Content-Type: multipart/mixed; boundary="-------------0403190925155" This is a multi-part message in MIME format. ---------------0403190925155 Content-Type: text/plain; name="04-89.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-89.keywords" Turbulence, dissipation, rigorous bounds ---------------0403190925155 Content-Type: application/postscript; name="Doering.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Doering.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: Doering.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX12 CMR10 CMR9 CMTT9 CMBX10 CMMI10 CMR7 CMMI7 CMSY10 %%+ MSBM10 CMEX10 CMBX7 CMSY7 CMMI5 CMR5 CMSS10 EUFM10 CMSY5 CMMIB10 %%+ CMSS8 CMTI10 EUFM7 CMBX9 CMMI9 CMTI9 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -Ppdf Doering -o Doering.ps %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2004.03.18:2226 %%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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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % 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 (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 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 175 /beta put dup 176 /gamma put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueXX 5087384 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a 757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4 ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821 f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89 02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4 30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c 61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f 1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42 483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693 f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68 f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84 ff7fbe77f6ddf9d06fa92b16ecebcbe0370b5cd9d450d0f2906a105cadf93ed0 0abc7fcf2c996e7c15e452006e35390d99b9cfc59925f1444c20d9c3e1fc2910 32cf9fa9d580eac1bc956334da391b870a757c3bee6aa3e005b20988d8587876 3ced20c6edf2ac2b22890e37ff7aedeb0986d85ae05bc84339bf2116df48c5d1 cc888bb33d409b06dd70ffd0618b2080442aac439aeb39c20a87ad74ef10629c f1604db8611e8e4224c5b21ab0c7ebddc77fe9a283b3a8c6a2a9508f6836e3fc 3eae1366b4da4f44cb7a77fd81d278c17775d56cb28b70f18d894bfd1ec1827f fb177e1d46b0dc5afee78aaca1c43d03b7be6c8768bf025d45ad66f3bad7d11f feea2ff2565da8dead9b9da7cb5d16eb5a060bba3be261adc96ce6ca88ca6325 027570e89e728c70a094dbc145d19c9b510876c4f7651662b1687188cc0fd42a d808551b33ca1cf31115197a8b21e3a4ec6b01053772a325ee61c813e493ef7e a4ef35d6c3c12b2c8881dc68b1c6dac3cca12b5d675de6856319f9f2217f6cb2 357247c90edcc18fe76abaa52ea2518c5f6b4c93f4474a458cc4de3c1cf94b53 127097d6c362eecf6a4fc00a4e0270d20bcacebac2a04daaff9f9568f2842497 d9f63a764b2e72fdb273c4d2683ad6ebda254eb779f7245651ff31ae01e933d3 9ebaa47b97adcd4aa71556dba069c6ca84de4df3936822d0a1b508f801609fcc 06c6e70cd562db755739f9cd026c13273dc13d19d8731d086fb43a82905816c5 167282c355f0d4c320492407b2d0fd380013b5d4bf994244463eef90f341a0ce 18434049c8b4ef1407a53842caf35fb3623ecce35d8bd14b0b3863f04693414d 7694b9ad0f9a582b32127ee9dc8d235108e1672057054219a3cf3e4fa9ad7e0e 76f15442926de7e0218905f1b31309203f2f9365b30b12020e0d4b57ed6d0890 53e0eaba0c3fca546a5f734c41797cd20736afb81874ad8ce0fb68cabc571f0c 4ae8834d18c47e4076805710b2f74f5895beefd30f286485dbf2ca742f3bf142 0a54eddcb3b55e7d2f04686027dbe77fadca98a020f2a6f5d907d0684c16dcf0 b35bfcb2e8834af798fb880aa6d7b8f5bd73acb7112beb5e6bd44ba235b8a5c4 ec44f5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % 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 (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 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 175 /fi put dup 176 /fl put dup 46 /period put dup 49 /one put dup 70 /F put dup 103 /g put dup 105 /i put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d55fd4dda249cff0b56b9f3aff e9d0de215c02a52a6bc77155ff6b8cba5cd6646ba331254ac58ace650a967d3b 272331b87b6df06d5ab9d80fabe9f9ceac10139b61244814dd9fc295ed42d1b5 cd11c2e4beab318b20f51ca2c2930657e5343ab7bcf0e8870a0d12de4ffacb6c b3fdbdda481c2fcb84408d3d902e9a32070b2af6cd9317a33a42a43857c114b3 f4c3005cef9401f1c2bad3e69150d7145b79f95c9cfaf7a335b277e6435ab374 f6a3e78e124ac1e4615511f743ad65c5d778403a840310ac4902985f107fd33c 0049623e4c496cd353d2ae2a4804110c6a420a38ece5d5b235c5e35886a0987d 284e6110527b653b1b2c68c636ef423536180acadb954843eff4d9a82568a713 b682c574e30f793f093aef755c650e0e7175c2e3138695212d9fea7bd4b5805c a90985b134c6bc15a19afae0bfb3066363ca3e2568c2ac4559a69fc32feb443b 61243b4508b7524d974636855c83c8149d489b68fe18bd497116a953431251df bd09fa1d2ef66c85b997ab2f6b7c6d9d096cb43931379ff9782fa00c5f3cbd06 04265d16891ffc4f66e4a0307765d384c32aa83a4e4f89ac79ef8e76eed08450 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7a85814f4d2cfee3d50f7323125e922308c165d64168de81a705cae872cea46f 8da6ca53765023ae5232dc3f3c39b95368394a4bdc43a145e439e22abf6734e9 b5459267d838a0015e2b4c23439de6f76063819699dd390ad3560f4d2a324b30 effca6e002975b95fc708b8d3c7fa9b7f809bd7dd0abb19b8c90780ff8f64dca c2ff791e8609cfa6712e9cd72faabc72749ac8303e3fa92acd8d00a6f42d31fd c5966f475aa5e96de492043a7c51a8ff56ca229dc93f3b3eae861e690b76df24 bfd0b40011f7db5e613839658d7099d7991a2c12ce59cfb45d6f8e9820cf3e0a 4abee9bc46e26b2be8965e7929b5dd75a34aef768d318b2a5ac771f2bcad3912 93e09f3ab235f5f7d6ceb8dcf7a54be38ccd8c9c5102c38f83ed826452f2277f 7e4290030ef6875da4bf5d9963f4f535a9f89d1684b5e0c5483a035efd07078b dbc0dab39eb13d13613280bc8fb9a45c74076abb7ed83fcf01021e4d0239a727 71330ea3ff652337403ac714f246e2fa8c9e1cae825ee535f6787d475eadeb5b 307f85f3cb98df6ffeccdf79e9facef6557d0fe0ba8a43161c28ad 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) 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 (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 112 /p put readonly def /FontBBox{0 -250 1193 750}readonly def /UniqueXX 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 a11d8b1b8184a69389665f063bb953dc1a8061fec0dc5ac78d19d6a06f0d3384 8484800aee7c387a735741818f70e5fb2e27893c5bce37ecf91b5a4c8a0f9de2 0837b88c944cc5882c3b3e976d1d1916404bd9b4eb5e4b0ce0f5c14742b95072 b252c9cc753a95fc4ef32a9619a95a3093b7535adbbdf56d135178d85459411a 1272e88b94481b98c5d7d207cb9f1ba23e9094c033abd374e50704e69316c0fb 20893d8e8772e89ac577c4255b67df31a70c8106b2c96f12330a5bd6617d3efe be2755861f389585186dcd98d04b69500d2ec9290e360a930f8608c1b891d866 716f364e18e11e7fd23e3bf018efed2fd26bd96a157b0dca27be65c3ce5b0eec 9bd67324678ee03cfd85ed52581105af6e85c697ac7245f83de0a79594cc86d8 4e03b06ea05c93bf7e61c8b4a52a5a6c15fc7a3fb7d9b6827637a724224832a9 283cfd020dc3a7b2066e8f7846a5fc0a26c9947d38093273aa81801f028c15bc 69037a40ef5b7053398c6b8eb8cf90798abefdb46cc7b1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 175 /fi put dup 176 /fl put dup 97 /a put dup 105 /i put dup 111 /o put dup 112 /p put dup 114 /r put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 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55fc0df002b7de6db37539b4a2aedcacb1b273d03dc7f1b471c258eee753ec2f d9fc012c5b59e712566dcf7d09d565b1cb6d9e6b036b1de55c20e9426bc1149c bd94b9f36cd955ce7a69ca194e6d6ffe59bbfff503678bf9461cd17d6fa448ed 11f27e310faf23017d7033b89108eee0bf4847b64f44a7bbccf23e600484f4c6 03e435e0818c6f2169a6b42d63cc91b60b2fe01503f885fdd51bcdb7bd1e49fe c3e113afa10b9859c90d5e09529002bbd5af221d4a9d5eebe51f24b1e71ccc77 f2b9390a802b40438bb48c9006d1482b526c9947270c9036d49efaf876beb46a 0a569880a5da3360bb60c2da512662ed5a41332e20bfe24769200f8820889a21 20b74bcb7bbb883ed315e7d1be1eb1171da6de6be1866ef1284ee633c13ba907 b0e6cf0d721c5464ffeda28b6c6e3b6ddda1f52d9814d508ee1590dfa0ef21b8 1b0ba32e4d9617df1c97f0c635e14cd5181d42d5d3e55faa477002736ba0cfa3 502f58c6a5444393981de6b0e65616e7810fb1ec59531ed13787c1088f5f99a3 49606177c567732828d1c0a39974079e36d614dae09b06488e8789cc65613b12 590a74ca1f512009fcd1368bf542942de9ebd4be932145736e61a0eb69e2c453 e9f23f0efa1b992c58c8038a52966de8e4f90f43ba337019171a6e67f859457c 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS8 %!PS-AdobeFont-1.1: CMSS8 1.0 %%CreationDate: 1991 Aug 20 17:34:12 % 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 (CMSS8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS8 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 175 /fi put dup 176 /fl put dup 82 /R put dup 101 /e put readonly def /FontBBox{-65 -250 1062 761}readonly def /UniqueXX 5000801 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cddfaf2ed604ab4eafe1b34aa4 31dcb3f73f83d75ec7227c48db19b78c44fb70b482ee1dbcb1d7fb08e9785c6d a62bee427908096a5b8f86f98d9152081f1747b469511b7f68cc2fda6418133f 75e6ee5850bb15a694473f719dedd4eb3fdc523956ae5514f74fde80f202176d 3e75352d77200ff5199c73b37488f46538df1b6acbc3e17af9850bd8b89fc663 0e6787916e0c266869f1f8202a1cb2f5bf4546ed3de9873bd1e9bb1572197b7e 0fcb8d4c206846f1794d1b79e43c77983b03421deeeb0205c9d8f85b747baf25 c3118fec3dc1a69697e20a28951030a31b5fd44d8400022b2a09032c8f116186 d0b3bf0084651683d1f4353d366419e9aa005f18b37ee47664f1f4761802c131 35ea7a68dfd58cd20584d8b452ff7d6ced0f0f3261ace39c8ed6da7619041f7d 7ed502e80cc367ee7b4789f6fd5f2a08a6d1d8c2890bb58895e89cabc039cd1f 676d04fda04e8074e4afb4af3ed0dd2dc308d7ac12cbc1c86474e6080de6b5ee cf6d60c29277593334367d368e31b49fa6a021ba69434d42bd32f07d145c38dc 8e25e08ac4d21eaad81a51865a6095b275fa248287d5bcf4bb1197f508102c50 e2dc98863474a0ee4ce3f76d3db05a5b9b09603e15dd24621f88cc54a91c3565 cebebf88085c447b7865225ec22e77b3e5e1b040f172fc5e208766916ea0e2da aa12c34ed4cbacd23b756dc57fc0b85554e94385fe48bd972971f482910f9a54 f566833fb543c420b5668e1b128d05cbe166f43e8b4eacde00b8a092ed646f3f d76539e42738796a22da10c0055d5d9d3fdf5cf9c116b9c0f3cb028db9a37021 72617d588e1aa7ddb54971c0ae4c07fc5396228125b962ae6e772a9d03ca3035 ba67911cb8716ecbac2314fade7ef1732e08c6d03973dca95fb670226ae5473e 374133c6b3a57372ab9821f0aa6db884b69e4dfc3bec6d1f2912341d28f319cf ec1071df15cd16bf8859f1c4937e697527b036efde2447df7e0258f8e96fda87 df9c33b0a20a058c5e38a20dd90d037d008dd4b92e6bac5d92cbb1a6a7606b3a e383662b2c0c3cdd96894c31829efc662816f0338fc322baf0f4c24e91b0a590 6b94bb8e8f07b7937021baaf884d2ed0d000827b5672808c912a2739fecf2e81 4965bb3b98ff502e3451e725efc7471e51f99192b748532a537d0e644986cf32 c9ab242188711f6e4a285241fc7456bf502bb8cc72aff0d0e8ba40b9df1ffe07 7031782f3634a20cb76b945149c13386e3636ffcb7df86a1c8b463624a6ec2d1 91ec472c5d41fc64ff69fb847a2f72f328d23568f22e84e93ed8350c82a12e4c 38f7a93225288911bc989666729e0f2bc77f340925e57d888df2d97243f3221b 1feb3ddfc4e0b337c3fbe94e61a87bfd716f26ff99f37129b6cc94594b33ad75 27d03f51aa4cfda5a746d66f8830b5ab1e7c7bc0fb569bee2f1e7e091f19c7f1 df75c5749d978b09d1dfd6894f8ae6221e105ee243fdc33ef5b17f95c5f437c9 f0bef6c47b4af941ef79cae1eae25682035872f5c3f12305390f6947041339b3 19cd013ef93527977b49cd4ed7e2d698675238f9d222d06cc9adc5f7dcc88275 49e7b5d5c48ff0dced2ff06ba9f3748fafd25b0d61070800f73f1d703e8b9665 6890344113d750eb5f513846de07db8a7539b555dd95fad3503e0e77df13b42e a7fce6d9c80aaa09deb01c8b7e1b1b93e0fc865de57090fdf83097bf3eee7fa5 269613c2a1bfdc6ce267a2c0ef7eb06c3db004bd06f7c04a24d74ca47aea5433 eae3fb251853830b264939 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % 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 (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 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 175 /beta put dup 176 /gamma put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueXX 5087392 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041490e364babe4b85935b8c9c7758c2dbe253653c 892b1fc2c6a01103e0b8553f847bb38d8e4fcd563ebe51cb7d5f0877af29249d b61636618fb31eeb6cbb4ea4db687fd77ed1574da8c9f9d33b592ec0e38d798c 498a205cab252f7e2f1ddb82a38f331f917b8452af11b2b93e34c1ef55ee005c e8418dbcd0fb9d4d3fa8cb388ec91f16c8864913ad3fc8960d3c424650bdd12c 4db4049367faae97c660f00021f712e9eb6366b7ce74255ff62b72396ca43287 7c77fecdc53883427c90c1c3ff7bd46e472cea9bd72eef0e1be36abb3a50a7bf 6f5d460fa2fc81466014df9ee1e15365642c2de78706dfa740e035b4f28f290d 79b8ba16e5bca13fd9c3eb7eb54006ac2c1cf0bf363b3b69e923797a95b76515 073892c75cf733da7c07da8ed1a8d1ded902f784764c6df6fcd0fd28083d88c8 4c41aeaa6c2c2c1bb10219f4feaab75ee904f4314fc0b9de5e96054f2472ad86 42140315385400686cb07a0585d922ae4b1b25ae722edc6b4afe053560fc9ac9 20a1d2fb8d0921c52c9468d34dba9bed42e3a8308742d36186ed0a3b43f690a4 dca6bb2af8bd698fb303fd68df53edc5e01912cf007dd31ca7481ce844be1258 7002d4aafb204a8075fc6df86f22249d61dd840e7ef87362d72e35f4e8ece044 95ae41ee5c02d6aafaad37141935867a8770fbd9e9e894ea6cc5cf3770f35d98 09be73c56fb053ebb622cd4a3826bc95c192bc2248e1a30e641799994debd48f c5a0ca09be0b2831672271e6a087154d1541899171bc12c8ae00dac586f5c0dc a9c8f4bc7910fe68531c2adf25f29002b74151ec41cfe904b25dc975f97ca163 59d6ea5787a3b0529b3a7a7f8b5b8606cf11dfa1029106881e531349e8317d6d 256ecbe471ffe359862eb0963554899beeb630f328f058328c7154377cfd3f1c 51963a34fad0f223a6f3cee7bdd8738e8fe266233d67d78785b5483d8a1f1f1d c5206465b30c24fe6e6c9074f88a26433c201206293145b62a7251b0cec8b2d0 df778c720519f1a20038ad5d741225dd875305a57c0ceecd591e770f50433d9e 264c8d92a5ec96ee64633cb9ea6e1e78d2f36b3c6b8081d180d5bf3496a63a63 952a23a231a826c549ee0492880f66316b263eb19e0765e2d00c6b247502cc25 94f686c50243d57ca88d73350c3d8f7d7e9304650b8592c79666f306b05671ee ea214cc2854ad45a0fe1b0f0584806371a5f07fb29f395f1a166fc633e108c7e ec0c68234ce4b43108f5a0186be05f74868f6e1db85db4de1ced750e08d2200b f3b58cc0374e5f22233577ff54f245bd1afb35f1ff3659439f752af9bdd12f57 7afd6b1ce6fb7fdafa42648805aae290e3565a86d42efc63796d1f3333bd8168 da88fccc7ff26bf850c30094b5b8079752f66d55f1a481c7b1d6380b4cb65b59 992998a25e418c248a9142e4068fa8d98ae1c0474daca10b155bee28492f5090 92e8a485890faacbc8af919a060dd3cb301413866c613f5ca7cdb17fe1f75437 b3351785e19392b133c7e772d7ac39d975be43d417ead89e7b130b46eee90e4d 165454ccce3f1407f182e19c3bf8a6ab82f26baed5f3aab28d77cfdc3fa49fee 02f1c2047a83d806288a4a4655aa8f09eb8c8e372e359e03a30a20998e85487f 0b132dbcbfe4677e0ed991b725afef14571bbfd54dcc42dc48da 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 175 /circledot put dup 176 /circlecopyrt put dup 48 /prime put dup 112 /radical put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueXX 5000815 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6784decd2fb36dec8f 7478da853762e00bc9c52ba86ef50d222ff142abc18e4fb95b86b3e57d9390ca 86e8de6347bf7f48f93322a372c5d7830521b14e8fa0771961b027c81365426d d95d16b950e216a90f28ce806244ff28dd969cb512a23e05045e7b2bcaf7d6f0 ca8b51494f2ec0681bdfde60420628d9bce98a0ca1ecca9140f452a88db19a30 ed46ae881b098c843a51d06f9a153489357fd24de6a0c36cb5a9eb9b3b64dd75 18f83018ae7cefa1c12fd205df6880a705e28457af7b869a6dd28f6b37d82cc3 e51cba348dcdb34efb119b8ce5a996f15492b0f5d34538850a2c1b6a509fe5fa 015eceaf28b0223cb57ac422cc75ea5af6535ee85ace82cd367adcd086f7d7ee 37c56fdc061cfde0ae74f776bcb9aacd3e0d0629ac0f37be535623db73b9654d b5cbeab79140d5136fc7432c1e199a15b22dae7f4a5c8a89e39482d0f8723c41 a2c2e713d6b392703cd19bf94cc57cb052a885fb2e521120612c3bd50bb53045 487d82118963a915ee9abf76398602eff7c924ddebe5a424e8aa396900977af4 7832d84ddd1afdb005a0bf3fdfad3a28a6b45b11b083bd275b1ecafdb7b92302 df7ddb1dde8be65dba93d1c27a005f274ed1eaaf3dee9117da7d1f3d46b30e4c a7781557f9ac7a81b9b1123cd6b25d7a5b00ff61e3758e2dac0e8f965436c64c f5d837dae664f1f4cf97062e47a2edf6ed6edb14b73aedd3473e6c9fc36b7586 942a2544c4ec4e00f85f748a31bd8ebac442cc2cd559e525c4443ed438292712 e2f684166974db9a05ab41ef969895d9ff218777a0cf35221447a40cadcc04cc f29e7a3f932541c90112970294a644329dd7ece82d32f1f48202a654f7b882d4 ea7932315772398e1114494dc46231e3d80fd21a616ca8b40673937cc79d686c 8d450aae06ba9f050b26d8422b47fb35babfdb6b37ec650097c69c9eb09c85b8 c681cbc4cc040d42b93497dedf66019ddbc5ce5103c2d213ee30639b6d9adfcc 6bbe98f20c5fb5b41042635bf7d1f9f49938fe58e435bbb411fb89c88ab6074b b8f823b78e99ec14a41c9608163227b74627c70828bcc005938bffb4c1adc407 c423a7d58548f18abfff156c68b4740063494623061685229a1c994534ab5fba c362e56bbf04a85788560e53b7afd38ab9d3b55fd571882b2cc3305ce2c01c95 54b78dd5196875c1450190c9eaae58a7c150fa51a5339399b768a188b09d177d 8c17d9d56745574cb09069a050ba01a0c1c3d276ed681549949f936c292cdc58 a68debab29e779bac9bc1ec8a43e307dac4fe3 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) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 112 /p put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueXX 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 f1b6fa57a9b0a2440bae0797790f91733970b16e742e6341d95faa40c583dac5 13a84eb181d2946b5d0075f71db8a991dc1a809cd3cfec573514392567a82e75 946ccf6e14f4a968313b3b6d727c83018ed58b882b96db208ebd27f7d30ffbc8 ab11e10a0f81425a62bdf7eed9f618c746103dc2d1c3e1f37d27083f4068a30e 099c92685e320266ff8047e81140658a63a6b52e4cd63e95d1b83fde2655d8b5 7dc0c494c0f8ff83dcb169f698180aa3af44eacdafe3c615fcea307f3fd88d08 f3398c5d9c7d91ec5b371e6b212b4a84d3bc6e0524cff6ae6b96747f61db355a 2e015eb6841a922466889f22e15ffe37925927f17bf0f427f2adc5cb2a8c03e7 01139846f4b21ffa534410a785a07db36f40228fef9cabbec348fdc0a697c0b4 eda95799880d4ad5f891e8e2d9c0b1576d7787cd3a5091814ddaad9b11fac91d 4302088380de1560b251c307fad523cbd5ef5af0a35f335bcbb7616b8ebf1d86 5084d5afee180c3ce52feca1cda5bfbba7e494c4aabffb89807fe05cc5edd133 e6b10efb5acf801702b1dd8f48cf66b315b90e1a1f7537ae9ffa2b7ec0635021 514a10214140b6b27f68d034e5cfb030fd5892a529263ae4325f6ac82ca7364c fc82688cbabaf07484a2c90a95630a5dae252cc95de9b18dbf765ab647cea950 56eb908de30493b3bdbd5c8358e5df9d3deaf4e0e659cbb19f3a78753f3cb8b7 5ea90ffa2d3f306ce1ae95958f682d6683ed769f8a82b9 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 175 /fi put dup 176 /fl put dup 82 /R put dup 101 /e put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueXX 5000803 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d43275929a6669eca687892476 7868f7357418bea5258a0ce230bd4a90e4c2449c1bb0b09a003fcc1550cc30c0 074be252faae7ebbb4540870d857f3fa917fbc959e50a1005453d38380bb2050 ab7166ae895122c76d0fe468acb4209a6a4732c83c7b3efd4a48f01a0095a944 70612ba2a396dd6f90875a7b48a6806c6d7b781c419e0404c494a7531556efd1 08e97e770410e56fe92b45557101548925cb121fe6c80914681803e6a43f603a 7a5a56dc73ad61f0e07d23b83519d73df4bbb2095c0b43c63ef3839135866235 3fdc68c810d53b36757496e93e0278a3e9ecfb064693408c428ccb882e25cbd8 0a6816f0f43d82cd7e7f65836756fd2bba49cb58c838fedcbd066007a0d05031 7bd08ed1ee6852e941da15d26b694f786dd9aa403dd448eb7459c1f1be275dcf da8d9eea3ce8c4590ffb24f7b35ba9486d675c2c05388d903335b7ca38d54a8b dfb43f0aa7d4c553f962fadf9f7515bd713d93bdb45e1917d291116d3fe3c7b1 7a0303886591e6248ca7862a83feccf080a54fc9780f848d95bae09126f5c52c 88ff1344328249a2bed8726f05890eb9988e69258044b9521bc6a56ba837d06f 28f244e71c374e76aacb5c16a0713c104b38e48a94bcaf268f27a90dc7bcd5f2 f579ad458fd22ce0ddbd9aef2cb40cb76686ea2380f985ec361517d0c488173e 6ba28e55b37c3dde4ab214f8ba90d1c86968eaf684f58125d056be4ba1ffb276 aa5910aa52a1f27e7fdb93db1689aa98404cdb94185ff6e3881aeb9427d41231 b90246e1d3e0b229160fd017197b75052f46fdb53266bc9cd275ccfdb703409b aa3554e863dfe7c5f18e4857576946cc84eaf43dbf1e7633b7245071464f5e74 e8be65b252244ec46133761189dd1a343913e74fe0d52e3182e83327a1027604 15f75b08f24feddf4b39b2a6b3902cb0eba3df529afef14a0bb37a71def309b2 d73136e9f75e3ea980892c37e526dd45cd7350a5d1d4a4d76dfd91503b2f40f7 93380bb2c6ceef89d6f67cb947b531c13b55f75f3df34789dcda20e1f3fbeeb2 bf38cce3b2e6fe501c4a7ede470bbe768c7edc6c9225a639d53664fb6f5fc000 808d23bcc8cd7f2985c05f0af2942d83c748a382215cd0af7530a44f5c94f8e6 e20eebe6d7a8878a791c94aac230975798893870a1fa1217a5dfc96f0c1ae22e fdbb1883153265dc7029ddce32c5afd50e624466b67122b8d3fa115014e4c756 5709b9d434fed50320ffdfedeeb5c0f9cf4597d5c87907dd31ca19e89fa8c573 adb83c6bdbd31fffa4c3225e90d249230246b6586f6478af4e4bfe37c981a03a 5de521685aff2b25e1ff684f594ca46b367838ec9429274c1c787511af0abad6 8ba2c29b38d4acd81dae9bb4977353fd43f53d55ec41ff84054aa6c613b6d576 2596d2766f60fb703d42692c42bd1dc434cbd00332f4d03babe8a7b09835fbe3 a1398c0fbb015898ff6cd34105e5e810fe1a9c712cdcd3fd42a396026e74a249 ff13bdd090f3097e667dc3db02f880c512420eff4d35fa512ddb95889ed04c56 b93b43d3e197757ada25d72ab9610afd1dbff3966adeb91d2bf85d39e15e4d47 4bad1ad571b636158e4b720cfe954079a18f99cb579015bdc1a106e9cdd5c38a 94810cbf4f6682cba709e2bac24e7b3fd5650846c9c6ffa74fee48b4ebd95bb4 260c6e23b5959447eb757c9c418dafff411d489e2de970d170c379c47eb075d9 97adb2c1393ef0a643b9547c7842cd937c152f6f49d567aae88a7cf171cfd67b 0f22b2e5580f9695570b99 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 175 /arrowdown put dup 176 /quotesingle put dup 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 56 /eight put dup 105 /i put dup 109 /m put dup 110 /n put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueXX 5000788 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4a71813d2ffb26 445026f89b4787516ecd1afc78f8bd19e91e9ccc9402e8c36d2449c1ff850a8a f61165aac3fe931332dd28e261b91b05edd18f44ea7d58a8f35fe88493b64aad 6bfac3a0136215fc2f4ca8e91d70c5010e6f4013e6d63b44f6fb00afdbd7cdb4 5ec5b1d9736f45cefc8a0124b815987cebd81bbe0d44dedb2d5ef37923b3d551 abb6a1cefca7868fc7bf3814ef7d7b6b1ae6e869cb77aa29e3d90b12b0dc3ff6 ec945922b5899bbf2f12e92731486d2ef1230c528bf8d7e0ae09ad7632a38966 5963de49d1ef3d65bc483e4a577b927c940f5e121169ba52f6576c85793e5fd7 7f5863c488e55bdefd5d8b2514795533aabbc12e7f51816c7e1484f1c441aa9a 66a5dc77158e79cd6692d299b95e8058b35e771a6972d2b5eb1cd6d2bb8e835d 361a6eac0c90c906aea1cd75c4412a1339dc1439f93e59917311bf20af4f2bc8 bba5a4626f75f28a47d4595c37f4019df480d9385975159142618e22e964f019 d88125210e2ef21d65baf500adf802297b24eebbf4e93c617a613f856bd0d45f e17a9480980ef83950bdb8ebf208c895ebc4a7132f0765b7c19a332ebbf8a3c9 ab65063a42e19ca9d43dec3de7aba46b9a5d24fb93d615c0a1726ab7e31c378e ab77150858535b91362ab0e2b968dee1c539964126d937f9d4980ccefa92bc81 b054996a65a13995c9c9d819ff05511cfc89cbfe67447c940405001d61be633b b771eff383fc6977ec06af30f981504260de7b9ec97359974734f495ac073935 fb30e3700679092ef5d971b6b2da0e15960f2391fa6b63c33e7f56b4a9b86951 1d3686a5e8e613a69a0add8b8c73b127ddcd397a48d785079e786d24b0e21dc3 7581f78d4e85fc184eccacce639ef264b5612ac30ad63e948779c9a9c60c650c 184d894dd59bf94051eee070cd6d5bc7ac353fa523c705a755b5b5dc5521c99a e8ec90e023d0a6f342238c87e2e81cda8a6c62e5c4858b18c67bd6c24d3d7f1f 08bda03868da2b79f2d3665df3b0286b94670f760308ffcbd6ae9f29a7c53881 492eb81fab9ea47f91838e0455c1b1a6c1a8509b4354a1832c020eacf4f121e6 0ac7bdba5220e6f42457abe1a803dd5e68bee162649f844b751b016e350fb5ec 2bd92a7f8d03f97750006d5cc640120472ace1d7fccc61d1dd880a6c5224a896 1f61b56c45c27287c73d84d88ab9e74fcaf9e29756173f7913c13fadf9876178 2fc90b9d338f6faf665743110ce38005f3b743e06d9dc1b67131862ddc316543 4e346999cb309b2664a442da54ac0ea224c25fc1c427d0a06c6b0d39fbbeb10e d91737aa8988494ada6c86f4e4958f574d9677b7397501d2e878d11080d32538 96c614b99745be2e76ffe5d8d4a7b8cfd67012915bc41e237c9c3cc34c4e033b d4061c5dbe4e317d41f9b73f04b327894a55b41ddd359b92800a8a47bc2aae5f 8c9287df1509e39d7eee06b861453bd571b3f7aadd855cc81382fb9e37736c1e 7e55f6b6a5219aaeb5a162853625dbfd9300246acb366765b45b40ac7091b968 32958e90ac942a9d5fb5064755eba18521d2569fa70778c722a5df6e6b11950c 89dd72e2d6fd4dd07d6f455977aa1a5e6eb245d37b5be8075776cc1ffcfca549 3255565e0c0e98abd078da329c25cc6190de652cd8b8ae6eb4063be3cd7766b3 a5172a626be0713eb9a55a541380c3dd4f8d3f35637cf09227e417174059445b 8908759f212536bcfef256bbabbb4ca43863b486867e97e1ffd6e434a812f169 e18b39b8e51abc25eecbc67adad5101437e7c6ee3da3d5f6958f0e3f618d51cc 72a9c12851407b92510c1341242e4868890f0b0082b47bd0d06956f7d460404c 7d1d4ddfe765364ba80bb9dadc0b79e8b55509125b309071f89f58d7aa33e755 078a55092ecd041d96177e0e1ce2436b175655772cd7d3296acbde6e80076d04 1d4d9c5a3a95b0b93a8275f4cfc9f98578ec0a0d20bfae9130b04d19b2d53d4b 36e0c857f80c4949764d8691444812cd1f100895f215dcdd2dd1b9a85dee2690 a91b458b58beeaaa2168e52dc03c15e290ff38cdd9359f6fe63275039d19b9d3 cb0cb00b7519acb815f3471d91e0273189f92da5cf4cceeea99085cb3e389bf1 8bb0d3d41155afa11ac6668ce58b6a71b3bd8d7b0b298ab816d830de4f3bfccc 4e14fd9650e78c4436b44e11119e305f01e8497c79be49757b846049b6bac4f6 ccfc9f45ec2f31299efa49a5ba436b34741a53bccb37b6f08a8c1654ac475e7e 0dc40be33c761cd1f2a7dbd4cb64f30982da9f19f93e7ef468bf66a43ffe9926 56cf9ad167bf4fa6dcaee7267abb75c9083e50bc7b68f8df5778df4da5808630 8b1cac011ff254129949c915877570a99f93c7a42b9fb14e5a96bd7e790cc9ba b7afa6d5b21f8422336d49452deb910ae9a8a9fe6b819f82fe9bc58c165e1c34 e318c8d87eaeb8bbf2c678574b6e74aa358cdbe8d4c88934901ba2939ef1a38d 0eed8d6c894ac11653fc5bb7a8cbae89a2030c7f2283777db453f0a4d8a4354b cd56bb7467ccd806d15a64ae823ba1c00bb0d5bd684a5deb74f2ec414fde1514 95119637c4df9d014ae5e7114104d6c25c5d04c2696d0cdc359fd92e46c53302 b88711db761b9a62ddb559fd5785bfa44f5ff6b33be9f8c93157676893cafc35 361d72fabcae959851beac4297f34b84fa34dd2a3ecd5aaf29f0fd40c7adc86a 599129bf4e006f0a588bad166252193f4d8541df54102c510c13867de94add6d 5eed95862b9259a7e735f8d18ef1338824406373a8e57d9ed8f59a556ca0c461 1b39d7800dc6f288ef23bf96a78a21295fb4bf434afac986bbaef9c0d955bdb2 f4c8a037702e4fb92c794be9fd2cfe9d3b10ceff56b1d882cca8d85a034a9d6b c17cd4e7d9e8c5c980cb7d6995e445e191da51f754e2fadad01e4ce607b7f8f4 5cac9bd64e096f24ff16a44e1a88e43233caa04cde7979db1af9c8a7a050cfbf 1dacfc2f62373ecced938b75f5f970545db313322d84a93026e162acaceccb9b 46423ca4cdca013e62fa7f824b899f18b52b6a1045c84662f3eaac75395fa966 1126eea489d59da2986775ea7de736eaf0b835bbff2d41f23b0bc3f478d6324d d0bd323425946111b8849a37f5c7abf2d214a39ea5dac74311c37ac08b047d83 28df18dad1b7409d46c8190681902ae432cc5796494bedb74594e7b632ce20e7 8c8a41fff8a2180e59880f0aa3b25513aed01932878fd1333a105c78ca118c8e f2cf36ef5a0fa1657ee0236111c305af1e56b1508c1749277e43ce15e7c0b138 d65eb3b6d8fefa6c2e5b61824fde7239e2c1e2f431e48885677742872f451f49 dd205114d47a3638b025e1fba192ed6e98c19a148baa53af4dfb4880fe4b2927 5a2c881607f2d39732c865cc2fa9e03275127fc5fa3fd740b65cf92e205d1d0f 3dd3f7f842 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 175 /beta put dup 176 /gamma put dup 186 /nu put dup 188 /pi put dup 96 /lscript put dup 100 /d put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueXX 5087380 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311e252234d51741e18db3a68e8ad10242 29e5817a10e796a78d2c7f7c1f50961b9a57aa604c9f821dbf5a9295197bc666 31678d7d2c7e1f8f2151ce0c29efce46270570f4301c5dad1b38884732e53dad 05dfc36b020e726ca575f71f04abf2b49e1f1d6d2a08a477658ca9a48f1c8cce 14382f0a42201de56e2821ee2b0e91a818b1b753d810ec2428dae5153b66af66 9442192024becf743a8f6264a58a0b3aa823510a4957d1bab3e1b83135362888 3e392f49926471a8021fdb48637baf0abcf31204b1b214f48c99f44af7782323 69d772ae4f49be53a1bf584747bf29b94f530d59a5be5370b8dd0691e32a21ba 9d0d592cf3bb50a99a3ecd18d6c4114cb4cfecc49705da90d7edb10e3a28f9eb a49347a09d31eec896f2a28e9607d99d42914aea16545c16e136bdd0b75fe486 61e24c7a9e9b233a76754c760822d0a88c575e08ae3e3f081d7bfb80ec4c03ac a08b65fb6474f71fc95c7c2462f2eb3754e647c29498288f2ced0bd3a2bca5c3 2f80a61fa667802d376cacd34de1f9572d1b3ab09d6f352750db4a768f869638 a87457889aa502850427b40e1294c5ba33e6b17532b2d13b5f50e71582f93daa 231e86597872a2a968127afb0f36257a76ce1eb24e6c4f29fce2aaf6532fb5cf df84da03f03a45b915209f67d398c7c4f7a3b0623750259087a478dca684b29e a8b7f52060bae9394369ed1cecc645d113cca3772a8dc36c6d916b5c5e65454c 0a188a33395fd3da67ad0a31ddab6a8434dd80f0bd0ea1a2a62eecc331d88b3e 369552daa1c575a98fe84383548626b65be7c24ae7eb61159f149872cfd87cf7 6c1a7c155c7186c7600e58cb61b8cb0c5dea98268a39e928bf6fc53985eaa763 2b28c1eb3d82e4d3fe225223f4266d2b6147e344aad2d4884a9308aadc7801af a606838925e3e50ee7aaf73f090baefcfd4e34b795cd92d83c944d91a4940f2f c955d727ea5bd76f0c8057b12621eceb0947b0a5dd10dbcbc52957dd978d7db0 c794660afdd4e946b3d7fc1ba60907fb3f756aab0406c0e7bce5a2238fb3e12e 07e2c0a7f465e90057642d704434ae0b57bd46c8ea91ab2a386e24c6deaf9cb0 8cdaa8fc4ec3fadc06bf28659cb878453db16f4b03925b2127b83be8fc240f33 23ea950b51d70c8fe861e30c346efa0a0125137598caca5478991e35f5bbbc19 4c787488ba339830bca15f8333431902e82b66a514a41c0bff92719a6a0d9587 4cff62c622fc61a0308a69f9fb7ef51bb274ce9e059c04b64e817abdbedfdd61 297ff457627f7db9b97155c55930bf854013c20a9a321d830157a9d91be8ce8b 42d95616724b3e1344416e405919a57d8793b600d6f63ffba9afc8e02f9ba556 41cc9031bd0d6d2b5316f96a6d848500e87501c7281998ff695fc334dd6da803 ce9a077c0201168e1760ffeeb644138fdc76c242eae146aa942726bb4db1d642 1bfc5fe890f4d4734c9d83925504217b7ef59c6e96488832225868b440c32b6f 0ceea0e4d90abb91ac76f190a39b93faaa17a012a2ba685837534b3689c0ad64 da1f705464ec7c553ee5ac50f594ada8a91409e66ccd02f31f38713013fb7a89 746bf5f7f688f116099dce741d29eba1d43061d74ca69cb50b2d55957f320f53 c16214b958e26aba2d5045fe1363ff8f894c249adc60d7e0993187891669ef55 67d57bba974243f43b839e12d4487356689774d63c4706d7dba357bbb6e8ae16 573ae56a1699516f3c8dfea5f4b4dee303f16b23046a77fead3a9c7bb6950beb 5651354c58605f2b9dd7c81d0bbc7e11d1a6e6285729614d3bbf99c123a4a0b2 f92b996c9ce536420f66f3e7519d508d08e9f11321e167f4a5154019a2b0c4d1 ef9c68f1a160e98474a861dcc4233c47ef4ce6ea74576ea5cd6a810721ec1b7a d58699465be5f44226f2eeba8f6707f32a50f8c4312aa6ca60262a4f38e48b25 91857f843f1d4b8abc276677a64f3b0354fb5edbb9468328f87bcab9cb98ba88 c58b9e225cf398906cb54cf3d4d6cb36f7963ca7378431aaafe330d3e96dbaaa 4565afc4026bdbc864ee5b935eb436f03d8ec4e5e0d5968a7b5fefe89856edaa d777e9815c8afd3d5444cce940092f6e34bd66945747c980649770e6df0d14e2 542f838474ebc459ce67b591b4a23500af7b7c6fd21e94f22cc58ae942eef66c 62f2e0ca52720f9defcc48f07db48c4f10ce6fb4cdb0ba54dfd1752e32cc07c9 07f9698ea51bd026da7d0038129c80840d822eb16c1561f3a67197d6c1366f95 a2226e97ef9e815934cf0a3317287c459e4b32d76bbf2cc5b59d33c3e53d98b4 99c7c4818445008df99f94a12c8544a451095d22b9b1cddeaa034d39cd03ca9d 249777e83367ff485134bdb8bfbfbc3dc5cabbc3879769ab9196771b32fbb04a e8c8169393c270b8248aadb98fbc66a3b7677525990839fd24391910ab239bda f261af1420619f4f2eeef975d90353afab5ea84e23ea9fdb02f0b50de033bdb7 3deacac7d8bca0e56dd46ae1e729b835cce09f256fdb1b2e705184d71b1d9100 8e657cbebd49da27c2bb28d5192a12d00b5ab744f2cf85ae067f30bd1310eb1f 9bfe7b3dad26c07fcb169fc12633c1bc73e1e6240b217c13db44941b753c6158 65e17372fee1a5dfdaf4e35398eb69554deb88e0c4e1afef0096c59b70bfca39 bdcff650e88ba09a16a52f4b6748633a212e291845a5932f7889c1c77b1a774c 7db4be30314d44c1c24f484ff84d9acf53279099ea05ce65c009dda96eec3df2 c6a0c37d586d3ccc3832c3479216d4cba04bf5feef498364c481f537c49ac803 88a83b00a326f2bfe6fc974962612144d1f64c46482f48bcc44f34318e456b59 0498a54671b49cc7927d7fbda8254c359e415f9b012c35450ce2dbaeaa017d76 efa7c499367db5ba2cce66083620856d05001c110c39972b50ac044ad5c08fcd 0ca44e2edab9d4accb3a2f728e6ebb0ac97f9cb0d740ef4dc243d06029cd5332 458515e4015f0576aea16fb6341ca2f140f6af6c2e8e7eb20fb0915f4b20dc37 d8e40a48176ac28afe07017c935ad8c400790ab305645df8b17b9c9559eafc4d 55403a74f18a6040a979cea52de5cf18fb8426eb26f32bc9127bd30e3bd3c276 4113db629dab716c82b1bf67a8725bec4115db96e18dd274df8bab7ff46b9e24 5b83567b13263e2672df1c948e49b24aba893a026850dde9b024efd2abbfc0e1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /minus put dup 162 /periodcentered put dup 164 /asteriskmath put dup 175 /circledot put dup 176 /circlecopyrt put dup 186 /followsequal put dup 188 /approxequal put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 76 /L put dup 80 /P put dup 104 /angbracketleft put dup 105 /angbracketright put dup 107 /bardbl put dup 112 /radical put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b87123038f7859ead991bc89f56703cf31c393da6f5b9f255cee55ff15 21c2879219ae38967e0c9c9f346fc5c95e953da9b395357b7483a8cc041cf0dc 58ec77355caebd19519bac5c5782035b73401f7a3d5bd27ebf1e0fac587934cb eb3745dc8711ad2553af4316bc0bacb511a630c80594d0741ab596e70ac7ef11 b785c037b54045e7d2f669aa49fa9833ad3e14d9bd7d8f302db66a20a09f8221 5d12b04aee95ccce19ae8f5891b674164d03da2a24720ecc64d050f201365d0c e10db2421c0df4cbeb482a71b3dbf0c614b715287f803af0baf02dd88f526484 71792222a2ee63e22ce8194e246f46744898d4402a54bb0bab3cc27855fa63b8 cac59c2a588010fc6a0414a8c23ff10450fd1737d15ef0ed7281d9b0b7bb2dac 060e18cf1c9e284bc767f90026dfb43c640603b426edc7fe03a8d0616bbc27fe aecdc08a044712705dac12076ba25e2e30e3f61108a0711c8e4a7fa4651e341f 71ea3fca4c787bfc952ed6ef61b60220060625b36b893299ee341f3b4f2dc874 167732f59b9ef82d2daa65b49fafcaee87f937b2ea55a05ba4cb4a49f9431a9c f9082f2d665fab38045d2242676832b19302f1641ce060bfe75a490364ace7a1 189adb2925ded286b573ba4fa3acd57df803fda29fa51d36976f18fa0f391001 c964052cc6dc61756ab03a94d31c68cf039f1e6522adfddcd0cfa7070bc5df87 bc7e10657ba4eae1815b82a74abc5d0df304e1d3cfbe0d71a563e6950346ee89 bfb19d6efec12647f38fb2a0e847bc96a21afdfb8dbb95dd6004167821505890 863f52abd7d93e571e2a17b42c0879edd6ffc99fbe6f8f04a49a55c8f9c889b1 5683e036b264d57c6418db5ebc9234c6505cdaee2be3cde22f977db5ea310036 4c5ebddea6458205dd094163de5ca80d97842cef39a2f1bf11031c72b9a101b6 67d2995c92a58d4235d3792df64415bd65daa21b92e2dc412e59e2cd0c9e6c7b d867606e45ddb50093c3bfb538911b0813cd590a7d0693c3db75477fd9dc6d2b ac2058ea310a45a2ff40f51a1ac000f556c9da1e1569e0db5c7eb85bea389c0b ecd95f7a2e0240dde8d00770a36661647a608c85d32e27a25839b2f986c0d23d fda168a507e9b20cd6d98d3361dbf9ef6e369597d258d629907073c68524f523 1a5b5535db1c6fbbe7fb1185458c218f23532ee6e78826a50c200ff44e160bde d94c6c1db7f7b03e3ead1565b27c999d6298527a4fde602980d768b3c6bb249e 8f8d9145bd0de4c84a2a0055294450e9860d2387e3dce4f6d0f117740594bcaa af6f8bc2f28a4f8594ba6bac86db087bd94c13f30ab3df69e8ec9f6ffd5cb157 f2e3caa4d14984ba78b8b432794d1187eb89ed68ee06ae5c6f1e39e4d1d79700 f51c2fb694015d80f441473e2fc5d6804da5bc6e4a1165e7cf7cc477d3fd1825 238f47247eb9246004d395d765b956a0b17a0a321028d7e645cf6d3ebff2b3bd cc3e6ed397f383aff475cd6cd79f595c06569a13351d8a7c4044d32a945592ec a8456b827a7c40ca81b86ce0c64bb15fb2651799975854bc7cf4d816c288b4c2 7caf41eebcd175c9c6e2e00ea16519d7531c74bf51f9d9e5d3387d04193ba505 e47a0751b0b434bc1c677e0adf030af75cd6b6149eb624d2272b9b617e2dac2c e9d7ed4c6523079cbd7a46fb116788077b76adab0b2157d723670dd63df70ccc f186b593d8191af509fe6c071f5f3efe35f3fcb85315719c7eb4f70a6fcfd3f7 a2345ef81de09c497f155de393397161441762557e9729239b435423081caab7 9584cc3b9270d6af8c7d857a344cde09cb4597ccce400251cb6e9901a2b8f3c1 2a3a99c2cc1697792f34340e18a34bdcdc97af3f7a18d67a3f8c24d3b1a3d39b 13a07d7c4ff8e641a56475cdab90183a88c5498ddb19893b7ac86eeb01aea494 0476c03270f396d1f49e5d3200053979e89b475c588ba48c84edd606bdf393cf 75d116bee5ea47be89b756578c70164a6512fcd5dfc771e4c067850e68c8d0a6 53bf051838a68dd1a7031d40a347dad0144497789a101aac36b0b949bba67887 9524c8889c8155c4edae838f069645ef8291e7925bbc9bca30f56663b0cbb641 96d2added878c2ec0c501180a1808a0e7eee7736e91e461f085536052b70c198 d167dac69114b9c05d26357cd2d92144504a770cdddd90843eec2e467d2ef31e b0bc5f545997a74c06772461a74999f441ea9dad544796ae0e4f2a9880a7088b 6b1295c0ac4c0e7f5f0cdfc81f89bd7dc6fa10450bc12aa2eb9a2d7460531a04 e7746234de38d703a756eb4dc048fda94bb0c4056b57b144579fddfaf86ec4b2 08cf651b544db7061a66a39093c23cdc115f4e2649be33a8e425c98e7c281c7c 02552347d860dc49767ca4c47e4c52355ca0756d0fa91c3c0c31f2a8bf2b09bf e63f274dd02bb312f9335b7cf780c1042a6c5481162e4e2f8f98850309dc2f7a 9f394a8ede3784f8c429118ec619b19932006c7dd513cded5160298dd7949144 be32cf4a17960e3633feb06bda2738ab774fc27f5add33247c5dcf0ebb4c9d44 58170df771484f4e07d1dbfde854a7a6a5b2bb2024904db356bea8c4882d9582 48887b7fd1694ddfb784cc3188ed4b6321d409199caee8a9efefd8c8d119bf86 611facf4dba58afd39a10d3a99073c7c321172565bd9207a9f12eb9729b73e5e fce2afcda1733e43180c1fbf1f019e590e49e38d80ec0accfcad473ffde6dafa c666d6186db6191821d4a4714154a3cbb9269e47dfd9f05ff5f913c0c7d434ba fe6139ca2f0012aba90cbaee1e05ab2f6aa3baef85e986006e7ed95e360e2b98 644ef29d86779804bf4d62f756b39e961323d55004b27192226a3a8738ff572e f37c8cea7e416ff576aa501057e389909ca599bcaa2152ee58090f85b8aabc92 f4006e8ea97b6b0046c4084ae97c0b584faa530bc2d32b591f5cf4a908857fcf 49df36e5ae37a08858e96b0db803859eb6d9c351c1072759d7f6e1f4773dce07 c40c22a5e79ecbc4ddcbad21e15bcbf5b91083b4cd80da341a4bd03d399887ac 3c47550b194c112ac8c4e1c71a5376cdd05bb4ec99e209ec516807c5db14584e 52340d0a59faa150c9a343f4e72b588235a074b67048b5186938e803478f2374 41fb5624ffe6c0e4aaf649ad853e6905279d85eac67e11953f0c4de8b86463ae f0846ed17e5710b9cf4295b2dcaf6f5285f38867b2845e6de7fac462d9bd7387 d3fe3b7de1bfc2b315406c410582368804bf01198b6029eef8f053f545a9e4dd a48e8bcc4a2fabf683c1606281f2bd663d01aa7019780da7ed498753b7a929d9 456e71916532deca985e85a20d16f006f1f840f46d8bb97b2c54c90c37b06997 f804fd475b546014072afaaee3451810fb3661ed6547d24c86122365583379e0 ebd903207f7fa0755b5dd47b8a68e063c1c8c1638aa6f28ed5538fbdd79f01f3 b41b2cb30f265da95992a8ef491feaee87a02439a7df11c307c7f997e5f551c1 525881d8efa4f4fe7d62d46fe894f065e75bc3a06ee49f4da33290cdcf4a4c65 62 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % 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 (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 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 161 /Gamma put dup 162 /Delta put dup 164 /Lambda put dup 175 /fi put dup 176 /fl put dup 186 /ring put dup 188 /germandbls put dup 107 /k put dup 117 /u put dup 120 /x put readonly def /FontBBox{-55 -250 1289 751}readonly def /UniqueXX 5000765 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b1ee2d9de5f5346241e154574f14a4532b35968596ef7a20 102dad629475cf5d654585d4caac68ba7b2ff21b103a98af3e9ec01fae180804 26b73d62e93f0328ce7775e81898de587dd0fbcfe98934a58afb1aa4dd8c6eec d19373ddd360a5e85cdd4b752b2f2baa13b48a282214a05632d28e915ec90824 21ff8f2166e940c7122c583f235bfd098f8aac0f1dbb9a625b02bd889869664e f1856608899ba509d6eb8ece665afc34a459dd5b54dc7711f6f04a288214efe4 53095e239bf19cd36b7028d46c07a2b8c17d452d8563ea88a3bc5e5ea29a9ea9 a7e38481679f893f9e6a983ccb5512bed4aca5888793526701796b3fcac0fb62 f69c66d0688eede0fefd590fbce954b2cdd2abc9017390077a2cf6f6fa7d0db2 dcb4b0963e3dfbf02be1dca9cad104f3d29495d19337fbffdd745e1729e7c0a6 41fdd3bf42c30d715670b3ade44f481d795071f1b24f4f03dff59d91bf9d678b 4560da27ad826c9fc8f8cd9a333248cb2007b4ac0a9e2d5c044774124f1ee23c 0e3e005a4a16e1d0cba15797fc42fa75cb45b24fcf8a8cf41de8e06388b5f995 04454646c3246074f495564cfc8ad75a949cc477ecf03f0511b90b6a7456b730 cf09773b5544f6ec17a9a179714e47e2eb1142d8005bd228affaa375eed7fb1b 075b3023be6386f3805aee05b47c7f370e8ad41011068687c6fa7c2b11d42ba3 1ecc8cf8c62889c3fb1f8f9c2ccbdccd2416d5690676bee515ef20362af7068a 8c781216a819eeda5f565b69a9befabbc64a4922496d357b61416d785c42d2e7 08cfa7baf4f3eee660eb4775caf210654b0c56599a8eed6f14b5409b734f57db df65731f1f2fc467b9c5838958b3bb1e6077bd74f44b87d9d51ed2be552ba31f 8313156cb711894bae461f6bd83a19845e51f5cea0b4580e9496d1c1e063a649 62d4e839c828fe68cbae9ad5cd15df83fc660bbaefeb4dbd720e534095a6e71a 10ca3c66c2141781fa72d67beb4a3c7e5405d5710376155d7a0573535ebcf5f0 a961ec9af7a50964d386a66b1cedcb0623a58166aa6f4102c21a315ee27ad749 a7367180a2d9aee6dbf7b2b524d6149c3947db4f578573d19a57a9ecd653a424 5f6a9dcc8b72c710f93e9e67a3f07d6fa376957da6c4b63013ea1549983ce57d 7a1d83af80912d8e6982801d67f93600472c497ef6e27de104fc4223c2ff3f05 f9826e6ab1364aa7839f5b99f816f2852a52e6cfe096c25c6941aefb19f2153d 03514d29b7d4da8429d8c42edf3fe99a926bf9e8c91b2c1cc17ae7a7c9320d9a 507f180a623271572170bfbf440042c26f84cf3c2fe5f63685cf24ae42926e8a 59d1e207b0722f34fee2b4bb0e661e630119e895cf714c9719d01ef19f47bde5 574b27f44269677fdd63a7d30a51ff0552c01438f586bd4d33ba6df32b60a3fb 9d7a4e7d192c420b7747f319f119d215564715ec6ff223465637ecc0742d5fee 2a6f88b85b7257d61c39f7243d400bb655d9866ca722739461130077c7c706c1 4d4a3f704df0c76ec70d965810dd4ba9ad7d5b652b63f6f965ca65a9deee9e09 b95d27eb8489a985baf367321075418cb5ecfb06e8ca6a320d001addd4517cd0 2d50c3404efab9ce466422c7d5e5f86e61fd63525bf786e48efd61927ef1e471 029f3aeb24f9d6bc00ebd7298ae26166ed3acccc28312dcc6aee5ad09413d86f df4f816616b618ff4034b9c283461417e0f2f3e427f74398606233cd42d5fecf b64ddff2c4a2a83a7b91e57d0c604bc6aa5c88a3a0e71dccb25591ea586ce496 103d97a31bfa99015754d5cbf1d57f125ab9ff30a6fc4fb2d769680d4d864698 2bc6699ede313a082838f1bd21223d25515b5fff70c6913bab1e08e144951483 293760c3f3e189294c3e0fb6b5190df11b58b6ba5a588e63c4ef6d9c1fec30b9 f64a3e01cc6149bc8cef3c370ea2bd4f2782c6aed3bdf26e6ac72ae2f65caddd 968c2c566b9bd872855312954415966a616b47901a2a9579ef7124d9404a5feb 99177344022facd9168b10367b5e742cc0abf1755e6cabea18dcdfb324d998e4 3fa48f67a234ebbd02d19f03a77049b03f572b7dbe8e8a8abc4017daa8705d5e 2509218ef5a758723a8089232392fc40ba6c3fdaaf427c92b9f3214f4c128e8d 049815aaa398cfb989989806ee0e7c93ace83693a8cf78d5d6d8074ba939af5c 425a2cb1a3d534a83f33fd885aea1dc29ae7a262c298ff4f5c46b37d87c26846 707ceeedd90e741452576172aae219a3a4ecca4f18f47186e12ef3340fa05ef2 8dd467e87f2b15caef47d5883400ff84e978c2c0f765e2b55c7c4fd24b2e0feb fe7293cf2101f2bd9b0eea38fce9bb65f848b4774583aee459647615db710c8b f45b74f9a6261e2bb86e750c947cb1e2935a1d521f4cfb51468ab7bd0f546a3a eb6807fe2f63fbda9e3f91b739f957788928ad1874e5a4b09b209fc5b788ae66 0ca57da343aa617da738379b17dccc953eb43b812d9d2735aa5059b43e80a36b fb9650304fd99e40b4993688e725f2a47f2287340a9a269ae6ef57a2f3ed7015 80489bf055d88f45a4e8cb95293bf349dfbb45508cd68e684ea5256d438f98c0 5e3d71ebd7cb3454e0355cd608b46408daed3d12612be4b7f5be89c2280da3f8 33d40e51e73ac86b470d059f55d0c4234c8ed94434f7c214cd8920c96c96c508 efef29d5056929e547052fa75c24dd7ca9cc067dff543526e687a78660dc4b51 9b22ab1d419e0ef8128b7f507f367ad5857b41247179d11471d1ffb34be57b62 39f808a211f435fa0d3ee776cdb2030a4faa1026e0fce116e35ef98c33fde2d8 549d9b14e040ba25308dea1d5bec18d9d4e334c51679ce76c04be0ad7603b8c2 eca8bb8e88d3e2a9f2b8de05245f0ac98f4ebf713194ba855c7833c894130a91 95c24c8f470d94eca648747199fd8b22492c81245c84848c3d2fbc990381e94e 81bbce458b6a68af83dac8786714ec24d6b7d8224bca935b842bbe8db6bae4f6 64f9999b2d35a5608b2cbd32ad64661dbcc41bb8f06a9c50d99cbcc2d00e6838 5fcf7eda5bf63209e21dffd34ea2f86dc6430117249cd12deaed2d8c342859d6 f7b69c2973d50bb7ce83f870fb70fb4b10da78f6050d6cb7bd3aea475f72a0e8 1b092502dd8cd3d93b27116b1e69698d650ceffaba2be0858bc9f22fda4cafb3 da8c7b6f76f330c16eba0012c67a9d9d6a35e576c784b019d3a3fbafadf74551 a2529d1954e14c5589311236b53ce958294a1014f9cf07660d60f1bed30fa643 db28de9d0f5e965c27335d9e0b4617dd6bd776883be4a3f47752dc0f78eafffa 9c89a81b4bc22ff14ca97a6ec9221999437c3abc6f2dcf 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 161 /parenleftbig put dup 162 /parenrightbig put dup 163 /bracketleftbig put dup 164 /bracketrightbig put dup 169 /braceleftbig put dup 170 /bracerightbig put dup 175 /vextendsingle put dup 176 /vextenddouble put dup 179 /parenleftBig put dup 180 /parenrightBig put dup 181 /parenleftbigg put dup 182 /parenrightbigg put dup 183 /bracketleftbigg put dup 184 /bracketrightbigg put dup 186 /floorrightbigg put dup 188 /ceilingrightbigg put dup 191 /angbracketleftbigg put dup 192 /angbracketrightbigg put dup 195 /parenleftBigg put dup 33 /parenrightBigg put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 112 /radicalbig put dup 113 /radicalBig put dup 115 /radicalBigg 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 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fe3c35a5e4206f60b2b4f567b948f7ac54e3ed16b58e137958bb0c141e411b c1c47810add8abfba9f5ef95f96d064cbea94293bf05dc6979c6001553e168fc 75fc6cffc105d3eecca34913cebaad61f3a0949cc0c6768d5795ac7405b64118 0c28dd9d2fbba6debe3de789753f299b268de623c58dd73f912c935c525fabd5 a8a45699842cb930cc3a9fc92d950210de61d71d4457d71b3788acf2afe5ecce 8ac9e714628742820e52127239253ac17b853d8d03e0530d0f53ca9d2e0f7830 daa082f471eb27eb9f2b2f4b06aeccc1b80c0895128e0724fdfe44d7a47e72a1 eca3df3411b50056b6811b41d513597d04f5c2ef0794c38971ae5a662330983d d76e5bd67dbb1836cb7dd48bdb38b59309a82edfa5e1aa1a4ab74694c6d1975b 7c73d3c5be222139b25c7b2ad2f252004a7f1f092028da2845ef8fec8e10ef4f a24b69875b40fbe542e3a8da32f8de8f686c191989b59636f56d596d83735ddc 4647b7cf8a3666f02fefb4f4191515edd0fbd12a8848ae29a5f27182981e0da9 6f8d15449cdc7d47a0b331e29157a8e7265fbd4ba59b316889d764201e67ff81 e808a12bf2f08f4059721c776947462aa30a2131cce0fd37245f6a25d781aa7c b497c37464e28ab126832fa9021e961d42874e4224894a21ed10e768032cf471 616afb23741c911eac42df462c932cf5ed9206de4f82d77ed69476308659473b 014a0c6b26dcbec4caf5a9275f84bcc07a998a321fe1737b6293c685d6f38e2f 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01ecde4ab9b59649d58a532d04c428446685e44ff3dedbbf790c092c0f790efa dd72ac15e1014ef60117d275e65a12407cd7455fb68b38f051ba44a09a320dad 80f3b2c5dc63f60bab775a2c7aa186d413a34db4f14b476d83b442a72aee85a3 c66c71be9acfbb49da0188f162a98c251e8b4079eb5f2ad12b6a384dd7a658e1 2b178d2271104e2e1f566bb84ce8ca98a506073e5bb6f12f8fe273e063ea09c0 6d643b75eb5b2da3595127559ad93bdc6f18f0e722b9dcdcd6cc3ed882a3e6a6 2dfb1bcd125f347d5a081a3c9842fa405428fa0c32137c9db58bfc584d86523d 8fe76ff09023931225e898007a91d711246229c4473a7d9d6973ce532f017ffb 53281ccb42b0eb1ed50ff05e72c7a28e96ca267f123c99a3f2c5d3190ee9d5d8 efc1cb6d21da6f4f7cdebee2759491a77fb50229f543d5346ae0ff71443a2027 4dad48cd97d1d66aeeb428eef4decd1ae4f7df261b7325c3f6c441194ef27254 f8e5b351d1ecd2c0037a383399702066dc7ab7285d43ef5793f19d715507dfb5 415fbeefb71effc1c84d54a2c290ea830cd06852c7290f958156c12b11c98a40 dcbcb2e53f291a11ea4e96b50f5afd2f26986f953e393a5226d1487db8f26326 918f181d2cb3f6dbf35fda53f1ba66bc9afcb86db61e372747781f2741d2b0de 4f0577b052d8b8d285ed1afc553d66a601d6414dfb9956f7555f3419d09e8590 cd344bdaae1285f0b99c5df9df04031281a53332604b9bb0478612f3260e40e3 05c24ef4c172416733cf955bc26c149a900e4d820dab896ea1ef715c9ae01b25 705663a31c36f1ee5d9ce407c2cab6afe897e799175aeebe372378a1768b853c 4336aca21cad7a5bdffa2a5fbb9d7790c29ea30a9ed62edc86f71a60310fbf32 1b9feb56043a441c5e231c7bc3e85fa49c8332034bc29a1a89603be87c5a7310 6c240fb2fe1d2e763a4170568edd337f6185226f9822dd6b279ffbf6ba42e044 215c25f69e2e237d35e2b15671999b5c68bf483cc42af44e9c9cc7d24af1b5eb 6256dae363bc2beeefd95f06d4e815ea541624d9b8b06482c8356f776a6b7325 c7dc711dfccd4f7fe7a124be0283147de6b63f2c8856edfed1180836f61ddb85 a24f3ed6137656e931cf8377cae83f7fe3620274bd47451fc7cf66ab04b65831 e72e6cfd673b25003f27a569b6d5982dd31bc6d2be6be6866aa9bfa72cc30edd bb494f59f3b568b9e388d02bfee19ff678e5b7a96f59642ad0350d8d14360d27 85e29b096a202786c3ee2a73dda45d7eeb3d2d3044c93d91b6960f4759756d83 a13650bb5c76d295eb8ff64d361a2bdd8be98df22b363fdd56fad986a3b64209 11e61d55973231a27bd7ce72dd2a8a4bbe4f90dd0d6555088d88ee69308b342f 3929b1aefa098ba1ad5a820349e55a3b1b3581482b5665d976f16a485a480b9d 225d65c19f205322138eba9070ca375b49a4d9eb5c967e386db5d40c11fb6bac 16ce9ff087bd5d13723dafa2a73a713d3cb1cee8a46f90dc1010239d7945dfc5 25f8d5d4c3c7fc6420cc93e07a74b5082b50c3a0d5255624db9580446dbe68bc 4f909bd789f997dc83e0f19a3423f871440183c10e43fe51906061d035632214 90af3d34facb5299f9d81f8619689900420a75c369e13966dae0fbe2ea38bb9a 67b09f5854d41fa59f6a600ca70555b8c64944072ab7807c4ccf0f9ea5f3d3cd 869ec6c1840c73eec03fe41f1bc02d6472ccb5cef78f1c3dc45207c6eff8951f e72fc8aef2e04bd853bc04d17a5ebcb784a07cac6495f27f30eadd75d8cb6a01 a49d566a0b63c93dcb6b31647d8397c75ba9721bf3e5933142afd608c6d87cd3 ac34208d290169b2ed24b80395e5c72ce51702be3193606b3a1d5ffd014ef367 15b57cbb0177c17a07b22f9164468c1db07a3d41bb2ba6b0ddedc12e086d4c6e 7125629996efd44dc9310bd367b7d4019819fc65bc65823d104c31ed6f0c7da8 cd49adc7b9bb68e724848fddf9beb73e8f335bf19f0f65db4f79eb5d4af08bd9 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b76e5bb4405d2f19ba069d7a83457212da82c7f0ec4d11f7fd15a0a3f9fd5e7e 36def4a98842db1e82dd5a7e19a8f14b2cc2a7324faa94f2e4a901b08ef97bbc d8de1c0b5dc28e18eb5be0e6df9a561262107b2329c68ac6f115d59e929d855b 9f7337f3e96d393b9b0a1a86ccb69470fe390fd8720ab95cb230862ae815a34b b13fa07fb88daf9e821600861ecf8f129eec05d9e1bbd98bd28115fa99f4f66c 7de311701b8364d0e6f36d6ac3b40c6bb3cbcea358f2d65ab8229fb920ffd203 3ee66a8c83496ca53d2835abc86c5170d24fc9e10344b88ab29d4a9a9c481531 e02271bf3f544f27e7abd145a119c09cad3282dce06ceb86ab308859bcede554 7371a0e28107615890500c57ce06639b976ab3000aeb56122532561e81175264 7cb76470db1d19a96fc729abb036061121eba3b8090aaa693d5a0ed2bf0439fc 0b6492e1b80886941322150cfa3cfd9cc48a663a626b59778a8c526d534c8804 52e8bcb18c85164f7510e23b94f1877f59173b738df6bd60a179c263654ec7df 2c3cc5613bb5eda188d00dda72c211ddd27b8898f0c8a85fde180bc7d9d04e11 a836e112313d61cad6547499a92e27ffd7a3d7922e56c29e55bf4200944565e8 e302c0ab34f72bc429b8df4741499e5b2c8bf473e85df62e48f722769ec59d2b b1b5c23489b815a5859d12ebb1f2a72f3040eb 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) 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 161 /lessornotequal put dup 162 /greaterornotequal put dup 163 /notlessequal put dup 164 /notgreaterequal put dup 169 /lessornotdbleql put dup 170 /greaterornotdbleql put dup 175 /lessnotequal put dup 176 /greaternotequal put dup 179 /precedeornoteqvlnt put dup 180 /followornoteqvlnt put dup 181 /lessornotsimilar put dup 182 /greaterornotsimilar put dup 183 /notlessdblequal put dup 184 /notgreaterdblequal put dup 186 /follownotslnteql put dup 188 /follownotdbleqv put dup 191 /notsimilar put dup 192 /notapproxequal put dup 195 /notsubsetoreql put dup 90 /Z 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 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aebd32bf1b3f75bda0bb41a73fb6922596f070fff12e35450318f2192509cca2 68d321d5fb5f92d3db22857e41691568a360ef2c0c012eef 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 161 /minus put dup 162 /periodcentered put dup 163 /multiply put dup 164 /asteriskmath put dup 167 /plusminus put dup 169 /circleplus put dup 170 /circleminus put dup 175 /circledot put dup 176 /circlecopyrt put dup 177 /openbullet put dup 179 /equivasymptotic put dup 180 /equivalence put dup 181 /reflexsubset put dup 182 /reflexsuperset put dup 183 /lessequal put dup 184 /greaterequal put dup 186 /followsequal put dup 187 /similar put dup 188 /approxequal put dup 191 /lessmuch put dup 192 /greatermuch put dup 195 /arrowleft put dup 50 /element put dup 76 /L put dup 80 /P put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 112 /radical put dup 114 /nabla 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 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 191 /tau put dup 192 /upsilon put dup 195 /psi put dup 59 /comma put dup 61 /slash put dup 62 /greater put dup 85 /U put dup 96 /lscript put dup 100 /d put dup 106 /j put dup 107 /k put dup 109 /m put dup 112 /p put dup 116 /t put dup 122 /z put readonly def /FontBBox{0 -250 1171 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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 191 /oslash put dup 192 /AE put dup 195 /suppress put 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 56 /eight put dup 61 /equal put dup 75 /K put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a 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 116 /t put dup 119 /w put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueXX 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950 93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21 c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644 7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e 13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03 22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56 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96490ea8f5c755ac1b2a2e4fff3194ea332a336470bab6d1208637a0dc7e2e9c cfd18e312c370bf3efa4e426c6d9a665713a03d1263a5b67cc1644d617ffdbc3 b59190d47b96b291fe98810e6fbfede944dcee350f176d9af35801e3 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /beta put dup 176 /gamma put dup 177 /delta put dup 178 /epsilon1 put dup 179 /zeta put dup 180 /eta put dup 181 /theta put dup 182 /iota put dup 183 /kappa put dup 184 /lambda put dup 186 /nu put dup 187 /xi put dup 188 /pi put dup 189 /rho put dup 191 /tau put dup 192 /upsilon put dup 193 /phi put dup 195 /psi put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 67 /C put dup 69 /E put dup 76 /L put dup 85 /U put dup 86 /V put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 100 /d put dup 103 /g put dup 107 /k put dup 112 /p put dup 116 /t put dup 117 /u put dup 122 /z 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 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 195 /suppress put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 67 /C put dup 76 /L put dup 79 /O put dup 85 /U put dup 97 /a put dup 98 /b 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 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 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f0c8c8f0c7d3c402ddb7dfaa106664f10d74b2fa5b280aa07fde59ff4344777e 9fc87be30cf1e24179e719b2905e727e5251fa96dbb260cafe90e17cacfbbbc2 8b8eaccafcf8154ad4b31e31ef3a36079493f943eebb9ce2db91105591ad01b9 294f1df91dcfc8bb8430309e243858b874c523876cabbbb5631b50ff9a05a6c6 20ad8b9e92a5c1e69784a1303e96465d4a2e4c633e274c7b29da4e846f2a097a fa619bc944fbb78f 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 195 /suppress put dup 45 /hyphen put dup 49 /one put dup 50 /two put dup 51 /three put dup 65 /A put dup 68 /D put dup 73 /I put dup 76 /L put dup 82 /R 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 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueXX 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT9 %!PS-AdobeFont-1.1: CMTT9 1.0 %%CreationDate: 1991 Aug 20 16:46:24 % 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 (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 175 /arrowdown put dup 176 /quotesingle put dup 177 /exclamdown put dup 178 /questiondown put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 195 /visiblespace put dup 46 /period put dup 64 /at put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put readonly def /FontBBox{-6 -233 542 698}readonly def /UniqueXX 5000831 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be465959b1188f76df7824c135a7fb382c4e1 1b0ddfe856b6f34552ca48c24b57dd8448fac257c4d93fb122e1218fd36b99b2 d79dadb8a66613ef11039be77816a7a2d6781fe0d69cecc36232ae87a172afe0 95532a8c7ff40bdd4a5fcfb6ccfd8f73c572231734e0609c6743ee11010f6579 820b367c49069ac1d45760c0ce8dc1e67e2beb72be6d287910547e1b4bb52465 b75947d224998223275a2c340a1c14c04328cc2935c53ee2723f1de6357a291e 14863f6c1411477b3ea074052b30a4c1ef03ab324d678307e1cb02c7aaffa90b 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fb20c545c75424b5992eefa4cf830338c56ba68b9eb46a8dc0b2c9fc44335340 dbb59a4e578028b2d64a8161d5ea3faf0955a00ac8433cf2173839dc544ab10c 052b137cf327f4b1f282a92ec1e4010b3b8022fd0cfb80ddea86a72a435ece7e 7c6cd0ed885ffaea1b32d5a8c4288de1e2408d5e496b23fd30f848e6961173bd 9497df75577f005c6ed108b6cb5996113dc2d79d 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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 195 /suppress put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 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 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 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 dup 122 /z put dup 123 /endash put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 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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 161 /Gamma put dup 162 /Delta put dup 163 /Theta put dup 164 /Lambda put dup 167 /Sigma put dup 169 /Phi put dup 170 /Psi put dup 174 /ff put dup 175 /fi put dup 176 /fl put dup 177 /ffi put dup 178 /ffl put dup 179 /dotlessi put dup 180 /dotlessj put dup 181 /grave put dup 182 /acute put dup 183 /caron put dup 184 /breve put dup 186 /ring put dup 187 /cedilla put dup 188 /germandbls put dup 189 /ae put dup 191 /oslash put dup 192 /AE put dup 193 /OE put dup 195 /suppress 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 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12 cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e 4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618 99b8ea06b092c3c1e503e6e436e0a9fa22576c8930ab3dc8c20f5d82b69cddf8 ff4dacfa9c54bed5a3aa3ea5b129fe96be632843b9b6bc91b615581a985db56b 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Fo(X)24288 57644 y Fn(k)p Fm(2L)26288 56298 y Fy(^)26211 56313 y Fu(u)p Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))g(e)30017 55856 y Fs(i)p Fn(k)p Fm(\242)p Fn(x)32015 56313 y Ft(:)10431 b Fy(\(1\))6974 59776 y(Ob)-31 b(viously)-92 b(,)390 b Fq(P)479 b Fy(maps)389 b Ft(L)17329 59374 y Fs(2)18214 59776 y Fy(in)-31 b(to)390 b Ft(L)21231 59374 y Fs(2)22116 59776 y Fy(v)-31 b(ector)390 b(\257elds;)e(in)h(fact,)h Fq(P)91 b Fu(u)388 b Fy(is)h Ft(C)36401 59374 y Fm(1)37727 59776 y Fy(in)g(the)g(spatial)6974 61104 y(v)-61 b(ariables.)400 b(The)f(pro)61 b(jection)400 b(also)g(preserv)-31 b(es)398 b(the)h(incompressibilit)-31 b(y)401 b(prop)31 b(ert)-31 b(y)-92 b(.)399 b(That)6974 62433 y(is,)369 b(if)h Fq(r)247 b(\242)f Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))309 b(=)f(0,)370 b(then)f Fq(r)247 b(\242)f(P)91 b Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))309 b(=)f(0.)p eop %%Page: 2 2 2 1 bop 6974 1328 a Fx(2)3041 b(Charles)341 b(R.)h(Do)28 b(ering)342 b(and)f(Nik)-28 b(ola)341 b(P)-85 b(.)342 b(P)-28 b(etro)g(v)8634 3764 y Fy(The)370 b(Na)-31 b(vier-Stok)g(es)371 b(equation)g(is)17776 6644 y(_)17576 6659 y Fu(u)246 b Fy(+)g(\()p Fu(u)h Fq(\242)f(r)p Fy(\))p Fu(u)h Fy(+)25129 5910 y(1)p 25119 6404 573 45 v 25119 7418 a Ft(\275)25824 6659 y Fq(r)p Ft(p)308 b Fy(=)g Ft(\272)70 b(\242)p Fu(u)247 b Fy(+)f Fu(f)489 b Ft(;)9188 b Fy(\(2\))6974 9681 y(with)370 b Fu(f)121 b Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))370 b(tak)-31 b(en)371 b(in)e(the)h(form)19411 12755 y Fu(f)121 b Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))309 b(=)e Ft(\262)25758 12006 y Fq(P)91 b Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))p 24588 12500 6333 45 v 24918 13132 a Fs(1)p 24721 13313 836 45 v 24721 13964 a Fr(`)25092 13742 y Fl(d)25689 13568 y Fq(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)30421 13187 y Fs(2)30421 13863 y(2)31423 12755 y Ft(:)11023 b Fy(\(3\))6974 16503 y(where)369 b Fq(k)246 b(\242)h(k)12081 16669 y Fs(2)12947 16503 y Fy(stands)369 b(for)g(the)h Ft(L)20757 16101 y Fs(2)21254 16503 y Fy(-norm,)g Fq(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)29556 16669 y Fs(2)30363 16503 y Fy(:=)31839 15606 y Fo(\243)32300 15611 y(R)33223 16503 y Fq(jP)91 b Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))p Fq(j)37828 16101 y Fs(2)38511 16503 y Fy(d)39126 16101 y Fr(d)39643 16503 y Fu(x)40315 15606 y Fo(\244)40909 15538 y Fk(1)p 40909 15661 377 38 v 40909 16102 a(2)41473 16503 y Fy(.)8634 17831 y(This)370 b(c)-31 b(hoice)370 b(of)g(forcing)g(ensures)e(that)i(the)f(input)h(p)31 b(o)-31 b(w)g(er)370 b(is)f(constan)-31 b(t:)18709 19264 y Fo(Z)20000 20771 y Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))248 b Fq(\242)f Fu(f)121 b Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))g(d)27664 20314 y Fr(d)28182 20771 y Fu(x)307 b Fy(=)g Ft(`)30790 20314 y Fr(d)31307 20771 y Ft(\262)369 b(:)10321 b Fy(\(4\))6974 23772 y(In)320 b(this)h(approac)-31 b(h)322 b Ft(\262)p Fy(,)f Ft(\272)391 b Fy(and)321 b Ft(`)f Fy(are)h(the)g(\(only\))h(con)-31 b(trol)323 b(parameters.)e(On) g(a)-31 b(v)g(erage,)322 b(the)6974 25100 y(p)31 b(o)-31 b(w)g(er)370 b(input)f(is)h(the)f(viscous)g(energy)h(dissipation)h (rate:)15011 28183 y Ft(\262)308 b Fy(:=)17589 27434 y(1)p 17377 27928 978 45 v 17377 28942 a Ft(`)17838 28622 y Fr(d)18672 26676 y Fo(Z)19963 28183 y Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))248 b Fq(\242)e Fu(f)121 b Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))g(d)27626 27726 y Fr(d)28144 28183 y Fu(x)308 b Fy(=)f Ft(\272)31227 27434 y Fq(hkr)p Fu(u)p Fq(k)34392 27032 y Fs(2)34392 27709 y(2)34890 27434 y Fq(i)p 31227 27928 4095 45 v 32785 28942 a Ft(`)33246 28622 y Fr(d)35823 28183 y Ft(;)6623 b Fy(\(5\))6974 31184 y(where)412 b Fq(h\242i)h Fy(stands)g(for)f(the)g (long)i(time)f(a)-31 b(v)g(erage.)414 b(The)f(non-dimensional)i (measure)d(of)6974 32512 y(energy)369 b(dissipation)i(is)e(de\257ned)g (as)23179 35463 y Ft(\257)d Fy(:=)26011 34714 y Ft(\262`)p 25780 35208 1374 45 v 25780 36222 a(U)26657 35902 y Fs(3)27655 35463 y Ft(;)14791 b Fy(\(6\))6974 38414 y(whic)-31 b(h)382 b(is)f(a)g(function)h(of)g Fj(Re)327 b Fy(:=)20994 37978 y Fr(U)83 b(`)p 20994 38159 1057 45 v 21275 38796 a(\272)22183 38414 y Fy(,)382 b(the)f(Reynolds)g(n)-31 b(um)g(b)31 b(er,)382 b(where)e Ft(U)502 b Fy(is)380 b(the)i(r.m.s.)6974 40161 y(v)-31 b(elo)31 b(cit)-31 b(y)375 b(de\257ned)e(b)-31 b(y)374 b Ft(U)17303 39760 y Fs(2)18113 40161 y Fy(:=)19728 39597 y Fm(hk)p Fn(u)p Fm(k)21551 39263 y Fk(2)21551 39818 y(2)21982 39597 y Fm(i)p 19728 39907 2613 45 v 20616 40557 a Fr(`)20987 40336 y Fl(d)22473 40161 y Fy(,)f(a)h(measure) f(of)g(the)h(total)h(kinetic)g(energy)e(of)g(the)6974 41490 y(\260uid.)346 b(Our)f(analysis)h(will)h(establish)f(limits)i(on) d(the)h(relationship)h(b)31 b(et)-31 b(w)g(een)346 b Ft(\257)404 b Fy(and)345 b Fj(Re)p Fy(.)8634 42818 y(Because)413 b(w)-31 b(e)414 b(will)h(study)e(the)h(\\lo)-31 b(w-)p Ft(k)35 b Fy(")415 b(F)-92 b(ourier)413 b(mo)31 b(des)413 b(\(i.e.,)i(mo)31 b(des)413 b(with)i(w)-31 b(a)g(v)g(e)6974 44147 y(v)g(ectors)266 b(in)h Fq(L)p Fy(\),)g(w)-31 b(e)267 b(also)g(in)-31 b(tro)31 b(duce)267 b(the)g(r.m.s.)g(v)-31 b(elo)31 b(cit)-31 b(y)268 b Ft(V)512 b Fy(con)-31 b(tained)268 b(in)f(these)f(mo)31 b(des,)21497 47291 y Ft(V)22389 46834 y Fs(2)23193 47291 y Fy(:=)24802 46542 y Fq(hkP)91 b Fu(u)p Fq(k)27906 46140 y Fs(2)27906 46817 y(2)28404 46542 y Fq(i)p 24802 47036 4033 45 v 26330 48050 a Ft(`)26791 47730 y Fr(d)29337 47291 y Ft(:)13109 b Fy(\(7\))6974 50037 y(The)369 b(b)31 b(ounds)369 b(on)g(the)h(dissipation)h Ft(\257)428 b Fy(will)370 b(b)31 b(e)369 b(in)h(terms)f(of)g Fj(Re)g Fy(and)h(the)f(quan)-31 b(tit)g(y)13790 53550 y Fi(p)307 b Fy(:=)16260 52801 y Ft(V)p 16260 53295 892 45 v 16268 54309 a(U)17592 53550 y Fq(\273)18761 51558 y Fo(s)p 19867 51558 16808 45 v 20000 52801 a Fy(\\lo)-31 b(w-)p Ft(k)35 b Fy(")372 b(kinetic)f(energy)e(of)h(the)f(\260uid)p 20000 53295 16543 45 v 20583 54309 a(T)-92 b(otal)371 b(kinetic)f(energy)g(of)f(the)h(\260uid)37044 53550 y Ft(:)5402 b Fy(\(8\))6974 56821 y(The)445 b(case)f Fi(p)434 b Fq(\274)f Fy(1)445 b(corresp)31 b(onds)443 b(to)j(laminar)g(\260o)-31 b(w,)446 b(when)f(the)g(turbulen)-31 b(t)446 b(cascade)f(is)6974 58149 y(inop)31 b(erativ)-31 b(e.)p eop %%Page: 3 3 3 2 bop 14553 1328 a Fx(Lo)-28 b(w-w)g(a)g(v)g(en)g(um)g(b)28 b(er)339 b(forcing)i(and)g(turbulen)-28 b(t)341 b(energy)h(dissipation) 3042 b(3)6974 3764 y Fv(2)554 b(Deriv)-83 b(ation)499 b(of)f(the)h(b)42 b(ounds)6974 6420 y Fu(2.1)554 b(Lo)-35 b(w)g(er)425 b(b)35 b(ounds)426 b(on)f(the)g(energy)h(dissipation)6974 8856 y Fy(T)-92 b(o)486 b(obtain)h(lo)-31 b(w)g(er)486 b(b)31 b(ounds)485 b(on)g(the)h(energy)f(dissipation,)j(w)-31 b(e)486 b(pro)31 b(ceed)484 b(as)i(usual)f(b)-31 b(y)6974 10184 y(m)g(ultiplying)514 b(the)c(Na)-31 b(vier-Stok)g(es)512 b(equation)g(\(2\))f(b)-31 b(y)511 b Fu(u)p Fy(\()p Fu(x)p Ft(;)184 b(t)p Fy(\))512 b(and)e(in)-31 b(tegrating)513 b(o)-31 b(v)g(er)6974 11512 y(the)369 b(v)-31 b(olume)371 b(of)f(the)f(\260uid)h(to)g(obtain)h(the)e(instan)-31 b(taneous)371 b(p)31 b(o)-31 b(w)g(er)370 b(balance,)16432 13714 y(1)p 16432 14208 554 45 v 16432 15222 a(2)17451 13714 y(d)p 17251 14208 1015 45 v 17251 15222 a(d)p Ft(t)18583 14463 y Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)22454 14006 y Fs(2)22454 14737 y(2)23262 14463 y Fy(=)307 b Fq(\241)p Ft(\272)255 b Fq(kr)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)30886 14006 y Fs(2)30886 14737 y(2)31632 14463 y Fy(+)246 b Ft(`)33200 14006 y Fr(d)33717 14463 y Ft(\262)369 b(;)7911 b Fy(\(9\))6974 17939 y(where)369 b Fq(kr)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)14968 17537 y Fs(2)14968 18213 y(2)15776 17939 y Fy(:=)17252 17047 y Fo(R)18174 16666 y(\257)18174 17330 y(\257)18174 17994 y(\257)18543 17108 y(P)19712 17382 y Fr(d)19712 18271 y(j)m(;m)p Fs(=1)22484 17939 y Ft(@)23072 18105 y Fr(j)23538 17939 y Ft(u)24172 18105 y Fr(m)25013 17939 y Fy(\()p Fu(x)p Ft(;)g(t)p Fy(\))27436 16666 y Fo(\257)27436 17330 y(\257)27436 17994 y(\257)27806 16939 y Fs(2)28487 17939 y Fy(d)29102 17537 y Fr(d)29618 17939 y Fu(x)p Fy(.)8634 19599 y(No)-31 b(w)425 b(w)-31 b(e)424 b(use)e(the)i(facts)g(that)g(the)g(lengths)g (of)f(w)-31 b(a)g(v)g(ev)g(ectors)426 b Fu(k)520 b Ft(=)-676 b Fq(2)398 b(L)424 b Fy(are)f(at)h(least)6974 20927 y(2)p Ft(\274)8198 20012 y Fq(p)p 9121 20012 554 45 v 9121 20927 a Fy(2)p Ft(=`)p Fy(,)e(and)f(that)i Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))283 b Fq(\241)e(P)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)24994 20526 y Fs(2)24994 21202 y(2)25887 20927 y Fy(=)394 b Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)31013 20526 y Fs(2)31013 21202 y(2)31793 20927 y Fq(\241)281 b(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)37667 20526 y Fs(2)37667 21202 y(2)38167 20927 y Fy(,)421 b(to)h(deriv)-31 b(e)421 b(a)6974 22256 y(lo)-31 b(w)g(er)370 b(b)31 b(ound)369 b(on)h Fq(kr)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)19611 21854 y Fs(2)19611 22530 y(2)20111 22256 y Fy(:)12139 25257 y Fq(kr)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)g(t)p Fy(\))p Fq(k)16932 24800 y Fs(2)16932 25530 y(2)17764 25257 y Fy(=)18957 23750 y Fo(Z)20249 25257 y Fq(jr)p Fu(u)p Fy(\()p Fu(x)p Ft(;)g(t)p Fy(\))p Fq(j)24915 24800 y Fs(2)25599 25257 y Fy(d)26214 24800 y Fr(d)26730 25257 y Fu(x)308 b Fy(=)f Ft(`)29339 24800 y Fr(d)30040 24205 y Fo(X)30575 26588 y Fn(k)31823 25257 y Ft(k)32434 24800 y Fs(2)32931 25257 y Fq(j)33315 25242 y Fy(^)33238 25257 y Fu(u)q Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))p Fq(j)36676 24800 y Fs(2)17764 29709 y Fy(=)332 b Ft(`)19418 29252 y Fr(d)20304 27816 y Fo(\303)21250 28657 y(X)21180 31040 y Fn(k)p Fm(2L)23104 29709 y Ft(k)23715 29252 y Fs(2)24211 29709 y Fq(j)24595 29694 y Fy(^)24518 29709 y Fu(u)q Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))p Fq(j)27956 29252 y Fs(2)28701 29709 y Fy(+)29878 28657 y Fo(X)29808 31083 y Fn(k)97 b Fr(=)-551 b Fm(2)o(L)31731 29709 y Ft(k)32342 29252 y Fs(2)32839 29709 y Fq(j)33223 29694 y Fy(^)33146 29709 y Fu(u)q Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))p Fq(j)36584 29252 y Fs(2)37082 27816 y Fo(!)17764 34263 y Fq(\270)332 b Ft(`)19418 33806 y Fr(d)20252 33514 y Fy(4)p Ft(\274)21476 33112 y Fs(2)p 20252 34008 1721 45 v 20634 35022 a Ft(`)21095 34702 y Fs(2)22290 32370 y Fo(\303)23237 33211 y(X)23167 35594 y Fn(k)p Fm(2L)25090 34263 y Fq(j)25474 34248 y Fy(^)25397 34263 y Fu(u)q Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))p Fq(j)28835 33806 y Fs(2)29579 34263 y Fy(+)246 b(2)31494 33211 y Fo(X)31423 35637 y Fn(k)97 b Fr(=)-551 b Fm(2)q(L)33348 34263 y Fq(j)33732 34248 y Fy(^)33655 34263 y Fu(u)q Fy(\()p Fu(k)p Ft(;)184 b(t)p Fy(\))p Fq(j)37093 33806 y Fs(2)37591 32370 y Fo(!)17764 38529 y Fy(=)19090 37780 y(4)p Ft(\274)20314 37378 y Fs(2)p 19090 38274 V 19472 39288 a Ft(`)19933 38969 y Fs(2)21128 37632 y Fo(\241)21636 38529 y Fq(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)26368 38072 y Fs(2)26368 38803 y(2)27114 38529 y Fy(+)246 b(2)184 b Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)g(t)p Fy(\))249 b Fq(\241)d(P)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)37811 38072 y Fs(2)37811 38803 y(2)38311 37632 y Fo(\242)17764 42011 y Fy(=)19090 41262 y(4)p Ft(\274)20314 40860 y Fs(2)p 19090 41756 V 19472 42770 a Ft(`)19933 42451 y Fs(2)21128 41114 y Fo(\241)21636 42011 y Fy(2)g Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)g(t)p Fy(\))p Fq(k)26244 41554 y Fs(2)26244 42285 y(2)26991 42011 y Fq(\241)246 b(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)32830 41554 y Fs(2)32830 42285 y(2)33330 41114 y Fo(\242)34390 42011 y Ft(:)7503 b Fy(\(10\))6974 44818 y(F)-92 b(rom)369 b(\(9\))h(and)g(\(10\))g(w)-31 b(e)370 b(obtain)h(the)e(di\256eren)-31 b(tial)371 b(inequalit)-31 b(y)15808 47214 y(1)p 15808 47708 554 45 v 15808 48722 a(2)16827 47214 y(d)p 16627 47708 1015 45 v 16627 48722 a(d)p Ft(t)17959 47963 y Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)21830 47505 y Fs(2)21830 48236 y(2)22637 47963 y Fq(\267)308 b(\241)p Ft(\272)25601 47214 y Fy(4)p Ft(\274)26825 46812 y Fs(2)p 25601 47708 1721 45 v 25983 48722 a Ft(`)26444 48402 y Fs(2)27640 47963 y Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)31511 47505 y Fs(2)31511 48236 y(2)32256 47963 y Fy(+)246 b Ft(`)33824 47505 y Fr(d)34341 47963 y Ft(\262)369 b(;)6974 50708 y Fy(from)h(whic)-31 b(h,)370 b(using)g(Gron)-31 b(w)g(all's)371 b(inequalit)-31 b(y)-92 b(,)372 b(w)-31 b(e)370 b(deduce)10048 53042 y(1)p 10048 53536 554 45 v 10048 54550 a(2)10919 53791 y Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)14790 53334 y Fs(2)14790 54065 y(2)15597 53791 y Fq(\267)16899 53042 y Fy(1)p 16899 53536 V 16899 54550 a(2)17770 53791 y Fq(k)p Fu(u)p Fy(\()p Fq(\242)p Ft(;)g Fy(0\))p Fq(k)21794 53334 y Fs(2)21794 54065 y(2)22479 53791 y Fy(e)22971 53289 y Fm(\241)23795 52992 y Fk(8)p Fl(\274)24652 52769 y Fk(2)25084 52992 y Fl(\272)p 23795 53115 1722 38 v 24275 53672 a(`)24606 53509 y Fk(2)25650 53289 y Fr(t)26286 53791 y Fy(+)246 b Ft(`)27854 53334 y Fr(d)28370 53791 y Ft(\262)29642 53042 y(`)30103 52640 y Fs(2)p 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b(with)h(the)e(long)h(time)h (a)-31 b(v)g(erage)371 b(exists\))f(is)f(indeed)g(giv)-31 b(en)370 b(b)-31 b(y)385 b(\(5\))r(.)8634 61982 y(T)-92 b(aking)371 b(the)f(time)g(a)-31 b(v)g(erage)371 b(of)456 b(\(10\))q(,)370 b(w)-31 b(e)370 b(obtain)g(the)g(b)31 b(ound)p eop %%Page: 4 4 4 3 bop 6974 1328 a Fx(4)3041 b(Charles)341 b(R.)h(Do)28 b(ering)342 b(and)f(Nik)-28 b(ola)341 b(P)-85 b(.)342 b(P)-28 b(etro)g(v)20244 3558 y Fy(4)p Ft(\274)21468 3156 y Fs(2)21965 3558 y Ft(\272)p 20244 4052 2339 45 v 20934 5066 a(`)21395 4746 y Fs(2)22900 4307 y Fy(\(2)p Ft(U)24760 3850 y Fs(2)25503 4307 y Fq(\241)246 b Ft(V)27501 3850 y Fs(2)27998 4307 y Fy(\))308 b Fq(\267)f Ft(\262)370 b(;)6974 7052 y Fy(whic)-31 b(h)370 b(in)f(non-dimensional)j(v)-61 b(ariables)370 b(reads)21383 9171 y(4)p Ft(\274)22607 8769 y Fs(2)p 21383 9665 1721 45 v 21640 10679 a Fj(Re)23237 9920 y Fy(\(2)246 b Fq(\241)g Fi(p)26127 9463 y Fs(2)26624 9920 y Fy(\))308 b Fq(\267)f Ft(\257)428 b(:)12309 b Fy(\(12\))6974 13441 y 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Fo(Z)24526 20005 y Ft(@)p 24326 20499 1049 45 v 24326 21513 a(@)61 b(t)25508 20753 y Fy(\()p Fq(P)91 b Fu(u)p Fy(\))247 b Fq(\242)f(P)91 b Fu(u)184 b Fy(d)31103 20296 y Fr(d)31620 20753 y Fu(x)308 b Fy(=)33901 20005 y(1)p 33901 20499 554 45 v 33901 21513 a(2)34720 20005 y(d)184 b Fq(kP)91 b Fu(u)p Fy(\()p Fq(\242)p Ft(;)184 b(t)p Fy(\))p Fq(k)40251 20171 y Fs(2)p 34720 20499 6032 45 v 37228 21513 a Fy(d)p Ft(t)41253 20753 y(:)6974 23837 y Fy(F)-92 b(or)368 b(the)i(viscosit)-31 b(y)371 b(term)e(w)-31 b(e)370 b(obtain)h(\(in)-31 b(tegrating)372 b(b)-31 b(y)370 b(parts\))11931 26982 y Ft(\272)12732 25475 y Fo(Z)13839 26982 y Fy(\()p Ft(\242)p Fu(u)p Fy(\))248 b Fq(\242)18064 26233 y(P)91 b Fu(u)p 17262 26727 3172 45 v 17262 27741 a Fq(kP)g Fu(u)p Fq(k)19936 27907 y Fs(2)20751 26982 y Fy(d)21366 26525 y Fr(d)21883 26982 y Fu(x)307 b Fy(=)g Fq(\241)p Ft(\272)25826 26233 y Fq(krP)91 b Fu(u)p Fq(k)29422 25831 y Fs(2)29422 26508 y(2)p 25826 26727 4095 45 v 26287 27741 a Fq(kP)g Fu(u)p 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Fq(\267)28313 55806 y Fs(1)p 28313 55987 442 45 v 28313 56624 a(2)28887 56242 y Fy(\()p Ft(z)49 b(a)30466 55840 y Fs(2)31179 56242 y Fy(+)32396 55806 y Fs(1)p 32389 55987 455 45 v 32389 56624 a Fr(z)32977 56242 y Ft(b)33452 55840 y Fs(2)33948 56242 y Fy(\))355 b(whic)-31 b(h)355 b(holds)f(for)h(an)-31 b(y)6974 57570 y Ft(z)356 b(>)307 b Fy(0:)p eop %%Page: 5 5 5 4 bop 14553 1328 a Fx(Lo)-28 b(w-w)g(a)g(v)g(en)g(um)g(b)28 b(er)339 b(forcing)i(and)g(turbulen)-28 b(t)341 b(energy)h(dissipation) 3042 b(5)8855 2657 y Fo(\257)8855 3321 y(\257)8855 3985 y(\257)8855 4649 y(\257)9224 2755 y(Z)10331 4262 y Fy([\()p Fu(u)247 b Fq(\242)g(r)p Fy(\))p Fu(u)p Fy(])g Fq(\242)16677 3513 y Fu(p)p 15875 4007 2311 45 v 15875 5021 a Fq(k)p Fu(p)p Fq(k)17688 5187 y Fs(2)18504 4262 y Fy(d)19119 3805 y Fr(d)19635 4262 y Fu(x)20307 2657 y Fo(\257)20307 3321 y(\257)20307 3985 y(\257)20307 4649 y(\257)20983 4262 y Fy(=)22152 2657 y Fo(\257)22152 3321 y(\257)22152 3985 y(\257)22152 4649 y(\257)22521 2755 y(Z)23627 4262 y Fy([)p Fu(p)g Fy(+)f(\()p Fu(u)h Fq(\241)f Fu(p)p Fy(\)])h Fq(\242)31204 3513 y(r)p Fu(p)p 30863 4007 V 30863 5021 a Fq(k)p Fu(p)p Fq(k)32676 5187 y Fs(2)33553 4262 y Fq(\242)f Fy([)p Fu(p)h Fy(+)f(\()p Fu(u)h Fq(\241)f Fu(p)p Fy(\)])184 b(d)41208 3805 y Fr(d)41725 4262 y Fu(x)42397 2657 y Fo(\257)42397 3321 y(\257)42397 3985 y(\257)42397 4649 y(\257)12005 8167 y Fq(\267)13787 7418 y Fy(2)p Ft(\274)15011 6475 y Fq(p)p 15934 6475 577 45 v 15934 7418 a Ft(d)p 13306 7912 3685 45 v 13306 8946 a(`)13767 8626 y Fs(1+\()p Fr(d=)p Fs(2\))17308 6660 y Fo(Z)18599 7270 y(\241)19107 8167 y Fy(2)g Fq(j)p Fu(p)p Fq(j)g(j)p Fu(u)249 b Fq(\241)d Fu(p)p Fq(j)h Fy(+)f Fq(j)p Fu(u)g Fq(\241)g Fu(p)p Fq(j)29468 7710 y Fs(2)29966 7270 y Fo(\242)30842 8167 y Fy(d)31457 7710 y Fr(d)31973 8167 y Fu(x)12005 11974 y Fq(\267)13787 11225 y Fy(2)p Ft(\274)15011 10281 y Fq(p)p 15934 10281 577 45 v 15934 11225 a Ft(d)p 13306 11719 3685 45 v 13306 12753 a(`)13767 12433 y Fs(1+\()p Fr(d=)p 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45 v 27728 57746 a Ft(d)185 b(\301)p Fy(\()p Fi(p)p Ft(;)f(z)49 b Fy(\))370 b Ft(;)9905 b Fy(\(17\))6974 60051 y(where)369 b(w)-31 b(e)369 b(ha)-31 b(v)g(e)371 b(in)-31 b(tro)31 b(duced)370 b(the)f(function)14145 62045 y Ft(\301)p Fy(\()p Fi(p)p Ft(;)184 b(z)49 b Fy(\))308 b(:=)g(min)21088 61148 y Fo(\251)21734 62045 y Fi(p)p Ft(;)22964 61148 y Fo(\241)23611 61609 y Fs(1)p 23604 61790 455 45 v 23604 62427 a Fr(z)24438 62045 y Fy(+)246 b(1)26098 61148 y Fo(\242)26790 62045 y Fi(p)g Fy(+)28697 61148 y Fo(\241)29204 62045 y Ft(z)295 b Fq(\241)31260 61609 y Fs(1)p 31254 61790 V 31254 62427 a Fr(z)32087 62045 y Fq(\241)246 b Fy(1)33747 61148 y Fo(\242)34439 62045 y Fi(p)34993 61588 y Fs(3)35490 61148 y Fo(\252)36689 62045 y Ft(:)5204 b Fy(\(18\))p eop %%Page: 6 6 6 5 bop 6974 1328 a Fx(6)3041 b(Charles)341 b(R.)h(Do)28 b(ering)342 b(and)f(Nik)-28 b(ola)341 b(P)-85 b(.)342 b(P)-28 b(etro)g(v)6974 3764 y Fu(2.3)554 b(Compatibilit)-35 b(y)423 b(of)i(the)g(lo)-35 b(w)g(er)425 b(and)g(upp)35 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