This is a multi-part message in MIME format. ---------------0211220904828 Content-Type: text/plain; name="02-479.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-479.keywords" Nonlinear wave equation; Periodic solutions; Lindstedt series method; Tree formalism; Perturbation theory ---------------0211220904828 Content-Type: application/postscript; name="gm-pde.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="gm-pde.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: gm-pde.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMBX12 CMSY7 CMR10 CMCSC10 CMTI10 CMTI8 CMR8 %%+ CMMI10 CMEX10 CMMI7 CMSY10 CMR7 MSBM10 CMMI5 CMR5 CMMI8 CMMI6 CMSY8 %%+ CMSL10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o gm-pde.ps gm-pde %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.11.22:1602 %%BeginProcSet: texc.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/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/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]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/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: texps.pro %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a7a227d51386469ec9ef415f3bb849d30411890d93a520e8cbc872f7 5a1b270af78e4653c99aa3789047f53c76ff56afc6306cbdeaead1bcb2484152 b10628e1a9c2612385057a7ae1156d95f88e2027f458ae327d2a8ededcf7db80 b3dfd75653ab4fa1661d655d3b472612d657f1971ca7df759f73ce7030cbe7f3 1a7d106e017f6163a95fac4a6058a6dc1988ab70346c84db0c27686672df86d3 27f0b397e332dbb89b138ed4a863d2b05dcaed1cf2ca9a1e63259fbe20376c72 bdf0232208376a879200705834b7351794ada9fa926c176351 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 59 /comma put dup 107 /k put dup 109 /m put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 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2f747531eddef7e2628c410fb63fcef62f7ffa9f762e785c890677bc568f093d 9f58480fea003dcaebeaac5ceb919226e3d840aadc8fe629cfaf97dbf913f363 622dca8ebb652c0cf48dbbaea9f19025fa9a2fdd684462dbacf1eb1ef806f388 0fce751e6ddffb13507bcf8be21c7efaa9e3c3c26a15741abea42357f7410f21 3e5bda226805459e60c36d31037f4898ef594586de8ba75db5fcab0a7e749d73 b46e2ed10a78595a7e0c506b5110f315fef747b8e76b08dd472e605d8aa7b750 7631195fe2846201ff04949e7eb8e80522bd92805d258e3f65d9bfb48ae39e81 e57b927fdefac28c94f735efa0ea14fa71746db0768799f6a48e5f10a810bb8a bdac8b43e82916176cf864de87ba01b3b939b1f36ac09cdbdb13dc80e78ca7bc 436d0eb532c0a50c46efc0a1288b63ec300764ea6e085957fd4a24b5a5aba9bb 5df6126c9b6070a2bf7acf55695970ab36fc706d01f5d5ba6dce92e01435c97a 7a8c1e008cca371525735061c9838e1ad7a7bf0325e837cde65e50d6408d877a 094e80cbc81e6d8e4ad29372b8439f8f00ed4f137474890db5d46a682b0235bb 2707312330f9f875e8d1bf7557ebed34285cf93a2017d880f61d0f4727d09d2c 84de54944adfadac754f6e8283099b2b2ca0d4fe43504c816024e82e0ffcb4a0 224fa9fd711747e757938f3ac28256d888611c5d67535114c2f022d79ef1f31e 11d8d94b8633580927f14ccae20c74adf02b045d36041670e7b449179ac9e35b 598632cee6451c56e391ebb14afae13323edffd220ec3bd8e3169081069f22cd 292424eed4020096d4d43d46285a05f46cb69f027c03c997cad30d6db6ffc2a5 0338f7d813e81da47eeba42eb404281e4f32c8055b262c5140aa39e568e6b988 f86d1f9df15d652da5c7c3715d7e88aaa8d626f2f4f5253b2c314d167c4d1e9a 72169c6b0c6790837fe32b65493e70e8681d88e670c7e20c6f8a35b2d6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 69 /E put dup 76 /L put dup 86 /V put dup 107 /k put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31 aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638 12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c 366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6 4729b84ffb21a57faf172aa6716b257bd42d15dd1145035aaf8addd9035f8352 a969d3171cbd9eaed1543388d36481d4276f294fe08be73e838731edd6b7926c 4ce622988501109915ed4e0b7cf10047c0f59516dd21deabf765b7ad2b2386ea 1771835003d59330c151578b290da617ee7c3be3f7146cf3c7ee277574ac879a 16942eb9162b68ddcfd46b00dac70bd88334e689fbc6e48528c18b723069a04f 82edafb40f93b0a809241bfff8e436f910f1455ce69c6c62ae759c0d2d7edb8b 9201100fddb90a38583eeeda24ee9a24a10ee27388006cb1021f72b49f7fc41a 1995ff2fbf613f89887cfcc89172b708fe8cf30cc768fbb1ee3d49b36aaef65f 2840b8518251827a9b111e0d6f1e2d3ef1db2d6eb56921ea1569f5e3e3e38529 97e2585fef8489129fb3a004b43750ae01e73a0734af387393642d2cfd8ea44a 657622ba3616e912df996d59f42b84e85679b649dbc328381be3b738010ab1f5 fab2fca1419aaf478a2f808850993fa8994005826f42583bc2cf0d5e13b3245e 9c7e39e125f66f6572dac62c3b4248e3338d214bb828e40ddf84dea21f3ebdc3 84fc3d3e348f56efaf40ea69b9fca80cd4315bbfa29318f1c3ba656b29dc0194 d35229ccb3f47540671d3e3c0dcaa649ac4a80f34578b6aebc22c716c1bce91a 2dab2264e0d5b678fb1ef763428ac1ebd753f880258c3ef20c7c8840c7fb71ea 61d783840c6c48eb0f03191c22d76cb9d52b8f02521d5645594921ad28bff54a 9d9929c17debca0f5d166a1ff49c860fa9953dc1eb30cf4e47460602c07f4261 2a161068e9cef3da99ab00d90330387c3669e2f0e3e99d988ea357f2ded573c0 4b6352ec9655653fc2ceafb3a9b1d50119d5298016a9f77ac1a1ef40865835ce d2ad6ee3806d1e01129ee84d48be88960232815fe8b155d33200207a2976f69b 0a748be2ef49e0802ceea1a1453a1f77d5e8f97e2558534f9ee9371438e16234 1b98c2ea23518b87cc99b2a2da28f3198c8b0d4bdc8189f4df73767dfa9fda66 d217bc5fa866650f721a934665a55414837c75dd580587f4e1a85cab62f21f65 0095ba6be24a8bfe94efa102b4e58e14cbc1bd60ea7fa526c07cdbb2ae707d15 f93b5a2230b401d13381700a0ac18ad9593a1dfc8bf9715d356d5dd6baed5960 6ac9d44b241a76781743e5d3dec82fd35201b7372977511d6595182945b6fa45 aa1c37501b3729f9a57c15ec28e892b8d5dc1f9fc248067a04e99035828cb982 5e42b6a2ccc5058d9e3f042877eca1f008127a5a9539f753cb0f94be75ff84a9 17085903ec71041d215ad30f3b1534cc78d968b3325a403b78c3e5e82c6b0b8c e03f1bc22947327d8e43b05183456c2399d55c80c98c9d9cfd5d62aa62ec6983 16ea8605f757e036c4e4d0916bdaf80971887db0c825ff754b63d00103c263e4 e8ba3ffc95ffccebf5e6da5495359eca239fc31bfb59d0182532a22676957afd 1bdc94067af0ba6f0adca471b20a4bdbae256c4dd4834c33096bf7ff015d2651 ea7e40085969a9d3e8830bd31718420628572adb46255965571c4aa2e282acbf 003650059199403ef8c8deaf12d4bff5635579a4c94476dbfe2e48818911304b 779881c1767625e82a639d05072bd7495af1ed949586b977a44628dea4635c2c 185f680956f30ac5c5f562884e4352a5eda6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % 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 (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 65 /A put dup 70 /F put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 109 /m put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueXX 5000772 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3037a112066957 7889d67fff57549064b985d67ede2fb03272083723541051ebe936eff01a4ab3 cd845d565dfdf25d9ddd2792db17f52f894bea484480f06c832140fdd6c3af0e fef0584c6b78b5e2bbb9a752f10581fd1c48cb498a822afb18cddebba34695b9 b418010368fdfb7bf758d50f3af03360b81c776325c33c9c81130b1e1be840cf 68c71ffd091dccc0df7b507fe8953dc3836af0da08ff9ff3e9cf7288d9eb8baf ffac546a0fd987ae8e0bcf7b759f4408e13524f478de5896d816cb0ad2904271 cbec82a5ca50f0598502b434ecd94531b4a65181b5b3afcb650904b15157737a a4386f1a7f1252caf2adbd5c8162bf3b065c01ca471d520c884ebbe1b29f9549 134e285dea2fe158c15a08a744cdda00bb6c62158262e24702803d9e1dc1d3a3 1383085631154b077fc20488ee3aa03f47ed2766644330b94133f2f9389b99b8 96d3707d1c5bb227fd3bbdf3a6ff572bf07164107c7a1c0710a5c7cfb67282f9 c238100fa138b75c553d7cbef17e2292a320d3d86a6210e6e3a1e590b10dac6e 177094d5dd163db623d7b344478752f6f3d7d5b3fa92e6bc72dc6fc343d2f946 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0b6bd53fa77c7acaff92aaeb8c063ae099f27158faef50d69b1199e8a5dba55e e1655b93130f1d4f76ea0eed48c4407d0e7a60d7076500bf3bab149ae8c060e2 826f94898dff07ba4876195b69c6a2f5ff0c7f346fc6b02840b7afe490b1d33b 0a8dabeb217d0bf2c93af6c4819ef70588f1f661ddec104864495bf40e8bc930 8076a1f4930e26f97e3c7f90b5de4a759ea43239b2fd6e175ca0b163a0e1e006 7dbe98ce9088bc817e2972d8ef1ad9ab2824d30ff4fbe15f1678ab43222e333a 7f033fc09ba4b5a43556bd6bb2193c06ec98b2c680276192985949c17b79e0b2 5a9f788486744d3d5b0217faf89c7754b2265e015b18f761f7006981ad5dcf62 bdff50a3fd35f373a2426e645290949393679039cba1f0374922b28aa80a5186 90068e55ef993dde212bca9ea850a09610215b6cac273df282e1b425eaa0db9c 5862b2ba12f8e74b07ccecd89ec42ca6b484526dada24f27ab7f0f8a91b8ded0 c0770527052640223952a10b541367df6159d7fc9ee154a603c2e521eefb2afe f0cf3131265a86d569d876065c402622b9d8b86f7985d7a4fa1c57d4b523aee5 b526c7903c3da7892136de892bd5d7d809ded113493a98b7c6b4d019d3e53fa3 1c0073e6083ae8b67742a2cb1d8ea13269eec326d6aa1e121a7b7b8133a920d6 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c907ffcb9145601354915e1b95ed9b5a2a777ae290559b61b888d6a6014517ec 205cf92776e5bd69a39995a0ec955419b2384c6e93dc5feb93bda1b31481d8de 28d7ec2713b5612f77ffe311130a4f8abd58e58e20ff0e82266b0e419d61b0af 85ce209a707a2c6d95178f09eac8d0a02df5eac04e3a16317f887b69964eef79 07ca25878bdb805ccde215dee777856eb72ef8eef07d00eb56d39a43f496deb4 9a2bf155d3cbefcef2871f6f08bb4b225371ae6d578cf24208bc673f08264d16 970e40481c607f8ca12f241b5ccd88a4b41cb5068ab9296133e8a1dc70a8ed3f cda82e565ba3f98ee592d34a729863be7b7cf0784b22641a01571c3713778ea0 2ea82664cd807e7c7a57affad8c8abd31cc92fcbddc5a4d54a9f06006d230e52 629bbc1cb9a04ddf5311d3f80bcc33b0d0c347e1ce8803dfe94c524aaf3c1dbc 47f021f24de5000fa9cc4482cf9dd9833cc3722628c719c2a62f64e942c36b1e 63f81985c339646467b06c8b8993365f0cc9d7dd854e9478185d49e506dd54a7 106b1acf8261a52ec04c61f968f3974fb29d807ae70f4f7b57d46d821f293594 f588208b2841b713c867b00c31f853ee8b826fbbfcaa7f901929f30129eafbd1 f266eabdbf7d5623aacc8aa883270b926e45960496a68b7bea05d9d45ce40821 f82da0fe1ffd9df2e1faf650efc10dfb52bff894690a567de2d78dc19521a6f2 d6a5665446b701befaef606518258d8250de2e2ca32932d8bcfcade704aef76c 1b50cde2f826a3cd4597fe05528799ffbd4f97c23565be0e64d064081b75ee26 fcb3848136cd0e88ced89d644e3ea9209c1d2d05473fcb06bfed 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 43 /plus put dup 49 /one put dup 50 /two put dup 61 /equal 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 1d3686a5e8e613a69a0add8b8c73b127ddcd397a48d785079e786d24b4295a50 5b3021b490724909c1f4a2cfe4ed60e0147e07b10b981f3d853a9b90be98a63d fb3e257b0585a33779c92f35773ef58b8078ae78151be7895292169aea236257 e9c3cb0e8a9b188460c1f38488f3d237dde0bf4e6d6237fefc814d8e9fbca022 23479da2770b2c9e9d28ed15472756ae0f02bbb553b6f4ed04e1dda106974f25 53625eb3987c5686af5f2c947bca2b50365a5cea5d4fb284bdcb52ae3bd25665 55db867df8e760d23e18b3be721d945abf1fd0ed8ff627b8c82a69caef5609e3 3f03d047844786b3afe5bc045ed06f2e4a6b892a8048e64543251e4b66c1b572 c54082b158c3c39f5b5a252260e478219b8775a93c38ef38e5899d32d87d453f 81629efb137b29759b9ad9f81264344919a78538cf2151d2860b139e146bb791 a809120cb9df7462dac67f7552810810de79b5fb535a37ef31eb153835a16024 2fd6a737b115b1cb87337636ac551ea972edfe30147cf85ff465a5c67e6711d1 a32d106d4652fef7676233a0df7c8a5b5855351431d259193afe3e8b5e8d07af 362150348da9221dcd40ebf32f019bf856db3c088b6925cca881caa64da77525 827bd0520567f200dd1bb41212345e4b99d6bf74d5bb31ff6927b8124c657192 d470c3378ca5f99fbb8abdb55900355914fee0d642456949400e0352ca9621c3 3220f3d1b1b57fb1b16ff1e97a6f0fb38b2d2f001612dd966965d6f66741c1be 442df46f11d15e1e66b9d2a5fc4f61899cc8f730b7c850cfd8d475285518d658 6332733cc38652ae2387da06b11f1a096e160f1c97dee096d222d7d4fe5bbf07 be7ceb73f35c171f9b6673437acf1b9fa79925eaff05a4736bebb18ab6e6024a 8d4158459d92088c79a213ee6b7c4a48b8734bec99f3f0a58fc066ccdf396bdb 4039479de6 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 23 /nu put dup 58 /period put dup 59 /comma put dup 96 /lscript put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 118 /v 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 4cff62c622fc61a0308a69f9fb7ef51bb274ce9e059c04b64e817abdb818c8fe 74b9d30c0eff3513eb9a3937f55fd947d4616c5f9fcf5fbb6121f2d2b8a401c9 51c3905f5096883af0484e6f2b12c7c3d71b5408eb3ffbafb26f0276cb774931 55fb8e1c4be1ba6ef3d916a55dd948cdac44a566cf2601ec7854dffbd11f2694 6f0c0c7c3efcb28b5ac38f168ff9468431fb24d832fa8f05c02b3021096c7dd9 1f1a153f81d92ef8f7ded1d48580ef2681dee4c1c684dcb5c69ea1187644cba2 e18b9edc57c6ffc065528160c09d92375255ad57589782e92a81c085d5f0f360 3da5763e2fa5a4daaf2463c2503b865e22fe65fae86b868857c6658bf32b92ff 26b9b7b4f1a75442aa107771171a3701d2400c4aa3fc4ea4476b7f7f3409b2a2 7e8e3573227425bab25e05435c6a43c3f2b52d31386161b727a2100bf7910824 f144ff5820ba96b78313866aeee41e4d65da6f054553ac99a59ca2de5ebbb6b4 8ba5a6c2569ebcfacb9813199a7e360803ecb3761b6c9f2409345cb677d142cf a73585a375d899b6d2e0db6df10a0d979c920e394e0e7236502586ae665d253a 7cba89a880bbdb076798da787763f90a9d4d93dd91ecfdfa1872d0485fd864ed 6c91d827693e810d5bb00464e6bcfb5e9a3dee7dc218ec405173ea7cc7c2c81b 252b8515887bcf8ac2196991058510ead0bdb91dddbd1e265dbf8f2ade0693d7 59f832a36442880352556c552b3c29eb256205355edb41f82a85f420bf6f5379 50315e944125f33e111ee2ba0bcd7dd2f18db1ba98ad0a7d304f40421460d86d 2b2a82b42a0fda330cbb0a94d3cb59425ef03c061a0a754c533843a37c24f164 90cbc11b70b11289828e66481be7fe332a0f14e98caae300beb03ba87c283a66 544ecf1cc654ee27781b31a41c125bb114aee7a7387ca285edc16cca406ed841 a3e2680dd1b1a9854187ba7dec9d43c5c924b8c57797b3da2e07ac7e6e881ba8 437cfb0ed9b70359707c806cf7636ae047857adec4dd2ed1a266b70e85b7f147 8579b639c4edf3459113decb90a8148d5677442368bf8763ce4083f272b43013 da604aec71dbe0685521f62f0f9b14c23c242d23dd58f0c49c845a81c44245a2 131670c24f391da28bb84162996aa022fc9ba6db18b38a46c2ec618386e27c96 100ce49756544de573efc44ad735ed60423f8979dc019ca2f1e1d26339481bcc e373360472c2ae9dfbc3ed84dfadae2bc7ded7e8f8bbb46ffb4fd1fc5354e5ae 2ebb16cedc29e951442acd5a7bf1f55fc55271ca0c1f1519769776e1c1c284e8 7f924685de5ae4c414e0d124bd8998e6393a8dd6a4b230c7a1c1310a719edd78 6dcd08ddbad6fcaee0ee036af25102c4dc4829e1f57bc327dd45df493a2ec3e2 39784dd03c532b849b94c82b01d3a91a46216afd4212faa5812958d89f4f3a97 674bca817ddc0c617ff169348dd1c560971245b778824683783d2b070e4da7d1 dc33a54cb3f16ca436ae558fd48390b5e3f1f5d5a739efff41d2ff2d9d35aef9 375725960179f59de3b2ed4a669913e1fd3d6b0ea31a8442c67b831ce104a78a 8048664997d4cc447dd312b5d19caad982567b90dd54884c0af09f2b485e4f59 6bd7dd8806d25a36372d96066258864d9f0773b6aeb912d7bab4aeed81dd1a43 6de0b8a1079bbf8b588756cd9ca835155ec8e60fabd7ef61dd10120eb4155cd4 bc23a5710ded3f25868c2558a580afa47f5189ceb0d4abebc562cc1bd6b85d8e d4825f7209da6fb86c189d6a8411ef65b0912c4a8f271bedb6cd2865d0ec4a9a aa2d4770344186644a8056c894c20a42721d23b68dde34ef92f7279cf1b0a8ee 72a312d37291879f4d3743c46e8147e2d63a29ffe3b7b1dc2d938ff036795091 a1a37c4e22b6b61604e921ea21332b63aa443353e315e780cbf17fb1d4e904f0 c4297b2b5462ef92be93728c10308354c84d1bacfe825818a9668d4636c0dab5 9f8e96ab8dfd84da6769f78ce326f4bab8fb11629629a0fa029cec1748f7d898 03cf405051c736c8c1059a0fb0d90608b39330213e60904c469270a3cab5861a 503e303e62f27f3bf50818b49e3f2e1b42c9201ac12b617a3c1eaa55a362e058 2c4081f21f6421fff715547c38b73f800ad7975a34d5da2c27353ab0ca282ef4 8f12c3e9daf248ee28976718f59dc8b9045541c4becf079da8d98bb06bd7d5a6 eed606028b1d605fd9c09310500269f7864a7319667533d367cae0e07641be3c 4ac8e7654c3dbed288d03262ab67095c7efa8487ccfd75ff18f95b386de1acc3 a2a109c422fc6fdc30c9fef0a2e09be51cd3c8eecf3bea378c637c7404d8b948 d7506a0450cc43efa949043d3019b71cd1b96133b0610e0554e599f8a03eb398 f11c9215384c684bd1656e276a748ab743d5748cbfdbe9ad35b6477f615c4765 8e3c945c8ccf1510adb94d166cd8a8203bb02b7dc5d36aa51bd66244ee92426b 831736049cbf348eba9f0033e3c202cc2c24995f922a507afb8acc4e08d52bb1 6b45b64dac93b4cc37db3dd5d126590b41adc9e262797765c2cb08808dc8e8dd 53fe250941d36df5304bd6cefda2b44f96e022987fe99790aad6dc4708610e66 4cf322af8615650baf671e9253402e418631af91 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 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812b1188a10f6327c9e8714449de2ae636420f56a44cebd774f0b131c629 818455cc8dd8d40939f3ba8aa5abc54590c7286b172193c23adb1b4f9931a9f7 73b960b1f5b760438028478e4442dc93a567b07e20017c18fca2a1daa2649dee 5a6ec51fd6c3f4b27367c31e95a56ba4bbeda0493bc02306037e2ba69add9b94 373364db316691e73d6811cd76fbc92b0c67ca18dcdf05807f17d1b309456ea9 d113ea0fccd6eb73bd8dfdbd5905a5e38bbf61cfe58fb01ec95a4bdd9565433d 4a7abb8dca6f76c45e50c1c9ba538078a5b7b67307730c84cfc5f62677924a48 28a9bb5be0b65603fd59e525ee6d0fdbef578ed48c15b1a344bd3e748631dc30 08992697b3543551e2a8740b14bdcc1df5780e9b12aed9da00183a46d0f2c727 ba64ce49e2dc7ae49ddec532db0ff9043ad3307040d1c84f4f7904c6250e4190 3f3cc5b97aa240986d464d116eb09e28c4a357bfc705238f21d179c1e8efa07a e338e737da2d04db865b77e9a539e9499aef03ebf58dce169a522fe6d2b43aff 0d806a114cf5af8368256694185c39f8eb6f61376624e3fa5572e82b68906652 e42d01549282e0bed67ed3692a53d6089395fa4e372a7196284f4a37b4aac76a 7d19f6d54519f7a64ae37c7fadbce8df272ee002061751f313f906ad4b82a369 e62e5a44cd30f093041610781e37fe26053bcd33cb4f7c43f8d93f1c72f06351 db9d9094996a34a3a0c3916684e73225589777c316afb196c6103b3293a5b090 804a66ffd0475367489bd6e2841a51e34c58d9ab5dfd4cbab5a936045b0dc8d0 a1373f36ce854c064b92fb8fc747a0ef6b50905a8045c3e021562427bce79ee5 68e5fd5b8628f218ee8ef1356e812a8e074ab2f29ab0a266e311e825bbab8492 b52f3dc748460c5893217f5f86c964d3be470308ca3537d62c1c82725e028163 46b38f244b98524ae1d11643be7b15d34cb7d57a38e1bc8f3661be54c313203a 4033066015c7bc1ae389745acf5f3065a7143d53ec45f32f649d740eb9fa93e2 69b18c2428061d85f694864a2f66c22ca373b939e209cd47756e25aabbd801ca 634ff4c6eaea4eb07dd66e4e712d50ada69be1a022c494a536eab11e8dc947d9 e99ba412496e483e68f76e00dd155ae0f672b13de4b8018370e47abc106a205b c1d2bd518b0e9e3d52e4aa13cd6302d53300c0bc3f7ce08956336987ee0350f5 8236ae1fe20c5ae8575123b72e7434 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /Theta 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 61 /equal 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 25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1 c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2 b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e 2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd 6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4 07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331 51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6 0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3 d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1 34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec 015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a 418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e 5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd 977f844d32b43b0e48caed5a4bdabcefe71695d69ca784df9fd4b83e27ad50d7 d73f182199e62fe14809e02d737efcea29176caebe85b84cb258815b2039da9a 7e4b2d5f8f44b12fbd060637c19cb90a8c6bf4d5d32b046e7ccacb5d5c7140f7 e7c5857b29c6162afecc8738794c4d97b60611ad6b31dd49b4dcde130196ab38 676effd276a815a6ef173d84056f0fe44818fa81d8d4aa8366ddad45b931bf0f db974408d130c7be33403b759a5439422647fe6580f9bef130ed6636ca91c12b 4d91d28893d42bb1389a6c270e2a40051f8270c4875c970b70fd8f8350d79029 7a97aee226317bc39f85f8cb413ead419acb1ea1d01ca9821e7eea753ebdfe7e c5c6ced2f5e9a6ed7faf9b9a8aa0be8f828f1ba26e07d688388f198fbac479ae 7f673bcecd91ebeb9878298240171954526ea3cde32a560b0991c5fde844c42a 73b55cc6503e601f35990d3ac577f512e94ac736c8e9759edd4f94b21d5348c3 955ace17522335119152f73f667a64a30b6805bb33e2804b99ddd20d50554397 93c1aab06aca12352e77c6c12a5d9d86a6fa63f9700d58dd6676532d382685d7 0d1e97319b8290467307eb367d2dc0497dbec582dc9a38eb811e94a6c0b18606 f0b69ac26e71868b9ab3772f899c36387d252f1fb1f9a623b3c054ba829d5510 905019b9d9d8fb73a5e44d278164f0d15670eef797c6b960579e8af5a6efb2d8 94ef4059fb5a2705afc9647f6b46efb74bd31c04858c5923db59de66ec0e8361 38346b28d3a677aa5cc5eb7b124c644537829a8eb8fd1d6de9049bf285f6dcd2 f8c2582ac852ce3088fcbdf6179e1f0014e35d1deee7927787a469f4effce612 aa3aa2dc80004e3add6397e12415c85769f220648c599efc7d37a11fc61dd464 89817d44cde4cc7386150dedadc858a34034c4d95403aa43116b86d5ab53bceb 81b573e3202008ab0ecdb352e34166d0f372618fc98d1b8a67e9c6a9db598222 f1ae2ad4361ab1ea8821fc758156cb822be885edb784a9433ff6c97a4c667d46 8d2046489d474550340649304d080d2183b13d4d808581eb200c86ece42cec03 bacf8ba3c8fdd4288bff7f168f4bdf6354d50a049d68585f1192dae0a232eadb 10ccd14a39c8e44aa588e0386e743fa4777c462a35b6344b7b1047c49bb107ab d75dd28af379c8e54d3355626c5f6d92e4580f10849f575cbbab6a9ae5886b47 9f376ae6f1a9f0989dc9b60f3f2a5440d18141d6df9009c8e055eada3d0888f0 fe915a373e8f62c65db256a85e1b4a48cafba7075e53fb46d391738d77de8161 29a8550bcb4c1a9c113ff0419a2ff03e4e02ba85639986291a6ca7784ec24df6 235b9de4c3a32c26171de5b9d838b868e78cb73728c3e5d2665ed7db7410c5ad 7c63e46701a423fc6c9d430b6f44ac7d3ea75e8bb05e4ce834e6e13bc93cf82e 4675320af70f6de6ae6b2c32e92d9104d1ea986d0c3cdf023871cb3ea52184ff 320f67ab5c87103b9b983928de53a450bdaa9b44e715623c39073faacf7aaeff db17a37ecffd552c2ed11b8ff719c5da3174695b73a529dad35fac044ee6a3a4 ba048a1d68e843881f6f730ea7ffa8a32266b6d3708d3d53fbb14e8f4cf0247a 4ff2cbb7920136bf0daccb3cc7323083e3a46c60c4977281d07d135db7febe46 41d949b6deb5a5ce885d2bebbc07046629d0e376de5f85b8169db13bde2293e2 8062755c2189478b275ec3bf43c6ef1a3df04bcb728d09637e35b394153b0979 2f7e47393f2150f26667c3f8e10a6103c7398555dc8befa99c6d0d307ae34560 b2226b112a61f9976fcd3c791714f792804ce39ab95d06d59776fb7a9a26d3a3 9544a90ae55636da126dfaabcb01416c0b65a10eaf9b78e1a61fa4b92a71e0aa cf559505a3f5b35e7513d01a245539999751c7b4032353f43ae068cd4e1fba9a 79928d7f2c88c43890ea47586bbdd028f32c40473c2b86892e1bf6fa80471914 8e04ae47ea8bb151 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 69 /E put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c430287cb233252ee604a481d21f6d474de7d8e00f4a323e006534d427c7e 009f7e849bc2a88531b276e08b5d6f6fde870470208d64d7aaaeab7a7a9815c0 97929f04ceffe9863d487ab4b7161b9f8492d6e8047aea0f3ee75fe940f0060e 41a679461d4a91579cc5317e4527ac0b8231304f59182b0069a99effc64c7673 fd128c2a91f2b39532be66acb655db3601bf548074926a8c8929bb91a56675b5 dd2f4ca7999ecb21c693c1fa58e58ade4ecdf8ed178e1cbf1a0622cb7c0564da b0f509180cf4d35c09866f4f381a62d5cb2f3077c0dc0d5bd285641a61ec4b1a 8d59a0895598b4f1a9739888be8b3db9dc9747e47d49825d1936fd8538e2bdd0 425986bba8353866dd3207243c766c99eb035370e6e8f19f9f16d327bfcf8a1b 1a6198746ad9da81e65eb6f42a8c320bee20e1252e9c9ed10de343e14b7b9ec8 b6d9261bfa6beaf9bf4964e798550328a5e102bfbe1a190c216c0cdeaa3e2866 74e2a862702decb3beb8e0ac6858430220f655506fb75d20dcbd3e9434d538df 71131f935371de2223453b948ebac2b10cd10498801cd3e0bc2ff5e513e88452 a6987aecd13bf98d840421f2be3fbd084a98f7c3840f0512c7fd7f0515d4eca0 75cab67bddd72856917f57608d7cdff7a44839d6e1eb603015d53df29247b2e0 86749e210c9718891cecd58b0038a5c6d829d3f312b43bbb51670a6f1882ac16 0aa0134b0f0ae6863f7c37d76e385f3f0e892833f1137e4ea84cb1246543fd33 d626c5d4b4bc777d92297864827bd59631afccb19ec3cbe93fbbac67acdc2c20 c83a32d6650c240482eec2e25f35d142cc82bedcfc963223cbd97f4b2b20ea7a e56418bb627f98d2d5406e9d6c0d5abf10a89498d458f5657cd4fe0fac59e40e b7612488250c79379cb19732faf5e7f1d08a79a92da71c5aa1e79410237fe55e 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 23 /nu put dup 24 /xi put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 69 /E put dup 76 /L put dup 77 /M put dup 86 /V put dup 96 /lscript put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 115 /s put dup 116 /t put dup 118 /v put dup 119 /w put dup 120 /x put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 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6fa3e8efb812c9beba5124f5e5363ced55e8662a012f2bc0139547d1deed9edf 77bd78cb85c1c8d1e47c5e4ace24e1ec53071c34a9d5ea6728bdf4eaac3a3d4c ce252a085b2d34a9396a3f7266aabd167c775dff8c6f908c46a93d804b83754e d1b114d51048cf5ef2ec66dd84222c2c25fc7ef4cc23e37d6823a3e5b14d97b5 a63d9686ef3f471a282dd95037eecf472c33e894998ae5721eaf970f4312b532 f7f4d5f61ba8888fef1b376802fc1a9f2984c524fe15d631ef991598414b344a 0e6a1122f5d6e72af22a8e2ffad1f8e7581a4cda845032334b9e0c15ae11bb8f 8184f4b778154d7b7c0b1a2cdc52e8ddef023d5a852a6a39db33be048ca939e4 74e68bba7f9d1a00d27f541ebbc36b949bf736ff393fc4c06ed0cd9e0e206c75 9cd8d609a81182648b5ad15eed3e34ec0c034f361ef02d6fd47fd4f3594c6fc0 9f6bb9b94c5234b2ffb854181cb43b654067c8d5edb32d49e96b3be0315386ed 9046a19ea4280dc2002abe3519cb6b73af24d0df2fe31103417ee68bf83fb07a b27584036ac416354a290a9573aa07578ff76c04128ec024b51b6effcb5f7850 35d23d599ec55512136b3a54bc1355d5229291341bee7ce8fd0854f07120cb7f 67f031cf0ad5844d97baecb7b2455aea4d2642caaaa9a09e1062e26198b4e0b7 f64e25116bd41e2259394cead89d4bb426db69fe27b3dd8d909a184fa88c92ea 85649fe9acd8e35fd94560e3832dd2407799c3341ac3df228c8bc30113269875 026e6b0da7d68852b147bc414155574cb06c138a94e7fcacf4c27335e9c3f240 29758a2d80d569f1a5ef1213daef623e6a10b1c22986784d11fba39e8a7e4cfb 451365342d16dcd994241eb295ec8a9839d2e9a65f267174bfef6dbb0bcb5249 6efd22e9a8de29b94455589dbd0b15ee54ed9bdf6b4dec38c7e9d6b9317fcf45 19edaee72f5ddfe849eec12796598831f95e9baf4f922c49b50bb959ca62fe69 72e797ee0eefd081dabe00f980b59bd737791a2389a8b45224dc87d4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 12 /vextendsingle put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 88 /summationdisplay put dup 89 /productdisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 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11aa6139fe50ce13d8ef9784ba5873f464133f8fefbac7dbefecbad21fbae8c3 cd25c04d92a206e8b2243d5639397346f36e06a92a14d78487810123d80826ef 34ac5ff441d5e3c806c955ae1666fc595b7829b5b1fde24e359367673ad1ec5e 26d38ad994b2dae98e4d7cb1f9fa0ee96d98f0402f651339a6458b30649e6e64 0cd4e20b86ba14e59ec70c1db41b945a0cea34cf11903b8b8a5a2c273c923d34 600752f9cdec290060d0a3d3e23115fba5f09d4c62cfe778bc5b2b111ba08929 7179e4b002e8ba766790be6da11f8de2be9fde942f27d45a334b72c90f391f62 ee74a74f75eecfcf7260a6cc30e3e85afc3a52832eb77cedb0c1a7419f7c7f21 f0878eb03a728444d24dff56bfedd4e4ea28f52f5ae98ac40779c841984df8b2 620095c711e9c139c312bc90c84627552e944b808dfc99647482173444760dc1 95d5f99e6155d708d771be17ab69e94b6c49d3e97f66abbc351f83de288d5cef 61c143cd82e689735032210de9f97fa20607db281983ef1877b7f2ec621aec6d df8eac0cf2186cf6b326a2742a414a2d72166ad79d3d5f561f7d5830cdb25f5b 9163bb8559c218f30644d572dce5352b9e3927c7de04aefcdd3204daf656e0a0 ace93a69cde27f955c10a36643ac2ace1db41200bbaa60833dacdc7b2355d835 e966825ef025e67eacf28be7d4d858c988f966c722439740d27b112fbfcf08dd 3c16b4c14f858ac37131e44da4e226b8b9462547dff9bb142f28ef6e1983fb89 281140aeb7cfc01ff1894b99c0569676f2c08918975fa63408624e3008022b73 1dde1456da93c7d999764da8959bff08d7c8ac6c5888f5d348e395c847a4061f 6c5eb9a1af659a5fa76deea93d3787713d0a3874357b57fbdcf501f16f563784 13374ce15d0722733044897f267a7f45ba6a176d27a8e3c185d8b59471917740 fc37cd6ebda1da0f2e1a6224a36c3ac954eb40c6548ff3b41affdb6e787789a5 143d8683c08afd0c7b8abf22ad38757049156e23abded156f4da5ff5a213d5df a1cc767afdd875d4383303a2dc0509e8a8125d21651824edac697f2b8887f79c d234f6801d31110f922dd98fdb8a41a1401d46ff6e7f7a96694b8217a9f18d48 833b5d33b9ea90559818b6aff4a57c2fae12a4fef8495188cf3bcd21e69d3f48 85cdf5b6c8b879421e7ee75cff0e23d6883e3ee6f9c412ada2d9cc43501ac9db 81d18adea3cc9298793d383a202147d0a701a1f72a017986ccdfc939f6e9e8c6 c31eacfb6e946533aead50ea47628b34097896def849fe026f58ce8229cf3d13 14878191cd36d3a2be0b02bca2323b7290351d4609342c6c95182db6297d7343 1453b6a851568063c6be233e558dd7e3a1c851877b326b28b1f0ff415034ed61 d69e8f035898e418965cd5b13d1b816bc6b28f3aeb7df9d261c39864b6f49ab3 54077c2d5ad6e57067f472a9d3398f4fdf79db183c8545a6dc6424c646252ecf 1a61a7ac4644d1ce59af5fde3bce0f12e9d08724b2e50ec7ae5d923887d590ab e5653fac2fb9f1a1b10d8361763725cb700a423f577d2eb9a8279f066da415d1 293cc205de2e1004d0173a005acdcd2168236c6cb060cd46ac0238df1ac8603e b6a8e200c2020e06aca2fdfefd0027963f4664728080b75f3dd8f3513204606c ea150a8e6fb1b6845424d764ae0ada5f44d6cc6cac1a9f3ab023f3f384009e17 8bb33eda582b862f7832ad30a4ed12ad8ab93e4bde831dbb5e267f13c3225b60 8617d0424f593224b03d8b95d9a7a17e2ea744fb2ed9eca6b266da786cb0d4d1 410248aa32c0917d7a4b7626b17c6c43148d62c7a143aa3677c8b5c57fc7337d a2673d63b3510d402a1f172a6f34207dbcd91941be2958ebb06e50c96b47a0e9 eda22ae3d35e66d43b0898c1ed6053cb2258a845c2860f446525761d6ff16547 a65fa59ac5afc5cd3f3da0f886096233b2b5e2d650600ce78fe814142eee1d02 48b0b43314061b6aba54c817e741d89431a93fa60cec8d3d4bd84d5d2f94b396 84bd109c3ee06d68e576a24a6b663b8057d8fdbda084ca8973c0fc9729688488 1b6159619c395de7f6a373483bb43d1368ca9aebcd8b80933c31207d3b4b25ae 4eac55313032202ad2b1e03a8233a6f2e2f2a1a4de21d19c40446c7f841c4954 969871ad8f14c7801ee58f0717064ae78035a1786413365309317026ab5ea66c 5a01c6748f9f33697433ae332241507f1b2deab0e4b2f57c0034406e8412c563 bc23873a6a17a16fd237a493e93c824b3379ac9e415a9fdffdbdefe245786e25 0e0ba6d26b0aa34c765c3fa16ce4db177a4ad98170c03e4670035013638d505a 0a2fede710a1d3e4d0d0c2ca5572fbb48914ad9bcc7057c9d56f771afee74017 27b4f775af748a4b830ecd226f2cc6c31f370d99c2a827abb0e1f2c609f26a64 023e68828379d0a9492a083c744c017ab36f8e7a38f7c7810da71f09699764f3 901f07a502f18ea18b9fc54afd2728ecf1d870116281f3e0196dd8d2965b1680 04737a276464aa02478665fd532a10eb060b9e475a647627f83b275d8e983426 d94d4b2ad38c2494a24083a4d1a92d7a41e47d32d6eeadd1ece4ce537421bc8c 2b8b720d4bda3177abafc245523da504321c494bd3182efdad3cd04eb16ae309 418e342a06ac9c702584b3339e73cf42e230c18ee437e0278efdd535abe28d8f ce91e0bffca36c7600f5a884595278efddf5085f74c3d7d8e9beb3be3f7f6131 e8233b084b16dfda9cc778dc10adda42786156d707750d12c920cc297e8f5857 8d5084a86d68a5180a 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 13 /gamma put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 33 /omega put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 64 /partialdiff 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 76 /L put dup 77 /M put dup 79 /O put dup 84 /T put dup 86 /V put dup 96 /lscript put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 107 /k put dup 109 /m put dup 110 /n put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 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bd71820e535e62bf46760b32c2bdb5e4d289c90e52235ecc93194f5a7e6a7d1d 42250d6098ea57b110c1fedabef4cc61a38d65646503acaf7ff372832a543241 8a3b9d82e2b2a3efda176f15e8e1012999b198fa4edd9afcb671608e42 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 67 /C put dup 76 /L put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end 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0dd43ef4d308a0206da41cbecb5047ed3409b4e11a3df10861a77e8ff4cd275b 855803b4f087826e3dc3fb7d3c72b0a78ba4e7ebe19f72e70886e61c7ada34e3 c2e2464a4a49c493a42640d0c238022908833820a5647e5051c67d485fcce9bd ed8d61d56fc20b63548158acf7f22b260f3d77853c96f514803254568cada699 6d73 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /Theta put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 54 /six put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 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a85a080f5335a9744bdb785a1e265cbaa18f197a889206c0c44d4b9e1e078ffa 67a46cbaa697e51008f0946a1f51c6b113f8c72e989f5d940b8e0dd9d8ddedca e10a387e211ff5d7b0160457cae9bd63 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 75 /K put dup 100 /d put dup 101 /e put dup 111 /o put dup 114 /r put dup 115 /s put dup 119 /w put dup 121 /y put readonly def /FontBBox{-35 -250 1190 750}readonly def /UniqueXX 5000826 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36f6372968dbd0df8505aef5b22e57f2b9834fef2c2798f9d715aa323 3e09b183f8d92797bbd3a990980982018887612cdc5507a47581f07a1cf99a5c 587021d6b67b0524e780517e7a088a6388097ced01e5a59aa8779c6ad82af704 f6283c0a8b62d57cc5d24220e4d52a7c736389ff9d77df48c0de3d3db6482774 72a5e726bf4d83d29751b70eca9ee9d04a18fb7d011542a2b2737eff052a4eff 2800d8dbc1aeeb7273d9172927c2912b597c90faf4eb15f30201e026c5d06c94 122d69e4c81882d9f10b74f81d8a85a329a5946464c9765706a4e979e3b76913 83ea8ff66e4608e5c6fa0171e0c14bba3efb8fbcd0285e6ca408671bf068e1b9 f1c040e0417a92557f6b43a2b49c772c5d6e1e6fe0315378d71f1b762c987f29 6ada445624744ef29f727436345875bab3b78eff3a86027026983eae46ee5cb6 baefe7a95b00007094774550ad81f1b2c7e3c042a77548631e4baeacfb244b62 80922062c83c0f96d439448951a8f4e8bdf68d60245c60c8a8cf3e340644ff00 efbbcbd9abfe6018af21b3fe10b1381325d2599e22b2c5ad47bd6d5ecf1f55fc 7b382f2bf4889af9fb6beb58dc03087e9de3624e2e171c669acc08ff9a88f879 48749ad40d3c781c14e04ad93b147a89b1f29c82f756d9de7c26ded896aa4918 46e3376cb7cad2c19cd70be96eb4cc3509e812fe2aac63a59c3f5016fe6380ea fa2042e6b070a6a0e9ea6d4fdedbd9147fcc6eedee7b48bcfb29d09c214fd2d1 6297d9220ae3467eeecbaa9efd677e0964f8b737d0db9a5fafc7ecc4ff00bb8c c06359af9c0db731419186f985c3ab3f726a465d094c89610c370b44b90a79d1 80b160916ff13931fb86076ab0f7b4ac91747c9cd900050df39f1a12a9928697 d9a29aa5280a46bc76bf952efec06543b9d02a81cdfae407ece5ecc4ee5ccf26 01537ae0fbaf8e2578157dd1d488f12c309e48c4878fa1e46f15c8851678a94a 3c3baf91c7f58be3fb206c50b8f27baee4456aeda4b4de616106760c687f8e61 8d4c22307fbd789a155df77f1aa08bcf56c0e517798a68b13deeee9fa6476c91 008f35fffadb3e473dc6a9f5e28b3d593dd53a3752849ff9c422c030903bf4ca 36bed5d34af2867a8b08f93c98b1d683ca0d5ee290018d498f505a9a0c7c8f04 86e7feca1becacbadda27b8eec1f13a6ad129d2cf8464b8f839b5b9671c23317 477c22de71c813b78ece24544a3fab1cf98a3a6d4b4c86f022c776da6ded6d03 522e62b3535097bc3be076b79df9c3061151c916d93c72b4edc67e0c9c926cdf e4490d1ece41c3193e6fce004ad5b3258a915acdcc8d8707ded322767a7ee2f5 7b5bc59fd65baa1d7439166eb1ee0cb67d5ec9ffbaa307d827891880551ee31a 05f8d1c687c95b7f06701a9174410c310ec452fba58d4e0833b271433df3f072 9ab76150775f3c7410f9e6c7f0c2238ca6f5fd96a8dae95e86ca5e79b3bf3fa1 de5c57646604f51e37fd63f32189e4d257e2118f271422f57fd4e02e8686557f b963b1f05edaf00974ca62ca91d35b7e2f57176ef1a8227f26785f7bd5ec7346 2a0b99ee94e5c6421081e31d0a18ea520f9706cb52600aa9b40bcb3f855980cf ea599c4e9d05ec90b484a2f9684e171cd4484a81d96e38f3bd9d90a228b617e0 9dc35959bf537e664a36eded3f5caf8ad1b4f93dceb682d341dd9373094a84f7 e7d6cf38e8fcb2671fbe51a0d6dd3769a5aea062273021a472c9b76665ffc688 beb6b47858fc55d89038f02fb13dec32ae3d2ed2d043cad32dd6d485d4055442 421bc18f9853cf0acd6b1f70529b36b393cf55ba58f1158fcc7bdf2031c0ad70 dda20b32fcb7aeb3a96d8d8d611fac02326bc9f7140b384711ec4e00d62daa8d 81ab842170e990856af4012355500434ddac2a1fed3ec62138ac5287cdec1584 68cae1aa8b6125dc38687f9b77070214a02137797494b26dd3db78d041548a8f 6a8d7f13682e4dc6d42733241e49f5ad80f997a5df80d4397d21b4b93d832e67 64204b9f7183d73d0569c0b61c29a9095fd111eca2fab775af32ccb0c81998de cb652c906b05570d47a2532e64f1dfc1b1a54b0eae48043acfe88cc488edbe4f 1ba1a38afbff40e5a52aeb7ae91f7798d8af673939812a0784cb3b386c1c7b3f 20b39038cc4a0cc5b2aa3eb8a5b9cca596815b3671216edba412b434f4d82508 cdcdded8a54c463d7bf6a825f924fa0ec59e2d83be3d287e9142bb53467555a7 e4306d82b3cdd5fc08cbd3018e56246c847d553ea2e02ac207cadc5843e3b957 15e7148478e92999639c6a1cc169c34988ae87c6c5d980b4c20b033b20012719 93cc5a3f5de1b0b4a3d8db72cff741c9485c4b31e2dfad0b6b02d145a745de10 712b4b6c6e97464c4a7fdd83c62bb086c15c1cb6711eaf867cc11732f63d53ba 8dc95babece1663dd4c0025322a35178be8bbcb0fff64278a4c6d90029310cd3 49254274d02bfa23137a5da5406e62fd4a573c4187d8038e117c25fd6e5e3bb7 d835e085e471bf3bce285dc6c5df165f391f049376dec2e00b2d7578e024a05d 7a3548434c6da0211981e0d895e371d6899e33c8371b865903241f925a1af2a3 317b6a1ead56da3925aded0a2a773deb8b9a0ff25ae73c3a16265b41c2960816 1af1b9b3f8e1ac08d41973b9febbac2b38bbdc6ce370720379b526cb8ed62078 418f3993d09d92bc9c772c594610be27ee89bbb141424e65792059ea1f53de15 7fe5d3384a6bf38d442d43bebf2dc52cd6df62fac3430bf49dc593957b8f9e0e fcdb8e71d6adc08282fa3ea4c98994e6deb193dcf3fbe1273b0d3ae82911d275 1b2d5a9a8ea0b9cfdfa6165222a885a375b8bf5020b67bf40a2c8c4d39d3b691 62b9c070811ba78d6aa33b45b0dd1edea7ca17bbb37835db82e1e0c5dfaf53cc aa51e5a8f3c2a3fd25b76506d21c0199a7c10185ff1564aae52f15cf54eacd6a 5713e4af386ff2d2198fce3fec94d11ba0fc70dca186b05c6d92228d0618ae8c 069ae18bb2c53f319177fb445fb408456d62fd8cb0078027bcf34765e62b43c7 7d304a53e7e56a18d78e3d3f9f06fa10c5bafb6ebd83e3ec54a0338138c273a9 959e0c348f9012619041bac34e6ac2c2ced30c1a82f68316ef0b2f241b62952c 6a9e8f646001768d4309a47340b1715a205c819618b51893af8c9fd639a1255d cbea3fd3c7b05284df015813198b15f0562e0059a5ec9e096b41555f7d04c84e ddbfcc3a8fee12dc9355d6bfea3c438c71a9430ee590883d72ef219bdeb16a71 e1534bcacb281d87a08a8209d889f62952ee1477b7cd42 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 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 54 /six put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 7dbcc4a8e4e85cd3259f40d3caf55c742cbb40ad0db1044c20a4f122a63f7b81 1d945bfa69662189ce4d089464d2ead9f6ed60b581b04114d5d45e97be27a576 35154e9b8464f2a0df18da855eb51b8f64d3054b0b2e84621f025a0776d16fed b988a43d2d64c32768dd106b9f541ae8e68ac0bb7399e16f4d4ba074b2152d0a 4e9b5bfc21bfa0d531e28165e518ffc054dd4ed0d74eca079d20e79670419f92 e03bcbfeecf3554d661596f6f29e12170804d15a250d917ffe7a8b6e8fa53047 1ed97ba56481589a65ca13619129f1e26affe6c22f0c38540f8ce37efb6e9e9b 60b51a5a9cb4454fd7c7f92f2f9437159687ab590f35b946a54491a7739c9269 e0f1fb48b129811c82edb3171cbd5105fe65906974db8a7da92f4f43dc7f6b36 6981146d86d23613a0b38d9d6191db9fea0172e982cb1cc50e382f69da1b377c 1be9407f88a2a761b56f398467a057f35d18c01cc377e006182c891ec80272e2 2e3a5c7123cd27eccdc87392a9fdf63bb40f02b7649cfc53ef933c6518744cb8 9cbbd437830ef5b1d58b00b67bbcf4426dc1e6ef583b0b4ad3aebd741e3ff0f7 29ae271f032019b1e7268043fd215be590f9cf24da14a90f1683afcba8006cef 5d5632c2481fbc1bd8224e8952debb7c4596a237e5505ac143180956ca1f603e ec70cdb4a33e1c4ca174436a38b06fd9d2b9196f02114b77a9a5f66595727faa ba323668573ae328f1f84e529ef161eaf705993ed7a6e1a993182ced46036442 aaee9f3d1344c2b6756bf9ff90747f029de976a2e8553f38d4f61266c2552051 4d9d3a20e74bac1b73b60833f507f897991ca75ab422285a0120393acc94bd90 11ce4c3f45b7f1e7846f8af09d1939fd0146149551e63e656d790f6d32d07105 8488c29ee7536d7f2e5b66eed4d93f25850325d5b60625e37ecb33822d4b7b2d cc76bd405ba53af3ced9fc4bef9dab60b28c6f23daad431f85a5926a23ea91a1 2e6348bc2df346e89c2404a836c888c57aedcc762e44b077d0b6d7410fc776e9 c11817f33f8ce752fa9eecbf2ed168ea85eb0897db47edba45a75956c1f8b4ca b7413353d51d0b5ddd7ff3e01a32cdf9dacf141bf32bf3bf4926492b89d5075f d4bf2a6482d64d2934fb7c8cc9ada6b76bb51437e4105aad6ffb9f82c709f324 ff2579e219a691baebb0c6b3f8dbcbe607c1ee35b8c0a80ee34b866b2e81a18b a83d6683287c648878e19a542b35832cbd883544ac6724452bc0ed013ad11dea 153c6a880d7239486afc3201d246af739154422cf8dcf4eb5ac363030bf9b99a f71aaf35430a17611d72e10a692e2d14e2419eb4fd3905ed253a37a2d50f3818 9df17bce17afde520ce25eb3191e73c081847ad7394877ab201ff5d31413097a a4268864d5ddcbbfd99697d29b869882763f072a914d481f5c555e6d7304656e 2834b6c6ed4c3a96f09fade325a773f046888fb1909ad6088bbda74b53f31ae3 52fe4c57581ab7b4fbdd7c1c5e9efdd7b1b0c98b5b83350311d7bde2c7e5b708 1ed8053bead2ac86939ba1de52e061468add87665b928092ae640ec75f8abb29 06a7edf7f4e0e7a33988c2422c5930d76ea35d6787cde6c456fc393c4d0f490c 05b50276439deba7c08fb6fd75c5ee41e513a9bfb391ac65316d99a85dc8dd47 91fef041fd1981cc0188708f53638882a2e545dc35d230b00bee90abe558198f 5d830b1d2e1b2e747c09f60ef31da373621ba2aeba75ea1e29691f74ddef942b 812e505455ff2eb75ca73313f4bec094fadeaaa4bcfd2f2a6820feac7f029cdc 0335d1aa40503baa8a672ce9991eda58ee87aeea932db9ede03fa92e5585ea1a 728b0aef6e5649477ebfdd0fc534caef6512fc2643f350944bf58f901f175a9b 4dd35fec6978c1fbe13ff892ff73ea5a6d0ad4dfe824137aa0ac620bbdafba68 f1e047a5a6d48c1e83d1df44d555fff42301ab6fb27bbf5027946c7af468b9df 0e572e3e4fcea7188f92cf482d51534bebd2d206edfd3b6da1ae567a3019a508 c23528d05513ea54ff3f4d1377440cb2a19a2f16f1e8364dffab3d9cbc523fc0 73dbd6415450ccf9d3cb265f7f3945bcc36f1766294b10be5a1b9b4dc7822043 9a503e182012b8009efefa039bdacf7fa1c693bf433e53a825813d190506ab4a 4ee10f3ef5b3db884ecebd045d96e389860d940fb903caa668f839d91578686c 2931decc6007a88a80cbfde3c5e730a6212e9f3048c1143e21419721ebee5e87 9d0f3b57b4f448359da8d2ec1155b449f0582841496c21ffb0132a78e00dd458 1dcc306d287fafb7c70c65ef4adacd7a8e4d97c6b00b9206561bf79897b764dd 761b6c3230c466585c0e8318f33e515637b3cb66dc5b535c7562bfb9d6dd9ec8 a88e2fb3164f7fc3c0156494fa99403d2a3dac89f91a6cbbcd578e86d332bebc fce2fffff1530f4eb42578fa84b58261fd0947a6553388a715ffed72ae67e4b7 961140e54beaff3c32e4cb1c1a2ff4b85c9ac814b079bbeec8d9b37ebe646928 14b0179d0b8e6be653991edd0701097e0c91ccba71f1354416ded923459ad6d7 9c62ce4c26b577ba00e0eca38f8e7736392567848b34f1e548c9a60d9124f1f9 a4e990b553e91ca4db5dd2d34675d64a161d169d2b2cddf0906fc3c5ae4823ec 11897e549283f2347b96de0b7c80ebaa679bc4231001dbc25c420a6132af7210 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /Theta put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 18 /grave 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 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 126 /tilde put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 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d7c53d865fd8474ee6ff3c8f55a5e6c9c20eec1c972fe4c4fe7b4f80ccf49b17 af35a011f460868049a08c1da07b824279a1edf89fe97bad6f1640f1187764e3 2ccb81b7da387d482bc45006afaec938e269bb76f92ef2622c5e3660cd63d038 85324cc73b60e2 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 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 20 /lessequal put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 106 /bar put dup 121 /dagger 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 4a93d9b87124d146d8836482f73a24389afb8a74364f22077cc3fd6015cd4469 c34470c86925433a77fb3c838a1a7158139e96980de23ff461382df32c6cb4c8 59d292d187a7c919a1c3e51647cecd04d7e091b936aaf37b758d1de4f6846958 e6703fd60aeca4e5c38b34574b55b0e2671154366e5554dc12a98bd9581eec29 a866523ed5b825c2ede44f7369230a595721fa307787764add7beda87195e1ac bd494f6474d023bc194cded7c514920260f6af49909f64b316c6e7d0c9924fa4 50f4025d038ee4402adedb44aaab577adc7137de131167d35a1fe4c6dd18c577 9cdede365f8b102f3882f92b2ac3479fd2811bdec9d36e8d02e68781dfa05e4b 059cb3d8a2e1609ae17a1f4268ca66623fc5ef9edb6a4a643f6015a2b6afb34c 8d085138fe34fbe8632874127af55a641ae96f820c41fa6a6763ea4d4d2b504d 7a5a15cf3eb70a8962cc646cb7b7e859689a76d3c12b78f92b64a1ff94f21f50 cdc82dadfb69dc56336b98337be4364762b1ca5d93b58b205084ca33a6eb56d0 bae0e59803ad4b404bf9ee7eda597d3dfa5d8aa163cc75a7cca26d49d5845d1c 361b48db9d56acc01ba5eb2e0069bc6cd24900cc35844aea21ea6dd09fa79e5b 216319a8a049bcea6c706c582284d396b4947fc8837a62a1c615b65a99c22272 d3b7822338dddcdd485ebf476a87514f9ea581e839d94837752f8eab26c12fac c3983d5aee9bedee2dcc76a66c2c56ead99596b1ef9ecd5eeb6c31c23de8949c 41bcfea42a822c8091c9cb588a3ed179fe7f941e8f7b539369f7e09336c3b02e 96037569b70373e01343bee4dd02464490745b8206c26ded83ac36d457b350d4 66f03535912428533079448fa36cc772d88ae87b90899ccb4ed16bad2ad7d7c1 d4b072a84522b839b6417c4ddd3de4f67440a2e62fbddaac2cf7512095b56a0b e8125ec384cb84c456c233cab0dd043978650ffddbaa84c3794b0c3b5404b228 ba3a40865acc2d83f333536f2ecd134f3b18384608b5b220977986f5216a69e9 699cf8cec1b798297cac0f0b34e16a7b9939df7f4b37938933172ff72d1e9dfd e88fe3515a6a4d3963eb5d3443ded518aba492282f8cbfce8337f224981c79ec ec25d253bd476108b79e23ba53906b923643a4e7da79e64501e936ba6cea8cf7 6362393eeade1e7d9a6686122ce5b3d6cdab82e15e82e22f0d3375687f783a63 2278209cdc7811b6267afc0fa3fd5616c430fd4d7e1230ed9f499964f4dd78ed 6971cce9985dfaee1d9362723898f2d846a71129f65786300e218cce6c3b6725 fa4aaefaa713ca4a0a13b5c864a7f0eda07fc7004fec34424c23e6bebecb1262 11f97a45d61a90b8b5d39de3bd2003cc2b312ebd6fc917afe4006815529a62a1 cf8681fb367950f2b17bbf95207956da3c9bd0af3735d44599476b07743dd343 b39a26d198f71ac36838d2cf11aa421680a388a5447f92a0f7c5df6403f76635 1a477064afe07dabb5385fd1d718c0acef3e3b54fcd13a00d2399437366646b6 a9df42ca07286bcb950bbe38ef5d55c8aae65ddbda337c9f0b330a60f481c4cd 2022a22bace3a0b7eabb2270b6447b94c16fe6af354ec1ee44b514d66a0e731b 5dd073fe286399b6c2267824c9aa6348fc1a7bd965d8ec35af9fb9293292b5e4 25c0fcad615191e5d5cf9f7ebcc269f2d06acbd4ecf7603261ac2a86a43e74cf e246f65ba5703156bf68d52fe34218f802ac8c852ef85add102ea34098608d63 6e02f1606aaca0831ba6ef6e694cc705e415db66aa29b49795738dc24badde15 673cf18b6c9abb7aafa12a2a7a029d06cfc2e4b3558b9de1b4858e7453ce183d 60c9f83a8b2669289d1db59821db16bc9a98cb01bc97efa15700c7757f5c5367 ff04ce59a416633f193b9c3c93a0a28df0edb2011445f6fac2af1fbd64aed39b 612f405e041bf4ac7e40eac3a5fd8a867fc6a736e4bb22224e24b7f2f960b3b1 90f3322f684a103ae569e4ce81652df608e6dc2b4252c83b 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 46 /period put dup 49 /one put dup 50 /two put dup 71 /G put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 86 /V put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u 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 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea a29b69d1b622b1f0cffc58291248759607d91150cb0651120970dc9f743bebef 44f6ae92facec57658999c8bf01f60611560043962c0695e1bb87d090e0fdaab 659d6557208a660be9aeef8ae55f71b8bc76394d792967e41bd8023b6e7f8c3d 9987d5e54c53bf2bbb32855b946473b44833bd78873df8e4c7e668ffff25aabb 8da4148f744b9d0524d6cb8281247b3052cc5d66f3f1bcf8a56a3fb446ea587b 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y(course)29 b(this)i(follo)n(ws)f(also)g(from)g(the)h (more)f(general)f(results)h(of)g([3])h(and)f([2];)i(the)f(in)n(terest)f (of)h([1])f(is)h(ho)n(w)n(ev)n(er)118 4984 y(that)d(under)f(prop)r(er)g (assumptions)g(the)h(result)f(is)h(quite)g(simple)f(to)h(pro)n(v)n(e.) 189 5091 y(As)g(the)g(problem)g(of)g(the)g(existence)f(of)h (oscillatory)e(solutions)h(of)h(nonlinear)f(w)n(a)n(v)n(e)g(equations)g (is)g(naturally)118 5197 y(related)35 b(to)h(KAM)f(theory)-7 b(,)37 b(it)g(is)e(tempting)h(to)g(try)f(to)h(study)g(it)g(b)n(y)f(the) h Fq(Lindste)l(dt)h(series)g Fs(metho)r(d.)61 b(The)1869 5396 y(2)p eop %%Page: 3 3 3 2 bop 118 555 a Fs(in)n(v)-5 b(arian)n(t)27 b(tori)h(of)h(\014nite)f (dimensional)g(quasi-in)n(tegrable)e(Hamiltonian)j(systems)e(can)h(b)r (e)h(parameterized)e(as)118 662 y(p)r(o)n(w)n(er)21 b(series)f(in)i (the)g(p)r(erturbation)f(parameter)g(\(Lindstedt)h(series\))f(whic)n(h) h(can)f(b)r(e)h(pro)n(v)n(en)e(to)i(b)r(e)g(con)n(v)n(ergen)n(t)118 768 y(\(see)34 b(for)g(instance)g([5],)i([6],)g([7])e(and)g(man)n(y)g (other)g(pap)r(ers\).)56 b(The)35 b(Lindstedt)g(series)e(can)h(b)r(e)h (written)f(as)g(a)118 874 y(\\sum)29 b(o)n(v)n(er)e(trees")h(and)g(con) n(v)n(ergence)f(can)h(b)r(e)h(pro)n(v)n(ed)f(b)n(y)g(exploiting)h (suitable)g(cancellations)e(b)r(et)n(w)n(een)i(the)118 981 y(n)n(umerical)i(v)-5 b(alues)31 b(asso)r(ciated)f(to)i(the)g (trees.)48 b(It)32 b(is)f(naural)g(to)g(apply)g(a)g(similar)g(metho)r (d)h(to)g(the)g(searc)n(h)e(of)118 1087 y(p)r(erio)r(dic)35 b(or)e(quasi-p)r(erio)r(dic)h(solutions)g(of)h(partial)e(di\013eren)n (tial)i(equations.)57 b(As)35 b(a)f(\014rst)h(step)f(w)n(e)h(start)f(b) n(y)118 1193 y(studying)d(the)g(case)f(considered)g(in)h([1],)g(and)g (w)n(e)f(hop)r(e)h(to)g(pro)n(v)n(e)e(similar)h(results)g(under)h(the)g (more)f(general)118 1300 y(conditions)d(in)h([3])f(and)h([2].)189 1406 y(T)-7 b(o)26 b(\014nd)i(a)e(p)r(o)n(w)n(er)g(series)g(expansion)g (in)h Fm(")g Fs(seems)f(at)h(\014rst)f(sigh)n(t)h(hop)r(eless,)f(as)h (the)g(solution)f(of)h(\(1.6\))g(is)f(not)118 1512 y(exp)r(ected)d(to)g (b)r(e)h(analytic)e(in)h Fm(")p Fs(;)i(ho)n(w)n(ev)n(er)20 b(under)j(a)g(quite)g(sp)r(ecial)g(Diophan)n(tine)g(condition)g(on)f Fm(!)3224 1524 y Fk(")3283 1512 y Fs(considered)118 1618 y(in)29 b([1],)f(see)g(\(2.10\))f(b)r(elo)n(w,)h(considering)f Fm(!)1476 1630 y Fk(")1539 1618 y Fs(as)h(a)g(parameter,)f(w)n(e)h (shall)f(b)r(e)i(able)f(to)g(write)g(indeed)g(\(1.6\))g(as)g(a)118 1725 y(p)r(o)n(w)n(er)e(series)h(expansion.)189 1831 y(W)-7 b(e)28 b(shall)f(pro)n(v)n(e)f(the)i(follo)n(wing)f(result)g (\(see)g([1]\).)118 2008 y Fn(1.2.)35 b Fr(Theorem.)h Fq(F)-6 b(or)28 b Fm(\026)f Fq(smal)t(l)i(enough)f(ther)l(e)f(exist)g (a)h(set)g Fj(E)i(\032)23 b Fh(R)k Fq(having)i(zer)l(o)f(as)g(an)f(ac)l (cumulation)h(p)l(oint)118 2115 y(and,)40 b(for)e(for)g(any)f Fm(")f Fj(2)h(E)7 b Fq(,)39 b(a)f(numb)l(er)e Fm(!)1477 2127 y Fk(")1549 2115 y Fq(close)i(to)f Fm(!)1919 2127 y Fi(1)1993 2115 y Fq(within)h Fm(O)r Fs(\()p Fm(")2389 2084 y Fk(M)6 b Ft(\000)p Fi(1)2548 2115 y Fs(\))37 b Fq(such)g(that)g(ther)l(e)g(is)h(a)f(p)l(erio)l(dic)118 2221 y(solution)30 b(of)h(\(1.1\))g(of)f(the)g(form)h(\(1.6\))g(which)g (is)f(analytic)h(in)f Fm(x;)14 b(t)p Fq(.)118 2398 y Fn(1.3.)58 b Fq(R)l(emarks.)j Fs(\(1\))35 b(The)g(solutions)g(in)g ([1],)i(in)e(a)g(more)g(abstract)f(form)n(ulation)g(and)h(with)h(some)e (w)n(eak)n(er)118 2504 y(assumptions,)27 b(are)f(solutions)g(in)h(a)g Fq(we)l(ak)h Fs(sense)f(and)g(b)r(elong)f(to)h Fm(H)2274 2474 y Fi(1)2311 2504 y Fs(\([0)p Fm(;)14 b Fs(2)p Fm(\031)s(=!)2631 2516 y Fk(")2665 2504 y Fs(])p Fm(;)g(`)2760 2474 y Fi(2)2760 2525 y Fk(s)2797 2504 y Fs(\).)37 b(Instead,)27 b(w)n(e)g(are)f(in)n (ter-)118 2611 y(ested)h(in)h(pro)n(ving)e(the)h(existence)g(of)g(smo)r (oth)g(solutions:)36 b(this)28 b(accoun)n(ts)e(for)g(the)i(parit)n(y)e (assumptions)h(on)g Fm(f)9 b Fs(.)118 2717 y(\(2\))34 b(Along)g(the)h(pro)r(of)e(w)n(e)h(shall)g(see)f(that)i(the)f(solution) g Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(")p Fs(\))34 b(will)g(b)r(e)h(obtained)f(through)f(t)n(w)n(o)h(steps:)118 2823 y(\014rst,)25 b(b)n(y)f(constructing)f(a)h(suitable)g(function)30 b(~)-48 b Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(!)s(;)g(")p Fs(\))24 b(whic)n(h)g(will)h(b)r(e)f(analytic)g(in)g(the)h(argumen)n (ts)d Fm(x;)14 b(t;)g(")p Fs(,)118 2929 y(while)25 b(de\014ned)g(only)f (on)g(a)g(non-n)n(umerable)f(set)h(\012)h(of)f(v)-5 b(alues)24 b Fm(!)s Fs(;)i(then)f(b)n(y)f(\014xing,)h(for)f(all)g Fm(!)i Fj(2)d Fs(\012)h(close)g(enough)118 3036 y(to)36 b Fm(!)280 3048 y Fi(1)317 3036 y Fs(,)h(a)f(v)-5 b(alue)35 b Fm(")h Fs(=)h Fm(")p Fs(\()p Fm(!)s Fs(\))e(suc)n(h)h(that)41 b(~)-48 b Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(!)s(;)g(")p Fs(\()p Fm(!)s Fs(\)\))36 b(is)g(a)f(solution)g(of)h(\(1.1\).)61 b(As)35 b(the)h(corresp)r(ondence)118 3142 y(b)r(et)n(w)n(een)31 b Fm(")f Fs(and)h Fm(!)i Fs(will)e(b)r(e)h(sho)n(wn)e(to)g(b)r(e)h (one-to-one)e(\(for)i Fm(!)g Fj(2)d Fs(\012)j(and)g Fm(")d Fj(2)g(E)39 b Fs(for)30 b(a)g(suitable)h(subset)f Fj(E)39 b Fs(of)118 3248 y(the)31 b(real)e(line)i(ha)n(ving)e(zero)g(as)h(an)g (accum)n(ulation)g(p)r(oin)n(t\),)h(w)n(e)f(can)g(write)g Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(")p Fs(\))28 b(=)k(~)-47 b Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(!)3247 3260 y Fk(")3282 3248 y Fm(;)g(")p Fs(\),)31 b(for)f Fm(!)3626 3260 y Fk(")118 3355 y Fs(suc)n(h)d(that)h Fm(")p Fs(\()p Fm(!)608 3367 y Fk(")643 3355 y Fs(\))c(=)e Fm(")p Fs(.)1304 3603 y Fu(2.)50 b(Pro)s(of)37 b(of)h(the)f(theorem)118 3780 y Fn(2.1.)44 b Fq(Perturb)l(ative)33 b(exp)l(ansion.)46 b Fs(Let)31 b(us)f(replace)f Fm(!)1807 3792 y Fk(")1873 3780 y Fs(in)i(\(1.6\))f(with)h Fm(!)s Fs(,)g(i.e)f(with)h(a)f(quan)n (tit)n(y)g(that)h(w)n(e)f(shall)118 3886 y(consider)d(as)g(indep)r (enden)n(t)h(of)g Fm(")p Fs(:)36 b(this)28 b(means)f(that)h(w)n(e)f (shall)h(deal)f(with)h(a)f(function)983 4089 y Fm(u)p Fs(\()p Fm(x;)14 b(t)p Fs(;)g Fm(!)s(;)g(")p Fs(\))22 b(=)1517 3985 y Ft(1)1490 4010 y Fl(X)1487 4186 y Fk(n)p Fi(=1)1664 3985 y Ft(1)1638 4010 y Fl(X)1626 4186 y Fk(m)p Fi(=1)1788 4089 y Fs(~)-47 b Fm(u)1831 4101 y Fk(n;m)1954 4089 y Fs(\()p Fm(";)14 b(!)s Fs(\))g(cos)o(\()p Fm(n!)s(t)p Fs(\))g(sin\()p Fm(mx)p Fs(\))p Fm(;)695 b Fs(\(2)p Fm(:)p Fs(1\))118 4301 y(where)21 b Fm(!)i Fs(and)e Fm(")g Fs(are)f(seen)h(as) f(indep)r(enden)n(t)i(parameters.)33 b(In)21 b(the)h(follo)n(wing)d(w)n (e)i(shall)g(let)g(drop)f(the)i(argumen)n(ts)118 4407 y Fm(!)s(;)14 b(")27 b Fs(in)h(the)g(co)r(e\016cien)n(ts)k(~)-47 b Fm(u)984 4419 y Fk(m;n)1107 4407 y Fs(.)189 4514 y(Inserting)27 b(\(2.1\))g(in)n(to)h(\(1.1\))f(giv)n(es)980 4617 y Ft(1)953 4642 y Fl(X)950 4818 y Fk(n)p Fi(=1)1127 4617 y Ft(1)1101 4642 y Fl(X)1089 4818 y Fk(m)p Fi(=1)1251 4721 y Fs(~)-47 b Fm(u)1294 4733 y Fk(n;m)1431 4721 y Fs(cos)13 b Fm(n!)s(t)h Fs(sin)o(\()p Fm(mx)p Fs(\))2004 4653 y Fl(\002)2040 4721 y Fj(\000)p Fm(n)2155 4686 y Fi(2)2191 4721 y Fm(!)2246 4686 y Fi(2)2302 4721 y Fs(+)k Fm(!)2440 4686 y Fi(2)2437 4741 y Fk(m)2499 4653 y Fl(\003)2557 4721 y Fs(=)23 b Fm(f)9 b Fs(\()p Fm(u)p Fs(\))p Fm(;)661 b Fs(\(2)p Fm(:)p Fs(2\))118 4933 y(whic)n(h)28 b(can)f(b)r(e)h(also)e(written)1048 5016 y Ft(1)1021 5040 y Fl(X)976 5215 y Fk(n)p Fi(=)p Ft(\0001)1280 5016 y(1)1254 5040 y Fl(X)1200 5215 y Fk(m)p Fi(=)p Ft(\0001)1447 5119 y Fs(^)-48 b Fm(u)1489 5131 y Fk(n;m)1627 5119 y Fm(e)1666 5085 y Fk(in!)r(t)1803 5119 y Fm(e)1842 5085 y Fk(imx)1980 5052 y Fl(\002)2014 5119 y Fj(\000)p Fm(n)2129 5085 y Fi(2)2166 5119 y Fm(!)2221 5085 y Fi(2)2276 5119 y Fs(+)18 b Fm(!)2414 5085 y Fi(2)2411 5140 y Fk(m)2474 5052 y Fl(\003)2532 5119 y Fs(=)k Fm(f)9 b Fs(\()p Fm(u)p Fs(\))p Fm(;)687 b Fs(\(2)p Fm(:)p Fs(3\))1869 5396 y(3)p eop %%Page: 4 4 4 3 bop 118 555 a Fs(where)27 b(the)h(F)-7 b(ourier)27 b(co)r(e\016cien)n(ts)32 b(^)-47 b Fm(u)1257 567 y Fk(n;m)1408 555 y Fs(are)27 b(trivially)f(related)h(to)h(the)g(co)r(e\016cien)n(ts) k(~)-47 b Fm(u)2850 567 y Fk(n;m)2973 555 y Fs(.)37 b(By)28 b(writing)494 827 y Fm(f)9 b Fs(\()p Fm(u)p Fs(\))23 b(=)794 723 y Ft(1)767 748 y Fl(X)766 923 y Fk(\027)t Fi(=1)901 827 y Fm(f)942 839 y Fi(2)p Fk(\027)t Fi(+1)1186 723 y Ft(1)1159 748 y Fl(X)1114 922 y Fk(n)p Fi(=)p Ft(\0001)1419 723 y(1)1392 748 y Fl(X)1338 922 y Fk(m)p Fi(=)p Ft(\0001)1783 748 y Fl(X)1611 914 y Fg(n)1648 926 y Ff(1)1680 914 y(+)p Fg(:::)p Ff(+)p Fg(n)1860 927 y Ff(2)p Fg(\027)s Ff(+1)1995 914 y(=)p Fg(n)1590 972 y(m)1641 984 y Ff(1)1673 972 y(+)p Fg(:::)p Ff(+)p Fg(m)1867 985 y Ff(2)p Fg(\027)s Ff(+1)2002 972 y(=)p Fg(m)2125 827 y Fs(^)-47 b Fm(u)2168 839 y Fk(n)2209 847 y Ff(1)2241 839 y Fk(;m)2320 847 y Ff(1)2370 827 y Fm(:)14 b(:)g(:)19 b Fs(^)-47 b Fm(u)2529 839 y Fk(n)2570 847 y Ff(2)p Fg(\027)s Ff(+1)2705 839 y Fk(;m)2784 847 y Ff(2)p Fg(\027)s Ff(+1)2923 827 y Fm(e)2962 792 y Fk(in!)r(t)3100 827 y Fm(e)3139 792 y Fk(imx)3263 827 y Fm(;)205 b 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Fs(\))33 b(equal)g(to)f(\()p Fj(\006)p Fs(1)p Fm(;)14 b Fj(\006)p Fs(1\))31 b(ha)n(v)n(e)h(to)g(b)r(e)h (discarded)118 1122 y(\(as)28 b(already)f(tak)n(en)h(in)n(to)g(accoun)n (t)f(b)n(y)h(the)h(term)f Fm(c")1784 1092 y Fk(M)6 b Ft(\000)p Fi(1)1971 1122 y Fs(in)29 b(\(2.22\)\).)38 b(The)29 b(function)g Fm(G)p Fs(\()p Fm(";)14 b(!)s Fs(\))28 b(is)g(analytic)g(for)118 1228 y Fj(j)p Fm(")p Fj(j)23 b Fm(<)g(")353 1240 y Fi(0)417 1228 y Fs(and)28 b(of)f(order)g Fm(M)36 b Fs(in)28 b Fm(")p Fs(,)f(and)h(it)g(admits)f(the)h(b)r(ound) 1410 1497 y Fj(j)p Fm(G)p Fs(\()p Fm(";)14 b(!)s Fs(\))p Fj(j)23 b(\024)g Fm(A)1948 1393 y Ft(1)1921 1418 y Fl(X)1903 1597 y Fk(k)q Fi(=)p Fk(M)2074 1380 y Fl(\022)2164 1441 y Fm(")p 2145 1478 76 4 v 2145 1554 a(")2184 1566 y Fi(0)2231 1380 y Fl(\023)2292 1397 y Fk(k)2347 1497 y Fm(;)1079 b Fs(\(2)p Fm(:)p Fs(24\))118 1776 y(for)27 b(some)g(p)r(ositiv)n(e)g (constan)n(t)g Fm(A)h Fs(and)g(for)f(all)g Fm(!)j Fs(satisfying)d(the)h 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a Fu(References)118 960 y Fs([1])37 b(D.)25 b(Bam)n(busi:)35 b Fq(Lyapunov)28 b(c)l(enter)f(the)l(or)l(em)g (for)h(some)g(nonline)l(ar)f(PDE's:)38 b(a)28 b(simple)g(pr)l(o)l(of)p Fs(,)f(Ann.)37 b(Scuola)243 1066 y(Norm.)f(Sup.)h(Pisa)27 b(Cl.)37 b(Sci.)g(\(4\))28 b Fn(29)f Fs(\(2000\),)f(823{837.)118 1241 y([2])37 b(J.)18 b(Bourgain:)31 b Fq(Construction)21 b(of)h(p)l(erio)l(dic)i(solutions)d(of)h(nonline)l(ar)g(wave)h(e)l (quations)e(in)h(higher)h(dimension)p Fs(,)243 1347 y(Geom.)36 b(F)-7 b(unct.)38 b(Anal.)f Fn(5)27 b Fs(\(1995\),)g(629{639.)118 1521 y([3])37 b(W.)21 b(Craig)e(and)i(C.E.)f(W)-7 b(a)n(yne:)33 b Fq(Newton)-8 b('s)23 b(metho)l(d)h(and)g(p)l(erio)l(dic)h(solutions)f (of)g(nonline)l(ar)g(wave)h(e)l(quations)p Fs(,)243 1627 y(Comm.)36 b(Pure)27 b(Appl.)38 b(Math.)f Fn(46)27 b Fs(\(1993\),)f(1409{1501.)118 1802 y([4])37 b(S.B.)i(Kuksin:)58 b Fa(Nearly)38 b(in)n(tegrable)g(in\014nite)i(dimensional)e (Hamiltonian)g(systems)p Fs(,)k(Lecture)c(Notes)h(in)243 1908 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b(1973.)1869 5396 y(8)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0211220904828--