3381 y Fq(2)1994 3231 y Fn(\022)2065 3292 y Ft(\()p Fs(N)28 b Fr(\000)18 b Ft(2\))2349 3262 y Fq(2)p 2065 3329 321 4 v 2205 3405 a Ft(4)2414 3348 y Fr(\000)g Fs(\026)c(M)2651 3231 y Fn(\023)2726 3235 y(Z)2772 3424 y Fm(R)2814 3407 y Fl(N)2885 3348 y Fr(j)p Fs(J)2954 3360 y Fo(k)3009 3348 y Fs(u)p Fr(j)3080 3314 y Fq(2)3140 3348 y Fs(dx)23 b(:)390 3573 y Ft(On)k(the)h(other)f(hand,)h(w)n(e)f(kno)n(w)g(that)447 3829 y Fr(R)517 3841 y Fo(M)614 3829 y Fr(\025)c(\000)796 3773 y Ft(1)p 777 3810 81 4 v 777 3886 a Fs(d)820 3862 y Fq(2)920 3725 y Fo(M)895 3750 y Fn(X)894 3929 y Fo(k)q Fq(=1)1029 3716 y Fn(Z)1075 3904 y Fq(\012)1122 3913 y Fl(k)1177 3762 y Fn(\002)1211 3829 y Ft(\()p Fs(K)1314 3841 y Fq(2)1370 3829 y Ft(+)18 b(2)c Fs(\026)p Ft(\))k(+)g 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Fs(J)8 b Ft(\(dist\()p Fs(x;)14 b Ft(\000)1115 5377 y Fo(c)1115 5431 y(k)1157 5408 y Ft(\))p Fs(=d)1274 5420 y Fo(k)1314 5408 y Ft(\),)39 b(1)d Fr(\024)g Fs(k)j Fr(\024)d Fs(M)-5 b Ft(,)38 b(for)d(some)g(con)n(tin)n(uous)g(truncation)g(function)h Fs(J)44 b Ft(with)390 5507 y Fs(J)35 b Fr(\021)27 b Ft(1)j(in)h([1)p Fs(=)p Ft(2)p Fs(;)14 b Fr(1)p Ft(\),)29 b(0)e Fr(\024)g Fs(J)36 b Fr(\024)27 b Ft(1)i(and)h Fs(J)8 b Ft(\(0\))28 b(=)f(0.)44 b(F)-7 b(or)30 b(an)n(y)f Fs(k)h Ft(=)d(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)-5 b Ft(,)31 b Fs(J)2916 5519 y Fo(k)2987 5507 y Ft(is)f(supp)r(orted)g(in)g(the)390 5607 y(closure)c(of)i(\000)814 5619 y Fo(k)855 5607 y Ft(.)242 5706 y(\(4\))42 b(In)29 b(some)g(cases,)g(it)g(is)h(also)e(p)r (ossible)h(to)g(in)n(tro)r(duce)g(an)g(arti\014cial)f(singularit)n(y)g (in)h(the)h(comp)r(onen)n(t)f(\007,)390 5806 y(in)f(order)e(to)i(con)n (trol)e Fs(V)1133 5818 y Fo(M)1235 5806 y Ft(on)h(\007)g(b)n(y)h(an)f (additional)g(Hardy)g(inequalit)n(y)-7 b(.)p eop end %%Page: 8 8 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b(Prop)r(ert)n(y)26 b(\()p Fs(d)p Ft(\))j(implies)989 1752 y Fq(3)946 1776 y Fn(X)945 1955 y Fo(k)q Fq(=1)1080 1855 y Fr(jr)p Fs(J)1218 1867 y Fo(k)1259 1855 y Fr(j)1282 1821 y Fq(2)1342 1855 y Ft(=)1440 1799 y Fr(jr)p Fs(J)1578 1811 y Fq(1)1616 1799 y Fr(j)1639 1769 y Fq(2)p 1440 1836 236 4 v 1441 1912 a Ft(1)18 b Fr(\000)g Fs(J)1638 1884 y Fq(2)1630 1934 y(1)1704 1855 y Ft(+)1797 1799 y Fr(jr)p Fs(J)1935 1811 y Fq(2)1973 1799 y Fr(j)1996 1769 y Fq(2)p 1797 1836 V 1798 1912 a Ft(1)g Fr(\000)g Fs(J)1995 1884 y Fq(2)1987 1934 y(2)2066 1855 y Fr(\024)2164 1799 y Fs(\031)2214 1769 y Fq(2)p 2164 1836 88 4 v 2168 1912 a Fs(d)2211 1888 y Fq(2)2275 1855 y Fp(I)2307 1870 y Fq(supp\()p Fk(r)p Fo(J)2562 1878 y Fj(3)2594 1870 y Fq(\))2647 1855 y Fs(;)101 2092 y Ft(where)26 b Fp(I)372 2104 y Fq(\012)450 2092 y Ft(is)g(the)h(c)n(haracteristic)d(function)j(of)g(the)f(set)h (\012)c(=)f(\012)2101 2104 y Fq(1)2154 2092 y Fr([)17 b Ft(\012)2286 2104 y Fq(2)2323 2092 y Ft(.)36 b(Our)26 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5794 y Fq(2)997 5782 y Ft(\()p Fs(t)p Ft(\))24 b(=)1218 5726 y Fs(t)p 1212 5763 V 1212 5839 a Ft(2)1282 5782 y Fr(\000)18 b Ft(2)1407 5748 y Fk(\000)p Fq(4)p Fo(=)p Fq(3)1577 5782 y Ft(3)1619 5748 y Fk(\000)p Fq(2)p Fo(=)p Fq(3)1788 5782 y Fs(\032)1831 5748 y Fq(1)p Fo(=)p Fq(3)1936 5782 y Ft(\()p Fs(t)p Ft(\))c Fd(Re)2148 5690 y Fn(\020)2198 5782 y Ft(\(1)k(+)g Fs(i)2416 5710 y Fr(p)p 2485 5710 V 72 x Ft(3)o(\))c Fs(e)2611 5748 y Fo(i\022)r Fq(\()p Fo(t)p Fq(\))p Fo(=)p Fq(3)2816 5690 y Fn(\021)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 101 -103 a Fq(12)995 b(R.)22 b(BOSI,)g(J.)g(DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)101 96 y Ft(where)1246 237 y Fs(A)p Ft(\()p Fs(t)p Ft(\))i(=)e(9)14 b Fs(t)g Ft(\()p Fs(t)1675 203 y Fq(2)1730 237 y Fr(\000)k Ft(4\))23 b Fs(;)1246 372 y(B)t Ft(\()p Fs(t)p Ft(\))g(=)1518 297 y Fn(p)p 1601 297 1042 4 v 75 x Ft(3)14 b(\(5)g Fs(t)1775 349 y Fq(6)1830 372 y Fr(\000)k Ft(72)c Fs(t)2041 349 y Fq(4)2095 372 y Ft(+)k(432)c Fs(t)2348 349 y Fq(2)2402 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Fn(\020)2168 955 y Ft(\(1)k Fr(\000)g Fs(i)2386 883 y Fr(p)p 2455 883 V 72 x Ft(3)o(\))c Fs(e)2581 921 y Fo(i\022)r Fq(\()p Fo(t)p Fq(\))p Fo(=)p Fq(3)2786 863 y Fn(\021)2873 955 y Fs(;)1101 1176 y Ft(\026)-43 b Fs(a)1144 1188 y Fq(3)1181 1176 y Ft(\()p Fs(t)p Ft(\))23 b(=)1402 1120 y Fs(t)p 1396 1157 V 1396 1233 a Ft(2)1466 1176 y(+)18 b(2)1591 1142 y Fk(\000)p Fq(1)p Fo(=)p Fq(3)1760 1176 y Ft(3)1802 1142 y Fk(\000)p Fq(2)p Fo(=)p Fq(3)1972 1176 y Fs(\032)2015 1142 y Fq(1)p Fo(=)p Fq(3)2119 1176 y Ft(\()p Fs(t)p Ft(\))29 b(cos)o(\()p Fs(\022)r Ft(\()p Fs(t)p Ft(\))p Fs(=)p Ft(3\))23 b Fs(:)201 1364 y Ft(De\014ne)28 b(the)g(function)g Fs(\024)g Ft(b)n(y)760 1510 y Fs(\024)p Ft(\()p Fs(t)p Ft(\))23 b(=)g(0)249 b(if)83 b Fs(t)23 b Fr(\025)g Ft(2)1632 1437 y Fr(p)p 1700 1437 V 1700 1510 a Ft(2)46 b Fr(\()-14 b(\))46 b Fs(\026)23 b Fr(\024)g Ft(\()p Fs(N)28 b Fr(\000)18 b Ft(2\))2431 1475 y Fq(2)2468 1510 y Fs(=)p Ft(8)k Fs(;)519 1643 y(\024)p Ft(\()p Fs(t)p Ft(\))h(=)g Fs(g)s Ft(\()q(\026)-43 b Fs(a)891 1655 y Fq(2)928 1643 y Ft(\()p Fs(t)p Ft(\)\))250 b(if)83 b(2)23 b Fs(<)f(t)h(<)g Ft(2)1784 1570 y Fr(p)p 1853 1570 V 73 x Ft(2)45 b Fr(\()-14 b(\))47 b Ft(\()p Fs(N)27 b Fr(\000)18 b Ft(2\))2422 1609 y Fq(2)2459 1643 y Fs(=)p Ft(8)k Fs(<)h(\026)g(<)f Ft(\()p Fs(N)28 b Fr(\000)18 b Ft(2\))3097 1609 y Fq(2)3134 1643 y Fs(=)p Ft(4)k Fs(:)101 1784 y Ft(W)-7 b(e)28 b(ha)n(v)n(e)f(therefore)f(pro)n(v)n(ed)g(the)i (follo)n(wing)f(result.)101 1957 y Fz(Theorem)32 b(7.)40 b Ff(With)31 b(the)e(ab)l(ove)i(notations,)g(let)e Fs(K)6 b Ft(\()p Fs(\026;)14 b(N)9 b Ft(\))23 b(:=)2148 1925 y Fq(1)p 2148 1939 34 4 v 2148 1986 a(4)2205 1957 y Fs(\024)2267 1865 y Fn(\020)2326 1925 y Fo(N)6 b Fk(\000)p Fq(2)p 2326 1939 144 4 v 2350 1950 a Fk(p)p 2405 1950 41 3 v 36 x Fo(\026)2480 1865 y Fn(\021)2529 1957 y Ff(.)39 b(If)30 b Fs(\026)23 b Fr(2)h Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)27 b Fr(\000)18 b Ft(2\))3226 1927 y Fq(2)3263 1957 y Fs(=)p Ft(4\))p Ff(,)29 b(then)529 2182 y 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%527DFFFFA8FF7DFD1CFF537D7DFFFFFF7D7DA8FD0CFFA852A8FD0CFF7D7D %FD04FF7D7DA8FD0CFFA827FD0DFF527DFD04FF52AFFD0CFFA852A8FD20FF %A8FF7D7DFFFFFF7D52A8FD0DFF7D7DFD0DFF52FD04FF7D52FD0DFF52527D %FD0BFF7D5252FFFFFFA87D52A8FD0CFF537DA8FD20FF7D52A8FFA8FFA8A8 %52FD0DFF7D7DFD0CFFA852FFFFA8FFA87D7DFD0DFF27A8FD0CFF7D52FFA8 %7DFF7D7D7DFD0CFF7E52FD20FFA87D52A8FF7DFFA852A8FD0CFF7D7DA8FD %0BFFA87D7DFF84A8FFA852FD0FFFA8FD0DFFA8FFA8FFFFA8A8FD0DFFA8FD %FCFFFD0AFFFF %%EndData %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults %%BeginProlog %%BeginResource: procset Adobe_AGM_Utils 1.0 0 %%Version: 1.0 0 %%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Utils 68 dict dup begin put /bdf { bind def } bind def /nd{ null def }bdf /xdf { exch def }bdf /ldf { load def }bdf /ddf { put }bdf /xddf { 3 -1 roll put }bdf /xpt { exch put }bdf /ndf { exch dup where{ pop pop pop }{ xdf }ifelse }def /cdndf { exch dup currentdict exch known{ pop pop }{ exch def }ifelse }def /bdict { mark }bdf /edict { counttomark 2 idiv dup dict begin {def} repeat pop currentdict end }def /ps_level /languagelevel where{ pop systemdict /languagelevel get exec }{ 1 }ifelse def /level2 ps_level 2 ge def /level3 ps_level 3 ge def /ps_version {version cvr} stopped { -1 }if def /makereadonlyarray { /packedarray where{ pop packedarray }{ array astore readonly }ifelse }bdf /map_reserved_ink_name { dup type /stringtype eq{ dup /Red eq{ pop (_Red_) }{ dup /Green eq{ pop (_Green_) }{ dup /Blue eq{ pop (_Blue_) }{ dup () cvn eq{ pop (Process) }if }ifelse }ifelse }ifelse }if }bdf /AGMUTIL_GSTATE 22 dict def /get_gstate { AGMUTIL_GSTATE begin /AGMUTIL_GSTATE_clr_spc currentcolorspace def /AGMUTIL_GSTATE_clr_indx 0 def /AGMUTIL_GSTATE_clr_comps 12 array def mark currentcolor counttomark {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 3 -1 roll put /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 add def} repeat pop /AGMUTIL_GSTATE_fnt rootfont def /AGMUTIL_GSTATE_lw currentlinewidth def /AGMUTIL_GSTATE_lc currentlinecap def /AGMUTIL_GSTATE_lj currentlinejoin def /AGMUTIL_GSTATE_ml currentmiterlimit def currentdash /AGMUTIL_GSTATE_do xdf /AGMUTIL_GSTATE_da xdf /AGMUTIL_GSTATE_sa currentstrokeadjust def /AGMUTIL_GSTATE_clr_rnd currentcolorrendering def /AGMUTIL_GSTATE_op currentoverprint def /AGMUTIL_GSTATE_bg currentblackgeneration cvlit def /AGMUTIL_GSTATE_ucr currentundercolorremoval cvlit def currentcolortransfer cvlit /AGMUTIL_GSTATE_gy_xfer xdf cvlit / AGMUTIL_GSTATE_b_xfer xdf cvlit /AGMUTIL_GSTATE_g_xfer xdf cvlit /AGMUTIL_GSTATE_r_xfer xdf /AGMUTIL_GSTATE_ht currenthalftone def /AGMUTIL_GSTATE_flt currentflat def end }def /set_gstate { AGMUTIL_GSTATE begin AGMUTIL_GSTATE_clr_spc setcolorspace AGMUTIL_GSTATE_clr_indx {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 1 sub get /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 sub def} repeat setcolor AGMUTIL_GSTATE_fnt setfont AGMUTIL_GSTATE_lw setlinewidth AGMUTIL_GSTATE_lc setlinecap AGMUTIL_GSTATE_lj setlinejoin AGMUTIL_GSTATE_ml setmiterlimit AGMUTIL_GSTATE_da AGMUTIL_GSTATE_do setdash AGMUTIL_GSTATE_sa setstrokeadjust AGMUTIL_GSTATE_clr_rnd setcolorrendering AGMUTIL_GSTATE_op setoverprint AGMUTIL_GSTATE_bg cvx setblackgeneration AGMUTIL_GSTATE_ucr cvx setundercolorremoval AGMUTIL_GSTATE_r_xfer cvx AGMUTIL_GSTATE_g_xfer cvx AGMUTIL_GSTATE_b_xfer cvx AGMUTIL_GSTATE_gy_xfer cvx setcolortransfer AGMUTIL_GSTATE_ht /HalftoneType get dup 9 eq exch 100 eq or { currenthalftone /HalftoneType get AGMUTIL_GSTATE_ht /HalftoneType get ne { mark AGMUTIL_GSTATE_ht {sethalftone} stopped cleartomark } if }{ AGMUTIL_GSTATE_ht sethalftone } ifelse AGMUTIL_GSTATE_flt setflat end }def /get_gstate_and_matrix { AGMUTIL_GSTATE begin /AGMUTIL_GSTATE_ctm matrix currentmatrix def end get_gstate }def /set_gstate_and_matrix { set_gstate AGMUTIL_GSTATE begin AGMUTIL_GSTATE_ctm setmatrix end }def /AGMUTIL_str256 256 string def /AGMUTIL_src256 256 string def /AGMUTIL_dst64 64 string def /AGMUTIL_srcLen nd /AGMUTIL_ndx nd /agm_sethalftone { dup begin /_Data load /Thresholds xdf end level3 { sethalftone }{ dup /HalftoneType get 3 eq { sethalftone } {pop} ifelse }ifelse } def /rdcmntline { currentfile AGMUTIL_str256 readline pop (%) anchorsearch {pop} if } bdf /filter_cmyk { dup type /filetype ne{ exch () /SubFileDecode filter } { exch pop } ifelse [ exch { AGMUTIL_src256 readstring pop dup length /AGMUTIL_srcLen exch def /AGMUTIL_ndx 0 def AGMCORE_plate_ndx 4 AGMUTIL_srcLen 1 sub{ 1 index exch get AGMUTIL_dst64 AGMUTIL_ndx 3 -1 roll put /AGMUTIL_ndx AGMUTIL_ndx 1 add def }for pop AGMUTIL_dst64 0 AGMUTIL_ndx getinterval } bind /exec cvx ] cvx } bdf /filter_indexed_devn { cvi Names length mul names_index add Lookup exch get } bdf /filter_devn { 4 dict begin /srcStr xdf /dstStr xdf dup type /filetype ne{ 0 () /SubFileDecode filter }if [ exch [ /devicen_colorspace_dict /AGMCORE_gget cvx /begin cvx currentdict /srcStr get /readstring cvx /pop cvx /dup cvx /length cvx 0 /gt cvx [ Adobe_AGM_Utils /AGMUTIL_ndx 0 /ddf cvx names_index Names length currentdict /srcStr get length 1 sub { 1 /index cvx /exch cvx /get cvx currentdict /dstStr get /AGMUTIL_ndx /load cvx 3 -1 /roll cvx / put cvx Adobe_AGM_Utils /AGMUTIL_ndx /AGMUTIL_ndx /load cvx 1 /add cvx / ddf cvx } for currentdict /dstStr get 0 /AGMUTIL_ndx /load cvx /getinterval cvx ] cvx /if cvx /end cvx ] cvx bind /exec cvx ] cvx end } bdf /AGMUTIL_imagefile nd /read_image_file { AGMUTIL_imagefile 0 setfileposition 10 dict begin /imageDict xdf /imbufLen Width BitsPerComponent mul 7 add 8 idiv def /imbufIdx 0 def /origDataSource imageDict /DataSource get def /origMultipleDataSources imageDict /MultipleDataSources get def /origDecode imageDict /Decode get def /dstDataStr imageDict /Width get colorSpaceElemCnt mul string def /srcDataStrs [ imageDict begin currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse { Width Decode length 2 div mul cvi string } repeat end ] def imageDict /MultipleDataSources known {MultipleDataSources}{false} ifelse { /imbufCnt imageDict /DataSource get length def /imbufs imbufCnt array def 0 1 imbufCnt 1 sub { /imbufIdx xdf imbufs imbufIdx imbufLen string put imageDict /DataSource get imbufIdx [ AGMUTIL_imagefile imbufs imbufIdx get /readstring cvx /pop cvx ] cvx put } for DeviceN_PS2 { imageDict begin /DataSource [ DataSource /devn_sep_datasource cvx ] cvx def /MultipleDataSources false def /Decode [0 1] def end } if }{ /imbuf imbufLen string def Indexed_DeviceN level3 not and DeviceN_NoneName or { imageDict begin /DataSource [AGMUTIL_imagefile Decode BitsPerComponent false 1 / filter_indexed_devn load dstDataStr srcDataStrs devn_alt_datasource / exec cvx] cvx def /Decode [0 1] def end }{ imageDict /DataSource {AGMUTIL_imagefile imbuf readstring pop} put } ifelse } ifelse imageDict exch load exec imageDict /DataSource origDataSource put imageDict /MultipleDataSources origMultipleDataSources put imageDict /Decode origDecode put end } bdf /write_image_file { begin { (AGMUTIL_imagefile) (w+) file } stopped{ false }{ Adobe_AGM_Utils/AGMUTIL_imagefile xddf 2 dict begin /imbufLen Width BitsPerComponent mul 7 add 8 idiv def MultipleDataSources {DataSource 0 get}{DataSource}ifelse type / filetype eq { /imbuf imbufLen string def }if 1 1 Height { pop MultipleDataSources { 0 1 DataSource length 1 sub { DataSource type dup /arraytype eq { pop DataSource exch get exec }{ /filetype eq { DataSource exch get imbuf readstring pop }{ DataSource exch get } ifelse } ifelse AGMUTIL_imagefile exch writestring } for }{ DataSource type dup /arraytype eq { pop DataSource exec }{ /filetype eq { DataSource imbuf readstring pop }{ DataSource } ifelse } ifelse AGMUTIL_imagefile exch writestring } ifelse }for end true }ifelse end } bdf /close_image_file { AGMUTIL_imagefile closefile (AGMUTIL_imagefile) deletefile }def statusdict /product known userdict /AGMP_current_show known not and{ /pstr statusdict /product get def pstr (HP LaserJet 2200) eq pstr (HP LaserJet 4000 Series) eq or pstr (HP LaserJet 4050 Series ) eq or pstr (HP LaserJet 8000 Series) eq or pstr (HP LaserJet 8100 Series) eq or pstr (HP LaserJet 8150 Series) eq or pstr (HP LaserJet 5000 Series) eq or pstr (HP LaserJet 5100 Series) eq or pstr (HP Color LaserJet 4500) eq or pstr (HP Color LaserJet 4600) eq or pstr (HP LaserJet 5Si) eq or pstr (HP LaserJet 1200 Series) eq or pstr (HP LaserJet 1300 Series) eq or pstr (HP LaserJet 4100 Series) eq or { userdict /AGMP_current_show /show load put userdict /show { currentcolorspace 0 get /Pattern eq {false charpath f} {AGMP_current_show} ifelse } put }if currentdict /pstr undef } if /consumeimagedata { begin currentdict /MultipleDataSources known not {/MultipleDataSources false def} if MultipleDataSources { 1 dict begin /flushbuffer Width cvi string def 1 1 Height cvi { pop 0 1 DataSource length 1 sub { DataSource exch get dup type dup /filetype eq { exch flushbuffer readstring pop pop }if /arraytype eq { exec pop }if }for }for end } { /DataSource load type dup /filetype eq { 1 dict begin /flushbuffer Width Decode length 2 div mul cvi string def 1 1 Height { pop DataSource flushbuffer readstring pop pop} for end }if /arraytype eq { 1 1 Height { pop DataSource pop } for }if }ifelse end }bdf /addprocs { 2{/exec load}repeat 3 1 roll [ 5 1 roll ] bind cvx }def /modify_halftone_xfer { currenthalftone dup length dict copy begin currentdict 2 index known{ 1 index load dup length dict copy begin currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end def currentdict end sethalftone }{ currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end sethalftone pop }ifelse }def /clonearray { dup xcheck exch dup length array exch Adobe_AGM_Core/AGMCORE_tmp -1 ddf { Adobe_AGM_Core/AGMCORE_tmp AGMCORE_tmp 1 add ddf dup type /dicttype eq { AGMCORE_tmp exch clonedict Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf } if dup type /arraytype eq { AGMCORE_tmp exch clonearray Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf } if exch dup AGMCORE_tmp 4 -1 roll put }forall exch {cvx} if }bdf /clonedict { dup length dict begin { dup type /dicttype eq { clonedict } if dup type /arraytype eq { clonearray } if def }forall currentdict end }bdf /DeviceN_PS2 { /currentcolorspace AGMCORE_gget 0 get /DeviceN eq level3 not and } bdf /Indexed_DeviceN { /indexed_colorspace_dict AGMCORE_gget dup null ne { /CSD known }{ pop false } ifelse } bdf /DeviceN_NoneName { /Names where { pop false Names { (None) eq or } forall }{ false }ifelse } bdf /DeviceN_PS2_inRip_seps { /AGMCORE_in_rip_sep where { pop dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get /DeviceN eq level3 not and AGMCORE_in_rip_sep and { /currentcolorspace exch AGMCORE_gput false } { true }ifelse } { true } ifelse } { true } ifelse } bdf /base_colorspace_type { dup type /arraytype eq {0 get} if } bdf /doc_setup{ Adobe_AGM_Utils begin }bdf /doc_trailer{ currentdict Adobe_AGM_Utils eq{ end }if }bdf systemdict /setpacking known { setpacking } if %%EndResource %%BeginResource: procset Adobe_AGM_Core 2.0 0 %%Version: 2.0 0 %%Copyright: Copyright (C) 1997-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Core 216 dict dup begin put /nd{ null def }bind def /Adobe_AGM_Core_Id /Adobe_AGM_Core_2.0_0 def /AGMCORE_str256 256 string def /AGMCORE_save nd /AGMCORE_graphicsave nd /AGMCORE_c 0 def /AGMCORE_m 0 def /AGMCORE_y 0 def /AGMCORE_k 0 def /AGMCORE_cmykbuf 4 array def /AGMCORE_screen [currentscreen] cvx def /AGMCORE_tmp 0 def /AGMCORE_&setgray nd /AGMCORE_&setcolor nd /AGMCORE_&setcolorspace nd /AGMCORE_&setcmykcolor nd /AGMCORE_cyan_plate nd /AGMCORE_magenta_plate nd /AGMCORE_yellow_plate nd /AGMCORE_black_plate nd /AGMCORE_plate_ndx nd /AGMCORE_get_ink_data nd /AGMCORE_is_cmyk_sep nd /AGMCORE_host_sep nd /AGMCORE_avoid_L2_sep_space nd /AGMCORE_distilling nd /AGMCORE_composite_job nd /AGMCORE_producing_seps nd /AGMCORE_ps_level -1 def /AGMCORE_ps_version -1 def /AGMCORE_environ_ok nd /AGMCORE_CSA_cache 0 dict def /AGMCORE_CSD_cache 0 dict def /AGMCORE_pattern_cache 0 dict def /AGMCORE_currentoverprint false def /AGMCORE_deltaX nd /AGMCORE_deltaY nd /AGMCORE_name nd /AGMCORE_sep_special nd /AGMCORE_err_strings 4 dict def /AGMCORE_cur_err nd /AGMCORE_ovp nd /AGMCORE_current_spot_alias false def /AGMCORE_inverting false def /AGMCORE_feature_dictCount nd /AGMCORE_feature_opCount nd /AGMCORE_feature_ctm nd /AGMCORE_ConvertToProcess false def /AGMCORE_Default_CTM matrix def /AGMCORE_Default_PageSize nd /AGMCORE_currentbg nd /AGMCORE_currentucr nd /AGMCORE_gradientcache 32 dict def /AGMCORE_in_pattern false def /knockout_unitsq nd /AGMCORE_CRD_cache where{ pop }{ /AGMCORE_CRD_cache 0 dict def }ifelse /AGMCORE_key_known { where{ /Adobe_AGM_Core_Id known }{ false }ifelse }ndf /flushinput { save 2 dict begin /CompareBuffer 3 -1 roll def /readbuffer 256 string def mark { currentfile readbuffer {readline} stopped {cleartomark mark} { not {pop exit} if CompareBuffer eq {exit} if }ifelse }loop cleartomark end restore }bdf /getspotfunction { AGMCORE_screen exch pop exch pop dup type /dicttype eq{ dup /HalftoneType get 1 eq{ /SpotFunction get }{ dup /HalftoneType get 2 eq{ /GraySpotFunction get }{ pop { abs exch abs 2 copy add 1 gt{ 1 sub dup mul exch 1 sub dup mul add 1 sub }{ dup mul exch dup mul add 1 exch sub }ifelse }bind }ifelse }ifelse }if } def /clp_npth { clip newpath } def /eoclp_npth { eoclip newpath } def /npth_clp { newpath clip } def /add_grad { AGMCORE_gradientcache 3 1 roll put }bdf /exec_grad { AGMCORE_gradientcache exch get exec }bdf /graphic_setup { /AGMCORE_graphicsave save def concat 0 setgray 0 setlinecap 0 setlinejoin 1 setlinewidth [] 0 setdash 10 setmiterlimit newpath false setoverprint false setstrokeadjust Adobe_AGM_Core/spot_alias get exec /Adobe_AGM_Image where { pop Adobe_AGM_Image/spot_alias 2 copy known{ get exec }{ pop pop }ifelse } if 100 dict begin /dictstackcount countdictstack def /showpage {} def mark } def /graphic_cleanup { cleartomark dictstackcount 1 countdictstack 1 sub {end}for end AGMCORE_graphicsave restore } def /compose_error_msg { grestoreall initgraphics /Helvetica findfont 10 scalefont setfont /AGMCORE_deltaY 100 def /AGMCORE_deltaX 310 def clippath pathbbox newpath pop pop 36 add exch 36 add exch moveto 0 AGMCORE_deltaY rlineto AGMCORE_deltaX 0 rlineto 0 AGMCORE_deltaY neg rlineto AGMCORE_deltaX neg 0 rlineto closepath 0 AGMCORE_&setgray gsave 1 AGMCORE_&setgray fill grestore 1 setlinewidth gsave stroke grestore currentpoint AGMCORE_deltaY 15 sub add exch 8 add exch moveto /AGMCORE_deltaY 12 def /AGMCORE_tmp 0 def AGMCORE_err_strings exch get { dup 32 eq { pop AGMCORE_str256 0 AGMCORE_tmp getinterval stringwidth pop currentpoint pop add AGMCORE_deltaX 28 add gt { currentpoint AGMCORE_deltaY sub exch pop clippath pathbbox pop pop pop 44 add exch moveto } if AGMCORE_str256 0 AGMCORE_tmp getinterval show ( ) show 0 1 AGMCORE_str256 length 1 sub { AGMCORE_str256 exch 0 put }for /AGMCORE_tmp 0 def } { AGMCORE_str256 exch AGMCORE_tmp xpt /AGMCORE_tmp AGMCORE_tmp 1 add def } ifelse } forall } bdf /doc_setup{ Adobe_AGM_Core begin /AGMCORE_ps_version xdf /AGMCORE_ps_level xdf errordict /AGM_handleerror known not{ errordict /AGM_handleerror errordict /handleerror get put errordict /handleerror { Adobe_AGM_Core begin $error /newerror get AGMCORE_cur_err null ne and{ $error /newerror false put AGMCORE_cur_err compose_error_msg }if $error /newerror true put end errordict /AGM_handleerror get exec } bind put }if /AGMCORE_environ_ok ps_level AGMCORE_ps_level ge ps_version AGMCORE_ps_version ge and AGMCORE_ps_level -1 eq or def AGMCORE_environ_ok not {/AGMCORE_cur_err /AGMCORE_bad_environ def} if /AGMCORE_&setgray systemdict/setgray get def level2{ /AGMCORE_&setcolor systemdict/setcolor get def /AGMCORE_&setcolorspace systemdict/setcolorspace get def }if /AGMCORE_currentbg currentblackgeneration def /AGMCORE_currentucr currentundercolorremoval def /AGMCORE_distilling /product where{ pop systemdict/setdistillerparams known product (Adobe PostScript Parser) ne and }{ false }ifelse def level2 not{ /xput{ dup load dup length exch maxlength eq{ dup dup load dup length dup 0 eq {pop 1} if 2 mul dict copy def }if load begin def end }def }{ /xput{ load 3 1 roll put }def }ifelse /AGMCORE_GSTATE AGMCORE_key_known not{ /AGMCORE_GSTATE 21 dict def /AGMCORE_tmpmatrix matrix def /AGMCORE_gstack 32 array def /AGMCORE_gstackptr 0 def /AGMCORE_gstacksaveptr 0 def /AGMCORE_gstackframekeys 10 def /AGMCORE_&gsave /gsave ldf /AGMCORE_&grestore /grestore ldf /AGMCORE_&grestoreall /grestoreall ldf /AGMCORE_&save /save ldf /AGMCORE_gdictcopy { begin { def } forall end }def /AGMCORE_gput { AGMCORE_gstack AGMCORE_gstackptr get 3 1 roll put }def /AGMCORE_gget { AGMCORE_gstack AGMCORE_gstackptr get exch get }def /gsave { AGMCORE_&gsave AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core exch /AGMCORE_gstackptr xpt AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def /grestore { AGMCORE_&grestore AGMCORE_gstackptr 1 sub dup AGMCORE_gstacksaveptr lt {1 add} if Adobe_AGM_Core exch /AGMCORE_gstackptr xpt }def /grestoreall { AGMCORE_&grestoreall Adobe_AGM_Core /AGMCORE_gstackptr AGMCORE_gstacksaveptr put }def /save { AGMCORE_&save AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core begin /AGMCORE_gstackptr exch def /AGMCORE_gstacksaveptr AGMCORE_gstackptr def end AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def 0 1 AGMCORE_gstack length 1 sub { AGMCORE_gstack exch AGMCORE_gstackframekeys dict put } for }if level3 /AGMCORE_&sysshfill AGMCORE_key_known not and { /AGMCORE_&sysshfill systemdict/shfill get def /AGMCORE_&usrshfill /shfill load def /AGMCORE_&sysmakepattern systemdict/makepattern get def /AGMCORE_&usrmakepattern /makepattern load def }if /currentcmykcolor [0 0 0 0] AGMCORE_gput /currentstrokeadjust false AGMCORE_gput /currentcolorspace [/DeviceGray] AGMCORE_gput /sep_tint 0 AGMCORE_gput /devicen_tints [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] AGMCORE_gput /sep_colorspace_dict null AGMCORE_gput /devicen_colorspace_dict null AGMCORE_gput /indexed_colorspace_dict null AGMCORE_gput /currentcolor_intent () AGMCORE_gput /customcolor_tint 1 AGMCORE_gput << /MaxPatternItem currentsystemparams /MaxPatternCache get >> setuserparams end }def /page_setup { /setcmykcolor where{ pop Adobe_AGM_Core/AGMCORE_&setcmykcolor /setcmykcolor load put }if Adobe_AGM_Core begin /setcmykcolor { 4 copy AGMCORE_cmykbuf astore /currentcmykcolor exch AGMCORE_gput 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor pop }ndf /currentcmykcolor { /currentcmykcolor AGMCORE_gget aload pop }ndf /setoverprint { pop }ndf /currentoverprint { false }ndf /AGMCORE_deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt def /AGMCORE_cyan_plate 1 0 0 0 test_cmyk_color_plate def /AGMCORE_magenta_plate 0 1 0 0 test_cmyk_color_plate def /AGMCORE_yellow_plate 0 0 1 0 test_cmyk_color_plate def /AGMCORE_black_plate 0 0 0 1 test_cmyk_color_plate def /AGMCORE_plate_ndx AGMCORE_cyan_plate{ 0 }{ AGMCORE_magenta_plate{ 1 }{ AGMCORE_yellow_plate{ 2 }{ AGMCORE_black_plate{ 3 }{ 4 }ifelse }ifelse }ifelse }ifelse def /AGMCORE_have_reported_unsupported_color_space false def /AGMCORE_report_unsupported_color_space { AGMCORE_have_reported_unsupported_color_space false eq { (Warning: Job contains content that cannot be separated with on- host methods. This content appears on the black plate, and knocks out all other plates.) == Adobe_AGM_Core /AGMCORE_have_reported_unsupported_color_space true ddf } if }def /AGMCORE_composite_job AGMCORE_cyan_plate AGMCORE_magenta_plate and AGMCORE_yellow_plate and AGMCORE_black_plate and def /AGMCORE_in_rip_sep /AGMCORE_in_rip_sep where{ pop AGMCORE_in_rip_sep }{ AGMCORE_distilling { false }{ userdict/Adobe_AGM_OnHost_Seps known{ false }{ level2{ currentpagedevice/Separations 2 copy known{ get }{ pop pop false }ifelse }{ false }ifelse }ifelse }ifelse }ifelse def /AGMCORE_producing_seps AGMCORE_composite_job not AGMCORE_in_rip_sep or def /AGMCORE_host_sep AGMCORE_producing_seps AGMCORE_in_rip_sep not and def /AGM_preserve_spots /AGM_preserve_spots where{ pop AGM_preserve_spots }{ AGMCORE_distilling AGMCORE_producing_seps or }ifelse def /AGM_is_distiller_preserving_spotimages { currentdistillerparams/PreserveOverprintSettings known { currentdistillerparams/PreserveOverprintSettings get { currentdistillerparams/ColorConversionStrategy known { currentdistillerparams/ColorConversionStrategy get /LeaveColorUnchanged eq }{ true }ifelse }{ false }ifelse }{ false }ifelse }def /convert_spot_to_process where {pop}{ /convert_spot_to_process { dup map_alias { /Name get exch pop } if dup dup (None) eq exch (All) eq or { pop false }{ AGMCORE_host_sep { gsave 1 0 0 0 setcmykcolor currentgray 1 exch sub 0 1 0 0 setcmykcolor currentgray 1 exch sub 0 0 1 0 setcmykcolor currentgray 1 exch sub 0 0 0 1 setcmykcolor currentgray 1 exch sub add add add 0 eq { pop false }{ false setoverprint 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq }ifelse grestore }{ AGMCORE_distilling { pop AGM_is_distiller_preserving_spotimages not }{ Adobe_AGM_Core/AGMCORE_name xddf false Adobe_AGM_Core/AGMCORE_in_pattern known {Adobe_AGM_Core/ AGMCORE_in_pattern get}{false} ifelse not currentpagedevice/OverrideSeparations known and { currentpagedevice/OverrideSeparations get { /HqnSpots /ProcSet resourcestatus { pop pop pop true }if }if }if { AGMCORE_name /HqnSpots /ProcSet findresource /TestSpot get exec not }{ gsave [/Separation AGMCORE_name /DeviceGray {}]setcolorspace false currentpagedevice/SeparationColorNames 2 copy known { get { AGMCORE_name eq or}forall not }{ pop pop pop true }ifelse grestore }ifelse }ifelse }ifelse }ifelse }def }ifelse /convert_to_process where {pop}{ /convert_to_process { dup length 0 eq { pop false }{ AGMCORE_host_sep { dup true exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch dup (Black) eq 3 -1 roll or {pop} {convert_spot_to_process and}ifelse } forall { true exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch (Black) eq or and }forall not }{pop false}ifelse }{ false exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch dup (Black) eq 3 -1 roll or {pop} {convert_spot_to_process or}ifelse } forall }ifelse }ifelse }def }ifelse /AGMCORE_avoid_L2_sep_space version cvr 2012 lt level2 and AGMCORE_producing_seps not and def /AGMCORE_is_cmyk_sep AGMCORE_cyan_plate AGMCORE_magenta_plate or AGMCORE_yellow_plate or AGMCORE_black_plate or def /AGM_avoid_0_cmyk where{ pop AGM_avoid_0_cmyk }{ AGM_preserve_spots userdict/Adobe_AGM_OnHost_Seps known userdict/Adobe_AGM_InRip_Seps known or not and }ifelse { /setcmykcolor[ { 4 copy add add add 0 eq currentoverprint and{ pop 0.0005 }if }/exec cvx /AGMCORE_&setcmykcolor load dup type/operatortype ne{ /exec cvx }if ]cvx def }if AGMCORE_host_sep{ /setcolortransfer { AGMCORE_cyan_plate{ pop pop pop }{ AGMCORE_magenta_plate{ 4 3 roll pop pop pop }{ AGMCORE_yellow_plate{ 4 2 roll pop pop pop }{ 4 1 roll pop pop pop }ifelse }ifelse }ifelse settransfer } def /AGMCORE_get_ink_data AGMCORE_cyan_plate{ {pop pop pop} }{ AGMCORE_magenta_plate{ {4 3 roll pop pop pop} }{ AGMCORE_yellow_plate{ {4 2 roll pop pop pop} }{ {4 1 roll pop pop pop} }ifelse }ifelse }ifelse def /AGMCORE_RemoveProcessColorNames { 1 dict begin /filtername { dup /Cyan eq 1 index (Cyan) eq or {pop (_cyan_)}if dup /Magenta eq 1 index (Magenta) eq or {pop (_magenta_)}if dup /Yellow eq 1 index (Yellow) eq or {pop (_yellow_)}if dup /Black eq 1 index (Black) eq or {pop (_black_)}if }def dup type /arraytype eq {[exch {filtername}forall]} {filtername}ifelse end }def /AGMCORE_IsSeparationAProcessColor { dup (Cyan) eq exch dup (Magenta) eq exch dup (Yellow) eq exch (Black) eq or or or }def level3 { /AGMCORE_IsCurrentColor { gsave false setoverprint 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq grestore }def /AGMCORE_filter_functiondatasource { 5 dict begin /data_in xdf data_in type /stringtype eq { /ncomp xdf /comp xdf /string_out data_in length ncomp idiv string def 0 ncomp data_in length 1 sub { string_out exch dup ncomp idiv exch data_in exch ncomp getinterval comp get 255 exch sub put }for string_out }{ string /string_in xdf /string_out 1 string def /component xdf [ data_in string_in /readstring cvx [component /get cvx 255 /exch cvx /sub cvx string_out /exch cvx 0 /exch cvx /put cvx string_out]cvx [/pop cvx ()]cvx /ifelse cvx ]cvx /ReusableStreamDecode filter }ifelse end }def /AGMCORE_separateShadingFunction { 2 dict begin /paint? xdf /channel xdf begin FunctionType 0 eq { /DataSource channel Range length 2 idiv DataSource AGMCORE_filter_functiondatasource def currentdict /Decode known {/Decode Decode channel 2 mul 2 getinterval def}if paint? not {/Decode [1 1]def}if }if FunctionType 2 eq { paint? { /C0 [C0 channel get 1 exch sub] def /C1 [C1 channel get 1 exch sub] def }{ /C0 [1] def /C1 [1] def }ifelse }if FunctionType 3 eq { /Functions [Functions {channel paint? AGMCORE_separateShadingFunction} forall] def }if currentdict /Range known {/Range [0 1] def}if currentdict end end }def /AGMCORE_separateShading { 3 -1 roll begin currentdict /Function known { currentdict /Background known {[1 index{Background 3 index get 1 exch sub}{1}ifelse]/ Background xdf}if Function 3 1 roll AGMCORE_separateShadingFunction /Function xdf /ColorSpace [/DeviceGray] def }{ ColorSpace dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ /_black_] / DeviceCMYK {}] def }{ ColorSpace dup 1 get AGMCORE_RemoveProcessColorNames 1 exch put }ifelse ColorSpace 0 get /Separation eq { { [1 /exch cvx /sub cvx]cvx }{ [/pop cvx 1]cvx }ifelse ColorSpace 3 3 -1 roll put pop }{ { [exch ColorSpace 1 get length 1 sub exch sub /index cvx 1 / exch cvx /sub cvx ColorSpace 1 get length 1 add 1 /roll cvx ColorSpace 1 get length{/pop cvx} repeat]cvx }{ pop [ColorSpace 1 get length {/pop cvx} repeat cvx 1]cvx }ifelse ColorSpace 3 3 -1 roll bind put }ifelse ColorSpace 2 /DeviceGray put }ifelse end }def /AGMCORE_separateShadingDict { dup /ColorSpace get dup type /arraytype ne {[exch]}if dup 0 get /DeviceCMYK eq { exch begin currentdict AGMCORE_cyan_plate {0 true}if AGMCORE_magenta_plate {1 true}if AGMCORE_yellow_plate {2 true}if AGMCORE_black_plate {3 true}if AGMCORE_plate_ndx 4 eq {0 false}if dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading currentdict end exch }if dup 0 get /Separation eq { exch begin ColorSpace 1 get dup /None ne exch /All ne and { ColorSpace 1 get AGMCORE_IsCurrentColor AGMCORE_plate_ndx 4 lt and ColorSpace 1 get AGMCORE_IsSeparationAProcessColor not and { ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [ /Separation ColorSpace 1 get /DeviceGray [ ColorSpace 3 get /exec cvx 4 AGMCORE_plate_ndx sub -1 /roll cvx 4 1 /roll cvx 3 [/pop cvx]cvx /repeat cvx 1 /exch cvx /sub cvx ]cvx ]def }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { currentdict 0 false AGMCORE_separateShading }if }ifelse }{ currentdict ColorSpace 1 get AGMCORE_IsCurrentColor 0 exch dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading }ifelse }if currentdict end exch }if dup 0 get /DeviceN eq { exch begin ColorSpace 1 get convert_to_process { ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [ /DeviceN ColorSpace 1 get /DeviceGray [ ColorSpace 3 get /exec cvx 4 AGMCORE_plate_ndx sub -1 /roll cvx 4 1 /roll cvx 3 [/pop cvx]cvx /repeat cvx 1 /exch cvx /sub cvx ]cvx ]def }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { currentdict 0 false AGMCORE_separateShading /ColorSpace [/DeviceGray] def }if }ifelse }{ currentdict false -1 ColorSpace 1 get { AGMCORE_IsCurrentColor { 1 add exch pop true exch exit }if 1 add }forall exch dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading }ifelse currentdict end exch }if dup 0 get dup /DeviceCMYK eq exch dup /Separation eq exch / DeviceN eq or or not { exch begin ColorSpace dup type /arraytype eq {0 get}if /DeviceGray ne { AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { ColorSpace 0 get /CIEBasedA eq { /ColorSpace [/Separation /_ciebaseda_ /DeviceGray {}] def }if ColorSpace 0 get dup /CIEBasedABC eq exch dup /CIEBasedDEF eq exch /DeviceRGB eq or or { /ColorSpace [/DeviceN [/_red_ /_green_ /_blue_] /DeviceRGB {}] def }if ColorSpace 0 get /CIEBasedDEFG eq { /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ / _black_] /DeviceCMYK {}] }if currentdict 0 false AGMCORE_separateShading }if }if currentdict end exch }if pop dup /AGMCORE_ignoreshade known { begin /ColorSpace [/Separation (None) /DeviceGray {}] def currentdict end }if }def /shfill { clonedict AGMCORE_separateShadingDict dup /AGMCORE_ignoreshade known {pop} {AGMCORE_&sysshfill}ifelse }def /makepattern { exch dup /PatternType get 2 eq { clonedict begin /Shading Shading AGMCORE_separateShadingDict def currentdict end exch AGMCORE_&sysmakepattern }{ exch AGMCORE_&usrmakepattern }ifelse }def }if }if AGMCORE_in_rip_sep{ /setcustomcolor { exch aload pop dup 7 1 roll inRip_spot_has_ink not { 4 {4 index mul 4 1 roll} repeat /DeviceCMYK setcolorspace 6 -2 roll pop pop }{ Adobe_AGM_Core begin /AGMCORE_k xdf /AGMCORE_y xdf /AGMCORE_m xdf /AGMCORE_c xdf end [/Separation 4 -1 roll /DeviceCMYK {dup AGMCORE_c mul exch dup AGMCORE_m mul exch dup AGMCORE_y mul exch AGMCORE_k mul} ] setcolorspace }ifelse setcolor }ndf /setseparationgray { [/Separation (All) /DeviceGray {}] setcolorspace_opt 1 exch sub setcolor }ndf }{ /setseparationgray { AGMCORE_&setgray }ndf }ifelse /findcmykcustomcolor { 5 makereadonlyarray }ndf /setcustomcolor { exch aload pop pop 4 {4 index mul 4 1 roll} repeat setcmykcolor pop }ndf /has_color /colorimage where{ AGMCORE_producing_seps{ pop true }{ systemdict eq }ifelse }{ false }ifelse def /map_index { 1 index mul exch getinterval {255 div} forall } bdf /map_indexed_devn { Lookup Names length 3 -1 roll cvi map_index } bdf /n_color_components { base_colorspace_type dup /DeviceGray eq{ pop 1 }{ /DeviceCMYK eq{ 4 }{ 3 }ifelse }ifelse }bdf level2{ /mo /moveto ldf /li /lineto ldf /cv /curveto ldf /knockout_unitsq { 1 setgray 0 0 1 1 rectfill }def /level2ScreenFreq{ begin 60 HalftoneType 1 eq{ pop Frequency }if HalftoneType 2 eq{ pop GrayFrequency }if HalftoneType 5 eq{ pop Default level2ScreenFreq }if end }def /currentScreenFreq{ currenthalftone level2ScreenFreq }def level2 /setcolorspace AGMCORE_key_known not and{ /AGMCORE_&&&setcolorspace /setcolorspace ldf /AGMCORE_ReplaceMappedColor { dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get dup /Separation eq { pop dup length array copy dup dup 1 get current_spot_alias { dup map_alias { begin /sep_colorspace_dict currentdict AGMCORE_gput pop pop pop [ /Separation Name CSA map_csa dup /MappedCSA xdf /sep_colorspace_proc load ] dup Name end }if }if map_reserved_ink_name 1 xpt }{ /DeviceN eq { dup length array copy dup dup 1 get [ exch { current_spot_alias{ dup map_alias{ /Name get exch pop }if }if map_reserved_ink_name } forall ] 1 xpt }if }ifelse }if }def /setcolorspace { dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get /Indexed eq { AGMCORE_distilling { /PhotoshopDuotoneList where { pop false }{ true }ifelse }{ true }ifelse { aload pop 3 -1 roll AGMCORE_ReplaceMappedColor 3 1 roll 4 array astore }if }{ AGMCORE_ReplaceMappedColor }ifelse }if DeviceN_PS2_inRip_seps {AGMCORE_&&&setcolorspace} if }def }if }{ /adj { currentstrokeadjust{ transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform }if }def /mo{ adj moveto }def /li{ adj lineto }def /cv{ 6 2 roll adj 6 2 roll adj 6 2 roll adj curveto }def /knockout_unitsq { 1 setgray 8 8 1 [8 0 0 8 0 0] {} image }def /currentstrokeadjust{ /currentstrokeadjust AGMCORE_gget }def /setstrokeadjust{ /currentstrokeadjust exch AGMCORE_gput }def /currentScreenFreq{ currentscreen pop pop }def /setcolorspace { /currentcolorspace exch AGMCORE_gput } def /currentcolorspace { /currentcolorspace AGMCORE_gget } def /setcolor_devicecolor { base_colorspace_type dup /DeviceGray eq{ pop setgray }{ /DeviceCMYK eq{ setcmykcolor }{ setrgbcolor }ifelse }ifelse }def /setcolor { currentcolorspace 0 get dup /DeviceGray ne{ dup /DeviceCMYK ne{ dup /DeviceRGB ne{ dup /Separation eq{ pop currentcolorspace 3 get exec currentcolorspace 2 get }{ dup /Indexed eq{ pop currentcolorspace 3 get dup type /stringtype eq{ currentcolorspace 1 get n_color_components 3 -1 roll map_index }{ exec }ifelse currentcolorspace 1 get }{ /AGMCORE_cur_err /AGMCORE_invalid_color_space def AGMCORE_invalid_color_space }ifelse }ifelse }if }if }if setcolor_devicecolor } def }ifelse /sop /setoverprint ldf /lw /setlinewidth ldf /lc /setlinecap ldf /lj /setlinejoin ldf /ml /setmiterlimit ldf /dsh /setdash ldf /sadj /setstrokeadjust ldf /gry /setgray ldf /rgb /setrgbcolor ldf /cmyk /setcmykcolor ldf /sep /setsepcolor ldf /devn /setdevicencolor ldf /idx /setindexedcolor ldf /colr /setcolor ldf /csacrd /set_csa_crd ldf /sepcs /setsepcolorspace ldf /devncs /setdevicencolorspace ldf /idxcs /setindexedcolorspace ldf /cp /closepath ldf /clp /clp_npth ldf /eclp /eoclp_npth ldf /f /fill ldf /ef /eofill ldf /@ /stroke ldf /nclp /npth_clp ldf /gset /graphic_setup ldf /gcln /graphic_cleanup ldf currentdict{ dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and { bind }if def }forall /currentpagedevice currentpagedevice def /getrampcolor { /indx exch def 0 1 NumComp 1 sub { dup Samples exch get dup type /stringtype eq { indx get } if exch Scaling exch get aload pop 3 1 roll mul add } for ColorSpaceFamily /Separation eq { sep } { ColorSpaceFamily /DeviceN eq { devn } { setcolor }ifelse }ifelse } bind def /sssetbackground { aload pop setcolor } bind def /RadialShade { 40 dict begin /ColorSpaceFamily exch def /background exch def /ext1 exch def /ext0 exch def /BBox exch def /r2 exch def /c2y exch def /c2x exch def /r1 exch def /c1y exch def /c1x exch def /rampdict exch def /setinkoverprint where {pop /setinkoverprint{pop}def}if gsave BBox length 0 gt { newpath BBox 0 get BBox 1 get moveto BBox 2 get BBox 0 get sub 0 rlineto 0 BBox 3 get BBox 1 get sub rlineto BBox 2 get BBox 0 get sub neg 0 rlineto closepath clip newpath } if c1x c2x eq { c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse } { /slope c2y c1y sub c2x c1x sub div def /theta slope 1 atan def c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if } ifelse gsave clippath c1x c1y translate theta rotate -90 rotate { pathbbox } stopped { 0 0 0 0 } if /yMax exch def /xMax exch def /yMin exch def /xMin exch def grestore xMax xMin eq yMax yMin eq or { grestore end } { /max { 2 copy gt { pop } {exch pop} ifelse } bind def /min { 2 copy lt { pop } {exch pop} ifelse } bind def rampdict begin 40 dict begin background length 0 gt { background sssetbackground gsave clippath fill grestore } if gsave c1x c1y translate theta rotate -90 rotate /c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def /c1y 0 def /c1x 0 def /c2x 0 def ext0 { 0 getrampcolor c2y r2 add r1 sub 0.0001 lt { c1x c1y r1 360 0 arcn pathbbox /aymax exch def /axmax exch def /aymin exch def /axmin exch def /bxMin xMin axmin min def /byMin yMin aymin min def /bxMax xMax axmax max def /byMax yMax aymax max def bxMin byMin moveto bxMax byMin lineto bxMax byMax lineto bxMin byMax lineto bxMin byMin lineto eofill } { c2y r1 add r2 le { c1x c1y r1 0 360 arc fill } { c2x c2y r2 0 360 arc fill r1 r2 eq { /p1x r1 neg def /p1y c1y def /p2x r1 def /p2y c1y def p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto fill } { /AA r2 r1 sub c2y div def /theta AA 1 AA dup mul sub sqrt div 1 atan def /SS1 90 theta add dup sin exch cos div def /p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def /p1y p1x SS1 div neg def /SS2 90 theta sub dup sin exch cos div def /p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def /p2y p2x SS2 div neg def r1 r2 gt { /L1maxX p1x yMin p1y sub SS1 div add def /L2maxX p2x yMin p2y sub SS2 div add def } { /L1maxX 0 def /L2maxX 0 def }ifelse p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto L1maxX L1maxX p1x sub SS1 mul p1y add lineto fill } ifelse } ifelse } ifelse } if c1x c2x sub dup mul c1y c2y sub dup mul add 0.5 exp 0 dtransform dup mul exch dup mul add 0.5 exp 72 div 0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 1 index 1 index lt { exch } if pop /hires exch def hires mul /numpix exch def /numsteps NumSamples def /rampIndxInc 1 def /subsampling false def numpix 0 ne { NumSamples numpix div 0.5 gt { /numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def /rampIndxInc NumSamples 1 sub numsteps div def /subsampling true def } if } if /xInc c2x c1x sub numsteps div def /yInc c2y c1y sub numsteps div def /rInc r2 r1 sub numsteps div def /cx c1x def /cy c1y def /radius r1 def newpath xInc 0 eq yInc 0 eq rInc 0 eq and and { 0 getrampcolor cx cy radius 0 360 arc stroke NumSamples 1 sub getrampcolor cx cy radius 72 hires div add 0 360 arc 0 setlinewidth stroke } { 0 numsteps { dup subsampling { round cvi } if getrampcolor cx cy radius 0 360 arc /cx cx xInc add def /cy cy yInc add def /radius radius rInc add def cx cy radius 360 0 arcn eofill rampIndxInc add } repeat pop } ifelse ext1 { c2y r2 add r1 lt { c2x c2y r2 0 360 arc fill } { c2y r1 add r2 sub 0.0001 le { c2x c2y r2 360 0 arcn pathbbox /aymax exch def /axmax exch def /aymin exch def /axmin exch def /bxMin xMin axmin min def /byMin yMin aymin min def /bxMax xMax axmax max def /byMax yMax aymax max def bxMin byMin moveto bxMax byMin lineto bxMax byMax lineto bxMin byMax lineto bxMin byMin lineto eofill } { c2x c2y r2 0 360 arc fill r1 r2 eq { /p1x r2 neg def /p1y c2y def /p2x r2 def /p2y c2y def p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto fill } { /AA r2 r1 sub c2y div def /theta AA 1 AA dup mul sub sqrt div 1 atan def /SS1 90 theta add dup sin exch cos div def /p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def /p1y c2y p1x SS1 div sub def /SS2 90 theta sub dup sin exch cos div def /p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def /p2y c2y p2x SS2 div sub def r1 r2 lt { /L1maxX p1x yMax p1y sub SS1 div add def /L2maxX p2x yMax p2y sub SS2 div add def } { /L1maxX 0 def /L2maxX 0 def }ifelse p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto L1maxX L1maxX p1x sub SS1 mul p1y add lineto fill } ifelse } ifelse } ifelse } if grestore grestore end end end } ifelse } bind def /GenStrips { 40 dict begin /ColorSpaceFamily exch def /background exch def /ext1 exch def /ext0 exch def /BBox exch def /y2 exch def /x2 exch def /y1 exch def /x1 exch def /rampdict exch def /setinkoverprint where {pop /setinkoverprint{pop}def}if gsave BBox length 0 gt { newpath BBox 0 get BBox 1 get moveto BBox 2 get BBox 0 get sub 0 rlineto 0 BBox 3 get BBox 1 get sub rlineto BBox 2 get BBox 0 get sub neg 0 rlineto closepath clip newpath } if x1 x2 eq { y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse } { /slope y2 y1 sub x2 x1 sub div def /theta slope 1 atan def x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if } ifelse gsave clippath x1 y1 translate theta rotate { pathbbox } stopped { 0 0 0 0 } if /yMax exch def /xMax exch def /yMin exch def /xMin exch def grestore xMax xMin eq yMax yMin eq or { grestore end } { rampdict begin 20 dict begin background length 0 gt { background sssetbackground gsave clippath fill grestore } if gsave x1 y1 translate theta rotate /xStart 0 def /xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def /ySpan yMax yMin sub def /numsteps NumSamples def /rampIndxInc 1 def /subsampling false def xStart 0 transform xEnd 0 transform 3 -1 roll sub dup mul 3 1 roll sub dup mul add 0.5 exp 72 div 0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 1 index 1 index lt { exch } if pop mul /numpix exch def numpix 0 ne { NumSamples numpix div 0.5 gt { /numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def /rampIndxInc NumSamples 1 sub numsteps div def /subsampling true def } if } if ext0 { 0 getrampcolor xMin xStart lt { xMin yMin xMin neg ySpan rectfill } if } if /xInc xEnd xStart sub numsteps div def /x xStart def 0 numsteps { dup subsampling { round cvi } if getrampcolor x yMin xInc ySpan rectfill /x x xInc add def rampIndxInc add } repeat pop ext1 { xMax xEnd gt { xEnd yMin xMax xEnd sub ySpan rectfill } if } if grestore grestore end end end } ifelse } bind def }def /page_trailer { end }def /doc_trailer{ }def systemdict /findcolorrendering known{ /findcolorrendering systemdict /findcolorrendering get def }if systemdict /setcolorrendering known{ /setcolorrendering systemdict /setcolorrendering get def }if /test_cmyk_color_plate { gsave setcmykcolor currentgray 1 ne grestore }def /inRip_spot_has_ink { dup Adobe_AGM_Core/AGMCORE_name xddf convert_spot_to_process not }def /map255_to_range { 1 index sub 3 -1 roll 255 div mul add }def /set_csa_crd { /sep_colorspace_dict null AGMCORE_gput begin CSA map_csa setcolorspace_opt set_crd end } def /setsepcolor { /sep_colorspace_dict AGMCORE_gget begin dup /sep_tint exch AGMCORE_gput TintProc end } def /setdevicencolor { /devicen_colorspace_dict AGMCORE_gget begin Names length copy Names length 1 sub -1 0 { /devicen_tints AGMCORE_gget 3 1 roll xpt } for TintProc end } def /sep_colorspace_proc { Adobe_AGM_Core/AGMCORE_tmp xddf /sep_colorspace_dict AGMCORE_gget begin currentdict/Components known{ Components aload pop TintMethod/Lab eq{ 2 {AGMCORE_tmp mul NComponents 1 roll} repeat LMax sub AGMCORE_tmp mul LMax add NComponents 1 roll }{ TintMethod/Subtractive eq{ NComponents{ AGMCORE_tmp mul NComponents 1 roll }repeat }{ NComponents{ 1 sub AGMCORE_tmp mul 1 add NComponents 1 roll } repeat }ifelse }ifelse }{ ColorLookup AGMCORE_tmp ColorLookup length 1 sub mul round cvi get aload pop }ifelse end } def /sep_colorspace_gray_proc { Adobe_AGM_Core/AGMCORE_tmp xddf /sep_colorspace_dict AGMCORE_gget begin GrayLookup AGMCORE_tmp GrayLookup length 1 sub mul round cvi get end } def /sep_proc_name { dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or level2 not and has_color not and{ pop [/DeviceGray] /sep_colorspace_gray_proc }{ /sep_colorspace_proc }ifelse } def /setsepcolorspace { current_spot_alias{ dup begin Name map_alias{ exch pop }if end }if dup /sep_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def Adobe_AGM_Core/AGMCORE_sep_special Name dup () eq exch (All) eq or ddf AGMCORE_avoid_L2_sep_space{ [/Indexed MappedCSA sep_proc_name 255 exch { 255 div } /exec cvx 3 -1 roll [ 4 1 roll load /exec cvx ] cvx ] setcolorspace_opt /TintProc { 255 mul round cvi setcolor }bdf }{ MappedCSA 0 get /DeviceCMYK eq currentdict/Components known and AGMCORE_sep_special not and{ /TintProc [ Components aload pop Name findcmykcustomcolor /exch cvx /setcustomcolor cvx ] cvx bdf }{ AGMCORE_host_sep Name (All) eq and{ /TintProc { 1 exch sub setseparationgray }bdf }{ AGMCORE_in_rip_sep MappedCSA 0 get /DeviceCMYK eq and AGMCORE_host_sep or Name () eq and{ /TintProc [ MappedCSA sep_proc_name exch 0 get /DeviceCMYK eq{ cvx /setcmykcolor cvx }{ cvx /setgray cvx }ifelse ] cvx bdf }{ AGMCORE_producing_seps MappedCSA 0 get dup /DeviceCMYK eq exch / DeviceGray eq or and AGMCORE_sep_special not and{ /TintProc [ /dup cvx MappedCSA sep_proc_name cvx exch 0 get /DeviceGray eq{ 1 /exch cvx /sub cvx 0 0 0 4 -1 /roll cvx }if /Name cvx /findcmykcustomcolor cvx /exch cvx AGMCORE_host_sep{ AGMCORE_is_cmyk_sep /Name cvx /AGMCORE_IsSeparationAProcessColor load /exec cvx /not cvx /and cvx }{ Name inRip_spot_has_ink not }ifelse [ /pop cvx 1 ] cvx /if cvx /setcustomcolor cvx ] cvx bdf }{ /TintProc /setcolor ldf [/Separation Name MappedCSA sep_proc_name load ] setcolorspace_opt }ifelse }ifelse }ifelse }ifelse }ifelse set_crd setsepcolor end } def /additive_blend { 3 dict begin /numarrays xdf /numcolors xdf 0 1 numcolors 1 sub { /c1 xdf 1 0 1 numarrays 1 sub { 1 exch add /index cvx c1 /get cvx /mul cvx }for numarrays 1 add 1 /roll cvx }for numarrays [/pop cvx] cvx /repeat cvx end }def /subtractive_blend { 3 dict begin /numarrays xdf /numcolors xdf 0 1 numcolors 1 sub { /c1 xdf 1 1 0 1 numarrays 1 sub { 1 3 3 -1 roll add /index cvx c1 /get cvx /sub cvx /mul cvx }for /sub cvx numarrays 1 add 1 /roll cvx }for numarrays [/pop cvx] cvx /repeat cvx end }def /exec_tint_transform { /TintProc [ /TintTransform cvx /setcolor cvx ] cvx bdf MappedCSA setcolorspace_opt } bdf /devn_makecustomcolor { 2 dict begin /names_index xdf /Names xdf 1 1 1 1 Names names_index get findcmykcustomcolor /devicen_tints AGMCORE_gget names_index get setcustomcolor Names length {pop} repeat end } bdf /setdevicencolorspace { dup /AliasedColorants known {false}{true}ifelse current_spot_alias and { 6 dict begin /names_index 0 def dup /names_len exch /Names get length def /new_names names_len array def /new_LookupTables names_len array def /alias_cnt 0 def dup /Names get { dup map_alias { exch pop dup /ColorLookup known { dup begin new_LookupTables names_index ColorLookup put end }{ dup /Components known { dup begin new_LookupTables names_index Components put end }{ dup begin new_LookupTables names_index [null null null null] put end } ifelse } ifelse new_names names_index 3 -1 roll /Name get put /alias_cnt alias_cnt 1 add def }{ /name xdf new_names names_index name put dup /LookupTables known { dup begin new_LookupTables names_index LookupTables names_index get put end }{ dup begin new_LookupTables names_index [null null null null] put end } ifelse } ifelse /names_index names_index 1 add def } forall alias_cnt 0 gt { /AliasedColorants true def 0 1 names_len 1 sub { /names_index xdf new_LookupTables names_index get 0 get null eq { dup /Names get names_index get /name xdf name (Cyan) eq name (Magenta) eq name (Yellow) eq name (Black) eq or or or not { /AliasedColorants false def exit } if } if } for AliasedColorants { dup begin /Names new_names def /AliasedColorants true def /LookupTables new_LookupTables def currentdict /TTTablesIdx known not { /TTTablesIdx -1 def } if currentdict /NComponents known not { /NComponents TintMethod /Subtractive eq {4}{3}ifelse def } if end } if }if end } if dup /devicen_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def currentdict /AliasedColorants known { AliasedColorants }{ false } ifelse /TintTransform load type /nulltype eq or { /TintTransform [ 0 1 Names length 1 sub { /TTTablesIdx TTTablesIdx 1 add def dup LookupTables exch get dup 0 get null eq { 1 index Names exch get dup (Cyan) eq { pop exch LookupTables length exch sub /index cvx 0 0 0 } { dup (Magenta) eq { pop exch LookupTables length exch sub /index cvx 0 /exch cvx 0 0 } { (Yellow) eq { exch LookupTables length exch sub /index cvx 0 0 3 -1 /roll cvx 0 } { exch LookupTables length exch sub /index cvx 0 0 0 4 -1 /roll cvx } ifelse } ifelse } ifelse 5 -1 /roll cvx /astore cvx } { dup length 1 sub LookupTables length 4 -1 roll sub 1 add /index cvx /mul cvx /round cvx /cvi cvx /get cvx } ifelse Names length TTTablesIdx add 1 add 1 /roll cvx } for Names length [/pop cvx] cvx /repeat cvx NComponents Names length TintMethod /Subtractive eq { subtractive_blend } { additive_blend } ifelse ] cvx bdf } if AGMCORE_host_sep { Names convert_to_process { exec_tint_transform } { currentdict /AliasedColorants known { AliasedColorants not }{ false } ifelse 5 dict begin /AvoidAliasedColorants xdf /painted? false def /names_index 0 def /names_len Names length def Names { AvoidAliasedColorants { /currentspotalias current_spot_alias def false set_spot_alias } if AGMCORE_is_cmyk_sep { dup (Cyan) eq AGMCORE_cyan_plate and exch dup (Magenta) eq AGMCORE_magenta_plate and exch dup (Yellow) eq AGMCORE_yellow_plate and exch (Black) eq AGMCORE_black_plate and or or or { /devicen_colorspace_dict AGMCORE_gget /TintProc [ Names names_index /devn_makecustomcolor cvx ] cvx ddf /painted? true def } if painted? {exit} if }{ 0 0 0 0 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq { /devicen_colorspace_dict AGMCORE_gget /TintProc [ Names names_index /devn_makecustomcolor cvx ] cvx ddf /painted? true def exit } if } ifelse AvoidAliasedColorants { currentspotalias set_spot_alias } if /names_index names_index 1 add def } forall painted? { /devicen_colorspace_dict AGMCORE_gget /names_index names_index put }{ /devicen_colorspace_dict AGMCORE_gget /TintProc [ names_len [/pop cvx] cvx /repeat cvx 1 /setseparationgray cvx 0 0 0 0 () /findcmykcustomcolor cvx 0 /setcustomcolor cvx ] cvx ddf } ifelse end } ifelse } { AGMCORE_in_rip_sep { Names convert_to_process not }{ level3 } ifelse { [/DeviceN Names MappedCSA /TintTransform load] setcolorspace_opt /TintProc level3 not AGMCORE_in_rip_sep and { [ Names /length cvx [/pop cvx] cvx /repeat cvx ] cvx bdf }{ /setcolor ldf } ifelse }{ exec_tint_transform } ifelse } ifelse set_crd /AliasedColorants false def end } def /setindexedcolorspace { dup /indexed_colorspace_dict exch AGMCORE_gput begin currentdict /CSD known { CSD get_csd /Names known { CSD get_csd begin currentdict devncs AGMCORE_host_sep{ 4 dict begin /devnCompCnt Names length def /NewLookup HiVal 1 add string def 0 1 HiVal { /tableIndex xdf Lookup dup type /stringtype eq { devnCompCnt tableIndex map_index }{ exec } ifelse setdevicencolor currentgray tableIndex exch HiVal mul cvi NewLookup 3 1 roll put } for [/Indexed currentcolorspace HiVal NewLookup] setcolorspace_opt end }{ level3 { [/Indexed [/DeviceN Names MappedCSA /TintTransform load] HiVal Lookup] setcolorspace_opt }{ [/Indexed MappedCSA HiVal [ Lookup dup type /stringtype eq {/exch cvx CSD get_csd /Names get length dup /mul cvx exch / getinterval cvx {255 div} /forall cvx} {/exec cvx}ifelse /TintTransform load /exec cvx ]cvx ]setcolorspace_opt }ifelse } ifelse end }{ } ifelse set_crd } { /MappedCSA CSA map_csa def AGMCORE_host_sep level2 not and{ 0 0 0 0 setcmykcolor }{ [/Indexed MappedCSA level2 not has_color not and{ dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or{ pop [/DeviceGray] }if HiVal GrayLookup }{ HiVal currentdict/RangeArray known{ { /indexed_colorspace_dict AGMCORE_gget begin Lookup exch dup HiVal gt{ pop HiVal }if NComponents mul NComponents getinterval {} forall NComponents 1 sub -1 0{ RangeArray exch 2 mul 2 getinterval aload pop map255_to_range NComponents 1 roll }for end } bind }{ Lookup }ifelse }ifelse ] setcolorspace_opt set_crd }ifelse }ifelse end }def /setindexedcolor { AGMCORE_host_sep { /indexed_colorspace_dict AGMCORE_gget dup /CSD known { begin CSD get_csd begin map_indexed_devn devn end end }{ AGMCORE_gget/Lookup get 4 3 -1 roll map_index pop setcmykcolor } ifelse }{ level3 not AGMCORE_in_rip_sep and /indexed_colorspace_dict AGMCORE_gget /CSD known and { /indexed_colorspace_dict AGMCORE_gget /CSD get get_csd begin map_indexed_devn devn end } { setcolor } ifelse }ifelse } def /ignoreimagedata { currentoverprint not{ gsave dup clonedict begin 1 setgray /Decode [0 1] def /DataSource def /MultipleDataSources false def /BitsPerComponent 8 def currentdict end systemdict /image get exec grestore }if consumeimagedata }def /add_csa { Adobe_AGM_Core begin /AGMCORE_CSA_cache xput end }def /get_csa_by_name { dup type dup /nametype eq exch /stringtype eq or{ Adobe_AGM_Core begin 1 dict begin /name xdf AGMCORE_CSA_cache { 0 get name eq { exit }{ pop } ifelse }forall end end }{ pop } ifelse }def /map_csa { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSA_cache get exch get }if }def /add_csd { Adobe_AGM_Core begin /AGMCORE_CSD_cache xput end }def /get_csd { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSD_cache get exch get }if }def /pattern_buf_init { /count get 0 0 put } def /pattern_buf_next { dup /count get dup 0 get dup 3 1 roll 1 add 0 xpt get } def /cachepattern_compress { 5 dict begin currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def /patarray 20 dict def /string_size 16000 def /readbuffer string_size string def currentglobal true setglobal patarray 1 array dup 0 1 put /count xpt setglobal /LZWFilter { exch dup length 0 eq { pop }{ patarray dup length 1 sub 3 -1 roll put } ifelse {string_size}{0}ifelse string } /LZWEncode filter def { ReadFilter readbuffer readstring exch LZWFilter exch writestring not {exit} if } loop LZWFilter closefile patarray end }def /cachepattern { 2 dict begin currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def /patarray 20 dict def currentglobal true setglobal patarray 1 array dup 0 1 put /count xpt setglobal { ReadFilter 16000 string readstring exch patarray dup length 1 sub 3 -1 roll put not {exit} if } loop patarray dup dup length 1 sub () put end }def /add_pattern { Adobe_AGM_Core begin /AGMCORE_pattern_cache xput end }def /get_pattern { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_pattern_cache get exch get dup wrap_paintproc }if }def /wrap_paintproc { statusdict /currentfilenameextend known{ begin /OldPaintProc /PaintProc load def /PaintProc { mark exch dup /OldPaintProc get stopped {closefile restore end} if cleartomark } def end } {pop} ifelse } def /make_pattern { dup matrix currentmatrix matrix concatmatrix 0 0 3 2 roll itransform exch 3 index /XStep get 1 index exch 2 copy div cvi mul sub sub exch 3 index /YStep get 1 index exch 2 copy div cvi mul sub sub matrix translate exch matrix concatmatrix 1 index begin BBox 0 get XStep div cvi XStep mul /xshift exch neg def BBox 1 get YStep div cvi YStep mul /yshift exch neg def BBox 0 get xshift add BBox 1 get yshift add BBox 2 get xshift add BBox 3 get yshift add 4 array astore /BBox exch def [ xshift yshift /translate load null /exec load ] dup 3 /PaintProc load put cvx /PaintProc exch def end gsave 0 setgray makepattern grestore }def /set_pattern { dup /PatternType get 1 eq{ dup /PaintType get 1 eq{ currentoverprint sop [/DeviceGray] setcolorspace 0 setgray }if }if setpattern }def /setcolorspace_opt { dup currentcolorspace eq{ pop }{ setcolorspace }ifelse }def /updatecolorrendering { currentcolorrendering/Intent known{ currentcolorrendering/Intent get }{ null }ifelse Intent ne{ false Intent AGMCORE_CRD_cache { exch pop begin dup Intent eq{ currentdict setcolorrendering_opt end exch pop true exch exit }if end } forall pop not{ systemdict /findcolorrendering known{ Intent findcolorrendering pop /ColorRendering findresource dup length dict copy setcolorrendering_opt }if }if }if } def /add_crd { AGMCORE_CRD_cache 3 1 roll put }def /set_crd { AGMCORE_host_sep not level2 and{ currentdict/CRD known{ AGMCORE_CRD_cache CRD get dup null ne{ setcolorrendering_opt }{ pop }ifelse }{ currentdict/Intent known{ updatecolorrendering }if }ifelse currentcolorspace dup type /arraytype eq {0 get}if /DeviceRGB eq { currentdict/UCR known {/UCR}{/AGMCORE_currentucr}ifelse load setundercolorremoval currentdict/BG known {/BG}{/AGMCORE_currentbg}ifelse load setblackgeneration }if }if }def /setcolorrendering_opt { dup currentcolorrendering eq{ pop }{ begin /Intent Intent def currentdict end setcolorrendering }ifelse }def /cpaint_gcomp { convert_to_process Adobe_AGM_Core/AGMCORE_ConvertToProcess xddf Adobe_AGM_Core/AGMCORE_ConvertToProcess get not { (%end_cpaint_gcomp) flushinput }if }def /cpaint_gsep { Adobe_AGM_Core/AGMCORE_ConvertToProcess get { (%end_cpaint_gsep) flushinput }if }def /cpaint_gend { newpath }def /path_rez { dup 0 ne{ AGMCORE_deviceDPI exch div dup 1 lt{ pop 1 }if setflat }{ pop }ifelse }def /set_spot_alias_ary { /AGMCORE_SpotAliasAry where{ pop pop }{ Adobe_AGM_Core/AGMCORE_SpotAliasAry xddf true set_spot_alias }ifelse }def /set_spot_alias { /AGMCORE_SpotAliasAry where{ /AGMCORE_current_spot_alias 3 -1 roll put }{ pop }ifelse }def /current_spot_alias { /AGMCORE_SpotAliasAry where{ /AGMCORE_current_spot_alias get }{ false }ifelse }def /map_alias { /AGMCORE_SpotAliasAry where{ begin /AGMCORE_name xdf false AGMCORE_SpotAliasAry{ dup/Name get AGMCORE_name eq{ save exch /Adobe_AGM_Core currentdict def /CSD get get_csd exch restore exch pop true exit }{ pop }ifelse }forall end }{ pop false }ifelse }bdf /spot_alias { true set_spot_alias /AGMCORE_&setcustomcolor AGMCORE_key_known not { Adobe_AGM_Core/AGMCORE_&setcustomcolor /setcustomcolor load put } if /customcolor_tint 1 AGMCORE_gput Adobe_AGM_Core begin /setcustomcolor { dup /customcolor_tint exch AGMCORE_gput current_spot_alias{ 1 index 4 get map_alias{ mark 3 1 roll setsepcolorspace counttomark 0 ne{ setsepcolor }if pop pop }{ AGMCORE_&setcustomcolor }ifelse }{ AGMCORE_&setcustomcolor }ifelse }bdf end }def /begin_feature { Adobe_AGM_Core/AGMCORE_feature_dictCount countdictstack put count Adobe_AGM_Core/AGMCORE_feature_opCount 3 -1 roll put {Adobe_AGM_Core/AGMCORE_feature_ctm matrix currentmatrix put}if }def /end_feature { 2 dict begin /spd /setpagedevice load def /setpagedevice { get_gstate spd set_gstate } def stopped{$error/newerror false put}if end count Adobe_AGM_Core/AGMCORE_feature_opCount get sub dup 0 gt{{pop} repeat}{pop}ifelse countdictstack Adobe_AGM_Core/AGMCORE_feature_dictCount get sub dup 0 gt{{end}repeat}{pop}ifelse {Adobe_AGM_Core/AGMCORE_feature_ctm get setmatrix}if }def /set_negative { Adobe_AGM_Core begin /AGMCORE_inverting exch def level2{ currentpagedevice/NegativePrint known{ currentpagedevice/NegativePrint get Adobe_AGM_Core/ AGMCORE_inverting get ne{ true begin_feature true{ bdict /NegativePrint Adobe_AGM_Core/AGMCORE_inverting get edict setpagedevice }end_feature }if /AGMCORE_inverting false def }if }if AGMCORE_inverting{ [{1 exch sub}/exec load dup currenttransfer exch]cvx bind settransfer gsave newpath clippath 1 /setseparationgray where{pop setseparationgray}{setgray}ifelse /AGMIRS_&fill where {pop AGMIRS_&fill}{fill} ifelse grestore }if end }def /lw_save_restore_override { /md where { pop md begin initializepage /initializepage{}def /pmSVsetup{} def /endp{}def /pse{}def /psb{}def /orig_showpage where {pop} {/orig_showpage /showpage load def} ifelse /showpage {orig_showpage gR} def end }if }def /pscript_showpage_override { /NTPSOct95 where { begin showpage save /showpage /restore load def /restore {exch pop}def end }if }def /driver_media_override { /md where { pop md /initializepage known { md /initializepage {} put } if md /rC known { md /rC {4{pop}repeat} put } if }if /mysetup where { /mysetup [1 0 0 1 0 0] put }if Adobe_AGM_Core /AGMCORE_Default_CTM matrix currentmatrix put level2 {Adobe_AGM_Core /AGMCORE_Default_PageSize currentpagedevice/ PageSize get put}if }def /driver_check_media_override { /PrepsDict where {pop} { Adobe_AGM_Core /AGMCORE_Default_CTM get matrix currentmatrix ne Adobe_AGM_Core /AGMCORE_Default_PageSize get type /arraytype eq { Adobe_AGM_Core /AGMCORE_Default_PageSize get 0 get currentpagedevice/PageSize get 0 get eq and Adobe_AGM_Core /AGMCORE_Default_PageSize get 1 get currentpagedevice/PageSize get 1 get eq and }if { Adobe_AGM_Core /AGMCORE_Default_CTM get setmatrix }if }ifelse }def AGMCORE_err_strings begin /AGMCORE_bad_environ (Environment not satisfactory for this job. Ensure that the PPD is correct or that the PostScript level requested is supported by this printer. ) def /AGMCORE_color_space_onhost_seps (This job contains colors that will not separate with on-host methods. ) def /AGMCORE_invalid_color_space (This job contains an invalid color space. ) def end end systemdict /setpacking known { setpacking } if %%EndResource %%BeginResource: procset Adobe_CoolType_Core 2.23 0 %%Copyright: Copyright 1997-2003 Adobe Systems Incorporated. All Rights Reserved. %%Version: 2.23 0 10 dict begin /Adobe_CoolType_Passthru currentdict def /Adobe_CoolType_Core_Defined userdict /Adobe_CoolType_Core known def Adobe_CoolType_Core_Defined { /Adobe_CoolType_Core userdict /Adobe_CoolType_Core get def } if userdict /Adobe_CoolType_Core 60 dict dup begin put /Adobe_CoolType_Version 2.23 def /Level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if def Level2? not { /currentglobal false def /setglobal /pop load def /gcheck { pop false } bind def /currentpacking false def /setpacking /pop load def /SharedFontDirectory 0 dict def } if currentpacking true setpacking /@_SaveStackLevels { Adobe_CoolType_Data begin @opStackCountByLevel @opStackLevel 2 copy known not { 2 copy 3 dict dup /args 7 index 5 add array put put get } { get dup /args get dup length 3 index lt { dup length 5 add array exch 1 index exch 0 exch putinterval 1 index exch /args exch put } { pop } ifelse } ifelse begin count 2 sub 1 index lt { pop count 1 sub } if dup /argCount exch def dup 0 gt { exch 1 index 2 add 1 roll args exch 0 exch getinterval astore pop } { pop } ifelse count 1 sub /restCount exch def end /@opStackLevel @opStackLevel 1 add def countdictstack 1 sub @dictStackCountByLevel exch @dictStackLevel exch put /@dictStackLevel @dictStackLevel 1 add def end } bind def /@_RestoreStackLevels { Adobe_CoolType_Data begin /@opStackLevel @opStackLevel 1 sub def @opStackCountByLevel @opStackLevel get begin count restCount sub dup 0 gt { { pop } repeat } { pop } ifelse args 0 argCount getinterval {} forall end /@dictStackLevel @dictStackLevel 1 sub def @dictStackCountByLevel @dictStackLevel get end countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse } bind def /@_PopStackLevels { Adobe_CoolType_Data begin /@opStackLevel @opStackLevel 1 sub def /@dictStackLevel @dictStackLevel 1 sub def end } bind def /@Raise { exch cvx exch errordict exch get exec stop } bind def /@ReRaise { cvx $error /errorname get errordict exch get exec stop } bind def /@Stopped { 0 @#Stopped } bind def /@#Stopped { @_SaveStackLevels stopped { @_RestoreStackLevels true } { @_PopStackLevels false } ifelse } bind def /@Arg { Adobe_CoolType_Data begin @opStackCountByLevel @opStackLevel 1 sub get /args get exch get end } bind def currentglobal true setglobal /CTHasResourceForAllBug Level2? { 1 dict dup begin mark { (*) { pop stop } 128 string /Category resourceforall } stopped cleartomark currentdict eq dup { end } if not } { false } ifelse def /CTHasResourceStatusBug Level2? { mark { /steveamerige /Category resourcestatus } stopped { cleartomark true } { cleartomark currentglobal not } ifelse } { false } ifelse def setglobal /CTResourceStatus { mark 3 1 roll /Category findresource begin ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec { cleartomark false } { { 3 2 roll pop true } { cleartomark false } ifelse } ifelse end } bind def /CTWorkAroundBugs { Level2? { /cid_PreLoad /ProcSet resourcestatus { pop pop currentglobal mark { (*) { dup /CMap CTHasResourceStatusBug { CTResourceStatus } { resourcestatus } ifelse { pop dup 0 eq exch 1 eq or { dup /CMap findresource gcheck setglobal /CMap undefineresource } { pop CTHasResourceForAllBug { exit } { stop } ifelse } ifelse } { pop } ifelse } 128 string /CMap resourceforall } stopped { cleartomark } stopped pop setglobal } if } if } bind def /doc_setup { Adobe_CoolType_Core begin CTWorkAroundBugs /mov /moveto load def /nfnt /newencodedfont load def /mfnt /makefont load def /sfnt /setfont load def /ufnt /undefinefont load def /chp /charpath load def /awsh /awidthshow load def /wsh /widthshow load def /ash /ashow load def /sh /show load def end userdict /Adobe_CoolType_Data 10 dict dup begin /AddWidths? false def /CC 0 def /charcode 2 string def /@opStackCountByLevel 32 dict def /@opStackLevel 0 def /@dictStackCountByLevel 32 dict def /@dictStackLevel 0 def /InVMFontsByCMap 10 dict def /InVMDeepCopiedFonts 10 dict def end put } bind def /doc_trailer { currentdict Adobe_CoolType_Core eq { end } if } bind def /page_setup { Adobe_CoolType_Core begin } bind def /page_trailer { end } bind def /unload { systemdict /languagelevel known { systemdict/languagelevel get 2 ge { userdict/Adobe_CoolType_Core 2 copy known { undef } { pop pop } ifelse } if } if } bind def /ndf { 1 index where { pop pop pop } { dup xcheck { bind } if def } ifelse } def /findfont systemdict begin userdict begin /globaldict where { /globaldict get begin } if dup where pop exch get /globaldict where { pop end } if end end Adobe_CoolType_Core_Defined { /systemfindfont exch def } { /findfont 1 index def /systemfindfont exch def } ifelse /undefinefont { pop } ndf /copyfont { currentglobal 3 1 roll 1 index gcheck setglobal dup null eq { 0 } { dup length } ifelse 2 index length add 1 add dict begin exch { 1 index /FID eq { pop pop } { def } ifelse } forall dup null eq { pop } { { def } forall } ifelse currentdict end exch setglobal } bind def /copyarray { currentglobal exch dup gcheck setglobal dup length array copy exch setglobal } bind def /newencodedfont { currentglobal { SharedFontDirectory 3 index known { SharedFontDirectory 3 index get /FontReferenced known } { false } ifelse } { FontDirectory 3 index known { FontDirectory 3 index get /FontReferenced known } { SharedFontDirectory 3 index known { SharedFontDirectory 3 index get /FontReferenced known } { false } ifelse } ifelse } ifelse dup { 3 index findfont /FontReferenced get 2 index dup type /nametype eq {findfont} if ne { pop false } if } if { pop 1 index findfont /Encoding get exch 0 1 255 { 2 copy get 3 index 3 1 roll put } for pop pop pop } { dup type /nametype eq { findfont } if dup dup maxlength 2 add dict begin exch { 1 index /FID ne {def} {pop pop} ifelse } forall /FontReferenced exch def /Encoding exch dup length array copy def /FontName 1 index dup type /stringtype eq { cvn } if def dup currentdict end definefont def } ifelse } bind def /SetSubstituteStrategy { $SubstituteFont begin dup type /dicttype ne { 0 dict } if currentdict /$Strategies known { exch $Strategies exch 2 copy known { get 2 copy maxlength exch maxlength add dict begin { def } forall { def } forall currentdict dup /$Init known { dup /$Init get exec } if end /$Strategy exch def } { pop pop pop } ifelse } { pop pop } ifelse end } bind def /scff { $SubstituteFont begin dup type /stringtype eq { dup length exch } { null } ifelse /$sname exch def /$slen exch def /$inVMIndex $sname null eq { 1 index $str cvs dup length $slen sub $slen getinterval cvn } { $sname } ifelse def end { findfont } @Stopped { dup length 8 add string exch 1 index 0 (BadFont:) putinterval 1 index exch 8 exch dup length string cvs putinterval cvn { findfont } @Stopped { pop /Courier findfont } if } if $SubstituteFont begin /$sname null def /$slen 0 def /$inVMIndex null def end } bind def /isWidthsOnlyFont { dup /WidthsOnly known { pop pop true } { dup /FDepVector known { /FDepVector get { isWidthsOnlyFont dup { exit } if } forall } { dup /FDArray known { /FDArray get { isWidthsOnlyFont dup { exit } if } forall } { pop } ifelse } ifelse } ifelse } bind def /?str1 256 string def /?set { $SubstituteFont begin /$substituteFound false def /$fontname 4 index def /$doSmartSub false def end 3 index currentglobal false setglobal exch /CompatibleFonts /ProcSet resourcestatus { pop pop /CompatibleFonts /ProcSet findresource begin dup /CompatibleFont currentexception 1 index /CompatibleFont true setexception 1 index /Font resourcestatus { pop pop 3 2 roll setglobal end exch dup findfont /CompatibleFonts /ProcSet findresource begin 3 1 roll exch /CompatibleFont exch setexception end } { 3 2 roll setglobal 1 index exch /CompatibleFont exch setexception end findfont $SubstituteFont /$substituteFound true put } ifelse } { exch setglobal findfont } ifelse $SubstituteFont begin $substituteFound { false (%%[Using embedded font ) print 5 index ?str1 cvs print ( to avoid the font substitution problem noted earlier.]%%\n) print } { dup /FontName known { dup /FontName get $fontname eq 1 index /DistillerFauxFont known not and /currentdistillerparams where { pop false 2 index isWidthsOnlyFont not and } if } { false } ifelse } ifelse exch pop /$doSmartSub true def end { exch pop exch pop exch 2 dict dup /Found 3 index put exch findfont exch } { exch exec exch dup findfont dup /FontType get 3 eq { exch ?str1 cvs dup length 1 sub -1 0 { exch dup 2 index get 42 eq { exch 0 exch getinterval cvn 4 1 roll 3 2 roll pop exit } {exch pop} ifelse }for } { exch pop } ifelse 2 dict dup /Downloaded 6 5 roll put } ifelse dup /FontName 4 index put copyfont definefont pop } bind def /?str2 256 string def /?add { 1 index type /integertype eq { exch true 4 2 } { false 3 1 } ifelse roll 1 index findfont dup /Widths known { Adobe_CoolType_Data /AddWidths? true put gsave dup 1000 scalefont setfont } if /Downloaded known { exec exch { exch ?str2 cvs exch findfont /Downloaded get 1 dict begin /Downloaded 1 index def ? str1 cvs length ?str1 1 index 1 add 3 index putinterval exch length 1 add 1 index add ?str1 2 index (*) putinterval ?str1 0 2 index getinterval cvn findfont ?str1 3 index (+) putinterval 2 dict dup /FontName ?str1 0 6 index getinterval cvn put dup /Downloaded Downloaded put end copyfont dup /FontName get exch definefont pop pop pop } { pop } ifelse } { pop exch { findfont dup /Found get dup length exch ?str1 cvs pop ?str1 1 index (+) putinterval ?str1 1 index 1 add 4 index ?str2 cvs putinterval ?str1 exch 0 exch 5 4 roll ?str2 cvs length 1 add add getinterval cvn 1 dict exch 1 index exch /FontName exch put copyfont dup /FontName get exch definefont pop } { pop } ifelse } ifelse Adobe_CoolType_Data /AddWidths? get { grestore Adobe_CoolType_Data /AddWidths? false put } if } bind def /?sh { currentfont /Downloaded known { exch } if pop } bind def /?chp { currentfont /Downloaded known { pop } { false chp } ifelse } bind def /?mv { currentfont /Downloaded known { moveto pop pop } { pop pop moveto } ifelse } bind def setpacking userdict /$SubstituteFont 25 dict put 1 dict begin /SubstituteFont dup $error exch 2 copy known { get } { pop pop { pop /Courier } bind } ifelse def /currentdistillerparams where dup { pop pop currentdistillerparams /CannotEmbedFontPolicy 2 copy known { get /Error eq } { pop pop false } ifelse } if not { countdictstack array dictstack 0 get begin userdict begin $SubstituteFont begin /$str 128 string def /$fontpat 128 string def /$slen 0 def /$sname null def /$match false def /$fontname null def /$substituteFound false def /$inVMIndex null def /$doSmartSub true def /$depth 0 def /$fontname null def /$italicangle 26.5 def /$dstack null def /$Strategies 10 dict dup begin /$Type3Underprint { currentglobal exch false setglobal 11 dict begin /UseFont exch $WMode 0 ne { dup length dict copy dup /WMode $WMode put /UseFont exch definefont } if def /FontName $fontname dup type /stringtype eq { cvn } if def /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /Encoding 256 array dup 0 1 255 { /.notdef put dup } for pop def /FontBBox [ 0 0 0 0 ] def /CCInfo 7 dict dup begin /cc null def /x 0 def /y 0 def end def /BuildChar { exch begin CCInfo begin 1 string dup 0 3 index put exch pop /cc exch def UseFont 1000 scalefont setfont cc stringwidth /y exch def /x exch def x y setcharwidth $SubstituteFont /$Strategy get /$Underprint get exec 0 0 moveto cc show x y moveto end end } bind def currentdict end exch setglobal } bind def /$GetaTint 2 dict dup begin /$BuildFont { dup /WMode known { dup /WMode get } { 0 } ifelse /$WMode exch def $fontname exch dup /FontName known { dup /FontName get dup type /stringtype eq { cvn } if } { /unnamedfont } ifelse exch Adobe_CoolType_Data /InVMDeepCopiedFonts get 1 index /FontName get known { pop Adobe_CoolType_Data /InVMDeepCopiedFonts get 1 index get null copyfont } { $deepcopyfont } ifelse exch 1 index exch /FontBasedOn exch put dup /FontName $fontname dup type /stringtype eq { cvn } if put definefont Adobe_CoolType_Data /InVMDeepCopiedFonts get begin dup /FontBasedOn get 1 index def end } bind def /$Underprint { gsave x abs y abs gt { /y 1000 def } { /x -1000 def 500 120 translate } ifelse Level2? { [ /Separation (All) /DeviceCMYK { 0 0 0 1 pop } ] setcolorspace } { 0 setgray } ifelse 10 setlinewidth x .8 mul [ 7 3 ] { y mul 8 div 120 sub x 10 div exch moveto 0 y 4 div neg rlineto dup 0 rlineto 0 y 4 div rlineto closepath gsave Level2? { .2 setcolor } { .8 setgray } ifelse fill grestore stroke } forall pop grestore } bind def end def /$Oblique 1 dict dup begin /$BuildFont { currentglobal exch dup gcheck setglobal null copyfont begin /FontBasedOn currentdict /FontName known { FontName dup type /stringtype eq { cvn } if } { /unnamedfont } ifelse def /FontName $fontname dup type /stringtype eq { cvn } if def /currentdistillerparams where { pop } { /FontInfo currentdict /FontInfo known { FontInfo null copyfont } { 2 dict } ifelse dup begin /ItalicAngle $italicangle def /FontMatrix FontMatrix [ 1 0 ItalicAngle dup sin exch cos div 1 0 0 ] matrix concatmatrix readonly end 4 2 roll def def } ifelse FontName currentdict end definefont exch setglobal } bind def end def /$None 1 dict dup begin /$BuildFont {} bind def end def end def /$Oblique SetSubstituteStrategy /$findfontByEnum { dup type /stringtype eq { cvn } if dup /$fontname exch def $sname null eq { $str cvs dup length $slen sub $slen getinterval } { pop $sname } ifelse $fontpat dup 0 (fonts/*) putinterval exch 7 exch putinterval /$match false def $SubstituteFont /$dstack countdictstack array dictstack put mark { $fontpat 0 $slen 7 add getinterval { /$match exch def exit } $str filenameforall } stopped { cleardictstack currentdict true $SubstituteFont /$dstack get { exch { 1 index eq { pop false } { true } ifelse } { begin false } ifelse } forall pop } if cleartomark /$slen 0 def $match false ne { $match (fonts/) anchorsearch pop pop cvn } { /Courier } ifelse } bind def /$ROS 1 dict dup begin /Adobe 4 dict dup begin /Japan1 [ /Ryumin-Light /HeiseiMin-W3 /GothicBBB-Medium /HeiseiKakuGo-W5 /HeiseiMaruGo-W4 /Jun101-Light ] def /Korea1 [ /HYSMyeongJo-Medium /HYGoThic-Medium ] def /GB1 [ /STSong-Light /STHeiti-Regular ] def /CNS1 [ /MKai-Medium /MHei-Medium ] def end def end def /$cmapname null def /$deepcopyfont { dup /FontType get 0 eq { 1 dict dup /FontName /copied put copyfont begin /FDepVector FDepVector copyarray 0 1 2 index length 1 sub { 2 copy get $deepcopyfont dup /FontName /copied put /copied exch definefont 3 copy put pop pop } for def currentdict end } { $Strategies /$Type3Underprint get exec } ifelse } bind def /$buildfontname { dup /CIDFont findresource /CIDSystemInfo get begin Registry length Ordering length Supplement 8 string cvs 3 copy length 2 add add add string dup 5 1 roll dup 0 Registry putinterval dup 4 index (-) putinterval dup 4 index 1 add Ordering putinterval 4 2 roll add 1 add 2 copy (-) putinterval end 1 add 2 copy 0 exch getinterval $cmapname $fontpat cvs exch anchorsearch { pop pop 3 2 roll putinterval cvn /$cmapname exch def } { pop pop pop pop pop } ifelse length $str 1 index (-) putinterval 1 add $str 1 index $cmapname $fontpat cvs putinterval $cmapname length add $str exch 0 exch getinterval cvn } bind def /$findfontByROS { /$fontname exch def $ROS Registry 2 copy known { get Ordering 2 copy known { get } { pop pop [] } ifelse } { pop pop [] } ifelse false exch { dup /CIDFont resourcestatus { pop pop save 1 index /CIDFont findresource dup /WidthsOnly known { dup /WidthsOnly get } { false } ifelse exch pop exch restore { pop } { exch pop true exit } ifelse } { pop } ifelse } forall { $str cvs $buildfontname } { false (*) { save exch dup /CIDFont findresource dup /WidthsOnly known { dup /WidthsOnly get not } { true } ifelse exch /CIDSystemInfo get dup /Registry get Registry eq exch /Ordering get Ordering eq and and { exch restore exch pop true exit } { pop restore } ifelse } $str /CIDFont resourceforall { $buildfontname } { $fontname $findfontByEnum } ifelse } ifelse } bind def end end currentdict /$error known currentdict /languagelevel known and dup { pop $error /SubstituteFont known } if dup { $error } { Adobe_CoolType_Core } ifelse begin { /SubstituteFont /CMap /Category resourcestatus { pop pop { $SubstituteFont begin /$substituteFound true def dup length $slen gt $sname null ne or $slen 0 gt and { $sname null eq { dup $str cvs dup length $slen sub $slen getinterval cvn } { $sname } ifelse Adobe_CoolType_Data /InVMFontsByCMap get 1 index 2 copy known { get false exch { pop currentglobal { GlobalFontDirectory 1 index known { exch pop true exit } { pop } ifelse } { FontDirectory 1 index known { exch pop true exit } { GlobalFontDirectory 1 index known { exch pop true exit } { pop } ifelse } ifelse } ifelse } forall } { pop pop false } ifelse { exch pop exch pop } { dup /CMap resourcestatus { pop pop dup /$cmapname exch def /CMap findresource /CIDSystemInfo get { def } forall $findfontByROS } { 128 string cvs dup (-) search { 3 1 roll search { 3 1 roll pop { dup cvi } stopped { pop pop pop pop pop $findfontByEnum } { 4 2 roll pop pop exch length exch 2 index length 2 index sub exch 1 sub -1 0 { $str cvs dup length 4 index 0 4 index 4 3 roll add getinterval exch 1 index exch 3 index exch putinterval dup /CMap resourcestatus { pop pop 4 1 roll pop pop pop dup /$cmapname exch def /CMap findresource /CIDSystemInfo get { def } forall $findfontByROS true exit } { pop } ifelse } for dup type /booleantype eq { pop } { pop pop pop $findfontByEnum } ifelse } ifelse } { pop pop pop $findfontByEnum } ifelse } { pop pop $findfontByEnum } ifelse } ifelse } ifelse } { //SubstituteFont exec } ifelse /$slen 0 def end } } { { $SubstituteFont begin /$substituteFound true def dup length $slen gt $sname null ne or $slen 0 gt and { $findfontByEnum } { //SubstituteFont exec } ifelse end } } ifelse bind readonly def Adobe_CoolType_Core /scfindfont /systemfindfont load put } { /scfindfont { $SubstituteFont begin dup systemfindfont dup /FontName known { dup /FontName get dup 3 index ne } { /noname true } ifelse dup { /$origfontnamefound 2 index def /$origfontname 4 index def /$substituteFound true def } if exch pop { $slen 0 gt $sname null ne 3 index length $slen gt or and { pop dup $findfontByEnum findfont dup maxlength 1 add dict begin { 1 index /FID eq { pop pop } { def } ifelse } forall currentdict end definefont dup /FontName known { dup /FontName get } { null } ifelse $origfontnamefound ne { $origfontname $str cvs print ( substitution revised, using ) print dup /FontName known { dup /FontName get } { (unspecified font) } ifelse $str cvs print (.\n) print } if } { exch pop } ifelse } { exch pop } ifelse end } bind def } ifelse end end Adobe_CoolType_Core_Defined not { Adobe_CoolType_Core /findfont { $SubstituteFont begin $depth 0 eq { /$fontname 1 index dup type /stringtype ne { $str cvs } if def /$substituteFound false def } if /$depth $depth 1 add def end scfindfont $SubstituteFont begin /$depth $depth 1 sub def $substituteFound $depth 0 eq and { $inVMIndex null ne { dup $inVMIndex $AddInVMFont } if $doSmartSub { currentdict /$Strategy known { $Strategy /$BuildFont get exec } if } if } if end } bind put } if } if end /$AddInVMFont { exch /FontName 2 copy known { get 1 dict dup begin exch 1 index gcheck def end exch Adobe_CoolType_Data /InVMFontsByCMap get exch $DictAdd } { pop pop pop } ifelse } bind def /$DictAdd { 2 copy known not { 2 copy 4 index length dict put } if Level2? not { 2 copy get dup maxlength exch length 4 index length add lt 2 copy get dup length 4 index length add exch maxlength 1 index lt { 2 mul dict begin 2 copy get { forall } def 2 copy currentdict put end } { pop } ifelse } if get begin { def } forall end } bind def end end %%EndResource %%BeginResource: procset Adobe_CoolType_Utility_MAKEOCF 1.19 0 %%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. %%Version: 1.19 0 systemdict /languagelevel known dup { currentglobal false setglobal } { false } ifelse exch userdict /Adobe_CoolType_Utility 2 copy known { 2 copy get dup maxlength 25 add dict copy } { 25 dict } ifelse put Adobe_CoolType_Utility begin /ct_Level2? exch def /ct_Clone? 1183615869 internaldict dup /CCRun known not exch /eCCRun known not ct_Level2? and or def ct_Level2? { globaldict begin currentglobal true setglobal } if /ct_AddStdCIDMap ct_Level2? { { ((Hex) 57 StartData 0615 1e27 2c39 1c60 d8a8 cc31 fe2b f6e0 7aa3 e541 e21c 60d8 a8c9 c3d0 6d9e 1c60 d8a8 c9c2 02d7 9a1c 60d8 a849 1c60 d8a8 cc36 74f4 1144 b13b 77) 0 () /SubFileDecode filter cvx exec } } { { eexec } } ifelse bind def userdict /cid_extensions known dup { cid_extensions /cid_UpdateDB known and } if { cid_extensions begin /cid_GetCIDSystemInfo { 1 index type /stringtype eq { exch cvn exch } if cid_extensions begin dup load 2 index known { 2 copy cid_GetStatusInfo dup null ne { 1 index load 3 index get dup null eq { pop pop cid_UpdateDB } { exch 1 index /Created get eq { exch pop exch pop } { pop cid_UpdateDB } ifelse } ifelse } { pop cid_UpdateDB } ifelse } { cid_UpdateDB } ifelse end } bind def end } if ct_Level2? { end setglobal } if /ct_UseNativeCapability? systemdict /composefont known def /ct_MakeOCF 35 dict def /ct_Vars 25 dict def /ct_GlyphDirProcs 6 dict def /ct_BuildCharDict 15 dict dup begin /charcode 2 string def /dst_string 1500 string def /nullstring () def /usewidths? true def end def ct_Level2? { setglobal } { pop } ifelse ct_GlyphDirProcs begin /GetGlyphDirectory { systemdict /languagelevel known { pop /CIDFont findresource /GlyphDirectory get } { 1 index /CIDFont findresource /GlyphDirectory get dup type /dicttype eq { dup dup maxlength exch length sub 2 index lt { dup length 2 index add dict copy 2 index /CIDFont findresource/GlyphDirectory 2 index put } if } if exch pop exch pop } ifelse + } def /+ { systemdict /languagelevel known { currentglobal false setglobal 3 dict begin /vm exch def } { 1 dict begin } ifelse /$ exch def systemdict /languagelevel known { vm setglobal /gvm currentglobal def $ gcheck setglobal } if ? { $ begin } if } def /? { $ type /dicttype eq } def /| { userdict /Adobe_CoolType_Data known { Adobe_CoolType_Data /AddWidths? known { currentdict Adobe_CoolType_Data begin begin AddWidths? { Adobe_CoolType_Data /CC 3 index put ? { def } { $ 3 1 roll put } ifelse CC charcode exch 1 index 0 2 index 256 idiv put 1 index exch 1 exch 256 mod put stringwidth 2 array astore currentfont /Widths get exch CC exch put } { ? { def } { $ 3 1 roll put } ifelse } ifelse end end } { ? { def } { $ 3 1 roll put } ifelse } ifelse } { ? { def } { $ 3 1 roll put } ifelse } ifelse } def /! { ? { end } if systemdict /languagelevel known { gvm setglobal } if end } def /: { string currentfile exch readstring pop } executeonly def end ct_MakeOCF begin /ct_cHexEncoding [/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/ c10/c11/c12 /c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/ c23/c24/c25 /c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/ c36/c37/c38 /c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/ c49/c4A/c4B /c4C/c4D/c4E/c4F/c50/c51/c52/c53/c54/c55/c56/c57/c58/c59/c5A/c5B/ c5C/c5D/c5E /c5F/c60/c61/c62/c63/c64/c65/c66/c67/c68/c69/c6A/c6B/c6C/c6D/c6E/ c6F/c70/c71 /c72/c73/c74/c75/c76/c77/c78/c79/c7A/c7B/c7C/c7D/c7E/c7F/c80/c81/ c82/c83/c84 /c85/c86/c87/c88/c89/c8A/c8B/c8C/c8D/c8E/c8F/c90/c91/c92/c93/c94/ c95/c96/c97 /c98/c99/c9A/c9B/c9C/c9D/c9E/c9F/cA0/cA1/cA2/cA3/cA4/cA5/cA6/cA7/ cA8/cA9/cAA /cAB/cAC/cAD/cAE/cAF/cB0/cB1/cB2/cB3/cB4/cB5/cB6/cB7/cB8/cB9/cBA/ cBB/cBC/cBD /cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/ cCE/cCF/cD0 /cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/ cE1/cE2/cE3 /cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/ cF4/cF5/cF6 /cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def /ct_CID_STR_SIZE 8000 def /ct_mkocfStr100 100 string def /ct_defaultFontMtx [.001 0 0 .001 0 0] def /ct_1000Mtx [1000 0 0 1000 0 0] def /ct_raise {exch cvx exch errordict exch get exec stop} bind def /ct_reraise { cvx $error /errorname get (Error: ) print dup ( ) cvs print errordict exch get exec stop } bind def /ct_cvnsi { 1 index add 1 sub 1 exch 0 4 1 roll { 2 index exch get exch 8 bitshift add } for exch pop } bind def /ct_GetInterval { Adobe_CoolType_Utility /ct_BuildCharDict get begin /dst_index 0 def dup dst_string length gt { dup string /dst_string exch def } if 1 index ct_CID_STR_SIZE idiv /arrayIndex exch def 2 index arrayIndex get 2 index arrayIndex ct_CID_STR_SIZE mul sub { dup 3 index add 2 index length le { 2 index getinterval dst_string dst_index 2 index putinterval length dst_index add /dst_index exch def exit } { 1 index length 1 index sub dup 4 1 roll getinterval dst_string dst_index 2 index putinterval pop dup dst_index add /dst_index exch def sub /arrayIndex arrayIndex 1 add def 2 index dup length arrayIndex gt { arrayIndex get } { pop exit } ifelse 0 } ifelse } loop pop pop pop dst_string 0 dst_index getinterval end } bind def ct_Level2? { /ct_resourcestatus currentglobal mark true setglobal { /unknowninstancename /Category resourcestatus } stopped { cleartomark setglobal true } { cleartomark currentglobal not exch setglobal } ifelse { { mark 3 1 roll /Category findresource begin ct_Vars /vm currentglobal put ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec { cleartomark false } { { 3 2 roll pop true } { cleartomark false } ifelse } ifelse ct_Vars /vm get setglobal end } } { { resourcestatus } } ifelse bind def /CIDFont /Category ct_resourcestatus { pop pop } { currentglobal true setglobal /Generic /Category findresource dup length dict copy dup /InstanceType /dicttype put /CIDFont exch /Category defineresource pop setglobal } ifelse ct_UseNativeCapability? { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering (Identity) def /Supplement 0 def end def /CMapName /Identity-H def /CMapVersion 1.000 def /CMapType 1 def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } if } { /ct_Category 2 dict begin /CIDFont 10 dict def /ProcSet 2 dict def currentdict end def /defineresource { ct_Category 1 index 2 copy known { get dup dup maxlength exch length eq { dup length 10 add dict copy ct_Category 2 index 2 index put } if 3 index 3 index put pop exch pop } { pop pop /defineresource /undefined ct_raise } ifelse } bind def /findresource { ct_Category 1 index 2 copy known { get 2 index 2 copy known { get 3 1 roll pop pop} { pop pop /findresource /undefinedresource ct_raise } ifelse } { pop pop /findresource /undefined ct_raise } ifelse } bind def /resourcestatus { ct_Category 1 index 2 copy known { get 2 index known exch pop exch pop { 0 -1 true } { false } ifelse } { pop pop /findresource /undefined ct_raise } ifelse } bind def /ct_resourcestatus /resourcestatus load def } ifelse /ct_CIDInit 2 dict begin /ct_cidfont_stream_init { { dup (Binary) eq { pop null currentfile ct_Level2? { { cid_BYTE_COUNT () /SubFileDecode filter } stopped { pop pop pop } if } if /readstring load exit } if dup (Hex) eq { pop currentfile ct_Level2? { { null exch /ASCIIHexDecode filter /readstring } stopped { pop exch pop (>) exch /readhexstring } if } { (>) exch /readhexstring } ifelse load exit } if /StartData /typecheck ct_raise } loop cid_BYTE_COUNT ct_CID_STR_SIZE le { 2 copy cid_BYTE_COUNT string exch exec pop 1 array dup 3 -1 roll 0 exch put } { cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi dup array exch 2 sub 0 exch 1 exch { 2 copy 5 index ct_CID_STR_SIZE string 6 index exec pop put pop } for 2 index cid_BYTE_COUNT ct_CID_STR_SIZE mod string 3 index exec pop 1 index exch 1 index length 1 sub exch put } ifelse cid_CIDFONT exch /GlyphData exch put 2 index null eq { pop pop pop } { pop /readstring load 1 string exch { 3 copy exec pop dup length 0 eq { pop pop pop pop pop true exit } if 4 index eq { pop pop pop pop false exit } if } loop pop } ifelse } bind def /StartData { mark { currentdict dup /FDArray get 0 get /FontMatrix get 0 get 0.001 eq { dup /CDevProc known not { /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known { get } { pop pop { pop pop pop pop pop 0 -1000 7 index 2 div 880 } } ifelse def } if } { /CDevProc { pop pop pop pop pop 0 1 cid_temp /cid_CIDFONT get /FDArray get 0 get /FontMatrix get 0 get div 7 index 2 div 1 index 0.88 mul } def } ifelse /cid_temp 15 dict def cid_temp begin /cid_CIDFONT exch def 3 copy pop dup /cid_BYTE_COUNT exch def 0 gt { ct_cidfont_stream_init FDArray { /Private get dup /SubrMapOffset known { begin /Subrs SubrCount array def Subrs SubrMapOffset SubrCount SDBytes ct_Level2? { currentdict dup /SubrMapOffset undef dup /SubrCount undef /SDBytes undef } if end /cid_SD_BYTES exch def /cid_SUBR_COUNT exch def /cid_SUBR_MAP_OFFSET exch def /cid_SUBRS exch def cid_SUBR_COUNT 0 gt { GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval 0 cid_SD_BYTES ct_cvnsi 0 1 cid_SUBR_COUNT 1 sub { exch 1 index 1 add cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add GlyphData exch cid_SD_BYTES ct_GetInterval 0 cid_SD_BYTES ct_cvnsi cid_SUBRS 4 2 roll GlyphData exch 4 index 1 index sub ct_GetInterval dup length string copy put } for pop } if } { pop } ifelse } forall } if cleartomark pop pop end CIDFontName currentdict /CIDFont defineresource pop end end } stopped { cleartomark /StartData ct_reraise } if } bind def currentdict end def /ct_saveCIDInit { /CIDInit /ProcSet ct_resourcestatus { true } { /CIDInitC /ProcSet ct_resourcestatus } ifelse { pop pop /CIDInit /ProcSet findresource ct_UseNativeCapability? { pop null } { /CIDInit ct_CIDInit /ProcSet defineresource pop } ifelse } { /CIDInit ct_CIDInit /ProcSet defineresource pop null } ifelse ct_Vars exch /ct_oldCIDInit exch put } bind def /ct_restoreCIDInit { ct_Vars /ct_oldCIDInit get dup null ne { /CIDInit exch /ProcSet defineresource pop } { pop } ifelse } bind def /ct_BuildCharSetUp { 1 index begin CIDFont begin Adobe_CoolType_Utility /ct_BuildCharDict get begin /ct_dfCharCode exch def /ct_dfDict exch def CIDFirstByte ct_dfCharCode add dup CIDCount ge { pop 0 } if /cid exch def { GlyphDirectory cid 2 copy known { get } { pop pop nullstring } ifelse dup length FDBytes sub 0 gt { dup FDBytes 0 ne { 0 FDBytes ct_cvnsi } { pop 0 } ifelse /fdIndex exch def dup length FDBytes sub FDBytes exch getinterval /charstring exch def exit } { pop cid 0 eq { /charstring nullstring def exit } if /cid 0 def } ifelse } loop } def /ct_SetCacheDevice { 0 0 moveto dup stringwidth 3 -1 roll true charpath pathbbox 0 -1000 7 index 2 div 880 setcachedevice2 0 0 moveto } def /ct_CloneSetCacheProc { 1 eq { stringwidth pop -2 div -880 0 -1000 setcharwidth moveto } { usewidths? { currentfont /Widths get cid 2 copy known { get exch pop aload pop } { pop pop stringwidth } ifelse } { stringwidth } ifelse setcharwidth 0 0 moveto } ifelse } def /ct_Type3ShowCharString { ct_FDDict fdIndex 2 copy known { get } { currentglobal 3 1 roll 1 index gcheck setglobal ct_Type1FontTemplate dup maxlength dict copy begin FDArray fdIndex get dup /FontMatrix 2 copy known { get } { pop pop ct_defaultFontMtx } ifelse /FontMatrix exch dup length array copy def /Private get /Private exch def /Widths rootfont /Widths get def /CharStrings 1 dict dup /.notdef dup length string copy put def currentdict end /ct_Type1Font exch definefont dup 5 1 roll put setglobal } ifelse dup /CharStrings get 1 index /Encoding get ct_dfCharCode get charstring put rootfont /WMode 2 copy known { get } { pop pop 0 } ifelse exch 1000 scalefont setfont ct_str1 0 ct_dfCharCode put ct_str1 exch ct_dfSetCacheProc ct_SyntheticBold { currentpoint ct_str1 show newpath moveto ct_str1 true charpath ct_StrokeWidth setlinewidth stroke } { ct_str1 show } ifelse } def /ct_Type4ShowCharString { ct_dfDict ct_dfCharCode charstring FDArray fdIndex get dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not { ct_1000Mtx matrix concatmatrix concat } { pop } ifelse /Private get Adobe_CoolType_Utility /ct_Level2? get not { ct_dfDict /Private 3 -1 roll { put } 1183615869 internaldict /superexec get exec } if 1183615869 internaldict Adobe_CoolType_Utility /ct_Level2? get { 1 index } { 3 index /Private get mark 6 1 roll } ifelse dup /RunInt known { /RunInt get } { pop /CCRun } ifelse get exec Adobe_CoolType_Utility /ct_Level2? get not { cleartomark } if } bind def /ct_BuildCharIncremental { { Adobe_CoolType_Utility /ct_MakeOCF get begin ct_BuildCharSetUp ct_ShowCharString } stopped { stop } if end end end end } bind def /BaseFontNameStr (BF00) def /ct_Type1FontTemplate 14 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] def /FontBBox [-250 -250 1250 1250] def /Encoding ct_cHexEncoding def /PaintType 0 def currentdict end def /BaseFontTemplate 11 dict begin /FontMatrix [0.001 0 0 0.001 0 0] def /FontBBox [-250 -250 1250 1250] def /Encoding ct_cHexEncoding def /BuildChar /ct_BuildCharIncremental load def ct_Clone? { /FontType 3 def /ct_ShowCharString /ct_Type3ShowCharString load def /ct_dfSetCacheProc /ct_CloneSetCacheProc load def /ct_SyntheticBold false def /ct_StrokeWidth 1 def } { /FontType 4 def /Private 1 dict dup /lenIV 4 put def /CharStrings 1 dict dup /.notdef put def /PaintType 0 def /ct_ShowCharString /ct_Type4ShowCharString load def } ifelse /ct_str1 1 string def currentdict end def /BaseFontDictSize BaseFontTemplate length 5 add def /ct_matrixeq { true 0 1 5 { dup 4 index exch get exch 3 index exch get eq and dup not { exit } if } for exch pop exch pop } bind def /ct_makeocf { 15 dict begin exch /WMode exch def exch /FontName exch def /FontType 0 def /FMapType 2 def dup /FontMatrix known { dup /FontMatrix get /FontMatrix exch def } { /FontMatrix matrix def } ifelse /bfCount 1 index /CIDCount get 256 idiv 1 add dup 256 gt { pop 256} if def /Encoding 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for bfCount 1 255 { 2 copy bfCount put pop } for def /FDepVector bfCount dup 256 lt { 1 add } if array def BaseFontTemplate BaseFontDictSize dict copy begin /CIDFont exch def CIDFont /FontBBox known { CIDFont /FontBBox get /FontBBox exch def } if CIDFont /CDevProc known { CIDFont /CDevProc get /CDevProc exch def } if currentdict end BaseFontNameStr 3 (0) putinterval 0 1 bfCount dup 256 eq { 1 sub } if { FDepVector exch 2 index BaseFontDictSize dict copy begin dup /CIDFirstByte exch 256 mul def FontType 3 eq { /ct_FDDict 2 dict def } if currentdict end 1 index 16 BaseFontNameStr 2 2 getinterval cvrs pop BaseFontNameStr exch definefont put } for ct_Clone? { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def } if FontName currentdict end definefont ct_Clone? { gsave dup 1000 scalefont setfont ct_BuildCharDict begin /usewidths? false def currentfont /Widths get begin exch /CIDFont get /GlyphDirectory get { pop dup charcode exch 1 index 0 2 index 256 idiv put 1 index exch 1 exch 256 mod put stringwidth 2 array astore def } forall end /usewidths? true def end grestore } { exch pop } ifelse } bind def /ct_ComposeFont { ct_UseNativeCapability? { 2 index /CMap ct_resourcestatus { pop pop exch pop } { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CMapName 3 index def /CMapVersion 1.000 def /CMapType 1 def exch /WMode exch def /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering CMapName ct_mkocfStr100 cvs (Adobe-) search { pop pop (-) search { dup length string copy exch pop exch pop } { pop (Identity)} ifelse } { pop (Identity) } ifelse def /Supplement 0 def end def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } ifelse composefont } { 3 2 roll pop 0 get /CIDFont findresource ct_makeocf } ifelse } bind def /ct_MakeIdentity { ct_UseNativeCapability? { 1 index /CMap ct_resourcestatus { pop pop } { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CMapName 2 index def /CMapVersion 1.000 def /CMapType 1 def /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering CMapName ct_mkocfStr100 cvs (Adobe-) search { pop pop (-) search { dup length string copy exch pop exch pop } { pop (Identity) } ifelse } { pop (Identity) } ifelse def /Supplement 0 def end def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } ifelse composefont } { exch pop 0 get /CIDFont findresource ct_makeocf } ifelse } bind def currentdict readonly pop end end %%EndResource %%BeginResource: procset Adobe_CoolType_Utility_T42 1.0 0 %%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. %%Version: 1.0 0 userdict /ct_T42Dict 15 dict put ct_T42Dict begin /Is2015? { version cvi 2015 ge } bind def /AllocGlyphStorage { Is2015? { pop } { {string} forall } ifelse } bind def /Type42DictBegin { 25 dict begin /FontName exch def /CharStrings 256 dict begin /.notdef 0 def currentdict end def /Encoding exch def /PaintType 0 def /FontType 42 def /FontMatrix [1 0 0 1 0 0] def 4 array astore cvx /FontBBox exch def /sfnts } bind def /Type42DictEnd { currentdict dup /FontName get exch definefont end ct_T42Dict exch dup /FontName get exch put } bind def /RD {string currentfile exch readstring pop} executeonly def /PrepFor2015 { Is2015? { /GlyphDirectory 16 dict def sfnts 0 get dup 2 index (glyx) putinterval 2 index (locx) putinterval pop pop } { pop pop } ifelse } bind def /AddT42Char { Is2015? { /GlyphDirectory get begin def end pop pop } { /sfnts get 4 index get 3 index 2 index putinterval pop pop pop pop } ifelse } bind def end %%EndResource Adobe_CoolType_Core begin /$Oblique SetSubstituteStrategy end %%BeginResource: procset Adobe_AGM_Image 1.0 0 %%Version: 1.0 0 %%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Image 75 dict dup begin put /Adobe_AGM_Image_Id /Adobe_AGM_Image_1.0_0 def /nd{ null def }bind def /AGMIMG_&image nd /AGMIMG_&colorimage nd /AGMIMG_&imagemask nd /AGMIMG_mbuf () def /AGMIMG_ybuf () def /AGMIMG_kbuf () def /AGMIMG_c 0 def /AGMIMG_m 0 def /AGMIMG_y 0 def /AGMIMG_k 0 def /AGMIMG_tmp nd /AGMIMG_imagestring0 nd /AGMIMG_imagestring1 nd /AGMIMG_imagestring2 nd /AGMIMG_imagestring3 nd /AGMIMG_imagestring4 nd /AGMIMG_imagestring5 nd /AGMIMG_cnt nd /AGMIMG_fsave nd /AGMIMG_colorAry nd /AGMIMG_override nd /AGMIMG_name nd /AGMIMG_maskSource nd /invert_image_samples nd /knockout_image_samples nd /img nd /sepimg nd /devnimg nd /idximg nd /doc_setup { Adobe_AGM_Core begin Adobe_AGM_Image begin /AGMIMG_&image systemdict/image get def /AGMIMG_&imagemask systemdict/imagemask get def /colorimage where{ pop /AGMIMG_&colorimage /colorimage ldf }if end end }def /page_setup { Adobe_AGM_Image begin /AGMIMG_ccimage_exists {/customcolorimage where { pop /Adobe_AGM_OnHost_Seps where { pop false }{ /Adobe_AGM_InRip_Seps where { pop false }{ true }ifelse }ifelse }{ false }ifelse }bdf level2{ /invert_image_samples { Adobe_AGM_Image/AGMIMG_tmp Decode length ddf /Decode [ Decode 1 get Decode 0 get] def }def /knockout_image_samples { Operator/imagemask ne{ /Decode [1 1] def }if }def }{ /invert_image_samples { {1 exch sub} currenttransfer addprocs settransfer }def /knockout_image_samples { { pop 1 } currenttransfer addprocs settransfer }def }ifelse /img /imageormask ldf /sepimg /sep_imageormask ldf /devnimg /devn_imageormask ldf /idximg /indexed_imageormask ldf /_ctype 7 def currentdict{ dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and{ bind }if def }forall }def /page_trailer { end }def /doc_trailer { }def /imageormask_sys { begin save mark level2{ currentdict Operator /imagemask eq{ AGMIMG_&imagemask }{ use_mask { level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation} ifelse }{ AGMIMG_&image }ifelse }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load AGMIMG_&imagemask }{ BitsPerComponent ImageMatrix /DataSource load AGMIMG_&image }ifelse }ifelse cleartomark restore end }def /overprint_plate { currentoverprint { 0 get dup type /nametype eq { dup /DeviceGray eq{ pop AGMCORE_black_plate not }{ /DeviceCMYK eq{ AGMCORE_is_cmyk_sep not }if }ifelse }{ false exch { AGMOHS_sepink eq or } forall not } ifelse }{ pop false }ifelse }def /process_mask_L3 { dup begin /ImageType 1 def end 4 dict begin /DataDict exch def /ImageType 3 def /InterleaveType 3 def /MaskDict 9 dict begin /ImageType 1 def /Width DataDict dup /MaskWidth known {/MaskWidth}{/Width} ifelse get def /Height DataDict dup /MaskHeight known {/MaskHeight}{/Height} ifelse get def /ImageMatrix [Width 0 0 Height neg 0 Height] def /NComponents 1 def /BitsPerComponent 1 def /Decode [0 1] def /DataSource AGMIMG_maskSource def currentdict end def currentdict end }def /use_mask { dup type /dicttype eq { dup /Mask known { dup /Mask get { level3 {true} { dup /MaskWidth known {dup /MaskWidth get 1 index /Width get eq} {true}ifelse exch dup /MaskHeight known {dup /MaskHeight get 1 index /Height get eq}{true}ifelse 3 -1 roll and } ifelse } {false} ifelse } {false} ifelse } {false} ifelse }def /make_line_source { begin MultipleDataSources { [ Decode length 2 div cvi {Width string} repeat ] }{ Width Decode length 2 div mul cvi string }ifelse end }def /datasource_to_str { exch dup type dup /filetype eq { pop exch readstring }{ /arraytype eq { exec exch copy }{ pop }ifelse }ifelse pop }def /masked_image_simulation { 3 dict begin dup make_line_source /line_source xdf /mask_source AGMIMG_maskSource /LZWDecode filter def dup /Width get 8 div ceiling cvi string /mask_str xdf begin gsave 0 1 translate 1 -1 Height div scale 1 1 Height { pop gsave MultipleDataSources { 0 1 DataSource length 1 sub { dup DataSource exch get exch line_source exch get datasource_to_str } for }{ DataSource line_source datasource_to_str } ifelse << /PatternType 1 /PaintProc [ /pop cvx << /ImageType 1 /Width Width /Height 1 /ImageMatrix Width 1.0 sub 1 matrix scale 0.5 0 matrix translate matrix concatmatrix /MultipleDataSources MultipleDataSources /DataSource line_source /BitsPerComponent BitsPerComponent /Decode Decode >> /image cvx ] cvx /BBox [0 0 Width 1] /XStep Width /YStep 1 /PaintType 1 /TilingType 2 >> matrix makepattern set_pattern << /ImageType 1 /Width Width /Height 1 /ImageMatrix Width 1 matrix scale /MultipleDataSources false /DataSource mask_source mask_str readstring pop /BitsPerComponent 1 /Decode [0 1] >> imagemask grestore 0 1 translate } for grestore end end }def /imageormask { begin SkipImageProc { currentdict consumeimagedata } { save mark level2 AGMCORE_host_sep not and{ currentdict Operator /imagemask eq DeviceN_PS2 not and { imagemask }{ AGMCORE_in_rip_sep currentoverprint and currentcolorspace 0 get / DeviceGray eq and{ [/Separation /Black /DeviceGray {}] setcolorspace /Decode [ Decode 1 get Decode 0 get ] def }if use_mask { level3 {process_mask_L3 image}{masked_image_simulation}ifelse }{ DeviceN_NoneName DeviceN_PS2 Indexed_DeviceN level3 not and or or AGMCORE_in_rip_sep and { Names convert_to_process not { 2 dict begin /imageDict xdf /names_index 0 def gsave imageDict write_image_file { Names { dup (None) ne { [/Separation 3 -1 roll /DeviceGray {1 exch sub}] setcolorspace Operator imageDict read_image_file names_index 0 eq {true setoverprint} if /names_index names_index 1 add def }{ pop } ifelse } forall close_image_file } if grestore end }{ Operator /imagemask eq { imagemask }{ image } ifelse } ifelse }{ Operator /imagemask eq { imagemask }{ image } ifelse } ifelse }ifelse }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load /Adobe_AGM_OnHost_Seps where { pop imagemask }{ currentgray 1 ne{ currentdict imageormask_sys }{ currentoverprint not{ 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentdict ignoreimagedata }ifelse }ifelse }ifelse }{ BitsPerComponent ImageMatrix MultipleDataSources{ 0 1 NComponents 1 sub{ DataSource exch get }for }{ /DataSource load }ifelse Operator /colorimage eq{ AGMCORE_host_sep{ MultipleDataSources level2 or NComponents 4 eq and{ AGMCORE_is_cmyk_sep{ MultipleDataSources{ /DataSource [ DataSource 0 get /exec cvx DataSource 1 get /exec cvx DataSource 2 get /exec cvx DataSource 3 get /exec cvx /AGMCORE_get_ink_data cvx ] cvx def }{ /DataSource Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul /DataSource load filter_cmyk 0 () /SubFileDecode filter def }ifelse /Decode [ Decode 0 get Decode 1 get ] def /MultipleDataSources false def /NComponents 1 def /Operator /image def invert_image_samples 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentoverprint not Operator/imagemask eq and{ 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentdict ignoreimagedata }ifelse }ifelse }{ MultipleDataSources NComponents AGMIMG_&colorimage }ifelse }{ true NComponents colorimage }ifelse }{ Operator /image eq{ AGMCORE_host_sep{ /DoImage true def HostSepColorImage{ invert_image_samples }{ AGMCORE_black_plate not Operator/imagemask ne and{ /DoImage false def currentdict ignoreimagedata }if }ifelse 1 AGMCORE_&setgray DoImage {currentdict imageormask_sys} if }{ use_mask { level3 {process_mask_L3 image}{masked_image_simulation}ifelse }{ image }ifelse }ifelse }{ Operator/knockout eq{ pop pop pop pop pop currentcolorspace overprint_plate not{ knockout_unitsq }if }if }ifelse }ifelse }ifelse }ifelse cleartomark restore }ifelse end }def /sep_imageormask { /sep_colorspace_dict AGMCORE_gget begin /MappedCSA CSA map_csa def begin SkipImageProc { currentdict consumeimagedata } { save mark AGMCORE_avoid_L2_sep_space{ /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def }if AGMIMG_ccimage_exists MappedCSA 0 get /DeviceCMYK eq and currentdict/Components known and Name () ne and Name (All) ne and Operator /image eq and AGMCORE_producing_seps not and level2 not and { Width Height BitsPerComponent ImageMatrix [ /DataSource load /exec cvx { 0 1 2 index length 1 sub{ 1 index exch 2 copy get 255 xor put }for } /exec cvx ] cvx bind MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Name findcmykcustomcolor customcolorimage }{ AGMCORE_producing_seps not{ level2{ AGMCORE_avoid_L2_sep_space not currentcolorspace 0 get / Separation ne and{ [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if currentdict imageormask }{ currentdict Operator /imagemask eq{ imageormask }{ sep_imageormask_lev1 }ifelse }ifelse }{ AGMCORE_host_sep{ Operator/knockout eq{ currentdict/ImageMatrix get concat knockout_unitsq }{ currentgray 1 ne{ AGMCORE_is_cmyk_sep Name (All) ne and{ level2{ [ /Separation Name [/DeviceGray] { sep_colorspace_proc AGMCORE_get_ink_data 1 exch sub } bind ] AGMCORE_&setcolorspace /sep_tint AGMCORE_gget AGMCORE_&setcolor currentdict imageormask_sys }{ currentdict Operator /imagemask eq{ imageormask_sys }{ sep_image_lev1_sep }ifelse }ifelse }{ Operator/imagemask ne{ invert_image_samples }if currentdict imageormask_sys }ifelse }{ currentoverprint not Name (All) eq or Operator/imagemask eq and{ currentdict imageormask_sys }{ currentoverprint not { gsave knockout_unitsq grestore }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ currentcolorspace 0 get /Separation ne{ [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if currentoverprint MappedCSA 0 get /DeviceCMYK eq and Name inRip_spot_has_ink not and Name (All) ne and { imageormask_l2_overprint }{ currentdict imageormask }ifelse }ifelse }ifelse }ifelse cleartomark restore }ifelse end end }def /decode_image_sample { 4 1 roll exch dup 5 1 roll sub 2 4 -1 roll exp 1 sub div mul add } bdf /colorSpaceElemCnt { currentcolorspace 0 get dup /DeviceCMYK eq { pop 4 } { /DeviceRGB eq { pop 3 }{ 1 } ifelse } ifelse } bdf /devn_sep_datasource { 1 dict begin /dataSource xdf [ 0 1 dataSource length 1 sub { dup currentdict /dataSource get /exch cvx /get cvx /exec cvx /exch cvx names_index /ne cvx [ /pop cvx ] cvx /if cvx } for ] cvx bind end } bdf /devn_alt_datasource { 11 dict begin /srcDataStrs xdf /dstDataStr xdf /convProc xdf /origcolorSpaceElemCnt xdf /origMultipleDataSources xdf /origBitsPerComponent xdf /origDecode xdf /origDataSource xdf /dsCnt origMultipleDataSources {origDataSource length}{1}ifelse def /samplesNeedDecoding 0 0 1 origDecode length 1 sub { origDecode exch get add } for origDecode length 2 div div dup 1 eq { /decodeDivisor 2 origBitsPerComponent exp 1 sub def } if 2 origBitsPerComponent exp 1 sub ne def [ 0 1 dsCnt 1 sub [ currentdict /origMultipleDataSources get { dup currentdict /origDataSource get exch get dup type }{ currentdict /origDataSource get dup type } ifelse dup /filetype eq { pop currentdict /srcDataStrs get 3 -1 /roll cvx /get cvx / readstring cvx /pop cvx }{ /stringtype ne { /exec cvx } if currentdict /srcDataStrs get /exch cvx 3 -1 /roll cvx /xpt cvx } ifelse ] cvx /for cvx currentdict /srcDataStrs get 0 /get cvx /length cvx 0 /ne cvx [ 0 1 Width 1 sub [ Adobe_AGM_Utils /AGMUTIL_ndx /xddf cvx currentdict /origMultipleDataSources get { 0 1 dsCnt 1 sub [ Adobe_AGM_Utils /AGMUTIL_ndx1 /xddf cvx currentdict /srcDataStrs get /AGMUTIL_ndx1 /load cvx /get cvx / AGMUTIL_ndx /load cvx /get cvx samplesNeedDecoding { currentdict /decodeDivisor known { currentdict /decodeDivisor get /div cvx }{ currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvxs BitsPerComponent /decode_image_sample load /exec cvx } ifelse } if ] cvx /for cvx }{ Adobe_AGM_Utils /AGMUTIL_ndx1 0 /ddf cvx currentdict /srcDataStrs get 0 /get cvx /AGMUTIL_ndx /load cvx currentdict /origDecode get length 2 idiv dup 3 1 /roll cvx /mul cvx /exch cvx /getinterval cvx [ samplesNeedDecoding { currentdict /decodeDivisor known { currentdict /decodeDivisor get /div cvx }{ currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvx BitsPerComponent /decode_image_sample load /exec cvx Adobe_AGM_Utils /AGMUTIL_ndx1 /AGMUTIL_ndx1 /load cvx 1 /add cvx /ddf cvx } ifelse } if ] cvx /forall cvx } ifelse currentdict /convProc get /exec cvx currentdict /origcolorSpaceElemCnt get 1 sub -1 0 [ currentdict /dstDataStr get 3 1 /roll cvx /AGMUTIL_ndx /load cvx currentdict /origcolorSpaceElemCnt get /mul cvx /add cvx /exch cvx currentdict /convProc get /filter_indexed_devn load ne { 255 /mul cvx /cvi cvx } if /put cvx ] cvx /for cvx ] cvx /for cvx currentdict /dstDataStr get ] cvx /if cvx ] cvx bind end } bdf /devn_imageormask { /devicen_colorspace_dict AGMCORE_gget begin /MappedCSA CSA map_csa def 2 dict begin dup dup /dstDataStr exch /Width get colorSpaceElemCnt mul string def /srcDataStrs [ 3 -1 roll begin currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse { Width Decode length 2 div mul cvi string } repeat end ] def begin SkipImageProc { currentdict consumeimagedata } { save mark AGMCORE_producing_seps not { level3 not { Operator /imagemask ne { /DataSource [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse colorSpaceElemCnt /devicen_colorspace_dict AGMCORE_gget / TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def } if }if currentdict imageormask }{ AGMCORE_host_sep{ Names convert_to_process { CSA map_csa 0 get /DeviceCMYK eq { /DataSource Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse 4 /devicen_colorspace_dict AGMCORE_gget /TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx filter_cmyk 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode [1 0] def /DeviceGray setcolorspace currentdict imageormask_sys }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate { /DataSource [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse CSA map_csa 0 get /DeviceRGB eq{3}{1}ifelse / devicen_colorspace_dict AGMCORE_gget /TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def currentdict imageormask_sys } { gsave knockout_unitsq grestore currentdict consumeimagedata } ifelse } ifelse } { /devicen_colorspace_dict AGMCORE_gget /names_index known { Operator/imagemask ne{ MultipleDataSources { /DataSource [ DataSource devn_sep_datasource /exec cvx ] cvx def /MultipleDataSources false def }{ /DataSource /DataSource load dstDataStr srcDataStrs 0 get filter_devn def } ifelse invert_image_samples } if currentdict imageormask_sys }{ currentoverprint not Operator/imagemask eq and{ currentdict imageormask_sys }{ currentoverprint not { gsave knockout_unitsq grestore }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ currentdict imageormask }ifelse }ifelse cleartomark restore }ifelse end end end }def /imageormask_l2_overprint { currentdict currentcmykcolor add add add 0 eq{ currentdict consumeimagedata }{ level3{ currentcmykcolor /AGMIMG_k xdf /AGMIMG_y xdf /AGMIMG_m xdf /AGMIMG_c xdf Operator/imagemask eq{ [/DeviceN [ AGMIMG_c 0 ne {/Cyan} if AGMIMG_m 0 ne {/Magenta} if AGMIMG_y 0 ne {/Yellow} if AGMIMG_k 0 ne {/Black} if ] /DeviceCMYK {}] setcolorspace AGMIMG_c 0 ne {AGMIMG_c} if AGMIMG_m 0 ne {AGMIMG_m} if AGMIMG_y 0 ne {AGMIMG_y} if AGMIMG_k 0 ne {AGMIMG_k} if setcolor }{ /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def [/Indexed [ /DeviceN [ AGMIMG_c 0 ne {/Cyan} if AGMIMG_m 0 ne {/Magenta} if AGMIMG_y 0 ne {/Yellow} if AGMIMG_k 0 ne {/Black} if ] /DeviceCMYK { AGMIMG_k 0 eq {0} if AGMIMG_y 0 eq {0 exch} if AGMIMG_m 0 eq {0 3 1 roll} if AGMIMG_c 0 eq {0 4 1 roll} if } ] 255 { 255 div mark exch dup dup dup AGMIMG_k 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 1 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_y 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 2 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_m 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 3 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_c 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec pop pop pop counttomark 1 roll }{ pop }ifelse counttomark 1 add -1 roll pop } ] setcolorspace }ifelse imageormask_sys }{ write_image_file{ currentcmykcolor 0 ne{ [/Separation /Black /DeviceGray {}] setcolorspace gsave /Black [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 1 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Yellow /DeviceGray {}] setcolorspace gsave /Yellow [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 2 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Magenta /DeviceGray {}] setcolorspace gsave /Magenta [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 3 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Cyan /DeviceGray {}] setcolorspace gsave /Cyan [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore } if close_image_file }{ imageormask }ifelse }ifelse }ifelse } def /indexed_imageormask { begin save mark currentdict AGMCORE_host_sep{ Operator/knockout eq{ /indexed_colorspace_dict AGMCORE_gget dup /CSA known { /CSA get map_csa }{ /CSD get get_csd /Names get } ifelse overprint_plate not{ knockout_unitsq }if }{ Indexed_DeviceN { /devicen_colorspace_dict AGMCORE_gget /names_index known { indexed_image_lev2_sep }{ currentoverprint not{ knockout_unitsq }if currentdict consumeimagedata } ifelse }{ AGMCORE_is_cmyk_sep{ Operator /imagemask eq{ imageormask_sys }{ level2{ indexed_image_lev2_sep }{ indexed_image_lev1_sep }ifelse }ifelse }{ currentoverprint not{ knockout_unitsq }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ level2{ Indexed_DeviceN { /indexed_colorspace_dict AGMCORE_gget begin CSD get_csd begin }{ /indexed_colorspace_dict AGMCORE_gget begin CSA map_csa 0 get /DeviceCMYK eq ps_level 3 ge and ps_version 3015.007 lt and { [/Indexed [/DeviceN [/Cyan /Magenta /Yellow /Black] /DeviceCMYK {}] HiVal Lookup] setcolorspace } if end } ifelse imageormask Indexed_DeviceN { end end } if }{ Operator /imagemask eq{ imageormask }{ indexed_imageormask_lev1 }ifelse }ifelse }ifelse cleartomark restore end }def /indexed_image_lev2_sep { /indexed_colorspace_dict AGMCORE_gget begin begin Indexed_DeviceN not { currentcolorspace dup 1 /DeviceGray put dup 3 currentcolorspace 2 get 1 add string 0 1 2 3 AGMCORE_get_ink_data 4 currentcolorspace 3 get length 1 sub { dup 4 idiv exch currentcolorspace 3 get exch get 255 exch sub 2 index 3 1 roll put }for put setcolorspace } if currentdict Operator /imagemask eq{ AGMIMG_&imagemask }{ use_mask { level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation} ifelse }{ AGMIMG_&image }ifelse }ifelse end end }def /OPIimage { dup type /dicttype ne{ 10 dict begin /DataSource xdf /ImageMatrix xdf /BitsPerComponent xdf /Height xdf /Width xdf /ImageType 1 def /Decode [0 1 def] currentdict end }if dup begin /NComponents 1 cdndf /MultipleDataSources false cdndf /SkipImageProc {false} cdndf /HostSepColorImage false cdndf /Decode [ 0 currentcolorspace 0 get /Indexed eq{ 2 BitsPerComponent exp 1 sub }{ 1 }ifelse ] cdndf /Operator /image cdndf end /sep_colorspace_dict AGMCORE_gget null eq{ imageormask }{ gsave dup begin invert_image_samples end sep_imageormask grestore }ifelse }def /cachemask_level2 { 3 dict begin /LZWEncode filter /WriteFilter xdf /readBuffer 256 string def /ReadFilter currentfile 0 (%EndMask) /SubFileDecode filter /ASCII85Decode filter /RunLengthDecode filter def { ReadFilter readBuffer readstring exch WriteFilter exch writestring not {exit} if }loop WriteFilter closefile end }def /cachemask_level3 { currentfile << /Filter [ /SubFileDecode /ASCII85Decode /RunLengthDecode ] /DecodeParms [ << /EODCount 0 /EODString (%EndMask) >> null null ] /Intent 1 >> /ReusableStreamDecode filter }def /spot_alias { /mapto_sep_imageormask { dup type /dicttype ne{ 12 dict begin /ImageType 1 def /DataSource xdf /ImageMatrix xdf /BitsPerComponent xdf /Height xdf /Width xdf /MultipleDataSources false def }{ begin }ifelse /Decode [/customcolor_tint AGMCORE_gget 0] def /Operator /image def /HostSepColorImage false def /SkipImageProc {false} def currentdict end sep_imageormask }bdf /customcolorimage { Adobe_AGM_Image/AGMIMG_colorAry xddf /customcolor_tint AGMCORE_gget bdict /Name AGMIMG_colorAry 4 get /CSA [ /DeviceCMYK ] /TintMethod /Subtractive /TintProc null /MappedCSA null /NComponents 4 /Components [ AGMIMG_colorAry aload pop pop ] edict setsepcolorspace mapto_sep_imageormask }ndf Adobe_AGM_Image/AGMIMG_&customcolorimage /customcolorimage load put /customcolorimage { Adobe_AGM_Image/AGMIMG_override false put dup 4 get map_alias{ /customcolor_tint AGMCORE_gget exch setsepcolorspace pop mapto_sep_imageormask }{ AGMIMG_&customcolorimage }ifelse }bdf }def /snap_to_device { 6 dict begin matrix currentmatrix dup 0 get 0 eq 1 index 3 get 0 eq and 1 index 1 get 0 eq 2 index 2 get 0 eq and or exch pop { 1 1 dtransform 0 gt exch 0 gt /AGMIMG_xSign? exch def / AGMIMG_ySign? exch def 0 0 transform AGMIMG_ySign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch AGMIMG_xSign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch itransform /AGMIMG_llY exch def /AGMIMG_llX exch def 1 1 transform AGMIMG_ySign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch AGMIMG_xSign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch itransform /AGMIMG_urY exch def /AGMIMG_urX exch def [AGMIMG_urX AGMIMG_llX sub 0 0 AGMIMG_urY AGMIMG_llY sub AGMIMG_llX AGMIMG_llY] concat }{ }ifelse end } def level2 not{ /colorbuf { 0 1 2 index length 1 sub{ dup 2 index exch get 255 exch sub 2 index 3 1 roll put }for }def /tint_image_to_color { begin Width Height BitsPerComponent ImageMatrix /DataSource load end Adobe_AGM_Image begin /AGMIMG_mbuf 0 string def /AGMIMG_ybuf 0 string def /AGMIMG_kbuf 0 string def { colorbuf dup length AGMIMG_mbuf length ne { dup length dup dup /AGMIMG_mbuf exch string def /AGMIMG_ybuf exch string def /AGMIMG_kbuf exch string def } if dup AGMIMG_mbuf copy AGMIMG_ybuf copy AGMIMG_kbuf copy pop } addprocs {AGMIMG_mbuf}{AGMIMG_ybuf}{AGMIMG_kbuf} true 4 colorimage end } def /sep_imageormask_lev1 { begin MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ { 255 mul round cvi GrayLookup exch get } currenttransfer addprocs settransfer currentdict imageormask }{ /sep_colorspace_dict AGMCORE_gget/Components known{ MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Adobe_AGM_Image/AGMIMG_k xddf Adobe_AGM_Image/AGMIMG_y xddf Adobe_AGM_Image/AGMIMG_m xddf Adobe_AGM_Image/AGMIMG_c xddf AGMIMG_y 0.0 eq AGMIMG_m 0.0 eq and AGMIMG_c 0.0 eq and{ {AGMIMG_k mul 1 exch sub} currenttransfer addprocs settransfer currentdict imageormask }{ currentcolortransfer {AGMIMG_k mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_y mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_m mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_c mul 1 exch sub} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }ifelse }{ MappedCSA 0 get /DeviceGray eq { {255 mul round cvi ColorLookup exch get 0 get} currenttransfer addprocs settransfer currentdict imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 2 get} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 1 get} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 0 get} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }ifelse }ifelse }ifelse }ifelse end }def /sep_image_lev1_sep { begin /sep_colorspace_dict AGMCORE_gget/Components known{ Components aload pop Adobe_AGM_Image/AGMIMG_k xddf Adobe_AGM_Image/AGMIMG_y xddf Adobe_AGM_Image/AGMIMG_m xddf Adobe_AGM_Image/AGMIMG_c xddf {AGMIMG_c mul 1 exch sub} {AGMIMG_m mul 1 exch sub} {AGMIMG_y mul 1 exch sub} {AGMIMG_k mul 1 exch sub} }{ {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} }ifelse AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end }def /indexed_imageormask_lev1 { /indexed_colorspace_dict AGMCORE_gget begin begin currentdict MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ {HiVal mul round cvi GrayLookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceGray eq { {HiVal mul round cvi Lookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 2 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 1 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi Lookup exch get HiVal div} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }ifelse }ifelse }ifelse end end }def /indexed_image_lev1_sep { /indexed_colorspace_dict AGMCORE_gget begin begin {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end end }def }if end systemdict /setpacking known { setpacking } if %%EndResource currentdict Adobe_AGM_Utils eq {end} if %%EndProlog %%BeginSetup Adobe_AGM_Utils begin 2 2010 Adobe_AGM_Core/doc_setup get exec Adobe_CoolType_Core/doc_setup get exec Adobe_AGM_Image/doc_setup get exec currentdict Adobe_AGM_Utils eq {end} if %%EndSetup %%Page: Figure-1.eps 1 %%EndPageComments %%BeginPageSetup /currentdistillerparams where {pop currentdistillerparams /CoreDistVersion get 5000 lt} {true} ifelse { 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+ZqqppirsVUbu1ju7Wa2laRY50aN2hkkhkAYUJSWJkkRvBlYEdsVSq18m6Ba6NpmjQRTr&#x A;p2jyxTadEbq6Zo2t2LRKZGlMjxp0EbsUpRaUAGKtXPk3QbrV11W5W6nuUlS4SGS9vHtBNF T05BZt KbUMhUMp9PZhy674qnmKuxVa6K6MjV4sCDQkGh22I3GKpXoflbR9Ee4lsVnae 6Ea3Fzd3VzezMkX L009W6kmkCJ6jFVDUBYmm5xVNsVf/9k= application/postscript % &&end XMP packet marker&& [{ai_metadata_stream_123} <> /PUT AI11_PDFMark5 [/Document 1 dict begin /Metadata {ai_metadata_stream_123} def currentdict end /BDC AI11_PDFMark5 Adobe_AGM_Utils begin Adobe_AGM_Core/page_setup get exec Adobe_CoolType_Core/page_setup get exec Adobe_AGM_Image/page_setup get exec %%EndPageSetup Adobe_AGM_Core/AGMCORE_save save ddf 1 -1 scale 0 -147.355 translate [1 0 0 1 0 0 ] concat % page clip gsave newpath gsave % PSGState 0 0 mo 0 147.355 li 239.866 147.355 li 239.866 0 li clp [1 0 0 1 0 0 ] concat 0.25 lw 1 lc 1 lj 10 ml [] 0 dsh true sadj 59.1065 136.581 mo 59.1065 135.326 li false sop /0 [/DeviceCMYK] add_csa 0 0 0 1 cmyk @ /1 [/DeviceGray] add_csa 0 gry %ADOBeginSubsetFont: Courier Initial %ADOt1write: (1.0.21) 13 dict dup begin /FontType 1 def /FontName /Courier def /FontInfo 6 dict dup begin /Notice (Copyright (c) 1989, 1990, 1991, 1992, 1993, 1996, 1997, 1998 Adobe Systems Incorporated. All Rights Reserved.) def /Weight (Medium) def /ItalicAngle 0 def end def /PaintType 0 def /FontMatrix [0.001 0 0 0.001 0 0] def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 50 /two put dup 53 /five put def /UniqueID 44052 def /FontBBox {-6 -249 639 803} def end systemdict begin dup /Private 12 dict dup begin /|- {def} def /| {put} def /BlueValues [-14 0 572 585 434 448 782 803 626 626] def /OtherBlues [236 243 344 344 -195 -193] def /FamilyBlues [-14 0 572 585 434 448 782 803 626 626] def /FamilyOtherBlues [236 243 344 344 -195 -193] def /StdHW [55] def /StdVW [55] def /password 5839 def /MinFeature {16 16} def /OtherSubrs[{}{}{}{systemdict/internaldict known not{pop 3}{1183615869 systemdict/internaldict get exec dup/startlock known{/startlock get exec}{dup /strtlck known{/strtlck get exec}{pop 3}ifelse}ifelse}ifelse} executeonly]def /Subrs 5 array dup 0 <1C60D8A8CC31FE2BF6E07AA3E541E2> | dup 1 <1C60D8A8C9C3D06D9E> | dup 2 <1C60D8A8C9C202D79A> | dup 3 <1C60D8A849> | dup 4 <1C60D8A8CC3674F41144B13B77> | def put dup /CharStrings 4 dict dup begin /period <1C60D8A8C9B7C3C9E2345CC0A09E843899300080E14D3CB98CC3BBC 0C29D3B013ABE248643B3BE11462117> |- /two <1C60D8A8C9B7C3C9F8C9154D6A8DC0B5A14D7C9764E1D32F8B47964F00 BE2711C767014CAAEB2E2C14E358030C9FA9D12B6C7010D9FFD0B867A8D207AD 713C0EE2BC9C15F4D9BA1730BB0E25C11AFBBF4C94DC5FCE95F531436106A276 DB87479CA7DE307EB04211DF> |- /five <1C60D8A8C9B7C3C9E245A29234478819A3E444EA546AD389DCBB17E4E D8D3D23FAC09DC338224E0E5191FC6394CE0096AE15AE49EAC31D88FCA596B43 41A82E78AFB8A4B4B52E9339B539844548846CCA280B5C94DF10597EBDB19E10 06493CC80FD3B51E7A0BEA570> |- /.notdef <1C60D8A8C9B7C3C91B> |- end put end dup /FontName get exch definefont pop end %ADOEndSubsetFont /HOIGHP+Courier /Courier findfont def /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two 2{/.notdef}repeat / five 202{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 50.1138 144.864 mov (2.5) sh 92.5826 136.581 mo 92.5826 135.326 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin HOIGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /three <1C60D8A8C9B7C3C9ED1E508B97BC436759165685C1C8A9AC53DBA035 7D279BBA03A9C8AC3AC0B2CF89724437FD35A2065C1B4A1543426EF2A131129E 962BBCA2D8570D2A4353FE29E5CF6A9BEA32523F62E62811B6D9DB8667D55032 80FA66E892677423186D7DE88F7481E95BDA9B5E9D14AFCF71B5358FFFF87F71 4B9E5F4AC95DC8326D0CE414BB99F70E66CF963385AD25045EE41881239FD62F 1E54C5D74DC5D2E26D7AEB872659C69719C4ED78A2FCC3E990D024BAA42B20> |- systemdict /gcheck known {setglobal} if end {end} if end HOIGHP+Courier /Encoding get dup 51 /three put pop %ADOEndSubsetFont /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two /three /.notdef / five 202{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 89.6992 144.864 mov (3) sh 126.061 136.581 mo 126.061 135.326 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 117.037 144.864 mov (3.5) sh 159.538 136.581 mo 159.538 135.326 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin HOIGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /four <1C60D8A8C9B7C3C9E2A9C1E2334675B52B245B3FB81B2A53E0971A4EB 43480F24C1049BC43938DE3B4F14FF04140D6104E6959A8144078C86299C6C49 ABE7DCAC2E5F93D01D4092D55FA> |- systemdict /gcheck known {setglobal} if end {end} if end HOIGHP+Courier /Encoding get dup 52 /four put pop %ADOEndSubsetFont /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two /three /four /five 202{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 156.695 144.744 mov (4) sh 193.014 136.581 mo 193.014 135.326 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 184.09 144.744 mov (4.5) sh 226.491 136.581 mo 226.491 135.326 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 223.423 144.744 mov (5) sh 0.125 lw 219.797 136.581 mo 219.797 135.828 li 213.1 136.581 mo 213.1 135.828 li 206.405 136.581 mo 206.405 135.828 li 199.711 136.581 mo 199.711 135.828 li 186.319 136.581 mo 186.319 135.828 li 179.624 136.581 mo 179.624 135.828 li 172.928 136.581 mo 172.928 135.828 li 166.233 136.581 mo 166.233 135.828 li 152.842 136.581 mo 152.842 135.828 li 146.147 136.581 mo 146.147 135.828 li 139.452 136.581 mo 139.452 135.828 li 132.754 136.581 mo 132.754 135.828 li 119.366 136.581 mo 119.366 135.828 li 112.669 136.581 mo 112.669 135.828 li 105.974 136.581 mo 105.974 135.828 li 99.2789 136.581 mo 99.2789 135.828 li 85.8877 136.581 mo 85.8877 135.828 li 79.1929 136.581 mo 79.1929 135.828 li 72.4961 136.581 mo 72.4961 135.828 li 65.8013 136.581 mo 65.8013 135.828 li 52.4097 136.581 mo 52.4097 135.828 li 45.7154 136.581 mo 45.7154 135.828 li 39.0206 136.581 mo 39.0206 135.828 li 32.3238 136.581 mo 32.3238 135.828 li 0 0 0 1 cmyk @ 0.25 lw 25.629 121.064 mo 26.8843 121.064 li 25.629 136.581 mo 226.491 136.581 li @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin HOIGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /zero <1C60D8A8C9B7C3C9E24E60C489D70E052AE9976D225DE2CA07C0A15C7 572C0A27900A47AB835FD764D54712AF293EAC6A992E07FABF9E04B96CB97E81 26ED618067617499E5BB5F3713DE8C872F684616702B331643368CE1A1FA88E0 058FEBDA4A636AA060C2832DA59609247095D9766029BACE17AE02AF0FDD2726 B1401C3> |- systemdict /gcheck known {setglobal} if end {end} if end HOIGHP+Courier /Encoding get dup 48 /zero put pop %ADOEndSubsetFont /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period /.notdef /zero /.notdef /two /three /four /five 202{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 0 123.856 mov -0.000213623 0 50 (0.25) wsh 25.629 105.545 mo 26.8843 105.545 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6 108.338 mov (0.5) sh 25.629 90.0284 mo 26.8843 90.0284 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin HOIGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /seven <1C60D8A8C9B7C3C9E574151636E3B381F86B0B579AF1FA9D57DF37D4 F74244DD4CAC4D72A6FC13721A9E01D0A7A10C79F7E148> |- systemdict /gcheck known {setglobal} if end {end} if end HOIGHP+Courier /Encoding get dup 55 /seven put pop %ADOEndSubsetFont /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period /.notdef /zero /.notdef /two /three /four /five /.notdef /seven 200{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 0 92.8213 mov -0.000213623 0 55 (0.75) wsh 25.629 74.5098 mo 26.8843 74.5098 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin HOIGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /one <1C60D8A8C9B7C3C9E2E7C3E088DBE325C6F98B28B39F1FC9168EDC9CD4 F5243A7BD6F40E9C7EBD025D090D293B869BB7ED0B> |- systemdict /gcheck known {setglobal} if end {end} if end HOIGHP+Courier /Encoding get dup 49 /one put pop %ADOEndSubsetFont /HOIGHP+Courier*1 [ 46{/.notdef}repeat /period /.notdef /zero /one /two /three /four /five /.notdef /seven 200{/.notdef}repeat ] HOIGHP+Courier nfnt HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 17.9302 77.3623 mov (1) sh 25.629 58.9932 mo 26.8843 58.9932 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 0 61.7861 mov -0.000213623 0 50 (1.25) wsh 25.629 43.4747 mo 26.8843 43.4747 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6 46.2676 mov (1.5) sh 25.629 27.9581 mo 26.8843 27.9581 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 0 30.751 mov -0.000213623 0 55 (1.75) wsh 25.629 12.4415 mo 26.8843 12.4415 li 0 0 0 1 cmyk @ 0 gry HOIGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 18.2202 15.2939 mov (2) sh 0.125 lw 25.629 15.545 mo 26.3824 15.545 li 25.629 18.6485 mo 26.3824 18.6485 li 25.629 21.7515 mo 26.3824 21.7515 li 25.629 24.855 mo 26.3824 24.855 li 25.629 31.0616 mo 26.3824 31.0616 li 25.629 34.1651 mo 26.3824 34.1651 li 25.629 37.2681 mo 26.3824 37.2681 li 25.629 40.3716 mo 26.3824 40.3716 li 25.629 46.5801 mo 26.3824 46.5801 li 25.629 49.6836 mo 26.3824 49.6836 li 25.629 52.7867 mo 26.3824 52.7867 li 25.629 55.8902 mo 26.3824 55.8902 li 25.629 62.0967 mo 26.3824 62.0967 li 25.629 65.2002 mo 26.3824 65.2002 li 25.629 68.3033 mo 26.3824 68.3033 li 25.629 71.4068 mo 26.3824 71.4068 li 25.629 77.6133 mo 26.3824 77.6133 li 25.629 80.7168 mo 26.3824 80.7168 li 25.629 83.8223 mo 26.3824 83.8223 li 25.629 86.9249 mo 26.3824 86.9249 li 25.629 93.1319 mo 26.3824 93.1319 li 25.629 96.2354 mo 26.3824 96.2354 li 25.629 99.3389 mo 26.3824 99.3389 li 25.629 102.442 mo 26.3824 102.442 li 25.629 108.649 mo 26.3824 108.649 li 25.629 111.752 mo 26.3824 111.752 li 25.629 114.856 mo 26.3824 114.856 li 25.629 117.959 mo 26.3824 117.959 li 25.629 124.167 mo 26.3824 124.167 li 25.629 127.271 mo 26.3824 127.271 li 25.629 130.375 mo 26.3824 130.375 li 25.629 133.478 mo 26.3824 133.478 li 0 0 0 1 cmyk @ 0.25 lw 25.629 136.581 mo 25.629 12.4415 li @ gsave % PSGState 25.629 12.4415 mo 25.629 136.581 li 226.491 136.581 li 226.491 12.4415 li 25.629 12.4415 li clp 0.5 lw 25.629 118.401 mo 33.7779 117.819 li 38.0181 117.572 li 42.6641 117.346 li 46.9844 117.181 li 51.0098 117.069 li 53.2232 117.023 li 54.3121 117.005 li 55.3165 116.991 li 56.21 116.979 li 57.1944 116.968 li 58.1846 116.962 li 58.7271 116.959 li 59.2334 116.957 li 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%%ViewingOrientation: 1 0 0 1 %%EndDefaults %%BeginProlog %%BeginResource: procset Adobe_AGM_Utils 1.0 0 %%Version: 1.0 0 %%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Utils 68 dict dup begin put /bdf { bind def } bind def /nd{ null def }bdf /xdf { exch def }bdf /ldf { load def }bdf /ddf { put }bdf /xddf { 3 -1 roll put }bdf /xpt { exch put }bdf /ndf { exch dup where{ pop pop pop }{ xdf }ifelse }def /cdndf { exch dup currentdict exch known{ pop pop }{ exch def }ifelse }def /bdict { mark }bdf /edict { counttomark 2 idiv dup dict begin {def} repeat pop currentdict end }def /ps_level /languagelevel where{ pop systemdict /languagelevel get exec }{ 1 }ifelse def /level2 ps_level 2 ge def /level3 ps_level 3 ge def /ps_version {version cvr} stopped { -1 }if def /makereadonlyarray { /packedarray where{ pop packedarray }{ array astore readonly }ifelse }bdf /map_reserved_ink_name { dup type /stringtype eq{ dup /Red eq{ pop (_Red_) }{ dup /Green eq{ pop (_Green_) }{ dup /Blue eq{ pop (_Blue_) }{ dup () cvn eq{ pop (Process) }if }ifelse }ifelse }ifelse }if }bdf /AGMUTIL_GSTATE 22 dict def /get_gstate { AGMUTIL_GSTATE begin /AGMUTIL_GSTATE_clr_spc currentcolorspace def /AGMUTIL_GSTATE_clr_indx 0 def /AGMUTIL_GSTATE_clr_comps 12 array def mark currentcolor counttomark {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 3 -1 roll put /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 add def} repeat pop /AGMUTIL_GSTATE_fnt rootfont def /AGMUTIL_GSTATE_lw currentlinewidth def /AGMUTIL_GSTATE_lc currentlinecap def /AGMUTIL_GSTATE_lj currentlinejoin def /AGMUTIL_GSTATE_ml currentmiterlimit def currentdash /AGMUTIL_GSTATE_do xdf /AGMUTIL_GSTATE_da xdf /AGMUTIL_GSTATE_sa currentstrokeadjust def /AGMUTIL_GSTATE_clr_rnd currentcolorrendering def /AGMUTIL_GSTATE_op currentoverprint def /AGMUTIL_GSTATE_bg currentblackgeneration cvlit def /AGMUTIL_GSTATE_ucr currentundercolorremoval cvlit def currentcolortransfer cvlit /AGMUTIL_GSTATE_gy_xfer xdf cvlit / AGMUTIL_GSTATE_b_xfer xdf cvlit /AGMUTIL_GSTATE_g_xfer xdf cvlit /AGMUTIL_GSTATE_r_xfer xdf /AGMUTIL_GSTATE_ht currenthalftone def /AGMUTIL_GSTATE_flt currentflat def end }def /set_gstate { AGMUTIL_GSTATE begin AGMUTIL_GSTATE_clr_spc setcolorspace AGMUTIL_GSTATE_clr_indx {AGMUTIL_GSTATE_clr_comps AGMUTIL_GSTATE_clr_indx 1 sub get /AGMUTIL_GSTATE_clr_indx AGMUTIL_GSTATE_clr_indx 1 sub def} repeat setcolor AGMUTIL_GSTATE_fnt setfont AGMUTIL_GSTATE_lw setlinewidth AGMUTIL_GSTATE_lc setlinecap AGMUTIL_GSTATE_lj setlinejoin AGMUTIL_GSTATE_ml setmiterlimit AGMUTIL_GSTATE_da AGMUTIL_GSTATE_do setdash AGMUTIL_GSTATE_sa setstrokeadjust AGMUTIL_GSTATE_clr_rnd setcolorrendering AGMUTIL_GSTATE_op setoverprint AGMUTIL_GSTATE_bg cvx setblackgeneration AGMUTIL_GSTATE_ucr cvx setundercolorremoval AGMUTIL_GSTATE_r_xfer cvx AGMUTIL_GSTATE_g_xfer cvx AGMUTIL_GSTATE_b_xfer cvx AGMUTIL_GSTATE_gy_xfer cvx setcolortransfer AGMUTIL_GSTATE_ht /HalftoneType get dup 9 eq exch 100 eq or { currenthalftone /HalftoneType get AGMUTIL_GSTATE_ht /HalftoneType get ne { mark AGMUTIL_GSTATE_ht {sethalftone} stopped cleartomark } if }{ AGMUTIL_GSTATE_ht sethalftone } ifelse AGMUTIL_GSTATE_flt setflat end }def /get_gstate_and_matrix { AGMUTIL_GSTATE begin /AGMUTIL_GSTATE_ctm matrix currentmatrix def end get_gstate }def /set_gstate_and_matrix { set_gstate AGMUTIL_GSTATE begin AGMUTIL_GSTATE_ctm setmatrix end }def /AGMUTIL_str256 256 string def /AGMUTIL_src256 256 string def /AGMUTIL_dst64 64 string def /AGMUTIL_srcLen nd /AGMUTIL_ndx nd /agm_sethalftone { dup begin /_Data load /Thresholds xdf end level3 { sethalftone }{ dup /HalftoneType get 3 eq { sethalftone } {pop} ifelse }ifelse } def /rdcmntline { currentfile AGMUTIL_str256 readline pop (%) anchorsearch {pop} if } bdf /filter_cmyk { dup type /filetype ne{ exch () /SubFileDecode filter } { exch pop } ifelse [ exch { AGMUTIL_src256 readstring pop dup length /AGMUTIL_srcLen exch def /AGMUTIL_ndx 0 def AGMCORE_plate_ndx 4 AGMUTIL_srcLen 1 sub{ 1 index exch get AGMUTIL_dst64 AGMUTIL_ndx 3 -1 roll put /AGMUTIL_ndx AGMUTIL_ndx 1 add def }for pop AGMUTIL_dst64 0 AGMUTIL_ndx getinterval } bind /exec cvx ] cvx } bdf /filter_indexed_devn { cvi Names length mul names_index add Lookup exch get } bdf /filter_devn { 4 dict begin /srcStr xdf /dstStr xdf dup type /filetype ne{ 0 () /SubFileDecode filter }if [ exch [ /devicen_colorspace_dict /AGMCORE_gget cvx /begin cvx currentdict /srcStr get /readstring cvx /pop cvx /dup cvx /length cvx 0 /gt cvx [ Adobe_AGM_Utils /AGMUTIL_ndx 0 /ddf cvx names_index Names length currentdict /srcStr get length 1 sub { 1 /index cvx /exch cvx /get cvx currentdict /dstStr get /AGMUTIL_ndx /load cvx 3 -1 /roll cvx / put cvx Adobe_AGM_Utils /AGMUTIL_ndx /AGMUTIL_ndx /load cvx 1 /add cvx / ddf cvx } for currentdict /dstStr get 0 /AGMUTIL_ndx /load cvx /getinterval cvx ] cvx /if cvx /end cvx ] cvx bind /exec cvx ] cvx end } bdf /AGMUTIL_imagefile nd /read_image_file { AGMUTIL_imagefile 0 setfileposition 10 dict begin /imageDict xdf /imbufLen Width BitsPerComponent mul 7 add 8 idiv def /imbufIdx 0 def /origDataSource imageDict /DataSource get def /origMultipleDataSources imageDict /MultipleDataSources get def /origDecode imageDict /Decode get def /dstDataStr imageDict /Width get colorSpaceElemCnt mul string def /srcDataStrs [ imageDict begin currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse { Width Decode length 2 div mul cvi string } repeat end ] def imageDict /MultipleDataSources known {MultipleDataSources}{false} ifelse { /imbufCnt imageDict /DataSource get length def /imbufs imbufCnt array def 0 1 imbufCnt 1 sub { /imbufIdx xdf imbufs imbufIdx imbufLen string put imageDict /DataSource get imbufIdx [ AGMUTIL_imagefile imbufs imbufIdx get /readstring cvx /pop cvx ] cvx put } for DeviceN_PS2 { imageDict begin /DataSource [ DataSource /devn_sep_datasource cvx ] cvx def /MultipleDataSources false def /Decode [0 1] def end } if }{ /imbuf imbufLen string def Indexed_DeviceN level3 not and DeviceN_NoneName or { imageDict begin /DataSource [AGMUTIL_imagefile Decode BitsPerComponent false 1 / filter_indexed_devn load dstDataStr srcDataStrs devn_alt_datasource / exec cvx] cvx def /Decode [0 1] def end }{ imageDict /DataSource {AGMUTIL_imagefile imbuf readstring pop} put } ifelse } ifelse imageDict exch load exec imageDict /DataSource origDataSource put imageDict /MultipleDataSources origMultipleDataSources put imageDict /Decode origDecode put end } bdf /write_image_file { begin { (AGMUTIL_imagefile) (w+) file } stopped{ false }{ Adobe_AGM_Utils/AGMUTIL_imagefile xddf 2 dict begin /imbufLen Width BitsPerComponent mul 7 add 8 idiv def MultipleDataSources {DataSource 0 get}{DataSource}ifelse type / filetype eq { /imbuf imbufLen string def }if 1 1 Height { pop MultipleDataSources { 0 1 DataSource length 1 sub { DataSource type dup /arraytype eq { pop DataSource exch get exec }{ /filetype eq { DataSource exch get imbuf readstring pop }{ DataSource exch get } ifelse } ifelse AGMUTIL_imagefile exch writestring } for }{ DataSource type dup /arraytype eq { pop DataSource exec }{ /filetype eq { DataSource imbuf readstring pop }{ DataSource } ifelse } ifelse AGMUTIL_imagefile exch writestring } ifelse }for end true }ifelse end } bdf /close_image_file { AGMUTIL_imagefile closefile (AGMUTIL_imagefile) deletefile }def statusdict /product known userdict /AGMP_current_show known not and{ /pstr statusdict /product get def pstr (HP LaserJet 2200) eq pstr (HP LaserJet 4000 Series) eq or pstr (HP LaserJet 4050 Series ) eq or pstr (HP LaserJet 8000 Series) eq or pstr (HP LaserJet 8100 Series) eq or pstr (HP LaserJet 8150 Series) eq or pstr (HP LaserJet 5000 Series) eq or pstr (HP LaserJet 5100 Series) eq or pstr (HP Color LaserJet 4500) eq or pstr (HP Color LaserJet 4600) eq or pstr (HP LaserJet 5Si) eq or pstr (HP LaserJet 1200 Series) eq or pstr (HP LaserJet 1300 Series) eq or pstr (HP LaserJet 4100 Series) eq or { userdict /AGMP_current_show /show load put userdict /show { currentcolorspace 0 get /Pattern eq {false charpath f} {AGMP_current_show} ifelse } put }if currentdict /pstr undef } if /consumeimagedata { begin currentdict /MultipleDataSources known not {/MultipleDataSources false def} if MultipleDataSources { 1 dict begin /flushbuffer Width cvi string def 1 1 Height cvi { pop 0 1 DataSource length 1 sub { DataSource exch get dup type dup /filetype eq { exch flushbuffer readstring pop pop }if /arraytype eq { exec pop }if }for }for end } { /DataSource load type dup /filetype eq { 1 dict begin /flushbuffer Width Decode length 2 div mul cvi string def 1 1 Height { pop DataSource flushbuffer readstring pop pop} for end }if /arraytype eq { 1 1 Height { pop DataSource pop } for }if }ifelse end }bdf /addprocs { 2{/exec load}repeat 3 1 roll [ 5 1 roll ] bind cvx }def /modify_halftone_xfer { currenthalftone dup length dict copy begin currentdict 2 index known{ 1 index load dup length dict copy begin currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end def currentdict end sethalftone }{ currentdict/TransferFunction known{ /TransferFunction load }{ currenttransfer }ifelse addprocs /TransferFunction xdf currentdict end sethalftone pop }ifelse }def /clonearray { dup xcheck exch dup length array exch Adobe_AGM_Core/AGMCORE_tmp -1 ddf { Adobe_AGM_Core/AGMCORE_tmp AGMCORE_tmp 1 add ddf dup type /dicttype eq { AGMCORE_tmp exch clonedict Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf } if dup type /arraytype eq { AGMCORE_tmp exch clonearray Adobe_AGM_Core/AGMCORE_tmp 4 -1 roll ddf } if exch dup AGMCORE_tmp 4 -1 roll put }forall exch {cvx} if }bdf /clonedict { dup length dict begin { dup type /dicttype eq { clonedict } if dup type /arraytype eq { clonearray } if def }forall currentdict end }bdf /DeviceN_PS2 { /currentcolorspace AGMCORE_gget 0 get /DeviceN eq level3 not and } bdf /Indexed_DeviceN { /indexed_colorspace_dict AGMCORE_gget dup null ne { /CSD known }{ pop false } ifelse } bdf /DeviceN_NoneName { /Names where { pop false Names { (None) eq or } forall }{ false }ifelse } bdf /DeviceN_PS2_inRip_seps { /AGMCORE_in_rip_sep where { pop dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get /DeviceN eq level3 not and AGMCORE_in_rip_sep and { /currentcolorspace exch AGMCORE_gput false } { true }ifelse } { true } ifelse } { true } ifelse } bdf /base_colorspace_type { dup type /arraytype eq {0 get} if } bdf /doc_setup{ Adobe_AGM_Utils begin }bdf /doc_trailer{ currentdict Adobe_AGM_Utils eq{ end }if }bdf systemdict /setpacking known { setpacking } if %%EndResource %%BeginResource: procset Adobe_AGM_Core 2.0 0 %%Version: 2.0 0 %%Copyright: Copyright (C) 1997-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Core 216 dict dup begin put /nd{ null def }bind def /Adobe_AGM_Core_Id /Adobe_AGM_Core_2.0_0 def /AGMCORE_str256 256 string def /AGMCORE_save nd /AGMCORE_graphicsave nd /AGMCORE_c 0 def /AGMCORE_m 0 def /AGMCORE_y 0 def /AGMCORE_k 0 def /AGMCORE_cmykbuf 4 array def /AGMCORE_screen [currentscreen] cvx def /AGMCORE_tmp 0 def /AGMCORE_&setgray nd /AGMCORE_&setcolor nd /AGMCORE_&setcolorspace nd /AGMCORE_&setcmykcolor nd /AGMCORE_cyan_plate nd /AGMCORE_magenta_plate nd /AGMCORE_yellow_plate nd /AGMCORE_black_plate nd /AGMCORE_plate_ndx nd /AGMCORE_get_ink_data nd /AGMCORE_is_cmyk_sep nd /AGMCORE_host_sep nd /AGMCORE_avoid_L2_sep_space nd /AGMCORE_distilling nd /AGMCORE_composite_job nd /AGMCORE_producing_seps nd /AGMCORE_ps_level -1 def /AGMCORE_ps_version -1 def /AGMCORE_environ_ok nd /AGMCORE_CSA_cache 0 dict def /AGMCORE_CSD_cache 0 dict def /AGMCORE_pattern_cache 0 dict def /AGMCORE_currentoverprint false def /AGMCORE_deltaX nd /AGMCORE_deltaY nd /AGMCORE_name nd /AGMCORE_sep_special nd /AGMCORE_err_strings 4 dict def /AGMCORE_cur_err nd /AGMCORE_ovp nd /AGMCORE_current_spot_alias false def /AGMCORE_inverting false def /AGMCORE_feature_dictCount nd /AGMCORE_feature_opCount nd /AGMCORE_feature_ctm nd /AGMCORE_ConvertToProcess false def /AGMCORE_Default_CTM matrix def /AGMCORE_Default_PageSize nd /AGMCORE_currentbg nd /AGMCORE_currentucr nd /AGMCORE_gradientcache 32 dict def /AGMCORE_in_pattern false def /knockout_unitsq nd /AGMCORE_CRD_cache where{ pop }{ /AGMCORE_CRD_cache 0 dict def }ifelse /AGMCORE_key_known { where{ /Adobe_AGM_Core_Id known }{ false }ifelse }ndf /flushinput { save 2 dict begin /CompareBuffer 3 -1 roll def /readbuffer 256 string def mark { currentfile readbuffer {readline} stopped {cleartomark mark} { not {pop exit} if CompareBuffer eq {exit} if }ifelse }loop cleartomark end restore }bdf /getspotfunction { AGMCORE_screen exch pop exch pop dup type /dicttype eq{ dup /HalftoneType get 1 eq{ /SpotFunction get }{ dup /HalftoneType get 2 eq{ /GraySpotFunction get }{ pop { abs exch abs 2 copy add 1 gt{ 1 sub dup mul exch 1 sub dup mul add 1 sub }{ dup mul exch dup mul add 1 exch sub }ifelse }bind }ifelse }ifelse }if } def /clp_npth { clip newpath } def /eoclp_npth { eoclip newpath } def /npth_clp { newpath clip } def /add_grad { AGMCORE_gradientcache 3 1 roll put }bdf /exec_grad { AGMCORE_gradientcache exch get exec }bdf /graphic_setup { /AGMCORE_graphicsave save def concat 0 setgray 0 setlinecap 0 setlinejoin 1 setlinewidth [] 0 setdash 10 setmiterlimit newpath false setoverprint false setstrokeadjust Adobe_AGM_Core/spot_alias get exec /Adobe_AGM_Image where { pop Adobe_AGM_Image/spot_alias 2 copy known{ get exec }{ pop pop }ifelse } if 100 dict begin /dictstackcount countdictstack def /showpage {} def mark } def /graphic_cleanup { cleartomark dictstackcount 1 countdictstack 1 sub {end}for end AGMCORE_graphicsave restore } def /compose_error_msg { grestoreall initgraphics /Helvetica findfont 10 scalefont setfont /AGMCORE_deltaY 100 def /AGMCORE_deltaX 310 def clippath pathbbox newpath pop pop 36 add exch 36 add exch moveto 0 AGMCORE_deltaY rlineto AGMCORE_deltaX 0 rlineto 0 AGMCORE_deltaY neg rlineto AGMCORE_deltaX neg 0 rlineto closepath 0 AGMCORE_&setgray gsave 1 AGMCORE_&setgray fill grestore 1 setlinewidth gsave stroke grestore currentpoint AGMCORE_deltaY 15 sub add exch 8 add exch moveto /AGMCORE_deltaY 12 def /AGMCORE_tmp 0 def AGMCORE_err_strings exch get { dup 32 eq { pop AGMCORE_str256 0 AGMCORE_tmp getinterval stringwidth pop currentpoint pop add AGMCORE_deltaX 28 add gt { currentpoint AGMCORE_deltaY sub exch pop clippath pathbbox pop pop pop 44 add exch moveto } if AGMCORE_str256 0 AGMCORE_tmp getinterval show ( ) show 0 1 AGMCORE_str256 length 1 sub { AGMCORE_str256 exch 0 put }for /AGMCORE_tmp 0 def } { AGMCORE_str256 exch AGMCORE_tmp xpt /AGMCORE_tmp AGMCORE_tmp 1 add def } ifelse } forall } bdf /doc_setup{ Adobe_AGM_Core begin /AGMCORE_ps_version xdf /AGMCORE_ps_level xdf errordict /AGM_handleerror known not{ errordict /AGM_handleerror errordict /handleerror get put errordict /handleerror { Adobe_AGM_Core begin $error /newerror get AGMCORE_cur_err null ne and{ $error /newerror false put AGMCORE_cur_err compose_error_msg }if $error /newerror true put end errordict /AGM_handleerror get exec } bind put }if /AGMCORE_environ_ok ps_level AGMCORE_ps_level ge ps_version AGMCORE_ps_version ge and AGMCORE_ps_level -1 eq or def AGMCORE_environ_ok not {/AGMCORE_cur_err /AGMCORE_bad_environ def} if /AGMCORE_&setgray systemdict/setgray get def level2{ /AGMCORE_&setcolor systemdict/setcolor get def /AGMCORE_&setcolorspace systemdict/setcolorspace get def }if /AGMCORE_currentbg currentblackgeneration def /AGMCORE_currentucr currentundercolorremoval def /AGMCORE_distilling /product where{ pop systemdict/setdistillerparams known product (Adobe PostScript Parser) ne and }{ false }ifelse def level2 not{ /xput{ dup load dup length exch maxlength eq{ dup dup load dup length dup 0 eq {pop 1} if 2 mul dict copy def }if load begin def end }def }{ /xput{ load 3 1 roll put }def }ifelse /AGMCORE_GSTATE AGMCORE_key_known not{ /AGMCORE_GSTATE 21 dict def /AGMCORE_tmpmatrix matrix def /AGMCORE_gstack 32 array def /AGMCORE_gstackptr 0 def /AGMCORE_gstacksaveptr 0 def /AGMCORE_gstackframekeys 10 def /AGMCORE_&gsave /gsave ldf /AGMCORE_&grestore /grestore ldf /AGMCORE_&grestoreall /grestoreall ldf /AGMCORE_&save /save ldf /AGMCORE_gdictcopy { begin { def } forall end }def /AGMCORE_gput { AGMCORE_gstack AGMCORE_gstackptr get 3 1 roll put }def /AGMCORE_gget { AGMCORE_gstack AGMCORE_gstackptr get exch get }def /gsave { AGMCORE_&gsave AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core exch /AGMCORE_gstackptr xpt AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def /grestore { AGMCORE_&grestore AGMCORE_gstackptr 1 sub dup AGMCORE_gstacksaveptr lt {1 add} if Adobe_AGM_Core exch /AGMCORE_gstackptr xpt }def /grestoreall { AGMCORE_&grestoreall Adobe_AGM_Core /AGMCORE_gstackptr AGMCORE_gstacksaveptr put }def /save { AGMCORE_&save AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gstackptr 1 add dup 32 ge {limitcheck} if Adobe_AGM_Core begin /AGMCORE_gstackptr exch def /AGMCORE_gstacksaveptr AGMCORE_gstackptr def end AGMCORE_gstack AGMCORE_gstackptr get AGMCORE_gdictcopy }def 0 1 AGMCORE_gstack length 1 sub { AGMCORE_gstack exch AGMCORE_gstackframekeys dict put } for }if level3 /AGMCORE_&sysshfill AGMCORE_key_known not and { /AGMCORE_&sysshfill systemdict/shfill get def /AGMCORE_&usrshfill /shfill load def /AGMCORE_&sysmakepattern systemdict/makepattern get def /AGMCORE_&usrmakepattern /makepattern load def }if /currentcmykcolor [0 0 0 0] AGMCORE_gput /currentstrokeadjust false AGMCORE_gput /currentcolorspace [/DeviceGray] AGMCORE_gput /sep_tint 0 AGMCORE_gput /devicen_tints [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] AGMCORE_gput /sep_colorspace_dict null AGMCORE_gput /devicen_colorspace_dict null AGMCORE_gput /indexed_colorspace_dict null AGMCORE_gput /currentcolor_intent () AGMCORE_gput /customcolor_tint 1 AGMCORE_gput << /MaxPatternItem currentsystemparams /MaxPatternCache get >> setuserparams end }def /page_setup { /setcmykcolor where{ pop Adobe_AGM_Core/AGMCORE_&setcmykcolor /setcmykcolor load put }if Adobe_AGM_Core begin /setcmykcolor { 4 copy AGMCORE_cmykbuf astore /currentcmykcolor exch AGMCORE_gput 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor pop }ndf /currentcmykcolor { /currentcmykcolor AGMCORE_gget aload pop }ndf /setoverprint { pop }ndf /currentoverprint { false }ndf /AGMCORE_deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt def /AGMCORE_cyan_plate 1 0 0 0 test_cmyk_color_plate def /AGMCORE_magenta_plate 0 1 0 0 test_cmyk_color_plate def /AGMCORE_yellow_plate 0 0 1 0 test_cmyk_color_plate def /AGMCORE_black_plate 0 0 0 1 test_cmyk_color_plate def /AGMCORE_plate_ndx AGMCORE_cyan_plate{ 0 }{ AGMCORE_magenta_plate{ 1 }{ AGMCORE_yellow_plate{ 2 }{ AGMCORE_black_plate{ 3 }{ 4 }ifelse }ifelse }ifelse }ifelse def /AGMCORE_have_reported_unsupported_color_space false def /AGMCORE_report_unsupported_color_space { AGMCORE_have_reported_unsupported_color_space false eq { (Warning: Job contains content that cannot be separated with on- host methods. This content appears on the black plate, and knocks out all other plates.) == Adobe_AGM_Core /AGMCORE_have_reported_unsupported_color_space true ddf } if }def /AGMCORE_composite_job AGMCORE_cyan_plate AGMCORE_magenta_plate and AGMCORE_yellow_plate and AGMCORE_black_plate and def /AGMCORE_in_rip_sep /AGMCORE_in_rip_sep where{ pop AGMCORE_in_rip_sep }{ AGMCORE_distilling { false }{ userdict/Adobe_AGM_OnHost_Seps known{ false }{ level2{ currentpagedevice/Separations 2 copy known{ get }{ pop pop false }ifelse }{ false }ifelse }ifelse }ifelse }ifelse def /AGMCORE_producing_seps AGMCORE_composite_job not AGMCORE_in_rip_sep or def /AGMCORE_host_sep AGMCORE_producing_seps AGMCORE_in_rip_sep not and def /AGM_preserve_spots /AGM_preserve_spots where{ pop AGM_preserve_spots }{ AGMCORE_distilling AGMCORE_producing_seps or }ifelse def /AGM_is_distiller_preserving_spotimages { currentdistillerparams/PreserveOverprintSettings known { currentdistillerparams/PreserveOverprintSettings get { currentdistillerparams/ColorConversionStrategy known { currentdistillerparams/ColorConversionStrategy get /LeaveColorUnchanged eq }{ true }ifelse }{ false }ifelse }{ false }ifelse }def /convert_spot_to_process where {pop}{ /convert_spot_to_process { dup map_alias { /Name get exch pop } if dup dup (None) eq exch (All) eq or { pop false }{ AGMCORE_host_sep { gsave 1 0 0 0 setcmykcolor currentgray 1 exch sub 0 1 0 0 setcmykcolor currentgray 1 exch sub 0 0 1 0 setcmykcolor currentgray 1 exch sub 0 0 0 1 setcmykcolor currentgray 1 exch sub add add add 0 eq { pop false }{ false setoverprint 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq }ifelse grestore }{ AGMCORE_distilling { pop AGM_is_distiller_preserving_spotimages not }{ Adobe_AGM_Core/AGMCORE_name xddf false Adobe_AGM_Core/AGMCORE_in_pattern known {Adobe_AGM_Core/ AGMCORE_in_pattern get}{false} ifelse not currentpagedevice/OverrideSeparations known and { currentpagedevice/OverrideSeparations get { /HqnSpots /ProcSet resourcestatus { pop pop pop true }if }if }if { AGMCORE_name /HqnSpots /ProcSet findresource /TestSpot get exec not }{ gsave [/Separation AGMCORE_name /DeviceGray {}]setcolorspace false currentpagedevice/SeparationColorNames 2 copy known { get { AGMCORE_name eq or}forall not }{ pop pop pop true }ifelse grestore }ifelse }ifelse }ifelse }ifelse }def }ifelse /convert_to_process where {pop}{ /convert_to_process { dup length 0 eq { pop false }{ AGMCORE_host_sep { dup true exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch dup (Black) eq 3 -1 roll or {pop} {convert_spot_to_process and}ifelse } forall { true exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch (Black) eq or and }forall not }{pop false}ifelse }{ false exch { dup (Cyan) eq exch dup (Magenta) eq 3 -1 roll or exch dup (Yellow) eq 3 -1 roll or exch dup (Black) eq 3 -1 roll or {pop} {convert_spot_to_process or}ifelse } forall }ifelse }ifelse }def }ifelse /AGMCORE_avoid_L2_sep_space version cvr 2012 lt level2 and AGMCORE_producing_seps not and def /AGMCORE_is_cmyk_sep AGMCORE_cyan_plate AGMCORE_magenta_plate or AGMCORE_yellow_plate or AGMCORE_black_plate or def /AGM_avoid_0_cmyk where{ pop AGM_avoid_0_cmyk }{ AGM_preserve_spots userdict/Adobe_AGM_OnHost_Seps known userdict/Adobe_AGM_InRip_Seps known or not and }ifelse { /setcmykcolor[ { 4 copy add add add 0 eq currentoverprint and{ pop 0.0005 }if }/exec cvx /AGMCORE_&setcmykcolor load dup type/operatortype ne{ /exec cvx }if ]cvx def }if AGMCORE_host_sep{ /setcolortransfer { AGMCORE_cyan_plate{ pop pop pop }{ AGMCORE_magenta_plate{ 4 3 roll pop pop pop }{ AGMCORE_yellow_plate{ 4 2 roll pop pop pop }{ 4 1 roll pop pop pop }ifelse }ifelse }ifelse settransfer } def /AGMCORE_get_ink_data AGMCORE_cyan_plate{ {pop pop pop} }{ AGMCORE_magenta_plate{ {4 3 roll pop pop pop} }{ AGMCORE_yellow_plate{ {4 2 roll pop pop pop} }{ {4 1 roll pop pop pop} }ifelse }ifelse }ifelse def /AGMCORE_RemoveProcessColorNames { 1 dict begin /filtername { dup /Cyan eq 1 index (Cyan) eq or {pop (_cyan_)}if dup /Magenta eq 1 index (Magenta) eq or {pop (_magenta_)}if dup /Yellow eq 1 index (Yellow) eq or {pop (_yellow_)}if dup /Black eq 1 index (Black) eq or {pop (_black_)}if }def dup type /arraytype eq {[exch {filtername}forall]} {filtername}ifelse end }def /AGMCORE_IsSeparationAProcessColor { dup (Cyan) eq exch dup (Magenta) eq exch dup (Yellow) eq exch (Black) eq or or or }def level3 { /AGMCORE_IsCurrentColor { gsave false setoverprint 1 1 1 1 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq grestore }def /AGMCORE_filter_functiondatasource { 5 dict begin /data_in xdf data_in type /stringtype eq { /ncomp xdf /comp xdf /string_out data_in length ncomp idiv string def 0 ncomp data_in length 1 sub { string_out exch dup ncomp idiv exch data_in exch ncomp getinterval comp get 255 exch sub put }for string_out }{ string /string_in xdf /string_out 1 string def /component xdf [ data_in string_in /readstring cvx [component /get cvx 255 /exch cvx /sub cvx string_out /exch cvx 0 /exch cvx /put cvx string_out]cvx [/pop cvx ()]cvx /ifelse cvx ]cvx /ReusableStreamDecode filter }ifelse end }def /AGMCORE_separateShadingFunction { 2 dict begin /paint? xdf /channel xdf begin FunctionType 0 eq { /DataSource channel Range length 2 idiv DataSource AGMCORE_filter_functiondatasource def currentdict /Decode known {/Decode Decode channel 2 mul 2 getinterval def}if paint? not {/Decode [1 1]def}if }if FunctionType 2 eq { paint? { /C0 [C0 channel get 1 exch sub] def /C1 [C1 channel get 1 exch sub] def }{ /C0 [1] def /C1 [1] def }ifelse }if FunctionType 3 eq { /Functions [Functions {channel paint? AGMCORE_separateShadingFunction} forall] def }if currentdict /Range known {/Range [0 1] def}if currentdict end end }def /AGMCORE_separateShading { 3 -1 roll begin currentdict /Function known { currentdict /Background known {[1 index{Background 3 index get 1 exch sub}{1}ifelse]/ Background xdf}if Function 3 1 roll AGMCORE_separateShadingFunction /Function xdf /ColorSpace [/DeviceGray] def }{ ColorSpace dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ /_black_] / DeviceCMYK {}] def }{ ColorSpace dup 1 get AGMCORE_RemoveProcessColorNames 1 exch put }ifelse ColorSpace 0 get /Separation eq { { [1 /exch cvx /sub cvx]cvx }{ [/pop cvx 1]cvx }ifelse ColorSpace 3 3 -1 roll put pop }{ { [exch ColorSpace 1 get length 1 sub exch sub /index cvx 1 / exch cvx /sub cvx ColorSpace 1 get length 1 add 1 /roll cvx ColorSpace 1 get length{/pop cvx} repeat]cvx }{ pop [ColorSpace 1 get length {/pop cvx} repeat cvx 1]cvx }ifelse ColorSpace 3 3 -1 roll bind put }ifelse ColorSpace 2 /DeviceGray put }ifelse end }def /AGMCORE_separateShadingDict { dup /ColorSpace get dup type /arraytype ne {[exch]}if dup 0 get /DeviceCMYK eq { exch begin currentdict AGMCORE_cyan_plate {0 true}if AGMCORE_magenta_plate {1 true}if AGMCORE_yellow_plate {2 true}if AGMCORE_black_plate {3 true}if AGMCORE_plate_ndx 4 eq {0 false}if dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading currentdict end exch }if dup 0 get /Separation eq { exch begin ColorSpace 1 get dup /None ne exch /All ne and { ColorSpace 1 get AGMCORE_IsCurrentColor AGMCORE_plate_ndx 4 lt and ColorSpace 1 get AGMCORE_IsSeparationAProcessColor not and { ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [ /Separation ColorSpace 1 get /DeviceGray [ ColorSpace 3 get /exec cvx 4 AGMCORE_plate_ndx sub -1 /roll cvx 4 1 /roll cvx 3 [/pop cvx]cvx /repeat cvx 1 /exch cvx /sub cvx ]cvx ]def }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { currentdict 0 false AGMCORE_separateShading }if }ifelse }{ currentdict ColorSpace 1 get AGMCORE_IsCurrentColor 0 exch dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading }ifelse }if currentdict end exch }if dup 0 get /DeviceN eq { exch begin ColorSpace 1 get convert_to_process { ColorSpace 2 get dup type /arraytype eq {0 get}if /DeviceCMYK eq { /ColorSpace [ /DeviceN ColorSpace 1 get /DeviceGray [ ColorSpace 3 get /exec cvx 4 AGMCORE_plate_ndx sub -1 /roll cvx 4 1 /roll cvx 3 [/pop cvx]cvx /repeat cvx 1 /exch cvx /sub cvx ]cvx ]def }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { currentdict 0 false AGMCORE_separateShading /ColorSpace [/DeviceGray] def }if }ifelse }{ currentdict false -1 ColorSpace 1 get { AGMCORE_IsCurrentColor { 1 add exch pop true exch exit }if 1 add }forall exch dup not currentoverprint and {/AGMCORE_ignoreshade true def}if AGMCORE_separateShading }ifelse currentdict end exch }if dup 0 get dup /DeviceCMYK eq exch dup /Separation eq exch / DeviceN eq or or not { exch begin ColorSpace dup type /arraytype eq {0 get}if /DeviceGray ne { AGMCORE_report_unsupported_color_space AGMCORE_black_plate not { ColorSpace 0 get /CIEBasedA eq { /ColorSpace [/Separation /_ciebaseda_ /DeviceGray {}] def }if ColorSpace 0 get dup /CIEBasedABC eq exch dup /CIEBasedDEF eq exch /DeviceRGB eq or or { /ColorSpace [/DeviceN [/_red_ /_green_ /_blue_] /DeviceRGB {}] def }if ColorSpace 0 get /CIEBasedDEFG eq { /ColorSpace [/DeviceN [/_cyan_ /_magenta_ /_yellow_ / _black_] /DeviceCMYK {}] }if currentdict 0 false AGMCORE_separateShading }if }if currentdict end exch }if pop dup /AGMCORE_ignoreshade known { begin /ColorSpace [/Separation (None) /DeviceGray {}] def currentdict end }if }def /shfill { clonedict AGMCORE_separateShadingDict dup /AGMCORE_ignoreshade known {pop} {AGMCORE_&sysshfill}ifelse }def /makepattern { exch dup /PatternType get 2 eq { clonedict begin /Shading Shading AGMCORE_separateShadingDict def currentdict end exch AGMCORE_&sysmakepattern }{ exch AGMCORE_&usrmakepattern }ifelse }def }if }if AGMCORE_in_rip_sep{ /setcustomcolor { exch aload pop dup 7 1 roll inRip_spot_has_ink not { 4 {4 index mul 4 1 roll} repeat /DeviceCMYK setcolorspace 6 -2 roll pop pop }{ Adobe_AGM_Core begin /AGMCORE_k xdf /AGMCORE_y xdf /AGMCORE_m xdf /AGMCORE_c xdf end [/Separation 4 -1 roll /DeviceCMYK {dup AGMCORE_c mul exch dup AGMCORE_m mul exch dup AGMCORE_y mul exch AGMCORE_k mul} ] setcolorspace }ifelse setcolor }ndf /setseparationgray { [/Separation (All) /DeviceGray {}] setcolorspace_opt 1 exch sub setcolor }ndf }{ /setseparationgray { AGMCORE_&setgray }ndf }ifelse /findcmykcustomcolor { 5 makereadonlyarray }ndf /setcustomcolor { exch aload pop pop 4 {4 index mul 4 1 roll} repeat setcmykcolor pop }ndf /has_color /colorimage where{ AGMCORE_producing_seps{ pop true }{ systemdict eq }ifelse }{ false }ifelse def /map_index { 1 index mul exch getinterval {255 div} forall } bdf /map_indexed_devn { Lookup Names length 3 -1 roll cvi map_index } bdf /n_color_components { base_colorspace_type dup /DeviceGray eq{ pop 1 }{ /DeviceCMYK eq{ 4 }{ 3 }ifelse }ifelse }bdf level2{ /mo /moveto ldf /li /lineto ldf /cv /curveto ldf /knockout_unitsq { 1 setgray 0 0 1 1 rectfill }def /level2ScreenFreq{ begin 60 HalftoneType 1 eq{ pop Frequency }if HalftoneType 2 eq{ pop GrayFrequency }if HalftoneType 5 eq{ pop Default level2ScreenFreq }if end }def /currentScreenFreq{ currenthalftone level2ScreenFreq }def level2 /setcolorspace AGMCORE_key_known not and{ /AGMCORE_&&&setcolorspace /setcolorspace ldf /AGMCORE_ReplaceMappedColor { dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get dup /Separation eq { pop dup length array copy dup dup 1 get current_spot_alias { dup map_alias { begin /sep_colorspace_dict currentdict AGMCORE_gput pop pop pop [ /Separation Name CSA map_csa dup /MappedCSA xdf /sep_colorspace_proc load ] dup Name end }if }if map_reserved_ink_name 1 xpt }{ /DeviceN eq { dup length array copy dup dup 1 get [ exch { current_spot_alias{ dup map_alias{ /Name get exch pop }if }if map_reserved_ink_name } forall ] 1 xpt }if }ifelse }if }def /setcolorspace { dup type dup /arraytype eq exch /packedarraytype eq or { dup 0 get /Indexed eq { AGMCORE_distilling { /PhotoshopDuotoneList where { pop false }{ true }ifelse }{ true }ifelse { aload pop 3 -1 roll AGMCORE_ReplaceMappedColor 3 1 roll 4 array astore }if }{ AGMCORE_ReplaceMappedColor }ifelse }if DeviceN_PS2_inRip_seps {AGMCORE_&&&setcolorspace} if }def }if }{ /adj { currentstrokeadjust{ transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform }if }def /mo{ adj moveto }def /li{ adj lineto }def /cv{ 6 2 roll adj 6 2 roll adj 6 2 roll adj curveto }def /knockout_unitsq { 1 setgray 8 8 1 [8 0 0 8 0 0] {} image }def /currentstrokeadjust{ /currentstrokeadjust AGMCORE_gget }def /setstrokeadjust{ /currentstrokeadjust exch AGMCORE_gput }def /currentScreenFreq{ currentscreen pop pop }def /setcolorspace { /currentcolorspace exch AGMCORE_gput } def /currentcolorspace { /currentcolorspace AGMCORE_gget } def /setcolor_devicecolor { base_colorspace_type dup /DeviceGray eq{ pop setgray }{ /DeviceCMYK eq{ setcmykcolor }{ setrgbcolor }ifelse }ifelse }def /setcolor { currentcolorspace 0 get dup /DeviceGray ne{ dup /DeviceCMYK ne{ dup /DeviceRGB ne{ dup /Separation eq{ pop currentcolorspace 3 get exec currentcolorspace 2 get }{ dup /Indexed eq{ pop currentcolorspace 3 get dup type /stringtype eq{ currentcolorspace 1 get n_color_components 3 -1 roll map_index }{ exec }ifelse currentcolorspace 1 get }{ /AGMCORE_cur_err /AGMCORE_invalid_color_space def AGMCORE_invalid_color_space }ifelse }ifelse }if }if }if setcolor_devicecolor } def }ifelse /sop /setoverprint ldf /lw /setlinewidth ldf /lc /setlinecap ldf /lj /setlinejoin ldf /ml /setmiterlimit ldf /dsh /setdash ldf /sadj /setstrokeadjust ldf /gry /setgray ldf /rgb /setrgbcolor ldf /cmyk /setcmykcolor ldf /sep /setsepcolor ldf /devn /setdevicencolor ldf /idx /setindexedcolor ldf /colr /setcolor ldf /csacrd /set_csa_crd ldf /sepcs /setsepcolorspace ldf /devncs /setdevicencolorspace ldf /idxcs /setindexedcolorspace ldf /cp /closepath ldf /clp /clp_npth ldf /eclp /eoclp_npth ldf /f /fill ldf /ef /eofill ldf /@ /stroke ldf /nclp /npth_clp ldf /gset /graphic_setup ldf /gcln /graphic_cleanup ldf currentdict{ dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and { bind }if def }forall /currentpagedevice currentpagedevice def /getrampcolor { /indx exch def 0 1 NumComp 1 sub { dup Samples exch get dup type /stringtype eq { indx get } if exch Scaling exch get aload pop 3 1 roll mul add } for ColorSpaceFamily /Separation eq { sep } { ColorSpaceFamily /DeviceN eq { devn } { setcolor }ifelse }ifelse } bind def /sssetbackground { aload pop setcolor } bind def /RadialShade { 40 dict begin /ColorSpaceFamily exch def /background exch def /ext1 exch def /ext0 exch def /BBox exch def /r2 exch def /c2y exch def /c2x exch def /r1 exch def /c1y exch def /c1x exch def /rampdict exch def /setinkoverprint where {pop /setinkoverprint{pop}def}if gsave BBox length 0 gt { newpath BBox 0 get BBox 1 get moveto BBox 2 get BBox 0 get sub 0 rlineto 0 BBox 3 get BBox 1 get sub rlineto BBox 2 get BBox 0 get sub neg 0 rlineto closepath clip newpath } if c1x c2x eq { c1y c2y lt {/theta 90 def}{/theta 270 def} ifelse } { /slope c2y c1y sub c2x c1x sub div def /theta slope 1 atan def c2x c1x lt c2y c1y ge and { /theta theta 180 sub def} if c2x c1x lt c2y c1y lt and { /theta theta 180 add def} if } ifelse gsave clippath c1x c1y translate theta rotate -90 rotate { pathbbox } stopped { 0 0 0 0 } if /yMax exch def /xMax exch def /yMin exch def /xMin exch def grestore xMax xMin eq yMax yMin eq or { grestore end } { /max { 2 copy gt { pop } {exch pop} ifelse } bind def /min { 2 copy lt { pop } {exch pop} ifelse } bind def rampdict begin 40 dict begin background length 0 gt { background sssetbackground gsave clippath fill grestore } if gsave c1x c1y translate theta rotate -90 rotate /c2y c1x c2x sub dup mul c1y c2y sub dup mul add sqrt def /c1y 0 def /c1x 0 def /c2x 0 def ext0 { 0 getrampcolor c2y r2 add r1 sub 0.0001 lt { c1x c1y r1 360 0 arcn pathbbox /aymax exch def /axmax exch def /aymin exch def /axmin exch def /bxMin xMin axmin min def /byMin yMin aymin min def /bxMax xMax axmax max def /byMax yMax aymax max def bxMin byMin moveto bxMax byMin lineto bxMax byMax lineto bxMin byMax lineto bxMin byMin lineto eofill } { c2y r1 add r2 le { c1x c1y r1 0 360 arc fill } { c2x c2y r2 0 360 arc fill r1 r2 eq { /p1x r1 neg def /p1y c1y def /p2x r1 def /p2y c1y def p1x p1y moveto p2x p2y lineto p2x yMin lineto p1x yMin lineto fill } { /AA r2 r1 sub c2y div def /theta AA 1 AA dup mul sub sqrt div 1 atan def /SS1 90 theta add dup sin exch cos div def /p1x r1 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def /p1y p1x SS1 div neg def /SS2 90 theta sub dup sin exch cos div def /p2x r1 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def /p2y p2x SS2 div neg def r1 r2 gt { /L1maxX p1x yMin p1y sub SS1 div add def /L2maxX p2x yMin p2y sub SS2 div add def } { /L1maxX 0 def /L2maxX 0 def }ifelse p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto L1maxX L1maxX p1x sub SS1 mul p1y add lineto fill } ifelse } ifelse } ifelse } if c1x c2x sub dup mul c1y c2y sub dup mul add 0.5 exp 0 dtransform dup mul exch dup mul add 0.5 exp 72 div 0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 1 index 1 index lt { exch } if pop /hires exch def hires mul /numpix exch def /numsteps NumSamples def /rampIndxInc 1 def /subsampling false def numpix 0 ne { NumSamples numpix div 0.5 gt { /numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def /rampIndxInc NumSamples 1 sub numsteps div def /subsampling true def } if } if /xInc c2x c1x sub numsteps div def /yInc c2y c1y sub numsteps div def /rInc r2 r1 sub numsteps div def /cx c1x def /cy c1y def /radius r1 def newpath xInc 0 eq yInc 0 eq rInc 0 eq and and { 0 getrampcolor cx cy radius 0 360 arc stroke NumSamples 1 sub getrampcolor cx cy radius 72 hires div add 0 360 arc 0 setlinewidth stroke } { 0 numsteps { dup subsampling { round cvi } if getrampcolor cx cy radius 0 360 arc /cx cx xInc add def /cy cy yInc add def /radius radius rInc add def cx cy radius 360 0 arcn eofill rampIndxInc add } repeat pop } ifelse ext1 { c2y r2 add r1 lt { c2x c2y r2 0 360 arc fill } { c2y r1 add r2 sub 0.0001 le { c2x c2y r2 360 0 arcn pathbbox /aymax exch def /axmax exch def /aymin exch def /axmin exch def /bxMin xMin axmin min def /byMin yMin aymin min def /bxMax xMax axmax max def /byMax yMax aymax max def bxMin byMin moveto bxMax byMin lineto bxMax byMax lineto bxMin byMax lineto bxMin byMin lineto eofill } { c2x c2y r2 0 360 arc fill r1 r2 eq { /p1x r2 neg def /p1y c2y def /p2x r2 def /p2y c2y def p1x p1y moveto p2x p2y lineto p2x yMax lineto p1x yMax lineto fill } { /AA r2 r1 sub c2y div def /theta AA 1 AA dup mul sub sqrt div 1 atan def /SS1 90 theta add dup sin exch cos div def /p1x r2 SS1 SS1 mul SS1 SS1 mul 1 add div sqrt mul neg def /p1y c2y p1x SS1 div sub def /SS2 90 theta sub dup sin exch cos div def /p2x r2 SS2 SS2 mul SS2 SS2 mul 1 add div sqrt mul def /p2y c2y p2x SS2 div sub def r1 r2 lt { /L1maxX p1x yMax p1y sub SS1 div add def /L2maxX p2x yMax p2y sub SS2 div add def } { /L1maxX 0 def /L2maxX 0 def }ifelse p1x p1y moveto p2x p2y lineto L2maxX L2maxX p2x sub SS2 mul p2y add lineto L1maxX L1maxX p1x sub SS1 mul p1y add lineto fill } ifelse } ifelse } ifelse } if grestore grestore end end end } ifelse } bind def /GenStrips { 40 dict begin /ColorSpaceFamily exch def /background exch def /ext1 exch def /ext0 exch def /BBox exch def /y2 exch def /x2 exch def /y1 exch def /x1 exch def /rampdict exch def /setinkoverprint where {pop /setinkoverprint{pop}def}if gsave BBox length 0 gt { newpath BBox 0 get BBox 1 get moveto BBox 2 get BBox 0 get sub 0 rlineto 0 BBox 3 get BBox 1 get sub rlineto BBox 2 get BBox 0 get sub neg 0 rlineto closepath clip newpath } if x1 x2 eq { y1 y2 lt {/theta 90 def}{/theta 270 def} ifelse } { /slope y2 y1 sub x2 x1 sub div def /theta slope 1 atan def x2 x1 lt y2 y1 ge and { /theta theta 180 sub def} if x2 x1 lt y2 y1 lt and { /theta theta 180 add def} if } ifelse gsave clippath x1 y1 translate theta rotate { pathbbox } stopped { 0 0 0 0 } if /yMax exch def /xMax exch def /yMin exch def /xMin exch def grestore xMax xMin eq yMax yMin eq or { grestore end } { rampdict begin 20 dict begin background length 0 gt { background sssetbackground gsave clippath fill grestore } if gsave x1 y1 translate theta rotate /xStart 0 def /xEnd x2 x1 sub dup mul y2 y1 sub dup mul add 0.5 exp def /ySpan yMax yMin sub def /numsteps NumSamples def /rampIndxInc 1 def /subsampling false def xStart 0 transform xEnd 0 transform 3 -1 roll sub dup mul 3 1 roll sub dup mul add 0.5 exp 72 div 0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt 1 index 1 index lt { exch } if pop mul /numpix exch def numpix 0 ne { NumSamples numpix div 0.5 gt { /numsteps numpix 2 div round cvi dup 1 le { pop 2 } if def /rampIndxInc NumSamples 1 sub numsteps div def /subsampling true def } if } if ext0 { 0 getrampcolor xMin xStart lt { xMin yMin xMin neg ySpan rectfill } if } if /xInc xEnd xStart sub numsteps div def /x xStart def 0 numsteps { dup subsampling { round cvi } if getrampcolor x yMin xInc ySpan rectfill /x x xInc add def rampIndxInc add } repeat pop ext1 { xMax xEnd gt { xEnd yMin xMax xEnd sub ySpan rectfill } if } if grestore grestore end end end } ifelse } bind def }def /page_trailer { end }def /doc_trailer{ }def systemdict /findcolorrendering known{ /findcolorrendering systemdict /findcolorrendering get def }if systemdict /setcolorrendering known{ /setcolorrendering systemdict /setcolorrendering get def }if /test_cmyk_color_plate { gsave setcmykcolor currentgray 1 ne grestore }def /inRip_spot_has_ink { dup Adobe_AGM_Core/AGMCORE_name xddf convert_spot_to_process not }def /map255_to_range { 1 index sub 3 -1 roll 255 div mul add }def /set_csa_crd { /sep_colorspace_dict null AGMCORE_gput begin CSA map_csa setcolorspace_opt set_crd end } def /setsepcolor { /sep_colorspace_dict AGMCORE_gget begin dup /sep_tint exch AGMCORE_gput TintProc end } def /setdevicencolor { /devicen_colorspace_dict AGMCORE_gget begin Names length copy Names length 1 sub -1 0 { /devicen_tints AGMCORE_gget 3 1 roll xpt } for TintProc end } def /sep_colorspace_proc { Adobe_AGM_Core/AGMCORE_tmp xddf /sep_colorspace_dict AGMCORE_gget begin currentdict/Components known{ Components aload pop TintMethod/Lab eq{ 2 {AGMCORE_tmp mul NComponents 1 roll} repeat LMax sub AGMCORE_tmp mul LMax add NComponents 1 roll }{ TintMethod/Subtractive eq{ NComponents{ AGMCORE_tmp mul NComponents 1 roll }repeat }{ NComponents{ 1 sub AGMCORE_tmp mul 1 add NComponents 1 roll } repeat }ifelse }ifelse }{ ColorLookup AGMCORE_tmp ColorLookup length 1 sub mul round cvi get aload pop }ifelse end } def /sep_colorspace_gray_proc { Adobe_AGM_Core/AGMCORE_tmp xddf /sep_colorspace_dict AGMCORE_gget begin GrayLookup AGMCORE_tmp GrayLookup length 1 sub mul round cvi get end } def /sep_proc_name { dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or level2 not and has_color not and{ pop [/DeviceGray] /sep_colorspace_gray_proc }{ /sep_colorspace_proc }ifelse } def /setsepcolorspace { current_spot_alias{ dup begin Name map_alias{ exch pop }if end }if dup /sep_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def Adobe_AGM_Core/AGMCORE_sep_special Name dup () eq exch (All) eq or ddf AGMCORE_avoid_L2_sep_space{ [/Indexed MappedCSA sep_proc_name 255 exch { 255 div } /exec cvx 3 -1 roll [ 4 1 roll load /exec cvx ] cvx ] setcolorspace_opt /TintProc { 255 mul round cvi setcolor }bdf }{ MappedCSA 0 get /DeviceCMYK eq currentdict/Components known and AGMCORE_sep_special not and{ /TintProc [ Components aload pop Name findcmykcustomcolor /exch cvx /setcustomcolor cvx ] cvx bdf }{ AGMCORE_host_sep Name (All) eq and{ /TintProc { 1 exch sub setseparationgray }bdf }{ AGMCORE_in_rip_sep MappedCSA 0 get /DeviceCMYK eq and AGMCORE_host_sep or Name () eq and{ /TintProc [ MappedCSA sep_proc_name exch 0 get /DeviceCMYK eq{ cvx /setcmykcolor cvx }{ cvx /setgray cvx }ifelse ] cvx bdf }{ AGMCORE_producing_seps MappedCSA 0 get dup /DeviceCMYK eq exch / DeviceGray eq or and AGMCORE_sep_special not and{ /TintProc [ /dup cvx MappedCSA sep_proc_name cvx exch 0 get /DeviceGray eq{ 1 /exch cvx /sub cvx 0 0 0 4 -1 /roll cvx }if /Name cvx /findcmykcustomcolor cvx /exch cvx AGMCORE_host_sep{ AGMCORE_is_cmyk_sep /Name cvx /AGMCORE_IsSeparationAProcessColor load /exec cvx /not cvx /and cvx }{ Name inRip_spot_has_ink not }ifelse [ /pop cvx 1 ] cvx /if cvx /setcustomcolor cvx ] cvx bdf }{ /TintProc /setcolor ldf [/Separation Name MappedCSA sep_proc_name load ] setcolorspace_opt }ifelse }ifelse }ifelse }ifelse }ifelse set_crd setsepcolor end } def /additive_blend { 3 dict begin /numarrays xdf /numcolors xdf 0 1 numcolors 1 sub { /c1 xdf 1 0 1 numarrays 1 sub { 1 exch add /index cvx c1 /get cvx /mul cvx }for numarrays 1 add 1 /roll cvx }for numarrays [/pop cvx] cvx /repeat cvx end }def /subtractive_blend { 3 dict begin /numarrays xdf /numcolors xdf 0 1 numcolors 1 sub { /c1 xdf 1 1 0 1 numarrays 1 sub { 1 3 3 -1 roll add /index cvx c1 /get cvx /sub cvx /mul cvx }for /sub cvx numarrays 1 add 1 /roll cvx }for numarrays [/pop cvx] cvx /repeat cvx end }def /exec_tint_transform { /TintProc [ /TintTransform cvx /setcolor cvx ] cvx bdf MappedCSA setcolorspace_opt } bdf /devn_makecustomcolor { 2 dict begin /names_index xdf /Names xdf 1 1 1 1 Names names_index get findcmykcustomcolor /devicen_tints AGMCORE_gget names_index get setcustomcolor Names length {pop} repeat end } bdf /setdevicencolorspace { dup /AliasedColorants known {false}{true}ifelse current_spot_alias and { 6 dict begin /names_index 0 def dup /names_len exch /Names get length def /new_names names_len array def /new_LookupTables names_len array def /alias_cnt 0 def dup /Names get { dup map_alias { exch pop dup /ColorLookup known { dup begin new_LookupTables names_index ColorLookup put end }{ dup /Components known { dup begin new_LookupTables names_index Components put end }{ dup begin new_LookupTables names_index [null null null null] put end } ifelse } ifelse new_names names_index 3 -1 roll /Name get put /alias_cnt alias_cnt 1 add def }{ /name xdf new_names names_index name put dup /LookupTables known { dup begin new_LookupTables names_index LookupTables names_index get put end }{ dup begin new_LookupTables names_index [null null null null] put end } ifelse } ifelse /names_index names_index 1 add def } forall alias_cnt 0 gt { /AliasedColorants true def 0 1 names_len 1 sub { /names_index xdf new_LookupTables names_index get 0 get null eq { dup /Names get names_index get /name xdf name (Cyan) eq name (Magenta) eq name (Yellow) eq name (Black) eq or or or not { /AliasedColorants false def exit } if } if } for AliasedColorants { dup begin /Names new_names def /AliasedColorants true def /LookupTables new_LookupTables def currentdict /TTTablesIdx known not { /TTTablesIdx -1 def } if currentdict /NComponents known not { /NComponents TintMethod /Subtractive eq {4}{3}ifelse def } if end } if }if end } if dup /devicen_colorspace_dict exch AGMCORE_gput begin /MappedCSA CSA map_csa def currentdict /AliasedColorants known { AliasedColorants }{ false } ifelse /TintTransform load type /nulltype eq or { /TintTransform [ 0 1 Names length 1 sub { /TTTablesIdx TTTablesIdx 1 add def dup LookupTables exch get dup 0 get null eq { 1 index Names exch get dup (Cyan) eq { pop exch LookupTables length exch sub /index cvx 0 0 0 } { dup (Magenta) eq { pop exch LookupTables length exch sub /index cvx 0 /exch cvx 0 0 } { (Yellow) eq { exch LookupTables length exch sub /index cvx 0 0 3 -1 /roll cvx 0 } { exch LookupTables length exch sub /index cvx 0 0 0 4 -1 /roll cvx } ifelse } ifelse } ifelse 5 -1 /roll cvx /astore cvx } { dup length 1 sub LookupTables length 4 -1 roll sub 1 add /index cvx /mul cvx /round cvx /cvi cvx /get cvx } ifelse Names length TTTablesIdx add 1 add 1 /roll cvx } for Names length [/pop cvx] cvx /repeat cvx NComponents Names length TintMethod /Subtractive eq { subtractive_blend } { additive_blend } ifelse ] cvx bdf } if AGMCORE_host_sep { Names convert_to_process { exec_tint_transform } { currentdict /AliasedColorants known { AliasedColorants not }{ false } ifelse 5 dict begin /AvoidAliasedColorants xdf /painted? false def /names_index 0 def /names_len Names length def Names { AvoidAliasedColorants { /currentspotalias current_spot_alias def false set_spot_alias } if AGMCORE_is_cmyk_sep { dup (Cyan) eq AGMCORE_cyan_plate and exch dup (Magenta) eq AGMCORE_magenta_plate and exch dup (Yellow) eq AGMCORE_yellow_plate and exch (Black) eq AGMCORE_black_plate and or or or { /devicen_colorspace_dict AGMCORE_gget /TintProc [ Names names_index /devn_makecustomcolor cvx ] cvx ddf /painted? true def } if painted? {exit} if }{ 0 0 0 0 5 -1 roll findcmykcustomcolor 1 setcustomcolor currentgray 0 eq { /devicen_colorspace_dict AGMCORE_gget /TintProc [ Names names_index /devn_makecustomcolor cvx ] cvx ddf /painted? true def exit } if } ifelse AvoidAliasedColorants { currentspotalias set_spot_alias } if /names_index names_index 1 add def } forall painted? { /devicen_colorspace_dict AGMCORE_gget /names_index names_index put }{ /devicen_colorspace_dict AGMCORE_gget /TintProc [ names_len [/pop cvx] cvx /repeat cvx 1 /setseparationgray cvx 0 0 0 0 () /findcmykcustomcolor cvx 0 /setcustomcolor cvx ] cvx ddf } ifelse end } ifelse } { AGMCORE_in_rip_sep { Names convert_to_process not }{ level3 } ifelse { [/DeviceN Names MappedCSA /TintTransform load] setcolorspace_opt /TintProc level3 not AGMCORE_in_rip_sep and { [ Names /length cvx [/pop cvx] cvx /repeat cvx ] cvx bdf }{ /setcolor ldf } ifelse }{ exec_tint_transform } ifelse } ifelse set_crd /AliasedColorants false def end } def /setindexedcolorspace { dup /indexed_colorspace_dict exch AGMCORE_gput begin currentdict /CSD known { CSD get_csd /Names known { CSD get_csd begin currentdict devncs AGMCORE_host_sep{ 4 dict begin /devnCompCnt Names length def /NewLookup HiVal 1 add string def 0 1 HiVal { /tableIndex xdf Lookup dup type /stringtype eq { devnCompCnt tableIndex map_index }{ exec } ifelse setdevicencolor currentgray tableIndex exch HiVal mul cvi NewLookup 3 1 roll put } for [/Indexed currentcolorspace HiVal NewLookup] setcolorspace_opt end }{ level3 { [/Indexed [/DeviceN Names MappedCSA /TintTransform load] HiVal Lookup] setcolorspace_opt }{ [/Indexed MappedCSA HiVal [ Lookup dup type /stringtype eq {/exch cvx CSD get_csd /Names get length dup /mul cvx exch / getinterval cvx {255 div} /forall cvx} {/exec cvx}ifelse /TintTransform load /exec cvx ]cvx ]setcolorspace_opt }ifelse } ifelse end }{ } ifelse set_crd } { /MappedCSA CSA map_csa def AGMCORE_host_sep level2 not and{ 0 0 0 0 setcmykcolor }{ [/Indexed MappedCSA level2 not has_color not and{ dup 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or{ pop [/DeviceGray] }if HiVal GrayLookup }{ HiVal currentdict/RangeArray known{ { /indexed_colorspace_dict AGMCORE_gget begin Lookup exch dup HiVal gt{ pop HiVal }if NComponents mul NComponents getinterval {} forall NComponents 1 sub -1 0{ RangeArray exch 2 mul 2 getinterval aload pop map255_to_range NComponents 1 roll }for end } bind }{ Lookup }ifelse }ifelse ] setcolorspace_opt set_crd }ifelse }ifelse end }def /setindexedcolor { AGMCORE_host_sep { /indexed_colorspace_dict AGMCORE_gget dup /CSD known { begin CSD get_csd begin map_indexed_devn devn end end }{ AGMCORE_gget/Lookup get 4 3 -1 roll map_index pop setcmykcolor } ifelse }{ level3 not AGMCORE_in_rip_sep and /indexed_colorspace_dict AGMCORE_gget /CSD known and { /indexed_colorspace_dict AGMCORE_gget /CSD get get_csd begin map_indexed_devn devn end } { setcolor } ifelse }ifelse } def /ignoreimagedata { currentoverprint not{ gsave dup clonedict begin 1 setgray /Decode [0 1] def /DataSource def /MultipleDataSources false def /BitsPerComponent 8 def currentdict end systemdict /image get exec grestore }if consumeimagedata }def /add_csa { Adobe_AGM_Core begin /AGMCORE_CSA_cache xput end }def /get_csa_by_name { dup type dup /nametype eq exch /stringtype eq or{ Adobe_AGM_Core begin 1 dict begin /name xdf AGMCORE_CSA_cache { 0 get name eq { exit }{ pop } ifelse }forall end end }{ pop } ifelse }def /map_csa { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSA_cache get exch get }if }def /add_csd { Adobe_AGM_Core begin /AGMCORE_CSD_cache xput end }def /get_csd { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_CSD_cache get exch get }if }def /pattern_buf_init { /count get 0 0 put } def /pattern_buf_next { dup /count get dup 0 get dup 3 1 roll 1 add 0 xpt get } def /cachepattern_compress { 5 dict begin currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def /patarray 20 dict def /string_size 16000 def /readbuffer string_size string def currentglobal true setglobal patarray 1 array dup 0 1 put /count xpt setglobal /LZWFilter { exch dup length 0 eq { pop }{ patarray dup length 1 sub 3 -1 roll put } ifelse {string_size}{0}ifelse string } /LZWEncode filter def { ReadFilter readbuffer readstring exch LZWFilter exch writestring not {exit} if } loop LZWFilter closefile patarray end }def /cachepattern { 2 dict begin currentfile exch 0 exch /SubFileDecode filter /ReadFilter exch def /patarray 20 dict def currentglobal true setglobal patarray 1 array dup 0 1 put /count xpt setglobal { ReadFilter 16000 string readstring exch patarray dup length 1 sub 3 -1 roll put not {exit} if } loop patarray dup dup length 1 sub () put end }def /add_pattern { Adobe_AGM_Core begin /AGMCORE_pattern_cache xput end }def /get_pattern { dup type /nametype eq{ Adobe_AGM_Core/AGMCORE_pattern_cache get exch get dup wrap_paintproc }if }def /wrap_paintproc { statusdict /currentfilenameextend known{ begin /OldPaintProc /PaintProc load def /PaintProc { mark exch dup /OldPaintProc get stopped {closefile restore end} if cleartomark } def end } {pop} ifelse } def /make_pattern { dup matrix currentmatrix matrix concatmatrix 0 0 3 2 roll itransform exch 3 index /XStep get 1 index exch 2 copy div cvi mul sub sub exch 3 index /YStep get 1 index exch 2 copy div cvi mul sub sub matrix translate exch matrix concatmatrix 1 index begin BBox 0 get XStep div cvi XStep mul /xshift exch neg def BBox 1 get YStep div cvi YStep mul /yshift exch neg def BBox 0 get xshift add BBox 1 get yshift add BBox 2 get xshift add BBox 3 get yshift add 4 array astore /BBox exch def [ xshift yshift /translate load null /exec load ] dup 3 /PaintProc load put cvx /PaintProc exch def end gsave 0 setgray makepattern grestore }def /set_pattern { dup /PatternType get 1 eq{ dup /PaintType get 1 eq{ currentoverprint sop [/DeviceGray] setcolorspace 0 setgray }if }if setpattern }def /setcolorspace_opt { dup currentcolorspace eq{ pop }{ setcolorspace }ifelse }def /updatecolorrendering { currentcolorrendering/Intent known{ currentcolorrendering/Intent get }{ null }ifelse Intent ne{ false Intent AGMCORE_CRD_cache { exch pop begin dup Intent eq{ currentdict setcolorrendering_opt end exch pop true exch exit }if end } forall pop not{ systemdict /findcolorrendering known{ Intent findcolorrendering pop /ColorRendering findresource dup length dict copy setcolorrendering_opt }if }if }if } def /add_crd { AGMCORE_CRD_cache 3 1 roll put }def /set_crd { AGMCORE_host_sep not level2 and{ currentdict/CRD known{ AGMCORE_CRD_cache CRD get dup null ne{ setcolorrendering_opt }{ pop }ifelse }{ currentdict/Intent known{ updatecolorrendering }if }ifelse currentcolorspace dup type /arraytype eq {0 get}if /DeviceRGB eq { currentdict/UCR known {/UCR}{/AGMCORE_currentucr}ifelse load setundercolorremoval currentdict/BG known {/BG}{/AGMCORE_currentbg}ifelse load setblackgeneration }if }if }def /setcolorrendering_opt { dup currentcolorrendering eq{ pop }{ begin /Intent Intent def currentdict end setcolorrendering }ifelse }def /cpaint_gcomp { convert_to_process Adobe_AGM_Core/AGMCORE_ConvertToProcess xddf Adobe_AGM_Core/AGMCORE_ConvertToProcess get not { (%end_cpaint_gcomp) flushinput }if }def /cpaint_gsep { Adobe_AGM_Core/AGMCORE_ConvertToProcess get { (%end_cpaint_gsep) flushinput }if }def /cpaint_gend { newpath }def /path_rez { dup 0 ne{ AGMCORE_deviceDPI exch div dup 1 lt{ pop 1 }if setflat }{ pop }ifelse }def /set_spot_alias_ary { /AGMCORE_SpotAliasAry where{ pop pop }{ Adobe_AGM_Core/AGMCORE_SpotAliasAry xddf true set_spot_alias }ifelse }def /set_spot_alias { /AGMCORE_SpotAliasAry where{ /AGMCORE_current_spot_alias 3 -1 roll put }{ pop }ifelse }def /current_spot_alias { /AGMCORE_SpotAliasAry where{ /AGMCORE_current_spot_alias get }{ false }ifelse }def /map_alias { /AGMCORE_SpotAliasAry where{ begin /AGMCORE_name xdf false AGMCORE_SpotAliasAry{ dup/Name get AGMCORE_name eq{ save exch /Adobe_AGM_Core currentdict def /CSD get get_csd exch restore exch pop true exit }{ pop }ifelse }forall end }{ pop false }ifelse }bdf /spot_alias { true set_spot_alias /AGMCORE_&setcustomcolor AGMCORE_key_known not { Adobe_AGM_Core/AGMCORE_&setcustomcolor /setcustomcolor load put } if /customcolor_tint 1 AGMCORE_gput Adobe_AGM_Core begin /setcustomcolor { dup /customcolor_tint exch AGMCORE_gput current_spot_alias{ 1 index 4 get map_alias{ mark 3 1 roll setsepcolorspace counttomark 0 ne{ setsepcolor }if pop pop }{ AGMCORE_&setcustomcolor }ifelse }{ AGMCORE_&setcustomcolor }ifelse }bdf end }def /begin_feature { Adobe_AGM_Core/AGMCORE_feature_dictCount countdictstack put count Adobe_AGM_Core/AGMCORE_feature_opCount 3 -1 roll put {Adobe_AGM_Core/AGMCORE_feature_ctm matrix currentmatrix put}if }def /end_feature { 2 dict begin /spd /setpagedevice load def /setpagedevice { get_gstate spd set_gstate } def stopped{$error/newerror false put}if end count Adobe_AGM_Core/AGMCORE_feature_opCount get sub dup 0 gt{{pop} repeat}{pop}ifelse countdictstack Adobe_AGM_Core/AGMCORE_feature_dictCount get sub dup 0 gt{{end}repeat}{pop}ifelse {Adobe_AGM_Core/AGMCORE_feature_ctm get setmatrix}if }def /set_negative { Adobe_AGM_Core begin /AGMCORE_inverting exch def level2{ currentpagedevice/NegativePrint known{ currentpagedevice/NegativePrint get Adobe_AGM_Core/ AGMCORE_inverting get ne{ true begin_feature true{ bdict /NegativePrint Adobe_AGM_Core/AGMCORE_inverting get edict setpagedevice }end_feature }if /AGMCORE_inverting false def }if }if AGMCORE_inverting{ [{1 exch sub}/exec load dup currenttransfer exch]cvx bind settransfer gsave newpath clippath 1 /setseparationgray where{pop setseparationgray}{setgray}ifelse /AGMIRS_&fill where {pop AGMIRS_&fill}{fill} ifelse grestore }if end }def /lw_save_restore_override { /md where { pop md begin initializepage /initializepage{}def /pmSVsetup{} def /endp{}def /pse{}def /psb{}def /orig_showpage where {pop} {/orig_showpage /showpage load def} ifelse /showpage {orig_showpage gR} def end }if }def /pscript_showpage_override { /NTPSOct95 where { begin showpage save /showpage /restore load def /restore {exch pop}def end }if }def /driver_media_override { /md where { pop md /initializepage known { md /initializepage {} put } if md /rC known { md /rC {4{pop}repeat} put } if }if /mysetup where { /mysetup [1 0 0 1 0 0] put }if Adobe_AGM_Core /AGMCORE_Default_CTM matrix currentmatrix put level2 {Adobe_AGM_Core /AGMCORE_Default_PageSize currentpagedevice/ PageSize get put}if }def /driver_check_media_override { /PrepsDict where {pop} { Adobe_AGM_Core /AGMCORE_Default_CTM get matrix currentmatrix ne Adobe_AGM_Core /AGMCORE_Default_PageSize get type /arraytype eq { Adobe_AGM_Core /AGMCORE_Default_PageSize get 0 get currentpagedevice/PageSize get 0 get eq and Adobe_AGM_Core /AGMCORE_Default_PageSize get 1 get currentpagedevice/PageSize get 1 get eq and }if { Adobe_AGM_Core /AGMCORE_Default_CTM get setmatrix }if }ifelse }def AGMCORE_err_strings begin /AGMCORE_bad_environ (Environment not satisfactory for this job. Ensure that the PPD is correct or that the PostScript level requested is supported by this printer. ) def /AGMCORE_color_space_onhost_seps (This job contains colors that will not separate with on-host methods. ) def /AGMCORE_invalid_color_space (This job contains an invalid color space. ) def end end systemdict /setpacking known { setpacking } if %%EndResource %%BeginResource: procset Adobe_CoolType_Core 2.23 0 %%Copyright: Copyright 1997-2003 Adobe Systems Incorporated. All Rights Reserved. %%Version: 2.23 0 10 dict begin /Adobe_CoolType_Passthru currentdict def /Adobe_CoolType_Core_Defined userdict /Adobe_CoolType_Core known def Adobe_CoolType_Core_Defined { /Adobe_CoolType_Core userdict /Adobe_CoolType_Core get def } if userdict /Adobe_CoolType_Core 60 dict dup begin put /Adobe_CoolType_Version 2.23 def /Level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if def Level2? not { /currentglobal false def /setglobal /pop load def /gcheck { pop false } bind def /currentpacking false def /setpacking /pop load def /SharedFontDirectory 0 dict def } if currentpacking true setpacking /@_SaveStackLevels { Adobe_CoolType_Data begin @opStackCountByLevel @opStackLevel 2 copy known not { 2 copy 3 dict dup /args 7 index 5 add array put put get } { get dup /args get dup length 3 index lt { dup length 5 add array exch 1 index exch 0 exch putinterval 1 index exch /args exch put } { pop } ifelse } ifelse begin count 2 sub 1 index lt { pop count 1 sub } if dup /argCount exch def dup 0 gt { exch 1 index 2 add 1 roll args exch 0 exch getinterval astore pop } { pop } ifelse count 1 sub /restCount exch def end /@opStackLevel @opStackLevel 1 add def countdictstack 1 sub @dictStackCountByLevel exch @dictStackLevel exch put /@dictStackLevel @dictStackLevel 1 add def end } bind def /@_RestoreStackLevels { Adobe_CoolType_Data begin /@opStackLevel @opStackLevel 1 sub def @opStackCountByLevel @opStackLevel get begin count restCount sub dup 0 gt { { pop } repeat } { pop } ifelse args 0 argCount getinterval {} forall end /@dictStackLevel @dictStackLevel 1 sub def @dictStackCountByLevel @dictStackLevel get end countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse } bind def /@_PopStackLevels { Adobe_CoolType_Data begin /@opStackLevel @opStackLevel 1 sub def /@dictStackLevel @dictStackLevel 1 sub def end } bind def /@Raise { exch cvx exch errordict exch get exec stop } bind def /@ReRaise { cvx $error /errorname get errordict exch get exec stop } bind def /@Stopped { 0 @#Stopped } bind def /@#Stopped { @_SaveStackLevels stopped { @_RestoreStackLevels true } { @_PopStackLevels false } ifelse } bind def /@Arg { Adobe_CoolType_Data begin @opStackCountByLevel @opStackLevel 1 sub get /args get exch get end } bind def currentglobal true setglobal /CTHasResourceForAllBug Level2? { 1 dict dup begin mark { (*) { pop stop } 128 string /Category resourceforall } stopped cleartomark currentdict eq dup { end } if not } { false } ifelse def /CTHasResourceStatusBug Level2? { mark { /steveamerige /Category resourcestatus } stopped { cleartomark true } { cleartomark currentglobal not } ifelse } { false } ifelse def setglobal /CTResourceStatus { mark 3 1 roll /Category findresource begin ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec { cleartomark false } { { 3 2 roll pop true } { cleartomark false } ifelse } ifelse end } bind def /CTWorkAroundBugs { Level2? { /cid_PreLoad /ProcSet resourcestatus { pop pop currentglobal mark { (*) { dup /CMap CTHasResourceStatusBug { CTResourceStatus } { resourcestatus } ifelse { pop dup 0 eq exch 1 eq or { dup /CMap findresource gcheck setglobal /CMap undefineresource } { pop CTHasResourceForAllBug { exit } { stop } ifelse } ifelse } { pop } ifelse } 128 string /CMap resourceforall } stopped { cleartomark } stopped pop setglobal } if } if } bind def /doc_setup { Adobe_CoolType_Core begin CTWorkAroundBugs /mov /moveto load def /nfnt /newencodedfont load def /mfnt /makefont load def /sfnt /setfont load def /ufnt /undefinefont load def /chp /charpath load def /awsh /awidthshow load def /wsh /widthshow load def /ash /ashow load def /sh /show load def end userdict /Adobe_CoolType_Data 10 dict dup begin /AddWidths? false def /CC 0 def /charcode 2 string def /@opStackCountByLevel 32 dict def /@opStackLevel 0 def /@dictStackCountByLevel 32 dict def /@dictStackLevel 0 def /InVMFontsByCMap 10 dict def /InVMDeepCopiedFonts 10 dict def end put } bind def /doc_trailer { currentdict Adobe_CoolType_Core eq { end } if } bind def /page_setup { Adobe_CoolType_Core begin } bind def /page_trailer { end } bind def /unload { systemdict /languagelevel known { systemdict/languagelevel get 2 ge { userdict/Adobe_CoolType_Core 2 copy known { undef } { pop pop } ifelse } if } if } bind def /ndf { 1 index where { pop pop pop } { dup xcheck { bind } if def } ifelse } def /findfont systemdict begin userdict begin /globaldict where { /globaldict get begin } if dup where pop exch get /globaldict where { pop end } if end end Adobe_CoolType_Core_Defined { /systemfindfont exch def } { /findfont 1 index def /systemfindfont exch def } ifelse /undefinefont { pop } ndf /copyfont { currentglobal 3 1 roll 1 index gcheck setglobal dup null eq { 0 } { dup length } ifelse 2 index length add 1 add dict begin exch { 1 index /FID eq { pop pop } { def } ifelse } forall dup null eq { pop } { { def } forall } ifelse currentdict end exch setglobal } bind def /copyarray { currentglobal exch dup gcheck setglobal dup length array copy exch setglobal } bind def /newencodedfont { currentglobal { SharedFontDirectory 3 index known { SharedFontDirectory 3 index get /FontReferenced known } { false } ifelse } { FontDirectory 3 index known { FontDirectory 3 index get /FontReferenced known } { SharedFontDirectory 3 index known { SharedFontDirectory 3 index get /FontReferenced known } { false } ifelse } ifelse } ifelse dup { 3 index findfont /FontReferenced get 2 index dup type /nametype eq {findfont} if ne { pop false } if } if { pop 1 index findfont /Encoding get exch 0 1 255 { 2 copy get 3 index 3 1 roll put } for pop pop pop } { dup type /nametype eq { findfont } if dup dup maxlength 2 add dict begin exch { 1 index /FID ne {def} {pop pop} ifelse } forall /FontReferenced exch def /Encoding exch dup length array copy def /FontName 1 index dup type /stringtype eq { cvn } if def dup currentdict end definefont def } ifelse } bind def /SetSubstituteStrategy { $SubstituteFont begin dup type /dicttype ne { 0 dict } if currentdict /$Strategies known { exch $Strategies exch 2 copy known { get 2 copy maxlength exch maxlength add dict begin { def } forall { def } forall currentdict dup /$Init known { dup /$Init get exec } if end /$Strategy exch def } { pop pop pop } ifelse } { pop pop } ifelse end } bind def /scff { $SubstituteFont begin dup type /stringtype eq { dup length exch } { null } ifelse /$sname exch def /$slen exch def /$inVMIndex $sname null eq { 1 index $str cvs dup length $slen sub $slen getinterval cvn } { $sname } ifelse def end { findfont } @Stopped { dup length 8 add string exch 1 index 0 (BadFont:) putinterval 1 index exch 8 exch dup length string cvs putinterval cvn { findfont } @Stopped { pop /Courier findfont } if } if $SubstituteFont begin /$sname null def /$slen 0 def /$inVMIndex null def end } bind def /isWidthsOnlyFont { dup /WidthsOnly known { pop pop true } { dup /FDepVector known { /FDepVector get { isWidthsOnlyFont dup { exit } if } forall } { dup /FDArray known { /FDArray get { isWidthsOnlyFont dup { exit } if } forall } { pop } ifelse } ifelse } ifelse } bind def /?str1 256 string def /?set { $SubstituteFont begin /$substituteFound false def /$fontname 4 index def /$doSmartSub false def end 3 index currentglobal false setglobal exch /CompatibleFonts /ProcSet resourcestatus { pop pop /CompatibleFonts /ProcSet findresource begin dup /CompatibleFont currentexception 1 index /CompatibleFont true setexception 1 index /Font resourcestatus { pop pop 3 2 roll setglobal end exch dup findfont /CompatibleFonts /ProcSet findresource begin 3 1 roll exch /CompatibleFont exch setexception end } { 3 2 roll setglobal 1 index exch /CompatibleFont exch setexception end findfont $SubstituteFont /$substituteFound true put } ifelse } { exch setglobal findfont } ifelse $SubstituteFont begin $substituteFound { false (%%[Using embedded font ) print 5 index ?str1 cvs print ( to avoid the font substitution problem noted earlier.]%%\n) print } { dup /FontName known { dup /FontName get $fontname eq 1 index /DistillerFauxFont known not and /currentdistillerparams where { pop false 2 index isWidthsOnlyFont not and } if } { false } ifelse } ifelse exch pop /$doSmartSub true def end { exch pop exch pop exch 2 dict dup /Found 3 index put exch findfont exch } { exch exec exch dup findfont dup /FontType get 3 eq { exch ?str1 cvs dup length 1 sub -1 0 { exch dup 2 index get 42 eq { exch 0 exch getinterval cvn 4 1 roll 3 2 roll pop exit } {exch pop} ifelse }for } { exch pop } ifelse 2 dict dup /Downloaded 6 5 roll put } ifelse dup /FontName 4 index put copyfont definefont pop } bind def /?str2 256 string def /?add { 1 index type /integertype eq { exch true 4 2 } { false 3 1 } ifelse roll 1 index findfont dup /Widths known { Adobe_CoolType_Data /AddWidths? true put gsave dup 1000 scalefont setfont } if /Downloaded known { exec exch { exch ?str2 cvs exch findfont /Downloaded get 1 dict begin /Downloaded 1 index def ? str1 cvs length ?str1 1 index 1 add 3 index putinterval exch length 1 add 1 index add ?str1 2 index (*) putinterval ?str1 0 2 index getinterval cvn findfont ?str1 3 index (+) putinterval 2 dict dup /FontName ?str1 0 6 index getinterval cvn put dup /Downloaded Downloaded put end copyfont dup /FontName get exch definefont pop pop pop } { pop } ifelse } { pop exch { findfont dup /Found get dup length exch ?str1 cvs pop ?str1 1 index (+) putinterval ?str1 1 index 1 add 4 index ?str2 cvs putinterval ?str1 exch 0 exch 5 4 roll ?str2 cvs length 1 add add getinterval cvn 1 dict exch 1 index exch /FontName exch put copyfont dup /FontName get exch definefont pop } { pop } ifelse } ifelse Adobe_CoolType_Data /AddWidths? get { grestore Adobe_CoolType_Data /AddWidths? false put } if } bind def /?sh { currentfont /Downloaded known { exch } if pop } bind def /?chp { currentfont /Downloaded known { pop } { false chp } ifelse } bind def /?mv { currentfont /Downloaded known { moveto pop pop } { pop pop moveto } ifelse } bind def setpacking userdict /$SubstituteFont 25 dict put 1 dict begin /SubstituteFont dup $error exch 2 copy known { get } { pop pop { pop /Courier } bind } ifelse def /currentdistillerparams where dup { pop pop currentdistillerparams /CannotEmbedFontPolicy 2 copy known { get /Error eq } { pop pop false } ifelse } if not { countdictstack array dictstack 0 get begin userdict begin $SubstituteFont begin /$str 128 string def /$fontpat 128 string def /$slen 0 def /$sname null def /$match false def /$fontname null def /$substituteFound false def /$inVMIndex null def /$doSmartSub true def /$depth 0 def /$fontname null def /$italicangle 26.5 def /$dstack null def /$Strategies 10 dict dup begin /$Type3Underprint { currentglobal exch false setglobal 11 dict begin /UseFont exch $WMode 0 ne { dup length dict copy dup /WMode $WMode put /UseFont exch definefont } if def /FontName $fontname dup type /stringtype eq { cvn } if def /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /Encoding 256 array dup 0 1 255 { /.notdef put dup } for pop def /FontBBox [ 0 0 0 0 ] def /CCInfo 7 dict dup begin /cc null def /x 0 def /y 0 def end def /BuildChar { exch begin CCInfo begin 1 string dup 0 3 index put exch pop /cc exch def UseFont 1000 scalefont setfont cc stringwidth /y exch def /x exch def x y setcharwidth $SubstituteFont /$Strategy get /$Underprint get exec 0 0 moveto cc show x y moveto end end } bind def currentdict end exch setglobal } bind def /$GetaTint 2 dict dup begin /$BuildFont { dup /WMode known { dup /WMode get } { 0 } ifelse /$WMode exch def $fontname exch dup /FontName known { dup /FontName get dup type /stringtype eq { cvn } if } { /unnamedfont } ifelse exch Adobe_CoolType_Data /InVMDeepCopiedFonts get 1 index /FontName get known { pop Adobe_CoolType_Data /InVMDeepCopiedFonts get 1 index get null copyfont } { $deepcopyfont } ifelse exch 1 index exch /FontBasedOn exch put dup /FontName $fontname dup type /stringtype eq { cvn } if put definefont Adobe_CoolType_Data /InVMDeepCopiedFonts get begin dup /FontBasedOn get 1 index def end } bind def /$Underprint { gsave x abs y abs gt { /y 1000 def } { /x -1000 def 500 120 translate } ifelse Level2? { [ /Separation (All) /DeviceCMYK { 0 0 0 1 pop } ] setcolorspace } { 0 setgray } ifelse 10 setlinewidth x .8 mul [ 7 3 ] { y mul 8 div 120 sub x 10 div exch moveto 0 y 4 div neg rlineto dup 0 rlineto 0 y 4 div rlineto closepath gsave Level2? { .2 setcolor } { .8 setgray } ifelse fill grestore stroke } forall pop grestore } bind def end def /$Oblique 1 dict dup begin /$BuildFont { currentglobal exch dup gcheck setglobal null copyfont begin /FontBasedOn currentdict /FontName known { FontName dup type /stringtype eq { cvn } if } { /unnamedfont } ifelse def /FontName $fontname dup type /stringtype eq { cvn } if def /currentdistillerparams where { pop } { /FontInfo currentdict /FontInfo known { FontInfo null copyfont } { 2 dict } ifelse dup begin /ItalicAngle $italicangle def /FontMatrix FontMatrix [ 1 0 ItalicAngle dup sin exch cos div 1 0 0 ] matrix concatmatrix readonly end 4 2 roll def def } ifelse FontName currentdict end definefont exch setglobal } bind def end def /$None 1 dict dup begin /$BuildFont {} bind def end def end def /$Oblique SetSubstituteStrategy /$findfontByEnum { dup type /stringtype eq { cvn } if dup /$fontname exch def $sname null eq { $str cvs dup length $slen sub $slen getinterval } { pop $sname } ifelse $fontpat dup 0 (fonts/*) putinterval exch 7 exch putinterval /$match false def $SubstituteFont /$dstack countdictstack array dictstack put mark { $fontpat 0 $slen 7 add getinterval { /$match exch def exit } $str filenameforall } stopped { cleardictstack currentdict true $SubstituteFont /$dstack get { exch { 1 index eq { pop false } { true } ifelse } { begin false } ifelse } forall pop } if cleartomark /$slen 0 def $match false ne { $match (fonts/) anchorsearch pop pop cvn } { /Courier } ifelse } bind def /$ROS 1 dict dup begin /Adobe 4 dict dup begin /Japan1 [ /Ryumin-Light /HeiseiMin-W3 /GothicBBB-Medium /HeiseiKakuGo-W5 /HeiseiMaruGo-W4 /Jun101-Light ] def /Korea1 [ /HYSMyeongJo-Medium /HYGoThic-Medium ] def /GB1 [ /STSong-Light /STHeiti-Regular ] def /CNS1 [ /MKai-Medium /MHei-Medium ] def end def end def /$cmapname null def /$deepcopyfont { dup /FontType get 0 eq { 1 dict dup /FontName /copied put copyfont begin /FDepVector FDepVector copyarray 0 1 2 index length 1 sub { 2 copy get $deepcopyfont dup /FontName /copied put /copied exch definefont 3 copy put pop pop } for def currentdict end } { $Strategies /$Type3Underprint get exec } ifelse } bind def /$buildfontname { dup /CIDFont findresource /CIDSystemInfo get begin Registry length Ordering length Supplement 8 string cvs 3 copy length 2 add add add string dup 5 1 roll dup 0 Registry putinterval dup 4 index (-) putinterval dup 4 index 1 add Ordering putinterval 4 2 roll add 1 add 2 copy (-) putinterval end 1 add 2 copy 0 exch getinterval $cmapname $fontpat cvs exch anchorsearch { pop pop 3 2 roll putinterval cvn /$cmapname exch def } { pop pop pop pop pop } ifelse length $str 1 index (-) putinterval 1 add $str 1 index $cmapname $fontpat cvs putinterval $cmapname length add $str exch 0 exch getinterval cvn } bind def /$findfontByROS { /$fontname exch def $ROS Registry 2 copy known { get Ordering 2 copy known { get } { pop pop [] } ifelse } { pop pop [] } ifelse false exch { dup /CIDFont resourcestatus { pop pop save 1 index /CIDFont findresource dup /WidthsOnly known { dup /WidthsOnly get } { false } ifelse exch pop exch restore { pop } { exch pop true exit } ifelse } { pop } ifelse } forall { $str cvs $buildfontname } { false (*) { save exch dup /CIDFont findresource dup /WidthsOnly known { dup /WidthsOnly get not } { true } ifelse exch /CIDSystemInfo get dup /Registry get Registry eq exch /Ordering get Ordering eq and and { exch restore exch pop true exit } { pop restore } ifelse } $str /CIDFont resourceforall { $buildfontname } { $fontname $findfontByEnum } ifelse } ifelse } bind def end end currentdict /$error known currentdict /languagelevel known and dup { pop $error /SubstituteFont known } if dup { $error } { Adobe_CoolType_Core } ifelse begin { /SubstituteFont /CMap /Category resourcestatus { pop pop { $SubstituteFont begin /$substituteFound true def dup length $slen gt $sname null ne or $slen 0 gt and { $sname null eq { dup $str cvs dup length $slen sub $slen getinterval cvn } { $sname } ifelse Adobe_CoolType_Data /InVMFontsByCMap get 1 index 2 copy known { get false exch { pop currentglobal { GlobalFontDirectory 1 index known { exch pop true exit } { pop } ifelse } { FontDirectory 1 index known { exch pop true exit } { GlobalFontDirectory 1 index known { exch pop true exit } { pop } ifelse } ifelse } ifelse } forall } { pop pop false } ifelse { exch pop exch pop } { dup /CMap resourcestatus { pop pop dup /$cmapname exch def /CMap findresource /CIDSystemInfo get { def } forall $findfontByROS } { 128 string cvs dup (-) search { 3 1 roll search { 3 1 roll pop { dup cvi } stopped { pop pop pop pop pop $findfontByEnum } { 4 2 roll pop pop exch length exch 2 index length 2 index sub exch 1 sub -1 0 { $str cvs dup length 4 index 0 4 index 4 3 roll add getinterval exch 1 index exch 3 index exch putinterval dup /CMap resourcestatus { pop pop 4 1 roll pop pop pop dup /$cmapname exch def /CMap findresource /CIDSystemInfo get { def } forall $findfontByROS true exit } { pop } ifelse } for dup type /booleantype eq { pop } { pop pop pop $findfontByEnum } ifelse } ifelse } { pop pop pop $findfontByEnum } ifelse } { pop pop $findfontByEnum } ifelse } ifelse } ifelse } { //SubstituteFont exec } ifelse /$slen 0 def end } } { { $SubstituteFont begin /$substituteFound true def dup length $slen gt $sname null ne or $slen 0 gt and { $findfontByEnum } { //SubstituteFont exec } ifelse end } } ifelse bind readonly def Adobe_CoolType_Core /scfindfont /systemfindfont load put } { /scfindfont { $SubstituteFont begin dup systemfindfont dup /FontName known { dup /FontName get dup 3 index ne } { /noname true } ifelse dup { /$origfontnamefound 2 index def /$origfontname 4 index def /$substituteFound true def } if exch pop { $slen 0 gt $sname null ne 3 index length $slen gt or and { pop dup $findfontByEnum findfont dup maxlength 1 add dict begin { 1 index /FID eq { pop pop } { def } ifelse } forall currentdict end definefont dup /FontName known { dup /FontName get } { null } ifelse $origfontnamefound ne { $origfontname $str cvs print ( substitution revised, using ) print dup /FontName known { dup /FontName get } { (unspecified font) } ifelse $str cvs print (.\n) print } if } { exch pop } ifelse } { exch pop } ifelse end } bind def } ifelse end end Adobe_CoolType_Core_Defined not { Adobe_CoolType_Core /findfont { $SubstituteFont begin $depth 0 eq { /$fontname 1 index dup type /stringtype ne { $str cvs } if def /$substituteFound false def } if /$depth $depth 1 add def end scfindfont $SubstituteFont begin /$depth $depth 1 sub def $substituteFound $depth 0 eq and { $inVMIndex null ne { dup $inVMIndex $AddInVMFont } if $doSmartSub { currentdict /$Strategy known { $Strategy /$BuildFont get exec } if } if } if end } bind put } if } if end /$AddInVMFont { exch /FontName 2 copy known { get 1 dict dup begin exch 1 index gcheck def end exch Adobe_CoolType_Data /InVMFontsByCMap get exch $DictAdd } { pop pop pop } ifelse } bind def /$DictAdd { 2 copy known not { 2 copy 4 index length dict put } if Level2? not { 2 copy get dup maxlength exch length 4 index length add lt 2 copy get dup length 4 index length add exch maxlength 1 index lt { 2 mul dict begin 2 copy get { forall } def 2 copy currentdict put end } { pop } ifelse } if get begin { def } forall end } bind def end end %%EndResource %%BeginResource: procset Adobe_CoolType_Utility_MAKEOCF 1.19 0 %%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. %%Version: 1.19 0 systemdict /languagelevel known dup { currentglobal false setglobal } { false } ifelse exch userdict /Adobe_CoolType_Utility 2 copy known { 2 copy get dup maxlength 25 add dict copy } { 25 dict } ifelse put Adobe_CoolType_Utility begin /ct_Level2? exch def /ct_Clone? 1183615869 internaldict dup /CCRun known not exch /eCCRun known not ct_Level2? and or def ct_Level2? { globaldict begin currentglobal true setglobal } if /ct_AddStdCIDMap ct_Level2? { { ((Hex) 57 StartData 0615 1e27 2c39 1c60 d8a8 cc31 fe2b f6e0 7aa3 e541 e21c 60d8 a8c9 c3d0 6d9e 1c60 d8a8 c9c2 02d7 9a1c 60d8 a849 1c60 d8a8 cc36 74f4 1144 b13b 77) 0 () /SubFileDecode filter cvx exec } } { { eexec } } ifelse bind def userdict /cid_extensions known dup { cid_extensions /cid_UpdateDB known and } if { cid_extensions begin /cid_GetCIDSystemInfo { 1 index type /stringtype eq { exch cvn exch } if cid_extensions begin dup load 2 index known { 2 copy cid_GetStatusInfo dup null ne { 1 index load 3 index get dup null eq { pop pop cid_UpdateDB } { exch 1 index /Created get eq { exch pop exch pop } { pop cid_UpdateDB } ifelse } ifelse } { pop cid_UpdateDB } ifelse } { cid_UpdateDB } ifelse end } bind def end } if ct_Level2? { end setglobal } if /ct_UseNativeCapability? systemdict /composefont known def /ct_MakeOCF 35 dict def /ct_Vars 25 dict def /ct_GlyphDirProcs 6 dict def /ct_BuildCharDict 15 dict dup begin /charcode 2 string def /dst_string 1500 string def /nullstring () def /usewidths? true def end def ct_Level2? { setglobal } { pop } ifelse ct_GlyphDirProcs begin /GetGlyphDirectory { systemdict /languagelevel known { pop /CIDFont findresource /GlyphDirectory get } { 1 index /CIDFont findresource /GlyphDirectory get dup type /dicttype eq { dup dup maxlength exch length sub 2 index lt { dup length 2 index add dict copy 2 index /CIDFont findresource/GlyphDirectory 2 index put } if } if exch pop exch pop } ifelse + } def /+ { systemdict /languagelevel known { currentglobal false setglobal 3 dict begin /vm exch def } { 1 dict begin } ifelse /$ exch def systemdict /languagelevel known { vm setglobal /gvm currentglobal def $ gcheck setglobal } if ? { $ begin } if } def /? { $ type /dicttype eq } def /| { userdict /Adobe_CoolType_Data known { Adobe_CoolType_Data /AddWidths? known { currentdict Adobe_CoolType_Data begin begin AddWidths? { Adobe_CoolType_Data /CC 3 index put ? { def } { $ 3 1 roll put } ifelse CC charcode exch 1 index 0 2 index 256 idiv put 1 index exch 1 exch 256 mod put stringwidth 2 array astore currentfont /Widths get exch CC exch put } { ? { def } { $ 3 1 roll put } ifelse } ifelse end end } { ? { def } { $ 3 1 roll put } ifelse } ifelse } { ? { def } { $ 3 1 roll put } ifelse } ifelse } def /! { ? { end } if systemdict /languagelevel known { gvm setglobal } if end } def /: { string currentfile exch readstring pop } executeonly def end ct_MakeOCF begin /ct_cHexEncoding [/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/ c10/c11/c12 /c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/ c23/c24/c25 /c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/ c36/c37/c38 /c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/ c49/c4A/c4B /c4C/c4D/c4E/c4F/c50/c51/c52/c53/c54/c55/c56/c57/c58/c59/c5A/c5B/ c5C/c5D/c5E /c5F/c60/c61/c62/c63/c64/c65/c66/c67/c68/c69/c6A/c6B/c6C/c6D/c6E/ c6F/c70/c71 /c72/c73/c74/c75/c76/c77/c78/c79/c7A/c7B/c7C/c7D/c7E/c7F/c80/c81/ c82/c83/c84 /c85/c86/c87/c88/c89/c8A/c8B/c8C/c8D/c8E/c8F/c90/c91/c92/c93/c94/ c95/c96/c97 /c98/c99/c9A/c9B/c9C/c9D/c9E/c9F/cA0/cA1/cA2/cA3/cA4/cA5/cA6/cA7/ cA8/cA9/cAA /cAB/cAC/cAD/cAE/cAF/cB0/cB1/cB2/cB3/cB4/cB5/cB6/cB7/cB8/cB9/cBA/ cBB/cBC/cBD /cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/ cCE/cCF/cD0 /cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/ cE1/cE2/cE3 /cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/ cF4/cF5/cF6 /cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def /ct_CID_STR_SIZE 8000 def /ct_mkocfStr100 100 string def /ct_defaultFontMtx [.001 0 0 .001 0 0] def /ct_1000Mtx [1000 0 0 1000 0 0] def /ct_raise {exch cvx exch errordict exch get exec stop} bind def /ct_reraise { cvx $error /errorname get (Error: ) print dup ( ) cvs print errordict exch get exec stop } bind def /ct_cvnsi { 1 index add 1 sub 1 exch 0 4 1 roll { 2 index exch get exch 8 bitshift add } for exch pop } bind def /ct_GetInterval { Adobe_CoolType_Utility /ct_BuildCharDict get begin /dst_index 0 def dup dst_string length gt { dup string /dst_string exch def } if 1 index ct_CID_STR_SIZE idiv /arrayIndex exch def 2 index arrayIndex get 2 index arrayIndex ct_CID_STR_SIZE mul sub { dup 3 index add 2 index length le { 2 index getinterval dst_string dst_index 2 index putinterval length dst_index add /dst_index exch def exit } { 1 index length 1 index sub dup 4 1 roll getinterval dst_string dst_index 2 index putinterval pop dup dst_index add /dst_index exch def sub /arrayIndex arrayIndex 1 add def 2 index dup length arrayIndex gt { arrayIndex get } { pop exit } ifelse 0 } ifelse } loop pop pop pop dst_string 0 dst_index getinterval end } bind def ct_Level2? { /ct_resourcestatus currentglobal mark true setglobal { /unknowninstancename /Category resourcestatus } stopped { cleartomark setglobal true } { cleartomark currentglobal not exch setglobal } ifelse { { mark 3 1 roll /Category findresource begin ct_Vars /vm currentglobal put ({ResourceStatus} stopped) 0 () /SubFileDecode filter cvx exec { cleartomark false } { { 3 2 roll pop true } { cleartomark false } ifelse } ifelse ct_Vars /vm get setglobal end } } { { resourcestatus } } ifelse bind def /CIDFont /Category ct_resourcestatus { pop pop } { currentglobal true setglobal /Generic /Category findresource dup length dict copy dup /InstanceType /dicttype put /CIDFont exch /Category defineresource pop setglobal } ifelse ct_UseNativeCapability? { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering (Identity) def /Supplement 0 def end def /CMapName /Identity-H def /CMapVersion 1.000 def /CMapType 1 def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } if } { /ct_Category 2 dict begin /CIDFont 10 dict def /ProcSet 2 dict def currentdict end def /defineresource { ct_Category 1 index 2 copy known { get dup dup maxlength exch length eq { dup length 10 add dict copy ct_Category 2 index 2 index put } if 3 index 3 index put pop exch pop } { pop pop /defineresource /undefined ct_raise } ifelse } bind def /findresource { ct_Category 1 index 2 copy known { get 2 index 2 copy known { get 3 1 roll pop pop} { pop pop /findresource /undefinedresource ct_raise } ifelse } { pop pop /findresource /undefined ct_raise } ifelse } bind def /resourcestatus { ct_Category 1 index 2 copy known { get 2 index known exch pop exch pop { 0 -1 true } { false } ifelse } { pop pop /findresource /undefined ct_raise } ifelse } bind def /ct_resourcestatus /resourcestatus load def } ifelse /ct_CIDInit 2 dict begin /ct_cidfont_stream_init { { dup (Binary) eq { pop null currentfile ct_Level2? { { cid_BYTE_COUNT () /SubFileDecode filter } stopped { pop pop pop } if } if /readstring load exit } if dup (Hex) eq { pop currentfile ct_Level2? { { null exch /ASCIIHexDecode filter /readstring } stopped { pop exch pop (>) exch /readhexstring } if } { (>) exch /readhexstring } ifelse load exit } if /StartData /typecheck ct_raise } loop cid_BYTE_COUNT ct_CID_STR_SIZE le { 2 copy cid_BYTE_COUNT string exch exec pop 1 array dup 3 -1 roll 0 exch put } { cid_BYTE_COUNT ct_CID_STR_SIZE div ceiling cvi dup array exch 2 sub 0 exch 1 exch { 2 copy 5 index ct_CID_STR_SIZE string 6 index exec pop put pop } for 2 index cid_BYTE_COUNT ct_CID_STR_SIZE mod string 3 index exec pop 1 index exch 1 index length 1 sub exch put } ifelse cid_CIDFONT exch /GlyphData exch put 2 index null eq { pop pop pop } { pop /readstring load 1 string exch { 3 copy exec pop dup length 0 eq { pop pop pop pop pop true exit } if 4 index eq { pop pop pop pop false exit } if } loop pop } ifelse } bind def /StartData { mark { currentdict dup /FDArray get 0 get /FontMatrix get 0 get 0.001 eq { dup /CDevProc known not { /CDevProc 1183615869 internaldict /stdCDevProc 2 copy known { get } { pop pop { pop pop pop pop pop 0 -1000 7 index 2 div 880 } } ifelse def } if } { /CDevProc { pop pop pop pop pop 0 1 cid_temp /cid_CIDFONT get /FDArray get 0 get /FontMatrix get 0 get div 7 index 2 div 1 index 0.88 mul } def } ifelse /cid_temp 15 dict def cid_temp begin /cid_CIDFONT exch def 3 copy pop dup /cid_BYTE_COUNT exch def 0 gt { ct_cidfont_stream_init FDArray { /Private get dup /SubrMapOffset known { begin /Subrs SubrCount array def Subrs SubrMapOffset SubrCount SDBytes ct_Level2? { currentdict dup /SubrMapOffset undef dup /SubrCount undef /SDBytes undef } if end /cid_SD_BYTES exch def /cid_SUBR_COUNT exch def /cid_SUBR_MAP_OFFSET exch def /cid_SUBRS exch def cid_SUBR_COUNT 0 gt { GlyphData cid_SUBR_MAP_OFFSET cid_SD_BYTES ct_GetInterval 0 cid_SD_BYTES ct_cvnsi 0 1 cid_SUBR_COUNT 1 sub { exch 1 index 1 add cid_SD_BYTES mul cid_SUBR_MAP_OFFSET add GlyphData exch cid_SD_BYTES ct_GetInterval 0 cid_SD_BYTES ct_cvnsi cid_SUBRS 4 2 roll GlyphData exch 4 index 1 index sub ct_GetInterval dup length string copy put } for pop } if } { pop } ifelse } forall } if cleartomark pop pop end CIDFontName currentdict /CIDFont defineresource pop end end } stopped { cleartomark /StartData ct_reraise } if } bind def currentdict end def /ct_saveCIDInit { /CIDInit /ProcSet ct_resourcestatus { true } { /CIDInitC /ProcSet ct_resourcestatus } ifelse { pop pop /CIDInit /ProcSet findresource ct_UseNativeCapability? { pop null } { /CIDInit ct_CIDInit /ProcSet defineresource pop } ifelse } { /CIDInit ct_CIDInit /ProcSet defineresource pop null } ifelse ct_Vars exch /ct_oldCIDInit exch put } bind def /ct_restoreCIDInit { ct_Vars /ct_oldCIDInit get dup null ne { /CIDInit exch /ProcSet defineresource pop } { pop } ifelse } bind def /ct_BuildCharSetUp { 1 index begin CIDFont begin Adobe_CoolType_Utility /ct_BuildCharDict get begin /ct_dfCharCode exch def /ct_dfDict exch def CIDFirstByte ct_dfCharCode add dup CIDCount ge { pop 0 } if /cid exch def { GlyphDirectory cid 2 copy known { get } { pop pop nullstring } ifelse dup length FDBytes sub 0 gt { dup FDBytes 0 ne { 0 FDBytes ct_cvnsi } { pop 0 } ifelse /fdIndex exch def dup length FDBytes sub FDBytes exch getinterval /charstring exch def exit } { pop cid 0 eq { /charstring nullstring def exit } if /cid 0 def } ifelse } loop } def /ct_SetCacheDevice { 0 0 moveto dup stringwidth 3 -1 roll true charpath pathbbox 0 -1000 7 index 2 div 880 setcachedevice2 0 0 moveto } def /ct_CloneSetCacheProc { 1 eq { stringwidth pop -2 div -880 0 -1000 setcharwidth moveto } { usewidths? { currentfont /Widths get cid 2 copy known { get exch pop aload pop } { pop pop stringwidth } ifelse } { stringwidth } ifelse setcharwidth 0 0 moveto } ifelse } def /ct_Type3ShowCharString { ct_FDDict fdIndex 2 copy known { get } { currentglobal 3 1 roll 1 index gcheck setglobal ct_Type1FontTemplate dup maxlength dict copy begin FDArray fdIndex get dup /FontMatrix 2 copy known { get } { pop pop ct_defaultFontMtx } ifelse /FontMatrix exch dup length array copy def /Private get /Private exch def /Widths rootfont /Widths get def /CharStrings 1 dict dup /.notdef dup length string copy put def currentdict end /ct_Type1Font exch definefont dup 5 1 roll put setglobal } ifelse dup /CharStrings get 1 index /Encoding get ct_dfCharCode get charstring put rootfont /WMode 2 copy known { get } { pop pop 0 } ifelse exch 1000 scalefont setfont ct_str1 0 ct_dfCharCode put ct_str1 exch ct_dfSetCacheProc ct_SyntheticBold { currentpoint ct_str1 show newpath moveto ct_str1 true charpath ct_StrokeWidth setlinewidth stroke } { ct_str1 show } ifelse } def /ct_Type4ShowCharString { ct_dfDict ct_dfCharCode charstring FDArray fdIndex get dup /FontMatrix get dup ct_defaultFontMtx ct_matrixeq not { ct_1000Mtx matrix concatmatrix concat } { pop } ifelse /Private get Adobe_CoolType_Utility /ct_Level2? get not { ct_dfDict /Private 3 -1 roll { put } 1183615869 internaldict /superexec get exec } if 1183615869 internaldict Adobe_CoolType_Utility /ct_Level2? get { 1 index } { 3 index /Private get mark 6 1 roll } ifelse dup /RunInt known { /RunInt get } { pop /CCRun } ifelse get exec Adobe_CoolType_Utility /ct_Level2? get not { cleartomark } if } bind def /ct_BuildCharIncremental { { Adobe_CoolType_Utility /ct_MakeOCF get begin ct_BuildCharSetUp ct_ShowCharString } stopped { stop } if end end end end } bind def /BaseFontNameStr (BF00) def /ct_Type1FontTemplate 14 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] def /FontBBox [-250 -250 1250 1250] def /Encoding ct_cHexEncoding def /PaintType 0 def currentdict end def /BaseFontTemplate 11 dict begin /FontMatrix [0.001 0 0 0.001 0 0] def /FontBBox [-250 -250 1250 1250] def /Encoding ct_cHexEncoding def /BuildChar /ct_BuildCharIncremental load def ct_Clone? { /FontType 3 def /ct_ShowCharString /ct_Type3ShowCharString load def /ct_dfSetCacheProc /ct_CloneSetCacheProc load def /ct_SyntheticBold false def /ct_StrokeWidth 1 def } { /FontType 4 def /Private 1 dict dup /lenIV 4 put def /CharStrings 1 dict dup /.notdef put def /PaintType 0 def /ct_ShowCharString /ct_Type4ShowCharString load def } ifelse /ct_str1 1 string def currentdict end def /BaseFontDictSize BaseFontTemplate length 5 add def /ct_matrixeq { true 0 1 5 { dup 4 index exch get exch 3 index exch get eq and dup not { exit } if } for exch pop exch pop } bind def /ct_makeocf { 15 dict begin exch /WMode exch def exch /FontName exch def /FontType 0 def /FMapType 2 def dup /FontMatrix known { dup /FontMatrix get /FontMatrix exch def } { /FontMatrix matrix def } ifelse /bfCount 1 index /CIDCount get 256 idiv 1 add dup 256 gt { pop 256} if def /Encoding 256 array 0 1 bfCount 1 sub { 2 copy dup put pop } for bfCount 1 255 { 2 copy bfCount put pop } for def /FDepVector bfCount dup 256 lt { 1 add } if array def BaseFontTemplate BaseFontDictSize dict copy begin /CIDFont exch def CIDFont /FontBBox known { CIDFont /FontBBox get /FontBBox exch def } if CIDFont /CDevProc known { CIDFont /CDevProc get /CDevProc exch def } if currentdict end BaseFontNameStr 3 (0) putinterval 0 1 bfCount dup 256 eq { 1 sub } if { FDepVector exch 2 index BaseFontDictSize dict copy begin dup /CIDFirstByte exch 256 mul def FontType 3 eq { /ct_FDDict 2 dict def } if currentdict end 1 index 16 BaseFontNameStr 2 2 getinterval cvrs pop BaseFontNameStr exch definefont put } for ct_Clone? { /Widths 1 index /CIDFont get /GlyphDirectory get length dict def } if FontName currentdict end definefont ct_Clone? { gsave dup 1000 scalefont setfont ct_BuildCharDict begin /usewidths? false def currentfont /Widths get begin exch /CIDFont get /GlyphDirectory get { pop dup charcode exch 1 index 0 2 index 256 idiv put 1 index exch 1 exch 256 mod put stringwidth 2 array astore def } forall end /usewidths? true def end grestore } { exch pop } ifelse } bind def /ct_ComposeFont { ct_UseNativeCapability? { 2 index /CMap ct_resourcestatus { pop pop exch pop } { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CMapName 3 index def /CMapVersion 1.000 def /CMapType 1 def exch /WMode exch def /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering CMapName ct_mkocfStr100 cvs (Adobe-) search { pop pop (-) search { dup length string copy exch pop exch pop } { pop (Identity)} ifelse } { pop (Identity) } ifelse def /Supplement 0 def end def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } ifelse composefont } { 3 2 roll pop 0 get /CIDFont findresource ct_makeocf } ifelse } bind def /ct_MakeIdentity { ct_UseNativeCapability? { 1 index /CMap ct_resourcestatus { pop pop } { /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CMapName 2 index def /CMapVersion 1.000 def /CMapType 1 def /CIDSystemInfo 3 dict dup begin /Registry (Adobe) def /Ordering CMapName ct_mkocfStr100 cvs (Adobe-) search { pop pop (-) search { dup length string copy exch pop exch pop } { pop (Identity) } ifelse } { pop (Identity) } ifelse def /Supplement 0 def end def 1 begincodespacerange <0000> endcodespacerange 1 begincidrange <0000> 0 endcidrange endcmap CMapName currentdict /CMap defineresource pop end end } ifelse composefont } { exch pop 0 get /CIDFont findresource ct_makeocf } ifelse } bind def currentdict readonly pop end end %%EndResource %%BeginResource: procset Adobe_CoolType_Utility_T42 1.0 0 %%Copyright: Copyright 1987-2003 Adobe Systems Incorporated. %%Version: 1.0 0 userdict /ct_T42Dict 15 dict put ct_T42Dict begin /Is2015? { version cvi 2015 ge } bind def /AllocGlyphStorage { Is2015? { pop } { {string} forall } ifelse } bind def /Type42DictBegin { 25 dict begin /FontName exch def /CharStrings 256 dict begin /.notdef 0 def currentdict end def /Encoding exch def /PaintType 0 def /FontType 42 def /FontMatrix [1 0 0 1 0 0] def 4 array astore cvx /FontBBox exch def /sfnts } bind def /Type42DictEnd { currentdict dup /FontName get exch definefont end ct_T42Dict exch dup /FontName get exch put } bind def /RD {string currentfile exch readstring pop} executeonly def /PrepFor2015 { Is2015? { /GlyphDirectory 16 dict def sfnts 0 get dup 2 index (glyx) putinterval 2 index (locx) putinterval pop pop } { pop pop } ifelse } bind def /AddT42Char { Is2015? { /GlyphDirectory get begin def end pop pop } { /sfnts get 4 index get 3 index 2 index putinterval pop pop pop pop } ifelse } bind def end %%EndResource Adobe_CoolType_Core begin /$Oblique SetSubstituteStrategy end %%BeginResource: procset Adobe_AGM_Image 1.0 0 %%Version: 1.0 0 %%Copyright: Copyright (C) 2000-2003 Adobe Systems, Inc. All Rights Reserved. systemdict /setpacking known { currentpacking true setpacking } if userdict /Adobe_AGM_Image 75 dict dup begin put /Adobe_AGM_Image_Id /Adobe_AGM_Image_1.0_0 def /nd{ null def }bind def /AGMIMG_&image nd /AGMIMG_&colorimage nd /AGMIMG_&imagemask nd /AGMIMG_mbuf () def /AGMIMG_ybuf () def /AGMIMG_kbuf () def /AGMIMG_c 0 def /AGMIMG_m 0 def /AGMIMG_y 0 def /AGMIMG_k 0 def /AGMIMG_tmp nd /AGMIMG_imagestring0 nd /AGMIMG_imagestring1 nd /AGMIMG_imagestring2 nd /AGMIMG_imagestring3 nd /AGMIMG_imagestring4 nd /AGMIMG_imagestring5 nd /AGMIMG_cnt nd /AGMIMG_fsave nd /AGMIMG_colorAry nd /AGMIMG_override nd /AGMIMG_name nd /AGMIMG_maskSource nd /invert_image_samples nd /knockout_image_samples nd /img nd /sepimg nd /devnimg nd /idximg nd /doc_setup { Adobe_AGM_Core begin Adobe_AGM_Image begin /AGMIMG_&image systemdict/image get def /AGMIMG_&imagemask systemdict/imagemask get def /colorimage where{ pop /AGMIMG_&colorimage /colorimage ldf }if end end }def /page_setup { Adobe_AGM_Image begin /AGMIMG_ccimage_exists {/customcolorimage where { pop /Adobe_AGM_OnHost_Seps where { pop false }{ /Adobe_AGM_InRip_Seps where { pop false }{ true }ifelse }ifelse }{ false }ifelse }bdf level2{ /invert_image_samples { Adobe_AGM_Image/AGMIMG_tmp Decode length ddf /Decode [ Decode 1 get Decode 0 get] def }def /knockout_image_samples { Operator/imagemask ne{ /Decode [1 1] def }if }def }{ /invert_image_samples { {1 exch sub} currenttransfer addprocs settransfer }def /knockout_image_samples { { pop 1 } currenttransfer addprocs settransfer }def }ifelse /img /imageormask ldf /sepimg /sep_imageormask ldf /devnimg /devn_imageormask ldf /idximg /indexed_imageormask ldf /_ctype 7 def currentdict{ dup xcheck 1 index type dup /arraytype eq exch /packedarraytype eq or and{ bind }if def }forall }def /page_trailer { end }def /doc_trailer { }def /imageormask_sys { begin save mark level2{ currentdict Operator /imagemask eq{ AGMIMG_&imagemask }{ use_mask { level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation} ifelse }{ AGMIMG_&image }ifelse }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load AGMIMG_&imagemask }{ BitsPerComponent ImageMatrix /DataSource load AGMIMG_&image }ifelse }ifelse cleartomark restore end }def /overprint_plate { currentoverprint { 0 get dup type /nametype eq { dup /DeviceGray eq{ pop AGMCORE_black_plate not }{ /DeviceCMYK eq{ AGMCORE_is_cmyk_sep not }if }ifelse }{ false exch { AGMOHS_sepink eq or } forall not } ifelse }{ pop false }ifelse }def /process_mask_L3 { dup begin /ImageType 1 def end 4 dict begin /DataDict exch def /ImageType 3 def /InterleaveType 3 def /MaskDict 9 dict begin /ImageType 1 def /Width DataDict dup /MaskWidth known {/MaskWidth}{/Width} ifelse get def /Height DataDict dup /MaskHeight known {/MaskHeight}{/Height} ifelse get def /ImageMatrix [Width 0 0 Height neg 0 Height] def /NComponents 1 def /BitsPerComponent 1 def /Decode [0 1] def /DataSource AGMIMG_maskSource def currentdict end def currentdict end }def /use_mask { dup type /dicttype eq { dup /Mask known { dup /Mask get { level3 {true} { dup /MaskWidth known {dup /MaskWidth get 1 index /Width get eq} {true}ifelse exch dup /MaskHeight known {dup /MaskHeight get 1 index /Height get eq}{true}ifelse 3 -1 roll and } ifelse } {false} ifelse } {false} ifelse } {false} ifelse }def /make_line_source { begin MultipleDataSources { [ Decode length 2 div cvi {Width string} repeat ] }{ Width Decode length 2 div mul cvi string }ifelse end }def /datasource_to_str { exch dup type dup /filetype eq { pop exch readstring }{ /arraytype eq { exec exch copy }{ pop }ifelse }ifelse pop }def /masked_image_simulation { 3 dict begin dup make_line_source /line_source xdf /mask_source AGMIMG_maskSource /LZWDecode filter def dup /Width get 8 div ceiling cvi string /mask_str xdf begin gsave 0 1 translate 1 -1 Height div scale 1 1 Height { pop gsave MultipleDataSources { 0 1 DataSource length 1 sub { dup DataSource exch get exch line_source exch get datasource_to_str } for }{ DataSource line_source datasource_to_str } ifelse << /PatternType 1 /PaintProc [ /pop cvx << /ImageType 1 /Width Width /Height 1 /ImageMatrix Width 1.0 sub 1 matrix scale 0.5 0 matrix translate matrix concatmatrix /MultipleDataSources MultipleDataSources /DataSource line_source /BitsPerComponent BitsPerComponent /Decode Decode >> /image cvx ] cvx /BBox [0 0 Width 1] /XStep Width /YStep 1 /PaintType 1 /TilingType 2 >> matrix makepattern set_pattern << /ImageType 1 /Width Width /Height 1 /ImageMatrix Width 1 matrix scale /MultipleDataSources false /DataSource mask_source mask_str readstring pop /BitsPerComponent 1 /Decode [0 1] >> imagemask grestore 0 1 translate } for grestore end end }def /imageormask { begin SkipImageProc { currentdict consumeimagedata } { save mark level2 AGMCORE_host_sep not and{ currentdict Operator /imagemask eq DeviceN_PS2 not and { imagemask }{ AGMCORE_in_rip_sep currentoverprint and currentcolorspace 0 get / DeviceGray eq and{ [/Separation /Black /DeviceGray {}] setcolorspace /Decode [ Decode 1 get Decode 0 get ] def }if use_mask { level3 {process_mask_L3 image}{masked_image_simulation}ifelse }{ DeviceN_NoneName DeviceN_PS2 Indexed_DeviceN level3 not and or or AGMCORE_in_rip_sep and { Names convert_to_process not { 2 dict begin /imageDict xdf /names_index 0 def gsave imageDict write_image_file { Names { dup (None) ne { [/Separation 3 -1 roll /DeviceGray {1 exch sub}] setcolorspace Operator imageDict read_image_file names_index 0 eq {true setoverprint} if /names_index names_index 1 add def }{ pop } ifelse } forall close_image_file } if grestore end }{ Operator /imagemask eq { imagemask }{ image } ifelse } ifelse }{ Operator /imagemask eq { imagemask }{ image } ifelse } ifelse }ifelse }ifelse }{ Width Height Operator /imagemask eq{ Decode 0 get 1 eq Decode 1 get 0 eq and ImageMatrix /DataSource load /Adobe_AGM_OnHost_Seps where { pop imagemask }{ currentgray 1 ne{ currentdict imageormask_sys }{ currentoverprint not{ 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentdict ignoreimagedata }ifelse }ifelse }ifelse }{ BitsPerComponent ImageMatrix MultipleDataSources{ 0 1 NComponents 1 sub{ DataSource exch get }for }{ /DataSource load }ifelse Operator /colorimage eq{ AGMCORE_host_sep{ MultipleDataSources level2 or NComponents 4 eq and{ AGMCORE_is_cmyk_sep{ MultipleDataSources{ /DataSource [ DataSource 0 get /exec cvx DataSource 1 get /exec cvx DataSource 2 get /exec cvx DataSource 3 get /exec cvx /AGMCORE_get_ink_data cvx ] cvx def }{ /DataSource Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul /DataSource load filter_cmyk 0 () /SubFileDecode filter def }ifelse /Decode [ Decode 0 get Decode 1 get ] def /MultipleDataSources false def /NComponents 1 def /Operator /image def invert_image_samples 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentoverprint not Operator/imagemask eq and{ 1 AGMCORE_&setgray currentdict imageormask_sys }{ currentdict ignoreimagedata }ifelse }ifelse }{ MultipleDataSources NComponents AGMIMG_&colorimage }ifelse }{ true NComponents colorimage }ifelse }{ Operator /image eq{ AGMCORE_host_sep{ /DoImage true def HostSepColorImage{ invert_image_samples }{ AGMCORE_black_plate not Operator/imagemask ne and{ /DoImage false def currentdict ignoreimagedata }if }ifelse 1 AGMCORE_&setgray DoImage {currentdict imageormask_sys} if }{ use_mask { level3 {process_mask_L3 image}{masked_image_simulation}ifelse }{ image }ifelse }ifelse }{ Operator/knockout eq{ pop pop pop pop pop currentcolorspace overprint_plate not{ knockout_unitsq }if }if }ifelse }ifelse }ifelse }ifelse cleartomark restore }ifelse end }def /sep_imageormask { /sep_colorspace_dict AGMCORE_gget begin /MappedCSA CSA map_csa def begin SkipImageProc { currentdict consumeimagedata } { save mark AGMCORE_avoid_L2_sep_space{ /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def }if AGMIMG_ccimage_exists MappedCSA 0 get /DeviceCMYK eq and currentdict/Components known and Name () ne and Name (All) ne and Operator /image eq and AGMCORE_producing_seps not and level2 not and { Width Height BitsPerComponent ImageMatrix [ /DataSource load /exec cvx { 0 1 2 index length 1 sub{ 1 index exch 2 copy get 255 xor put }for } /exec cvx ] cvx bind MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Name findcmykcustomcolor customcolorimage }{ AGMCORE_producing_seps not{ level2{ AGMCORE_avoid_L2_sep_space not currentcolorspace 0 get / Separation ne and{ [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if currentdict imageormask }{ currentdict Operator /imagemask eq{ imageormask }{ sep_imageormask_lev1 }ifelse }ifelse }{ AGMCORE_host_sep{ Operator/knockout eq{ currentdict/ImageMatrix get concat knockout_unitsq }{ currentgray 1 ne{ AGMCORE_is_cmyk_sep Name (All) ne and{ level2{ [ /Separation Name [/DeviceGray] { sep_colorspace_proc AGMCORE_get_ink_data 1 exch sub } bind ] AGMCORE_&setcolorspace /sep_tint AGMCORE_gget AGMCORE_&setcolor currentdict imageormask_sys }{ currentdict Operator /imagemask eq{ imageormask_sys }{ sep_image_lev1_sep }ifelse }ifelse }{ Operator/imagemask ne{ invert_image_samples }if currentdict imageormask_sys }ifelse }{ currentoverprint not Name (All) eq or Operator/imagemask eq and{ currentdict imageormask_sys }{ currentoverprint not { gsave knockout_unitsq grestore }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ currentcolorspace 0 get /Separation ne{ [/Separation Name MappedCSA sep_proc_name exch 0 get exch load ] setcolorspace_opt /sep_tint AGMCORE_gget setcolor }if currentoverprint MappedCSA 0 get /DeviceCMYK eq and Name inRip_spot_has_ink not and Name (All) ne and { imageormask_l2_overprint }{ currentdict imageormask }ifelse }ifelse }ifelse }ifelse cleartomark restore }ifelse end end }def /decode_image_sample { 4 1 roll exch dup 5 1 roll sub 2 4 -1 roll exp 1 sub div mul add } bdf /colorSpaceElemCnt { currentcolorspace 0 get dup /DeviceCMYK eq { pop 4 } { /DeviceRGB eq { pop 3 }{ 1 } ifelse } ifelse } bdf /devn_sep_datasource { 1 dict begin /dataSource xdf [ 0 1 dataSource length 1 sub { dup currentdict /dataSource get /exch cvx /get cvx /exec cvx /exch cvx names_index /ne cvx [ /pop cvx ] cvx /if cvx } for ] cvx bind end } bdf /devn_alt_datasource { 11 dict begin /srcDataStrs xdf /dstDataStr xdf /convProc xdf /origcolorSpaceElemCnt xdf /origMultipleDataSources xdf /origBitsPerComponent xdf /origDecode xdf /origDataSource xdf /dsCnt origMultipleDataSources {origDataSource length}{1}ifelse def /samplesNeedDecoding 0 0 1 origDecode length 1 sub { origDecode exch get add } for origDecode length 2 div div dup 1 eq { /decodeDivisor 2 origBitsPerComponent exp 1 sub def } if 2 origBitsPerComponent exp 1 sub ne def [ 0 1 dsCnt 1 sub [ currentdict /origMultipleDataSources get { dup currentdict /origDataSource get exch get dup type }{ currentdict /origDataSource get dup type } ifelse dup /filetype eq { pop currentdict /srcDataStrs get 3 -1 /roll cvx /get cvx / readstring cvx /pop cvx }{ /stringtype ne { /exec cvx } if currentdict /srcDataStrs get /exch cvx 3 -1 /roll cvx /xpt cvx } ifelse ] cvx /for cvx currentdict /srcDataStrs get 0 /get cvx /length cvx 0 /ne cvx [ 0 1 Width 1 sub [ Adobe_AGM_Utils /AGMUTIL_ndx /xddf cvx currentdict /origMultipleDataSources get { 0 1 dsCnt 1 sub [ Adobe_AGM_Utils /AGMUTIL_ndx1 /xddf cvx currentdict /srcDataStrs get /AGMUTIL_ndx1 /load cvx /get cvx / AGMUTIL_ndx /load cvx /get cvx samplesNeedDecoding { currentdict /decodeDivisor known { currentdict /decodeDivisor get /div cvx }{ currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvxs BitsPerComponent /decode_image_sample load /exec cvx } ifelse } if ] cvx /for cvx }{ Adobe_AGM_Utils /AGMUTIL_ndx1 0 /ddf cvx currentdict /srcDataStrs get 0 /get cvx /AGMUTIL_ndx /load cvx currentdict /origDecode get length 2 idiv dup 3 1 /roll cvx /mul cvx /exch cvx /getinterval cvx [ samplesNeedDecoding { currentdict /decodeDivisor known { currentdict /decodeDivisor get /div cvx }{ currentdict /origDecode get /AGMUTIL_ndx1 /load cvx 2 /mul cvx 2 /getinterval cvx /aload cvx /pop cvx BitsPerComponent /decode_image_sample load /exec cvx Adobe_AGM_Utils /AGMUTIL_ndx1 /AGMUTIL_ndx1 /load cvx 1 /add cvx /ddf cvx } ifelse } if ] cvx /forall cvx } ifelse currentdict /convProc get /exec cvx currentdict /origcolorSpaceElemCnt get 1 sub -1 0 [ currentdict /dstDataStr get 3 1 /roll cvx /AGMUTIL_ndx /load cvx currentdict /origcolorSpaceElemCnt get /mul cvx /add cvx /exch cvx currentdict /convProc get /filter_indexed_devn load ne { 255 /mul cvx /cvi cvx } if /put cvx ] cvx /for cvx ] cvx /for cvx currentdict /dstDataStr get ] cvx /if cvx ] cvx bind end } bdf /devn_imageormask { /devicen_colorspace_dict AGMCORE_gget begin /MappedCSA CSA map_csa def 2 dict begin dup dup /dstDataStr exch /Width get colorSpaceElemCnt mul string def /srcDataStrs [ 3 -1 roll begin currentdict /MultipleDataSources known {MultipleDataSources {DataSource length}{1}ifelse}{1} ifelse { Width Decode length 2 div mul cvi string } repeat end ] def begin SkipImageProc { currentdict consumeimagedata } { save mark AGMCORE_producing_seps not { level3 not { Operator /imagemask ne { /DataSource [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse colorSpaceElemCnt /devicen_colorspace_dict AGMCORE_gget / TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def } if }if currentdict imageormask }{ AGMCORE_host_sep{ Names convert_to_process { CSA map_csa 0 get /DeviceCMYK eq { /DataSource Width BitsPerComponent mul 7 add 8 idiv Height mul 4 mul [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse 4 /devicen_colorspace_dict AGMCORE_gget /TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx filter_cmyk 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode [1 0] def /DeviceGray setcolorspace currentdict imageormask_sys }{ AGMCORE_report_unsupported_color_space AGMCORE_black_plate { /DataSource [ DataSource Decode BitsPerComponent currentdict / MultipleDataSources known {MultipleDataSources}{false} ifelse CSA map_csa 0 get /DeviceRGB eq{3}{1}ifelse / devicen_colorspace_dict AGMCORE_gget /TintTransform get dstDataStr srcDataStrs devn_alt_datasource /exec cvx ] cvx 0 () /SubFileDecode filter def /MultipleDataSources false def /Decode colorSpaceElemCnt [ exch {0 1} repeat ] def currentdict imageormask_sys } { gsave knockout_unitsq grestore currentdict consumeimagedata } ifelse } ifelse } { /devicen_colorspace_dict AGMCORE_gget /names_index known { Operator/imagemask ne{ MultipleDataSources { /DataSource [ DataSource devn_sep_datasource /exec cvx ] cvx def /MultipleDataSources false def }{ /DataSource /DataSource load dstDataStr srcDataStrs 0 get filter_devn def } ifelse invert_image_samples } if currentdict imageormask_sys }{ currentoverprint not Operator/imagemask eq and{ currentdict imageormask_sys }{ currentoverprint not { gsave knockout_unitsq grestore }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ currentdict imageormask }ifelse }ifelse cleartomark restore }ifelse end end end }def /imageormask_l2_overprint { currentdict currentcmykcolor add add add 0 eq{ currentdict consumeimagedata }{ level3{ currentcmykcolor /AGMIMG_k xdf /AGMIMG_y xdf /AGMIMG_m xdf /AGMIMG_c xdf Operator/imagemask eq{ [/DeviceN [ AGMIMG_c 0 ne {/Cyan} if AGMIMG_m 0 ne {/Magenta} if AGMIMG_y 0 ne {/Yellow} if AGMIMG_k 0 ne {/Black} if ] /DeviceCMYK {}] setcolorspace AGMIMG_c 0 ne {AGMIMG_c} if AGMIMG_m 0 ne {AGMIMG_m} if AGMIMG_y 0 ne {AGMIMG_y} if AGMIMG_k 0 ne {AGMIMG_k} if setcolor }{ /Decode [ Decode 0 get 255 mul Decode 1 get 255 mul ] def [/Indexed [ /DeviceN [ AGMIMG_c 0 ne {/Cyan} if AGMIMG_m 0 ne {/Magenta} if AGMIMG_y 0 ne {/Yellow} if AGMIMG_k 0 ne {/Black} if ] /DeviceCMYK { AGMIMG_k 0 eq {0} if AGMIMG_y 0 eq {0 exch} if AGMIMG_m 0 eq {0 3 1 roll} if AGMIMG_c 0 eq {0 4 1 roll} if } ] 255 { 255 div mark exch dup dup dup AGMIMG_k 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 1 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_y 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 2 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_m 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec 4 3 roll pop pop pop counttomark 1 roll }{ pop }ifelse AGMIMG_c 0 ne{ /sep_tint AGMCORE_gget mul MappedCSA sep_proc_name exch pop load exec pop pop pop counttomark 1 roll }{ pop }ifelse counttomark 1 add -1 roll pop } ] setcolorspace }ifelse imageormask_sys }{ write_image_file{ currentcmykcolor 0 ne{ [/Separation /Black /DeviceGray {}] setcolorspace gsave /Black [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 1 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Yellow /DeviceGray {}] setcolorspace gsave /Yellow [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 2 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Magenta /DeviceGray {}] setcolorspace gsave /Magenta [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {4 3 roll pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore }if 0 ne{ [/Separation /Cyan /DeviceGray {}] setcolorspace gsave /Cyan [{1 exch sub /sep_tint AGMCORE_gget mul} /exec cvx MappedCSA sep_proc_name cvx exch pop {pop pop pop 1 exch sub} /exec cvx] cvx modify_halftone_xfer Operator currentdict read_image_file grestore } if close_image_file }{ imageormask }ifelse }ifelse }ifelse } def /indexed_imageormask { begin save mark currentdict AGMCORE_host_sep{ Operator/knockout eq{ /indexed_colorspace_dict AGMCORE_gget dup /CSA known { /CSA get map_csa }{ /CSD get get_csd /Names get } ifelse overprint_plate not{ knockout_unitsq }if }{ Indexed_DeviceN { /devicen_colorspace_dict AGMCORE_gget /names_index known { indexed_image_lev2_sep }{ currentoverprint not{ knockout_unitsq }if currentdict consumeimagedata } ifelse }{ AGMCORE_is_cmyk_sep{ Operator /imagemask eq{ imageormask_sys }{ level2{ indexed_image_lev2_sep }{ indexed_image_lev1_sep }ifelse }ifelse }{ currentoverprint not{ knockout_unitsq }if currentdict consumeimagedata }ifelse }ifelse }ifelse }{ level2{ Indexed_DeviceN { /indexed_colorspace_dict AGMCORE_gget begin CSD get_csd begin }{ /indexed_colorspace_dict AGMCORE_gget begin CSA map_csa 0 get /DeviceCMYK eq ps_level 3 ge and ps_version 3015.007 lt and { [/Indexed [/DeviceN [/Cyan /Magenta /Yellow /Black] /DeviceCMYK {}] HiVal Lookup] setcolorspace } if end } ifelse imageormask Indexed_DeviceN { end end } if }{ Operator /imagemask eq{ imageormask }{ indexed_imageormask_lev1 }ifelse }ifelse }ifelse cleartomark restore end }def /indexed_image_lev2_sep { /indexed_colorspace_dict AGMCORE_gget begin begin Indexed_DeviceN not { currentcolorspace dup 1 /DeviceGray put dup 3 currentcolorspace 2 get 1 add string 0 1 2 3 AGMCORE_get_ink_data 4 currentcolorspace 3 get length 1 sub { dup 4 idiv exch currentcolorspace 3 get exch get 255 exch sub 2 index 3 1 roll put }for put setcolorspace } if currentdict Operator /imagemask eq{ AGMIMG_&imagemask }{ use_mask { level3 {process_mask_L3 AGMIMG_&image}{masked_image_simulation} ifelse }{ AGMIMG_&image }ifelse }ifelse end end }def /OPIimage { dup type /dicttype ne{ 10 dict begin /DataSource xdf /ImageMatrix xdf /BitsPerComponent xdf /Height xdf /Width xdf /ImageType 1 def /Decode [0 1 def] currentdict end }if dup begin /NComponents 1 cdndf /MultipleDataSources false cdndf /SkipImageProc {false} cdndf /HostSepColorImage false cdndf /Decode [ 0 currentcolorspace 0 get /Indexed eq{ 2 BitsPerComponent exp 1 sub }{ 1 }ifelse ] cdndf /Operator /image cdndf end /sep_colorspace_dict AGMCORE_gget null eq{ imageormask }{ gsave dup begin invert_image_samples end sep_imageormask grestore }ifelse }def /cachemask_level2 { 3 dict begin /LZWEncode filter /WriteFilter xdf /readBuffer 256 string def /ReadFilter currentfile 0 (%EndMask) /SubFileDecode filter /ASCII85Decode filter /RunLengthDecode filter def { ReadFilter readBuffer readstring exch WriteFilter exch writestring not {exit} if }loop WriteFilter closefile end }def /cachemask_level3 { currentfile << /Filter [ /SubFileDecode /ASCII85Decode /RunLengthDecode ] /DecodeParms [ << /EODCount 0 /EODString (%EndMask) >> null null ] /Intent 1 >> /ReusableStreamDecode filter }def /spot_alias { /mapto_sep_imageormask { dup type /dicttype ne{ 12 dict begin /ImageType 1 def /DataSource xdf /ImageMatrix xdf /BitsPerComponent xdf /Height xdf /Width xdf /MultipleDataSources false def }{ begin }ifelse /Decode [/customcolor_tint AGMCORE_gget 0] def /Operator /image def /HostSepColorImage false def /SkipImageProc {false} def currentdict end sep_imageormask }bdf /customcolorimage { Adobe_AGM_Image/AGMIMG_colorAry xddf /customcolor_tint AGMCORE_gget bdict /Name AGMIMG_colorAry 4 get /CSA [ /DeviceCMYK ] /TintMethod /Subtractive /TintProc null /MappedCSA null /NComponents 4 /Components [ AGMIMG_colorAry aload pop pop ] edict setsepcolorspace mapto_sep_imageormask }ndf Adobe_AGM_Image/AGMIMG_&customcolorimage /customcolorimage load put /customcolorimage { Adobe_AGM_Image/AGMIMG_override false put dup 4 get map_alias{ /customcolor_tint AGMCORE_gget exch setsepcolorspace pop mapto_sep_imageormask }{ AGMIMG_&customcolorimage }ifelse }bdf }def /snap_to_device { 6 dict begin matrix currentmatrix dup 0 get 0 eq 1 index 3 get 0 eq and 1 index 1 get 0 eq 2 index 2 get 0 eq and or exch pop { 1 1 dtransform 0 gt exch 0 gt /AGMIMG_xSign? exch def / AGMIMG_ySign? exch def 0 0 transform AGMIMG_ySign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch AGMIMG_xSign? {floor 0.1 sub}{ceiling 0.1 add} ifelse exch itransform /AGMIMG_llY exch def /AGMIMG_llX exch def 1 1 transform AGMIMG_ySign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch AGMIMG_xSign? {ceiling 0.1 add}{floor 0.1 sub} ifelse exch itransform /AGMIMG_urY exch def /AGMIMG_urX exch def [AGMIMG_urX AGMIMG_llX sub 0 0 AGMIMG_urY AGMIMG_llY sub AGMIMG_llX AGMIMG_llY] concat }{ }ifelse end } def level2 not{ /colorbuf { 0 1 2 index length 1 sub{ dup 2 index exch get 255 exch sub 2 index 3 1 roll put }for }def /tint_image_to_color { begin Width Height BitsPerComponent ImageMatrix /DataSource load end Adobe_AGM_Image begin /AGMIMG_mbuf 0 string def /AGMIMG_ybuf 0 string def /AGMIMG_kbuf 0 string def { colorbuf dup length AGMIMG_mbuf length ne { dup length dup dup /AGMIMG_mbuf exch string def /AGMIMG_ybuf exch string def /AGMIMG_kbuf exch string def } if dup AGMIMG_mbuf copy AGMIMG_ybuf copy AGMIMG_kbuf copy pop } addprocs {AGMIMG_mbuf}{AGMIMG_ybuf}{AGMIMG_kbuf} true 4 colorimage end } def /sep_imageormask_lev1 { begin MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ { 255 mul round cvi GrayLookup exch get } currenttransfer addprocs settransfer currentdict imageormask }{ /sep_colorspace_dict AGMCORE_gget/Components known{ MappedCSA 0 get /DeviceCMYK eq{ Components aload pop }{ 0 0 0 Components aload pop 1 exch sub }ifelse Adobe_AGM_Image/AGMIMG_k xddf Adobe_AGM_Image/AGMIMG_y xddf Adobe_AGM_Image/AGMIMG_m xddf Adobe_AGM_Image/AGMIMG_c xddf AGMIMG_y 0.0 eq AGMIMG_m 0.0 eq and AGMIMG_c 0.0 eq and{ {AGMIMG_k mul 1 exch sub} currenttransfer addprocs settransfer currentdict imageormask }{ currentcolortransfer {AGMIMG_k mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_y mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_m mul 1 exch sub} exch addprocs 4 1 roll {AGMIMG_c mul 1 exch sub} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }ifelse }{ MappedCSA 0 get /DeviceGray eq { {255 mul round cvi ColorLookup exch get 0 get} currenttransfer addprocs settransfer currentdict imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 2 get} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 1 get} exch addprocs 4 1 roll {255 mul round cvi ColorLookup exch get 0 get} exch addprocs 4 1 roll setcolortransfer currentdict tint_image_to_color }ifelse }ifelse }ifelse }ifelse end }def /sep_image_lev1_sep { begin /sep_colorspace_dict AGMCORE_gget/Components known{ Components aload pop Adobe_AGM_Image/AGMIMG_k xddf Adobe_AGM_Image/AGMIMG_y xddf Adobe_AGM_Image/AGMIMG_m xddf Adobe_AGM_Image/AGMIMG_c xddf {AGMIMG_c mul 1 exch sub} {AGMIMG_m mul 1 exch sub} {AGMIMG_y mul 1 exch sub} {AGMIMG_k mul 1 exch sub} }{ {255 mul round cvi ColorLookup exch get 0 get 1 exch sub} {255 mul round cvi ColorLookup exch get 1 get 1 exch sub} {255 mul round cvi ColorLookup exch get 2 get 1 exch sub} {255 mul round cvi ColorLookup exch get 3 get 1 exch sub} }ifelse AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end }def /indexed_imageormask_lev1 { /indexed_colorspace_dict AGMCORE_gget begin begin currentdict MappedCSA 0 get dup /DeviceRGB eq exch /DeviceCMYK eq or has_color not and{ {HiVal mul round cvi GrayLookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceGray eq { {HiVal mul round cvi Lookup exch get HiVal div} currenttransfer addprocs settransfer imageormask }{ MappedCSA 0 get /DeviceCMYK eq { currentcolortransfer {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }{ currentcolortransfer {pop 1} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 2 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi 1 add Lookup exch get HiVal div} exch addprocs 4 1 roll {3 mul HiVal mul round cvi Lookup exch get HiVal div} exch addprocs 4 1 roll setcolortransfer tint_image_to_color }ifelse }ifelse }ifelse end end }def /indexed_image_lev1_sep { /indexed_colorspace_dict AGMCORE_gget begin begin {4 mul HiVal mul round cvi Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 1 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 2 add Lookup exch get HiVal div 1 exch sub} {4 mul HiVal mul round cvi 3 add Lookup exch get HiVal div 1 exch sub} AGMCORE_get_ink_data currenttransfer addprocs settransfer currentdict imageormask_sys end end }def }if end systemdict /setpacking known { setpacking } if %%EndResource currentdict Adobe_AGM_Utils eq {end} if %%EndProlog %%BeginSetup Adobe_AGM_Utils begin 2 2010 Adobe_AGM_Core/doc_setup get exec Adobe_CoolType_Core/doc_setup get exec Adobe_AGM_Image/doc_setup get exec currentdict Adobe_AGM_Utils eq {end} if %%EndSetup %%Page: Figure-2.eps 1 %%EndPageComments %%BeginPageSetup /currentdistillerparams where {pop currentdistillerparams /CoreDistVersion get 5000 lt} {true} ifelse { userdict /AI11_PDFMark5 /cleartomark load put userdict /AI11_ReadMetadata_PDFMark5 {flushfile cleartomark } bind put} { userdict /AI11_PDFMark5 /pdfmark load put userdict /AI11_ReadMetadata_PDFMark5 {/PUT pdfmark} bind put } ifelse [/NamespacePush AI11_PDFMark5 [/_objdef {ai_metadata_stream_123} /type /stream /OBJ AI11_PDFMark5 [{ai_metadata_stream_123} currentfile 0 (% &&end XMP packet marker&&) /SubFileDecode filter AI11_ReadMetadata_PDFMark5 2006-10-16T20:42:31Z 2006-11-03T11:05:36Z Illustrator JPEG 256 188 /9j/4AAQSkZJRgABAgEASABIAAD/ 7QAsUGhvdG9zaG9wIDMuMAA4QklNA+0AAAAAABAASAAAAAEA AQBIAAAAAQAB/ +4ADkFkb2JlAGTAAAAAAf/ bAIQABgQEBAUEBgUFBgkGBQYJCwgGBggLDAoKCwoK DBAMDAwMDAwQDA4PEA8ODBMTFB QTExwbGxscHx8fHx8fHx8fHwEHBwcNDA0YEBAYGhURFRofHx8f Hx8fHx8fHx8fHx8fH x8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8f/ 8AAEQgAvAEAAwER AAIRAQMRAf/ EAaIAAAAHAQEBAQEAAAAAAAAAAAQFAwIGAQAHCAkKCwEAAgIDAQEBAQEAAAAAAAAA AQ ACAwQFBgcICQoLEAACAQMDAgQCBgcDBAIGAnMBAgMRBAAFIRIxQVEGE2EicYEUMpGhBxWxQi PB 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get exec Adobe_CoolType_Core/page_setup get exec Adobe_AGM_Image/page_setup get exec %%EndPageSetup Adobe_AGM_Core/AGMCORE_save save ddf 1 -1 scale 0 -161.115 translate [1 0 0 1 0 0 ] concat % page clip gsave newpath gsave % PSGState 0 0 mo 0 161.115 li 221.884 161.115 li 221.884 0 li clp [1 0 0 1 0 0 ] concat 0.25 lw 1 lc 1 lj 10 ml [] 0 dsh true sadj 60.6021 150.288 mo 60.6021 149.012 li false sop /0 [/DeviceCMYK] add_csa 0 0 0 1 cmyk @ /1 [/DeviceGray] add_csa 0 gry %ADOBeginSubsetFont: Courier Initial %ADOt1write: (1.0.21) 13 dict dup begin /FontType 1 def /FontName /Courier def /FontInfo 6 dict dup begin /Notice (Copyright (c) 1989, 1990, 1991, 1992, 1993, 1996, 1997, 1998 Adobe Systems Incorporated. All Rights Reserved.) def /Weight (Medium) def /ItalicAngle 0 def end def /PaintType 0 def /FontMatrix [0.001 0 0 0.001 0 0] def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 50 /two put def /UniqueID 44052 def /FontBBox {-6 -249 639 803} def end systemdict begin dup /Private 12 dict dup begin /|- {def} def /| {put} def /BlueValues [-14 0 572 585 434 448 782 803 626 626] def /OtherBlues [236 243 344 344 -195 -193] def /FamilyBlues [-14 0 572 585 434 448 782 803 626 626] def /FamilyOtherBlues [236 243 344 344 -195 -193] def /StdHW [55] def /StdVW [55] def /password 5839 def /MinFeature {16 16} def /OtherSubrs[{}{}{}{systemdict/internaldict known not{pop 3}{1183615869 systemdict/internaldict get exec dup/startlock known{/startlock get exec}{dup /strtlck known{/strtlck get exec}{pop 3}ifelse}ifelse}ifelse} executeonly]def /Subrs 5 array dup 0 <1C60D8A8CC31FE2BF6E07AA3E541E2> | dup 1 <1C60D8A8C9C3D06D9E> | dup 2 <1C60D8A8C9C202D79A> | dup 3 <1C60D8A849> | dup 4 <1C60D8A8CC3674F41144B13B77> | def put dup /CharStrings 3 dict dup begin /period <1C60D8A8C9B7C3C9E2345CC0A09E843899300080E14D3CB98CC3BBC 0C29D3B013ABE248643B3BE11462117> |- /two <1C60D8A8C9B7C3C9F8C9154D6A8DC0B5A14D7C9764E1D32F8B47964F00 BE2711C767014CAAEB2E2C14E358030C9FA9D12B6C7010D9FFD0B867A8D207AD 713C0EE2BC9C15F4D9BA1730BB0E25C11AFBBF4C94DC5FCE95F531436106A276 DB87479CA7DE307EB04211DF> |- /.notdef <1C60D8A8C9B7C3C91B> |- end put end dup /FontName get exch definefont pop end %ADOEndSubsetFont /ECEGHP+Courier /Courier findfont def /ECEGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two 205{/.notdef}repeat ] ECEGHP+Courier nfnt ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 51.7192 158.614 mov (2.2) sh 107.575 150.288 mo 107.575 149.012 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin ECEGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /four <1C60D8A8C9B7C3C9E2A9C1E2334675B52B245B3FB81B2A53E0971A4EB 43480F24C1049BC43938DE3B4F14FF04140D6104E6959A8144078C86299C6C49 ABE7DCAC2E5F93D01D4092D55FA> |- systemdict /gcheck known {setglobal} if end {end} if end ECEGHP+Courier /Encoding get dup 52 /four put pop %ADOEndSubsetFont /ECEGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two /.notdef /four 203 {/.notdef}repeat ] ECEGHP+Courier nfnt ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 98.6616 158.614 mov (2.4) sh 154.545 150.288 mo 154.545 149.012 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin ECEGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /six <1C60D8A8C9B7C3C9F9172BAADA8BC86C29843875037507636FA753BC24 58733B5F2A4DD1D5AE8B12E71051D1DB76D21AC30015BB36E349CD73F81AF377 78DFF3175129CD736781D2B349DD8C91A5AF1665246CBC86E4061D0ECB688BD8 2EB97447F94A0FE3CCBF7319B08D719A247AAC7BE864A9F915939A769B6EDF5A 88BA4CE131EF63A6FDF52B3D1023640FC4D6F67C60960CA1CAFB252058A90686 93D7EBD2B2E96909C6B3FBF27EBC0F06624222AEC591A6F841194A2EC6DF24C5 108C29514DE4681F78149A75AB1B4E33EF50E85C52FAC6765F41A4033E81321F 957BA01E0D8FF998486C461E9F18DD> |- systemdict /gcheck known {setglobal} if end {end} if end ECEGHP+Courier /Encoding get dup 54 /six put pop %ADOEndSubsetFont /ECEGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two /.notdef / four /.notdef /six 201{/.notdef}repeat ] ECEGHP+Courier nfnt ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 145.602 158.614 mov (2.6) sh 201.518 150.288 mo 201.518 149.012 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin ECEGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /eight <1C60D8A8C9B7C3C9E645C90E948096AFD30C38FBE873B1EB0FD5516A 25BEC848181359BE9B2D94FB060BB42210E95A0E40E6B6B49DA3F41251773058 C6B3969571E6CED62CFFBF324449A6D4F8BF768AEF3D1850AA57DC8B8F7038E9 65B6C6ADE55EA186CAF86F88A5779CEFAE943E8549824E225D86B6A988350746 2CDF0AB365BF7482DBEF126A0F419A547419232B88035C79841E90893A22C1EA 986D9C95BE348D68D7689E0423A257A103DB28AB3E6870247A4EBC7CAD69B94B 125BFAB4D6376286A8AAD1182E3A94484EF3B0FCAE6CDD335ACAFECC36422983 6E09D0D97F0DD56461FD6330129C19F2> |- systemdict /gcheck known {setglobal} if end {end} if end ECEGHP+Courier /Encoding get dup 56 /eight put pop %ADOEndSubsetFont /ECEGHP+Courier*1 [ 46{/.notdef}repeat /period 3{/.notdef}repeat /two /.notdef / four /.notdef /six /.notdef /eight 199{/.notdef}repeat ] ECEGHP+Courier nfnt ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 192.564 158.625 mov (2.8) sh 0.125 lw 189.775 150.288 mo 189.775 149.522 li 178.033 150.288 mo 178.033 149.522 li 166.29 150.288 mo 166.29 149.522 li 142.803 150.288 mo 142.803 149.522 li 131.06 150.288 mo 131.06 149.522 li 119.318 150.288 mo 119.318 149.522 li 95.8321 150.288 mo 95.8321 149.522 li 84.0894 150.288 mo 84.0894 149.522 li 72.3467 150.288 mo 72.3467 149.522 li 48.8594 150.288 mo 48.8594 149.522 li 37.1168 150.288 mo 37.1168 149.522 li 25.3741 150.288 mo 25.3741 149.522 li 0 0 0 1 cmyk @ 0.25 lw 13.6314 125.036 mo 14.9083 125.036 li 8.76758 150.288 mo 213.058 150.288 li @ 0 gry ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6.17969 127.888 mov (2) sh 13.6314 99.7847 mo 14.9083 99.7847 li 0 0 0 1 cmyk @ 0 gry ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6.11963 102.578 mov (4) sh 13.6314 74.5328 mo 14.9083 74.5328 li 0 0 0 1 cmyk @ 0 gry ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6.05957 77.3193 mov (6) sh 13.6314 49.2803 mo 14.9083 49.2803 li 0 0 0 1 cmyk @ 0 gry ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 6.03955 52.0732 mov (8) sh 13.6314 24.0303 mo 14.9083 24.0303 li 0 0 0 1 cmyk @ 0 gry %ADOBeginSubsetFont: Courier AddGlyphs %ADOt1write: (1.0.21) systemdict begin ECEGHP+Courier dup /Private get dup rcheck {begin true}{pop false}ifelse exch /CharStrings get begin systemdict /gcheck known {currentglobal currentdict gcheck setglobal} if /zero <1C60D8A8C9B7C3C9E24E60C489D70E052AE9976D225DE2CA07C0A15C7 572C0A27900A47AB835FD764D54712AF293EAC6A992E07FABF9E04B96CB97E81 26ED618067617499E5BB5F3713DE8C872F684616702B331643368CE1A1FA88E0 058FEBDA4A636AA060C2832DA59609247095D9766029BACE17AE02AF0FDD2726 B1401C3> |- /one <1C60D8A8C9B7C3C9E2E7C3E088DBE325C6F98B28B39F1FC9168EDC9CD4 F5243A7BD6F40E9C7EBD025D090D293B869BB7ED0B> |- systemdict /gcheck known {setglobal} if end {end} if end ECEGHP+Courier /Encoding get dup 48 /zero put dup 49 /one put pop %ADOEndSubsetFont /ECEGHP+Courier*1 [ 46{/.notdef}repeat /period /.notdef /zero /one /two /.notdef /four /.notdef /six /.notdef /eight 199{/.notdef}repeat ] ECEGHP+Courier nfnt ECEGHP+Courier*1 [10 0 -0 -10 0 0 ]mfnt sfnt 0 26.8232 mov (10) sh 0.125 lw 13.6314 30.3428 mo 14.3975 30.3428 li 13.6314 36.6553 mo 14.3975 36.6553 li 13.6314 42.9678 mo 14.3975 42.9678 li 13.6314 55.5933 mo 14.3975 55.5933 li 13.6314 61.9078 mo 14.3975 61.9078 li 13.6314 68.2203 mo 14.3975 68.2203 li 13.6314 80.8453 mo 14.3975 80.8453 li 13.6314 87.1582 mo 14.3975 87.1582 li 13.6314 93.4703 mo 14.3975 93.4703 li 13.6314 106.099 mo 14.3975 106.099 li 13.6314 112.411 mo 14.3975 112.411 li 13.6314 118.724 mo 14.3975 118.724 li 13.6314 131.349 mo 14.3975 131.349 li 13.6314 137.663 mo 14.3975 137.663 li 13.6314 143.976 mo 14.3975 143.976 li 0 0 0 1 cmyk @ 0.25 lw 13.6314 150.288 mo 13.6314 24.0303 li @ gsave % PSGState 8.76758 150.288 mo 213.058 150.288 li 213.058 24.0303 li 8.76758 24.0303 li 8.76758 150.288 li clp 0.5 lw 31.0391 24.0303 mo 32.2159 34.9249 li 34.1177 48.9678 li 36.3365 62.2632 li 38.3897 72.337 li 42.2896 87.2681 li 46.5303 99.2271 li 50.3423 107.426 li 54.5528 114.527 li 58.837 120.241 li 62.7657 124.488 li 70.6695 130.995 li 78.7632 135.734 li 86.5489 139.087 li 94.835 141.764 li 102.813 143.723 li 111.289 145.324 li 119.457 146.517 li 127.316 147.42 li 135.675 148.176 li 143.724 148.744 li 151.464 149.175 li 159.706 149.53 li 167.636 149.79 li 171.671 149.898 li 176.07 149.996 li 184.192 150.135 li 188.218 150.185 li 192.506 150.227 li 194.613 150.241 li 196.888 150.258 li 198.856 150.268 li 201.011 150.276 li 202.821 150.282 li 203.687 150.284 li 204.506 150.284 li 205.438 150.286 li 206.288 150.288 li 206.762 150.288 li 207.202 150.288 li 207.43 150.288 li 207.683 150.288 li 207.947 150.288 li 208.194 150.288 li @ grestore % PSGState 0 lc 0 lj 4 ml 194.25 150.351 mo 220.376 150.351 li @ 221.884 150.351 mo 221.174 150.614 220.293 151.063 219.748 151.539 cv 220.178 150.351 li 219.748 149.162 li 220.293 149.638 221.174 150.087 221.884 150.351 cv f 13.625 14.0376 mo 13.625 37.0376 li 0.949001 0.8275 0.8157 0.898001 cmyk f 13.625 14.0376 mo 13.625 37.0376 li 0 0 0 1 cmyk @ 13.625 12.5289 mo 13.8887 13.2388 14.3379 14.1197 14.8135 14.6656 cv 13.625 14.2354 li 12.4366 14.6656 li 12.9122 14.1197 13.3619 13.2388 13.625 12.5289 cv f gsave % PSGState 214.963 147.431 mo 214.963 139.75 li 219.763 139.75 li 219.763 147.431 li 214.963 147.431 li clp 214.963 139.75 mo 214.963 147.43 li 219.763 147.43 li 219.763 139.75 li gsave % PSGState clp [1 0 0 -1 0 161.115 ] concat /0 map_csa setcolorspace [4.80001 0 0 7.68 214.963 13.6853 ] concat snap_to_device Adobe_AGM_Image/AGMIMG_filter currentfile /ASCII85Decode filter / RunLengthDecode filter ddf bdict /ImageType 1 /Width 20 /Height 32 /ImageMatrix[20 0 0 -32 0 32 ] /MultipleDataSources true /BitsPerComponent 8 /Decode[0 1 0 1 0 1 0 1 ] /DataSource [ [AGMIMG_filter 20 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 20 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 20 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 20 string /readstring cvx /pop cvx] cvx ] /NComponents 4 /HostSepColorImage false /SkipImageProc {false} /Operator /colorimage edict img q>^Ssnn%:j!hIe=n,NNWcr'94!h&-NnGiZ&o(%t6!!?6Mds^`d!)WgEd!,![!s.NF/F`] BSau;JnGiZH e'gYR!!@i"cp7+$!^u/3n,NO!naZMWo`,&ge'mdd!i+,hn,NNqjlQ"4!u(4pXRQ8m&C] *unGiY%d*S0Q !;lfujlMj!!!?g'nWWJC"'*h!IdmC?:sdR4nGiXljlJ&`!!Ae^nknoW!f,7R! (-2U"+nnH5k+gU7-3P" !!9Ouo'cV\Usmf^!!8qBd-q#:ZK:3E!;lfu\+0% fnHJLRo'u:Fq>^Mnp^Mhp^N%p>l9\ q>^pe;Gg>Vna`2I;Gg=@q>^pZ6UF+fe'j.?6UF-aq>^OL570Y@GL4]e5X.Lu+8,[:/EPt \nGiZ^o("s6 !!A#*dk^Fn"+nnH0C]#D7-3P"!!Ke%jT#;O!!9(IbO>K5U!UgK!!9LghXLRJ'Ct [jnGiY&e'jWQ!!e'g)B!! @GlcnFnh!\EHp n,NNio&]?@!h.T]n,NNYd)PPT!h&0,r;cHi!qPlYn,NO=e!BJ'!mo;Vn,NOOja?Ru"&\X [L[b?H6IXD' p&P!j"$Y)YD"%E+jlI?L!!AGTnP\lW"+J_J6h(-YG0nT#nGiVAjlPt3! N,DfnbW:dAG6'*QIF=[!!$!m !!8;0d/*eC;"jqkI-'Je!!!&o!!;6PXS`&!;T/;0!m&i\qu?abYP/"uaO$=P!!#4`[.aP% h;t"#!!((7 !!=\@ns'%P!NLD>!!=Fods_,o!LdQo!!==id!,Bf!LdBi!!;9D/GoJKR0iWg"& \UZ;>gIq;RH9#rW!$e e'gY^!!,E^pAb:\d*P&V!!,?[p&P-SqZ$W%pAb:Zna]TW!!3kr4nepY1"4T=rW!!1b;/ el"#/*K5Q1Wa &]QKt!!;9D!;ulthXpjR`:7C=!%G:"o`,6#do?AJ,,AcB!!fmX:]LJ;UL3Zo!lsC'rVuu) $2"9&4m02: U;UU7!!Y4$Uj\B/<;lml!!Y+!UN_R%;"FYjhQe\>`rYc3";?$EGSK] K";#*lA.S52":nj`?P)`-!XUCa o`0RDJcLB&m/VY~> grestore % PSGState newpath % image grestore % PSGState gsave % PSGState 14.9625 11.5201 mo 14.9625 0 li 30.8028 0 li 30.8028 11.5201 li 14.9625 11.5201 li clp 14.9625 0 mo 14.9625 11.5201 li 30.8025 11.5201 li 30.8025 0 li gsave % PSGState clp [1 0 0 -1 0 161.115 ] concat /0 map_csa setcolorspace [15.84 0 0 11.5201 14.9625 149.595 ] concat snap_to_device Adobe_AGM_Image/AGMIMG_filter currentfile /ASCII85Decode filter / RunLengthDecode filter ddf bdict /ImageType 1 /Width 66 /Height 48 /ImageMatrix[66 0 0 -48 0 48 ] /MultipleDataSources true /BitsPerComponent 8 /Decode[0 1 0 1 0 1 0 1 ] /DataSource [ [AGMIMG_filter 66 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 66 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 66 string /readstring cvx /pop cvx] cvx [AGMIMG_filter 66 string /readstring cvx /pop cvx] cvx ] /NComponents 4 /HostSepColorImage false /SkipImageProc {false} /Operator /colorimage edict img JcLB&JcLB&aoDH>PjSMPP#Bj2!CD55!:g*jI7)Qc!C1ks!!.:.eGoS#mJm5lN$DS!=@lQ!!20fgAh:GD )!V)%)!0NQ!YaXpkPt[ajV7UmirB,laI;;m!h.:Ch>dTfaI;;m!h.+? h#IK3RHOVORGQa"!iGN;oDeqi P8!cm"98ENjegl7!g_:XoDeqZILu8S![>gRh>dV>clhr\"@.,@!!)iq![#FEh>dS (jmiBO/G9&EhL+2\ !`JT`oDek?!qGfEpAb8Ynkn'_03$!!9LU,4kj;ERWBHpAb7*e$@m3!OpDU +nPa:Cs^O: pAb7+d'hj4!QjHp!!=)"jU(V\!ThG`!!E9%Gk%O"!!B+gnL=/3!i#71iW'$jduj5%"- h9`,5)!92iW'#dj^7TZ!dj%jo`,&#jU(>To`,&nnR_:l!p/sjo`,% knZ:^M!hIe? o)Jj8e$&EE!^kG,o)S7[!gq>2o)Jj3d'WHG!^G&!iW'%JjT4rQ!oE%ZoDepRQhURI!!4V? `:Es254\6< oDesRnic%6![?*so)JkIe'jBM!!:6j1B%::!!47h[.=8"0[S1(oDes6cnFDZ!ThAm!!; 9D?M"3th#QQs !!8_^U@S?eL[st[oDerent"hA!f,6co)Jl5e'hh%!;um!O4/mF!!7c! MXpfMCXCF9oDerMd":^U2H'2)%!!h^q>^U/A:6f@!!^SknuD9]"/bVY'_25*Wq)n_!!^SRd$XD)"-LsW&Fof&Ra?ri!!; 9DRJd*d!OMb* !p/Mpq>^V)jd?,@!!7Q0jm`!!<4iduj5%!mB&hnGiWOe"-F;"&R@kG5_ICCnVC=!<45L!!&dg'_;;+[.0CQ!! >CSnXT+L!gN5^ r;[+Ye'gYa!0Njd/F"F!W1s[R=#kC!!;9D/ G&oDa5sYs!!4_5 jo,5gSFQ,I!!#oP`:EGg'D;D-o'qt;!!=\?nXT(K!gN9HrW!@`e'gV`!(1b4e'j- bp&G0Cds^lh"!Z4C M=:KHIFH[E!"=D)cp.R25A[RNd!uZ#!!:NoGPV=;!!==id"(Tc!dE#^Vpo("7-!;lfuWq)\Q!!Ae_nLJ/EQ!l!!**;qu?eejd5W?!jh"/qZ$W&p&G5`jd,rI". \rQ;Yg@qS+?(` rVutrAc)N0PjtjJ!!;`^UAOulPbRjO#d!T]!!%l)dmNs3",PFT&,lP0Qbd!#Hi7-3P+!! 5OLjo#/[Hia-F !\EH"o`,'Tj^.ib!A%UT!;lg%RcQ(#!4VLgq#CJtn\kD,!Yk/=qu?eDnacAR"&e [[Gl7UD'B^h!!3_Y&GuM0 @*m9o!!>L5csQ_O!Yn:+SPj<5g[kCr;ZkTGP2"B +jeRZ!!)-B ReZpbRH9k9!!*C5q>gQWq#L?ns5j.Y!FIDN!!;9D!!E:4na_q?!!7rHXSr2#`'4"t! lOP>pAb:/naTNV !!.>Oo`,8/n\bD-<7B2SFN++g6uo`, 5Id"q`&/EQ!f !!V68!!$=nq#CJ'j[AeB"%;6%!!3-gZLe,%6fhYT!+bYtpAb=FVXif4p](A+n\k)#"I $dp`0Bin#IO#4 !!$!IQM1@^,*p^!IJ^XLa5t>mo)JitjT4BA!ljanj8]6Eo#0Mf!OC/ S1?8E:1=NGd !!9UU0]W380@7)f!<)s!alVL^!ThA]!!8ASS`BbPSahI"!;QTrIaa)5!!7r)ET-s"G0kj %!!7c!D!qAr !!4_57-"=L7-,9F!!JoaMnee!9jL`hW+Y; hqm8k!gE2"jo>I-ns'(Qj8]71dq%S@!bBc.huEh%csPo8!FO1RGMiH&/EI3#!!3Jg/DgF/ [)NgF!!E9% 'Z@B8!!8t%&*Nup&$Mec!!8q(&FTVq!!3_=UYYtOZH;5/!QVM&!!5=RP4SbI!!8>R4l-/? 1=L[8!!7St 1>W!40[P%>!:TsiGL/#!!!214kPtW7jkKh=L[dM-!:0[e;XoLs!!7/h1?ni@6dp&1!! 6u`0BrN=5L=6% !!*qukPtYF(uYJl!!8nV'^Pf$'Bc+D!!88*&*s8t&B^*r!;6BoMoH=p!!3\RMqS.3@,C/ K!T%5L!:Tsi UU1^&!!3kDU=]GIOe`QV!!3\/OmW58!!8"P&+0E!&YY'6!!-H4li7'm? h49Z!!/:XmJm9^PL]^7IZWst !KV^(!8mhXG)Pbg!K)'O!!+WYmJm8o/GoL"!.k3&!.k3&!9F34!.k3&!:g,?~> grestore % PSGState newpath % image grestore % PSGState %ADOBeginClientInjection: EndPageContent "AI11EPS" userdict /annotatepage 2 copy known {get exec}{pop pop} ifelse %ADOEndClientInjection: EndPageContent "AI11EPS" % page clip grestore grestore % PSGState /ECEGHP+Courier*1 ufnt Adobe_AGM_Core/AGMCORE_save get restore %%PageTrailer [/EMC AI11_PDFMark5 [/NamespacePop AI11_PDFMark5 Adobe_AGM_Image/page_trailer get exec Adobe_CoolType_Core/page_trailer get exec Adobe_AGM_Core/page_trailer get exec currentdict Adobe_AGM_Utils eq {end} if %%Trailer Adobe_AGM_Image/doc_trailer get exec Adobe_CoolType_Core/doc_trailer get exec Adobe_AGM_Core/doc_trailer get exec %%EOF %AI9_PrintingDataEnd userdict /AI9_read_buffer 256 string put userdict begin /ai9_skip_data { mark { currentfile AI9_read_buffer { readline } stopped { } { not { exit } if (%AI9_PrivateDataEnd) eq { exit } if } ifelse } loop cleartomark } def end userdict /ai9_skip_data get exec %AI9_PrivateDataBegin %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(R) 11.0 %%AI8_CreatorVersion: 11.0.0 %%For: (CNRS) () %%Title: (Figure-2.eps) %%CreationDate: 3/11/06 12:05 %AI9_DataStream %Gb"-6l#%cgPpZ>1rXSj)J:r9gFLU'/@=V_g3N\lh8^K40?-T$-A[4q@@Zo9c9Qb-BIa7 \YA%kAc(sJdfH@V_7P7.t/b`3]*qsquj %(D!/,hr!:?J+<$s5KDEJ%GUGc,]c5c:c5]0(\8&p`e>Po9rpG)g2b \5(C)Qs7Df$LNb[!5AhS2*ZdQFr+u9) %lhe#<\c,pL\N]oNc/%3n^R\Zc?,-:&m$=]-qbO`oiUc*sc/\/KhgPL_LV) <1pZi2F^Pq&Vh;6sm4Zn2'rcFIPH^s]bntgj2-u[#B %o!b4ijo)g'cgPe$,Hne+s2trDogaCl^ZF@f]D;(jjs \OtjON"7q;Zsm:Z:JLrHUqH4cc4?gtd?Aqu6$Bce!A*Q&GYaq9jV;Fe8-h %-emBONt:ttJ%L"([(K(m!>k\*p#l4Aob1ShGY@OHaa*N'eG2qiE;#KF\\?gJ&0CM.? 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b(then)h Fs(\026)1087 367 y Fn(R)1126 464 y Fm(R)1168 447 y Fl(N)1239 434 y Fs(V)1287 446 y Fo(M)1375 434 y Fr(j)p Fs(u)p Fr(j)1469 404 y Fq(2)1535 434 y Fs(dx)22 b Fr(\000)1733 367 y Fn(R)1772 464 y Fm(R)1814 447 y Fl(N)1885 434 y Fr(jr)p Fs(u)p Fr(j)2048 404 y Fq(2)2115 434 y Fs(dx)34 b Ff(c)l(an)f(b)l(e)h(taken)f(arbitr)l(arily)i (lar)l(ge)g(for)f(a)g(wel)t(l)101 542 y(chosen)d Fs(u)22 b Fr(2)i Fs(H)598 512 y Fq(1)635 542 y Ft(\()p Fp(R)727 512 y Fo(N)790 542 y Ft(\))30 b Ff(with)g Fr(k)p Fs(u)p Fr(k)1164 558 y Fo(L)1210 541 y Fj(2)1241 558 y Fq(\()p Fm(R)1309 541 y Fl(N)1362 558 y Fq(\))1415 542 y Ft(=)23 b(1)p Ff(.)201 694 y Ft(The)34 b(pro)r(of)f(of)g(this)h(lemma)g(is)f (straighforw)n(ard)e(and)i(follo)n(ws)g(the)h(same)f(lines)h(as)f(the)h (one)f(of)h(Lemma)f(6.)101 793 y(The)28 b(b)r(est)g(constan)n(t)764 961 y Fs(L)22 b Ft(:=)335 b(sup)954 1036 y Fo(u)p Fk(2)p Fo(H)1096 1020 y Fj(1)1129 1036 y Fq(\()p Fm(R)1197 1020 y Fl(N)1251 1036 y Fq(\))p Fo(;)11 b Fk(k)p Fo(u)p Fk(k)1415 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b(to)f(the)h(original)e(co)r(ordinates)g(w)n(e)i(\014nd)635 3081 y(\()p Fs(x)19 b Fr(\000)f Fs(y)857 3093 y Fo(k)897 3081 y Ft(\))h Fr(\001)g Ft(\()p Fs(x)g Fr(\000)f Fs(y)1212 3093 y Fo(j)1247 3081 y Ft(\))p 635 3118 645 4 v 639 3194 a Fr(j)p Fs(x)h Fr(\000)f Fs(y)852 3206 y Fo(k)892 3194 y Fr(j)915 3170 y Fq(2)967 3194 y Fr(j)p Fs(x)h Fr(\000)f Fs(y)1180 3206 y Fo(j)1214 3194 y Fr(j)1237 3170 y Fq(2)1312 3137 y Fr(\024)k Fs(\014)1478 3020 y Fn(\022)1686 3081 y Ft(1)p 1550 3118 314 4 v 1550 3194 a Fr(j)p Fs(x)d Fr(\000)f Fs(y)1763 3206 y Fo(k)1803 3194 y Fr(j)1826 3170 y Fq(2)1892 3137 y Ft(+)2118 3081 y(1)p 1985 3118 308 4 v 1985 3194 a Fr(j)p Fs(x)h Fr(\000)f Fs(y)2198 3206 y Fo(j)2232 3194 y Fr(j)2255 3170 y Fq(2)2303 3020 y Fn(\023)2382 3137 y Ft(+)2475 3081 y(\(1)h Fr(\000)f Fs(\014)t Ft(\))2734 3051 y Fq(2)p 2475 3118 297 4 v 2598 3194 a Fs(\014)2955 3081 y Ft(1)p 2805 3118 343 4 v 2805 3194 a Fr(j)p Fs(y)2869 3206 y Fo(j)2922 3194 y Fr(\000)g Fs(y)3046 3206 y Fo(k)3087 3194 y Fr(j)3110 3170 y Fq(2)268 3350 y Fn(X)166 3528 y Fq(1)p Fk(\024)p Fo(j)s Fk(6)p Fq(=)p Fo(k)q Fk(\024)p Fo(M)515 3372 y Ft(\()p Fs(x)h Fr(\000)f Fs(y)737 3384 y Fo(k)777 3372 y Ft(\))h Fr(\001)g Ft(\()p Fs(x)g Fr(\000)f Fs(y)1092 3384 y Fo(j)1127 3372 y Ft(\))p 515 3409 645 4 v 519 3485 a Fr(j)p Fs(x)h Fr(\000)f Fs(y)732 3497 y Fo(k)772 3485 y Fr(j)795 3461 y Fq(2)847 3485 y Fr(j)p Fs(x)h Fr(\000)f Fs(y)1060 3497 y Fo(j)1094 3485 y Fr(j)1117 3461 y Fq(2)1252 3428 y Fr(\024)1502 3350 y Fn(X)1399 3528 y Fq(1)p Fk(\024)p Fo(j)s Fk(6)p Fq(=)p Fo(k)q Fk(\024)p Fo(M)1738 3311 y Fn(\024)1782 3428 y Fs(\014)1861 3311 y Fn(\022)2096 3372 y Ft(1)p 1932 3409 370 4 v 1932 3485 a(2)c Fr(j)p Fs(x)k Fr(\000)g Fs(y)2200 3497 y Fo(k)2241 3485 y Fr(j)2264 3461 y Fq(2)2330 3428 y Ft(+)2584 3372 y(1)p 2423 3409 364 4 v 2423 3485 a(2)c Fr(j)p Fs(x)k Fr(\000)g Fs(y)2691 3497 y Fo(j)2726 3485 y Fr(j)2749 3461 y Fq(2)2796 3311 y Fn(\023)2876 3428 y Ft(+)3052 3372 y(\(1)g Fr(\000)g Fs(\014)t Ft(\))3310 3342 y 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Fo(k)2103 4094 y Fr(j)2126 4070 y Fq(2)2191 4037 y Ft(+)g Fs(\015)2317 4049 y Fo(M)2414 4037 y Fs(;)101 4261 y Ft(where)k(w)n(e)h(set)f Fs(\014)625 4273 y Fo(M)722 4261 y Ft(:=)h(\()p Fs(M)17 b Fr(\000)8 b Ft(1\))14 b Fs(\014)t(;)97 b(\015)1338 4273 y Fo(M)1434 4261 y Ft(:=)23 b Fs(\014)1596 4231 y Fk(\000)p Fq(1)1699 4261 y Ft(\(1)8 b Fr(\000)g Fs(\014)t Ft(\))1937 4231 y Fq(2)1975 4261 y Fs(=)p Ft(\(4)14 b Fs(D)2176 4231 y Fq(2)2213 4261 y Ft(\),)24 b(where)e Fs(D)2598 4231 y Fk(\000)p Fq(2)2710 4261 y Ft(=)h(2)2854 4199 y Fn(P)2941 4286 y Fq(1)p Fk(\024)p Fo(j)s Fk(6)p Fq(=)p Fo(k)q Fk(\024)p Fo(M)3284 4261 y Fr(j)p Fs(y)3348 4273 y Fo(j)3391 4261 y Fr(\000)8 b Fs(y)3505 4273 y Fo(k)3545 4261 y Fr(j)3568 4231 y Fk(\000)p Fq(2)3658 4261 y Ft(.)101 4368 y(F)-7 b(rom)27 b(the)h(previous)f(estimate)g(and) h(\(5\))g(w)n(e)f(obtain)206 4521 y Fn(\002)241 4588 y Ft(\()p Fs(N)g Fr(\000)18 b Ft(2\))c Fs(\013)19 b Fr(\000)f Fs(\013)746 4553 y Fq(2)797 4588 y Ft(\(1)g(+)g Fs(\014)1019 4600 y 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b(related)g(b)n(y)1125 5806 y(1)22 b(=)h Fs(t)14 b(a)k Fr(\000)g Fs(a)1510 5772 y Fq(2)1561 5806 y Ft(\(1)g(+)g Fs(\014)g Ft(\()p Fs(M)28 b Fr(\000)18 b Ft(1\)\))23 b Fs(;)97 b(\014)27 b Fr(2)d Ft(\(0)p Fs(;)14 b Ft(1\))22 b Fs(;)p eop end %%Page: 15 15 TeXDict begin 15 14 bop 956 -103 a Fq(HARD)n(Y)30 b(INEQUALITIES)e (WITH)h(SEVERAL)g(SINGULARITIES)788 b(15)101 96 y Ft(whic)n(h)28 b(means)f(that)h(at)f Fs(t)h Ft(\014xed,)g Fs(a)f Ft(has)g(to)h(b)r(e)g (tak)n(en)f(suc)n(h)g(that)1293 238 y(\(1)19 b(+)f Fs(\014)g Ft(\()p Fs(M)27 b Fr(\000)18 b Ft(1\)\))c Fs(a)1921 203 y Fq(2)1977 238 y Fr(\000)k Fs(t)c(a)k Ft(+)g(1)k(=)h(0)g Fs(;)101 380 y Fh(i.e.,)28 b Ft(for)f(some)g Fs(\014)h Fr(2)23 b Ft(\(0)p Fs(;)14 b Ft(1\),)1171 551 y Fs(a)23 b Ft(=)g Fs(a)1370 516 y Fk(\006)1370 577 y Fo(\014)1449 551 y Ft(=)1546 494 y Fs(t)c Fr(\006)1678 423 y Fn(p)p 1761 423 794 4 v 71 x Fs(t)1791 470 y Fq(2)1846 494 y Fr(\000)f Ft(4)c(\(1)k(+)g Fs(\014)g Ft(\()p Fs(M)28 b Fr(\000)18 b Ft(1\)\))p 1546 532 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Fq(2)1004 1376 y Fr(\000)f Ft(4)1142 1309 y Fn(\001)1194 1376 y Fs(=)p Ft(4)p Fs(;)1315 1309 y Fn(\000)1352 1376 y Fs(t)g Ft(+)1483 1307 y Fr(p)p 1552 1307 V 69 x Fs(t)1582 1352 y Fq(2)1638 1376 y Fr(\000)g Ft(4)1776 1309 y Fn(\001)1828 1376 y Fs(=)p Ft(4)1912 1309 y Fn(\001)1949 1376 y Ft(.)37 b(De\014ne)29 b(the)f(function)g Fs(\024)2783 1388 y Fo(M)2884 1376 y Ft(b)n(y)658 1537 y Fs(\024)706 1549 y Fo(M)780 1537 y Ft(\()p Fs(t)p Ft(\))23 b(=)g(0)249 b(if)83 b Fs(t)23 b Fr(\025)g Ft(2)1604 1462 y Fr(p)p 1672 1462 90 4 v 1672 1537 a Fs(M)55 b Fr(\()-14 b(\))46 b Fs(\026)23 b Fr(\024)g Ft(\()p Fs(N)28 b Fr(\000)18 b Ft(2\))2451 1502 y Fq(2)2488 1537 y Fs(=)p Ft(\(4)c Fs(M)9 b Ft(\))22 b Fs(;)331 1672 y(\024)p Ft(\()p Fs(t)p Ft(\))h(=)g Fs(g)624 1684 y Fo(M)697 1672 y Ft(\()q(\026)-43 b Fs(a)773 1684 y Fq(2)p Fo(;M)900 1672 y Ft(\()p Fs(t)p Ft(\)\))250 b(if)83 b(2)23 b Fs(<)f(t)h(<)g Ft(2)1756 1597 y Fr(p)p 1824 1597 V 1824 1672 a Fs(M)55 b Fr(\()-14 b(\))47 b Ft(\()p Fs(N)27 b Fr(\000)18 b Ft(2\))2442 1637 y Fq(2)2479 1672 y Fs(=)p Ft(\(4)c Fs(M)9 b Ft(\))22 b Fs(<)h(\026)g(<)g Ft(\()p Fs(N)k Fr(\000)18 b Ft(2\))3285 1637 y Fq(2)3322 1672 y Fs(=)p Ft(4)k Fs(:)101 1814 y Ft(The)28 b(result)f(of)h(this)g(computation)f(can)g(b)r(e)h (summarized)f(in)n(to)g(the)h(follo)n(wing)f(statemen)n(t.)101 1988 y Fz(Theorem)37 b(10.)44 b Ff(With)34 b(the)h(ab)l(ove)g (notations,)h(let)e Fs(K)6 b Ft(\()p Fs(\026;)14 b(N)t(;)g(M)9 b Ft(\))31 b(:=)2475 1955 y Fq(1)p 2366 1969 251 4 v 2366 2016 a(4)11 b(\()p Fo(M)6 b Fk(\000)p Fq(1\))2641 1988 y Fs(\024)2689 2000 y Fo(M)2776 1895 y Fn(\020)2836 1955 y Fo(N)g Fk(\000)p Fq(2)p 2836 1969 144 4 v 2860 1980 a Fk(p)p 2915 1980 41 3 v 36 x Fo(\026)2989 1895 y Fn(\021)3039 1988 y Ff(.)52 b(If)35 b Fs(\026)c Fr(2)h Ft(\(0)p Fs(;)14 b Ft(\()p Fs(N)30 b Fr(\000)101 2117 y Ft(2\))175 2087 y Fq(2)212 2117 y Fs(=)p Ft(4\))p Ff(,)g(then)815 2272 y Fs(\026)879 2159 y Fn(Z)925 2348 y Fm(R)967 2331 y Fl(N)1038 2272 y Fs(V)1086 2284 y Fo(M)1174 2272 y Fr(j)p Fs(u)p Fr(j)1268 2238 y Fq(2)1328 2272 y Fs(dx)24 b Fr(\024)1529 2159 y Fn(Z)1575 2348 y Fm(R)1617 2331 y Fl(N)1689 2272 y Fr(jr)p Fs(u)p Fr(j)1852 2238 y Fq(2)1912 2272 y Fs(dx)19 b Ft(+)2114 2216 y Fs(K)6 b Ft(\()p Fs(\026;)14 b(N)t(;)g(M)9 b Ft(\))p 2114 2253 426 4 v 2272 2329 a Fs(D)2343 2305 y Fq(2)2563 2159 y Fn(Z)2609 2348 y Fm(R)2651 2331 y Fl(N)2723 2272 y Fr(j)p Fs(u)p Fr(j)2817 2238 y Fq(2)2877 2272 y Fs(dx)101 2451 y Ff(holds)31 b(for)g(any)f Fs(u)23 b Fr(2)g Fs(H)830 2421 y Fq(1)867 2451 y Ft(\()p Fp(R)959 2421 y Fo(N)1022 2451 y Ft(\))30 b Ff(and)h(any)f Fs(y)1446 2463 y Fq(1)1497 2451 y Fs(;)14 b(:)g(:)g(:)27 b(y)1699 2463 y Fo(M)1802 2451 y Ff(in)j Fp(R)1964 2421 y Fo(N)2027 2451 y Ff(.)910 2642 y Ft(3.)41 b Fu(Hard)n(y)31 b(inequalities)g(f)n(or)h(the)g(Dira)n(c)f(opera)-6 b(tor)101 2791 y Ft(3.1.)41 b Fz(The)49 b(Dirac-Coulom)m(b)f(op)s(erator.)41 b Ft(In)i(this)g(section)f(w)n(e)f(deal)h(with)h(Hardy-lik)n(e)e (inequalities)h(for)101 2891 y(the)35 b(Dirac)g(op)r(erator)e(with)i (the)g(m)n(ultip)r(olar)f(Coulom)n(b)g(p)r(oten)n(tial)h Fs(\027)19 b(W)2441 2903 y Fo(M)2501 2891 y Ft(,)37 b(with)e Fs(\027)41 b Fr(2)35 b Ft(\(0)p Fs(;)14 b Ft(1\))34 b(and)h Fs(W)3395 2903 y Fo(M)3469 2891 y Ft(\()p Fs(x)p Ft(\))h(=)101 2939 y Fn(P)189 2960 y Fo(M)189 3026 y(k)q Fq(=1)421 2969 y(1)p 338 2983 199 4 v 338 3030 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)482 3039 y Fl(k)517 3030 y Fk(j)547 3001 y Ft(.)61 b(Coulom)n(b)36 b(singularities)e(are)h(\014xed)h(at)g Fs(y)1970 3013 y Fq(1)2021 3001 y Fs(;)14 b(:)g(:)g(:)27 b(y)2223 3013 y Fo(M)2334 3001 y Fr(2)37 b Fp(R)2486 2971 y Fq(3)2523 3001 y Ft(.)62 b(The)36 b(Dirac-Coulom)n(b)e(op)r (erator)101 3110 y(tak)n(es)27 b(the)h(form)1383 3217 y Fs(H)1452 3229 y Fo(\027;W)1567 3237 y Fl(M)1657 3217 y Ft(:=)23 b Fs(H)i Fr(\000)18 b Fs(\027)h(W)2083 3229 y Fo(M)2157 3217 y Ft(\()p Fs(x)p Ft(\))14 b Fp(I)2314 3229 y Fq(4)2376 3217 y Fs(;)456 3402 y(H)30 b Ft(:=)22 b Fr(\000)p Fs(i)15 b(~)-43 b(\013)18 b Fr(\001)h(r)f Ft(+)g Fs(\014)88 b Ft(where)82 b Fs(\014)28 b Ft(:=)1671 3285 y Fn(\022)1732 3352 y Fp(I)1764 3364 y Fq(2)1931 3352 y Ft(0)1746 3451 y(0)97 b Fr(\000)p Fp(I)1982 3463 y Fq(2)2019 3285 y Fn(\023)2177 3402 y Fs(\013)2230 3414 y Fo(k)2294 3402 y Ft(:=)2405 3285 y Fn(\022)2489 3352 y Ft(0)106 b Fs(\033)2684 3364 y Fo(k)2466 3451 y Fs(\033)2513 3463 y Fo(k)2661 3451 y Ft(0)2726 3285 y Fn(\023)2800 3402 y Fs(;)37 b(k)26 b Ft(=)d(1)14 b Fs(;)36 b Ft(2)14 b Fs(;)37 b Ft(3)14 b Fs(:)101 3635 y Ft(Here)33 b Fp(I)335 3647 y Fo(n)413 3635 y Ft(the)g(iden)n(tit)n(y)g(matrix)f(in)h(\()p Fp(C)1342 3605 y Fq(3)1379 3635 y Ft(\))1411 3605 y Fo(n)1490 3635 y Ft(and)f Fs(\033)1703 3647 y Fq(1)1773 3635 y Ft(=)1869 3518 y Fn(\022)1930 3584 y Ft(0)82 b(1)1930 3684 y(1)g(0)2096 3518 y Fn(\023)2157 3635 y Ft(,)34 b Fs(\033)2261 3647 y Fq(2)2330 3635 y Ft(=)2426 3518 y Fn(\022)2488 3584 y Ft(0)82 b Fr(\000)p Fs(i)2494 3684 y(i)115 b Ft(0)2705 3518 y Fn(\023)2766 3635 y Ft(,)35 b Fs(\033)2871 3647 y Fq(3)2940 3635 y Ft(=)3036 3518 y Fn(\022)3097 3584 y Ft(1)115 b(0)3097 3684 y(0)83 b Fr(\000)p Ft(1)3328 3518 y Fn(\023)3422 3635 y Ft(are)31 b(the)101 3779 y(P)n(auli)c(matrices.)201 3921 y(If)j Fs(W)42 b Ft(is)30 b(a)f(b)r(ounded)i(function)f(whic)n(h)g(tends)g(to) g(0)f(at)h(in\014nit)n(y)-7 b(,)31 b(one)e(can)h(easily)f(pro)n(v)n(e)f (that)i(the)g(op)r(erator)101 4021 y Fs(H)f Fr(\000)22 b Fs(W)45 b Ft(with)34 b(domain)f Fs(H)981 3991 y Fq(1)1018 4021 y Ft(\()p Fp(R)1110 3991 y Fq(3)1147 4021 y Ft(\))h(is)f (self-adjoin)n(t.)54 b(If)33 b Fs(W)46 b Ft(has)32 b(singularities,)i (as)e(it)i(is)f(the)h(case)e(for)h(instance)101 4121 y(if)39 b Fs(W)53 b Ft(=)40 b Fs(\027)20 b(W)563 4133 y Fo(M)637 4121 y Ft(,)41 b(one)d(is)g(in)n(terested)g(in)g(de\014ning) h(self-adjoin)n(t)f(extensions)f(of)h(\()p Fs(H)33 b Fr(\000)25 b Fs(W)12 b Ft(\))17 b Fe(\026)e Fs(C)3213 4091 y Fk(1)3207 4141 y Fq(0)3284 4121 y Ft(\()p Fp(R)3376 4091 y Fq(3)3413 4121 y Ft(\).)70 b(The)101 4220 y(metho)r(d)25 b(used)g(to)f(do)g(this)h(dep)r(ends)g(on)f(the)h(singularit)n(y)-7 b(.)35 b(Let)24 b(us)h(for)f(instance)g(consider)f(Coulom)n(b)h(p)r (oten)n(tials)101 4320 y Fs(\027)19 b(W)239 4332 y Fq(1)277 4320 y Ft(\()p Fs(x)p Ft(\))27 b(=)f Fs(\027)5 b(=)p Fr(j)p Fs(x)p Fr(j)p Ft(,)31 b Fs(\027)g(>)26 b Ft(0.)42 b(Then)30 b(for)f Fs(\027)i Fr(2)c Ft(\(0)p Fs(;)14 b(\031)s(=)p Ft(2])29 b(one)g(can)g(use)g(the)h(pseudo-F)-7 b(riedric)n(h)28 b(extension)h(metho)r(d)101 4420 y(to)f(de\014ne)g(an)f(extension)g (whic)n(h)h(satis\014es)1236 4561 y Fr(D)r Ft(\()p Fs(H)1403 4573 y Fo(\027;W)1518 4581 y Fj(1)1556 4561 y Ft(\))23 b Fr(\032)g(D)r Ft(\()p Fr(j)p Fs(H)7 b Fr(j)1919 4527 y Fq(1)p Fo(=)p Fq(2)2024 4561 y Ft(\))23 b(=)g Fs(H)2243 4527 y Fq(1)p Fo(=)p Fq(2)2347 4561 y Ft(\()p Fp(R)2439 4527 y Fq(3)2477 4561 y Ft(\))14 b Fs(:)101 4706 y Ft(This)27 b(result)f(is)g(obtained)h(b)n(y)f(using)g(Kato's)f(inequalit)n(y)h(:) 37 b Fr(j)p Fs(H)7 b Fr(j)22 b(\025)2269 4673 y Fq(2)p 2221 4687 130 4 v 2221 4735 a Fo(\031)13 b Fk(j)p Fo(x)p Fk(j)2360 4706 y Ft(.)37 b(Actually)27 b(one)f(can)g(pro)n(v)n(e)f (that)h Fs(H)3528 4718 y Fo(\027;W)3643 4726 y Fj(1)101 4833 y Ft(is)i(essen)n(tially)e(self-adjoin)n(t)h(if)i Fs(\027)f(<)1243 4764 y Fr(p)p 1312 4764 42 4 v 69 x Ft(3)o Fs(=)p Ft(2)f(\([40)o(]\).)201 4937 y(When)21 b(the)g(singularities)e(are)g(stronger,)h(that)h(is)f(for)g Fs(\027)29 b Fr(\025)2025 4868 y(p)p 2095 4868 V 2095 4937 a Ft(3)o Fs(=)p Ft(2,)21 b(other)f(metho)r(ds)h(need)f(to)g(b)r(e) h(used.)35 b(V)-7 b(arious)101 5037 y(w)n(orks)28 b(ha)n(v)n(e)g(dealt) h(with)h(this)f(issue,)h(and)f(it)g(app)r(ears)g(that)g(for)g(p)r(oten) n(tials)g Fs(W)41 b Ft(whic)n(h)29 b(ha)n(v)n(e)f(a)h(singularit)n(y)f (at)101 5136 y(the)g(origin,)f(the)h(condition)101 5278 y(\(6\))1365 b(sup)1574 5349 y Fo(x)p Fk(6)p Fq(=0)1725 5278 y Fr(j)p Fs(x)p Fr(j)14 b Fs(W)e Ft(\()p Fs(x)p Ft(\))24 b Fs(<)f Ft(1)14 b Fs(;)101 5486 y Ft(is)37 b(su\016cien)n(t)g(to)g(de\014ne)g(a)f(distinguished)h(extension)f(of)h (\()p Fs(H)32 b Fr(\000)24 b Fs(W)12 b Ft(\))39 b Fe(\026)f Fs(C)2504 5456 y Fk(1)2498 5507 y Fq(0)2575 5486 y Ft(\()p Fp(R)2667 5456 y Fq(3)2704 5486 y Ft(\).)65 b(This)37 b(has)f(b)r(een)h(done)g(b)n(y)101 5586 y(v)-5 b(arious)30 b(metho)r(ds)i(:)45 b(see)31 b([47)o(,)g(48)o(,)h(49)o(])f(in)h(the)g (case)e(of)i(semib)r(ounded)f(p)r(oten)n(tials)g Fs(W)44 b Ft(and)31 b([39)o(])h(without)f(this)101 5696 y(assumption.)40 b(The)29 b(extension)1130 5675 y Fn(e)1116 5696 y Fs(T)40 b Ft(is)28 b(then)i(de\014ned)f(as)1883 5675 y Fn(e)1870 5696 y Fs(T)36 b Ft(:=)24 b Fs(T)2128 5666 y Fk(\003)2165 5696 y Fe(\026)p Fs(D)r Ft(\()p Fs(T)2364 5666 y Fk(\003)2401 5696 y Ft(\))c Fr(\\)f Fs(D)r Ft(\()p Fr(j)p Fs(x)p Fr(j)2723 5666 y Fk(\000)p Fq(1)p Fo(=)p Fq(2)2880 5696 y Ft(\).)41 b(On)28 b(the)i(other)e(hand,)101 5806 y(under)33 b(Assumption)g(\(6\)) q(,)h(Nenciu)g(pro)n(v)n(ed)d(in)i([38])g(the)g(existence)g(of)g(a)g (unique)g(extension)3139 5785 y Fn(e)3125 5806 y Fs(T)45 b Ft(with)33 b(domain)p eop end %%Page: 16 16 TeXDict begin 16 15 bop 101 -103 a Fq(16)995 b(R.)22 b(BOSI,)g(J.)g(DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)101 96 y Ft(con)n(tained)k(in)g Fs(H)647 66 y Fq(1)p Fo(=)p Fq(2)751 96 y Ft(\()p Fp(R)843 66 y Fq(3)880 96 y Fs(;)14 b Fp(C)977 66 y Fq(4)1014 96 y Ft(\).)37 b(Finally)-7 b(,)26 b(in)h(the)f(case)f(of)h(semib)r(ounded)g(p)r(oten)n(tials)g (satisfying)g(\(6\),)h(Klaus)e(and)101 195 y(W)r(\177)-44 b(ust)28 b(pro)n(v)n(ed)e(in)i([33)o(])g(that)g(the)g(aforemen)n (tioned)e(metho)r(ds)i(lead)g(to)f(the)h(same)f(self-adjoin)n(t)g (extension.)201 344 y(As)22 b(in)g(the)h(case)e(of)h(the)g(Sc)n(hr\177) -42 b(odinger)21 b(op)r(erator,)g(Hardy)g(inequalities)h(for)g(Dirac)f (op)r(erators)f(pro)n(vide)h(us)h(with)101 445 y(lo)n(w)n(er)j (estimates)g(for)g(some)h(eigen)n(v)-5 b(alues.)35 b(If)26 b Fs( )g Ft(=)1722 378 y Fn(\000)1761 408 y Fo(\036)1760 474 y(\037)1801 378 y Fn(\001)1865 445 y Ft(is)g(an)g(eigenfunction)g (of)f Fs(H)2730 457 y Fo(\027;W)2885 445 y Ft(with)i(eigen)n(v)-5 b(alue)25 b Fs(\025)p Ft(,)h(the)101 551 y(eigen)n(v)-5 b(alue)27 b(equation)g(can)g(b)r(e)h(rewritten)f(as)1400 699 y Fs(K)6 b(\037)18 b Ft(+)g Fs(\036)g Fr(\000)h Fs(W)25 b(\036)f Ft(=)e Fs(\025)14 b(\036)24 b(;)1409 824 y(K)6 b(\036)18 b Fr(\000)g Fs(\037)g Fr(\000)g Fs(W)26 b(\037)d Ft(=)g Fs(\025)14 b(\037)23 b(;)101 972 y Ft(where)k Fs(K)i Ft(:=)23 b Fr(\000)p Fs(i)12 b(~)-40 b(\033)20 b Fr(\001)f(r)p Ft(.)37 b(W)-7 b(e)28 b(can)f(eliminate)h(the)g(lo)n(w) n(er)e(comp)r(onen)n(t)h Fs(\037)p Ft(.)37 b(The)28 b(equation)f(for)g Fs(\036)h Ft(is)1269 1166 y Fs(K)1360 1049 y Fn(\022)1559 1110 y Fs(K)6 b(\036)p 1431 1147 383 4 v 1431 1223 a Ft(1)18 b(+)g Fs(\025)g Ft(+)h Fs(W)1823 1049 y Fn(\023)1903 1166 y Ft(+)f Fs(\036)h Fr(\000)f Fs(W)26 b(\036)d Ft(=)g Fs(\025)14 b(\036)101 1394 y Ft(and)33 b(so,)f Fs(\036)h Ft(app)r(ears)f(as)f(a)h(critical)g(p)r(oin)n(t)h(of)f Fs(\036)g Fr(7!)1771 1327 y Fn(R)1810 1423 y Fm(R)1852 1407 y Fj(3)1916 1353 y Fk(j)o Fo(~)-33 b(\033)r Fk(\001r)11 b Fo(\036)p Fk(j)2122 1328 y Fj(2)p 1912 1375 246 4 v 1912 1422 a Fq(1+)p Fo(\025)p Fq(+)p Fo(W)2199 1394 y Fs(dx)22 b Ft(+)f(\(1)h Fr(\000)f Fs(\025)p Ft(\))2673 1327 y Fn(R)2713 1423 y Fm(R)2755 1407 y Fj(3)2805 1394 y Fr(j)p Fs(\036)p Fr(j)2900 1363 y Fq(2)2969 1394 y Fs(dx)h Fr(\000)3168 1327 y Fn(R)3207 1423 y Fm(R)3249 1407 y Fj(3)3299 1394 y Fs(W)k Fr(j)p Fs(\036)p Fr(j)3498 1363 y Fq(2)3567 1394 y Fs(dx)p Ft(,)101 1495 y(with)i(critical)f(v)-5 b(alue)27 b(0.)36 b(Suc)n(h)27 b(a)g(functional)g(is)g(monotone)g (decreasing)e(as)i(a)f(function)i(of)f Fs(\025)p Ft(.)38 b(Hence)27 b(if)h(\003)22 b(=)h Fs(\025)3643 1507 y Fq(1)101 1595 y Ft(is)28 b(the)g(smallest)f(eigen)n(v)-5 b(alue)27 b(of)g Fs(H)1207 1607 y Fo(\027;W)1364 1595 y Ft(in)h(\()p Fr(\000)p Ft(1)p Fs(;)14 b Ft(1\),)26 b(then)101 1799 y(\(7\))876 1686 y Fn(Z)922 1875 y Fm(R)964 1858 y Fj(3)1058 1743 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)1346 1713 y Fq(2)p 1025 1780 393 4 v 1025 1856 a Ft(1)k(+)g(\003)g(+)g Fs(W)1450 1799 y(dx)h Ft(+)f(\(1)g Fr(\000)g Ft(\003\))1921 1686 y Fn(Z)1967 1875 y Fm(R)2009 1858 y Fj(3)2059 1799 y Fr(j)p Fs(\036)p Fr(j)2154 1765 y Fq(2)2215 1799 y Fs(dx)24 b Fr(\025)2417 1686 y Fn(Z)2463 1875 y Fm(R)2505 1858 y Fj(3)2555 1799 y Fs(W)i Fr(j)p Fs(\036)p Fr(j)2754 1765 y Fq(2)2815 1799 y Fs(dx)101 1994 y Ft(holds)e(with)h(\003)d(=)h Fs(\025)717 2006 y Fq(1)755 1994 y Ft(.)36 b(Recipro)r(cally)-7 b(,)23 b(for)h(a)g(large)e(class)i(of)g(p)r(oten)n(tials)f Fs(W)n Ft(,)i(an)n(y)f(eigen)n(v)-5 b(alue)23 b(of)h Fs(H)3185 2006 y Fo(\027;W)3338 1994 y Ft(in)h(\()p Fr(\000)p Ft(1)p Fs(;)14 b Ft(1\))101 2103 y(can)19 b(b)r(e)h(c)n(haracterized)e(as)h(a) g(min-max)g(of)h(the)g(Ra)n(yleigh)e(quotien)n(t)h(\()q Fs(H)2320 2115 y Fo(\027;W)2462 2103 y Fs( )s(;)14 b( )s Ft(\))h Fs(=)p Fr(k)p Fs( )s Fr(k)2843 2073 y Fq(2)2843 2130 y Fo(L)2889 2113 y Fj(2)2919 2130 y Fq(\()p Fm(R)2987 2113 y Fj(3)3019 2130 y Fo(;)p Fm(C)3081 2113 y Fj(4)3114 2130 y Fq(\))3163 2103 y Ft(where)k Fs( )26 b Ft(=)3563 2036 y Fn(\000)3602 2066 y Fo(\036)3601 2132 y(\037)3643 2036 y Fn(\001)101 2211 y Ft(is)39 b(decomp)r(osed)f(in)n(to)h(an)f (upp)r(er)h(comp)r(onen)n(t)g Fs(\036)g Ft(and)g(a)f(lo)n(w)n(er)f (one,)42 b Fs(\037)p Ft(.)70 b(Under)39 b(appropriate)e(conditions,)101 2310 y(see)27 b([13,)g(14)o(],)336 2512 y Fs(\025)398 2399 y Fn(Z)444 2587 y Fm(R)486 2571 y Fj(3)537 2512 y Fr(j)p Fs(\036)p Fr(j)632 2477 y Fq(2)693 2512 y Fs(dx)c Ft(=)g(max)951 2561 y Fo(\037)1110 2455 y Ft(\()p Fs(H)1211 2467 y Fo(\027;W)1340 2455 y Fs( )s(;)14 b( )s Ft(\))p 1095 2493 443 4 v 1095 2569 a Fr(k)p Fs( )s Fr(k)1236 2540 y Fq(2)1236 2597 y Fo(L)1282 2580 y Fj(2)1314 2597 y Fq(\()p Fm(R)1382 2580 y Fj(3)1414 2597 y Fo(;)p Fm(C)1476 2580 y Fj(4)1508 2597 y Fq(\))1571 2512 y Ft(=)1659 2399 y Fn(Z)1705 2587 y Fm(R)1747 2571 y Fj(3)1835 2455 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Fs(\036)p Fr(j)2124 2425 y Fq(2)p 1807 2493 383 4 v 1807 2569 a Ft(1)k(+)g Fs(\025)h Ft(+)f Fs(W)2223 2512 y(dx)h Ft(+)2415 2399 y Fn(Z)2461 2587 y Fm(R)2503 2571 y Fj(3)2554 2512 y Fr(j)p Fs(\036)p Fr(j)2649 2477 y Fq(2)2709 2512 y Fs(dx)24 b Fr(\025)2911 2399 y Fn(Z)2957 2587 y Fm(R)2999 2571 y Fj(3)3049 2512 y Fs(W)i Fr(j)p Fs(\036)p Fr(j)3248 2477 y Fq(2)3309 2512 y Fs(dx)e(;)101 2731 y Ft(whic)n(h)k(implicitly)g (determines)g Fs(\025)23 b Ft(=)g Fs(\025)p Ft([)p Fs(\036)p Ft(].)38 b(The)27 b(minimization)h(step)g(is)f(then)h(reduced)g(to)f (establish)g(that)1622 2879 y Fs(\025)1670 2891 y Fq(1)1730 2879 y Ft(=)c(min)1825 2933 y Fo(\036)p Fk(6)p Fq(=0)1970 2879 y Fs(\025)p Ft([)p Fs(\036)p Ft(])h Fs(:)101 3067 y Ft(This)31 b(completes)f(the)h(pro)r(of,)f(at)g(least)g(at)h(a)f (formal)f(lev)n(el,)i(that)g(\014nding)f(the)h(lo)n(w)n(est)e(eigen)n (v)-5 b(alue)30 b(of)g Fs(H)3452 3079 y Fo(\027;W)3611 3067 y Ft(in)101 3167 y(the)25 b(gap)f(\()p Fr(\000)p Ft(1)p Fs(;)14 b Ft(1\))24 b(is)h(equiv)-5 b(alen)n(t)24 b(to)h(getting)g(the)g(b)r(est)g(constan)n(t)f(in)h(Inequalit)n(y)g (\(7\).)36 b(It)26 b(w)n(as)d(pro)n(v)n(ed)h(in)h([13)o(,)g(14)o(])101 3266 y(that)g(for)g(a)f(large)g(class)g(of)h(p)r(oten)n(tials)f(with)i (at)e(most)h(one)g(singularit)n(y)-7 b(,)24 b(the)h(\014rst)g(eigen)n (v)-5 b(alue)24 b(of)h Fs(H)20 b Fr(\000)13 b Fs(W)36 b Ft(in)25 b(the)101 3366 y(sp)r(ectral)30 b(gap)f(\()p Fr(\000)p Ft(1)p Fs(;)14 b Ft(1\))29 b(is)h(the)h(largest)d(constan)n (t)i(\003)g(for)f(whic)n(h)h(\(7\))g(holds.)44 b(F)-7 b(or)30 b(instance,)g(in)h(the)f(case)f(of)h(the)101 3466 y(radial)d(Coulom)n(b)g(p)r(oten)n(tial,)g Fr(\000)p Fs(\027)5 b(=)p Fr(j)p Fs(x)p Fr(j)p Ft(,)28 b(for)f(all)g Fs(\027)i Fr(2)23 b Ft(\(0)p Fs(;)14 b Ft(1\),)101 3667 y(\(8\))736 3554 y Fn(Z)782 3743 y Fm(R)824 3726 y Fj(3)975 3611 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Fs(\036)p Fr(j)1264 3581 y Fq(2)p 884 3648 509 4 v 884 3724 a Ft(1)k(+)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))19 b(+)1325 3691 y Fo(\027)p 1305 3705 78 4 v 1305 3753 a Fk(j)p Fo(x)p Fk(j)1425 3667 y Fs(dx)h Ft(+)1618 3600 y Fn(\002)1652 3667 y Ft(1)e Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1961 3600 y Fn(\003)2010 3554 y(Z)2056 3743 y Fm(R)2098 3726 y Fj(3)2149 3667 y Fr(j)p Fs(\036)p Fr(j)2244 3633 y Fq(2)2295 3667 y Fs(dx)24 b Fr(\025)2497 3554 y Fn(Z)2543 3743 y Fm(R)2585 3726 y Fj(3)2669 3611 y Fs(\027)p 2645 3648 94 4 v 2645 3724 a Fr(j)p Fs(x)p Fr(j)2762 3667 y(j)p Fs(\036)p Fr(j)2857 3633 y Fq(2)2909 3667 y Fs(dx)g(;)101 3900 y Ft(where)30 b Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))29 b(:=)655 3831 y Fr(p)p 724 3831 227 4 v 69 x Ft(1)18 b Fr(\000)g Fs(\027)913 3876 y Fq(2)981 3900 y Ft(is)31 b(the)g(b)r(est)g(p)r(ossible)f(constan)n(t.)45 b(P)n(assing)29 b(to)h(the)h(limit)h Fs(\027)h Fr(!)28 b Ft(1)3068 3912 y Fk(\000)3124 3900 y Ft(,)j(Inequalit)n(y)h(\(8\))101 4000 y(also)27 b(holds)g(for)g Fs(\027)h Ft(=)23 b(1.)201 4099 y(In)37 b(this)g(section)g(w)n(e)f(sho)n(w)g(that)h(inequalities)g (lik)n(e)g(\(7\))g(can)f(b)r(e)i(pro)n(v)n(ed)d(for)h(the)i(m)n(ultip)r (olar)e(p)r(oten)n(tials)101 4199 y Fs(\027)19 b(W)239 4211 y Fo(M)340 4199 y Ft(and)27 b(pro)n(vide)e(us)i(with)g(lo)n(w)n (er)e(estimates)h(for)g(the)h(eigen)n(v)-5 b(alues)26 b(of)g Fs(H)e Fr(\000)16 b Fs(\027)j(W)2771 4211 y Fo(M)2872 4199 y Ft(in)26 b(the)h(in)n(terv)-5 b(al)26 b(\()p Fr(\000)p Ft(1)p Fs(;)14 b Ft(1\).)101 4299 y(W)-7 b(e)30 b(shall)g(use)f(the)i (IMS)f(metho)r(d)g(to)g(lo)r(calize)f(the)h(in)n(tegrals)e(and)i(to)f (reduce)h(the)g(problem)f(to)h(lo)r(cally)f(radial)101 4398 y(p)r(oten)n(tials.)101 4575 y(3.2.)41 b Fz(A)24 b(priori)g(estimates.)40 b Ft(Consider)20 b(as)g(in)i(Section)f(1)f(a)h (partition)g(of)g(unit)n(y)g(de\014ned)g(b)n(y)h(\(2\))q(.)34 b(The)21 b(op)r(erator)101 4681 y Fs(H)170 4693 y Fo(\027;W)285 4701 y Fl(M)380 4681 y Ft(acts)27 b(on)g(the)h(4-spinors)e Fs( )g Ft(=)1329 4614 y Fn(\000)1368 4645 y Fo(\036)1367 4710 y(\037)1408 4614 y Fn(\001)1470 4681 y Fr(2)d Fs(H)1624 4651 y Fq(1)1661 4681 y Ft(\()p Fp(R)1753 4651 y Fq(3)1791 4681 y Fs(;)14 b Fp(C)1888 4651 y Fq(4)1925 4681 y Ft(\).)37 b(If)28 b(w)n(e)f(write)h Fs(\036)23 b Ft(=)2595 4614 y Fn(\000)2633 4645 y Fo(\036)2673 4653 y Fj(1)2633 4710 y Fo(\036)2673 4718 y Fj(2)2705 4614 y Fn(\001)2771 4681 y Ft(with)28 b Fs(\036)3009 4693 y Fq(1)3047 4681 y Ft(,)g Fs(\036)3147 4693 y Fq(2)3207 4681 y Fr(2)c Fs(H)3362 4651 y Fq(1)3399 4681 y Ft(\()p Fp(R)3491 4651 y Fq(3)3528 4681 y Fs(;)14 b Fp(C)p Ft(\),)101 4809 y(the)24 b(expressions)d Fr(j)p Fs(\036)p Fr(j)763 4779 y Fq(2)801 4809 y Ft(,)j Fr(jr)p Fs(\036)p Fr(j)1012 4779 y Fq(2)1050 4809 y Ft(,)g Fr(j)n Fs(~)-40 b(\033)12 b Fr(\001)d(r)14 b Fs(\036)p Fr(j)1366 4779 y Fq(2)1427 4809 y Ft(denote)23 b(resp)r(ectiv)n(ely)f (the)i(quan)n(tities)e Fr(j)p Fs(\036)2727 4821 y Fq(1)2765 4809 y Fr(j)2788 4779 y Fq(2)2835 4809 y Ft(+)9 b Fr(j)p Fs(\036)2981 4821 y Fq(2)3018 4809 y Fr(j)3041 4779 y Fq(2)3078 4809 y Ft(,)3125 4747 y Fn(P)3213 4767 y Fq(3)3213 4834 y Fo(k)q Fq(=1)3352 4809 y Fr(j)p Fs(@)3419 4821 y Fo(k)3460 4809 y Fs(\036)3509 4821 y Fq(1)3547 4809 y Fr(j)3570 4779 y Fq(2)3616 4809 y Ft(+)101 4910 y Fr(j)p Fs(@)168 4922 y Fo(k)209 4910 y Fs(\036)258 4922 y Fq(2)296 4910 y Fr(j)319 4880 y Fq(2)383 4910 y Ft(and)27 b Fr(j)p Fs(@)611 4922 y Fq(3)648 4910 y Fs(\036)697 4922 y Fq(1)752 4910 y Ft(+)16 b Fs(@)877 4922 y Fq(1)914 4910 y Fs(\036)963 4922 y Fq(2)1018 4910 y Fr(\000)g Fs(i)e(@)1186 4922 y Fq(2)1223 4910 y Fs(\036)1272 4922 y Fq(2)1310 4910 y Fr(j)1333 4880 y Fq(2)1387 4910 y Ft(+)i Fr(j)p Fs(@)1535 4922 y Fq(1)1573 4910 y Fs(\036)1622 4922 y Fq(1)1676 4910 y Ft(+)g Fs(i)e(@)1844 4922 y Fq(2)1881 4910 y Fs(\036)1930 4922 y Fq(1)1985 4910 y Fr(\000)i Fs(@)2110 4922 y Fq(3)2147 4910 y Fs(\036)2196 4922 y Fq(2)2234 4910 y Fr(j)2257 4880 y Fq(2)2321 4910 y Ft(where)27 b(the)g(notation)f Fs(@)3078 4922 y Fo(k)3146 4910 y Ft(denotes)g Fs(@)5 b(=@)3580 4922 y Fo(x)3618 4931 y Fl(k)3658 4910 y Ft(,)101 5009 y Fs(k)26 b Ft(=)d(1,)k(2,)g(3.)37 b(Denoting)27 b(b)n(y)h Fs(L)22 b Ft(:=)h Fr(\000)p Fs(i)14 b Fr(r)k(^)g Fs(x)29 b Ft(the)e(angular)g(momen)n(tum)g(op)r(erator,)f(w)n(e)i (recall)e(that)101 5192 y(\(9\))1095 b Fs(~)-40 b(\033)22 b Fr(\001)c(r)24 b Ft(=)1594 5100 y Fn(\020)1642 5192 y Fs(~)-40 b(\033)22 b Fr(\001)1787 5136 y Fs(x)p 1764 5173 94 4 v 1764 5249 a Fr(j)p Fs(x)p Fr(j)1868 5100 y Fn(\021)o(\020)1967 5192 y Fs(@)2011 5204 y Fo(r)2066 5192 y Fr(\000)2159 5136 y Ft(1)p 2159 5173 42 4 v 2160 5249 a Fs(r)2223 5192 y(~)-41 b(\033)22 b Fr(\001)d Fs(L)2392 5100 y Fn(\021)2455 5192 y Fs(;)101 5389 y Ft(with)33 b Fs(r)g Ft(=)d Fr(j)p Fs(x)p Fr(j)j Ft(and)f Fs(@)796 5401 y Fo(r)864 5389 y Ft(=)969 5356 y Fo(x)p 969 5370 38 4 v 972 5418 a(r)1038 5389 y Fr(\001)21 b(r)p Ft(.)51 b(The)32 b(sp)r(ectrum)h(of)d Fs(~)-40 b(\033)25 b Fr(\001)c Fs(L)g Ft(+)g(1)32 b(is)g(the)g(discrete)g(set)g Fr(f)p Fs(l)g Fr(2)f Fp(Z)44 b Ft(:)h Fs(l)32 b Fr(6)p Ft(=)e(0)p Fr(g)p Ft(.)50 b(See)101 5493 y([12)o(])34 b(and)g([44)o(])g(for)f (more)g(details.)55 b(If)35 b Fs(P)1399 5505 y Fo(l)1458 5493 y Ft(is)f(the)g(sp)r(ectral)f(pro)5 b(jection)33 b(on)n(to)g(the)h(eigenspace)f(of)h Fs(H)3348 5463 y Fq(1)3385 5493 y Ft(\()p Fp(R)3477 5463 y Fq(3)3514 5493 y Fs(;)14 b Fp(C)3611 5463 y Fq(2)3648 5493 y Ft(\))101 5593 y(corresp)r(onding)25 b(to)i(the)g(eigen)n(v)-5 b(alue)26 b Fs(l)i Ft(of)d Fs(~)-40 b(\033)20 b Fr(\001)d Fs(L)f Ft(+)g(1,)27 b(then,)h(in)f(analogy)d(with)k(Lemma)e(5)h(of)f ([12)o(],)i(w)n(e)e(can)g(pro)n(v)n(e)101 5693 y(that)505 5806 y Fs(P)558 5818 y Fo(k)613 5806 y Ft(\()n Fs(~)-40 b(\033)22 b Fr(\001)d(r)p Ft(\))857 5772 y Fq(2)908 5806 y Fs(P)961 5818 y Fo(l)1010 5806 y Ft(=)k Fs(P)1151 5818 y Fo(l)1190 5806 y Ft(\()n Fs(~)-40 b(\033)22 b Fr(\001)d(r)p Ft(\))1434 5772 y Fq(2)1486 5806 y Fs(P)1539 5818 y Fo(k)1603 5806 y Fr(\021)j Ft(0)83 b(in)23 b Fs(H)1983 5772 y Fq(1)2020 5806 y Ft(\()p Fp(R)2112 5772 y Fq(3)2150 5806 y Fs(;)14 b Fp(C)2247 5772 y Fq(2)2284 5806 y Ft(\))83 b Fr(8)23 b Fs(k)17 b(;)37 b(l)24 b Fr(2)g Fp(Z)19 b Fr(n)f(f)p Ft(0)p Fr(g)c Fs(;)35 b(k)26 b Fr(6)p Ft(=)c Fs(l)j(:)p eop end %%Page: 17 17 TeXDict begin 17 16 bop 956 -103 a Fq(HARD)n(Y)30 b(INEQUALITIES)e (WITH)h(SEVERAL)g(SINGULARITIES)788 b(17)101 96 y Ft(This)38 b(implies)f(that)h Fr(h)p Fs(P)867 108 y Fo(k)922 96 y Fs(\036;)14 b(P)1061 108 y Fo(l)1101 96 y Fs(\036)p Fr(i)1182 111 y Fo(L)1228 94 y Fj(2)1261 111 y Fq(\()p Fm(R)1329 94 y Fj(3)1361 111 y Fo(;m)d(dx)p Fq(\))1592 96 y Ft(=)39 b(0,)g(for)e Fs(k)42 b Fr(6)p Ft(=)d Fs(l)g Ft(and)e(for)g(eac)n(h)f(measurable)g(radial)g(function)101 201 y Fs(m)23 b Ft(=)g Fs(m)p Ft(\()p Fr(j)p Fs(x)p Fr(j)p Ft(\).)37 b(Hence)27 b(the)g Fs(L)1020 171 y Fq(2)1057 201 y Ft(-norm)e(of)g Fs(~)-40 b(\033)19 b Fr(\001)e(r)p Fs(\036)27 b Ft(can)f(b)r(e)h(written)f(in)h(terms)f(of)h(the)g(ab)r(o) n(v)n(e-men)n(tioned)d(sp)r(ectral)101 301 y(decomp)r(osition)j(as)101 451 y(\(10\))41 b Fr(k)p Ft(\()n Fs(~)-40 b(\033)21 b Fr(\001)c(r)p Ft(\))d Fs(\036)p Fr(k)678 416 y Fq(2)678 473 y Fo(L)724 457 y Fj(2)756 473 y Fq(\()p Fm(R)824 457 y Fj(3)857 473 y Fo(;)d(m)g(dx)p Fq(\))1083 451 y Ft(=)1231 372 y Fn(X)1171 554 y Fo(l)p Fk(2)p Fm(Z)p Fk(nf)p Fq(0)p Fk(g)1425 451 y Fr(k)p Ft(\()n Fs(~)-40 b(\033)20 b Fr(\001)e(r)p Ft(\))c Fs(P)1775 463 y Fo(l)1801 451 y Fs(\036)p Fr(k)1892 416 y Fq(2)1892 473 y Fo(L)1938 457 y Fj(2)1970 473 y Fq(\()p Fm(R)2038 457 y Fj(3)2070 473 y Fo(;)d(m)g(dx)p Fq(\))2297 451 y Ft(=)2444 372 y Fn(X)2384 554 y Fo(l)p Fk(2)p Fm(Z)p Fk(nf)p Fq(0)p Fk(g)2638 451 y Fr(k)o Ft(\()q Fo(@)2747 459 y Fl(r)2781 451 y Fk(\000)2843 421 y Fj(\()p Fl(l)p Fi(\000)p Fj(1\))p 2843 437 139 3 v 2897 471 a Fl(r)2991 451 y Ft(\))j Fs(P)3090 463 y Fo(l)3116 451 y Fs(\036)g Fr(k)3220 409 y Fq(2)3220 475 y Fo(L)3266 459 y Fj(2)3298 475 y Fq(\()p Fm(R)3366 459 y Fj(3)3399 475 y Fo(;)d(m)g(dx)p Fq(\))3616 451 y Fs(;)101 685 y Ft(where)27 b(w)n(e)h(ha)n(v)n(e)e(used)i Fr(j)n Fs(~)-40 b(\033)21 b Fr(\001)e Fs(x=)p Fr(j)p Fs(x)p Fr(j)14 b(j)23 b Ft(=)g(1.)201 823 y(W)-7 b(e)31 b(no)n(w)f(decomp)r(ose)g(the)h(term)g Fr(j)n Fs(~)-40 b(\033)24 b Fr(\001)d(r)p Fs(\036)p Fr(j)1571 793 y Fq(2)1640 823 y Ft(b)n(y)30 b(using)g(the)i(partition)e(of)h(unit)n(y)g (de\014ned)g(in)g(Section)g(1)f(and)101 923 y(tak)n(e)d(adv)-5 b(an)n(tage)26 b(of)i(the)g(fact)f(that)h(the)g(function)h Fs(J)35 b Ft(is)28 b(scalar)e(and)h(tak)n(es)g(real)f(v)-5 b(alues.)101 1074 y Fz(Lemma)30 b(11.)40 b Ff(L)l(et)28 b Fr(f)p Fs(J)831 1086 y Fo(k)871 1074 y Fr(g)913 1038 y Fo(M)6 b Fq(+1)913 1099 y Fo(k)q Fq(=1)1099 1074 y Ff(b)l(e)29 b(any)g(p)l(artition)g(of)h(unity)e(such)g(that)h Ft(In)n(t)14 b(\(supp\()p Fs(J)2764 1086 y Fo(k)2805 1074 y Ft(\)\))j Fr(\\)f Ft(In)n(t)e(\(supp)q(\()p Fs(J)3359 1086 y Fo(l)3384 1074 y Ft(\)\))24 b(=)f Fr(;)28 b Ff(if)101 1174 y Ft(1)23 b Fr(\024)f Fs(k)k Fr(6)p Ft(=)d Fs(l)h Fr(\024)f Fs(M)9 b Ff(.)38 b(Then)916 1388 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Fs(\036)p Fr(j)1205 1354 y Fq(2)1266 1388 y Ft(=)1353 1284 y Fo(M)6 b Fq(+1)1370 1309 y Fn(X)1370 1488 y Fo(k)q Fq(=1)1521 1388 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Ft(\()p Fs(J)1815 1400 y Fo(k)1856 1388 y Fs(\036)p Ft(\))p Fr(j)1960 1354 y Fq(2)2017 1388 y Fr(\000)2100 1284 y Fo(M)6 b Fq(+1)2117 1309 y Fn(X)2116 1488 y Fo(k)q Fq(=1)2267 1388 y Fr(jr)p Fs(J)2405 1400 y Fo(k)2446 1388 y Fr(j)2469 1354 y Fq(2)2521 1388 y Fr(j)p Fs(\036)p Fr(j)2616 1354 y Fq(2)2676 1388 y Fs(:)101 1614 y Ff(Pr)l(o)l(of.)43 b Ft(W)-7 b(e)21 b(\014rst)f(denote)h(b)n(y)f Fs(J)29 b Ft(an)20 b(arbitrary)e(elemen)n (t)j(of)f(the)h(partition)f(of)h(unit)n(y)-7 b(.)34 b(By)21 b(applying)e(the)i(de\014nition)101 1717 y(of)28 b Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Ft(\()p Fs(J)8 b(\036)p Ft(\))p Fr(j)602 1687 y Fq(2)668 1717 y Ft(and)28 b(grouping)e(the)i (terms)f(with)h Fs(J)1793 1687 y Fq(2)1831 1717 y Ft(,)1881 1655 y Fn(P)1969 1676 y Fq(3)1969 1742 y Fo(a)p Fq(=1)2107 1717 y Fr(j)p Fs(@)2174 1729 y Fo(a)2214 1717 y Fs(J)8 b Fr(j)2291 1687 y Fq(2)2356 1717 y Ft(and)28 b Fs(J)22 b(@)2630 1729 y Fo(a)2670 1717 y Fs(J)8 b Ft(,)28 b(w)n(e)f(obtain)g (the)h(follo)n(wing:)298 1860 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Ft(\()p Fs(J)8 b(\036)p Ft(\))p Fr(j)705 1826 y Fq(2)766 1860 y Ft(=)23 b Fs(J)908 1826 y Fq(2)959 1860 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)p Fs(\036)p Fr(j)1233 1826 y Fq(2)1290 1860 y Ft(+)g Fr(jr)p Fs(J)8 b Fr(j)1542 1826 y Fq(2)1579 1860 y Fr(j)p Fs(\036)p Fr(j)1674 1826 y Fq(2)1731 1860 y Ft(+)18 b Fs(f)1855 1872 y Fq(1)1892 1860 y Ft(\()p Fs(\036)p Ft(\))c(\()p Fs(J)23 b(@)2164 1872 y Fq(1)2201 1860 y Fs(J)8 b Ft(\))19 b(+)f Fs(f)2430 1872 y Fq(2)2467 1860 y Ft(\()p Fs(\036)p Ft(\))c(\()p Fs(J)23 b(@)2739 1872 y Fq(2)2776 1860 y Fs(J)8 b Ft(\))19 b(+)f Fs(f)3005 1872 y Fq(3)3042 1860 y Ft(\()p Fs(\036)p Ft(\))c(\()p Fs(J)23 b(@)3314 1872 y Fq(3)3351 1860 y Fs(J)8 b Ft(\))23 b Fs(;)101 1998 y Ft(with)28 b Fs(f)331 2010 y Fq(1)368 1998 y Ft(,)g Fs(f)460 2010 y Fq(2)497 1998 y Ft(,)g Fs(f)589 2010 y Fq(3)653 1998 y Ft(the)g(real)f(v)-5 b(alued)27 b(functions)348 2136 y Fs(f)389 2148 y Fq(1)426 2136 y Ft(\()p Fs(\036)p Ft(\))84 b(:=)f(2)14 b Fd(Re)f Ft(\()p Fr(h)p Fs(\036)1067 2148 y Fq(2)1105 2136 y Fs(;)h(@)1186 2148 y Fq(1)1223 2136 y Fs(\036)1272 2148 y Fq(2)1328 2136 y Fr(\000)k Fs(i)c(@)1498 2148 y Fq(2)1535 2136 y Fs(\036)1584 2148 y Fq(2)1640 2136 y Ft(+)k Fs(@)1767 2148 y Fq(3)1805 2136 y Fs(\036)1854 2148 y Fq(1)1891 2136 y Fr(i)p Ft(\))h(+)f(2)c Fd(Re)f Ft(\()p Fr(h)p Fs(\036)2330 2148 y Fq(1)2368 2136 y Fs(;)h(@)2449 2148 y Fq(1)2487 2136 y Fs(\036)2536 2148 y Fq(1)2592 2136 y Ft(+)k Fs(i)c(@)2762 2148 y Fq(2)2799 2136 y Fs(\036)2848 2148 y Fq(1)2904 2136 y Fr(\000)k Fs(@)3031 2148 y Fq(3)3068 2136 y Fs(\036)3117 2148 y Fq(2)3155 2136 y Fr(i)p Ft(\))28 b Fs(;)348 2261 y(f)389 2273 y Fq(2)426 2261 y Ft(\()p Fs(\036)p Ft(\))84 b(:=)f(2)14 b Fd(Re)f Ft(\()p Fr(h\000)p Fs(i)h(\036)1175 2273 y Fq(2)1212 2261 y Fs(;)g(@)1293 2273 y Fq(1)1330 2261 y Fs(\036)1379 2273 y Fq(2)1435 2261 y Fr(\000)k Fs(i)c(@)1605 2273 y Fq(2)1642 2261 y Fs(\036)1691 2273 y Fq(2)1747 2261 y Ft(+)k Fs(@)1874 2273 y Fq(3)1912 2261 y Fs(\036)1961 2273 y Fq(1)1998 2261 y Fr(i)p Ft(\))h(+)f(2)c Fd(Re)f Ft(\()p Fr(h)p Fs(i)h(\036)2480 2273 y Fq(1)2518 2261 y Fs(;)g(@)2599 2273 y Fq(1)2636 2261 y Fs(\036)2685 2273 y Fq(1)2741 2261 y Ft(+)k Fs(i)c(@)2911 2273 y Fq(2)2948 2261 y Fs(\036)2997 2273 y Fq(1)3053 2261 y Fr(\000)k Fs(@)3180 2273 y Fq(3)3218 2261 y Fs(\036)3267 2273 y Fq(2)3304 2261 y Fr(i)p Ft(\))29 b Fs(;)348 2385 y(f)389 2397 y Fq(3)426 2385 y Ft(\()p Fs(\036)p Ft(\))84 b(:=)f(2)14 b Fd(Re)f Ft(\()p Fr(h)p Fs(\036)1067 2397 y Fq(1)1105 2385 y Fs(;)h(@)1186 2397 y Fq(1)1223 2385 y Fs(\036)1272 2397 y Fq(2)1328 2385 y Fr(\000)k Fs(i)c(@)1498 2397 y Fq(2)1535 2385 y Fs(\036)1584 2397 y Fq(2)1640 2385 y Ft(+)k Fs(@)1767 2397 y Fq(3)1805 2385 y Fs(\036)1854 2397 y Fq(1)1891 2385 y Fr(i)p Ft(\))h(+)f(2)c Fd(Re)f Ft(\()p Fr(h\000)p Fs(\036)2395 2397 y Fq(2)2433 2385 y Fs(;)h(@)2514 2397 y Fq(1)2551 2385 y Fs(\036)2600 2397 y Fq(1)2656 2385 y Ft(+)k Fs(i)c(@)2826 2397 y Fq(2)2863 2385 y Fs(\036)2912 2397 y Fq(1)2968 2385 y Fr(\000)k Fs(@)3095 2397 y Fq(3)3133 2385 y Fs(\036)3182 2397 y Fq(2)3219 2385 y Fr(i)p Ft(\))29 b Fs(;)101 2523 y Ft(where)h Fr(h)p Fs(a;)14 b(b)p Fr(i)28 b Ft(=)p 645 2477 44 4 v 27 w Fs(a)14 b(b)30 b Ft(and)h Fd(Re)o Ft(\()p Fs(z)t Ft(\))f(denotes)g(the)h(real)f(part)g(of)g(the)h(complex)f(n)n(um)n(b)r (er)g Fs(z)t Ft(.)45 b(T)-7 b(o)30 b(obtain)g(the)h(result)101 2633 y(w)n(e)h(ha)n(v)n(e)e(to)i(sum)f(o)n(v)n(er)f(all)i(the)g (indexes)f Fs(k)i Ft(=)c(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)j Ft(+)21 b(1)31 b(and)h(remem)n(b)r(er)f(that)2853 2571 y Fn(P)2940 2592 y Fo(M)6 b Fq(+1)2940 2658 y Fo(k)q Fq(=1)3112 2633 y Fs(J)3158 2645 y Fo(k)3212 2633 y Fs(@)3256 2645 y Fo(a)3297 2633 y Fs(J)3343 2645 y Fo(k)3413 2633 y Ft(=)30 b(0)h(for)101 2733 y Fs(a)23 b Ft(=)g(1,)k(2,)g(3.)3616 2833 y Fe(\003)201 3003 y Ft(The)g(next)h(result)f(is)g(a)g(lo)r(cal)f (estimate)h(on)g(domains)g(where)g(the)g(p)r(oten)n(tial)h Fs(W)39 b Ft(admits)27 b(a)g(radial)f(dominan)n(t)101 3103 y(p)r(oten)n(tial.)101 3254 y Fz(Lemma)g(12.)37 b Ff(L)l(et)25 b Fs(W)35 b Fr(\025)22 b Ft(0)j Ff(and)h Fs(J)31 b Fr(2)24 b Fs(W)1403 3224 y Fq(1)p Fo(;)p Fk(1)1526 3254 y Ft(\()p Fp(R)1618 3224 y Fq(3)1655 3254 y Ft(\))i Ff(b)l(e)f(such)h(that)f(for)i(some)f Fs(z)g Fr(2)d Fp(R)2700 3224 y Fq(3)2737 3254 y Ff(,)k Fs(C)2848 3266 y Fo(W)2947 3254 y Fr(2)c Fp(R)3085 3224 y Fq(+)3166 3254 y Ff(and)j Fs(\027)i Fr(2)c Ft(\(0)p Fs(;)14 b Ft(1\))p Ff(,)101 3413 y Ft(\(11\))941 b Fs(W)12 b Ft(\()p Fs(x)p Ft(\))25 b Fr(\024)1609 3357 y Fs(\027)p 1513 3394 238 4 v 1513 3470 a Fr(j)p Fs(x)19 b Fr(\000)f Fs(z)t Fr(j)1779 3413 y Ft(+)g Fs(C)1921 3425 y Fo(W)2082 3413 y Ff(on)85 b Ft(supp\()p Fs(J)8 b Ft(\))23 b Fs(:)101 3605 y Ff(Then,)31 b(for)g(any)f Fs(\036)23 b Fr(2)h Fs(H)862 3575 y Fq(1)899 3605 y Ft(\()p Fp(R)991 3575 y Fq(3)1028 3605 y Fs(;)14 b Fp(C)1125 3575 y Fq(2)1162 3605 y Ft(\))30 b Ff(and)h(any)f Fs(\025)23 b(>)g Fr(\000)p Ft(1)p Ff(,)864 3683 y Fn(Z)911 3871 y Fm(R)953 3855 y Fj(3)1038 3740 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Ft(\()p Fs(J)8 b(\036)p Ft(\))p Fr(j)1444 3710 y Fq(2)p 1013 3777 495 4 v 1013 3853 a Ft(1)18 b(+)g Fs(\025)h Ft(+)f Fs(W)12 b Ft(\()p Fs(x)p Ft(\))1541 3796 y Fs(dx)23 b Fr(\025)1742 3683 y Fn(Z)1788 3871 y Fm(R)1830 3855 y Fj(3)1881 3796 y Fs(W)i Fr(j)p Fs(J)8 b(\036)p Fr(j)2133 3762 y Fq(2)2185 3796 y Fs(dx)19 b Fr(\000)f Fs(C)2436 3808 y Fq(1)2488 3683 y Fn(Z)2534 3871 y Fm(R)2576 3855 y Fj(3)2626 3796 y Fr(j)p Fs(J)8 b(\036)p Fr(j)2775 3762 y Fq(2)2827 3796 y Fs(dx)101 4007 y Ff(wher)l(e)31 b Fs(C)395 4019 y Fq(1)455 4007 y Ft(=)23 b Fs(C)602 4019 y Fq(1)640 4007 y Ft(\()p Fs(\025;)14 b(C)816 4019 y Fo(W)892 4007 y Ft(\))23 b(:=)g(\(1)18 b(+)g Fs(\025)h Ft(+)f Fs(C)1442 4019 y Fo(W)1518 4007 y Ft(\))1564 3940 y Fn(\002)1599 4007 y Ft(1)g Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1908 3940 y Fn(\003)1943 3957 y Fq(2)1980 4007 y Fs(=\027)2068 3973 y Fq(2)2124 4007 y Ft(+)18 b Fs(C)2266 4019 y Fo(W)2342 4007 y Ff(.)101 4159 y(Pr)l(o)l(of.)43 b Ft(The)28 b(pro)r(of)f(is)h(divided)f(in)n(to) h(three)f(steps.)101 4297 y Ff(Step)j(1:)39 b(Sp)l(e)l(ctr)l(al)30 b(de)l(c)l(omp)l(osition.)39 b Ft(F)-7 b(rom)27 b(\(11\),)g(w)n(e)h (kno)n(w)e(that)1023 4375 y Fn(Z)1069 4563 y Fm(R)1111 4547 y Fj(3)1196 4431 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Ft(\()p Fs(J)8 b(\036)p Ft(\))p Fr(j)1603 4401 y Fq(2)p 1171 4468 V 1171 4544 a Ft(1)18 b(+)g Fs(\025)h Ft(+)f Fs(W)12 b Ft(\()p Fs(x)p Ft(\))1699 4488 y Fs(dx)24 b Fr(\025)1901 4375 y Fn(Z)1947 4563 y Fm(R)1989 4547 y Fj(3)2184 4431 y Fr(j)n Fs(~)-40 b(\033)21 b Fr(\001)e(r)p Fs(')p Fr(j)2463 4401 y Fq(2)p 2049 4468 587 4 v 2049 4544 a Ft(1)f(+)g Fs(\025)h Ft(+)f Fs(C)2401 4556 y Fo(W)2495 4544 y Ft(+)2588 4512 y Fo(\027)p 2588 4526 38 4 v 2590 4573 a(r)2668 4488 y Fs(dx)101 4682 y Ft(for)i Fs(')p Ft(\()p Fs(x)p Ft(\))k(:=)f(\()p Fs(J)8 b(\036)p Ft(\)\()p Fs(x)t Ft(+)t Fs(z)t Ft(\).)35 b(In)20 b(order)f(to)h(apply)g(\(10\))g (to)g(the)h(last)f(in)n(tegral,)g(w)n(e)g(write)g Fs(')h Ft(as)e(a)h(linear)g(com)n(bination)101 4781 y(of)32 b(eigenfunctions)f Fs(')800 4793 y Fo(l)856 4781 y Ft(:=)e Fs(P)1026 4793 y Fo(l)1066 4781 y Fs(')j Ft(of)f(the)h(op)r(erator)c Fs(~)-40 b(\033)25 b Fr(\001)c Fs(L)g Ft(+)f(1)31 b(with)i(corresp)r (onding)c(eigen)n(v)-5 b(alues)31 b Fs(l)g Fr(2)f Fp(Z)21 b Fr(n)g(f)p Ft(0)p Fr(g)p Ft(.)101 4881 y(Set)28 b Fs(g)s Ft(\()p Fs(r)r Ft(\))c(:=)f(1)p Fs(=)p Ft(\()p Fs(b)14 b(r)20 b Ft(+)e Fs(\027)5 b Ft(\),)28 b Fs(b)23 b Ft(=)g(1)18 b(+)g Fs(\025)g Ft(+)g Fs(C)1458 4893 y Fo(W)1534 4881 y Ft(,)28 b(and)f(use)h(\(9\))g(to)f(get)252 4959 y Fn(Z)298 5148 y Fm(R)340 5131 y Fj(3)522 5016 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)p Fs(')778 5028 y Fo(l)804 5016 y Fr(j)827 4986 y Fq(2)p 400 5053 587 4 v 400 5129 a Ft(1)g(+)g Fs(\025)h Ft(+)f Fs(C)752 5141 y Fo(W)846 5129 y Ft(+)939 5096 y Fo(\027)p 939 5110 38 4 v 941 5158 a(r)1019 5072 y Fs(dx)24 b Ft(=)1221 4959 y Fn(Z)1267 5148 y Fm(R)1309 5131 y Fj(3)1369 5016 y Fs(r)17 b Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(')1693 5028 y Fo(l)1719 5016 y Fr(j)1742 4986 y Fq(2)p 1369 5053 411 4 v 1456 5129 a Fs(b)g(r)20 b Ft(+)e Fs(\027)1812 5072 y(dx)340 5304 y Ft(=)488 5191 y Fn(Z)534 5379 y Fm(R)576 5363 y Fj(3)626 5304 y Fs(g)s Ft(\()p Fs(r)r Ft(\))c Fs(r)841 5208 y Fn(\014)841 5258 y(\014)841 5308 y(\014)868 5304 y Fs(@)912 5316 y Fo(r)949 5304 y Fs(')1003 5316 y Fo(l)1047 5304 y Fr(\000)k Ft(\()p Fs(l)j Fr(\000)d Ft(1\))1388 5248 y(1)p 1388 5285 42 4 v 1389 5361 a Fs(r)1453 5304 y(')1507 5316 y Fo(l)1533 5208 y Fn(\014)1533 5258 y(\014)1533 5308 y(\014)1561 5229 y Fq(2)1612 5304 y Fs(dx)340 5536 y Ft(=)488 5423 y Fn(Z)534 5612 y Fm(R)576 5595 y Fj(3)626 5536 y Fs(g)s Ft(\()p Fs(r)r Ft(\))c Fs(r)k Fr(j)p Fs(@)908 5548 y Fo(r)945 5536 y Fs(')999 5548 y Fo(l)1024 5536 y Fr(j)1047 5502 y Fq(2)1098 5536 y Fs(dx)i Ft(+)1291 5423 y Fn(Z)1337 5612 y Fm(R)1379 5595 y Fj(3)1439 5480 y Ft(\()p Fs(l)g Fr(\000)e Ft(1\))1673 5450 y Fq(2)p 1439 5517 272 4 v 1555 5593 a Fs(r)1734 5536 y(g)s Ft(\()p Fs(r)r Ft(\))c Fr(j)p Fs(')1971 5548 y Fo(l)1998 5536 y Fr(j)2021 5502 y Fq(2)2072 5536 y Fs(dx)19 b Ft(+)f(\()p Fs(l)i Fr(\000)e Ft(1\))2512 5423 y Fn(Z)2558 5612 y Fm(R)2600 5595 y Fj(3)2650 5444 y Fn(\020)2700 5536 y Fs(g)2743 5502 y Fk(0)2766 5536 y Ft(\()p Fs(r)r Ft(\))h(+)2981 5480 y(2)14 b Fs(g)s Ft(\()p Fs(r)r Ft(\))p 2981 5517 203 4 v 3063 5593 a Fs(r)3194 5444 y Fn(\021)3257 5536 y Fr(j)p Fs(')3334 5548 y Fo(l)3360 5536 y Fr(j)3383 5502 y Fq(2)3434 5536 y Fs(dx)340 5764 y Ft(=)488 5651 y Fn(Z)534 5839 y Fm(R)576 5823 y Fj(3)626 5764 y Fs(g)s Ft(\()p Fs(r)r Ft(\))g Fs(r)k Fr(j)p Fs(@)908 5776 y Fo(r)945 5764 y Fs(')999 5776 y Fo(l)1024 5764 y Fr(j)1047 5729 y Fq(2)1098 5764 y Fs(dx)i Ft(+)1291 5651 y Fn(Z)1337 5839 y Fm(R)1379 5823 y Fj(3)1429 5672 y Fn(h)1468 5764 y Ft(\()p Fs(l)1527 5729 y Fq(2)1583 5764 y Fr(\000)e Ft(1\))1763 5708 y Fs(g)s Ft(\()p Fs(r)r Ft(\))p 1763 5745 147 4 v 1817 5821 a Fs(r)1939 5764 y Ft(+)g(\()p Fs(l)i Fr(\000)e Ft(1\))c Fs(g)2313 5729 y Fk(0)2335 5764 y Ft(\()p Fs(r)r Ft(\))2438 5672 y Fn(i)2479 5764 y Fr(j)p Fs(')2556 5776 y Fo(l)2582 5764 y Fr(j)2605 5729 y Fq(2)2656 5764 y Fs(dx)24 b(;)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 101 -103 a Fq(18)995 b(R.)22 b(BOSI,)g(J.)g(DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)101 96 y Ft(where)i(w)n(e)f(ha)n(v)n(e)g(in)n(tegrated)g(b)n(y)h(parts)f (in)h(the)h(v)-5 b(ariable)23 b Fs(r)r Ft(.)36 b(Since)24 b(the)h(last)f(in)n(tegral)e(is)i(non-negativ)n(e)e(for)i(ev)n(ery)101 195 y Fs(l)h Fr(2)e Fp(Z)c Fr(n)f(f)p Ft(0)p Fr(g)p Ft(,)26 b(w)n(e)h(obtain)1121 242 y Fn(Z)1167 430 y Fm(R)1209 414 y Fj(3)1269 298 y Fs(r)17 b Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(')1593 310 y Fo(l)1619 298 y Fr(j)1642 268 y Fq(2)p 1269 335 411 4 v 1356 411 a Fs(b)g(r)20 b Ft(+)e 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a Fo(\027)685 1313 y Ft(,)j(it)g(holds)876 1427 y Fn(Z)922 1616 y Fm(R)964 1599 y Fj(3)1014 1540 y Fs(g)s Ft(\()p Fs(r)r Ft(\))14 b Fs(r)k Fr(j)p Fs(@)1296 1552 y Fo(r)1333 1540 y Fs(')1387 1552 y Fo(l)1412 1540 y Fr(j)1435 1506 y Fq(2)1486 1540 y Fs(dx)24 b Fr(\025)1688 1427 y Fn(Z)1734 1616 y Fm(R)1776 1599 y Fj(3)1826 1448 y Fn(\020)1886 1484 y Fs(\027)p 1886 1521 47 4 v 1889 1597 a(r)1961 1540 y Fr(\000)2054 1479 y Fs(b)2104 1411 y Fn(\002)2138 1479 y Ft(1)18 b Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))2447 1411 y Fn(\003)2482 1429 y Fq(2)p 2054 1521 466 4 v 2244 1597 a Fs(\027)2290 1573 y Fq(2)2529 1448 y Fn(\021)2592 1540 y Fr(j)p Fs(')2669 1552 y Fo(l)2695 1540 y Fr(j)2718 1506 y Fq(2)2769 1540 y Fs(dx)24 b(:)101 1728 y Ft(Hence)30 b(w)n(e)e(ha)n(v)n(e)g(sho)n(wn)h(that)g(for)g(ev)n (ery)f Fs(l)f Fr(2)f Fp(Z)20 b Fr(n)f(f)p Ft(0)p Fr(g)p Ft(,)28 b(for)h(ev)n(ery)f Fs(b)d(>)h Ft(0,)j(the)h(eigenfunction)f Fs(')3203 1740 y Fo(l)3258 1728 y Ft(satis\014es)f(the)101 1827 y(inequalit)n(y)736 1869 y Fn(Z)783 2057 y Fm(R)825 2041 y Fj(3)885 1926 y Fs(r)16 b Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)d(r)14 b Fs(')1209 1938 y Fo(l)1235 1926 y Fr(j)1258 1895 y Fq(2)p 885 1963 411 4 v 971 2039 a Fs(b)g(r)21 b Ft(+)d Fs(\027)1328 1982 y(dx)24 b Fr(\025)1529 1869 y Fn(Z)1576 2057 y Fm(R)1618 2041 y Fj(3)1678 1926 y Fs(\027)p 1678 1963 47 4 v 1681 2039 a(r)1748 1982 y Fr(j)p Fs(')1825 1994 y Fo(l)1851 1982 y Fr(j)1874 1947 y Fq(2)1925 1982 y Fs(dx)19 b Fr(\000)f Fs(b)2177 1926 y Ft([1)g Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\)])2532 1895 y Fq(2)p 2177 1963 393 4 v 2331 2039 a Fs(\027)2377 2015 y Fq(2)2593 1869 y Fn(Z)2639 2057 y Fm(R)2681 2041 y Fj(3)2732 1982 y Fr(j)p Fs(')2809 1994 y Fo(l)2835 1982 y Fr(j)2858 1947 y Fq(2)2909 1982 y Fs(dx)23 b(:)101 2193 y Ff(Step)30 b(3.)39 b(R)l(e)l(c)l(omp)l(osition.)f Ft(A)28 b(sum)g(o)n(v)n(er)d Fs(l)g Fr(2)e Fp(Z)c Fr(n)f(f)p Ft(0)p Fr(g)26 b Ft(giv)n(es)777 2274 y Fn(Z)823 2463 y Fm(R)865 2446 y Fj(3)925 2331 y Fs(r)17 b Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)p Fs(')p Fr(j)1258 2301 y Fq(2)p 925 2368 371 4 v 992 2444 a Fs(b)c(r)21 b Ft(+)d Fs(\027)1329 2387 y(dx)24 b Fr(\025)1531 2274 y Fn(Z)1577 2463 y Fm(R)1619 2446 y Fj(3)1679 2331 y Fs(\027)p 1679 2368 47 4 v 1682 2444 a(r)1749 2387 y Fr(j)p Fs(')p Fr(j)1849 2353 y Fq(2)1910 2387 y Fs(dx)19 b Fr(\000)2112 2331 y Fs(b)14 b Ft([1)j Fr(\000)h Fs(S)5 b Ft(\()p Fs(\027)g Ft(\)])2516 2301 y Fq(2)p 2112 2368 443 4 v 2291 2444 a Fs(\027)2337 2420 y Fq(2)2578 2274 y Fn(Z)2624 2463 y Fm(R)2666 2446 y Fj(3)2717 2387 y Fr(j)p Fs(')p Fr(j)2817 2353 y Fq(2)2868 2387 y Fs(dx)24 b(:)101 2580 y Ft(No)n(w)d(w)n(e)g(return)g(to)g(the)h (original)e(co)r(ordinates)f(with)j Fs(b)h Ft(=)g(1)6 b(+)g Fs(\025)g Ft(+)g Fs(C)2241 2592 y Fo(W)2315 2580 y Ft(,)23 b(w)n(e)e(add)g(and)g(subtract)g Fs(C)3168 2592 y Fo(W)3258 2513 y Fn(R)3297 2609 y Fm(R)3339 2593 y Fj(3)3389 2580 y Fr(j)p Fs(J)8 b(\036)p Fr(j)3538 2550 y Fq(2)3590 2580 y Fs(dx)101 2685 y Ft(to)23 b(the)h(righ)n(t)e(hand)h (side.)35 b(F)-7 b(rom)23 b(a)f(last)h(application)f(of)h(\(11\))g(w)n (e)g(get)g(the)g(result)g(with)g Fs(C)2909 2697 y Fq(1)2970 2685 y Ft(=)g Fs(b)14 b Ft([1)9 b Fr(\000)g Fs(S)c Ft(\()p Fs(\027)g Ft(\)])3445 2655 y Fq(2)3482 2685 y Fs(=\027)3570 2655 y Fq(2)3616 2685 y Ft(+)101 2785 y Fs(C)160 2797 y Fo(W)236 2785 y Ft(.)3357 b Fe(\003)101 2955 y Ft(3.3.)41 b Fz(Case)22 b Fs(d)h Fz(large.)40 b Ft(W)-7 b(e)20 b(consider)e(an)h (arbitrary)f(con\014guration)f(of)j(p)r(oles)f Fs(y)2555 2967 y Fo(k)2618 2955 y Fr(2)24 b Fp(R)2757 2925 y Fq(3)2794 2955 y Ft(,)d(and)e(de\014ne)h(the)g(follo)n(wing)101 3055 y(quan)n(tities)28 b(:)971 3235 y Fs(a)23 b Ft(:=)1159 3178 y Fs(\027)c(M)p 1159 3215 150 4 v 1212 3292 a(d)1342 3235 y(;)97 b(b)22 b Ft(:=)1641 3106 y Fn(\002)1676 3173 y Ft(1)c Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1985 3106 y Fn(\003)2020 3123 y Fq(2)p 1641 3215 416 4 v 1807 3292 a Fs(\027)1853 3268 y Fq(2)2090 3235 y Fs(;)97 b(c)23 b Ft(:=)g(2)2445 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Fs(;)101 3810 y Ft(with)28 b Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))24 b(=)568 3740 y Fr(p)p 637 3740 227 4 v 70 x Ft(1)18 b Fr(\000)g Fs(\027)826 3786 y Fq(2)891 3810 y Ft(and)27 b Fs(d)d Ft(:=)e(min)1368 3822 y Fo(i)p Fk(6)p Fq(=)p Fo(k)1497 3810 y Fr(j)p Fs(y)1561 3822 y Fo(i)1607 3810 y Fr(\000)c Fs(y)1731 3822 y Fo(j)1765 3810 y Fr(j)p Fs(=)p Ft(2.)101 3963 y Fz(Theorem)43 b(13.)j Ff(With)39 b(the)f(ab)l(ove)i(notations,)h(for)f(al)t(l)f Fs(\027)44 b Fr(2)c Ft(\(0)p Fs(;)14 b Ft(1\))p Ff(,)40 b Fs(M)48 b Fr(\025)38 b Ft(2)p Ff(,)j(if)e Fs(d)g Fr(\025)g Fs(d)3042 3932 y Fk(\003)3080 3963 y Ft(\()p Fs(\027)5 b Ft(\))p Ff(,)42 b(then)c(for)i(al)t(l)101 4062 y Fs(\036)24 b Fr(2)f Fs(H)328 4032 y Fq(1)365 4062 y Ft(\()p Fp(R)457 4032 y Fq(3)495 4062 y Fs(;)14 b Fp(C)592 4032 y Fq(2)629 4062 y Ft(\))30 b Ff(we)g(have)723 4143 y Fn(Z)769 4332 y Fm(R)811 4315 y Fj(3)980 4200 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)1268 4170 y Fq(2)p 871 4237 544 4 v 871 4313 a Ft(1)k(+)g Fs(\025)1062 4289 y Fk(\003)1119 4313 y Ft(+)g Fs(\027)h(W)1340 4325 y Fo(M)1424 4256 y Fs(dx)h Ft(+)e(\(1)g Fr(\000)g Fs(\025)1840 4222 y Fk(\003)1878 4256 y Ft(\))1924 4143 y Fn(Z)1971 4332 y Fm(R)2013 4315 y Fj(3)2063 4256 y Fr(j)p Fs(\036)p Fr(j)2158 4222 y Fq(2)2210 4256 y Fs(dx)23 b Fr(\025)g Fs(\027)2471 4143 y Fn(Z)2517 4332 y Fm(R)2559 4315 y Fj(3)2610 4256 y Fs(W)2688 4268 y Fo(M)2776 4256 y Fr(j)p Fs(\036)p Fr(j)2871 4222 y Fq(2)2922 4256 y Fs(dx)h(:)101 4444 y Ff(We)30 b(observe)h(that)f Fs(\025)764 4414 y Fk(\003)825 4444 y Fs(>)23 b Fr(\000)p Ft(1)29 b Ff(for)h(every)h Fs(d)23 b Fr(\025)g Fs(d)1598 4414 y Fk(\003)1636 4444 y Ft(\()p Fs(\027)5 b Ft(\))31 b Ff(and)f(that)g Fs(\025)2156 4414 y Fk(\003)2217 4444 y Ft(=)23 b(0)29 b Ff(for)839 4624 y Fs(d)24 b Ft(=)1008 4602 y(\026)993 4624 y Fs(d)g Ft(:=)1249 4567 y(1)p 1180 4605 179 4 v 1180 4681 a Fs(c)19 b Fr(\000)f Ft(2)1392 4531 y Fn(\020)1460 4624 y Fr(\000)1553 4567 y Ft(1)p 1553 4605 42 4 v 1553 4681 a(2)1618 4624 y Fs(M)23 b(\027)c(c)f Fr(\000)1919 4549 y Fn(p)p 2002 4549 831 4 v 75 x Fs(M)2092 4600 y Fq(2)2143 4624 y Ft(\()p Fs(c)h Fr(\000)f Ft(1\))g Fr(\000)g Fs(\031)2538 4600 y Fq(2)2589 4624 y Ft(\()p Fs(c)h Fr(\000)f Ft(2\))2847 4531 y Fn(\021)2919 4624 y Fs(:)101 4824 y Ff(Pr)l(o)l(of.)43 b Ft(Let)38 b Fr(f)p Fs(J)608 4836 y Fo(k)648 4824 y Fr(g)690 4789 y Fo(M)6 b Fq(+1)690 4849 y Fo(k)q Fq(=1)885 4824 y Ft(b)r(e)37 b(a)g(partition)g(of)g(unit)n(y)h(supp)r(orted)f(on) g(balls)g(de\014ned)g(as)g(in)g(Section)h(1,)h(namely)101 4968 y Fs(J)147 4980 y Fo(k)188 4968 y Ft(\()p Fs(x)p Ft(\))24 b(=)f Fs(J)8 b Ft(\()p Fr(j)p Fs(x)15 b Fr(\000)g Fs(y)703 4980 y Fo(k)743 4968 y Fr(j)p Fs(=d)p Ft(\))26 b(for)f(all)h Fs(x)d Fr(2)g Fp(R)1356 4938 y Fq(3)1394 4968 y Ft(,)j(1)c Fr(\024)h Fs(k)j Fr(\024)d Fs(M)-5 b Ft(,)26 b(with)g Fs(J)34 b Ft(as)25 b(in)h(\(2\))f(and)h Fs(J)2676 4980 y Fo(M)6 b Fq(+1)2857 4968 y Ft(=)2944 4864 y Fn(q)p 3027 4864 318 4 v 42 x(P)3115 4926 y Fo(M)3115 4993 y(k)q Fq(=1)3254 4968 y Fs(J)3308 4939 y Fq(2)3300 4993 y Fo(k)3345 4968 y Ft(.)36 b(F)-7 b(or)25 b(an)n(y)101 5098 y Fs(k)h Ft(=)d(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)-5 b Ft(,)27 b(the)h(function)g Fs(J)1115 5110 y Fo(k)1184 5098 y Ft(is)f(supp)r(orted)h(in)p 1755 5025 294 4 v 28 w Fs(B)t Ft(\()p Fs(y)1895 5110 y Fo(k)1936 5098 y Fs(;)14 b(d)p Ft(\).)37 b(Note)28 b(that)577 5392 y Fs(\027)19 b(W)715 5404 y Fo(M)789 5392 y Ft(\()p Fs(x)p Ft(\))24 b Fr(\024)1012 5172 y Fn(8)1012 5247 y(>)1012 5271 y(>)1012 5296 y(<)1012 5446 y(>)1012 5471 y(>)1012 5496 y(:)1252 5225 y Fs(\027)p 1137 5262 277 4 v 1137 5338 a Fr(j)p Fs(x)19 b Fr(\000)f Fs(y)1350 5350 y Fo(k)1391 5338 y Fr(j)1442 5281 y Ft(+)1535 5225 y Fs(M)27 b Fr(\000)18 b Ft(1)p 1535 5262 233 4 v 1630 5338 a Fs(d)1791 5281 y(\027)199 b Ft(on)51 b(supp\()p Fs(J)2419 5293 y Fo(k)2460 5281 y Ft(\))83 b Fr(8)24 b Fs(k)h Ft(=)e(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)32 b(;)1250 5440 y(\027)p 1137 5477 273 4 v 1137 5553 a Fr(j)p Fs(x)19 b Fr(\000)f Fs(y)1350 5565 y 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y Fq(2)1630 4892 y(1)1704 4813 y Ft(+)1797 4757 y Fr(jr)p Fs(J)1935 4769 y Fq(2)1973 4757 y Fr(j)1996 4727 y Fq(2)p 1797 4794 V 1798 4870 a Ft(1)g Fr(\000)g Fs(J)1995 4841 y Fq(2)1987 4892 y(2)2066 4813 y Fr(\024)2164 4757 y Fs(\031)2214 4727 y Fq(2)p 2164 4794 88 4 v 2168 4870 a Fs(d)2211 4846 y Fq(2)2275 4813 y Fp(I)2307 4828 y Fq(supp\()p Fk(r)p Fo(J)2562 4836 y Fj(3)2594 4828 y Fq(\))2647 4813 y Fs(:)-2569 b Ft(\(14\))101 5027 y(Moreo)n(v)n(er,)25 b(w)n(e)i(ha)n(v)n(e)g(the)h (estimate)101 5312 y(\(15\))898 b Fs(W)1225 5324 y Fq(2)1263 5312 y Ft(\()p Fs(x)p Ft(\))24 b Fr(\024)1486 5092 y Fn(8)1486 5167 y(>)1486 5192 y(>)1486 5217 y(<)1486 5366 y(>)1486 5391 y(>)1486 5416 y(:)1677 5134 y Fq(1)p 1611 5148 165 4 v 1611 5195 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)r Fk(j)1804 5167 y Ft(+)1898 5134 y Fq(1)p 1897 5148 35 4 v 1897 5195 a Fo(d)2107 5167 y Ft(on)f(supp\()p Fs(J)2467 5179 y Fq(1)2505 5167 y Ft(\))g Fs(;)1676 5272 y Fq(1)p 1611 5286 164 4 v 1611 5334 a Fk(j)p Fo(x)p Fq(+)p Fo(y)r 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Fq(2)2215 5806 y Ft(\()p Fs(\025;)14 b(\027)q(;)g(d;)g Ft(2\))28 b(replaced)e(b)n(y)i Fs(K)3107 5818 y Fq(2)3143 5806 y Ft(\()p Fs(\025;)14 b(\027)q(;)g(d;)g Ft(1\).)100 b Fe(\003)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 101 -103 a Fq(20)995 b(R.)22 b(BOSI,)g(J.)g(DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)201 96 y Ft(In)39 b(the)h(case)f Fs(M)51 b(>)42 b Ft(2,)g(if)e(one)f(w)n (an)n(ts)f(to)h(impro)n(v)n(e)f(on)h(Theorem)g(13,)i(one)e(has)g(to)g (mak)n(e)g(a)g(geometric)101 195 y(assumption,)27 b(whic)n(h)h(is)f (alw)n(a)n(ys)f(satis\014ed)h(for)g Fs(M)32 b Ft(=)23 b(2.)101 345 y Fz(Corollary)38 b(15.)44 b Ff(L)l(et)33 b Fs(M)39 b Fr(\025)30 b Ft(2)p Ff(.)50 b(Assume)33 b(that)h(ther)l(e)g (exists)g(a)g(p)l(artition)h(of)f(unity)g Fr(f)p Fs(J)2938 357 y Fo(k)2978 345 y Fr(g)3020 309 y Fo(M)6 b Fq(+1)3020 370 y Fo(k)q Fq(=1)3211 345 y Ff(such)34 b(that)g(for)101 446 y(some)c Fs(z)352 458 y Fq(1)403 446 y Fs(;)14 b(:)g(:)g(:)28 b(z)604 458 y Fo(M)677 446 y Fs(;)g(z)767 458 y Fo(M)6 b Fq(+1)947 446 y Fr(2)23 b Fp(R)1085 416 y Fq(3)1123 446 y Ff(,)684 627 y Fs(W)762 639 y Fo(M)836 627 y Ft(\()p Fs(x)p Ft(\))h Fr(\024)1185 571 y Ft(1)p 1069 608 275 4 v 1069 684 a Fr(j)p Fs(x)19 b Fr(\000)f Fs(z)1280 696 y Fo(k)1320 684 y Fr(j)1372 627 y Ft(+)1465 571 y(\()p Fs(M)27 b Fr(\000)18 b Ft(1\))p 1465 608 298 4 v 1592 684 a Fs(d)1857 627 y Ff(on)23 b Ft(supp\()p Fs(J)2218 639 y Fo(k)2259 627 y Ft(\))85 b Fr(8)24 b Fs(k)i Ft(=)c(1)14 b Fs(;)g(:)g(:)g(:)27 b(M)g Ft(+)18 b(1)23 b Fs(;)101 829 y Ff(and)274 767 y Fn(P)362 788 y Fo(M)6 b Fq(+1)362 854 y Fo(k)q Fq(=1)533 829 y Fr(jr)p Fs(J)671 841 y Fo(k)712 829 y Fr(j)735 799 y Fq(2)816 829 y Fr(\024)44 b Fs(\031)975 799 y Fq(2)1012 829 y Fs(=d)1097 799 y Fq(2)1134 829 y Ff(.)73 b(Then)42 b(the)f(r)l(esults)g(of)h(The)l(or)l(em)g(13)g (hold)h(with)e Fs(a)j Ft(=)f(\()p Fs(M)36 b Fr(\000)26 b Ft(1\))14 b Fs(\027)5 b(=d)41 b Ff(and)101 929 y Fs(d)144 899 y Fk(\003)183 929 y Ft(\()p Fs(\027)5 b Ft(\))24 b(=)e Fs(\027)d(c)14 b Ft(\()p Fs(M)27 b Fr(\000)18 b Ft(1\))p Fs(=)p Ft(2)g(+)g Fs(\031)1060 869 y Fr(p)p 1129 869 36 4 v 60 x Fs(c)p Ff(.)101 1078 y(Pr)l(o)l(of.)43 b Ft(One)38 b(pro)r(ceeds)e(as)h(in)h(the)g(pro)r(of)f(of)h(Theorem)e (13,)k(with)e Fs(K)2377 1090 y Fq(2)2451 1078 y Ft(replaced)f(b)n(y)g Fs(K)2985 1090 y Fq(2)3022 1078 y Ft(\()p Fs(\025;)14 b(\027)q(;)g(d;)g(M)34 b Fr(\000)25 b Ft(1\))39 b(=)101 1178 y Fs(K)172 1190 y Fq(1)209 1178 y Ft(\()p Fs(\025;)14 b(\027)q(;)g(d;)g(M)9 b Ft(\).)2986 b Fe(\003)201 1349 y Ft(Theorem)27 b(13)f(has)h(sev)n(eral)f(consequences.)36 b(Assume)28 b(\014rst)f(that)h Fs(b)2312 1361 y Fo(M)2408 1349 y Ft(=)23 b Fs(M)9 b Ft(.)101 1498 y Fz(Corollary)35 b(16)f Ft(\(Asymptotics)29 b(for)g Fs(\025)1350 1468 y Fk(\003)1389 1498 y Ft(\))p Fz(.)42 b Ff(F)-6 b(or)32 b Fs(\027)f Fr(!)26 b Ft(1)p Ff(,)32 b(we)g(\014nd)2234 1476 y Ft(\026)2219 1498 y Fs(d)26 b Fr(!)g Ft(+)p Fr(1)31 b Ff(and)h Fs(d)2782 1468 y Fk(\003)2821 1498 y Ft(\()p Fs(\027)5 b Ft(\))27 b Fr(!)f Fs(b)3103 1510 y Fo(M)3196 1498 y Ft(+)19 b Fs(\031)3330 1430 y Fr(p)p 3399 1430 42 4 v 68 x Ft(2)p Ff(,)32 b(while)101 1598 y(for)f Fs(\027)d Fr(!)23 b Ft(0)p Ff(,)521 1576 y Ft(\026)506 1598 y Fs(d)g Fr(!)g Fs(\031)33 b Ff(and)e Fs(d)963 1568 y Fk(\003)1001 1598 y Ft(\()p Fs(\027)5 b Ft(\))24 b Fr(!)f Fs(\031)s Ff(.)39 b(Mor)l(e)l(over,)32 b(for)e(\014xe)l(d)f Fs(\027)g Fr(2)23 b Ft(\(0)p Fs(;)14 b Ft(1\))p Ff(,)30 b Fs(M)h Fr(\025)23 b Ft(2)p Ff(,)1041 1782 y Fs(\025)1089 1748 y Fk(\003)1150 1782 y Ft(=)1238 1701 y Fn(p)p 1321 1701 227 4 v 81 x Ft(1)18 b Fr(\000)g Fs(\027)1510 1758 y Fq(2)1566 1782 y Fr(\000)g Fs(b)1685 1794 y Fo(M)1782 1726 y Fs(\027)p 1782 1763 47 4 v 1784 1839 a(d)1857 1782 y Ft(+)g Fs(O)2019 1665 y Fn(\022)2110 1726 y Ft(1)p 2090 1763 81 4 v 2090 1839 a Fs(d)2133 1815 y Fq(2)2181 1665 y Fn(\023)2340 1782 y Ff(as)24 b Fs(d)f Fr(!)g(1)g Fs(:)201 1982 y Ft(Under)34 b(the)g(assumption)f(of)g(Corollaries)e(14) i(\()p Fs(M)42 b Ft(=)33 b(2\))g(and)h(15,)g(w)n(e)g(can)f(tak)n(e)g Fs(b)2870 1994 y Fo(M)2976 1982 y Ft(=)g Fs(M)e Fr(\000)22 b Ft(1.)55 b(W)-7 b(e)34 b(also)101 2081 y(observ)n(e)26 b(that)h Fs(\025)624 2051 y Fk(\003)690 2081 y Ft(pro)n(vides)f(a)h(lo) n(w)n(er)e(b)r(ound)j(for)f(the)g(lo)n(w)n(est)f(eigen)n(v)-5 b(alue)27 b(in)g(the)h(sp)r(ectral)e(gap)h(of)g Fs(H)3344 2093 y Fo(\027;W)3459 2101 y Fl(M)3526 2081 y Ft(.)37 b(As)101 2189 y Fs(d)30 b Fr(!)g Ft(+)p Fr(1)p Ft(,)i Fs(\025)538 2159 y Fk(\003)608 2189 y Ft(con)n(v)n(erges)d(to)i Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))31 b(=)1380 2120 y Fr(p)p 1449 2120 227 4 v 69 x Ft(1)18 b Fr(\000)g Fs(\027)1638 2165 y Fq(2)1707 2189 y Ft(and)32 b(one)f(reco)n(v)n(ers)d(the)k (Hardy-lik)n(e)e(inequalit)n(y)j(\(8\))e(for)g(the)101 2289 y(1-p)r(ole)c(p)r(oten)n(tial.)101 2438 y(3.4.)41 b Fz(F)-8 b(urther)35 b(estimates.)k Ft(One)29 b(can)g(actually)g(use)g (Lemma)h(12)e(to)h(obtain)h(sligh)n(tly)e(di\013eren)n(t)i (inequalities)101 2538 y(whic)n(h)d(are)g(not)g(Hardy)f(inequalities)h (for)g(Dirac)g(op)r(erators)e(as)h(\(7\).)37 b(The)27 b(di\013erence)g(lies)h(in)f(the)h(fact)f(that)g(the)101 2638 y(co)r(e\016cien)n(t)c(in)f(fron)n(t)g(of)h(the)f Fs(L)1057 2607 y Fq(2)1117 2638 y Ft(term)g(is)g(tak)n(en)g(bigger)f (than)i(in)f(\(7\).)36 b(Suc)n(h)22 b(inequalities)g(are)g(v)-5 b(alid)22 b(for)g(all)g Fs(d)h(>)g Ft(0)101 2737 y(and)28 b(are)e(useful)i(to)g(obtain)f(asymptotics)g(b)r(oth)h(in)g(the)g (cases)e Fs(d)e Fr(!)f Ft(+)p Fr(1)k Ft(and)g Fs(d)d Fr(!)f Ft(0,)k(for)g Fs(\027)33 b Ft(small)27 b(enough.)201 2872 y(With)h(the)g(same)f(notations)g(as)g(in)h(Corollary)d(16,)i(let) 1093 3063 y(\003\()p Fs(d;)14 b(\027)5 b Ft(\))24 b(:=)1486 3002 y(2)1542 2934 y Fn(\002)1575 3002 y Ft(1)18 b Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1884 2934 y Fn(\003)p 1486 3044 435 4 v 1651 3120 a Fs(\027)19 b(d)1943 3063 y(b)1979 3075 y Fo(M)2071 3063 y Ft(+)2355 3007 y Fs(\031)2405 2977 y Fq(2)p 2164 3044 469 4 v 2164 3120 a Fs(d)2207 3096 y Fq(2)2258 3120 y Ft(\(1)g(+)f Fs(S)5 b Ft(\()p Fs(\027)g Ft(\)\))2666 3063 y Fs(:)101 3246 y Ft(By)26 b(taking)f Fs(\025)f Ft(=)e Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))27 b(instead)f(of)g Fs(\025)1262 3216 y Fk(\003)1326 3246 y Ft(in)g(\(12\),)g(w)n(e)g(obtain)g(the)g(follo)n(wing)f(result.) 36 b(Note)26 b(that)g(for)f Fs(d)f Fr(!)f(1)p Ft(,)j(one)101 3346 y(reco)n(v)n(ers)f(the)j(Hardy-lik)n(e)e(inequalit)n(y)j(\(8\))e (for)g(1-p)r(ole.)101 3495 y Fz(Corollary)33 b(17.)41 b Ff(F)-6 b(or)30 b(al)t(l)h Fs(\036)23 b Fr(2)h Fs(H)1192 3465 y Fq(1)1229 3495 y Ft(\()p Fp(R)1321 3465 y Fq(3)1358 3495 y Fs(;)14 b Fp(C)1455 3465 y Fq(2)1492 3495 y Ft(\))30 b Ff(and)g Fs(\027)f Fr(2)23 b Ft(\(0)p Fs(;)14 b Ft(1\))p Ff(,)203 3570 y Fn(Z)249 3759 y Fm(R)291 3742 y Fj(3)556 3627 y Fr(j)n Fs(~)-40 b(\033)22 b Fr(\001)c(r)c Fs(\036)p Fr(j)844 3597 y Fq(2)p 352 3664 736 4 v 352 3740 a Ft(1)j(+)i Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))19 b(+)f Fs(\027)h(W)901 3752 y Fo(M)975 3740 y Ft(\()p Fs(x)p Ft(\))1120 3683 y Fs(dx)g Ft(+)1312 3616 y Fn(\002)1347 3683 y Ft(1)f Fr(\000)g Fs(S)5 b Ft(\()p Fs(\027)g Ft(\))1656 3616 y Fn(\003)1705 3570 y(Z)1751 3759 y Fm(R)1793 3742 y Fj(3)1843 3683 y Fr(j)p Fs(\036)p Fr(j)1938 3649 y Fq(2)1990 3683 y Fs(dx)19 b Ft(+)f(\003\()p Fs(d;)c(\027)5 b Ft(\))2444 3570 y Fn(Z)2490 3759 y Fm(R)2532 3742 y Fj(3)2583 3683 y Fr(j)p Fs(\036)p Fr(j)2678 3649 y Fq(2)2729 3683 y Fs(dx)24 b Fr(\025)f Fs(\027)2991 3570 y Fn(Z)3037 3759 y Fm(R)3079 3742 y Fj(3)3129 3683 y Fs(W)3207 3695 y Fo(M)3295 3683 y Fr(j)p Fs(\036)p Fr(j)3390 3649 y Fq(2)3442 3683 y Fs(dx)h(:)201 3881 y Ft(Motiv)-5 b(ated)39 b(b)n(y)g(the)h (asymptotics)e(corresp)r(onding)f(to)i Fs(d)k Ft(=)f Fr(j)p Fs(y)2277 3893 y Fq(2)2340 3881 y Fr(\000)26 b Fs(y)2472 3893 y Fq(1)2509 3881 y Fr(j)42 b(!)h Ft(0)c(in)g(case)g Fs(M)51 b Ft(=)41 b(2,)h(w)n(e)d(can)101 3981 y(pro)n(v)n(e)31 b(another)h(inequalit)n(y)h(for)f(the)h(bip)r(olar)g(Coulom)n(b)f(p)r (oten)n(tial,)i(whic)n(h)f(also)f(holds)g(for)h(an)n(y)f Fs(d)g(>)f Ft(0.)53 b(Let)101 4081 y Fs(W)179 4093 y Fq(2)217 4081 y Ft(\()p Fs(x)p Ft(\))24 b(=)515 4048 y Fq(1)p 450 4062 165 4 v 450 4109 a Fk(j)p Fo(x)p Fk(\000)p Fo(y)r Fk(j)639 4081 y Ft(+)794 4048 y Fq(1)p 728 4062 164 4 v 728 4109 a Fk(j)p Fo(x)p Fq(+)p Fo(y)r Fk(j)928 4081 y Ft(with)i Fs(y)g Ft(=)d(\()p Fs(d;)14 b Ft(0)p Fs(;)g Ft(0\))22 b Fr(2)i Fp(R)1696 4050 y Fq(3)1733 4081 y Ft(,)i Fs(d)e(>)e Ft(0)k(and)f(de\014ne)h(\012\()p Fs(d)p Ft(\))e(:=)f Fr(f)p Fs(x)g Fr(2)g Fp(R)2953 4050 y Fq(3)3027 4081 y Ft(:)37 b Fr(j)p Ft(\()p Fs(x)16 b Fr(\001)f Fs(y)s Ft(\))p Fr(j)23 b(\024)g Fs(d)3496 4050 y Fq(2)3533 4081 y Fs(=)p Ft(2)p Fr(g)p Ft(.)101 4250 y Fz(Theorem)32 b(18.)40 b Ff(With)30 b(the)g(ab)l(ove)h(notations,)f (for)h(any)f Fs(\027)f Fr(2)23 b Ft(\(0)p Fs(;)14 b Ft(1)p Fs(=)p Ft(2\))28 b Ff(and)i(any)h Fs(\036)23 b Fr(2)h Fs(H)2916 4219 y Fq(1)2953 4250 y Ft(\()p Fp(R)3045 4219 y Fq(3)3082 4250 y Fs(;)14 b Fp(C)3179 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b(BOSI,)g(J.)g(DOLBEA)n(UL)-5 b(T,)23 b(AND)f(M.J.)g(ESTEBAN)101 96 y Fy([16])35 b Fw(T.)c(Duyckaer)l(ts)p Fy(,)e Fg(Op)l(er)l(ateur)i (de)f(schr)l(o)l(dinger)i(ave)l(c)e(p)l(otentiel)h(singulier)f(multi-p) l(olair)l(e)i(\(schr)l(o)l(dinger)g(op)l(er)l(ator)g(with)e(a)246 179 y(p)l(otential)d(including)f(sever)l(al)g(inverse-squar)l(e)f (singularities\))p Fy(,)f(2004.)101 262 y([17])p 246 249 191 4 v 226 w(,)f Fg(Stabilization)k(of)e(the)h(line)l(ar)g(system) f(of)h(magneto)l(elasticity)p Fy(,)d(2004.)101 345 y([18])35 b Fw(H.)22 b(Egnell)p Fy(,)e Fg(El)t(liptic)i(b)l(oundary)i(value)f(pr) l(oblems)g(with)g(singular)g(c)l(o)l(e\016cients)f(and)h(critic)l(al)f (nonline)l(arities)p Fy(,)f(Indiana)g(Univ.)246 428 y(Math.)j(J.,)f(38) h(\(1989\),)h(pp.)f(235{251.)101 511 y([19])35 b Fw(V.)23 b(Felli,)i(E.)e(M.)g(Mar)o(chini,)f(and)h(S.)g(Terra)o(cini)p Fy(,)e Fg(On)i(Schr\177)-36 b(odinger)24 b(op)l(er)l(ators)i(with)d (multip)l(olar)j(inverse-squar)l(e)d(p)l(oten-)246 594 y(tials)p Fy(.)h(Preprin)n(t,)f(2006.)101 677 y([20])35 b Fw(V.)d(Felli)f(and)g(S.)g(Terra)o(cini)p Fy(,)f Fg(F)-5 b(ountain-like)31 b(solutions)h(for)f(nonline)l(ar)i(el)t(liptic)d(e)l (quations)i(with)f(critic)l(al)h(gr)l(owth)g(and)246 760 y(Har)l(dy)27 b(p)l(otential)p Fy(,)d(Comm)n(un.)f(Con)n(temp.)i (Math.,)e(7)h(\(2005\),)h(pp.)e(867{904.)101 843 y([21])p 246 830 V 226 w(,)f Fg(El)t(liptic)i(e)l(quations)h(with)g (multi-singular)f(inverse-squar)l(e)g(p)l(otentials)i(and)f(critic)l (al)f(nonline)l(arity)p Fy(,)e(Comm.)g(P)n(artial)246 926 y(Di\013eren)n(tial)i(Equations,)g(31)g(\(2006\),)h(pp.)f(469{495.) 101 1009 y([22])35 b Fw(S.)21 b(Filipp)l(as)f(and)h(A.)f(Ter)l(tikas)p Fy(,)g Fg(Optimizing)h(impr)l(ove)l(d)i(Har)l(dy)f(ine)l(qualities)p Fy(,)d(J.)g(F)-6 b(unct.)19 b(Anal.,)g(192)h(\(2002\),)h(pp.)e (186{233.)101 1092 y([23])35 b Fw(F.)21 b(Gazzola,)h(H.-C.)f(Gr)o(una)o (u,)e(and)i(E.)f(Mitidieri)p Fy(,)h Fg(Har)l(dy)g(ine)l(qualities)h 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y(pp.)f(P)n(ap)r(er)g(6,)f (11)h(pp.)g(\(electronic\).)101 1756 y([27])35 b Fw(M.)e (Hoffmann-Ostenhof,)f(T.)h(Hoffmann-Ostenhof,)g(and)f(A.)h(Laptev)p Fy(,)f Fg(A)h(ge)l(ometric)l(al)g(version)f(of)h(Har)l(dy's)g(in-)246 1839 y(e)l(quality)p Fy(,)23 b(J.)h(F)-6 b(unct.)24 b(Anal.,)f(189)h (\(2002\),)i(pp.)d(539{548.)101 1922 y([28])35 b Fw(M.)30 b(Hoffmann-Ostenhof,)g(T.)h(Hoffmann-Ostenhof,)f(A.)g(Laptev,)i(and)e (J.)g(Tidblom)p Fy(,)f Fg(Har)l(dy's)i(typ)l(e)f(ine)l(qualities)246 2005 y(for)c(many)g(p)l(articles)p Fy(.)e(Preprin)n(t,)f(2006.)h (Preprin)n(t.)101 2088 y([29])35 b Fw(H.)g(Kalf,)h(U.-W.)f(Schmincke,)h (J.)e(W)-8 b(al)l(ter,)37 b(and)d(R.)h(W)1960 2082 y(\177)1958 2088 y(ust)p Fy(,)g Fg(On)f(the)g(sp)l(e)l(ctr)l(al)i(the)l(ory)e(of)g (Schr\177)-36 b(odinger)35 b(and)g(Dir)l(ac)246 2171 y(op)l(er)l(ators)23 b(with)e(str)l(ongly)g(singular)h(p)l(otentials)p Fy(,)e(in)e(Sp)r(ectral)h(theory)g(and)g(di\013eren)n(tial)g(equations) g(\(Pro)r(c.)g(Symp)r(os.,)g(Dundee,)246 2254 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y(\(1981\),)h(pp.)f(L167{L171.)101 3417 y([37])35 b Fw(B.)30 b(Muckenhoupt)p Fy(,)e Fg(Har)l(dy's)i(ine)l (quality)f(with)g(weights)p Fy(,)g(Studia)f(Math.,)h(44)f(\(1972\),)i (pp.)d(31{38.)i(Collection)f(of)g(articles)246 3500 y(honoring)c(the)h (completion)g(b)n(y)f(An)n(toni)g(Zygm)n(und)g(of)g(50)g(y)n(ears)g(of) f(scien)n(ti\014c)i(activit)n(y)-6 b(,)24 b(I.)101 3583 y([38])35 b Fw(G.)27 b(Nenciu)p Fy(,)f Fg(Self-adjointness)i(and)h (invarianc)l(e)f(of)g(the)f(essential)h(sp)l(e)l(ctrum)h(for)f(Dir)l (ac)g(op)l(er)l(ators)i(de\014ne)l(d)e(as)g(quadr)l(atic)246 3666 y(forms)p Fy(,)c(Comm.)f(Math.)h(Ph)n(ys.,)f(48)h(\(1976\),)h(pp.) f(235{247.)101 3749 y([39])35 b Fw(U.-W.)26 b(Schmincke)p Fy(,)d Fg(Distinguishe)l(d)j(selfadjoint)g(extensions)g(of)g(Dir)l(ac)f (op)l(er)l(ators)p Fy(,)h(Math.)d(Z.,)g(129)i(\(1972\),)g(pp.)e (335{349.)101 3832 y([40])p 246 3819 V 226 w(,)33 b Fg(Essential)g (selfadjointness)g(of)g(Dir)l(ac)f(op)l(er)l(ators)j(with)d(a)h(str)l 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