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DA8E5AB309F1814EEB711AB72F2F504F322D6C00E1C16AFFBC02BED
28C3840E50FCBE0C6F3CFC95BD5F89A51CDB63098EAE17289AAF79
cleartomark
%%BeginFont: EUEX10
%!PS-AdobeFont-1.1: EUEX10 2.1
%%CreationDate: 1993 Sep 17 17:38:59
% Extended Computer Modern fonts were designed by the American Mathematical Society with assistance from Donald E. Knuth.
% 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 (EUEX10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 33 /arrowright put
readonly def
/FontBBox{-24 -1}readonly def
/UniqueID 5031983 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A4EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEEAB91B58F29A4D79EEB0FBBB6D4F4EC35014F
D2DECBADF0C6EBA7DCB4C19B
469A6CADDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CFBDC9E14E6B1B4D536B17074CB4
54AB2C1B7FB83E160A8B2DC7A5829B3ACCDF203FC9E8F25D82A362E
22B51EFCE4BDBA8A5ED6FC
2FCEA8E6F827FA7CD01FCB293A6AF6928B
D28815DAA3A19C7AD6DEC9CB0D80AD0D1667
195870CCDFF46E9694831FDE64B489EBDFA39CC690DE4
93ADEE0EAB10B
33CB208B52BB3AAFC3BEE2D14CB2ACE72179AAE1A
2C5D03CDD96FFBCB49A157B627EACEF69DE
7FB131C97BD84C745DFCC68112FDF027259CAD55D70
8737CF3CDEA7AD895B1F19EA897E4E8F0E6CB5EF31
6F907A3BAADFABCBB1DBF341DCA164F02F938
9ABDDC6E3C76B81D4B5CBCF
62F15CE398D0F2FCE56B4B55BEB176
466A37014CEA0FCDCB8FCE9C293A15BBE31A9FB74CB6
B43E1A72AD43AA249ADD
2A04FCE400A5CE0CE62B0E
B60A8E137D1E6BE30BE8C79FE8A4E6BADBA
D5E8F03C12D7E0B65E037CB4676FCCCF29C13C88108DAC0CBDECA5
59BCFD17EF375A1FF37E10A8CA1132967C
503B79C029DA20CD15EF6B3DF44D515B3688B16AEB1B52BB1EE256
5A8FBB8EE58B6B6C1E9B69EA60CC168
C6E5E5C61B25E05E1AF3E43DB15EACAAD1F8D118EAEB
D5AFAC31825FECEDCAD998B53C15A3708ECEE62BBF65F77AA07640
7F5CC60DACE426AFC3B26D530E82CA4E69FDB66CE1C152E0CE447
FB54A7EAB70E7CFC2D200CA7DAAEFEC34DED4C6768BF
9A83BBF1B20D6A6C39E83628DBF6FACD1251
cleartomark
%%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 /.notdef put
readonly def
/FontBBox{-29 -960 }readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D74A4EAA1E2B58ECA633B8D4E8C5EF4
A213ACB58AA0ABF2EDA960DFE2B27EA49C
E21B3ABF72E39A87FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DDDDE7D31FF2B87F97C73D63EECDDA4CA
27DF461F6E40A5DB51E641C1D4E8E4F8CBF
5B78EC1DC453A678F58A7E1B7BD7CAEB8DA1F57C4F09
0ABF1D42C5DDD0C384C7E22F8FC1CC8E3B4E
DEB819CB6AE455B1AF3187FFEA41D44EC7A
71A7BB3DFD2E4BB69859EFA4BBC30BD6BBD
4ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4ED7C
515DB70A8D4FDC1E5DE8BC570317AAEA74A842CFD26FA0
9B4EAD712F4278EF5AEB8DEE60CA4AC372EEE8BCF912C5
7FC5D575CADB6EEDD9C4BAE71B13C32BF5D
F64E9DD5ABBCBAA3DDA8DC221E501D9AFB8
7C0324758ADD857FFEAA74D7A1A6F2D5E849C54D792
D8ED0B54BD1EDBEB73FE195FA82EBCD5A5C807B9D70B
FF52A2CD408BDCB30BFDDCE15A54D86EEAB77D127438
E4D7F3CB7F9697AFC9CEAC4D3CBA700AC9F71F1A7DD7A
1CED1C50CC4EEFFA0BA37FB741C
20AEBF49AD2EBF6F5B72E3E3D194EFCFC53FA03C4C
BA2AC5BB289F5D065E9EB4ECF7FF3FF4414AD56AAB0C4CF3F615C3E4B9C0D0A4
7C332A7FCF3B97DA953D18D9BE00AAA22CD60FC5C6A8
E92C27D1D4B654ADA8DB9B9B34BB012A74490DB11EFA10BE27ECEB
8F242C5B81667DE4AEF180D3FF449D6F2B90C31AAD0EF5F5AFB312E0FD496FBF
5177999EBA15A448E6BBA45F5460FA0E
cleartomark
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% 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 (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 82 /R put
readonly def
/FontBBox{-55 -420 }readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A4EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEEAB91B58F29A4D79EEB0FBBB6D4F4EC35014F
D2DECBADF0C6EBA7DCB4C19B
469A6CADDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66AF68BFF326D
1D432B0D064B56C598F81D78E1629A31ECA5DDC383
D10F04E2CF25B81CD9A158EABD3C6849ABA86F
1F25CE79BCC50D9A3FEAB534EB9721003
DBFEEFD050F3AC62A9A531ECEC0FE946D21CAA771D30
A6C27ECBA196BF9DCFE7AE1
160EFCC206F28BA544FF
D85FD89D6F43D66B5DCE676503EDFAE84D12A71E77
1F4F3F50D2C57EDDB8E76A7EF413EDC
16A3B65CDD2F9FEC4E662D54DAA43CFAAFB68
ED4C8C493D6DACD010A74FECD7D12D72AE16C26194AF
21AFEEE092F09C19959BAAA9F263CD391E3
74DD1D1B4CD4D75273CAA4E37F68CFA35AD34C0AFB1
854D16CE1C375FD159A337E221A6FF1CFFBEBB58C
AD92DD9EAA355998BCC48ADD0E7A4BCF
A1FEF6075033BCD422EEE7C223D5AD4D5B
95CE4D6DDE819BC579EDF743F2C74C95F717FAA6154FADC3FE2975
F59CFB1C1AC48505BAEADE18E46E610C868A257173ED
0D30EAA4C78E92D0ADABAC770FE26D70E72F
90CCFAADFA75A299EF090B93F8CA49FEADB79026CBAA539F56CB
3E44D9E5F7FD8D7AF7D18A8A1DC7AA072CE1CF7C157F236E5F11673F
CAAC6A3C6EC9F76CF77DDB3B66F38DBDCF5CBAE516C
24B3B4ACFF3132FCFAC78426FBDABB5ABE4
37E890FFFB40FDE97DAD3ADFC5C3AE67DAE5D781301
A9C19FF598FAE6E55DDEAFE1BF0BAC9DD0CA4C1EBEACC34
C380FE7EE00BD0B9FEE0EC50A17084
97425BEA1FCFECEBBDD14D8C280A5B533FF41D3C1
6901EEAB8E6CAB73A29CAF3ECFF9F1FC5AB1A6A238
7FA9B02EEC35C9C31C52BD69DD46FEF423B7A0C9A272E0
F0BF7CD8CEFF7EB8B11E99E9CF
0F200FA69B4D6F2D473F7A020E68A0BDBBE5646F43CE
C24B052AA797C4BDBAC28F027DCE7B1
C9CBBB262EDDB3DD374EDFB66A0E2448C
1AC53A4EA28CD8E6A34C5DE3E6ED0B4C530D3D8A6F44D
A548FDDA8A964FD94CD7FBA725E37DAD5AA5A6B127C774E0B9C38
66A43E5F3E572F9B59CDAAE48ED93841B
31A3D9EEDF67F16B39B2DCEB0A7146446FAA97BE30F73DFEAFE28C2B415D960D
3ABE131E61FD7DE250CA728A9E1F37D17A7C141AA8C629B73BB524
A923A0B49CD5AD3ACAEE7CA8B650C280807FEBC6F0F8DFC50E6C7E
03F15C7BDACF3FB82A38FC57A44F434ECCF652F616001FDF76CC97
3E62BAD7F8F631E7F3FDA62B0EEC24C8B173AFF
cleartomark
%%BeginFont: EURM7
%!PS-AdobeFont-1.1: EURM7 2.1
%%CreationDate: 1992 Nov 20 17:36:39
% Euler fonts were designed by Hermann Zapf.
% 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 (EURM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EURM7 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 18 /theta put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 64 /partialdiff put
dup 102 /f put
dup 105 /i put
dup 110 /n put
dup 122 /z put
readonly def
/FontBBox{0 -250 }readonly def
/UniqueID 5031990 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A4EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEEAB91B58F29A4D79EEB0FBBB6D4F4EC35014F
D2DECBADF0C6EBA7DCB4C19B
469A6CADDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CFBC1F2E73FECA8A4
87100FB1FFC4C8AF409BE605DAEA1A455F
D1F017CECB9BCDDEAF93A4FCF4140B4
F4BAD1FA07FB156DCB7EA9F1
B0AFDE5EA7A41DCA5D6380BB4
1BFF36E1DEC4FB9D55FDC9FA3A57C8E
CC9CF2D24DABA5A3C417DD
9D06DA9EE996FED422B6E35AF5D9A5B19CFEF1A4BFF14FE66B6C
FC999505DBEB9FC61D71A2A8C266FA89F2
B865D16EB2636DCE29ACDCBE1DB7EBE91C
0D6ABE7743860AFBCF3DAD06BA306CB714F2
C520F3BC5C7CDB0CB6B54E7E148E61D1BC63BCEE9D558
761ACECCA5DE92BDB0B9E0F8205AFDAA5F5DC5796D
AC76207AAF34CF1E8398EDA6A42C9BDD82B1DECA882E9243202C
76D01C9AE6C68F7C2635EC92EAC1DD32B0D2ED1C399
618C2B5BFF4C7B3D6CAC6FED76F908AA97FFB2E749B
BF6077B9AEED790A98BB8F2E021F52B11D2CDD5C218BF84EC864B6AD98F74FD0
37431CACDCCAF8AFE2DCB926E9AC0AB7CAE3EE8BE4639622BDB471F
322E3C6E8DD3B1398001DFF57DC85E93C7DFA5D24
081C21AF0FEBC6BC436BCBDE910A54
A1F7CCD2D8D3EA8FEB5A1928AEEA1AB814B3AA5B2
F23B24DDF2F4B047EB8B62DEB90BAC77038BEE39C78
29A7D8B21A310EABAABE9E9F2E250824F
D5E351D20C369A089B1C9AF017912DCD03EFA174FCADF6BB6B40703
FD02DA17A9E6FB7DA4D7DAD5F43D68
B57FCCFB7E94E7BFEF449DDCF31A5A1167BACFB354
ACBAB950C1B71EE9BAAD5DA22F5FAE3F1EAD7FD5D6F
FFAE42DF3FB58A787C5C
4A9A5FBB983CFBFEA0FC13E
8DFCABCFC704CA8B4F813BF7BDFEF9015A9
670E76DC4AA1F93CC3EDA9AFA47BED4DE37C6F
EDAAB9283DBBD3FFFB3FDDAA31431CCBCC275D4EC9
CDCD94EFACDFACBCFBEFBE095C6FF888E
CB0E21DAAA83D7FBE8F494EDFFE8B54EF82D6CE04B25309B
4D92F7FB317E622BBED568F2AC559ACF3B0C78A4D57DDF682F8AAC5E
2BA4AC3E4C757DBFF8AA09E14B731DC32AA7CD8F
619ACBBD89BD9E976E469D9DCEBF5C82B2A53DE909081FCEF495B7
E37009EDCA4F9DB40DDC528DA0136DD7EAE7237F61ACDA
253B04D585D2BDBF99BBA07C9B3F48E006A8A5BB14
9F42FBD8FD99D83FA4CCD0C661CE1BE67EC65D9F313A0DA959ECA338
3953A8CEFFF940C23B66776DFCEEFCD10D4
EF90C1C15DC374DE63FA9491A8CDF3F1BB993ACC49FBADC869D1D
F94EFCB015E1FACFA094BFA0D880036E
04DB65CE1FF09CE0A06E12F63CD69E57CEEF
CEEC4F634A854CDAFC5F53
ACBBCD8FB70B1D1D6E13EF5DBEFCBD0C9DF
A0BEED78AD4D9EA78ACB195
873D0EFF62B410D993B3FFFBBC6341A2FDA50DFC952B
9926CB30DABCC16CEF254C635906EFC457DFCF6D3DB
926BAF97E111EBB92EA4DE8B1C2CF0B7DDF3C44A03
C6E97B93DA91F24EFFDE8148EEFE517CBD7B6400E
1CCB50CDF23AB2E53DAA009B3FA2E551B7B15624AEBEE61D
DA2BF57DAC3A7EA854B2EFC91D8C9FCC81CCD9923270C
D39CBF4F92C72B055E125D328CDBF7E683CC9DFAC40DB5BCA6FB22
B6CBA7E0E4DBEF422C0C945DED6FDA3B12C8745CA0
464F88CAAC49BF47DCF4ABA6B5C10A3B1
7CF37A7B7F301DDA90ACFE50380CAA88E7DFE25F78B2C0DBC3DBEF
451EC90AED87CBF91A62EC7FE1C1FC59BCC
5EFFAF26EFB5AAAD784E0DF9EEE537BD352C41B29
FF1DA1D1AACE89903FDD73BD94DCCA6D34E07D27A63D
DA7BFCEDA7BE32FF73F3B253CCE08A3D0D500DC322E5B8F8CF2286
E1D5ED6EEF7F47CB911B55D40462F0BDD7A5EED204D925748DCB1
16DF62ACEE9C7DFBC1B3C572FEC1C8A8AEECE76EB72307
3C1EF9D4C8DA23CCCC76BE85AA3B261E519BBA
0A4CEF5F8D51FD760D82FC7EF859F8BC458EC09315
BCC033CE534CAB9852ACD72A7B48C97BEBDD56DD76D3EBE6C14C1B
07DCE5036CCD3D461E317FCBC057E5F62EC2B15DEE307BABFBF70
F81A37CCBBA60BF968D401CB30B297E9
497A4EB16FF90863FDA6E9111A5CFD34F5D81FFE27F
A279DBA2ACBB3BBF6F4D4E
4D796C3DC3EEBB0E133F9FC00E51D61B464BF3C9AB8105
4B5B2C32CCBA1B99B5E7FF4DF51BAB88CD4C705D247D0
8F22F360B707F00BD71E2F7FB0DDF2B4DA
B855F5FCC77ABEB49C5B73EC3F973DC41
DB6FF09D3EABBD28F95C42CD2D68C782E934CBD6359D
F243ABDD0C92E8CAD5B48DE978E0BF976B7A4E09D67A64A3132F
AEABF7A5DB30B97A29DD84E43F0785A3
C93FE7129FDF1EC8EAFE89DB170C0F5D19D94ACA8F
D6AE29FDC2F5BCBC21C2D113F82DB54E4237BCFA89
EC860E44A1BF652AB8FC4BBD50CD5DB2C73
cleartomark
%%BeginFont: EUFM10
%!PS-AdobeFont-1.1: EUFM10 2.1
%%CreationDate: 1992 Nov 20 17:36:20
% Euler fonts were designed by Hermann Zapf.
% 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 (EUFM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUFM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 45 /minus put
dup 58 /colon put
dup 61 /equal put
dup 91 /bracketleft put
dup 93 /bracketright put
readonly def
/FontBBox{-26 -224 }readonly def
/UniqueID 5031986 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A4EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEEAB91B58F29A4D79EEB0FBBB6D4F4EC35014F
D2DECBADF0C6EBA7DCB4C19B
469A6CADDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CFDA4FF164169FBB
D2FB69E0E5E617BC06F3BB47E731AE1
0B406AB3C86AA1A83C171DA0
C020AAADC1A6A56FFD3C4B33F6B0E977B7C760F8816
4A6F13E415D902E653B81AEF60FE07C4ABC376BB2
6BAB3851178BEB6AA92FE582EFCFA3A22C6795DCAAFAFCA0F3E79D
270BB779E2071AFDF30D3FAEDF90940B6DAA1F34BAC0E9AA
8D9EB615A972BBD0B8EAA09B5D88859
BF0D6B8C64EE022AF457F4E063E40F3
FA1F8C2CF0C7C49EC374E22B0A865A90FDC5CE762D7AC4CA872A23
9CA95AE336A8D3C10BBC8BA47B1DD8DAC76B3F7B4E34DA11B11F27E
5CC1B7DCC5E194DD545B39C060A69CFC2145AFED8242A9FEA65F
ED03FC2DA7CDD3ADC394D32F5C356A7
1EA231A6AE8B779BFBB6F7E01D44C6A1
8422BACAA4C2B6BA95F232A5B3B9DE2EFF97C276B4
691C2E88AAD4FF004B53C12CC6BEDDDACCE965BF81A8
8518AD8EAAD03CCF67CA8BA8A2B26BACAE757CB7C3BAE0532181
ACEF7B3ABCFD2BCFD278A34AB
27FBDEFD188D97D419AC2486AAB33B073D9EDA1ABF2B2339F56C
02B150C69E56B6C84E1CCFBA0A500FAEA9703DEFE9
FAED265E96BCB30F450F546F4DA8D8FE
DCB8A667AAA31C447EB928D8989214EDBD1B7B329B37E
8ECFCC46ECDDD3E3D7D1EFE
752F9ACF5C1ACF3A794D679CB72D458A1EE62B74A1B876CD9F13AD
C7D920F40CC369B42BCA58ADBAE76CA
689D610F895D0EFAB69D463E4DF427E214FAB47D618BE2AB6BCD6F
DBFE7B9E3DA166BB0B99DD663ABEFD04
65D8CFDF950AB7FEBDA1AD44AAD0920B7
35E92F63F0D7FAD2EBCB78D8240CD02BEC944CE2994A
95C426EDBFE4B199ACB5A8E9B0C5651
596FF9F48A16F1A3ADB25A6FE250B98AEE6C7F9AAAE8D
2A4E326EC794F4C1E83D673CDEAEC45D481CCA363D561
8BF57B2AA2F3BF31EBFB9EDC72CF9DD1FE0B2095D1FA
417B587D2D950486DCD45D17BDEF5B4AB382BDEB628B
0E74C347F0EFFC7BFDBBF84A7B09DDB4
0DBF8B27F904FE7FB6D357EEE0FEE62AFC2C82EFCA147D
FAE3A168DFE7F9AEE53B1FFAC8D2E392F948
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dup 68 /D put
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dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-32 -206 }readonly def
/UniqueID 5031984 def
currentdict end
currentfile eexec
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1918 y(@f)p
a(@)q Fe(\026)g
Fk(z) y Fj(+) y Fk(@g)p 4
a(@)13 b Fe(\026)-55 b Fk(w) y(@)2301
1899 y Fe(\026) y Fk(f)p
2031 a(@)q Fe(\026)-43 b Fk(z) y(:)456 2160
y Fm(4.)41 b Fl(P)n(olar)28 b(co)r(ordinates)e Fj(\()p
Fk(r;)14 b(\022)p Fj(\))30 b Fl(on)f Fh(C) y
Fd(\002) y Fj(=)d Fh(C)20 b Fc(n)f(f)p Fk(0)p
Fc(g)29 b Fl(are)g(de\034ned)g(b)n(y)g Fk(x)d Fj(=)g
Fk(r)14 b Fe(cos)e Fk(\022)p Fl(,)30 b Fk(y)d Fj(=)f
Fk(r)14 b Fe(sin)e Fk(\022)p Fl(,)456 2268 y(or)26 b(equiv)-5
b(alen)n(tly)26 b Fk(z)d Fj(=)g Fk(re) y Fi(i\022)1318
2268 y Fl(.)647 2435 y(\(i\))41 b(Sho)n(w)33 b(that)g(in)g(p)r(olar)f
(co)r(ordinates)e(the)k(Cauc)n(h)n(y-Riemann)29 b(equations)i(tak)n(e)j
(the)776 2543 y(form) y Fk(@u)p 0
a(@r) y Fj(=) y Fk(1)p
a(r) y(@v)p 1706
a(@\022) y(;)
a(r) y(@u)p
a(@\022) y Fj(=)23
b(-) y Fk(@v)p
2664 y(:)623 2811 y Fl(\(ii\))41 b(Let)35 b Fk(\012)1004
2823 y Fi(0) y Fl(b)r(e)f(the)g(region)e Fk(r)i(>)g(0)g
Fl(and)f Fj(-)p Fk(\031)h(<)g(\022)g(<)g(\031)p Fl(.)56
b(De\034ne)34 b Fe(log)9 b Fj(:)30 b Fk(\012)
y Fi(0) y Ff(!)35 b Fh(C)f Fl(b)n(y)776 2919
y Fe(log)14 b Fk(z)28 b Fj(=)g Fe(log)14 b Fk(r)20 b
Fj(+)g Fk(i\022)p Fl(.)47 b(Sho)n(w)30 b(that)g Fe(log)h
Fl(is)f(holomorphic.)42 b(Find)29 b(a)i(region)d Fk(\012)3213
2931 y Fi(1) y Fl(suc)n(h)776 3027 y(that)g
Fe(exp)9 b Fj(:)27 b Fk(\012) y Fi(1)
y Ff(!)d Fk(\012) y Fi(0) y Fl(is)j(bijectiv)n(e)f
(and)h Fe(log)g Fl(is)g(its)g(in)n(v)n(erse.)456 3189
y Fm(5.)40 b Fl(De\034ne)28 b Fk(f)9 b Fj(:)27 b Fh(C)c
Ff(!)h Fh(C)j Fl(b)n(y)g Fk(f)p Fj(\()p Fk(x)19 b Fj(+)f
Fk(iy)p Fj(\))23 b(=) y Fb(p)p 0
4 v 71 x Fg(j)p Fk(xy)p Fg(j)p Fl(.)647 3355 y(\(i\))41
b(Sho)n(w)29 b(that)g Fk(f)h Fl(satis\034es)e(the)i(Cauc)n(h)n
(y-Riemann)25 b(equations)i(at)j(the)f(origin,)e(but)i(is)776
3463 y(not)e(holomorphic)c(at)28 b(the)f(origin.)623
3571 y(\(ii\))41 b(Explain)30 b(wh)n(y)i(this)f(do)r(es)g(not)g(con)n
(tradict)e(the)j(theorem)e(that)h Fk(f)h Fl(is)f(holomorphic)776
3679 y(at)d Fk(a)f Fl(if)h(and)e(only)h(if)g(it)h(is)f(real)f
(di\033eren)n(tiable)e(at)j Fk(a)h Fl(and) y
a(@)s Fa(\026)-36
b Fi(z) y Fj(\()p Fk(a)p Fj(\))23 b(=)g Fk(0)p
Fl(.)456 3841 y Fm(6.)40 b Fl(Let)28 b Fk(f)f Fl(b)r(e)g(holomorphic)c
(in)j(a)h(region)e Fk(\012)p Fl(.)37 b(Assume)26 b(that)h(one)f(of)h
(the)g(follo)n(wing)e(assump-)456 3949 y(tions)h(holds,)647
4116 y(\(i\))41 b Fe(Re)14 b Fk(f)27 b Fl(is)g(constan)n(t,)f(or)623
4224 y(\(ii\))41 b Fe(Im)14 b Fk(f)27 b Fl(is)g(constan)n(t,)f(or)600
4332 y(\(iii\))40 b Fg(j)p Fk(f)p Fg(j)28 b Fl(is)f(constan)n(t,)456
4499 y(and)f(conclude)f(that)j Fk(f)f Fl(is)g(constan)n(t.)p
eop end end
userdict /end-hook known{end-hook}if}