Content-Type: multipart/mixed; boundary="-------------0401201602532" This is a multi-part message in MIME format. ---------------0401201602532 Content-Type: text/plain; name="04-13.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-13.keywords" absolutely continuous spectrum, slowly decaying potentials, Schrodinger operators ---------------0401201602532 Content-Type: application/postscript; name="1.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="1.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: 1.dvi %%CreationDate: Tue Jan 20 14:01:13 2004 %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMR10 CMR9 CMTI10 CMMI10 CMSY10 CMSY8 MSBM10 %%+ CMMI8 CMR8 CMEX10 CMMI6 MSBM7 CMR6 CMCSC10 CMTI9 CMBX9 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 -p1 -l4 1 %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2004.01.20:1359 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}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{A A 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/IEn 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 IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/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 A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 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 A 1 get A mul exch 0 get A 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/IEn 256 array N 2 string 0 1 255{IEn S A 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/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A 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 Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/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: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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%%CreationDate: 1991 Aug 18 21:08:07 % 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 (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 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 14 /ffi put dup 45 /hyphen put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 127 /dieresis put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueXX 5000827 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3036f2ed7bb65d cc883aff8d6350d6e8af1a9c1d2d7fcddc4c554c7e350f2420586f43e2124611 487cdb176d453854b51cb8f9100bf241899bbef87d57f1135e589813995c4d86 ce91db2b3757948f365186c2a4f32d845f659a8e95028f9c0168851997135c67 ce7654f2de4f22f51311aa78f440e5fc2c58f6df901fd071b2d53b2697bfcebc 43fe4508828b4756ebbe1f3e8512514162b3bb44493a65f11ab56deaf152fd01 bc8b642e6021af01998edc76b6a1929fbb9fa4fd1a430bfd4464b53f75075f66 c726fc037fc23cf09a178ffc60908f77d8ea9dea79c1e21fcb5a6a994e5a8e5c 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put dup 99 /c put dup 101 /e put dup 102 /f put dup 110 /n put dup 114 /r put dup 115 /s put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueXX 5000772 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3037a112066957 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907df3729bba47439a6a22e78673f94e3f43cdd26d2ccf2e8ca46682b76e3044 00655e0c17969d9fdd9f94af56db000220d8af638b3cea49a07009ccb68db482 a3c065a1abda3912928ce3fe0154a99578504eaad72454dbe16ecdb4b52695d3 c9e752a083f8bda74d08e1b15295d85039168bbd662ffeb3b8c427c9befad97c 0e9a319dfceb62621479b0dd9d169e71187190dedc3255c3584ccadb664a10d8 7ec0e6585ab351ab4b4860ebc2742b504d182a4e2c2b18bf4c 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 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523dfa618d367b001af bfc9543651fadf6389c92ef4a113933bfb4ce45b9ec1da149da8266d7ae816ac 591763c1ce0975ca2c6fad4dbf00da2d5ea9005dfe188787b84606f607dcb299 dbd62d54c0d9a3f63151b4605487b20b6612bacb429274d9c41584d6b0364b8e 3d9974f806134b12b859a7d761a1cf69b88c3b8fcd7df349ecea60c16041cf86 b3759ca18300e771a59922287a619d7d1e85a6c05fd807d62fb128a85222d66a 5ffdfc23a68bf4b49d6cb703a4b61c83a49b8e965c46262f03314b3b201179ba 4523b7f14bc486d8c369a8681b7a2837f5f82810d48ab9c8063598298c56340e 20e031c2603386b7564b3ff929be77050ce216cf7ccca14fd4916821b5e568bc 46c3ae7c6c63e4bb5f9cff87417005f6403af598ac4fbf73ff557e9124485569 1327cc0942e6061e12c0f107926d130a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b48d5d21d6c29aee4faca71bd775bb9defa37ff627f1e4926f10d59313e 77d81a511027ef9a8ed5b7fa9b5bd67758cd13bab6ac18411c974a65d0c90085 67bf5860d0930d7f43e557ee45e76ecb2806d21f4732bb282ac8b591f2b8775d 4b3ce2a37ebb371cb74a3cc513bdd70a0115de4760c21f034f5080d769f7ff83 554af524184702a02e534d1eb98dd3f7c5d51900409354dea37de4ac74a12c3a 69320913de6a728bd887c57f4ee5dcb8772249587ce3190bb662ac853abcff77 d4bd77985a4a805f44f8cc8597416c488866ff8429f65cd0edeec1fe2f0015a3 2bb098b0b3d8c913007f5846ca593c491e1efabc8f420a5fa338c47fd2427813 3279d27f12022195e15827797fe71d898f17b8af955e5bd5ce1da5fae7b3ece8 87aa52db81daa819242c6acb7fbed098d59a27bbcb12dca67e16915a4709fa5e 16311a55ddda46359ab51be5964874f1d3612ec10d2444576c508ae6a285a57f b978458b6f5f93c00882f2227d43d42c648437715a27cefd8d4ffb490e3e9980 1d1b4f1cacbc8b9e59c04c677a04047cc4b655fd8985d8e619a99e71cad67c94 2744577e185ac8b225e5352ae93ef0d804b73b943353266c74677b899d45b286 869cbe8ce9ad231007381de74bd3c6c84958f07ffce0620e42902a01fd15c98a 421ff110e5de48cd65568060afaa1e11e9893e720f22b754c47c334a1f5d0933 9b1b1b91b036b981a6be8a3276634fd4e39af829e2f2ac2b2dde35379abd1bf5 3a1071f07537db5fff44d145fce9713d8a9e2660900c41b83f948e16731d3048 2c8fa2aef8de49e3cf649e8ff62a2748cd9e299c7b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /delta put dup 100 /d put dup 114 /r put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 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 93971def6fc0aed1bcd3e15825f528f4afa81d64383e1066384024033abbd4d6 44bf6f3e73adb1f9d0fb8c2844674fdb9500142eedeabdf59c8d6ec31beb79be 0977b9eec00265af3813efcc342464eb6baebfba3ffae422877b7b2c172dbc1f f926f7bf99ea95eb161f0fbd27549a6dd07e59eceb9db25bdb577590c8220aed 64a36640fc65ed6c8af9f2e0f1c0ee6e902445095e0895e8c85eabd4170f9fd2 c244f69f347d1e755f18b1948d1009fb51959dfacce4bc45c952adc0ac3ac220 f989af705a0f76d27befecd9fa812d8291992c740402f38122a7d1477fece6d9 5d24b37929cfecf63f9dab7787217fef1fc323ec57001f2d45cfa8a68db3a09e ad80b56d275824330bb59aad8bff35c72482f90b1811226a3f56477a556705e5 06c726410c5418622dcde859e88f8df051db6557e78d39c76bdbec269ed42308 648ba05de003df90d65db25ccde7ae2b904ada3dcceaca1315f21ab40d611c57 73d37f47c3b5652f562cf8f387ac9b8d83fb2e4fe91600d915f1e3b471699f2b f6cdd1fb3ebe80df67f9dfa7b812c27369d1369c53474dca15e2851c1b3c4f9f fe80fb2c7c25290d58577099f7b5326422b37aff3736be111450ede10e61ee41 4b15a7a7e760755387bd9654bc56a6514e26f984ae1346152f59585021fd8dc0 4a8fb64b870bc3e116757424ac6485a232d805850b9f31dbbc34d5cc2730ef47 b8781a1c81f5b90953fa1922eea803c6856b72f52bb75764a5b0147eda2d01b0 736a2229b83b838da11b9954b93e6d6a4ee48432bf596e5da86fa8e9fadd49d0 69067decebfb32ad99ef1f9c00f0e6b152bc9aabe1cd94334a9693a606b3596d 496d03e9e68ec0ff28e26427b1120d4b3d4acd2fb69d00b58aa8e8158ec7dc62 7fdde8c91ce4883dbe0561673460d4ed25965e15a75526654d45b106276f9eb3 e543982ceca6632cc0113e28f3bab4a3d2acbc2e9790c0eade5cf5d9e98ddf39 84c753dcede9723096905a1a2496197dced1fa94c4a4d2afc9b8e0b99d062ac5 cdbc64464e3b5507 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 16 /parenleftBig put dup 17 /parenrightBig put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 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 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92986e683562f67567cabff69fe7afc26242d8c4f2be76058343336d261ad97e 0169614c45ad56f5fa102f589038d2935fe9717a00be13e56b256b3f737b35f0 92fa190c1812e5208dbe138a94a201b3f6b0374bd66f66ddc68028f132315d7d 011f894ad519646257a16acfec66ded1e6e3f3c4e90bc17c0f38690473d00499 7e51b4d06f1e8de06b2c5289ff0b11fd57b3768dfa07b9b9acaef0eb60faafc8 edd4985d6148ad9b7ae5bb83951e740e7a1f64df9abc4b4dc27726c9379ff352 46f8dc22146abc7a513737c23af2424a7cbdbb88ecd831806c9b40d3d8c9bbd0 e5131bfeb43afe9df5dbfe1c78eb4e524ec0134db5dc15aeb3c78ccf67ff137a 215247aedf252ffa5ede2087d2fb9a191757f0fa6e512a736850b8ea8ebbbc97 71ef4ded2da2018acdf152ce74ea22c9e978fe45fdcbb62f717f2281795e6e3a bd9b692f7a08888e0aa58d137b600c01bd4730eab9df5a7028fb614cf8d152c7 28296836d1fefe9000a90f286ba4a4ab4a97ffd101b0e252d23ed3d985e08529 41345dbddeaaaea178161945057cab77ccb2619d8f2031405523e9e357283799 07da7f8e9b4f949edd2261a4a16232dd014d80826b554b10f04feec1fb555f38 c6950722c699c7662c77a50ccb122ceeba25e34c74fe9a374b46aee71f7df7f8 271837240a043b826d9cd45423a778a487e7c6220ba5994e3ca1677e3da70892 4534301c46c847cdd8d29b230a54506597325661d26c8a75c5e50be92f967236 06ebf9784301154cc9d274e7d55f9085b48d3df67c202bb3b2a7e61d66a5b625 1a239ed5936a123e7f645ff998b76a0fa3f742c204c74efb0459befef28d47a0 ccefe1d9d439b8be5d205dacf27d1afcd599ad7fe42e540d23e9f94487fbf40b d9c5898a2cf86ee2c1412735f24ad1f3836546ff9dc60fa57f4ea11f725e803a 6d5e425d5f3052a2fc11983760be3aa06711a29377cc118296caa236d587ab61 2a69d44a4ed1926c725412c2f1d7f63c2113057efd67ae3b33eee79eaec8eb7d 904b85fd067557ea0a88fa6f5e9c6c826fcf6b1d1cad2795b3a7dab8530a74bc 67dcdb86ce4a670b5eebeb7a44f94da5eea2acb2896e5a80872e519d3c625ed5 edda576b3e29344c32ff344d1b1ec1e2d3bb8a1df96d5952320ddca0c5086c1a 61a4aadf2b8d2c4204873bb9452a558b096ace094da6e24db29205eb 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus 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 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 76 /L put dup 78 /N put dup 79 /O put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 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081c4c832a335081c941cf42c844d75f11545d19bf69ac8c1d6c146dac0ba9e3 02478f8aa72304dd3b2d29d0fb73a0d4871814923c4e7540afce929c9d108a0d 261c2aecee97abe4509494278e5b0dfabfa9fea1526606c3fb3783c6eea53f27 56d14f1f08da7db22a7a9ac2950c16f280b1413f6d4a3ee9206473d7b30d18cb a1eaacead7bde38b7c7f4ae5d61fa5ec4d12ebfcccac7932c2b9244ab9a3598c 22190b1bbbce28f7aab09e0266474d66e17096ac88fac314182e8959c200147e 82f53ddf13bebf3cd60ca102a2b20ba1d4f9dc51254f35f9d0d8078701368820 348a5af4f46aa0558eab9014d4c7fd25a5f9aaca329f3ae489cf82347fdde917 bca031c3f0ef9c80ba939f598cd7ed2abc83e840e45de6f629038bf6d67c4c1f a6a316e398653ead36054f4bdf52acf08547e347e0fd95586247b400ab2eb237 20cfa5bbe976db2e3921ab5eedc80ded4edcc1cb9c490aac384ff217a1b650a3 46fec32bf81df1808e72821a38bb97cef3feb5b53f9b3c2ccb165ff4ccca442a 4fc0c90178f2c96f5f8af81d026737906dc12b27be944146789452890ca9006b ff197bcf54fcd86d3b24e4964a3df01f2474721093abe3690efc302cfb5e3367 c6dce2980f030ec8cfea2d0b704a70e5775e80ce0e6156fc452cad60c08e93a5 1cf5587a394366e379b2c8938c9050a178b1117df039e9094d62d6fd0579ca7d 242273cc0da65cf52640b23e4ca4e8b9b98b44e127d225f8a06b88a013d48208 afd9518e97b0f429497bbb815d1415c49faeec039fe86fbce51b1681ee485bce 3d21a1e68f37825093a616b220c2d222cf8c4d6873d1371e6354102f9ee9bf00 8be615f50a9d88bf13816fba123b7e93fc79d0566438c6980f381dcae2194b71 6e97f3c22b665f3d4ec284038ae911b81326132bac2ff496fbde6e0a4d47b3ac 67fd903432c60c5d1eb621f5fcc3c185a80f366cbdd670d9eda0917190196c23 31c54f2bd44293634d9f34a5540e63c0d777d6e63f35a6d1da15dcda920a7b84 935385275a45a6e9df5ad1f49d6d1a6360e1677f6dafc58742077d1da7b586ab 9b73408787a2e641aa321bf6f7b46f01015e7a96bfd511ea479da42f3e86593a 94303bc4f0e633005caf48a63c1e6875e2511bdeedaa30bdae108f54f9b62c6e 824652db25ebd2f9cb71748056032ba0dc91808f2952ca25f5592e7bee855966 d24a0d7d32c8ee6833f9fe799b2f930ce05735b369ee6987c5262630267ded20 80f801993d1ba22ebb49b2cb9880c2fa5bc2d5d442ad7e4a2991c189dca80ed3 e0b1508ef3b4a53ac32e5a66a2b146a3ff5bfe06cc6e2cfba3607fbf64747eee 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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 14 /delta put dup 24 /xi put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 66 /B put dup 72 /H put dup 84 /T put dup 100 /d put dup 106 /j put dup 112 /p put dup 114 /r put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 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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) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 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: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 49 /infinity put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a368f97cc4b552b0cb393586ef85adfbe8b725cd15e9c696e58e1b11 21c368ba02f172045741e4815d8cca8af35469573ec88979a32605484af842c7 c8113b9e8ed45959f6509328d38df9339718d0330e7678d6f8dd1eda9c64e8e9 5386e11244041426e100bb8e8a37f3b65096c3610428646e73f5efa5d3c4e61c 14fdcd7ea9eba748a3a13442e01b14e62bee9269bd5a418b0c16014994ea181c e732ef0c7cb86441f64334e2b2be5ae7675114909aff96971eef01cf53193b05 d2bf8bc8d031eb3d13ed5478eb94ab493beed5ffa631a038f3116a2ae0fd5364 01299390e966530184007284ae5a57ffeca47258e1dd77c988d1fa6e0a175e5d a17039d980d9898c7236bf82b688351b5073f2cf958a787fdd6dc83f7968b61f 3719a9ddd5e871258948e9fc6de07fb9c5fd903080c2e498a986bf523ce1878f 7889546c3bdbc93c386db4c4911d725019dbf04befa2d5e4d1983fee741e0f63 86e107c94e1f60f432e93920f38656b0935cd068233f781d3634c75330ba122c a6f33bac80edab4c3e6def6996b07a3728610455acaf7865f8adacfb707ddbe7 b9e15c3cf4c1a5463f7a73bb461b728725853bbf2bc7f8520a1d4000c2bc4488 88ccbf3315fd29da1037fd1b4b17ee899946a5d45f611b40a8a434ac05c7e92f f761094279eb80f43c216c6cc3bfc01a4ebc6e54bc04685f63386ce174e23dca ac4a2a0f3f54285cb270b3cccd65ba9933b30dca92d3d6cd9d30ffc02eec27d3 78a9789824e07b01f390e2a97c0200b3ab8b160b77e83b2b965770b2f6b4513a 19fc66f143f676b678704b6df69ad71c9db72436dc12f68471bda8c1a924ba17 ec53443e50be172aa60551d99ab8dc180f4be72c1fdf6fc4604d4c579eaa95e9 25c95ac2af561af83d2242ab2be4429a2eaf9778e5bcc6e5e8d2a2eb4734d86f 85507a9693a252834ebc50d172ccd5d0b5900484a70b4861e4483a3a1857890f 38b5a726daad1f9b7f78ecbdb3797de24a7a94917b166fd0592b97857fc3a490 ff0826a07f068f31ff21b8b5bb5dd3ab729e5edd2355c7e654984b50e66808be 76d12df93632ec1018e1d558592f3e85be2737a2d5c13de23021715fc1cae332 fcfdce37333888533833bfee6525bb9bee05 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 56 /universal put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c4302813551ec0153be72f1f9695b56a658dabe99f86661b49303d6565988 88bfe2c6ad3f28b68ea9b83725ea102a0b9393a25f33efc29df1996ac4dd61f5 f873f5babe16171ad53ce606645dd09e9afb6d3941bdc0cd7ebb88f03299f85d 7e956540734911f7754de74b8c7cbae69278a0770b300d116d8408eb28eb9185 15af0e18d71489f51eb20cb4102ce31371359d513266eb5301fed3910f27938d 31939b21f90328d46e695b1548ebc59fca9760ee05df9f2a9f67c75ace46f809 7f71c5e88ed2ac14b5492067df5ef80a67a4fb685337ba4d9cda053f7216f5b0 0c415292e3f1812968914c58152abb4344a468e892235f5103a0f22466a2fac5 f486039e056a6dc8580a146da607ed43fa27f3bd561d95ccbcfd50cb9b7066d7 a98c68a6a818e74286548b5188c37ca9722b9009c0fdf820be478cbd4b74b776 ec0f7fd51562e5ecee374907f729de5425de9d8c8e4ce4e6bec941f1055fc818 7d9033d8b7bcb452889a122bd53929516a7ab7133dd109918a0fbfe1527ca67c 9bda5364517d8e6a09bc8c35b9c27c4ed215a192daea05c916be1026afffdf6f a3a3904f25f88ee9df38163a82a9446ce924850e9514474be8a018453f40cbea 0b8196a7474843f8cbd475b312683f7429a07c510b00b237d2c367104f372239 dd866a235ad7207eff719c8609e87e0348caca9eeccefa44bab29f09f8e46b3d 5fd35ffac36831dc755851e1eb4f4319d0a0675e56ec0187c1cb25db801279b1 4fc204c8471b4b717120a4d9b692a82fa02e54498d2acf8acf5c87914c2c572c 9e1efd6d671bc879c94039f8407f03584447bdd45ecd6948e7898f49f60a3e87 35bd551e2907a9bfc90882f37cd5d798b9b64a15b76e1eef3e32647ade738823 7f6f306a3da1af73c0ec0ddd790f03c49a4416044b63015d9c6d12be4a5ff0e1 442413a114d2193f3ec618fa10b0c978e58538be3b6c517ae2ea6d59e03ba150 6a58bb936524c0eef05b1ffbccf0a8e4a9ad7afab703c9152c16c01b555aa2e7 e07b0c3632ccabb18c6f0802f0f6a1f485e1c6780dd3feb9c9a41b88edd0ccf8 02ee20627de5433733beb3ecc01eb65d5a798429c6cf6c3a58cb5b6275dc0d3e 90a6c26524a58f30ee6ef9330c83a3c7bd1252e17d8b4f2c5fb29fd46d7934d5 95f9fc970981142e204ba4e748bbeb6dcb3d7aa80fc1fc7081716be1d8d98a3a 1b054a358ac948d28755f8d8511119eac1c805a5a3c9a7f7df454912444d1dcc f87111c2a11e6d4ba2f0c5bc05bf6766572709cc35e448c7126ddff25a85d941 b87d8e3e8b680601f195330a786ada387759771c1040e86f753e97ce6e6e0c58 7f4037828ca42cccb3148b4ca9503f17b47a5e51a76f530552942fba68dc0c77 36062ac97b8a1284bc3e7f93f27c3b20e2bc7ee47dbee7b458291ae71a1fc494 25bb0f58ccd2ce313a42955776c74e85ca97c23f7ecb7751b351681bb0307599 a4aa33a6bb1ad222ea1f375e9b805c08d9a70e1f6b8b2037260cb3292758c6b6 79c689d4cf2fb4a62ca65131dd111ab13e26654dd352003f2564bf7a554113e4 4a98086631519cbfc936aa04aac86aa12d4c9354912aca6e28ffbe314c6364d6 69c8936674ae6af523921d1246ecaa13a4c1b8c27e83f46a959b6bc04c175aae 098b6c0a55eb824a5fd768e1eac98d248ae27cbc24c578c4c41ebad1df620d5d 8f2cb3501c0cb556ff9e6b18618fc6a47855358597f014a1d7f193ed665633c1 b57afe9a547a545938b2461661457792256aebf70d0b1d195d33b41be6b2008f a4de5027bcdc454ee5071f63af09cb8b1df9380f7500e65dcecfe95c4ef39b88 9c462d93ca4fefbc82d310840ed4c5c49698d1af34893d576d04429fc300955e 20d9ab7ecb00b9ec50573ee0040d41f7cfe02b8a6dd0c7072833f65385b0bb8e 08d37b4a274d0584c484b733c69e3a29743572bb42851e86f60ec51c1a5f0ec2 d21b2bff64421b11dbb389f8062034d2259fc3a9fb5f7dad2deab27bc4eab6d5 4c2fd5d7e69f8fdb35d090754d32104bd122e4651e037428000e708eb36508d1 22a58ddc8f509f096857de6084ef8effce7c54ba482696b83744b7d1ba33e4d8 79c48ed440d1cff44d787b37aef5fa0b0e26e2a333849f7ca45401defb616fc9 4ca9d984a5ef2072b2fb124a339017489ef159ff83b63ad07fcfdaf819a84120 f705f3a7dcd34c533611aff020b10c37ddae094628a6dec818a00f9fd42f39f1 a30c3cbc50a11072039b45ccbc671449559df2606216e76ba42f225b569b5fc7 5a4db0c95f92e578dc0f272df88f70590b39965389efee8cc604df6556588e70 2de5df9011ec7eb69079cd005ea658388d6055106319eb0ffa0c8cfafc8f350c 829a1e5e6626ada05c35fb3e938e0387474d8e352196cefc18ee4946538d22a2 a2c038f5fb844f8e437f420450e3c0a177ae1365f593d0ec4695234612236cc8 c26dc15424ff5d07a868885b5ff7cdeb50b8323b2533def8dc973b1ae84fa0a2 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 14 /delta put dup 21 /lambda put dup 24 /xi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 62 /greater put dup 66 /B put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 76 /L put dup 80 /P put dup 84 /T put dup 86 /V put dup 99 /c put dup 100 /d put dup 101 /e put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 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 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd45416d f3459365434123a76ccf883a4973bab19807e1f0c4bab03a45f7ed69ff2660ff 3963e4def11001eec4238c368a39d874fd30b3c14f4186ec7700fbce22abe468 eb32baf7b0164f8f21a9b5e706b91411faaa44467cb2180ab03de375c1ab93e9 76e11ab92fdd4a7280a6d1a8dc65c4c89d04c8ed6988045a2a3de9a4c7b1efd3 75b788255adb8b108285db827957adb0b64b68aba5b07e01468719002d6d7b0f 6a30bf0518533cbc75c64f97b6576b22cfc5106a8a712a181cab7ccac6a8417c 0a0d3d9ffec69d24f2462582b24d5c1633b126c12baff98b07b180157f7d992f 74e49a9b468d7ab640bd0334d70a6dc792458102ebdcea963f27d3a287b16c80 c66f4bf737df07986dafecacf6dc4f90e382336c025317babdf4f4c26ea5e593 97892411406ace27c91397d78ec6f98937d8c5a2d8eff804b4defb03569bd542 26e57aaed88d3c47bfaa9a41d3e3449fd300938d846698b5fdb63c1a03596509 13c76740d62466ed190f66f8edd50848ae430645a6b94c079db9906d3d8ffb13 cdf338367e1005e692ed69f169c189eab12539cf8c6aa166ef87e1df24d55796 d3c1d35b0942fbc7902a00867e3dacb951731ba47ee5b3c92bac83c7f906f222 31dc7bcc461d901c08b90e7b1b965b2a62e227014c36c7282e443387659e3221 c8d0a0ae2e4ea1cea9ff3fcb72596cf8e629bf58782cb13f8eed2868368ff4ee 0f08b97779db81977cf48362ae771b8ab05f87a00ae875f6b8671eaf598b1ea3 721bd46a2234b31679f26e0b46fee4af368ff0fcd5c69bd75918aa9954a6f239 0b0b2e4e38cc10cc36c2ef5b4c2832f8739f433983dec6cc72d22e62d3a33a9c fc9c9bb5157ead6b48a621853bf85aff35e0d75956d49889982f392c5efa5328 8d06b3b53ae0224c493f9cf4d500ad94373f62b553722234beaaf46711c0aa9a 70a0b7111417dead7eb894e0fc03aefd9e7d2c55d076b6d46ee52f4af5afec18 38c9d8205e19a11c44f41f62dc49ab88e71310e21f8446ee5953e1ea4b83fd9c afe5f1ea72a923eca966470f67d73feca7ab0b8773b895d8f54ad8bbdf5b89e1 136c8e67d1f77fb2173de0ba9b784cf9c01d8992fa68096ec415ab53bdbf234c 73c12bfb95e986df829ef46a539d1fd312f1ddd5f6523c85da771707c88291a2 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 65 /A put dup 70 /F put dup 73 /I put dup 76 /L put dup 80 /P put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 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{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 7dbcc4a8e4e85cd3259f40d3caf55c742cbb40ad0db1044c20a4f122a63f7b81 1d945bfa69662189ce4d089464d2ead9f6ed60b581b04114d5d45e97be27a576 35154e9b8464f2a0df18da855eb51b8f64d3054b0b2e84621f025a0776d16fed 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65a8905b23845581698e3838df709a711f7c90271ed3a75b5b9228d25b8dd711 00b7f49fb2f593ae01a7b7b7b84cdff088fe3baaa0ec3832dd47787ea361728c abe9d193f511e2e8e62ed24907b328a53d8b7c52900767499481b43e6dda42f9 90a376a9384721c87d740462e46fb5fccfbe2d2f127d74f54e35d25923a3982c 01a821d33a6fe349d91a4c7daa65ddeb628a76ffbd518f072428847da2164bbe c1ce02b74d022da23d62a13126a889 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % 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 (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 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 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 dcf4871a5d023c9ef57d3362d9f2d7a440bb69bf653364105f16f4d0f03582f9 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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 1 /Delta put dup 10 /Omega put dup 12 /fi put dup 33 /exclam 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 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 66 /B put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 78 /N put dup 80 /P put dup 83 /S put dup 84 /T put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex 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 readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 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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 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 75 /K put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 101 /e put dup 104 /h put dup 109 /m put dup 111 /o put dup 114 /r put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 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b Fm(s)p Fp(\))30082 52648 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)32281 53149 y Fm(P)168 b(V)270 b(P)168 b Fp(\()p Fm(H)369 b Fp(+)269 b Fm(s)p Fp(\))39249 52648 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)43434 50991 y Fp(\(0.2\))6075 55279 y(No)-34 b(w,)398 b(let)d(us)h(in)-34 b(tro)34 b(duce)396 b(the)g(p)34 b(oten)-34 b(tial)397 b Fm(V)25733 55461 y Fh(0)26654 55279 y Fp(whose)g(F)-101 b(ourier)395 b(transform)h(is)g(the)g(c)-34 b(har-)6075 56718 y(acteristic)386 b(function)i(of)f(the)h(ball)f Fm(B)22676 56915 y Fh(2)p Fi(\016)24038 56718 y Fp(m)-34 b(ultiplied)388 b(b)-34 b(y)387 b(the)g(F)-101 b(ourier)387 b(transform)h(of)f Fm(V)270 b Fp(.)6075 58157 y(Note)404 b(that)h(then)21990 59782 y Fm(E)70 b(V)269 b(E)406 b Fp(=)336 b Fm(E)70 b(V)28183 59964 y Fh(0)28709 59782 y Fm(E)g(:)6075 61660 y Fp(Therefore)8313 63789 y(\()p Fm(H)368 b Fp(+)269 b Fm(s)p Fp(\))12411 63288 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)14610 63789 y Fm(V)g Fp(\()p Fm(H)368 b Fp(+)269 b Fm(s)p Fp(\))19684 63288 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)22220 63789 y Fp(=)337 b(\()p Fm(H)367 b Fp(+)269 b Fm(s)p Fp(\))27597 63288 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)29797 63789 y Fm(V)30504 63971 y Fh(0)31029 63789 y Fp(\()p Fm(H)368 b Fp(+)269 b Fm(s)p Fp(\))35127 63288 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)37596 63789 y Fp(+)g Fm(T)168 b Fp(\()p Fm(s)p Fp(\))2240 b(\(0.3\))6075 65918 y(where)404 b Fm(T)168 b Fp(\()p Fm(s)p Fp(\))405 b(satis\014es)g(the)g(estimate:) 6681 67207 y Fg(Z)7893 67557 y Fh(+)p Fk(1)7354 69956 y Fh(0)10442 68036 y Fp(1)p 9956 68578 1579 49 v 9956 68820 a Fl(p)p 10966 68820 569 49 v 873 x Fm(s)11667 68856 y(n)p Fp(\(1)p Fm(;)202 b Fp(\()p Fm(T)168 b Fp(\()p Fm(s)p Fp(\)\))202 b Fm(ds)339 b Fl(\024)d Fm(C)87 b Fp(\()p Fm(\016)46 b Fp(\))22838 67511 y Fg(\020)23563 67207 y(Z)24236 69956 y Fe(R)24876 69703 y Ff(d)25615 68856 y Fl(j)p Fm(V)269 b Fl(j)27265 68356 y Fi(d)p Fh(+1)29007 68856 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)66 b Fp(+)33243 67207 y Fg(Z)33915 69956 y Fe(R)34555 69703 y Ff(d)35294 68856 y Fl(j)p Fm(V)36338 69038 y Fh(0)36864 68856 y Fl(j)37201 68356 y Fi(d)p Fh(+1)38943 68856 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)42104 67511 y Fg(\021)43434 68856 y Fp(\(0.4\))p eop %%Page: 3 3 3 2 bop 17660 3345 a Fh(ONE)407 b(CONSEQUENCE)f(OF)h(THE)g(LNS)11522 b(3)6075 6001 y Fp(It)404 b(m)-34 b(ust)405 b(b)34 b(e)404 b(noted)h(here)f(that)14930 6865 y Fg(Z)15604 9614 y Fe(R)16244 9362 y Ff(d)16983 8515 y Fl(j)p Fm(V)18027 8697 y Fh(0)18552 8515 y Fl(j)18889 8015 y Fi(p)19418 8515 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)337 b Fl(\024)f Fm(C)25061 8712 y Fi(\016)-19 b(;p)26249 8515 y Fp([)26586 6865 y Fg(Z)27259 9614 y Fk(j)p Fi(\030)35 b Fk(j)p Fi(<)p Fh(2)p Fi(\016)30140 8515 y Fl(j)30662 8209 y Fp(^)30477 8515 y Fm(V)269 b Fp(\()p Fm(\030)56 b Fp(\))p Fl(j)33318 8015 y Fh(2)34046 8515 y Fm(d\030)g Fp(])35600 8015 y Fi(p=)p Fh(2)6075 11541 y Fp(for)404 b(an)-34 b(y)405 b(2)336 b Fm(<)h(p)f(<)h Fl(1)p Fp(.)7403 12992 y(Indeed,)372 b(to)365 b(pro)-34 b(v)g(e)364 b(\(0.4\))h(w)-34 b(e)365 b(remark)e(that)i Fl(jj)p Fp(\()p Fm(H)288 b Fp(+)190 b Fm(s)p Fp(\))32226 12552 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)34424 12992 y Fm(P)168 b Fp(\()p Fm(H)289 b Fp(+)190 b Fm(s)g Fp(+)g Fm(\016)46 b Fp(\))41218 12552 y Fh(1)p Fi(=)p Fh(2)42683 12992 y Fl(jj)336 b Fm(<)g(C)6075 14431 y Fp(is)476 b(b)34 b(ounded)479 b(uniformly)e(in)f Fm(s)p Fp(.)757 b(Therefore)477 b(w)-34 b(e)477 b(ha)-34 b(v)g(e)478 b(the)f(follo)-34 b(wing)477 b(inequalit)-34 b(y)477 b(for)6075 15870 y(an)-34 b(y)404 b(\014xed)h(n)-34 b(um)g(b)34 b(er)405 b Fm(t)336 b(>)h Fp(0)6075 17154 y Fg(Z)7287 17505 y Fh(+)p Fk(1)6748 19903 y Fh(0)10139 17984 y Fp(1)p 9350 18525 2185 49 v 9350 19641 a(2)9956 18768 y Fl(p)p 10966 18768 569 49 v 873 x Fm(s)11667 18804 y(n)p Fp(\()p Fm(t)13304 18304 y Fh(2)13829 18804 y Fm(;)202 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))17927 18304 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)20127 18804 y Fm(P)168 b(V)269 b(P)168 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))26554 18304 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)28754 18804 y Fp(\))202 b Fm(ds)338 b Fl(\024)32243 17154 y Fg(Z)33455 17505 y Fh(+)p Fk(1)32916 19903 y Fh(0)36307 17984 y Fp(1)p 35518 18525 2185 49 v 35518 19641 a(2)36124 18768 y Fl(p)p 37134 18768 569 49 v 873 x Fm(s)37835 18804 y(n)p Fp(\()p Fm(C)39987 18304 y Fk(\000)p Fh(1)41245 18804 y Fm(t;)202 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(+)p Fm(\016)46 b Fp(\))47309 18304 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)49507 18804 y Fl(j)p Fm(V)269 b Fl(j)51157 18304 y Fh(1)p Fi(=)p Fh(2)52624 18804 y Fp(\))202 b Fm(ds)6075 21850 y Fp(The)282 b(righ)-34 b(t)282 b(hand)h(side)e(can)h(b)34 b(e)281 b(estimated)h(b)-34 b(y)27064 20874 y Fg(R)28074 21850 y Fl(j)p Fm(V)269 b Fl(j)29724 21410 y Fi(d)p Fh(+1)31668 21850 y Fm(dx)281 b Fp(due)h(to)g(the)g(Lieb-Thirring)6075 23289 y(estimate)9435 24651 y Fg(X)11387 24369 y(q)p 12600 24369 6527 49 v 12600 25803 a Fl(j)p Fm(\025)13644 25985 y Fi(j)14130 25803 y Fp(\()p Fm(\016)316 b Fl(\000)269 b(j)p Fm(V)g Fl(j)p Fp(\))p Fl(j)336 b(\024)h Fm(C)21897 24153 y Fg(Z)23109 25803 y Fp(\()p Fl(j)p Fm(V)269 b Fl(j)h(\000)f Fm(\016)46 b Fp(\))27768 25164 y Fh(\()p Fi(d)p Fh(+1\))p Fi(=)p Fh(2)27768 26114 y(+)31384 25803 y Fm(dx)337 b Fl(\024)f Fm(C)35190 26000 y Fi(\016)35897 24153 y Fg(Z)37311 25803 y Fl(j)p Fm(V)270 b Fl(j)38962 25303 y Fi(d)p Fh(+1)40905 25803 y Fm(dx:)6075 28553 y Fp(The)404 b(estimate)h(for)13439 29601 y Fg(Z)14651 29952 y Fh(+)p Fk(1)14112 32350 y Fh(0)17503 30431 y Fp(1)p 16714 30972 2185 49 v 16714 32088 a(2)17320 31214 y Fl(p)p 18330 31214 569 49 v 874 x Fm(s)19031 31251 y(n)p Fp(\()p Fm(t;)202 b Fp(\()p Fm(H)368 b Fp(+)269 b Fm(s)p Fp(\))25305 30750 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)27504 31251 y Fm(E)70 b(V)269 b(P)168 b Fp(\()p Fm(H)368 b Fp(+)269 b Fm(s)p Fp(\))34489 30750 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)36688 31251 y Fp(\))202 b Fm(ds)6075 34346 y Fp(is)542 b(more)g(straigh)-34 b(tforw)g(ard,)579 b(since)543 b Fl(jj)p Fm(P)168 b Fp(\()p Fm(H)460 b Fp(+)361 b Fm(s)p Fp(\))28660 33906 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)30859 34346 y Fl(jj)567 b(\024)h Fm(\016)34196 33906 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)36394 34346 y Fp(.)954 b(In)542 b(this)i(case)e(w)-34 b(e)6075 35785 y(obtain)6075 36834 y Fg(Z)7287 37184 y Fh(+)p Fk(1)6748 39583 y Fh(0)10139 37664 y Fp(1)p 9350 38205 2185 49 v 9350 39320 a(2)9956 38447 y Fl(p)p 10966 38447 569 49 v 873 x Fm(s)11667 38484 y(n)p Fp(\()p Fm(t;)202 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))17402 37983 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)19601 38484 y Fm(E)70 b(V)269 b(P)168 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))26047 37983 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)28247 38484 y Fp(\))202 b Fm(ds)337 b Fl(\024)31735 36834 y Fg(Z)32947 37184 y Fh(+)p Fk(1)32409 39583 y Fh(0)35800 37664 y Fp(1)p 35010 38205 2185 49 v 35010 39320 a(2)35616 38447 y Fl(p)p 36627 38447 569 49 v 36627 39320 a Fm(s)37328 38484 y(n)p Fp(\()p Fm(c)p Fp(\()p Fm(\016)46 b Fp(\))p Fm(t;)202 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))45115 37983 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)47313 38484 y Fm(E)70 b(V)269 b Fp(\))202 b Fm(ds)337 b Fl(\024)16179 42261 y(\024)17459 41109 y Fg(X)19412 40821 y(q)p 20624 40821 6209 49 v 1440 x Fl(j)p Fm(\025)21668 42443 y Fi(j)22154 42261 y Fp(\()p Fl(\000)p Fm(C)87 b(V)25498 41911 y Fh(2)26024 42261 y Fp(\))p Fl(j)p Fm(;)2626 b(C)424 b Fp(=)336 b Fm(C)87 b Fp(\()p Fm(t;)202 b(\016)46 b Fp(\))6075 44409 y(The)533 b(latter)g(sum)h(of)g(eigen)-34 b(v)-67 b(alues)532 b(can)h(b)34 b(e)533 b(estimated)h(due)g(to)f(the)h(Lieb-Thirring)6075 45848 y(estimate)16421 46706 y Fg(X)18374 46418 y(q)p 19586 46418 5256 49 v 1440 x Fl(j)p Fm(\025)20630 48040 y Fi(j)21117 47858 y Fp(\()p Fl(\000)p Fm(V)23507 47508 y Fh(2)24033 47858 y Fp(\))p Fl(j)337 b(\024)f Fm(C)27612 46208 y Fg(Z)29026 47858 y Fl(j)p Fm(V)269 b Fl(j)30676 47357 y Fi(d)p Fh(+1)32418 47858 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)7403 50423 y Fp(Finally)404 b(w)-34 b(e)404 b(apply)h(one)f(of) g(the)h(results)f(of)g([11])g(to)g(conclude)h(that)6075 51774 y Fg(Z)7287 52125 y Fh(+)p Fk(1)6748 54523 y Fh(0)9836 52604 y Fp(1)p 9350 53145 1579 49 v 9350 53388 a Fl(p)p 10360 53388 569 49 v 873 x Fm(s)11061 53424 y(n)11789 53606 y Fh(+)12576 53424 y Fp(\(1)p Fm(;)202 b Fp(\()p Fm(H)98 b Fp(+)p Fm(s)p Fp(\))17751 52924 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)19950 53424 y Fm(V)20657 53606 y Fh(0)21183 53424 y Fp(\()p Fm(H)g Fp(+)p Fm(s)p Fp(\))24742 52924 y Fk(\000)p Fh(1)p Fi(=)p Fh(2)26941 53424 y Fp(\))202 b Fm(ds)338 b Fl(\024)e Fm(C)87 b Fp(\()p Fm(\016)46 b Fp(\))32910 52079 y Fg(\020)33634 51774 y(Z)34308 54523 y Fi(B)35018 54679 y Fd(2)p Ff(\016)36135 53424 y Fl(j)36657 53118 y Fp(^)36472 53424 y Fm(V)269 b Fl(j)37785 52924 y Fh(2)38311 53424 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)p Fp(+\()42886 51774 y Fg(Z)43559 54523 y Fi(B)44269 54679 y Fd(2)p Ff(\016)45387 53424 y Fl(j)45909 53118 y Fp(^)45724 53424 y Fm(V)269 b Fl(j)47037 52924 y Fh(2)47562 53424 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)p Fp(\))51194 52924 y Fh(2)51721 52079 y Fg(\021)52445 53424 y Fm(:)6075 56385 y Fp(Indeed)398 b(this)h(estimate)f(is)g(a)g(consequence)g(of)h (the)f(follo)-34 b(wing)399 b(statemen)-34 b(t)400 b(of)e(Laptev-)6075 57824 y(Nab)34 b(ok)-34 b(o-Safrono)g(v)405 b([11])6075 60126 y Fq(Theorem)464 b(0.3.)554 b Fn(L)-62 b(et)433 b Fp(\012)17683 60323 y Fi(\016)18622 60126 y Fn(b)-62 b(e)433 b(the)f(domain)18593 62318 y Fp(\012)19468 62515 y Fi(\016)20310 62318 y Fp(=)337 b Fl(f)202 b Fm(\030)393 b Fl(2)336 b Fj(R)25340 61817 y Fi(d)26217 62318 y Fp(:)538 b Fl(j)p Fp(\()p Fm(\030)56 b(;)202 b(e)p Fp(\))p Fl(j)338 b Fm(<)e(\016)248 b Fl(g)6075 64540 y Fn(wher)-62 b(e)399 b Fm(e)i Fn(is)e(a)h(\014xe)-62 b(d)400 b(ve)-62 b(ctor)398 b(in)j Fj(R)21348 64100 y Fi(d)22288 64540 y Fn(of)e(norm)i(1.)546 b(It)400 b(holds)e(for)h(the)g(eigenvalues)e(of)j(the)6075 65979 y(Shcr\177)-620 b(odinger)432 b(op)-62 b(er)g(ator)431 b(that)9558 67577 y Fg(X)11511 67295 y(q)p 12723 67295 3787 49 v 1433 x Fl(j)p Fm(\025)13767 68910 y Fi(j)14254 68728 y Fp(\()p Fm(V)269 b Fp(\))p Fl(j)337 b(\024)g Fm(C)87 b Fp(\()p Fm(\016)46 b Fp(\))20606 67383 y Fg(\020)21330 67078 y(Z)22003 69827 y Fh(\012)22683 69983 y Ff(\016)23395 68728 y Fl(j)23917 68422 y Fp(^)23732 68728 y Fm(V)269 b Fl(j)25045 68228 y Fh(2)25570 68728 y Fp(\()p Fm(\030)56 b Fp(\))202 b Fm(d\030)326 b Fp(+)30000 67078 y Fg(Z)31414 68728 y Fl(j)p Fm(V)269 b Fl(j)33064 68228 y Fh(4)33589 68728 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)36750 67383 y Fg(\021)37474 68728 y Fm(;)1441 b(d)337 b Fl(\025)f Fp(3)p Fm(:)p eop %%Page: 4 4 4 3 bop 6075 3345 a Fh(4)16124 b(O.)314 b(SAFR)-26 b(ONO)g(V)6075 6043 y Fn(In)434 b(p)-62 b(articular,)431 b(if)14936 5736 y Fp(^)14751 6043 y Fm(V)606 b Fp(=)336 b(0)434 b Fn(outside)d(of)i(the)f(b)-62 b(al)62 b(l)433 b Fm(B)29122 6240 y Fi(\016)30060 6043 y Fn(then)10677 7391 y Fg(X)12630 7109 y(q)p 13842 7109 3787 49 v 1433 x Fl(j)p Fm(\025)14886 8724 y Fi(j)15373 8542 y Fp(\()p Fm(V)269 b Fp(\))p Fl(j)337 b(\024)g Fm(C)87 b Fp(\()p Fm(\016)46 b Fp(\))21725 7197 y Fg(\020)22449 6893 y(Z)23122 9642 y Fi(B)23832 9798 y Ff(\016)24544 8542 y Fl(j)25066 8236 y Fp(^)24881 8542 y Fm(V)269 b Fl(j)26194 8042 y Fh(2)26719 8542 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)270 b Fp(+)f(\()31833 6893 y Fg(Z)32507 9642 y Fi(B)33217 9798 y Ff(\016)33928 8542 y Fl(j)34450 8236 y Fp(^)34265 8542 y Fm(V)h Fl(j)35579 8042 y Fh(2)36104 8542 y Fp(\()p Fm(x)p Fp(\))202 b Fm(dx)p Fp(\))39736 8042 y Fh(2)40262 7197 y Fg(\021)40986 8542 y Fm(:)22466 11744 y Fc(References)7099 13894 y Fo([1])512 b(M.)574 b(Christ)e(and)g(A.)h(Kiselev,)633 b Fb(A)-26 b(bsolutely)580 b(c)-52 b(ontinuous)577 b(sp)-52 b(e)g(ctrum)579 b(for)f(one-dimensional)8691 15112 y(Schr\177)-523 b(odinger)559 b(op)-52 b(er)g(ators)557 b(with)g(slow)52 b(ly)558 b(de)-52 b(c)g(aying)558 b(p)-52 b(otentials:)853 b(Some)559 b(optimal)e(r)-52 b(esults)p Fo(,)604 b(J.)8691 16330 y(Amer.)342 b(Math.)g(So)28 b(c.)342 b Fa(11)h Fo(\(1998\),)f(771{797.)7099 17547 y([2])512 b(D.)316 b(Damanik,)321 b(R.)315 b(Killip)i(and)d(B.Simon)i Fb(Ne)-52 b(c)g(essary)342 b(and)f(su\016cient)h(c)-52 b(onditions)340 b(in)i(the)f(sp)-52 b(e)g(c-)8691 18765 y(tr)g(al)366 b(the)-52 b(ory)365 b(of)h(Jac)-52 b(obi)365 b(matric)-52 b(es)367 b(and)e(Schrdinger)i(op)-52 b(er)g(ators)p Fo(,)341 b(to)h(app)28 b(ear)341 b(in)h(IMRN)7099 19983 y([3])512 b(P)-85 b(.)426 b(Deift)g(and)f(R.)g(Killip,)449 b Fb(On)443 b(the)g(absolutely)h(c)-52 b(ontinuous)442 b(sp)-52 b(e)g(ctrum)444 b(of)e(one-dimensional)8691 21200 y(Schr\177)-523 b(odinger)464 b(op)-52 b(er)g(ators)461 b(with)g(squar)-52 b(e)464 b(summable)g(p)-52 b(otentials)p Fo(,)472 b(Comm.)447 b(Math.)g(Ph)-28 b(ys.)446 b Fa(203)8691 22418 y Fo(\(1999\),)342 b(341{347.)7099 23636 y([4])512 b(S.A.)395 b(Deniso)-28 b(v,)409 b Fb(On)415 b(the)f(c)-52 b(o)g(existenc)g(e)416 b(of)e(absolutely)h(c)-52 b(ontinuous)414 b(and)g(singular)h(c)-52 b(ontinuous)8691 24853 y(c)g(omp)g(onents)383 b(of)g(the)g(sp)-52 b(e)g(ctr)g(al)383 b(me)-52 b(asur)g(e)384 b(for)e(some)i(Sturm-Liouvil)52 b(le)385 b(op)-52 b(er)g(ators)382 b(with)g(squar)-52 b(e)8691 26071 y(summable)368 b(p)-52 b(otentials)p Fo(,)341 b(Comm)-28 b(un.)341 b(Math.)h(Ph)-28 b(ys.)7099 27289 y([5])512 b(S.A.)280 b(Deniso)-28 b(v,)293 b Fb(On)308 b(the)h(absolutely)g(c)-52 b(ontinuous)308 b(sp)-52 b(e)g(ctrum)309 b(of)f(the)h(Dir)-52 b(ac)309 b(op)-52 b(er)g(ator)p Fo(,)291 b(preprin)-28 b(t.)7099 28506 y([6])512 b(D.)438 b(Hundertmark)f(and)f(B.)i(Simon,)462 b Fb(Lieb-Thirring)455 b(ine)-52 b(qualities)454 b(for)f(Jac)-52 b(obi)454 b(matric)-52 b(es)p Fo(,)462 b(J.)8691 29724 y(Apro)-28 b(x.)341 b(Theory)-85 b(.)7099 30942 y([7])512 b(R.)492 b(Killip,)531 b Fb(Perturb)-52 b(ations)503 b(of)g(one-dimensional)h(Schr\177)-523 b(odinger)505 b(op)-52 b(er)g(ators)503 b(pr)-52 b(eserving)505 b(the)8691 32159 y(absolutely)367 b(c)-52 b(ontinuous)365 b(sp)-52 b(e)g(ctrum)p Fo(,)342 b(IMRN.)7099 33377 y([8])512 b(R.)f(Killip)h (and)e(B.Simon,)554 b Fb(Sum)522 b(rules)g(for)f(Jac)-52 b(obi)521 b(matric)-52 b(es)522 b(and)f(their)g(applic)-52 b(ations)520 b(to)8691 34595 y(sp)-52 b(e)g(ctr)g(al)367 b(the)-52 b(ory)p Fo(,)341 b(Annals)g(of)g(Math.)h Fa(158)h Fo(\(2003\),)f(253-321)7099 35812 y([9])512 b(A.)396 b(Kiselev,)411 b Fb(A)-26 b(bsolutely)417 b(c)-52 b(ontinuous)414 b(sp)-52 b(e)g(ctrum)416 b(of)f(one-dimensional)h(Schr\177)-523 b(odinger)416 b(op)-52 b(er)g(a-)8691 37030 y(tors)338 b(and)f(Jac)-52 b(obi)338 b(matric)-52 b(es)338 b(with)e(slow)52 b(ly)338 b(de)-52 b(cr)g(e)g(asing)339 b(p)-52 b(otentials)p Fo(,)316 b(Comm.)311 b(Math.)g(Ph)-28 b(ys.)311 b Fa(179)8691 38247 y Fo(\(1996\),)342 b(377{400.)6587 39465 y([10])512 b(A.)287 b(Kiselev,)300 b Fb(Imb)-52 b(e)g(dde)g(d)316 b(Singular)g(Continuous)f(Sp)-52 b(e)g(ctrum)316 b(for)f(Schr\177)-523 b(odinger)316 b(Op)-52 b(er)g(ators)p Fo(,)298 b(pre-)8691 40683 y(pin)-28 b(t.)6587 41900 y([11])512 b(A.)405 b(Laptev,)422 b(S.)404 b(Nab)28 b(ok)-28 b(o,)421 b(and)404 b(O.)i(Safrono)-28 b(v,)419 b Fb(A)-26 b(bsolutely)425 b(c)-52 b(ontinuous)423 b(sp)-52 b(e)g(ctrum)425 b(of)e(multi-)8691 43118 y(dimensional)453 b(Schr\177)-523 b(odinger)452 b(op)-52 b(er)g(ators)452 b(with)f(slow)52 b(ly)452 b(de)-52 b(c)g(aying)452 b(oscilating)g(p)-52 b(otentials)p Fo(,)458 b(sub-)8691 44336 y(mitted.)6587 45553 y([12])512 b(E.H.)364 b(Lieb)f(and)g(W.)g(Thirring,)368 b Fb(Bound)385 b(for)h(the)f(kinetic)i(ener)-52 b(gy)386 b(of)g(fermions)g(which)f(pr)-52 b(oves)8691 46771 y(the)324 b(stability)f(of)g(matter)p Fo(,)305 b(Ph)-28 b(ys.)296 b(Rev.)g(Lett.)g Fa(35)h Fo(\(1975\),)305 b(687{689.)295 b(Errata)g Fa(35)h Fo(\(1975\),)305 b(1116.)6587 47989 y([13])512 b(E.H.)540 b(Lieb)g(and)e(W.)i(Thirring,)588 b Fb(Ine)-52 b(qualities)548 b(for)f(the)h(moments)h(of)e(the)g (eigenvalues)j(of)8691 49206 y(the)481 b(Schr\177)-523 b(odinger)481 b(Hamiltonian)e(and)g(their)i(r)-52 b(elation)479 b(to)h(Sob)-52 b(olev)481 b(ine)-52 b(qualities)p Fo(,)497 b(in)466 b(\\Stud-)8691 50424 y(ies)289 b(in)f(Mathematical)h(Ph)-28 b(ysics.)288 b(Essa)-28 b(ys)287 b(in)h(Honor)e(of)i(V)-85 b(alen)-28 b(tine)288 b(Bargmann,")f(pp.)h(269{303,)8691 51642 y(Princeton)342 b(Univ)-28 b(ersit)g(y)342 b(Press,)f(Princeton,) h(NJ,)f(1976.)6587 52859 y([14])512 b(C.)493 b(Remling,)531 b Fb(The)505 b(absolutely)g(c)-52 b(ontinuous)504 b(sp)-52 b(e)g(ctrum)506 b(of)e(one-dimensional)g(Schr\177)-523 b(odinger)8691 54077 y(op)-52 b(er)g(ators)366 b(with)e(de)-52 b(c)g(aying)366 b(p)-52 b(otentials)p Fo(,)341 b(Comm.)h(Math.)g(Ph)-28 b(ys.)341 b Fa(193)i Fo(\(1998\),)f(151{170.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0401201602532--