This is a multi-part message in MIME format. ---------------0305231415354 Content-Type: text/plain; name="03-237.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-237.comments" Corrected version of 03-119. Notational ambig ity corrected. ---------------0305231415354 Content-Type: text/plain; name="03-237.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-237.keywords" Casimir operators, Lie algebra, representations ---------------0305231415354 Content-Type: application/postscript; name="Camp2201.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Camp2201.ps" %!PS-Adobe-2.0 %%Creator: dvips 5.72 Copyright 1997 Radical Eye Software (www.radicaleye.com) %%Title: C:\PCTeXv4\AMSLTX12\Camp2201.DVI %%CreationDate: Fri May 02 18:03:56 2003 %%Pages: 17 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: cmbx12 cmbsy10 cmsy10 cmr10 cmtt10 cmbx10 EUFM10 cmmi10 %%+ cmmi7 cmr7 EUFM7 cmr12 cmmi12 cmmi8 MSBM10 eufm8 cmr8 cmex10 cmsy8 %%+ cmr6 cmmi6 cmti12 cmti10 %%DocumentPaperSizes: A4 %%EndComments %DVIPSCommandLine: dvips -@p1 -@t42 -M -T8.263889in,11.694444in -p=1 %+ -n17 -c1 -r0 -D600 -oC:\PCTeXv4\AMSLTX12\Camp2201.ps %+ C:\PCTeXv4\AMSLTX12\Camp2201.DVI %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2003.05.02:1803 %%BeginProcSet: tex.pro %! /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]{ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]} if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{ cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 2 string 0 1 255{IE S dup 360 add 36 4 index cvrs cvn put}for pop 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /V{}B /RV /v{/ruley X /rulex X V}B statusdict begin /product where{pop false[ (Display)(NeXT)(LaserWriter 16/600)]{dup length product length le{dup length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail {dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M} B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{ 4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{ p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmti12 %!PS-AdobeFont-1.1: cmti12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmti12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /cmti12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 14 /ffi put dup 44 /comma put dup 45 /hyphen put dup 46 /period 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 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 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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 105 /i put dup 106 /j put dup 110 /n put dup 113 /q put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f bcea9907a04cf93c12727ec40db3f2f77596dca477862747435bdedacd9b2311 6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a 84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711 de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e 93964fa67d27fae86cba2166fd5bcdea975949a3e06d6894a539161012fb486f 12b96d638c731f3f21f0e03cac4a795d88b7f7c6c37e03bbcd84e3dfc6fa0903 f471ce1992428ee75c286b0b35c4f3ace3b47dbd42db7e56e95b6098ee9a3cc9 d7a37e6ff95bfe2c0b20f14839cc38284949143f2095aa85fb5f83b9dd6ba529 0af876a0d087822c2fcb297190d917f3833f453855344ccb2e1d41987fcb1794 b8d8c380474be157f848a218197b208c38b3879beb3f96dc4dd823c15f0ef7da 0cb320df4ee1b11852b68fd47b2744ebec4de0539bc86a57c7a2a4a0a7fca1eb f89de0f3bfe28ab67236bb5ff74f79a0014063d898d689107baebb7575089568 120ed6cbcb7f208bd81c2ff57e24936d3dda56ee92629099ff2ebfec5316ba81 6db64df9d032527ad71b8da53fff524d52d8aaa745b86accf003317423f8b1db 956b249cbb229e315aba3b760df2b046ca3c1864b8cb43a9e16f8d97a021a991 0d9589e9e7448f184e4d7c659c6884ed36a486b5cbdd1f75cfb528d110c5f503 1cba982eb6670e00234c51557b5297ed3a8fdb33cccc62727c97c884e9fc9b6c f2dcbbfbf4fc37259e21e559262d6eff29a02525fb59479dfde0115e2c32ef69 7f1752fa7b8f547fb963b66e3f4f748d6f3e6bb724bdfa6cad59aff43c9257ac e05353949ff3f4a899ccfbb6ec9dc7e059dd2e9095f236471110e66b6bba4c79 ee68b2b3c191fd3410ca496e97348a7b720eb34d8da4b6d6d8963e7b95c53ab0 a0ff9e01804315a2710a7282c1850f367a796610357d0d7862173ecc7fb1079b 0a4d36b31b3c4f916a708a694b08cfaaf12c1f0ef977e985e3a45ea02f45cd9a 1f81d341ee40e079c0e1268613dd008f03be329654b1269d55e42030ac4761c5 76aba4fa997b762f6df97cb2c63453c12ce4dc3907029299e68d4760aa7dc68a de9bfba7f1582d8f6039b3170df4ca94e60575d0aeefc555a03478fd48bb45a5 997871404904612c1592faed2eaed8bc6b747604df54ad8a41ec96902af84af3 840bcc82f31aee56528fa93249c973212024b67d714c050081baa93e307ae29c 88ec5cbc3400e2b67e92c6593d7bc6e4a1e41969bea2aa3bb76539e5a9da8606 112006ad35b4895f54ebe6dc31717c9a52830f189e0f6b318dea2148681aed6c 00004ca48a9c9a0a0982304a0de17c427017b4b6d1980311da9fb8b482b6ccca 9ea6bd4308d36116fe3023a83280e75b4aba09b2d554831547d0377820de1794 8d0a086e839433951d41c48570a541ecc66d9ceb7dde2b66ed16d4c8b5cdfa58 1d2b75ae02919dcf548322ebd7050c44896ca1d37dd770e988e46e76510cedca 9d235886c4ee1a494bce078c8ed3e7df14f8bb55fe750167009b82ad40 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmr6 %!PS-AdobeFont-1.1: cmr6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmr6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /cmr6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d98f2e44ef37ad46 282d7a587974734c2b1e24d854562df98bbe4af15005486cbaffcbcffec311bd e91d2cadb4d2d0835a77c4f73bdee2dd107a4700b60cf0bff46d3d25dfaf0551 8e363c1e95736e70a5c950a2152ce2c3f5c44389518fcb2cc85003fc99994abd 691177ab02601cc9e72a98c68c487b6251ee3b4b649aa85afa307fa744c5baa1 6bd6170fa6404f15b42eb9d417e3fb0f48335c6db453bb0a46a730ab26c3f903 9db1f048f083a04fd61a35caef7d527d21ae534ea61c9798e5c1c802796207f4 89c987f0d56276e362a5347f3b005aab26da5ab14d146d495dd58daedc16fee1 bbd150e48676b71b6cc41348b2526346ff01806a0143c9ed4deb60706f4e34ce 46615c7501249491edb50dc52846399ce5e2a406f7449488d54f6bfa9e1c2bb6 17a90981965b9de4db15b0afe8f45b3882eab15a0c8e5f79c3b2ee8518b0fe62 3bf01f7307d234cadb7d2a0fa3106a51e358ff843df209a9ac21b085d85486d1 294c4703dbba4d7e87d6d534c8c57640530f21a659f6627ee65d9d8a6259e1f3 c4e49b7b475f2cf3811da2863c314146d835b045fe89196581d4a25eb2451356 e234d3e173047a7dae601dfb357131be9b8099688c3039507b46e692e58fd35e 72ee7c8093254fb3138bebc6b5370cba404919b7760eb0c4b0524b2f56ba7673 3a5c7bcba15bbc1d5ba98e5f426e91586683bcdf974b824c76cd302d0843e130 52c69d22034b0a5c9fbf20702c06370b2073de16ae3a459371f9591be5cf651f 1a24912c63330430ef6e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmsy8 %!PS-AdobeFont-1.1: cmsy8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmsy8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /cmsy8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 8 /circleplus put dup 20 /lessequal put dup 21 /greaterequal put dup 48 /prime put dup 49 /infinity put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a25ad4f81f70a4699b36ad0292e61eb54422c13ee7266ce8fbbde4ef da0f829dd430a038260f2e92f668f3a3e39fdb35d5e11ae25b119b10985bf3fd 12ffb2982f230d02c675bf6de332e2f593defc379506d71b85f707504a5b4941 92dc5c1fec66f4dccece85b6ec2825f0852d820437806a7d42e60addf725c2d4 a9160bd0b0dfe92fe33662306ac14b7c5c5a32edcd7de847fb77d81b1c026817 538adf114427a69b55f5a2b2864a1741f5769138eb28d28b719b6bca5ceb1f09 a709f0256d65921a9a9ec7d1dfd0a4176258c97fd1e8dd7fff4b9239162b7100 bcab850b3baec51df2bc9078c814df60351fb5b0fe58c5964c3d07f82ceeebf0 8477b32601b94a5d1454ee7c64c66a5ca2bca4ee0b50192d28cbccd56925b6d8 a7c96b9ec5936e842f1becb11a01fe323f4b623374975071312770d53354496a a6ff67a0c1d7f601b6be6a350d795633921106ec9c7670ad4580e340fb478ca7 27b71a509a9be4de2ad835df0b526d06edc4df2b80057a90704a9f016bf720f4 e6cba77e8b02b8cbd638b5b4c3a79ae9bab500955e89d5067f15c3f133dbf8dc 44787f1d1b1d2f464949f6a2f90613891e071a03d9227291412e05a7192594aa fc68aa36de2d9f0502f75aa7cafcabdbab866a00ea17002a2bf3d96c1b277964 dda15ee8193abf6cc88510f10a3269d51d446cf50d870a95e256be32be1e690a be55890aebbdd84a2e7ef8794515538404c7def815047a36ab824d1588c5d712 3cb3e753f674613a6408293c9e399f448dc7b2e1a1a73b82b89a969b176c47f7 82f8f0d7f94311aa13815d59810af4b843563a9773ffa4099063b682dac007c6 c0a0b26c8bbe938a1ceef66016200d2e3b0488d63bfdcec5121bca456b42921c 0ab099f293f8cadd7f1e1b52682720436ea0380da7e16ea19150545d27b810fa 9c841cfec2d77f8ede0808856efc25a682381e5f673a15aebd37d0a2273f1c1d 8ffa679707949410409836a209e9028807ffc01cbae573a1487140e3ff74dd6b 330f4744026a4b2a6d6786c58c730b1c5e29b6c5eb49942b818b463cb5e2548b 7d5ef4b4dd61759deb2cb51c8f650eb322491f1db2b3711c39f36e29b7a4dd5a 2776dc7444a95be475dfe359587ab2fc523c5690e5b3de2350a15f1e01af7d4c 6ba1505f705609bbe8dd115bc85242d3d5756d89dbd0a6cb03acb286ff4e614b afbe301e00d44a290d9bccce7d50ae7f0bc42b62b958d34bc53f05749cb14ba6 69d74114f9c3ac77231c3f422a66ed2dd545d9aef6b76b995c2720a1b40227fa b4d48c5379aa9d10ce7e7898ad0e42fb947e5cb2c5b4d5f1697691be83ac0e42 ed1fde4afa0c0c89cf23574624c7be487fe12c3ef326396132a801f86d847686 61b97fb9189757738f1df3bdd88d1972eb6cbae57cb83360241af9379c281edf c97146e9fe923306607c936d63f81c8ee3be7b233fd2d494ba42a8c95f7796b7 7540a1792ded02f03fe367a080b03fa3e3991a083076b03c4682c8d19ce6dc4c 61270bdeabab28e9e228dc929a28c0ae8e8d76e9642663a875463075249687fd 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmex10 %!PS-AdobeFont-1.1: cmex10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 40 /braceleftBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 80 /summationtext put dup 83 /uniontext put dup 88 /summationdisplay put dup 98 /hatwide put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fe3c35a5e4206f60b2b4f567b948f7ac54e3ed16b58e137958bb0c141e411b c1c47810add8abfba9f5ef95f96d064cbea94293bf05dc6979c6001553e168fc 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmr8 %!PS-AdobeFont-1.1: cmr8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmr8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /cmr8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus 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 82 /R put dup 100 /d put dup 101 /e put dup 103 /g put dup 105 /i put dup 109 /m put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: eufm8 %PPR-don't-cache %!PS-TrueTypeFont-1.0-1.0 %%Title: eufm8 %%Copyright: Copyright (C) 1994, 1995, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-C. %%Creator: Converted from TrueType to type 42 by PPR 15 dict begin /FontName /eufm8 def /PaintType 0 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[-26 -223 1094 742]def /FontType 42 def /Encoding [ /dadv /dalt /fnos /falt /galt /kalt /talt /ualt /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /quoteleft /quoteright /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /exclam /.notdef /.notdef /.notdef /.notdef /ampersand /quotesingle /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /.notdef /equal /.notdef /question /.notdef /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /.notdef /bracketright /asciicircum /.notdef /.notdef /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /.notdef /.notdef /quotedbl /.notdef /onealt /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ]def /FontInfo 10 dict dup begin /FamilyName (eufm8) def /FullName (eufm8) def /Notice (Copyright (C) 1994, 1995, Basil K. Malyshev. All Rights Reserved.012BaKoMa Fonts Collection, Level-C. ) def /Weight (Regular) def /Version (1.2/19-Jan-95) def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -133 def /UnderlineThickness 20 def end readonly def /sfnts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def /CharStrings 97 dict dup begin /.notdef 0 def /.null 1 def /nonmarkingreturn 2 def /comma 3 def /nine 4 def /quoteleft 5 def /quotesingle 6 def /M 7 def /Z 8 def /g 9 def /t 10 def /dalt 11 def /exclam 12 def /period 13 def /semicolon 14 def /B 15 def /O 16 def /i 17 def /v 18 def /falt 19 def /zero 20 def /equal 21 def /D 22 def /Q 23 def /k 24 def /x 25 def /kalt 26 def /two 27 def /question 28 def /F 29 def /S 30 def /m 31 def /z 32 def /ualt 33 def /quoteright 34 def /four 35 def /H 36 def /U 37 def /bracketleft 38 def /b 39 def /o 40 def /minus 41 def /hardspace 42 def /parenright 43 def /six 44 def /J 45 def /W 46 def /bracketright 47 def /d 48 def /q 49 def /plus 50 def /eight 51 def /L 52 def /Y 53 def /f 54 def /s 55 def /dadv 56 def /space 57 def /colon 58 def /A 59 def /N 60 def /h 61 def /u 62 def /fnos 63 def /quotedbl 64 def /slash 65 def /C 66 def /P 67 def /j 68 def /w 69 def /galt 70 def /one 71 def /E 72 def /R 73 def /l 74 def /y 75 def /talt 76 def /ampersand 77 def /three 78 def /G 79 def /T 80 def /a 81 def /n 82 def /onealt 83 def /parenleft 84 def /five 85 def /I 86 def /V 87 def /c 88 def /p 89 def /asterisk 90 def /seven 91 def /K 92 def /X 93 def /asciicircum 94 def /e 95 def /r 96 def end readonly def systemdict/resourcestatus known {42 /FontType resourcestatus {pop pop false}{true}ifelse} {true}ifelse {/TrueDict where{pop}{(%%[ Error: no TrueType rasterizer ]%%)= flush}ifelse /FontType 3 def /TrueState 271 string def TrueDict begin sfnts save 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt cvi 0 72 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt cvi 3 -1 roll restore TrueState initer end /BuildGlyph{exch begin CharStrings dup 2 index known {exch}{exch pop /.notdef}ifelse get dup xcheck {currentdict systemdict begin begin exec end end} {TrueDict begin /bander load cvlit exch TrueState render end} ifelse end}bind def /BuildChar{ 1 index /Encoding get exch get 1 index /BuildGlyph get exec }bind def }if FontName currentdict end definefont pop %%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 8 /circleplus put dup 10 /circlemultiply put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 70 /F put dup 77 /M put dup 78 /N put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 121 /dagger put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 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27c3e781d604054f467ab9a9eac67288441f0f37c4e6b52cb78fc8d146c950 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%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) 1991, 1992 Y&Y, Inc. All rights reserved. % Copyright (C) 1991, 1992 Blue Sky Research, Inc. All rights reserved. % Please note: this font is not in the public domain. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (c) 1991, 1992 Blue Sky Research Inc and Y&Y, Inc. All rights reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812eae30521c3c775adf1959595a43d8a9c4e12d9f9ece27a0c9b5f45e38 8e26a39cb0ad4e25ab8f21b25ad1b106ed22af7947ea8ae4dc17b9facbc5e22e 89a91b046ba4cddde69c1997fa7f4cd949ba3ac4b6e001475daf165b9432dc70 6e30aeead8cc342d94b20a4045a331175655d6aa279627efc0fb53a4ce66b68f a45b5765f0c1368c02c39418366880efada9c81e9dfcee2a9443eadb1c3d2644 736aca103a5a3571f285d37f28f172cea414b1a8ff59c97990a065817703841a cde9d9f92a1511564aa7124acb4d690be1be46bf1e2f05d1eccb8980e1c01e0b 9ff57dc4573f9a105b96073d91b65983fb3cc0ede3c9eeb72411ac9107c06c87 02d1431267a919f2f34e4880c3ff606a8f4c15b6b401a0f32841385ec46fbfb5 70fc46069ec8c47745ed68a8af084a442c8b6c5699983acee943dc23634147ea ee1d861307e78a8dfc3a913acf76c67a802d2526b4fa06e98e4f461689a91c0f cf231549abcc99a5c0bb1d2d085c51b5a991b64e0080950a3337bf768adc1fb7 f1b787042f5f0a6f5b0abf6b00f0eb51443b1fa58f3dd2ac9146c3f85d115412 6ddb09fa4c28b69e723854a59b41008622f629c993633a38e8b06995405564bd 2a0047c4ae6d387d0a0e60e655ebd5993957d10d0b9263625e1b9d93a246f9ad 449e44c53963ef9efea23d0c219515a65aaf2b4ed699b7bd075af0b592adfb12 a1447799d128290030dfabf8ada2240e954d54745b774d883c7288882f6c926e c00692b953c002c4227b66eb5120cb2117bad0a89abbd5c604ef284311d74824 f44c9865eb5c008ad4bda519a3e278a02f359d41 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%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) 1991, 1992 Y&Y, Inc. All rights reserved. % Copyright (C) 1991, 1992 Blue Sky Research, Inc. All rights reserved. % Please note: this font is not in the public domain. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (c) 1991, 1992 Y&Y, Inc and Blue Sky Research Inc. 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 70 /F put dup 85 /U put dup 97 /a put dup 103 /g put dup 104 /h put dup 108 /l put dup 111 /o put dup 114 /r put dup 115 /s put dup 117 /u put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueID 5031986 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e320fe93acc64a4016412366d1ad2 8776cfdce37d3a89b95e5bb9373a99730cba9c11192589e22438b44f4ecc6a8d 1f72a7ea6a698d9580bcafcc2366c5964e5d3094b67d86eec82e16761e4b6f4d fd245d3c0b4188a0543ee88fa787fb10793268e415e389ff071cdd46bf6b260e 1e9c9ac037edba327c6379836655308ddf35e4a4488ad32d3ab301c67a2fa71e 8ae00daeead4271df276f5ce395a57e414f85237cf8f1be070309ed5c3078506 c9d38c2adeeac618d04c0be2ff891dcfc9ada7588efb91f739188a933e1d37bf 632cf042106df1bae0cdfb79c578e565014cead123bf856cc0c14983f5548a20 c0d45446e0dd2b017f528e46d394a88a2d5f86fc669ac7d489f1851c100b29a0 ee3ec82faf87eba944a57dc14ebc94f2445a8a21ee68eef1848d534bdd192ea1 181220351ff93c51e53fcd5ee6ec92bd644d121eac52bc163acb6948a7a4c256 7243c7113b1b5650aeeedb14ffd9b6ce33605907595230a06db01bfb510a460e 76598fb2bb67498f79f0f5b5c5fdb5515cf2257aad324ef1a877a296e2851d38 f8995123e527c4956247fc8ab910206a9ce8736563ff0d4cd5d00579d60bca51 650af348ac4d6422c4cd74d924b532d4a28ba95eff24aca4b3cd1d28e207c7f8 906f8dd99aa04c135fe46c1dc8ee89bd768df17240a70f1a96382defcc180b9a 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9a84d40e43e0d280b21a4549086c51821a2777e1136379143c14ee8a1a5be020 de300b254bbc7e90799ac52c125c6621f8f19fa4c3dd65e7946cf595c0b72636 4921c8920164191bf908b6f6bc3a882d89bf1a5bee13056f496068d7bdef7306 9a89566592b20fb2cf9437787d7f29c9c63b5d60935b58d8bda05ac0c2fc75f5 8283e674dfe56795697c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmmi8 %!PS-AdobeFont-1.1: cmmi8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmmi8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /cmmi8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 58 /period put dup 59 /comma put dup 60 /less put dup 67 /C put dup 68 /D put dup 82 /R put dup 84 /T put dup 97 /a put dup 100 /d put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 114 /r put dup 116 /t put dup 118 /v put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmmi12 %!PS-AdobeFont-1.1: cmmi12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmmi12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /cmmi12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 15 /epsilon1 put dup 17 /eta put dup 21 /lambda put dup 26 /rho put dup 34 /epsilon 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 67 /C put dup 68 /D put dup 70 /F put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 78 /N put dup 82 /R put dup 83 /S put dup 86 /V put dup 87 /W put dup 88 /X put dup 90 /Z put dup 97 /a put dup 100 /d put dup 102 /f 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 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put 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3d6350520694160dd657ae921a6024e55c8321a07ccb319164c0d67ce049a02b 0bc9dd02f445b4e7923212a26b4bdbd1947b8498ffb41bab1935f8960e5b2362 72501528c018a0776b6624ffaf12bf84123e9e0c29a30c28335151e49dc0b97f 8f0a9dec7359ac5d67cc300573ee2eb1058239127eca8dfadb9d9c6f6b22df5e bc94e2e78abcded3631ac726258454058ab283bffb37767eed327676fcb99966 b371ed51676d4c4026c9fffa5dfb 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmr12 %!PS-AdobeFont-1.1: cmr12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmr12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /cmr12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl 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 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 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 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 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83e778e300f4bcec3c63d950aba6a8ae27ac365e32 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: EUFM7 %!PS-AdobeFont-1.1: EUFM7 2.1 %%CreationDate: 1992 Nov 20 17:36:25 % Euler fonts were designed by Hermann Zapf. % Copyright (C) 1991, 1992 Y&Y, Inc. All rights reserved. % Copyright (C) 1991, 1992 Blue Sky Research, Inc. All rights reserved. % Please note: this font is not in the public domain. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (c) 1991, 1992 Y&Y, Inc and Blue Sky Research Inc. All rights reserved) readonly def /FullName (EUFM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM7 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 115 /s put readonly def /FontBBox{0 -250 1193 750}readonly def /UniqueID 5031992 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e320fe93acc64a4016412366d1ad2 8776cfdce37d3a89b95e5bb9373a99730cba9c11192589e22438b44f4ecc6a8d 1f72a7ea6a698d9580bcafcc2366c5964e5d3094b67d86eec82e16761e4b6f4d fd245d33c9b9c2e5efaf6b70fc1b26729242663b094e125b63b03099ae89aef3 960574bed8d38d9a5871585daeef1a4fee999d512520a302e184ec3fc9a08570 7c490d9d92ba9e23eb831c6f0d09095f97e570e19fbc20e2a04ae15de9836754 0071fa98cd0a687c158288903e7daecf04f31701e4e2f9e7f89f9444063548bf 107761142c46af966926ad8888abae91da9af232c3560a8f044ec566f2797b20 4c66aab3d13785980b5f6cd6edc225a2d939b5e3c6c2dcf7e85c911ec4be45fd ecf273f14f93bc789e2d567f6413fa3c0d46239dee0c7e98faaeb9643481b0de dc7821817e01bb2c4d14d6eb348422a86e7168ca0b0783312dd2c985805b1cf8 3048b9b127262460901ff6291c5c8540daaf8d3e370c1e1580a2eaee60acd2f2 20843291cf3bc3c8fbc397444ce5651559001ebd115ece976b74f40d75ac9a0e be0b5a33d5fb7a5ad3888af240cec5b189aa907095f26a83f21347a20dc6a274 070b50b813f007bd6ec6bf3dc7e6ca22e2b334770791a822f530efca26ae1d67 72f29c2372bcca17e57f13d88cdaa448255f9160bb173dbae40a205e7e4ea2e5 eae10ae90a9d46855cbc2e3a8fee8ae0a6d9c193b8223a89d6d64acf98a0f30d da3e845f80654229284286633e0a99290ca56f27900ecdf0e3e671a8bb4effd9 4ae4a57bdb1959d1e466e7071b2059e1e153939897702414815d1aaea56b2a71 7f464f4344355e9ce5c38746dd5439241f72ebbf2c6528bb5b7a31b72467edcd 835a91658b27b76237aa3a20ffad24b7ce6b10bcb41c58396f4216303115faa9 a11d8b1b8184a69389665c9aa3c2c3a0a38a59eb4089aee54941ec83bc3dd41e 5ff0db2465fb1c70b41a70b2edc2539685de69a614e3dc93b4bc02338b2c6947 2962ce82e4e8e0d72ab13ea292b3bc0ce2195219635a6edca521a88ec4a4e08d b3610b28fd97cc524c17f939d75252f95973eab7d2c3a55d1edc77061df526aa ab074d33b95e41ef03770f44f7172293916959597edbcef68646a91a1dd15b11 7494b09a901e3dd83b6c1beff1b43ea6feede04dbcf12664975dc8c1d2aab0c0 7a2841b5662e651340fbc80aaf43b25f8cf0453f06b79dc1f2f4f19784376472 b39f7c686337038baf7cea0432dd29cac5486b31c46435d318e4dfe4289ff676 fb12b0ca0e2d91af98137fa212221b8524171437b861e1bc3f1d4a7e442985a7 2e15fe4ed9b950e6e71982a97120ad681e57868862b1c0e6937aa9922ce27a4c dd88768b31b80e81a8f5b0b96e0e04577f9ec5606f4a3d04067efc5b93503e93 b5b31d1d42834b9322689f1edd6009e125a5f1988a9a19486a47b24662a9427b 93c7d1120251d9fd4c97ffe8 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 40 /parenleft put dup 41 /parenright put dup 49 /one put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950 93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21 c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644 7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e 13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03 22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56 25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1 c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2 b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e 2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd 6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4 07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331 51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6 0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3 d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1 34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec 015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a 418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e 5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd 977f844d32b43b0e48caed5a4bdabcefe71695d69ca784db55ff8fd5c5c42e30 40097ef70580328190679608c08431469efbadc20f49f69637dd68f9033f909e 92849d34d41de7d21c6286ee60b234d8583679c709ab83d4ffb30adbe0fc3a66 b335178add894f65b0fdaf1863a1ea5cf0872044d74a92217bcd3edabaa09a6e 2e312c6869aed800266698e8cf064ef7dfb47bf5ec2168f0c31e4a5cb747df4a 65ca9702cec34d67c53ff8e8fe0f3e8ff8c6663c2779b6b2993ef4d8539ea670 98e15a96440884ffd15a9941385d05aa2de72372009cdfcd5d4dfe06c5eb80d4 61eb63013627f8fc52d73c14c0440e797f348bb850c17817976e0e70bc2c5b1f a651fd41ea8ba0db57779d00f6636ba7128511f0ed50afb7a93ad1893e64b944 2313a61361ffa04a0110de544da4c075786c2c8d686bbc4a340487ff46850465 62715f6aa12d64feab629666bcaad4e5c26c1be70bc793262258aca2b7e96524 17646271007cbafff6ccb3dde26a6271be0ac35ad2275bf17937e7d7a7b5db66 cb5882c8c3a3c033738365673b4e27a10f2211e8ada5ad73d4dd17525b0a01ec e6a6262ecdabb578c79c1d5f5ccbcdbd52c949bf1a7ce80ac4fc3acaf355c69f 47dfcc532370d53bf7978cb1c0a5b05c8f21e68fefa6ed2c4db6d588340d77e6 64145b94acd8a48b16d0e31812e205b26d96b72b4802abb51f2fe1f9550a48d6 f214cc785c9b916891b8ef5a7cb916ff8b6446cb0e01b2907acc595b92e95007 1fcbccacd0c598b4adf735d85a66c5a8e8ae21ada18a328ded4d9150fc856caf 666ef0b6dbf0e7fca3f564ab9ef4b3fcb743f55c384f1a4a32ba36d13a0dd3f0 9a8f1cbcd26847846690d34f965e0b9ac8c8f026b25fe364ce3f7f7e9dc8d1f8 1c30718cd20b4ded26c5d033747880d620769c0d7c7c797fc023cd33a441c36a 6a59e8cb3d4daf4361 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 82 /R put dup 97 /a put dup 100 /d put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82 ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96 0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0 24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772 0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2 364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba 0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279 617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a12ac1 d8764421dfef5dfa13fbee58f5ecd4deeb4cda9fe9483c229ab29460b05559b0 35c73d6b88f6a384de0e2dfae4b1886f91e522d800b0ad40eae57f680490fea4 a2eda9f8f57aea1a4315674be45989c2293362dfbd0b5d90a523a7b79de04d6f 7b9ffa9f9ff2f2f7a1645e6b6e199c88c8430208a7df1f8f8839769a44b3922b 18294062582dfb8eb65d087635f1b602efbd5aa1d63676616822ac40947e58d4 49f3226143efd388f810db12077f5cbbd8d6cfee0ad3ef2426bdd29bc2cff5ef 5c8cb8d23ce3652705c542faafc8a6de949546ed69c7fc80eb313749e45341bf 43b8f56aa289196ae975055a60326f2985cbfefb9033578942156ae062521110 0a05b9a794e9f7422dddf1a8a0db03e708e23ee59efd0ca76618e7ce6e0fc8ce 1246fc98b327c715d4e72aedf70712756aa345b6a118664ffcbdad6e15bd4c77 6d6e701fb2729f7defdfca28ae52871bac41586ffc7e30432c34fb9584220d4f fbc74be7db156ce942f252f043b2d773f436a971b34f7a7d93fc0fbbc9811498 29298692207d722a862deb6a2daed4f076067389ff8e388306445621805504b6 1f6a688e005fb119760c69502b8326b048a050ed39d67747814a0f8c77414100 15c85dfa722c39a0e95bc3fcc05d5021455d43f3f753feff99a92589a8f080cc 538ee7a7e05871664ca5b562cde6d16dd36e979637c4f2f41d2956bb0eeefca1 108bbdd6e30b3385b560adb126dea43e2a4e82445bd67c73d1a89f19488e09a3 17e3ceb5d477c7c19796a96f7339216e8f167f4268249104a1e0a7634ee3d57e 6def2e327a3446af730f90a0dd6ada5722f35c04374cec49be59264e85306ba3 a050248d8ff12e480479154cef8e154c062c9e0a8baaae99553631fc54ed444c 97625b9c49162e5326ccefede08a86afa0a1bd40d57187eb197e88d4a457e61c 1288cd03ae393819f5d2fd3d01fd744eb1fe65aa70ef8cf5fc3a82091b03c52f ba722cfc624bee64669331aecf7dd6f4cc252bc57ae5ca2916b4d9d3e5fe0c15 d173ebbed1799270688dbd5bf6d9c05674843cb2652dd01e69888535182e27af 035d5092792d46da57c6d5a1f9d56849053a8f98702dc8847f35ea28ef415fd9 8e217d5c191b774e8d38d8e4142f816a596ebfa6994d2de8aa253d07ee92f6e6 0761318a62d932c7a7f8728032ef680bdbedea60176d6a6a275fd2cf94a72ea6 ea0a4cd7d3a95ac231d99d4be3f03a669da58650d21ba3383db912aaeed16607 dede319514adccb24879493e4972e35bca93dcd80ff17cdc3043bc8cd6088afd 70f3725b6cc8cb5039ee33a60d6683d5d98d02b8eee7e9b72f2c5b9378f68e16 5fa6988a5301d0de22beae31b479c87e2b211b45fea6869fee128c71b8ea734e 529136ff1f980b32637c5221fdb0d6c04c0f372e6ceed62c9efcf89151176ae6 2c2dd1fd4f4c8fa811a583a00cbe316e422255a9c45983372c2b997353f15ae8 8bd9fa6671b74324823a305e11457b94ef7e60a622388a7fbe92ab2ce376 0000000000000000000000000000000000000000000000000000000000000000 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 65 /A put dup 76 /L put dup 82 /R put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2 b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc 55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7 8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316 ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325 e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd47deb8 5405d720de0bb4dcae731a8e27bdbb6e6be38d168b7daff815acfc32ce367374 bf9fd98c0ae5ba1bccdb84d94b5c173abc92f7d18e19a68f64a2241a0a163910 8dc46b8a04ead17662b7bbff3d3d9a95d5937698573bfac64973dc8d8b8d9f68 c52d0c133119eca4fae72f7553d276c817003234a98337d7c037c0f1bce8a804 57113bcd97515c002d20f836fa086a3277727873ec2b64a92bedb01193491134 b6692a08de4a201a3f11dbe070d797f7629ad487d2b8dbf89a0631956c93864a 41c887c7f8a5bc1894692fc1e7311f2444795da2c55aa8aedf734558a0d784fb 714df24ea224adc89184f1719a75755d5f3b3b2babe532fd295dc3d41ea6ff78 2f87b3d169da6bddbb4d05d82ed0a89d8ed9740e1462aeed292d740f9211a188 0dfc8b0f0eff5f7cd55812fec2a96c2adb98c5fe319304e26655913e04c95228 40d02a935081e3a7b92f71214eb55a044adf79c9d4ff440d40e8c9e303e23993 3ccb9fc46f80810942c495ff19366b0e9a679ddaf5f86158d1fc05d33d78d5fd 80fac1339ae1248d4b55da30387759eeec5a072e17b96f7db18b7aa6c1cd1d33 97c3ce8e0fc36e584d52691c500b0811e4076dd3df7ef62073748e92354fb811 f697f31196771c6a87b160de11edcc285cdd1ac0aabbce9cca0d8d2cb724977f 5a55eb8c9cb832a45bf25e394ae4bb5050df1ab164981c3aaf103b3257401712 6194b520aca6807790565f95c137c0ac891d4df2f0ae806adffcdc32672bea8e 8b58c60b73bc410de0ea02e97988a2dd1c25b64c48ad4eddf1e8c87c23db1ebf b3f8e210c178f95c5672c19b4f70411d14f2944f27d931b5b43bd625b3c0cafd 58c067d9362329164f055dafd37cb36ffd5a4bf0b0fe055ce1084772830b31ff 08f9dc1743d1d8f6ac9e11eeb41cfe7f906a105b89fbcefa5bd05595a035ecd6 1e09ef26cc54829cd4bb251bfd83ce7892f124b0d7f6192e2ca47615a90753a7 eb8d7e59259af991af2e66371bde64063544393dc630f2b9f7c32d5c0ddeb89d ac2b391f4079362c5c32729c2970072eff8bb9a10807fae22e2e7513bc6a6603 c2feff4e368a3e91c431a66a63b04dfc43e92a921d3c59b76169287bec144cf9 1c4528cb44d834ea925c31dc795d520a02fbfffaa87d7e1b85423fa0eefef8e9 a8a81844b860f557787460a1179da585f98873fe57831f84dd34950f53fa6e33 86ac43294ddca8c6e6e687ea9f7729484527a83713340590b6488b1540a76ef6 5005486cb4e93950557a0d95b1da8783dd3196d44d0755b9bd15326cbc9d1975 7522d3763b548e2d667c0e1a86544ee68e5013a96191b5e31a7f41b3dd6ecdb7 941be9afe5f697d3f419b547a85921e0c8f795a94bfb0048ba8f9987bcf81507 5827eb4af9c1e3291d5386c09e1c47b405b5a8bd0aff 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 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 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 108 /l put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 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037fc4792072bea4bac472d53709272fd4966ccc76191709f2a57ba2cf982995 778f99eea5116fb3ca59fbc881b83a0a7a28aafed528d346f9cd51ef889add52 09d74989ea345de6bb087cfdcefa74d3d108aed2a1adf7a67d1ab4a86efb6180 c19be87ea46e6d43ac01038e7e500d63ef0cceaa18e73de7a3c12caaf608a469 11fc43c50a81e08701c47d59e1ce3c6858d24fc1ca9414b88e4dbc9606d1bad4 4f41f4a2dfd3a5931e964fdf6ffb6d56140c5b3550a1fb530a76ddedf27508ee 6e27c995cb51e8a306bb1c796147c522403ed2f8b50be2d6ee65459df7d0c92b da022f8442772c00e64e0ba7989b2783cbe4e15f4fb98c1eb920159389c84f15 3adbecc2dc1399883a59c32ad10ca42de06dcbb9c6f0b7bf8e480f84cb767fb8 29a23609957c6a97eb54c19d68117bf6d60a08a71005812f4791cbe38d0ddc9d 5d26c3554bcbfa9abfb5a20e13bd589d248e3375b00af2e59d26e46313b19b60 1be56688b0275e1ac287705d0031a4b43f803f8ac8fbd576d48902721c3ef0c4 eb82471e84eb70c82c08c755d2e092394f0e467472c5280f0090d5ca4ecf957c 98f4c434806586290dceefa3244faa3530adc68703c91b1360549f719a37da99 0cd965ea5b64c8457ff9e4c006ae84327dd19ae9ea0cc4f9ef5c756b58623dab c3acb47f8a9f3e6c3c7297053840c07487ee12921591d623941ac0c8c7b11741 9c5e15137975bedcb003207f7fa7a688d98b1e38b6ddfbf0a3cfaef49d98799c 8230d147c54a78fff14ebdc43aa61a290dd742b6de4597d94fda3904ec94f06d f95b4dea5dacad50f1b6b880a22fea500f2004d82360295a6f103bca47a631f7 19004e1fb676e15fa79933a1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmtt10 %!PS-AdobeFont-1.1: cmtt10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % 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 (cmtt10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /cmtt10 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 46 /period put dup 64 /at put dup 67 /C put dup 82 /R put dup 97 /a put dup 102 /f put dup 104 /h put dup 109 /m put dup 111 /o put dup 112 /p put dup 114 /r put dup 117 /u put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 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35a275557273cde7b3443b8718d91dd39865981f6791fa293606790b5a58f3c9 249687f683648463d990f2a48fdbec6dc698fc50b711afa8c36bf9b71784de6d a8db38120da087782d0bbd763df25ea9daa7fb7ea5a336ef8cea5b109fa5d0ae 63defeeba9d529a124f168170e2d58c205a66e0f07003803d9e6a9d4a613715d df5e590804fb4d54eee3016de14b911a3284257c8e4d50b687b81f294d424da1 612929dd8afd675dfd6d51646182b6ce8452bb75657d020d37f264ab67661332 76f0da04b1999f94a2fa6400ebef2033866a34fb31dc89ff47840280dd91e33f f2819f974ca36638a3c4a8fb01ba863b54d555ee7f5250eff7f3b16dd8477304 05cdd95a54a6d02bbe219ef1e72f9b44a780b207086123803b1af70f2776d227 c8e57015f76f2f9825def661dcc9976a0e0867524b8e72d807102e79668c264b 0c57d9677bb3a423cef3a4682e3b69ff803a80f9a07850c5193ce29705a96a12 6bc2d2520aaa8b2380f8c9f844e1128d1dea9569e98383285be7c422e17481b9 294e0c9ec58d884f9d74d6b264096cc11764507f17a00968cc3cadf60e6f5abf 2e18dd86082799468fce58834af0e456894fc52090f37929ee3b1eb74f2be403 b5cc33067245de8d89e692d25794e6b25f2ad5226d79bc6de361c2075a696777 7c444e1126ff52e9983e4ffa4437bb1de1a42b7327707d07ed7636e492578bd9 a01067b51bf5e2f79317a3386173a3a02595022efbdea10fa73f6f99759d12ff b2767bb78380179e7d89b6d5df3d4059d677213cc5627dfd56f5f5f9a9dc3d2c 535615b2c7da19f62d3c6f3bcba0a34b798b14aa52de93457243b10cb817f23b 657de89b889c955511fb7953776e36e64e592b87c8c6503f373666e3ecf72884 c79516c30badf15e08ef38c0b8086e4a872e19c7c0df5a9098c698b0790eed61 83d8cfe2eb81dd8bed72985ea96d091efedc2435f7d4c9cd9be3a881034d1941 4eae8b432efbc78a40a56fc2fc0ce581561b7d957db0e26ca9ed7386791d237b 862ec616261cdb38872fd48a8bec4e226cb81b58155729f800d1b45e3e5c310e f15788bce0e139a8510aac2b25223ecb89c3fcec9b1c839bd7198174fbdc2c35 47e309936a7bdf2d41b67e5375efda42c9467e91b3798007f9416c0064cfa315 4293ec2799223adaf6cf2244e96c318d508f89083b77cfe78ca182ad3e891e03 8f314091b3b53621b6c91c1edaebd14a81ffbe9055d14265efd536af7a0b0549 b0cba03ad3e5a94831d5a6bf050ec066b6ff5470c2e5b6649801818dafc10066 d196797e149bba6b9f34f66cc4daafbe1c70c0f18edfe6496229b4ea23716b92 20d22f174e61a7dcf0bbcf4348f86516d9e0feb43fa126a699ddea3140d0c9e8 35f1951211cdf7cacee297b07949771cb400d83f6ea38dae855b2e9b50d0fdc8 8b6b0387dc76f91fad5b228bdd74109750f121f08d84e05d8de9499b1e4b3695 77ac91ce85014e885b94c5d2d393f5d219ee5e380f5c46f9597311c7654ca961 f441048798c7ffecb00a86f9f758aaef67a4bb71d051df77ade607c0434f094c 1cd4929fbe6ba223b43ca323c609ccab9ac36cd8dfa43d35e5f48b75d9b42654 d86e56c1798a583d84ce07779ad56c931afd0b67abcc01972c2b7b8ee829cd9e fe06060344da8d5aea479dabcd07bd3ebb86e3da457a8e5cd5595ab259f3c899 a489890b2f205c58bddac0c330b8ad0793fa750bbc9d610d9786bc205c0c78ac 20c948d8d099f83e4e340bea34659140c4de51e51bd536634eddaeac836060ec 05a8c13421e01026998874e239f1b91f4276b84d6775cac030737a3fd3644440 51db0d1fbe03d8dbc4e564cb0d49339c626166bf0b29927f6034f6e8ed44bd88 648518e3e8854314fdbb1bdb221fb2e0923e958872524fde3908ae03ef9e789f 0e2271eb0b339e2b17acaeed208a4a94613cf47e64ed5b77fff0193b61112a94 2bccd106df4b97f61284e5628e2b55cbd48f23344949c2e39f2e8b729a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 12 /fi put dup 18 /grave put dup 19 /acute 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 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 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmbsy10 %!PS-AdobeFont-1.1: cmbsy10 1.00 %%CreationDate: 1992 Jul 23 21:21:18 % 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 (cmbsy10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /cmbsy10 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 121 /dagger put readonly def /FontBBox{-27 -940 1332 825}readonly def /UniqueID 5000762 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc691c7bbdc230332e4e15db130d783c5d60b3 4fa0c677b6fc914a4213ae7799999a2d0021fd62c387d3bb675576611b2ec495 a9caa4ef4a1bf07cf81eafedfce403b646248cf8361b876f5c8d87de5fcc236f 2b2f12c78a15541fa8126c733d02cf50fe3dfb4fa7697d214dac2976bf91bc19 25c44f6936d68343d88dd537315a255cb7fc437bac2edb80f1fedfb4969ccde2 833a78ed57203109de46d94ee67e9d14d007992d2b9eabe7849bfbd36d1dd5de 5610f8e81efba96bffe4771de37e4b90ab0fa5d00300e3061eaf81cfea33be39 4d62e8f0c0aa19ebe3828f6fde9e61b73c470cef9b4d7a6787b150ff08f15a83 ed6b0acf36782e41acca43713187dd752c77547e2528d18dc4134fa3be0437e0 410f753832c5a527637c0036f79decaa84d1336c08eb69278ec4cc6521f89d17 554615b1b9116bfd0206cf7a1df3f28001205ae025f815296036c964a2021b70 f0337f2f2a90c1470b16ed8e150bfc7e005bd2ea03ad6bfe9d6b5a3c65b14e6c be22923c1eb4580708cfef29efdf90e536a526e574800e33e8da7df629c95160 7d35f46dee446052fe9d16b548e706ed1cd2134dacf1de546eb986db5dcb2720 3cdb731c7cd3dcdb09fc306c72e30b6ac4ba92e01172b6b7c3ab05eefc76f18b 88634a00cda21f9aa8b49697f29a3a933ecf906ecbbc18dd666400ba4a5cee1f 93a7c2b839d974432d0870b95bae5aab09bfdbdc34239645738efa9614940fde e7a133e719de5158aebf878bfd7fbb18ab3ed796980110cc963a15e698f86115 9d6bacf7eaa215c7fe350c691b0197e44771431566e5cea887ffc56f020cfc7a 0e65beec65e69680575f81eaa9650a9c6b3afe7dfd807eb036cb2ed43f20fa78 0b0461d49b390806959f5a6cf78bcd36ee4ed2f44769a8e0e680914d92b1c5a6 427a7f2dc26de250b549c88d9024ad5a8ca41cf7cb03f7f38356d5baec9b3caa f866034678e92301181c91c92f683ca9832714d13413a4b170d1a4d7c7dba482 b3aeb7428965fdb9a4accf0f25649c0ebc24560a60ab72480119860c34d33b0f 698dd803ab086ec82efe3aa1381080c6b9d483e95c1d97a9283afec4cfe2f36b cf1c4fc6ea0a6fa264fcb82e124d17b6d627e60b261d8841ced2c360b6d53390 24e9436cb298eeb6b1134fda88a92cf8737f9e545fa54fad15bfe688bf4ad4fd 154bc33286047f0a034b22e8d06ea0eb763e14a94b4a796d8a80c771936111f5 91b387b304d952b6902ea843dc6743a87bcd662c7a80fee1dc47788abb42d98c 05399302f24d9b9a10679f0949c300e799b24d05a15ff27ca17a19b08c1c91f3 7a45a8537431b240af368d45bc7c99caf33fbc9f8d64b9a80565a08e8f2f775e dfe1b25be654fe7aad2e057428b68e2d6830f2ee0ca384fb862813bad48832ec 89991fa5e6bf9d3135378f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: cmbx12 %!PS-AdobeFont-1.1: cmbx12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (cmbx12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /cmbx12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 76 /L put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U 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 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{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea a29b69d1b622b1f0cffc58291248759607d91150cb0651120970dc9f743bebef 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y(\010)2693 4259 y Fl(R)2751 4244 y Fk(r)34 b Fn(b)s(e)h(a)g(p)s(erfect)g(algebra,)0 4377 y Fi(f)p Fm(X)131 4392 y Fg(1)170 4377 y Fm(;)17 b(::;)g(X)393 4392 y Fl(n)440 4377 y Fi(g)32 b Fn(a)g(basis)i(of)e Fk(s)p Fn(,)h(and)f Fi(f)p Fm(X)1378 4392 y Fg(1+)p Fl(n)1515 4377 y Fm(;)17 b(::;)g(X)1738 4392 y Fl(n)p Fg(+)p Fl(m)1902 4377 y Fi(g)32 b Fn(a)h(basis)g(of)f Fk(r)p Fn(.)44 b(W)-8 b(e)33 b(de\014ne)g(the)g(matrix:)598 4560 y Fm(\032)648 4575 y Fl(R)706 4560 y Fn(\()p Fk(s)p Fn(\))27 b(:=)984 4479 y Ff(\000)1030 4560 y Fi(\000)p Fm(C)1184 4518 y Fl(n)p Fg(+)p Fl(k)1177 4585 y(i;n)p Fg(+)p Fl(j)1355 4560 y Fm(x)1410 4575 y Fl(k)r Fg(+)p Fl(n)1551 4479 y Ff(\001)1596 4602 y Fg(1)p Fe(\024)p Fl(i)p Fe(\024)p Fl(n;)p Fg(1)p Fe(\024)p Fl(j;k)r Fe(\024)p Fl(m)2143 4560 y Fm(;)1411 b Fn(\(8\))0 4742 y(that)42 b(is,)k(the)d(matrix)g Fm(\032)914 4757 y Fl(R)972 4742 y Fn(\()p Fk(s)p Fn(\))g(comprises)h (the)f(action)g(of)f(the)h(Levi)g(part)g(on)f Fk(r)g Fn(with)i(resp)s(ect)f(to)0 4875 y(the)38 b(represen)m(tation)h Fm(R)q Fn(.)59 b(In)38 b(what)g(follo)m(ws,)h(und)f(unless)i(otherwise) f(stated,)g(w)m(e)g(will)f(implicitly)0 5008 y(assume)c(that)e Fm(R)i Fn(do)s(es)f(not)f(con)m(tain)i(copies)f(of)f(the)h(trivial)g (represen)m(tation)i Fm(D)2969 5023 y Fg(0)3041 5008 y Fn(of)d Fk(s)p Fn(.)0 5216 y Fy(Prop)s(osition)38 b(2)48 b Fb(F)-7 b(or)34 b(the)h(Lie)g(algebr)-5 b(a)34 b Fk(g)28 b Fn(=)f Fk(s)1780 5166 y Fi(\000)-77 b(!)1791 5216 y(\010)1880 5231 y Fl(R)1938 5216 y Fk(r)34 b Fb(fol)5 b(lowing)34 b(ine)-5 b(quality)35 b(holds:)598 5398 y Fi(N)15 b Fn(\()p Fk(g)p Fn(\))27 b Fi(\024)h Fn(dim)17 b Fk(r)22 b Fn(+)g(dim)17 b Fk(h)22 b Fi(\000)h Fn(rank)p Fm(\032)1886 5413 y Fg(R)1943 5398 y Fn(\()p Fk(s)p Fn(\))p Fm(:)1491 b Fn(\(9\))p eop %%Page: 8 8 8 7 bop 3657 17 a Fn(8)195 232 y Fy(Pro)s(of.)63 b Fn(Let)40 b Fm(A)p Fn(\()p Fk(g)p Fn(\))f(b)s(e)h(the)f(comm)m(utator)h(matrix)g (of)f Fk(g)p Fn(.)63 b(This)41 b(matrix)e(can)h(b)s(e)f(seen)i(as)e(a)0 365 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(information)f(ab)s(out)g(the)h(structure)h(of)e(the)g(radical.)86 b(One)0 2402 y(could)39 b(b)s(e)g(tempted)g(to)f(use)h(the)g(decomp)s (osition)h(of)e Fm(R)h Fn(in)m(to)g(irreducible)h(represen)m(tations,)i (and)0 2535 y(to)h(dev)m(elop)i(a)d(similar)i(argumen)m(t)g(lik)m(e)g (in)g(the)f(preceding)i(prop)s(osition.)75 b(Ho)m(w)m(ev)m(er,)48 b(a)43 b(further)0 2668 y(sub)s(division)i(will)f(so)s(on)g(lead)g(to)f (false)h(results,)j(as)d(can)g(b)s(e)f(seen)i(for)e(the)h(follo)m(wing) f(example.)0 2801 y(Let)g Fk(s)j Fn(=)g Fk(sl)p Fn(\(2)p Fm(;)17 b Fj(R)p Fn(\))42 b(and)h(consider)i(the)e(tensor)h(pro)s(duct) f(represen)m(tation)i Fm(R)i Fn(=)e Fm(D)3172 2816 y Fg(2)3241 2801 y Fi(\012)30 b Fm(D)3429 2816 y Fg(1)3469 2801 y Fn(.)75 b(W)-8 b(e)0 2933 y(ha)m(v)m(e)46 b Fm(R)j Fn(=)f Fm(D)565 2948 y Fg(3)634 2933 y Fi(\010)31 b Fm(D)823 2948 y Fg(2)893 2933 y Fi(\010)g Fm(D)1082 2948 y Fg(1)1121 2933 y Fn(,)48 b(and)c(the)h(represen)m(tation)h(is)g(of)e(dimension)i (15.)79 b(If)44 b(w)m(e)i(assume)0 3066 y(that)37 b Fk(r)e Fn(=)g(15)p Fm(L)565 3081 y Fg(1)604 3066 y Fn(,)j(then)g Fk(s)940 3016 y Fi(\000)-77 b(!)951 3066 y(\010)1039 3081 y Fl(R)1097 3066 y Fn(15)p Fm(L)1261 3081 y Fg(1)1337 3066 y Fn(has)38 b(t)m(w)m(elv)m(e)h(Casimir)f(op)s(erators.)57 b(The)38 b(upp)s(er)f(b)s(ound)g(ab)s(o)m(v)m(e)0 3199 y(pro)m(vides)d(the)f(appro)m(ximation:)598 3382 y Fi(N)15 b Fn(\()p Fk(s)777 3332 y Fi(\000)-77 b(!)788 3382 y(\010)876 3397 y Fl(R)934 3382 y Fk(r)p Fn(\))27 b Fi(\024)h Fn(15)22 b(+)g(1)g Fi(\000)g Fn(rank)q Fm(\032)1774 3397 y Fg(R)1830 3382 y Fn(\()p Fk(s)p Fn(\))28 b(=)f(13)p Fm(;)1327 b Fn(\(13\))0 3564 y(and)42 b(b)m(y)h(parit)m(y)g(of)e(the)i(dimension)g (the)g(v)-5 b(alue)42 b(is)h(at)e(most)i(12.)71 b(An)m(y)43 b(further)f(reduction)h(that)0 3697 y(considers)32 b(the)f(decomp)s (osition)h(of)e Fm(R)i Fn(in)m(to)f(irreducible)h(comp)s(onen)m(ts)g(w) m(ould)g(giv)m(e)f(a)g(v)-5 b(alue)31 b(whic)m(h)0 3830 y(is)f(lo)m(w)m(er)i(than)e(the)g(n)m(um)m(b)s(er)h(of)f(Casimir)h(op)s (erators)f(of)f(the)h(algebra.)43 b(Although)30 b(the)h(b)s(ound)f (\(11\))0 3963 y(cannot)36 b(b)s(e)h(re\014ned)g(using)g(the)f(decomp)s (osition)h(of)f Fm(R)q Fn(,)h(w)m(e)g(can)f(impro)m(v)m(e)i(it)e(b)m(y) h(considering)h(the)0 4096 y(parit)m(y)-8 b(,)33 b(as)g(in)g(the)g (preceding)h(example.)45 b(If)32 b(w)m(e)i(de\014ne:)598 4348 y Fm(\017)p Fn(\()p Fk(g)p Fn(\))28 b(:=)922 4177 y Ff(\()1043 4283 y Fn(1)83 b(if)90 b(rank)p Fm(\032)1564 4298 y Fg(R)1621 4283 y Fn(\()p Fk(s)p Fn(\))27 b Fi(\021)i Fn(1)97 b(\(mo)s(d2\))1043 4416 y(0)83 b(if)90 b(rank)p Fm(\032)1564 4431 y Fg(R)1621 4416 y Fn(\()p Fk(s)p Fn(\))27 b Fi(\021)i Fn(0)97 b(\(mo)s(d2\))3533 4348 y(\(14\))0 4605 y(then)33 b(form)m(ula)g(\(11\))f(is)h(rewritten)h(as)598 4788 y Fi(N)15 b Fn(\()p Fk(g)p Fn(\))27 b Fi(\024)h Fn(dim)17 b Fk(r)22 b Fn(+)g(dim)17 b Fk(h)22 b Fi(\000)h Fn(rank)p Fm(\032)1886 4803 y Fg(R)1943 4788 y Fn(\()p Fk(s)p Fn(\))f 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Fn(\(3\))2211 5502 y Fi(\000)-77 b(!)2222 5551 y(\010)p 2310 5523 58 3 v 2310 5577 a Fl(R)2385 5471 y Ff(\000)2430 5551 y Fn(deg)p 2594 5471 76 4 v 18 w Fm(R)2670 5471 y Ff(\001)2732 5551 y Fm(L)2798 5566 y Fg(1)2838 5471 y Ff(\001)2900 5551 y Fm(;)606 b Fn(\(16\))p eop %%Page: 9 9 9 8 bop 3657 17 a Fn(9)598 278 y Ft(T)-8 b(able)32 b(1.)k Fv(Ev)-5 b(aluation)27 b(of)g(\(15\))g(for)g Fs(s)c Fv(=)g Fs(su)p Fv(\(3\).)p 0 340 2912 9 v -2 498 4 133 v 207 458 a Fm(R)p 488 498 V 258 w Fn(dim)33 b Fk(g)p 833 498 V 100 w Fn(rank)g(A\()p Fk(g)p Fn(\))p 1356 498 V 100 w Fi(N)e Fn(\()p Fk(g)p Fn(\))p 1695 498 V 100 w(upp)s(er)i(b)s(ound)g (\(15\))p 2548 498 V 99 w Fi(M)17 b Fn(\()o Fk(g)p Fn(\))p 2910 498 V 0 501 2912 4 v -2 634 4 133 v 220 594 a(3)p 488 634 V 344 w(11)p 833 634 V 336 w(10)p 1356 634 V 358 w(1)p 1695 634 V 547 w(2)p 2548 634 V 558 w(0)p 2910 634 V 0 638 2912 4 v -2 770 4 133 v 135 731 a(3)22 b Fi(\010)h Fn(3)p 488 770 V 258 w(14)p 833 770 V 336 w(12)p 1356 770 V 358 w(2)p 1695 770 V 547 w(2)p 2548 770 V 558 w(0)p 2910 770 V 0 774 2912 4 v -2 907 4 133 v 135 867 a(3)f Fi(\010)p 306 791 49 4 v 23 w Fn(3)p 488 907 4 133 v 258 w(14)p 833 907 V 336 w(12)p 1356 907 V 358 w(2)p 1695 907 V 547 w(3)p 2548 907 V 558 w(1)p 2910 907 V 0 910 2912 4 v -2 1043 4 133 v 220 1003 a(6)p 488 1043 V 344 w(14)p 833 1043 V 336 w(12)p 1356 1043 V 358 w(2)p 1695 1043 V 547 w(3)p 2548 1043 V 558 w(1)p 2910 1043 V 0 1046 2912 4 v -2 1179 4 133 v 220 1139 a(8)p 488 1179 V 344 w(16)p 833 1179 V 336 w(12)p 1356 1179 V 358 w(4)p 1695 1179 V 547 w(4)p 2548 1179 V 558 w(2)p 2910 1179 V 0 1182 2912 4 v -2 1315 4 133 v 135 1275 a(6)g Fi(\010)h Fn(3)p 488 1315 V 258 w(17)p 833 1315 V 336 w(16)p 1356 1315 V 358 w(1)p 1695 1315 V 547 w(3)p 2548 1315 V 558 w(1)p 2910 1315 V 0 1318 2912 4 v -2 1451 4 133 v 135 1411 a(6)f Fi(\010)p 306 1335 49 4 v 23 w Fn(3)p 488 1451 4 133 v 258 w(17)p 833 1451 V 336 w(14)p 1356 1451 V 358 w(3)p 1695 1451 V 547 w(3)p 2548 1451 V 558 w(1)p 2910 1451 V 0 1455 2912 4 v 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b(!)1115 3492 y(\010)1204 3507 y Fl(R)1261 3492 y Fk(r)35 b Fb(b)-5 b(e)35 b(a)f(p)-5 b(erfe)g(ct)35 b(Lie)g(algebr)-5 b(a.)43 b(Then)598 3672 y Fi(N)31 b Fn(\()p Fk(g)p Fn(\))d Fi(\024)g Fn(dim)17 b Fk(r)22 b Fn(+)g(dim)17 b Fk(h)p Fi(\000)p Fm(r)s(ank)s(\032)1876 3687 y Fl(R)1951 3672 y Fn(\()p Fk(s)p Fn(\))22 b Fi(\000)h Fm(")17 b Fn(\()o Fk(g)p Fn(\))g Fm(:)195 3875 y Fy(Pro)s(of.)59 b Fn(Let)38 b Fi(f)o Fm(X)867 3890 y Fg(1)907 3875 y Fm(;)17 b(::;)g(X)1130 3890 y Fl(n)1176 3875 y Fm(;)g(X)1301 3890 y Fl(n)p Fg(+1)1438 3875 y Fm(;)g(::;)g(X)1661 3890 y Fl(n)p Fg(+)p Fl(m)1825 3875 y Fi(g)37 b Fn(b)s(e)h(a)g(basis)g(of)g Fk(g)f Fn(suc)m(h)i(that)f Fi(f)p Fm(X)3158 3890 y Fg(1)3197 3875 y Fm(;)17 b(::;)g(X)3420 3890 y Fl(n)3467 3875 y Fi(g)37 b Fn(is)h(a)0 4008 y(basis)44 b(of)e Fk(s)h Fn(and)g Fi(f)p Fm(X)789 4023 y Fl(n)p Fg(+1)926 4008 y Fm(;)17 b(::;)g(X)1149 4023 y Fl(n)p Fg(+)p Fl(m)1313 4008 y Fi(g)43 b Fn(is)g(a)g(basis)g(of)g Fk(r)p Fm(:)f Fn(Let)2270 3927 y Ff(\010)2329 4008 y Fm(C)2406 3971 y Fl(k)2399 4032 y(ij)2459 3927 y Ff(\011)2517 4049 y Fg(1)p Fe(\024)p Fl(i;j;k)r Fe(\024)p Fl(n)p Fg(+)p Fl(m)2999 4008 y Fn(b)s(e)h(the)h(structure)0 4140 y(constan)m(ts)34 b(of)e Fk(g)h Fn(o)m(v)m(er)g(this)h(basis.)44 b(If)33 b(w)m(e)g(consider)h(the)f(c)m(hange)h(of)e(basis)h(de\014ned)h(b)m(y:) 639 4308 y Fm(X)728 4272 y Fe(0)720 4333 y Fl(i)779 4308 y Fn(:=)28 b Fm(X)991 4323 y Fl(i)1019 4308 y Fm(;)44 b Fn(1)28 b Fi(\024)g Fm(i)g Fi(\024)g Fm(n;)639 4441 y(X)728 4405 y Fe(0)720 4466 y Fl(n)p Fg(+)p Fl(j)882 4441 y Fn(:=)1026 4402 y Fg(1)p 1023 4418 43 4 v 1023 4475 a Fl(n)1076 4441 y Fm(X)1157 4456 y Fl(n)p Fg(+)p Fl(j)1291 4441 y Fm(;)44 b Fn(1)28 b Fi(\024)g Fm(j)33 b Fi(\024)28 b Fm(m;)3533 4373 y Fn(\(17\))0 4605 y(then,)33 b(with)g(resp)s(ect)h(to)f(this)g(c)m(hange,)g(the)g(brac)m(k)m(ets)i (of)d(the)h(algebra)f(c)m(hange)i(to:)639 4692 y Ff(\002)681 4773 y Fm(X)770 4737 y Fe(0)762 4798 y Fl(i)793 4773 y Fm(;)17 b(X)926 4737 y Fe(0)918 4798 y 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y Fm(;)17 b(X)979 5652 y Fe(0)971 5718 y Fl(n)p Fg(+)p Fl(j)1105 5613 y Ff(\003)1174 5693 y Fn(=)1292 5626 y(1)p 1288 5670 59 4 v 1288 5762 a Fm(n)1356 5693 y(C)1433 5652 y Fl(n)p Fg(+)p Fl(k)1426 5719 y(n)p Fg(+)p Fl(i;n)p Fg(+)p Fl(j)1701 5693 y Fm(X)1790 5652 y Fe(0)1782 5718 y Fl(n)p Fg(+)p Fl(k)1923 5693 y Fm(;)44 b Fn(1)27 b Fi(\024)i Fm(i;)17 b(j;)g(k)31 b Fi(\024)d Fm(m:)897 b Fn(\(19\))p eop %%Page: 10 10 10 9 bop 3609 17 a Fn(10)0 232 y(Therefore,)34 b(for)e Fm(n)c Fi(!)f(1)32 b Fn(w)m(e)i(obtain:)598 331 y Ff(\002)639 411 y Fm(X)728 370 y Fe(0)720 436 y Fl(n)p Fg(+)p Fl(i)846 411 y Fm(;)17 b(X)979 370 y Fe(0)971 436 y Fl(n)p Fg(+)p Fl(j)1105 331 y Ff(\003)1174 411 y Fn(=)28 b(0)p Fm(:)0 590 y Fn(This)g(sho)m(ws)g(that)f(the)g(Lie)g(algebra)f Fk(s)1396 540 y Fi(\000)-77 b(!)1407 590 y(\010)1496 605 y Fl(R)1554 590 y Fm(mL)1705 605 y Fg(1)1771 590 y Fn(is)27 b(a)g(In\177)-49 b(on)s(\177)e(u-Wigner)26 b(con)m(traction)h(of)f Fk(g)h Fn([23].)41 b(Using)0 723 y(either)36 b(the)f(w)m(ell)h(kno)m(wn)g(fact)e(that)h(the)g(n)m (um)m(b)s(er)h(of)f(Casimir)g(op)s(erators)g(of)f(a)h(con)m(traction)g (is)g(at)0 856 y(least)i(that)g(of)f(the)h(con)m(tracted)h(algebra)f (or)f(the)h(general)g(form)m(ulae)h(giv)m(en)f(in)g([24])g(for)f (arbitrary)0 989 y(t)m(yp)s(es)e(of)e(in)m(v)-5 b(arian)m(ts,)34 b(w)m(e)f(conclude)h(that:)598 1168 y Fi(N)d Fn(\()p Fk(g)p Fn(\))d Fi(\024)g(N)1083 1087 y Ff(\000)1128 1168 y Fk(s)1172 1118 y Fi(\000)-77 b(!)1183 1168 y(\010)1272 1183 y Fl(R)1330 1168 y Fm(mL)1481 1183 y Fg(1)1521 1087 y Ff(\001)1583 1168 y Fm(;)1923 b Fn(\(20\))0 1346 y(and)33 b(the)g(assertion)g(follo)m(ws)h(from)e(prop)s(osition)h(2.)p 1980 1346 49 49 v 195 1479 a(W)-8 b(e)34 b(no)m(w)h(analyze)g(the)f (blo)s(c)m(k)h(matrix)f(\(10\))g(more)g(closely)-8 b(,)36 b(in)e(order)g(to)f(extract)i(additional)0 1612 y(information)66 b(on)h(the)g(constitution)g(of)g(the)g(Casimir)g(op)s(erators)g(in)f (dep)s(endence)j(of)e(the)0 1745 y(represen)m(tation)34 b Fm(R)q Fn(.)0 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