Content-Type: multipart/mixed; boundary="-------------0009210745249" This is a multi-part message in MIME format. ---------------0009210745249 Content-Type: text/plain; name="00-375.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-375.keywords" Standard map, KAM, Analyticity Domain, Pade' Approximants, Natural Boundary ---------------0009210745249 Content-Type: application/postscript; name="bfg1.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="bfg1.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: bfg1.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMR9 CMCSC10 CMMI9 CMR10 CMMI10 CMMI8 MSBM10 %%+ CMSY10 CMEX10 CMSY8 CMR8 CMTI10 MSBM7 CMSY6 Helvetica CMBX9 CMTI9 %%+ CMTT9 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips bfg1 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.09.21:1434 %%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 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 66 /B put dup 69 /E put dup 82 /R put dup 97 /a 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueXX 5000827 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e 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ca5782f99062e096f0b6ba6dd18f496cff152dad838247045bf56f1a1bc4827c 4ea24592a678b95db350865a68e440d3c2f163b8d6f3e95d71fbdaf40fe6cb00 405de3c71249c0de408f088c74c8c32ef6fccb47c501f99c8d7928d1fd9c21be 8dcaf74b3088704dbe3fa5312551d78c25e495d4dde09eb4eda611f1adb0b2c1 9668f062b08e7f85269c99630d674aabe22af784e3a94b6f914dab054615891f 373bd032ccc763f8fd7a87055148343a9c040faba874def60fd3a44b4d01c95b b7afa173e729b197576df1687042e5b8304871106f7521144141f8ac31d58910 387dd6a1c26bec92cc924f8d8ad6c2756f7deba429f93ff179bb7abb6229a4e9 3d9d35b4ff6941229ae0e271952f566055a9b5adb1b9fee84f9e667b8905cc07 b51da96906a4185181c75706f08911547d8c014762e1db58ff632f334c81792c 4c4bf4120babb7412eebdfa0c4ccbeb31663acb193986992276907a09821c465 2cfbe63c6345f971d962c110c1d836a7a8c82ef6e043e033e5997431532fe440 d7b943520c3c04fda2914c7d39e16208b7cc8562ff6f97f5293df84c19532451 eaa80a705ff3c8ea8c56c9970b04ea512028df5176280ecaf728ab00ebc3d147 76a9a6223727afaabdb64e64cf39756d439dae4aadcc16f63e813e77eb75ae09 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69e7dacf7d3e1e8a90a724503ef3a0c0c95d9a77306044aa7e4d21db283ba223 302c84908829d5fabcc8a79e15779c9e47f9c3291e50f08004677550e41e68ca 167372b4d47a571c43be8df336a9c7419df4112278a4e89e6d26db9aa4e7ba2e dafb7d7fc83b7fbb0ca50f21bd145a017136b5ab31c233444a66832534032bbc 51e69f5f69cc319a8ffeb0111ce2d9e23e27e663fb2251d0c3ff62980efbbfef 0497eff301304d203287393e6f572ede9128091967d7b45cbb1e337a84393b5f 553233dd7a90a7e3736f42f1d764c015d9153443254dddc1b4f4c5a6d92502f7 948e690187ea68a69158462622bd8feb8dffbd896e368ca54a2b5912899fb674 21fa0e6add98bbc72e1e4fdf535aef82834040f6c528e2d0964719cd614bfcb1 27b3eb8a5a8618a964499461d7f24bd2fa6260a6a9abfd0c8df8f0d18a20b626 9fa236f26dc5762b4ae1ecf7a33822a481d9a221901aaa50f514566fd96501b6 065154e547ef2180393cef7ec07c28ac9df8effe26cabf3a133a7a2702f525e9 a9484355071041e2c9264422058f0bc9c0f94b5e1d851666db269101527d16a9 6be03641a2f5fc2dd617540c8d21d1e5625c0ec81aa7ce986a1dd6ba98d62431 6a97ba920d05f1172328ccbe9b896b722194d252d0d0e11a9e4c9fdd0b1c8fda ecc1baa9fee0bf2bbc91bf2ebc2bb7a3fa6afb690b0d198cee7d7f4d85136628 8dd7276545db68ce32d83a3b347d3647b18268630c8450315bd656149d38c384 d073034453b6430bdeb938dcf6bc8553169ec0ee6b9c7e0cfdfe53483b4e53a8 e68192d1474583e84c3346ef205f144868b92726d6c98016215d6e89ad435678 8e20218ba96f545343e7f744a7cb770ff88e94e926e561bba267b123575d74 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d55fd4dda249cff0b56b9f3aff e9d0de215c02a52a6bc77155ff6b8cba5cd6646ba331254ac58ace650a967d3b 272331b87b6df06d5ab9d80fabe9f9ceac10139b61244814dd9fc295ed42d1b5 cd11c2e4beab318b20f51ca2c2930657e5343ab7bcf0e8870a0d12de4ffacb6c b3fdbdda481c2fcb84408d3d902e9a32070b2af6cd9317a33a42a43857c114b3 f4c3005cef9401f1c2bad3e69150d7145b79f95c9cfaf7a335b277e6435ab374 f6a3e78e124ac1e4615511f743ad65c5d778403a840310ac4902985f107fd33c 0049623e4c496cd353d2ae2a4804110c6a420a38ece5d5b235c5e35886a0987d 284e6110527b653b1b2c68c636ef423536180acadb954843eff4d9a82568a713 b682c574e30f793f093aef755c650e0e7175c2e3138695212d9fea7bd4b5805c a90985b134c6bc15a19afae0bfb3066363ca3e2568c2ac4559a69fc32feb443b 61243b4508b7524d974636855c83c8149d489b68fe18bd497116a953431251df bd09fa1d2ef66c85b997ab2f6b7c6d9d096cb43931379ff9782fa00c5f3cbd06 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359e33b85c2a8fb36425d6187cd33c556b6edde3a0dc152bcf1f374c1de50a63 0f3d914a3a3b6267627f80a3c841701870faade7eb3f38ceb375acc1ede0cb1e 3c5b3284b39af3e0334d9f446b559a966209bdf971bac582a0811ed030514d54 0f0f64e5c98c5c3dd77f46ee100d53824905e014baa95932492edee6ebc969a2 3135d64a98f056ee48e85db1f233b2f09fbf603c9fadde8f829b409e3595a969 f1bec1a86962b58e8adabf580f0ce4ccbc90e3b402a35cdea8dfdf5d75fd574a e378bf44bd7351de42fa85fc196051078d02bbc08757c830913803ebfd9eeeb9 e02be72d0490e34fe6a1f798a9934008b358f2ad4743813cfede70bbe32b725f b29f5b63c0a257b1904e9ae76f30fe47d856d6fa0149b3a9cdb2194e50f01cc1 67d2650f94e10314db2b4d5eb28b528f7fb01599d187e97779472c9742a2a7df cf0a2ad2d80d4a9b2aef6b30d05d7a9d1ad060083282c2a3c177b2e1faa6dc40 a179898d2abbbec82d4cde36ba9d39ad396371e341204b53716c9743939c076d f5651ac84c8a25ec59320a2e999d4e8272c8b7b03bdf4f2425051422502d0408 729f0fa3614929ddd3ea225f2303685b1bdafd4820ec38f1ab1576228bb388c8 0f22d8d4470f1717f3a67e47a06983580afd6aa6db37ccf7c02fb677396f7256 07d829c03038ce85909f6ca22ef68dee5934abe0a80a208d89119c05a52da04a 012bdca9744aab1f8f12d2c991334edffa805b0ad747f90eeee003a997349c11 aa4683b491132cd5f18cf0268e4a333fb6bdfacd2057a1dca4c26f185d605bec 01121dd08f6e3052b1e1b232f9b31c6cb627179b7865a2ed84ee6b0277897790 1d8a0f34e7d8094cec3081e10c6af5d604c7393ccc8449d285435d3eca427ca2 4e46e6c313824d32a6815d86f090b2f2dbf27b03711572b50e76c9968e9aff18 ca6688ee210c24e1de74156432bc5568ad768a70e514a3c0d5b919f5e59c999f 33eb9a0eb124afb977bc9b29ae40ce94f2ed9ffde911696dd270b2d851b2517b f795740362820aada1dda499d4d1c40bd544cc276dae3673fc36164654472d48 9c5bb772c5be22309d1cb134b316721731d149be7bf7917091dc2c4de5a00988 57c0a29d5caf6f34e9bd992c8aa1b9e06cfccb593aedc771be54436835420375 005afc405f84b60e44c237db8245b72638c739908672ed0034672e2a306b8f5d f79b406b83dbf1739ed2346bda474d0c6a79a98bd1bb12805975ca3661c75a00 60cd7fb95cc2216b2464e80d24363e7ba774c9b94e415e3aa85cfa9227fd892c d11ebedfb4bdd59b81c777744a8f6656f5abcff0f55ce3cb070b24c0e4edb4b1 7fe53ac35de79fffc665a99b133ccd53ac4b1637233e7c8115e54beed2fafb0f da21a2b0b474020b81b9c8079fd01fc9a60013dbe6172fc9bfe4ec782b0ab5bd 7fc065323e074d173ddf6e0abf077b3bb13bb95104e76e5bd3189b62839d7157 f7eb1cc34351bb3d20f8c268c8a43d8528c5f7e59188e5cefde5614d6ce0fe40 da917fa8b9276468a6e125f43832d59b2435d47a1727db22a7babc182f1e3d9f e500b3034ccb946f6fb87e380b4ab6b3026b566c6db2960aa1ca71e4b301cb9d efe588bf2171657dd9f807eb9045ffdced9b0b7020fb44ce7fedeffe2b58a655 feeba2945a60aea3c1ed97a99bee63d9e19fd30b1b4e6a48e9eb59109cb18e44 618d89155f56f6641b0bd6e21f80ebec5547a3c19565d257bd5c0cb9a2da0954 068c8359890abef945ddac62db1f2c10db7286f7a4e8d668451fde12553f19a8 9eb9fa54267efebec5cf0d57a0a57ea16bd825e3fbfc3eed15c9c015eb5a83d6 471356f18d6f04db5fa3c8894aa9c3b730924d501a4ae9ae4be0790e7362dd49 2bdb07c72a052bbb 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 18 /grave put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 73 /I put dup 76 /L put dup 77 /M put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V 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 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 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueXX 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e28519671e8def84a1526a8b89450ef2bd624857da91e67a35269b877f161 ead3b9314f0ebb23d1a803608fb8bed47522b2a7814eba409f33973ca88ebb86 148d3d0d91d8056e573e23f17b04c8dfeb3d040cab25f1da3caad77b904b64f1 98dc18b1abbbeb700e3bcad39189c15c31bdc0009f94094d223f303408ab2800 533c624b77a8b576fcb13a492a5aac1035d7766bf5e2ba738c1de82bcb395cb4 344d6f452463521d7a6d8d979625e6900ac2b993de3d6a15cf4473176be41862 e61b3f9e109d500405e6f01936bd4cd77ca687b490df2a2e501e141fbecc7082 86f85fa428a8121af362ef3bee57af 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 84 /T put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b48d5d21d6c29aee4faca71bd775bb9defa37ff627f1e4926f10d59313e 77d81a511027ef9a8ed5b7fa9b5bd67758cd13bab6ac18411c974a65d0c90085 67bf5860d0930d7f43e557ee45e76ecb2806d21f4732bb282ac8b591f2b8775d 4b3ce2a37ebb371cb74a3cc513bdd70a0115de4760c21f034f5080d769f7ff83 554af524184702a02e534d1eb98dd3f7c5d51900409354dea37de4ac72c4128f b7c08af8a17f2033761abc7ce4578d50960ba229f0bbde72a750e61ebf32f961 f519c386735f979944540cdbe8c8e2ef8a191839e033fffae82e797b6d99eb09 96caf6191f6824680f0aa167fa3670df501492d493d04da4e0d40c579bc98f69 1368624f1beefe7c681a84f0122a97651ffc905047fcec9abc49089fd5be8cc2 aef34559b180555eda5ee38056cb66ff3c179cf5715dacb4b66b8a695434dbd8 fab68a01da044cba0abe634c035c19d20a8113a66ef4bf6f80b8332f2edca065 eb99277c1ad03f15837aaa9bb52f5f63c73de2760c253efe0533e75467f968f4 0847ada5c4e097b1096db482b171b8397131a4d797896ae8361281c3a70e55e5 71a1c17b23a4203a62adaa8f8bd4491db48f60541846f0776653b8bcfdf845e1 4197d51ede41b129e79157e9c6597d52ab4460ea133d48d02cd32c43b3f02e97 19954b9ff25fdf 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 46 /period put dup 66 /B 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 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-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 ec70cdb4a33e1c4ca1744adc0e2605cfc5cf8028f4a1acb9dd2350c61e6070f9 693748698b56e743c435e5f6a1679797b805ba7cf6435aefdc67b6be80dde9e0 11a8199092b061e43a6071347f2aeb6a21d6b8781609d31b340a25e4e68204f8 ed72ab88ded65642c336c6a66cf3b7a9c14b8e663739c9ac9ae3af8e1f27c71c 390c32ec8c213ff12a2661cc9fca8d2d3a507f574d6e7ab8a91d13adcee54236 4362f8a62e13ad9ba8f85e07562905fc6c3c69f29d07ce1fc7b4d758ac717acd 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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 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal put dup 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 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 89 /Y put dup 99 /c put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end 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%%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 20 /lessequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 106 /bar put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03ad78e7fe3ede25ebd7b90e10c8ffdb9b6b4b460b11e84d5d1ed2c307 f30f1dd56f09206083aeb1e5c4efa99c7550086966a11485846744c64511501b 824efac74c4f7f82a5899bd4661ec1e8799ed0d5c8127cc83617f26d23e8e824 b06180183d6adce567cf9bcec941b8c0d8b3a5b44273518ea2ac28d4fddeb752 df1ffaa62c2bdfea0eb0eac2043cddfe94bb84420675a100fecc29d669e5fefe ff613dcd55334fb1636f257861b27dc34776f6a7f5e8c51e251195c397164de6 eac281be7d19eabdbd5c203d019be9cda987b987e99688b3be801a38dda97b45 7fda8906e6217a48ca7a340650b020e917832dde468bd45de0eae63402f3d64a f50b97dec2256a7cec82059518c0322bd2ca2252b47c48539da8d8287fd75058 5df60452618b7ecdf334a7f2adde679afca090dc04535f49fbbaa827b2663d04 0a8015ba58bfcdfadf775c9730fcde0c8e752c9833903dc1f2f7db4b71c643a8 7115d271300ea670dd2bf1961cf7c1c6ebbb8fe7cc7bae3dc8a3a257080a6fa6 010a85528eaf3835d4b4034c9d9dc1bc6cc9b1f697d86aeab40cda2e5f1b4152 aef6d9fe20f2b5c8c81239328c3cac0cbfb12f712332b847cc60cccefd3e9771 5417d83a4155212c20e47f6497ef4ceb720b9dea025033fe709a1d8b819413f6 af515ed857309780f09461bc3c99a30a7ccddf5308191fdbaa5615b5a43db1f7 a919f42ef3a4326cd1607cd5ca87e4f4eff5252a89508298e5bdbae73ca3bca6 df3108c00b5ed05795c8936e27ac1ee57e094f2ebe46eee150635aae406075af 10b5b640704fedcef61273337bdd924c081cabd2a132a714cd672661a0eade6a ec2044819cca1df7e18d096343050a5d1a1e99a1e53292cdbbef4c00fb49f8f3 a40c03079893539d47e43cf9d0fc834bba867b3c9b7d74306698938dbd72e4f4 7b97451f7f2d5bbf2a390aa1fd68b0776be70e0ef6efbd109ca62555715a4a14 a00a2e46a1af16cf10bbf6bd5111be82705a85e03c20efb1abef9b80a96d6efd b80c423ea436d276da5a83e944ca150e9de9ef5a0b3ec5e240fff2c4bf303250 b7575076ef10a472d9d9de6acaaaf8f8c16074dc3c7105ae93b5d24a527964df 684e446eb6a6e06d886350e9bcefae47ca0013b976363e4b3bbb2ded7dda2ace 219838c61df01c0ff6e205bcf0a8802d50a4972555a529d7768bada4f8c8bd1b 32440a9bb8eb425a9e8c7154557838f5c4cfba4a6885877d5737705d7f54e067 7569c6779cf5f19053fa11014a931245de7abeb122325fdd746be554e2a133e3 091c9cc5c22e076641d2547c307ca7632da46570b13ad402e4075f8dfb0437b8 56620c39b9c585c13c68db2e70e1a5f1d05508ea3523c742def1f0ec36ce57f5 f97c42027f0217b064e8b762952894d625 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 12 /vextendsingle put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 88 /summationdisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fd04735fc902fa2d6ac5e867bf7e9c6afb91cf07d29eeea04e40ebfc834622 b6708e5be32302597bdf5c6e1ac8569e7399ba1fbe4631deda2d9409ee4fad26 1ec8370e49afc455f918d9492a6f642ee8a18c648ef87fb6510b2eda370c046b 82a3e4a1d4bb2a2226130f7e659aac7e39b2a32c43f2d58729ce2fbc7bf2a145 86668fc997ba51ee07cd114aab976ebf984949475f447d5bab8ce7ddd385c3d6 d1c5270e3b9707e59ecf94d749c852c79f36b9f0daf1dc39c2615ad578fcbcd5 98db52a04e136e84fe7c365ad5914528b0d1fda64ed4647ec12d6a7782184294 8e9fa28ead878311af037a730a47696e636f7f0e387558473f9e03bcdc1b2b4a 1dd089cf8add3d270da36e3fc99dd464d2185e46bda978d066ccfa10346617c4 3563321c1fee329e637cb6c2c6b3ff63159c1dbcdfec31b41094b380b3e2eb61 4897b536ba0851d48e21a5828ec3fc0d165ef1a51ed2174b81abdf54ead448f3 1d18ba61aef143cfd99338e0b94c7863c5b870ec60135d09aaf08a6f6109cc08 864d96f4a5140788bd5cacbd13a63c30b5e8c824f8dc188218292a971a0937f7 67bf7307f3e7a33af4b6d2f114f7a96bea396af9b4a618f88e7554d460002bf7 b2afc2acb292bf045b35b4e54cfc7df37725e5228f597d31184d9fe908942ed1 822c8d441ef1ea844e2e8ec910957c7a7ea2b1b453a865f440132a99783f4ddf 807e8d4f976961583dbbbe32705082d1d260baeb599fec3e8050d59d106fcc33 3475c54ba29f34b9430cffe53593b6fcb995ccc1177cb84f423a2828d181b7ac ddb393c284c7fa8178036adc3ff8d1e152bd2d2acbb9dd1854ed2e21ecccd4af b82a4299f9a544521e64b1c6164e7dcb2e11c3711f5c3fed67e4d53a0aba67d6 8875c0cdb8a33a768b4070f4d6dc939e6bfebff19b07645584e3e60f42ed2c14 392322b8af2aeb23f2cc4fbe2aa09caa01247197d9a3f84bd5825c63d1ece4ce df857271c1d1eaa8df52819a6987802b7640fdd000ee1b5c1f3bf163e306cdd9 e94885d6f3c819b67b18afc32e2252a13e6c44ead544cbe2b65f7b6732f9135d 41e85e51abd82904bcc966816bb0ed06185287d326fb7f788b6a0ab145eb7a60 e6eab859213471993e687026672a1ae86eeea7069b8ee827a9f4de4fc346d224 fbe31eeacb22b5d05aef1af3c8eeafdb0511b6a062c17df999d12ced43d4ccfb ebd90f59a515a9aac943a849838239f1d2ff15c2afa36b8d8f0e92aa64602a44 72434130e6fa6facbb12c902c8a32fa8b3fdcb4d2fb32a83bf428764f8575102 aec5b45d3f0448712c330286705c5da23f47713af5f7a8ae7d97a968d537b485 83f9c9b675a8cbd977b8fc74d4e3d851deeb67932f0e503135c5079272f8ae50 9fc384886cf3f1c69e46502df8f7877c022e9f73b82adfe24d14cc8bd41148ce 35e693072558386612f0bc2c4c257ec486c4e3c59feb3436bac3f73b80d67820 07e072790294975c7b02b800243dd28bea29e1a22d80d6102067956269e7fe95 06ee9d86ee0decf201d947e4147e0fb4952d6b08b5c933c916226c3360cbc7a6 025acaef12b31a3e9a69399f581f22f6a6abda634ba72a5020e04768e2ecd6eb 9120b3ef13840049a666183283922f0965a98fab52c0ce3a0e8eff307803a3a9 e417dbd804980b4da70afe07afed7e713fdfd2ac112c0c57af09510440b170c1 a205c3414029f03f53dec5a9d8653272f4fdc09b4fe784e86c76141f4c9f0c47 16032944e69ab8cbdc2c5b9850db3813a2d07eddb33180f7ce0dd5b52872b931 6a59aa8842fe888e30d802bae5fc9a2139b5b1c6e09035e3dd50c87eb6626f3b 6faf9369529273638c2cd7839d2241d4f09159c8e7e49d25f4ee6f23c4bc8a98 98fbb347def42b6be55da47c661c5b370e6511bc11ad5a28ee3edf294afee43c 3865581cc25c98a27b11e869b69de1d191517488cb8ab32e3c8277cb956330d5 5a9981a0e5932c68d1254a1fa74b578a9e10554995a3d7ac6eb5a563e0d32353 c9cfd57ac39c6d2c4780421b54b338702965323f3ff5ae590851498d7360f119 9e88af76b1a79d5eca621b45196c9d0dd3dca13825c0ca637efbc2c53d4cbd93 be8b25d10bf6ea4c11a6ec860a1f1958450cacf0eb1aa7fbb8d7c90d7c14f43d 58290e35a7b3915af1919d57b780fc62a46ccf604618783e36a6069b0abb7642 85b2755205b5a1888cc45f1709da2ad890c688390d02c7c473c45541ff13c7f9 33894eb0144ba10577c44fd1bfa7128c142348f9100fc12a3b4f52c8e0018ad1 c165fb97e3105ed2a64c2e6f5bb6813123e666ff15f22d95a939bf499d819024 7d1b2fd8cd2aa681a0a820534e24abdd70a2169ed6271c391c365e5132a94669 669e475e2bb326b728d0246e25027fb6979c4d5720107f470db4433d5c495b97 c50efa285ae82483aadf8abb31c1ce98bd1b51ebf6b53615ffdf104c62f9fdac d0bbfe2f0b2fa278572c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 20 /lessequal put dup 21 /greaterequal put dup 25 /approxequal put dup 33 /arrowright put dup 55 /mapsto put dup 56 /universal put dup 67 /C put dup 102 /braceleft put dup 103 /braceright 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 b64c4302863dc92ad516760fed6c99c9eed6070c194e87ca5a7fb5c80918a70e cdf9fefc4083039192acc025cec8b4bd8ca5161a383aa8ccaa5e0c2e1f9f8df2 e7526391dbf6bf133961829699e1e530db23d7998b6a0e2cf42b82de7fdedd8a f829bae921d6f90d3f069cec380565de237294cd4df6240414aeb2ddb626952a 4b92549edb7c2a2345ad0a68b28e4cbb9b73daf1cfe44f4f53bc72a7e2063db0 06ef51a07769e3166a641ee96e1bf746195cfa65df1df564cc2a4c917eb68734 6dc3d534a005a813eb1775431372515e83f017481059eaa1306b321ef6f4ffb7 a0984862aae0258eac25348857ceb482a71388211d41e2614cc5e0d20c7ce437 8b145cbbfc14823e753762312ca47d2e1f84efee0bef5b099ae9acf73216cb8d 0a9058152b378941724c980fe18683aee95084558d31cf388140766fa23c10ce 0b4e2ce06fd596306f79f12489cfbc84b354e0a10f2e903a68ca7a2c0f4ae3f0 e7e8799d1369a1d875a99236e16c5581571cb4e8c919a82af193d3fdc502b818 967713c22eaf22145beb2b5bda49ae79d9c84cda19641f303df15c9266910d25 e14149d46d057a8dea7ea90606c3f0b95e8012f8d26fd29546eada8ec3e4ac02 a9bb3083f9dee40bcf9049cbeed4934593e231c26a2e2e4c501eb5d04c31d6f0 e9d2954906bf02af081e5741242c3e913bfb19384ad2fb7e23da0a21f1e09a8c 3902431b0925031ebe1b2121bde6644829f9f1b1e4e6c024de4b22a35050a09c ab43b3d4b231f75901ee9cbb4074570b654be45ad7626ac4b67db981da373f98 097e9c3905d771152ad6d1c754891c013c12b9f56d35cbdf452c98418812298f 603df9c0b7becab2d60c41b2a9c28bcb43555182a9fa9f2f4bdc93a7c40a17a7 8f8775101fa21a3cd560a0a60c1828df101ed47f59670677e48db4388aabbc7b 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92b1bfe1e0fd6e333f140744cfda09ed994a4407a195134c8168bb5c577d6f66 3f9f406813c68bbcbbac8b93d371ea45d9625caf6dc2ab28be9f8964d3374bc4 186ce3331b4bd40205e67bfb7a330c028bd67ff60ad95eb7028d9b37dbfadbea 4e43e95e3ba82f89717fbd390f21c76e59851d41f3d3e440bc1fd7f477434f81 cf63a8d32f8b8b3aafb882218f315e490b88c47d96db3e6526dfdf8cd85ecd00 4eefd2bcff33354088824edbd47f712b2d4fe059890c8bc4d4f01872e3de548f 60bf8546571bc3ed0026b7716931ba46c10e86cc22fbc67985cc174e31676f56 ac8758c042c1871ef4c1b0bd5e6bdf9047f93d682ad737d67a07c70ae45667f1 ddcfe6b12da74f5624bd8d309f4e1404cc8a4e63b499b6aed9ec966e2545d730 28e085934d2b1a62e88dd40553424712d5b445c17c325ae4a1102de55593cda6 a1724016a5d18a371d0df555290980e55c17cdcee70287345c747d9746bcdfc6 c819591f0f4092bbab97b06f155f4ba6907bb9d28623c39a6a789971d602f0ad b12b3bf9c1c0e27c57c6df847f370ae3754a2f4d1c98131ce2b40bd06ac1fffd 4f76f142c572ac34b4accd08b98e6c2eb3d17ee20d0e007f4ad89e1f8bf7ab5f 06a64f671cc4cfa170a7507c58e76757521acc05e129eede127daa3a163b3a5c 913c6911fd9870865bcf385ca0b4a33daf1b760d1f06aefae9ec95467c1b1c82 b8a24fdfc32028f77a686e15e13d4c5ea791c8f1c4660cef72bbda40febd41aa f3347ec7ea6c65b933a820f36ec3c204e2dc5835901db38d0a5dedc8e592ed90 9374e15cfa2d099a8995f9ea5081a41eb527542da6cc806d4978504bfc299f81 c497af1a2c19549acf11edee7e3a80b9eabed1236c25efb07d6a554cca2bcf0c 2fdafda08b8453d3829ea41391a089c629d5cfd335e9bbe498cbbd17de1b6214 b3550f051ea7fc8ef6147bc5560eb8eeae8b711d0d9d6300d63f539cd459d9be 10422c6a4cd3efb33dbf1734471e5754cf4b15fafcbaed11ac19391b43af60f7 2ad6d629a4dfbed5dcca6f6881adf8399655f3d71a4b0b177f567b78211e0015 18976350200a1de7d86556a038683b75bb073681a77d505917c81aa071e9339d 1e85d1143adc81f87f1286946dd3ddabdc825fe573c85b7ff7053a4f25b88ddf 15aa086459f289298b0a9ce19c1b213748aacf45b4a3ecdea1c18832cc1dabcf 1b6df164839ef456876e 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 82 /R put dup 84 /T put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812eae30521c3c775adf1959595a43d8a9c4e12d9f9ece27a0c9b5f45e38 8e26a39cb0ad4e25ab8f21b25ad1b106ed22af7947ea8ae4dc17b9facbc5e22e 89a91b046ba4cddde69c1997fa7f4cd949ba3ac4b6e001475daf165b9432dc70 6e30aeead8cc342d94b20a4045a331175655d6aa279627efc0fb53a4ce66b68f a45b5765f0c1368c0392eb2e0e75cae373c613a428b5e5b9f5da85536890738a 85d25d468958470a9cc9a469e8f303fd9b2b9d15efe95466fc26e61950815a08 8154a539a6bd4cae4a88970fa556e9e8606c4ae99580864178f34978088107ac c9940c7292f531b0d912942d06d02037d9c51ebd66bc4e32c80d4b0171b34a9f a92320d9991cdf78d0d59b3f3080e0cd85db0512b14d5658a84ecb42973cdcf1 12b5edb46d15050d2a757cc2c9cc7d349b7dd04bd3d5d8e9d0c4988f86344fac 48ff4d289f6aa4a32d69fba0152ee4ea988bfbe059ee9405132a3289d3e3431c 0c61d8c19992e35e4c3b13780011ed8f511f36ab71bf5848dd4bde3a9beeb182 bcb9be67a9dc21a89511ac7dce1098f3b284006d801a2dec1e84be1cde27957c ff887aec7c7ac3ccc10c5665e12639ef161f3c41974ba20cb2a854e21b6e266d 38adc9d1e019c0d23d292ab46e6c3a533914519da54f82ffcf4674065eb738c4 5570cb3172b45437b475a96c2e0d3901ef1cf6d9a5ff71585e75c973cd9f2c6c 693f65cc341f2f34bb26d4e89c2234e95f211fc315cb2926348fcfc058354504 2e72e644ba6eae12dd893055797c09ecb7e74caec66ff0f7535b7425993aec97 aaca80f8065b2d5162d43460eef3a444e5ead93c694988d13c99bf5e150fda2a 900d4011483ca800a1490abf190c03c02c9c47a8775d6d90d6e529338da8e5c3 425855c27381063c05e9ee7549e1faeea4a20e9cfe75dc00862d53dabb9379e3 16a46ec93d06c5c9a01ef1f04fcca0bfa7059e21af370c86f3115125f564a72e fd61ac3b489822e4e1f8c377dbe57a84a69056f9e09fde38510f5c7e1f9994d4 9055a59e6662ec3014b6ba9aca9cffb4aee72d270773b69344a701c8603cb806 27dcc0fd04f0e501e2a87edfacf9a51d210af370554aed3e8d642f280c9ad441 b3f6 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 11 /alpha put dup 17 /eta put dup 23 /nu put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 80 /P put dup 99 /c put dup 105 /i put dup 107 /k put dup 110 /n put dup 112 /p put dup 113 /q 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 472e951a11a8159b61756503160b8fd0f3d9fc51113424391e27f029882859e2 8984370eeedbcdd59f98bc1fafe3b274a02294259821124c2c17d113e0dd1ab0 22548e45dad95eb8ab0dd97783d6145e7f403695c00e2485a2087977b8e0d668 24d09a5ac0213270decb05bfc0d25e1bd9484e13d4e513cb4068a207d52c28c5 4d42423bd278fd416b00d8bc7983c467b72f1ec42a0612e6a51d54128daf0ed2 a3a7b4f178c39d51d9a90ec9f8105536d14d06e5b9c6c41f8ca9a6eb785a9ec8 9d3e092560afdb21461b9ef9d2d25e9977f715c946f3d6e5d5e124be36e74609 3b49cec7caeedc04893103aeb179dfe44f6bc322736ba0f6989bb39611191263 8f55d9edad1e1479bcef1938e302350f6d38a9ac4b8ce35fd90a58560739e0a8 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b66d8e3fcaeb2f92221974396cd364507d447105ca05f4342a729f41464fd1e5 7f4d61378014af4fd049c47f38d17ee5431c0e24afdc0d306fe30447e6adcf68 dc45a541bd484a73f177dccc2809fed10782a8a312bb46d0ad44110720efad7f 36da6abae37d244d49f36e0656675ebf258c49e4ad119e09527e9e459bc2e558 ab03b47928999f4aad400b228775697d6d4536e1c006cb2621 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 11 /alpha put dup 13 /gamma put dup 17 /eta put dup 21 /lambda put dup 23 /nu put dup 25 /pi put dup 26 /rho 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 62 /greater put dup 67 /C put dup 68 /D put dup 84 /T put dup 97 /a put dup 101 /e put dup 107 /k put dup 112 /p put dup 113 /q put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 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e94376f7a3661c0978ad674c709f56b9c22b3c5d10538a875cadf74ccea38fa2 850e01438ac50515ef11bd8e920a2449d38ed9ff276721a68ba266d0935544b4 59a020058ce7e27b90aadfa7c93b384c0aede040abe65cde1d679bd68394bb1b ca810b2c7bf983d9517724b8d59b51c4aee408fbb15e4407adca 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 22 /macron 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 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 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 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 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 readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 61 /slash put dup 112 /p put dup 113 /q put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueXX 5087384 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a 757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4 ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821 f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89 02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4 30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c 61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f 1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42 483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693 f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68 f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84 ff7fbe77f6ddf9d06fa92b16ecebcbe0370b5cd9d450d0f2906a105cadf93ed0 0abc7fcf2c996e7c15e452006e35390d99b9cfc59925f1444c20d9c3e1fc2910 32cf9fa9d580eac1bc956334da391b870a757c3bee6aa3e005b20988d8587876 3ced20c6edf2ac2b22890e37ff7aedeb0986d85ae05bc84339bf2116df48c5d1 cc888bb33d409b06dd70ffd0618b2080442aac439aeb39c20a87ad74ef10629c f1604db8611e8e4224c5b21ab0c7ebddc77fe9a283b3a8c6a2a9508f6836e3fc 3eae1366b4da4f44cb7a77fd81d278c17775d56cb28b70f18d894bfd1ec1827f fb1099ea73d550aae6858f31b1b18cd32c08de80883057e8c801ad8a355a932a 3b389f803390a9d43418ce79f6be95eb1ec91a1e0b99c3d564a0ea2a0d3da719 98fa1019e61f5633b2c41e907b4af9b2eabf619bf661453b425dff70eb2844d3 1dfbb58803f958463c68b04d4bc9a123155886af4af7730e8575202e9f160fd0 061f46c49789d6e98a97fdcf48320b74b88b96df3dc70aeade4850f9252c57d7 2705e29d63337e2b6d19d6958491528448839d2c6560caf283345835d217dec3 8dc102f9c16c26a858e36811fd8d8a1890db16f9add8fea9a12a10380298f7fd 1c7dd6c0924e51eba67400c09d16250b677542a19391939f70723eb4562c37d2 007b409e86983444d0f7692692abe1f790f3151a77ab7927aa7b62340e4b42ba 24f3c96e0422a995e4723acf4c76aa7bf1bb32e2badf61dfb2596aa859569484 99cb1546fa5724433d460fe72e51a0b5e320e465f681fd0aebe7623ec66ad184 e98f5ab00df0df192686601e1eee6315cd579977f0bc6f5e7b3462dbd2498687 bea4a5aee680bd279a1a10849e4b70747a7ca1636159d7d8b79390e4ebeda07a aadd9edc46632c6ea1937b8f7cd51b0517149d2458b3dfaafc2521259d03c029 cd165d0993584c94f47df17310e74df25c343695719f6b600c69bb827ba5d067 ceec2c5fecbf0bf1565beca65079d8ab1e1d17c1f2abaf6b090e51d04b08caf5 1c40a27f9e8adf4cf4db5a52153bf1f8a0a52a10896f8615544e172eb7318939 c45ee4938b792bbcb5fa4499c5b941f9913cacc8f19cc23eb02850e5d963c351 956f086e36dfb82d06e8967a96c2efa22b30a42aafed063a1afb7b47176afbe6 1642950775dfbb9d9d02e2b96faed093cd370835f386298b2ec453d3fdb92604 a907d3ebaa96038941a08fc96acbfc7c18b21a8648766b5bb9373afafac50fbf 270d587417a2d72b4972faa6a6d513746c39a8fa627da5a723b8acd7ab9b9e34 711b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 18 /grave put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon 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 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 dcf4871a5d023c9ef57d3362d9f2d7a440bb69bf653364105f16f4d0f03582f9 aced3d05cc76489b16e3fa8a446094d30038b06ecceda269f2eab9d19a99c7f9 39f9548f206c5a457a19270b2b82c43b091dfc5573468eaa3e7a4a32f8042891 d85e4b180fcbcb3091d2800e54c87d84ce9cad6869b5aabbbe47f40c68799893 d22b765295e1e69e33aa048b7ed98ba480ceca91f3ebf8ef85fe9a3976909626 b95ac5940d53f9b02215d84a44837ba25ed15cce0d504f1d335065594f3bc824 5405407591cccb11cfd4645da60d960c0b93f187b0cf7b105543c0b70f89af5d 264b6c026e3ae646acf145950202ec73282111e3e601cf2bcde22ce3edf6db23 516481420f26552ff4472d749811f27768150450d0d0ebe3c79f999e99b5c0f2 2eaebb12d97782b1bd91b2a1f62a76412548ad53c0dd411d4a08c0f071c2c218 63d9adb75a4621803ecb84c2bb235b620b658984b2d8e0c4637e2811bc8f0d04 6c8935afc70141e1b2d9c23bdb251d304b3378faf8928bd09686aa0340fb0cb1 dc48c996ef91530ff078666fad227a3589f50b605267212d3a65ebc1019a8eec 9a0739a00279471a01e1505c17658c10030fae32f274fdc8c8774b0d5406c384 a1d17068dcb0c2575c562fdc5a2176609bad9a2c255e426a4325a4fc3053c7b3 2f35f7bbc9aa50135f30223360fa2fbf019294b2e1d1405e078341097090ddba 1561f22f8738fe105c0e3b84532bed145d51428c9cb1807e655408807dc69161 1109a98af82680d6dccc987cb312835dec4ea0645f47a15b6707d654ae54846b 3d3301d61150fdea8ae2da33e79976812c7764050a3e86a2a819ffd3c64c38ec 16b2d0bec3922847fde375ffdd82f8f8bcdfa39c53068da393b35277ba7af682 9e48b1607f22eeefd7d0eea93ba1e2fb9b5ecc6c6fe1075db980999f0be7a232 c0918c6b795e560e98140046cb852abb26e37434ca125d334c56d82548bb8817 56eb534f80b13a8220e6c6246e3452ddd32a8b0f7bd882e20ca5defb24b20ab0 fa76a8d1e276476732729ba46f04d1fb39db048b8179141e7b5991ec6842aa00 e2daa5e70d4e391b3704a163e68cfbf8da102240af1522b5b520a67486cebf14 c6a7d5aa97fcabd5819cd417afa52f840e361858ca54c10cddf010256b2db8cb 911a6b1c115c2ad4fad0a048874de6958fe680393a5ffbfffadfba02d2bc454d f3ac55e1fa85c5d263cf3e5edba49b842f5279d060f3102c691f71cb035c57fc ae9d4a415957969b45e165bd31f27e2ba9aac0bdf03b19aacc25624c979dcf5c 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fdcb677863aea62cf677db59aa87338cd39ef4e5e5f793e74d099c7a26b3bdbe ff962473ebd57d59cbba937f3eadf617f168ca56f6bd8f3d4fb99e6d9d499a27 1bb756478eda3c17a2aabf5fb22f29266a3f12ae39eab43db18c0a896f27a66e f0a39060f99103f9cd6462ff1b371d6f50c97b1b948a18c3458afd5c8428b773 44092ae95ba03104b345d2ecbb92827625f419d2d47f4b8ac0cc057e180c9787 231b 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 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 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 89 /Y put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 115 /s put dup 116 /t put dup 119 /w put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 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(the)g(curv)m(e)g Fk(C)2542 280 y Fm(";!)2681 266 y Fo(is)g(giv)m(en)h (b)m(y)f(rotations)390 395 y Fn(\013)448 409 y Fm(n)p Fh(+1)612 395 y Fo(=)27 b Fn(\013)768 409 y Fm(n)836 395 y Fo(+)20 b(2)p Fn(\031)s(!)s Fo(;)33 b(the)e(function)h Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\),)34 b(called)e(the)g Fg(c)-5 b(onjugating)34 b(function)p Fo(,)e(sat-)390 525 y(is\014es)e(the)h(functional)g(equation)643 603 y Fj(\000)685 676 y Fn(D)763 639 y Fh(2)760 699 y Fm(!)811 676 y Fn(u)863 603 y Fj(\001)920 676 y Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\))27 b(=)e Fn(u)p Fo(\()p Fn(\013)c Fo(+)f(2)p Fn(\031)s(!)s(;)15 b(";)g(!)s Fo(\))22 b Fk(\000)e Fo(2)p Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\))23 b(+)d Fn(u)p Fo(\()p Fn(\013)h Fk(\000)f Fo(2)p Fn(\031)s(!)s(;)15 b(";)g(!)s Fo(\))1257 838 y(=)25 b Fn(")15 b Fo(sin\()p Fn(\013)21 b Fo(+)f Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\)\))p Fn(;)3394 761 y Fo(\(1\))390 1003 y(whose)22 b(solutions)h(are)f(formally)h(unique)e(if)h(w)m(e)h(imp)s(ose)e(that)i Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\))24 b(has)e(zero)h(a)m(v)m (erage)390 1133 y(in)g(the)g Fn(\013)g Fo(v)-5 b(ariable.)40 b(The)22 b(study)g(of)i(the)f(in)m(v)-5 b(arian)m(t)24 b(curv)m(es)f Fk(C)2455 1147 y Fm(";!)2581 1133 y Fo(and)f(of)h(their)g (smo)s(othness)390 1262 y(prop)s(erties)32 b(ma)m(y)i(then)e(b)s(e)h (reduced)f(to)h(the)h(study)e(of)h(the)g(existence)h(and)e(smo)s (othness)390 1392 y(of)f(the)f(solutions)h(of)f(the)h(functional)g (equation)g(\(1\))q(.)490 1521 y(The)d(solutions)i(of)36 b(\(1\))30 b(can)f(b)s(e)g(studied)f(p)s(erturbativ)m(ely)h(b)m(y)g (expanding)g Fn(u)g Fo(in)g(T)-8 b(a)m(ylor)390 1651 y(series)29 b(in)g Fn(")h Fo(and)e(in)h(F)-8 b(ourier)30 b(series)f(in)g Fn(\013)p Fo(:)40 b(the)30 b(resulting)f(series)g(is)h (called)g(the)f Fg(Lindste)-5 b(dt)390 1780 y(series)879 1940 y Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\))28 b(=)1395 1826 y Fi(1)1365 1853 y Fj(X)1366 2051 y Fm(k)r Fh(=1)1511 1940 y Fn(")1553 1902 y Fm(k)1612 1940 y Fn(u)1664 1902 y Fh(\()p Fm(k)r Fh(\))1761 1940 y Fo(\()p Fn(\013;)15 b(!)s Fo(\))27 b(=)2142 1826 y Fi(1)2112 1853 y Fj(X)2113 2051 y Fm(k)r Fh(=1)2258 1940 y Fn(")2300 1902 y Fm(k)2379 1853 y Fj(X)2358 2055 y Fi(j)p Fm(\027)t Fi(j\024)p Fm(k)2545 1940 y Fn(e)2587 1902 y Fm(i\027)t(\013)2715 1940 y Fn(u)2767 1902 y Fh(\()p Fm(k)r Fh(\))2767 1962 y Fm(\027)2865 1940 y Fo(\()p Fn(!)s Fo(\);)390 2180 y(b)m(y)i(inserting)f(the)h (expansion)g(in)f(\(1\))i(w)m(e)f(can)g(deriv)m(e)g(recursion)f (relations)i(for)e(the)h(co)s(ef-)390 2309 y(\014cien)m(ts)e Fn(u)744 2261 y Fh(\()p Fm(k)r Fh(\))744 2321 y Fm(\027)841 2309 y Fo(\()p Fn(!)s Fo(\),)h(whic)m(h,)f(b)s(esides)e(imp)s(osing)h (the)g(restriction)h(on)f(the)g(range)g(of)h(the)f(sum)390 2439 y(o)m(v)m(er)j Fn(k)s Fo(,)f(are)g(useful)f(for)h(n)m(umerical)g (calculations)h(and)e(form)h(also)g(the)g(basis)f(of)h(the)g Fg(tr)-5 b(e)g(es)390 2568 y(exp)g(ansions)37 b Fo(pionereed)26 b(in)h([9)q(].)40 b(It)27 b(is)g(the)g(in)m(v)m(ersion)g(of)g(the)h(op) s(erator)f Fn(D)2926 2535 y Fh(2)2923 2591 y Fm(!)3000 2568 y Fo(when)f(solving)390 2698 y(the)h(functional)f(equation)i (\(1\))f(whic)m(h)f(giv)m(es)i(rise)e(to)h(the)g(so)g(called)g Fg(smal)5 b(l)30 b(denominators)390 2827 y(pr)-5 b(oblem)p Fo(,)27 b(app)s(earing)d(as)g(the)g(presence)g(in)f(the)h(expressions)g (for)f(the)h(co)s(e\016cien)m(ts)i Fn(u)3282 2779 y Fh(\()p Fm(k)r Fh(\))3282 2839 y Fm(\027)3379 2827 y Fo(\()p Fn(!)s Fo(\))390 2957 y(of)31 b(the)f(k)m(ernel)h(of)g(the)f(op)s (erator)h Fn(D)1623 2924 y Fi(\000)p Fh(2)1620 2979 y Fm(!)1717 2957 y Fo(,)f(giv)m(en)i(b)m(y)e(1)p Fn(=)p Fo(4)15 b(sin)2399 2922 y Fh(2)2454 2957 y Fn(\027)6 b(\031)s(!)s Fo(.)490 3086 y(T)-8 b(o)37 b(c)m(haracterize)i(the)e (breakdo)m(wn)f(of)g(an)h(in)m(v)-5 b(arian)m(t)37 b(curv)m(e)g Fk(C)2694 3100 y Fm(";!)2833 3086 y Fo(w)m(e)g(in)m(tro)s(duce)g(the) 390 3216 y Fg(r)-5 b(adius)34 b(of)f(c)-5 b(onver)g(genc)g(e)38 b Fo(of)30 b(the)h(Lindstedt)f(series:)1167 3435 y Fn(\032)p Fo(\()p Fn(!)s Fo(\))c(=)38 b(inf)1466 3496 y Fm(\013)p Fi(2)p Ff(T)1618 3307 y Fj(\022)1685 3435 y Fo(lim)15 b(sup)1734 3514 y Fm(k)r Fi(!1)1978 3331 y Fj(\014)1978 3385 y(\014)1978 3440 y(\014)2008 3435 y Fn(u)2060 3398 y Fh(\()p Fm(k)r Fh(\))2158 3435 y Fo(\()p Fn(\013;)g(!)s Fo(\))2386 3331 y Fj(\014)2386 3385 y(\014)2386 3440 y(\014)2418 3357 y Fh(1)p Fm(=k)2531 3307 y Fj(\023)2598 3330 y Fi(\000)p Fh(1)2707 3435 y Fn(;)390 3640 y Fo(and)30 b(the)g Fg(critic)-5 b(al)34 b(function)785 3815 y Fn(")827 3829 y Fh(c)863 3815 y Fo(\()p Fn(!)s Fo(\))26 b(=)f(sup)o Fk(f)p Fn(")1339 3777 y Fi(0)1388 3815 y Fk(\025)g Fo(0)h(:)50 b Fk(8)15 b Fn(")1738 3777 y Fi(00)1806 3815 y Fn(<)25 b(")1944 3777 y Fi(0)1993 3815 y Fk(C)2041 3830 y Fm(")2074 3811 y Fe(00)2114 3830 y Fm(;!)2209 3815 y Fo(exists)31 b(and)f(is)h(analytic)q Fk(g)p Fo(;)390 3990 y(clearly)i Fn(\032)p Fo(\()p Fn(!)s Fo(\))28 b Fk(\024)f Fn(")1027 4004 y Fh(c)1063 3990 y Fo(\()p Fn(!)s Fo(\).)45 b(In)31 b(particular,)i(the)f(radius)f(of)h(con)m(v)m(ergence)i(of)e(the)f (Lindstedt)390 4119 y(series)36 b(is)g(zero)h({)f(so)g(no)g(KAM)g(in)m (v)-5 b(arian)m(t)37 b(curv)m(e)f(exists)h({)f(when)f Fn(!)k Fo(is)d(rational;)k(when)390 4249 y Fn(!)e Fo(satis\014es)f(an)e (irrationalit)m(y)j(condition)e(kno)m(wn)f(as)h(the)g Fg(Bryuno)i(c)-5 b(ondition)p Fo(,)39 b(instead,)390 4378 y(it)d(can)f(b)s(e)g(pro)m(v)m(ed)g(that)h Fn(\032)p Fo(\()p Fn(!)s Fo(\))e Fn(>)f Fo(0)j({)g(so)f(that)h(analytic)h(in)m(v) -5 b(arian)m(t)36 b(curv)m(es)g(exist)g(for)f Fn(")390 4508 y Fo(small.)490 4637 y(The)26 b(analytic)i(structure)d(of)i Fn(u)f Fo(in)h Fn(")f Fo(is)h(of)f(particular)h(in)m(terest,)i(since)d (it)h(ma)m(y)g(explain,)390 4767 y(among)40 b(other)f(things,)j(the)d (relation)i(b)s(et)m(w)m(een)f Fn(\032)p Fo(\()p Fn(!)s Fo(\))g(and)e Fn(")2560 4781 y Fh(c)2596 4767 y Fo(\()p Fn(!)s Fo(\).)68 b(It)39 b(is)h(b)s(eliev)m(ed,)i(on)390 4896 y(the)j(basis)g(of)g([10)q(,)g(11)q(,)g(12)q(],)k(that)c Fn(u)g Fo(has)f(a)i(natural)f(b)s(oundary)d(on)j(the)g(complex)h Fn(")390 5026 y Fo(plane,)h Fg(i.e.)d Fo(that)g(its)g(domain)f(of)h (analyticit)m(y)i(is)e(b)s(ounded)d(b)m(y)j(a)f(con)m(tin)m(uous)i (curv)m(e)390 5155 y(where)39 b(singularities)i(are)g(dense,)h (obstructing)e(analytic)h(con)m(tin)m(uation;)47 b(this)40 b(natural)p eop %%Page: 3 3 3 2 bop 1188 66 a Fh(SHAPE)31 b(OF)f(ANAL)-6 b(YTICITY)31 b(DOMAINS)883 b(3)270 266 y Fo(b)s(oundary)33 b(app)s(ears)i(to)h(b)s (e)e(indep)s(enden)m(t)g(on)i Fn(\013)p Fo(.)55 b(Its)36 b(shap)s(e)e(determines)h(the)h(relation)270 395 y(b)s(et)m(w)m(een)g Fn(\032)p Fo(\()p Fn(!)s Fo(\))g(and)f Fn(")1063 409 y Fh(c)1099 395 y Fo(\()p Fn(!)s Fo(\):)51 b(in)35 b(fact,)j Fn(\032)p Fo(\()p Fn(!)s Fo(\))e(is)g(giv)m(en)g(b)m(y)g(the)f (distance)i(of)e(the)h(natural)270 525 y(b)s(oundary)43 b(from)h(the)h(origin,)k(while)c Fn(")1689 539 y Fh(c)1725 525 y Fo(\()p Fn(!)s Fo(\))g(is)g(giv)m(en)h(b)m(y)e(its)i(in)m (tersection)g(with)f(the)270 654 y(real,)d(p)s(ositiv)m(e)e(axis)f (\(and)g(for)f(the)h(standard)f(map)h(the)g(natural)g(b)s(oundary)e(m)m (ust)i(b)s(e)270 784 y(symmetric)31 b(with)f(resp)s(ect)g(to)h(the)g (imaginary)g(axis\).)370 913 y(F)-8 b(or)25 b(some)g(rotation)h(n)m(um) m(b)s(ers,)f(lik)m(e)h(the)e(golden)i(mean)e Fn(\015)31 b Fo(=)25 b(\()2519 838 y Fk(p)p 2595 838 46 4 v 75 x Fo(5)9 b Fk(\000)g Fo(1\))p Fn(=)p Fo(2,)27 b(the)e(natural)270 1043 y(b)s(oundary)f(w)m(as)j(found)e(to)i(b)s(e)f(roughly)g(circular)h ([10)q(,)f(11)q(],)i(with)e(a)h(v)m(ery)f(sligh)m(t)i(lengh)m(ten-)270 1172 y(ing)k(along)g(the)g(imaginary)g(axis)g(for)f(the)g(golden)h (mean)g([12)q(],)g(so)g(that)g(one)g(w)m(ould)f(ha)m(v)m(e)270 1302 y Fn(")312 1316 y Fh(c)348 1302 y Fo(\()p Fn(!)s Fo(\))26 b(=)f Fn(\032)p Fo(\()p Fn(!)s Fo(\).)39 b(Qualitativ)m(ely)-8 b(,)30 b(w)m(e)c(can)g(note)g(that)g(suc)m(h)g(a)g(situation)g (practically)i(arises)270 1431 y(for)41 b(Diophan)m(tine)h(n)m(um)m(b)s (ers)e(of)i(the)f(form)g Fn(!)47 b Fo(=)c([)p Fn(a)2124 1445 y Fh(1)2164 1431 y Fn(;)15 b(a)2252 1445 y Fh(2)2291 1431 y Fn(;)g(a)2379 1445 y Fh(3)2419 1431 y Fn(;)g(:)g(:)g(:)r Fo(],)44 b(with)d(small)h(partial)270 1561 y(quotien)m(ts)29 b Fn(a)710 1576 y Fm(k)753 1561 y Fo(:)40 b(in)28 b(this)g(sense)g(the) h(golden)f(mean)h(is)f(the)h(b)s(est)f(p)s(ossible)f(case.)41 b(F)-8 b(ollo)m(wing)270 1690 y(hin)m(ts)34 b(from)g([15)q(,)g(16)q(],) i(w)m(e)e(can)h(exp)s(ect)f(to)h(see)g(a)g(sharp)e(di\013erence)h(b)s (et)m(w)m(een)h Fn(\032)p Fo(\()p Fn(!)s Fo(\))g(and)270 1820 y Fn(")312 1834 y Fh(c)348 1820 y Fo(\()p Fn(!)s Fo(\))e(when)e Fn(!)k Fo(is)d(close)h(to)g(a)f(rational)i(n)m(um)m(b)s (er)d(\(w)m(e)i(shall)f(come)h(bac)m(k)g(later)g(on)f(what)270 1949 y(\\close")h(really)e(means\).)370 2079 y(Here)22 b(w)m(e)g(determine)g(n)m(umerically)-8 b(,)25 b(using)c(P)m(ad)m(\023) -43 b(e)24 b(appro)m(ximan)m(ts,)g(the)e(natural)g(b)s(ound-)270 2208 y(ary)h(for)h(the)f(Lindstedt)g(series)h(of)f(the)h(standard)f (map)g(in)g(the)g(complex)h Fn(")g Fo(v)-5 b(ariable,)26 b(when)270 2338 y Fn(!)38 b Fo(is)d(a)g(Diophan)m(tine)h(n)m(um)m(b)s (er)e(close)i(to)g(a)f(rational)i(one:)50 b(see)36 b([10)q(,)f(11)q(])g (for)g(the)g(use)g(of)270 2467 y(P)m(ad)m(\023)-43 b(e)34 b(appro)m(ximan)m(ts)e(in)g(this)f(con)m(text)j(and)e(further)e (references;)j(it)g(is)f(enough)f(here)h(to)270 2597 y(recall)g(that)g(the)f(p)s(oles)g(of)g(the)g(P)m(ad)m(\023)-43 b(e)33 b(appro)m(ximan)m(ts)e(mo)s(del)g(the)g(shap)s(e)g(of)g(the)g (natural)270 2726 y(b)s(oundary)d(of)j(the)f(function)h(b)s(eing)e (appro)m(ximated.)370 2856 y(In)39 b(the)h(follo)m(wing)i(\014gures)d (w)m(e)h(plot)h(the)f(p)s(oles)g(in)g(the)g(complex)h Fn(")f Fo(plane)g(of)h(some)270 2985 y(P)m(ad)m(\023)-43 b(e)32 b(appro)m(ximan)m(ts)e(for)g Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(!)s Fo(\))33 b(for)d Fn(\013)25 b Fo(=)g(1)31 b(and)e(selected)j(v)-5 b(alues)30 b(of)h Fn(!)i Fo(near)d(ratio-)270 3115 y(nal)f(v)-5 b(alues.)41 b(W)-8 b(e)30 b(sho)m(w)f(only)g(the)g (data)h(coming)g(from)e(high)h(order)g(P)m(ad)m(\023)-43 b(e)30 b(appro)m(ximan)m(ts)270 3244 y(\([240)p Fn(=)p Fo(240]\),)e(computed)21 b(using)f(high)h(precision)g(arithmetic)i (\(480)g(digits\),)h(though)d(lo)m(w)m(er)270 3374 y(order)26 b(P)m(ad)m(\023)-43 b(e)28 b(appro)m(ximan)m(ts)f(and)f(lo)m(w)m(er)h (precision)g(arithmetic)g(sho)m(w)g(the)f(same)h(results.)270 3504 y(Spurious)f(p)s(ole/zero)k(pairs)e(ha)m(v)m(e)h(b)s(een)e(c)m (hec)m(k)m(ed)j(for)e(and)g(deleted.)41 b(The)27 b(indep)s(endence)270 3633 y(of)f(the)g(analyticit)m(y)i(domain)d(on)h Fn(\013)g Fo(has)f(b)s(een)g(tested)h(b)m(y)g(computing)f(the)h(P)m(ad)m(\023)-43 b(e)27 b(appro)m(xi-)270 3763 y(man)m(ts)g(for)f(some)h(selected)h(v)-5 b(alues)27 b(of)g Fn(\013)p Fo(,)h(and)e(v)m(erifying)h(that)g(the)g (shap)s(e)e(of)i(the)g(natural)270 3892 y(b)s(oundary)h(is)j(essen)m (tially)h(the)f(same.)370 4022 y(In)j(\014gure)h(1)g(w)m(e)h(see)f(the) h(shap)s(e)e(of)h(the)h(natural)f(b)s(oundary)e(when)h Fn(!)i Fo(=)d([10)p Fn(;)15 b Fo(1)3184 3989 y Fi(1)3261 4022 y Fo(])33 b(=)270 4151 y(1)p Fn(=)p Fo(\(10)28 b(+)d Fn(\015)5 b Fo(\),)42 b(where)c Fn(\015)45 b Fo(=)39 b(\()1271 4076 y Fk(p)p 1347 4076 V 75 x Fo(5)26 b Fk(\000)f Fo(1\))p Fn(=)p Fo(2)41 b(is)e(the)g(golden)g(mean;)k(note)d(that)f (suc)m(h)f(an)h Fn(!)270 4281 y Fo(is)h(close)h(to)g(0.)69 b(W)-8 b(e)41 b(clearly)g(see)g(that)f(singularities)h(close)g(to)g (the)f(origin)g(app)s(ear)f(on)270 4410 y(the)f(imaginary)g(axis,)j(so) d(that)g Fn(\032)p Fo(\()p Fn(!)s Fo(\))g Fn(<)f(")1776 4424 y Fh(c)1812 4410 y Fo(\()p Fn(!)s Fo(\))h(strictly)h(in)e(this)h (case.)64 b(Note)39 b(also)g(the)270 4540 y(t)m(w)m(o-lob)s(ed)d(shap)s (e)f(of)g(the)g(domain,)h(generated)g(b)m(y)f(the)g(t)m(w)m(o)i(lines)e (of)g(singularities)h(on)270 4669 y(the)31 b(imaginary)g(axis)f (cutting)i(deep)e(in)m(to)h(the)g(analyticit)m(y)i(domain.)370 4799 y(In)c(\014gure)g(2)i(w)m(e)f(see)h(the)f(shap)s(e)f(of)h(the)g (natural)g(b)s(oundary)e(when)h Fn(!)f Fo(=)d([2)p Fn(;)15 b Fo(10)p Fn(;)g Fo(1)3191 4766 y Fi(1)3269 4799 y Fo(])25 b(=)270 4928 y(\(10)j(+)e Fn(\015)5 b Fo(\))p Fn(=)p Fo(\(21)28 b(+)f(2)p Fn(\015)5 b Fo(\),)43 b(whic)m(h)c(is)h(close)h (to)f(1)p Fn(=)p Fo(2.)70 b(Again)41 b Fn(\032)p Fo(\()p Fn(!)s Fo(\))g Fn(<)g(")2697 4942 y Fh(c)2733 4928 y Fo(\()p Fn(!)s Fo(\))f(strictly)-8 b(,)44 b(and)270 5058 y(observ)m(e)f(the)f(four-lob)s(ed)f(shap)s(e)h(of)g(the)g(domain,)j (with)d(four)f(lines)h(of)h(singularities,)270 5187 y(disp)s(osed)24 b(radially)i(as)g(the)f(4-th)h(ro)s(ots)g(of)f Fk(\000)p Fo(1,)i(cutting)f(in)m(to)g(the)g(domain)f(of)h(analyticit)m(y)-8 b(.)p eop %%Page: 4 4 4 3 bop 390 66 a Fh(4)330 b(ALBER)-6 b(TO)23 b(BERRETTI,)g(CORRADO)g(F) -8 b(ALCOLINI,)24 b(AND)f(GUIDO)h(GENTILE)896 2166 y @beginspecial 163 @llx 299 @lly 416 @urx 537 @ury 2530 @rwi @setspecial %%BeginDocument: fig1.eps %!PS-Adobe-3.0 EPSF-3.0 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currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix 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def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe 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@e 1148.5 1984.5 4.5 @i 1148.5 1984.5 4 @e 1148.5 1420.5 4.5 @i 1148.5 1420.5 4 @e 1172.5 1972.5 4.5 @i 1172.5 1972.5 4 @e 1172.5 1432.5 4.5 @i 1172.5 1432.5 4 @e 1189.5 1966.5 4.5 @i 1189.5 1966.5 4 @e 1189.5 1438.5 4.5 @i 1189.5 1438.5 4 @e 1190.5 1959.5 4.5 @i 1190.5 1959.5 4 @e 1190.5 1445.5 4.5 @i 1190.5 1445.5 4 @e 1191.5 1953.5 4.5 @i 1191.5 1953.5 4 @e 1191.5 1451.5 4.5 @i 1191.5 1451.5 4 @e 1191.5 1948.5 4.5 @i 1191.5 1948.5 4 @e 1191.5 1456.5 4.5 @i 1191.5 1456.5 4 @e 1191.5 1918.5 4.5 @i 1191.5 1918.5 4 @e 1191.5 1486.5 4.5 @i 1191.5 1486.5 4 @e 1191.5 1918.5 4.5 @i 1191.5 1918.5 4 @e 1191.5 1486.5 4.5 @i 1191.5 1486.5 4 @e 1191.5 1919.5 4.5 @i 1191.5 1919.5 4 @e 1191.5 1485.5 4.5 @i 1191.5 1485.5 4 @e 1191.5 1921.5 4.5 @i 1191.5 1921.5 4 @e 1191.5 1483.5 4.5 @i 1191.5 1483.5 4 @e 1191.5 1922.5 4.5 @i 1191.5 1922.5 4 @e 1191.5 1482.5 4.5 @i 1191.5 1482.5 4 @e 1191.5 1923.5 4.5 @i 1191.5 1923.5 4 @e 1191.5 1481.5 4.5 @i 1191.5 1481.5 4 @e 1191.5 1925.5 4.5 @i 1191.5 1925.5 4 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md/setpagedevice undef SC_topddict realstpgdev }bd /stpgdev { SC_topddict dup 3 -1 roll { SC_spdict 2 index known { SC_spdict 2 index get dup 3 -1 roll { put dup }forall pop put dup }{ put dup }ifelse }forall pop pop }bd /ststpgdev { md/setpagedevice/stpgdev load put /SC_topddict 0 dict store /SC_spdict 3 dict begin /InputAttributes 0 dict def /Policies 0 dict def /OutputAttributes 0 dict def currentdict end store }def /sfcl/sfcl2 ld /efcl/efcl2 ld level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { mT $m currentmatrix mTS concatmatrix pop /pm save store mT concat }bd /endp { pm restore }bd /adjRect { dup 2 mul 6 2 roll 4 index sub exch 5 -1 roll sub exch 4 2 roll 4 index add exch 5 -1 roll add exch 4 2 roll }bd /frame1up { gS mTS setmatrix QDframwid lw /setstrokeadjust where{pop T setstrokeadjust}if clippath pathbbox 2 index sub exch 3 index sub exch currentlinewidth framewidth mul adjRect numframes dup 0 lt{pop 0}if { 4 copy rS currentlinewidth framewidth mul 4 mul adjRect }repeat pop pop pop pop gR }bd /$c devr def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile level3 startnoload %%BeginFile: lw8_safeclipL12-1.0 /rectclip where { pop/rCa/rectclip ld }{ /rCa { np 0 1 index length 4 idiv { 2 copy 4 getinterval aload pop 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K 4 add }repeat clip np pop pop }bd }ifelse /savedstack Z /subsavedstack Z /execstring Z /saferCa { /execstring xs /odictstk countdictstack store /oopstk 0 store count 0 ne { savedstack 0 eq{ count 100 gt{count}{100}ifelse array/savedstack xs }{ count savedstack length gt { count array/savedstack xs }if }ifelse count savedstack 0 3 -1 roll getinterval astore/subsavedstack xs }{ /subsavedstack 0 store }ifelse execstring cvx stopped { $error/newerror F put newpath }if fcl subsavedstack 0 ne{ subsavedstack aload pop }if }bd %%EndFile level3 endnoload level3 not startnoload %%BeginFile: lw8_safeclipL3-1.0 /saferCa/pop ld %%EndFile level3 not endnoload %%BeginFile: lw8_level1_colorspace-2.0 /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /$cs Z /:rg{devr :ss}bd /:sc{$cs :ss}bd /:dc { dup type/arraytype eq{0 get}if dup/DeviceCMYK eq { pop devc }{ /DeviceGray eq { devg }{ devr }ifelse }ifelse /$cs xdf }bd /:sgl{}def /:dr{}bd /:fCRD{pop}bd /:ckcs{}bd /:ss{/$c xdf}bd %%EndFile level2 startnoload %%BeginFile: lw8_level1_patterns-2.0 /patfreq Z /patangle Z /bk Z /fg Z /docolorscreen Z /graystring Z /pattransf{}def /initQDpatterns { /patfreq 9.375 store /patangle 1 0 $m defaultmatrix dtransform exch atan por not {90 add}if normland{180 add}if store :a }def /docolorscreen /setcolorscreen where { pop/currentcolorscreen where { pop/setcmykcolor where { pop T }{ F }ifelse }{ F }ifelse }{ F }ifelse def /setgraypattern { /graystring xs patfreq patangle { 1 add 4 mul cvi graystring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and }setscreen 64 div setgray }bd /:b { /pattransf load settransfer pop pop pop setgraypattern }bd docolorscreen startnoload /screensave 5 array def /:a{currentgray currentscreen currenttransfer screensave astore pop}bd /:e{screensave aload pop settransfer setscreen setgray}bd /:d { pop pop pop /pattransf load settransfer setgraypattern 8{pop}repeat }bd /:c /:d ld docolorscreen endnoload docolorscreen not startnoload /screensave 20 array def /:a{currentcmykcolor currentcolorscreen currentcolortransfer screensave astore pop}bd /:e{screensave aload pop setcolortransfer setcolorscreen setcmykcolor}bd /rstring Z /grstring Z /blstring Z /convroll{64 div 4 -1 roll}bd /setcolorpattern { /graystring xs /blstring xs /grstring xs /rstring xs patfreq patangle { 1 add 4 mul cvi rstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi grstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi blstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi graystring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } setcolorscreen convroll convroll convroll convroll setcmykcolor }bd /:d { pop pop pop /pattransf load settransfer pop pop setcolorpattern }bd /:c /:d ld docolorscreen not endnoload %%EndFile level2 endnoload level2 not startnoload %%BeginFile: lw8_level2_patterns-2.0 /pmtx Z /BGnd Z /FGnd Z /PaintData Z /PatternMtx Z /PatHeight Z /PatWidth Z /$d Z /savecolor 4 array def /savecolorspace Z /patDecode Z /:a{ mark 0 0 0 currentcolor savecolor astore pop cleartomark /savecolorspace currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix makepattern gR }bd /:u { 14 dict begin /$d 8 dict def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PaintData xdf /PatHeight xdf /PatWidth xdf /PatternMtx[PatWidth 0 0 PatHeight 0 0]def $d begin /ImageType 1 def /MultipleDataSource F def /Height PatHeight def /Width PatWidth def /Decode patDecode def /ImageMatrix PatternMtx def /DataSource PaintData def /BitsPerComponent 8 def end /PaintProc { begin $d image end }def currentdict PatternMtx end gS $c setcolorspace pmtx setmatrix makepattern gR }bd /bk[1 1 1]def /fg[0 0 0]def /:b{ :t setpattern pop pop }bd /:d{ :t setpattern 10{pop}repeat }bd /:c{ :u setpattern 10{pop}repeat }bd %%EndFile level2 not endnoload %%BeginFile: lw8_uniform_graphics-2.0 /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /@c { moveto 0 rlineto stroke }bd /@w { moveto 0 exch rlineto stroke }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: lw8_basic_text-2.0 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld /mT[.24 0 0 -.24 10.56 830.179]def initQDpatterns /sD 16 dict def %%IncludeFont: Helvetica /f135/Helvetica :mre /f151 f135 42 scf /Courier findfont[10 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1307 2155 1 1 1306 1254 @b -1 -1 1419 2155 1 1 1418 1254 @b -1 -1 1532 2155 1 1 1531 1254 @b -1 -1 1644 2155 1 1 1643 1254 @b :e .176 G 26 743 2154.5 @c 26 743 2042.5 @c 26 743 1929.5 @c 26 743 1817.5 @c 26 743 1704.5 @c 26 743 1591.5 @c 26 743 1479.5 @c 26 743 1366.5 @c 26 743 1254.5 @c 13 743 2126.5 @c 13 743 2098.5 @c 13 743 2070.5 @c 13 743 2014.5 @c 13 743 1985.5 @c 13 743 1957.5 @c 13 743 1929.5 @c 13 743 1901.5 @c 13 743 1873.5 @c 13 743 1845.5 @c 13 743 1789.5 @c 13 743 1760.5 @c 13 743 1732.5 @c 13 743 1676.5 @c 13 743 1648.5 @c 13 743 1620.5 @c 13 743 1563.5 @c 13 743 1535.5 @c 13 743 1507.5 @c 13 743 1451.5 @c 13 743 1423.5 @c 13 743 1395.5 @c 13 743 1338.5 @c 13 743 1310.5 @c 13 743 1282.5 @c 26 1618 2154.5 @c 26 1618 2042.5 @c 26 1618 1929.5 @c 26 1618 1817.5 @c 26 1618 1704.5 @c 26 1618 1591.5 @c 26 1618 1479.5 @c 26 1618 1366.5 @c 26 1618 1254.5 @c 13 1631 2126.5 @c 13 1631 2098.5 @c 13 1631 2070.5 @c 13 1631 2014.5 @c 13 1631 1985.5 @c 13 1631 1957.5 @c 13 1631 1929.5 @c 13 1631 1901.5 @c 13 1631 1873.5 @c 13 1631 1845.5 @c 13 1631 1789.5 @c 13 1631 1760.5 @c 13 1631 1732.5 @c 13 1631 1676.5 @c 13 1631 1648.5 @c 13 1631 1620.5 @c 13 1631 1563.5 @c 13 1631 1535.5 @c 13 1631 1507.5 @c 13 1631 1451.5 @c 13 1631 1423.5 @c 13 1631 1395.5 @c 13 1631 1338.5 @c 13 1631 1310.5 @c 13 1631 1282.5 @c 26 743.5 2129 @w 26 855.5 2129 @w 26 968.5 2129 @w 26 1080.5 2129 @w 26 1193.5 2129 @w 26 1306.5 2129 @w 26 1418.5 2129 @w 26 1531.5 2129 @w 26 1643.5 2129 @w 13 771.5 2142 @w 13 799.5 2142 @w 13 827.5 2142 @w 13 883.5 2142 @w 13 912.5 2142 @w 13 940.5 2142 @w 13 968.5 2142 @w 13 996.5 2142 @w 13 1024.5 2142 @w 13 1052.5 2142 @w 13 1108.5 2142 @w 13 1137.5 2142 @w 13 1165.5 2142 @w 13 1221.5 2142 @w 13 1249.5 2142 @w 13 1277.5 2142 @w 13 1334.5 2142 @w 13 1362.5 2142 @w 13 1390.5 2142 @w 13 1446.5 2142 @w 13 1474.5 2142 @w 13 1502.5 2142 @w 13 1559.5 2142 @w 13 1587.5 2142 @w 13 1615.5 2142 @w 26 743.5 1254 @w 26 855.5 1254 @w 26 968.5 1254 @w 26 1080.5 1254 @w 26 1193.5 1254 @w 26 1306.5 1254 @w 26 1418.5 1254 @w 26 1531.5 1254 @w 26 1643.5 1254 @w 13 771.5 1254 @w 13 799.5 1254 @w 13 827.5 1254 @w 13 883.5 1254 @w 13 912.5 1254 @w 13 940.5 1254 @w 13 968.5 1254 @w 13 996.5 1254 @w 13 1024.5 1254 @w 13 1052.5 1254 @w 13 1108.5 1254 @w 13 1137.5 1254 @w 13 1165.5 1254 @w 13 1221.5 1254 @w 13 1249.5 1254 @w 13 1277.5 1254 @w 13 1334.5 1254 @w 13 1362.5 1254 @w 13 1390.5 1254 @w 13 1446.5 1254 @w 13 1474.5 1254 @w 13 1502.5 1254 @w 13 1559.5 1254 @w 13 1587.5 1254 @w 13 1615.5 1254 @w 901 743.5 1254 @w 901 1643.5 1254 @w 901 743 2154.5 @c 901 743 1254.5 @c 0 G 756.5 1704.5 4.5 @i 756.5 1704.5 4 @e 803.5 1717.5 4.5 @i 803.5 1717.5 4 @e 803.5 1691.5 4.5 @i 803.5 1691.5 4 @e 807.5 1732.5 4.5 @i 807.5 1732.5 4 @e 807.5 1676.5 4.5 @i 807.5 1676.5 4 @e 808.5 1774.5 4.5 @i 808.5 1774.5 4 @e 808.5 1634.5 4.5 @i 808.5 1634.5 4 @e 811.5 1762.5 4.5 @i 811.5 1762.5 4 @e 811.5 1646.5 4.5 @i 811.5 1646.5 4 @e 812.5 1740.5 4.5 @i 812.5 1740.5 4 @e 812.5 1668.5 4.5 @i 812.5 1668.5 4 @e 814.5 1780.5 4.5 @i 814.5 1780.5 4 @e 814.5 1628.5 4.5 @i 814.5 1628.5 4 @e 824.5 1808.5 4.5 @i 824.5 1808.5 4 @e 824.5 1600.5 4.5 @i 824.5 1600.5 4 @e 825.5 1795.5 4.5 @i 825.5 1795.5 4 @e 825.5 1613.5 4.5 @i 825.5 1613.5 4 @e 828.5 1823.5 4.5 @i 828.5 1823.5 4 @e 828.5 1585.5 4.5 @i 828.5 1585.5 4 @e 831.5 2087.5 4.5 @i 831.5 2087.5 4 @e 831.5 1321.5 4.5 @i 831.5 1321.5 4 @e 838.5 1845.5 4.5 @i 838.5 1845.5 4 @e 838.5 1563.5 4.5 @i 838.5 1563.5 4 @e 847.5 1857.5 4.5 @i 847.5 1857.5 4 @e 847.5 1551.5 4.5 @i 847.5 1551.5 4 @e 853.5 1885.5 4.5 @i 853.5 1885.5 4 @e 853.5 1524.5 4.5 @i 853.5 1524.5 4 @e 860.5 1858.5 4.5 @i 860.5 1858.5 4 @e 860.5 1550.5 4.5 @i 860.5 1550.5 4 @e 867.5 1883.5 4.5 @i 867.5 1883.5 4 @e 867.5 1525.5 4.5 @i 867.5 1525.5 4 @e 877.5 1891.5 4.5 @i 877.5 1891.5 4 @e 877.5 1517.5 4.5 @i 877.5 1517.5 4 @e 894.5 1910.5 4.5 @i 894.5 1910.5 4 @e 894.5 1498.5 4.5 @i 894.5 1498.5 4 @e 907.5 1911.5 4.5 @i 907.5 1911.5 4 @e 907.5 1497.5 4.5 @i 907.5 1497.5 4 @e 911.5 1919.5 4.5 @i 911.5 1919.5 4 @e 911.5 1489.5 4.5 @i 911.5 1489.5 4 @e 933.5 1932.5 4.5 @i 933.5 1932.5 4 @e 933.5 1476.5 4.5 @i 933.5 1476.5 4 @e 937.5 1963.5 4.5 @i 937.5 1963.5 4 @e 937.5 1446.5 4.5 @i 937.5 1446.5 4 @e 957.5 1940.5 4.5 @i 957.5 1940.5 4 @e 957.5 1468.5 4.5 @i 957.5 1468.5 4 @e 964.5 2001.5 4.5 @i 964.5 2001.5 4 @e 964.5 1407.5 4.5 @i 964.5 1407.5 4 @e 964.5 1933.5 4.5 @i 964.5 1933.5 4 @e 964.5 1476.5 4.5 @i 964.5 1476.5 4 @e 969.5 1969.5 4.5 @i 969.5 1969.5 4 @e 969.5 1439.5 4.5 @i 969.5 1439.5 4 @e 969.5 1928.5 4.5 @i 969.5 1928.5 4 @e 969.5 1480.5 4.5 @i 969.5 1480.5 4 @e 973.5 1924.5 4.5 @i 973.5 1924.5 4 @e 973.5 1484.5 4.5 @i 973.5 1484.5 4 @e 976.5 1921.5 4.5 @i 976.5 1921.5 4 @e 976.5 1487.5 4.5 @i 976.5 1487.5 4 @e 978.5 1919.5 4.5 @i 978.5 1919.5 4 @e 978.5 1490.5 4.5 @i 978.5 1490.5 4 @e 980.5 1994.5 4.5 @i 980.5 1994.5 4 @e 980.5 1414.5 4.5 @i 980.5 1414.5 4 @e 980.5 1916.5 4.5 @i 980.5 1916.5 4 @e 980.5 1492.5 4.5 @i 980.5 1492.5 4 @e 982.5 1915.5 4.5 @i 982.5 1915.5 4 @e 982.5 1494.5 4.5 @i 982.5 1494.5 4 @e 984.5 1913.5 4.5 @i 984.5 1913.5 4 @e 984.5 1495.5 4.5 @i 984.5 1495.5 4 @e 985.5 1911.5 4.5 @i 985.5 1911.5 4 @e 985.5 1497.5 4.5 @i 985.5 1497.5 4 @e 986.5 1910.5 4.5 @i 986.5 1910.5 4 @e 986.5 1498.5 4.5 @i 986.5 1498.5 4 @e 987.5 1909.5 4.5 @i 987.5 1909.5 4 @e 987.5 1499.5 4.5 @i 987.5 1499.5 4 @e 988.5 1908.5 4.5 @i 988.5 1908.5 4 @e 988.5 1500.5 4.5 @i 988.5 1500.5 4 @e 989.5 1908.5 4.5 @i 989.5 1908.5 4 @e 989.5 1500.5 4.5 @i 989.5 1500.5 4 @e 989.5 1907.5 4.5 @i 989.5 1907.5 4 @e 989.5 1501.5 4.5 @i 989.5 1501.5 4 @e 990.5 1907.5 4.5 @i 990.5 1907.5 4 @e 990.5 1501.5 4.5 @i 990.5 1501.5 4 @e 990.5 1907.5 4.5 @i 990.5 1907.5 4 @e 990.5 1502.5 4.5 @i 990.5 1502.5 4 @e 993.5 2010.5 4.5 @i 993.5 2010.5 4 @e 993.5 1398.5 4.5 @i 993.5 1398.5 4 @e 1013.5 2029.5 4.5 @i 1013.5 2029.5 4 @e 1013.5 1379.5 4.5 @i 1013.5 1379.5 4 @e 1017.5 2002.5 4.5 @i 1017.5 2002.5 4 @e 1017.5 1407.5 4.5 @i 1017.5 1407.5 4 @e 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1176.5 1316.5 4.5 @i 1176.5 1316.5 4 @e 1188.5 2094.5 4.5 @i 1188.5 2094.5 4 @e 1188.5 1314.5 4.5 @i 1188.5 1314.5 4 @e 1208.5 2084.5 4.5 @i 1208.5 2084.5 4 @e 1208.5 1324.5 4.5 @i 1208.5 1324.5 4 @e 1216.5 2097.5 4.5 @i 1216.5 2097.5 4 @e 1216.5 1312.5 4.5 @i 1216.5 1312.5 4 @e 1234.5 2094.5 4.5 @i 1234.5 2094.5 4 @e 1234.5 1315.5 4.5 @i 1234.5 1315.5 4 @e 1238.5 2081.5 4.5 @i 1238.5 2081.5 4 @e 1238.5 1327.5 4.5 @i 1238.5 1327.5 4 @e 1246.5 2131.5 4.5 @i 1246.5 2131.5 4 @e 1246.5 1277.5 4.5 @i 1246.5 1277.5 4 @e 1264.5 2085.5 4.5 @i 1264.5 2085.5 4 @e 1264.5 1323.5 4.5 @i 1264.5 1323.5 4 @e 1275.5 2081.5 4.5 @i 1275.5 2081.5 4 @e 1275.5 1327.5 4.5 @i 1275.5 1327.5 4 @e 1293.5 2074.5 4.5 @i 1293.5 2074.5 4 @e 1293.5 1335.5 4.5 @i 1293.5 1335.5 4 @e 1305.5 2067.5 4.5 @i 1305.5 2067.5 4 @e 1305.5 1342.5 4.5 @i 1305.5 1342.5 4 @e 1314.5 2050.5 4.5 @i 1314.5 2050.5 4 @e 1314.5 1358.5 4.5 @i 1314.5 1358.5 4 @e 1318.5 2066.5 4.5 @i 1318.5 2066.5 4 @e 1318.5 1343.5 4.5 @i 1318.5 1343.5 4 @e 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currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix makepattern gR }bd /:u { 14 dict begin /$d 8 dict def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PaintData xdf /PatHeight xdf /PatWidth xdf /PatternMtx[PatWidth 0 0 PatHeight 0 0]def $d begin /ImageType 1 def /MultipleDataSource F def /Height PatHeight def /Width PatWidth def /Decode patDecode def /ImageMatrix PatternMtx def /DataSource PaintData def /BitsPerComponent 8 def end /PaintProc { begin $d image end }def currentdict PatternMtx end gS $c setcolorspace pmtx setmatrix makepattern gR }bd /bk[1 1 1]def /fg[0 0 0]def /:b{ :t setpattern pop pop }bd /:d{ :t setpattern 10{pop}repeat }bd /:c{ :u setpattern 10{pop}repeat }bd %%EndFile level2 not endnoload %%BeginFile: lw8_uniform_graphics-2.0 /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /@c { moveto 0 rlineto stroke }bd /@w { moveto 0 exch rlineto stroke }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: lw8_basic_text-2.0 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld /mT[.24 0 0 -.24 10.56 830.179]def initQDpatterns /sD 16 dict def %%IncludeFont: Helvetica /f135/Helvetica :mre /f151 f135 42 scf /Courier findfont[10 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Fn(=)p Fo(240],)64 b Fn(!)k Fo(=)569 2538 y([3)p Fn(;)15 b Fo(12)p Fn(;)g Fo(1)854 2505 y Fi(1)931 2538 y Fo(],)31 b Fn(\013)26 b Fo(=)f(1.)41 b(Greene's)31 b(metho)s(d)f(giv)m(es)i Fn(")2269 2552 y Fm(c)2304 2538 y Fo(\()p Fn(!)s Fo(\))26 b(=)f(0)p Fn(:)p Fo(7047.)370 2769 y(As)40 b(w)m(e)h(tak)m(e)i (rotation)f(n)m(um)m(b)s(ers)d(close)j(to)g(other)e(rational)i(n)m(um)m (b)s(ers)e Fn(p=q)s Fo(,)j(w)m(e)e(see)270 2898 y(2)p Fn(q)s Fo(-lob)s(ed)30 b(analyticit)m(y)i(domains)d(generated)i(b)m(y)f (2)p Fn(q)j Fo(lines)c(of)h(singularities,)h(disp)s(osed)e(as)270 3028 y(the)i(2)p Fn(q)s Fo(-th)f(ro)s(ots)h(of)f Fk(\000)p Fo(1:)41 b(w)m(e)31 b(call)h Fg(dominant)41 b Fo(suc)m(h)30 b(singularities.)370 3157 y(F)-8 b(or)42 b(example,)k(in)c(\014gure)f (3)h(w)m(e)h(see)f(the)h(shap)s(e)e(of)h(the)g(natural)g(b)s(oundary)e (when)270 3287 y Fn(!)c Fo(=)d([3)p Fn(;)15 b Fo(12)p Fn(;)g Fo(1)752 3254 y Fi(1)830 3287 y Fo(])33 b(=)g(\(12)25 b(+)e Fn(\015)5 b Fo(\))p Fn(=)p Fo(\(37)25 b(+)e(3)p Fn(\015)5 b Fo(\),)38 b(close)e(to)g(1)p Fn(=)p Fo(3,)i(and)c(in)h (\014gure)g(4)g(w)m(e)h(see)g(the)270 3416 y(shap)s(e)42 b(of)g(the)h(natural)f(b)s(oundary)e(when)i Fn(!)48 b Fo(=)c([4)p Fn(;)15 b Fo(14)p Fn(;)g Fo(1)2328 3383 y Fi(1)2406 3416 y Fo(])45 b(=)g(\(15)30 b(+)e Fn(\015)5 b Fo(\))p Fn(=)p Fo(\(61)30 b(+)e(4)p Fn(\015)5 b Fo(\),)270 3546 y(close)35 b(to)f(1)p Fn(=)p Fo(4:)49 b(observ)m(e)34 b(the)g(shap)s(es)f(of)g(the)h(natural)g(b)s(oundaries)e(and)h(their)h (relations)270 3675 y(with)k Fn(q)s Fo(.)63 b(It)38 b(app)s(ears)f (that)i(there)f(is)g(no)g(relev)-5 b(an)m(t)39 b(dep)s(endence)e(of)i (the)f(shap)s(e)f(on)h(the)270 3805 y(n)m(umerator)29 b Fn(p)p Fo(:)40 b(for)29 b(example)h(in)f(\014gure)g(5)h(w)m(e)g(see)g (the)f(shap)s(e)g(of)g(the)h(natural)f(b)s(oundary)270 3934 y(when)j Fn(!)h Fo(=)c([2)p Fn(;)15 b Fo(2)p Fn(;)g Fo(12)p Fn(;)g Fo(1)1070 3901 y Fi(1)1149 3934 y Fo(])30 b(=)f(\(25)23 b(+)f(2)p Fn(\015)5 b Fo(\))p Fn(=)p Fo(\(62)25 b(+)c(5)p Fn(\015)5 b Fo(\),)35 b(whic)m(h)e(is)g(close)h(to)g(2)p Fn(=)p Fo(5;)i(a)e(similar)270 4064 y(shap)s(e)c(is)g(obtained)h(for)f (a)h(rotation)g(n)m(um)m(b)s(er)e(close)j(to)f(1)p Fn(=)p Fo(5.)370 4193 y(In)e([13)q(,)i(14)q(])f(it)h(w)m(as)g(sho)m(wn)f(that) h(there)f(exists)1033 4368 y(\026)-51 b Fn(u)1079 4387 y Fm(p=q)1188 4368 y Fo(\()p Fn(\013;)15 b(")p Fo(\))27 b(=)34 b(lim)1521 4426 y Fm(\021)r Fi(!)p Fh(0)1680 4368 y Fn(u)p Fo(\()p Fn(\013;)15 b Fo(\(2)p Fn(\031)s(\021)s Fo(\))2083 4331 y Fh(2)p Fm(=q)2195 4368 y Fn(";)g(p=q)24 b Fo(+)c Fn(\021)s Fo(\))p Fn(;)642 b Fo(\(2\))270 4570 y(where)29 b(the)h(limit)h(is)f(tak)m(en)h(along)g(an)m(y)f(path)g(in)f (the)h(complex)h Fn(!)i Fo(plane)d(tending)f(to)i Fn(p=q)270 4699 y Fo(non-tangen)m(tially)i(to)e(the)f(real)h(axis.)42 b(In)29 b(particular)i(this)f(implies)809 4874 y Fn(u)p Fo(\()p Fn(\013;)15 b(";)g(p=q)25 b Fo(+)20 b Fn(\021)s Fo(\))26 b(=)31 b(\026)-51 b Fn(u)1581 4893 y Fm(p=q)1690 4874 y Fo(\()p Fn(\013;)15 b Fo(\(2)p 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Z /grstring Z /blstring Z /convroll{64 div 4 -1 roll}bd /setcolorpattern { /graystring xs /blstring xs /grstring xs /rstring xs patfreq patangle { 1 add 4 mul cvi rstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi grstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi blstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi graystring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } setcolorscreen convroll convroll convroll convroll setcmykcolor }bd /:d { pop pop pop /pattransf load settransfer pop pop setcolorpattern }bd /:c /:d ld docolorscreen not endnoload %%EndFile level2 endnoload level2 not startnoload %%BeginFile: lw8_level2_patterns-2.0 /pmtx Z /BGnd Z /FGnd Z /PaintData Z /PatternMtx Z /PatHeight Z /PatWidth Z /$d Z /savecolor 4 array def /savecolorspace Z /patDecode Z /:a{ mark 0 0 0 currentcolor savecolor astore pop cleartomark /savecolorspace currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix makepattern gR }bd /:u { 14 dict begin /$d 8 dict def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PaintData xdf /PatHeight xdf /PatWidth xdf /PatternMtx[PatWidth 0 0 PatHeight 0 0]def $d begin /ImageType 1 def /MultipleDataSource F def /Height PatHeight def /Width PatWidth def /Decode patDecode def /ImageMatrix PatternMtx def /DataSource PaintData def /BitsPerComponent 8 def end /PaintProc { begin $d image end }def currentdict PatternMtx end gS $c setcolorspace pmtx setmatrix makepattern gR }bd /bk[1 1 1]def /fg[0 0 0]def /:b{ :t setpattern pop pop }bd /:d{ :t setpattern 10{pop}repeat }bd /:c{ :u setpattern 10{pop}repeat }bd %%EndFile level2 not endnoload %%BeginFile: lw8_uniform_graphics-2.0 /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /@c { moveto 0 rlineto stroke }bd /@w { moveto 0 exch rlineto stroke }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: lw8_basic_text-2.0 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld /mT[.24 0 0 -.24 10.56 830.179]def initQDpatterns /sD 16 dict def %%IncludeFont: Helvetica /f135/Helvetica :mre /f151 f135 42 scf /Courier findfont[10 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4.5 @i 829.5 1626.5 4 @e 843.5 1848.5 4.5 @i 843.5 1848.5 4 @e 843.5 1561.5 4.5 @i 843.5 1561.5 4 @e 849.5 1829.5 4.5 @i 849.5 1829.5 4 @e 849.5 1579.5 4.5 @i 849.5 1579.5 4 @e 867.5 1884.5 4.5 @i 867.5 1884.5 4 @e 867.5 1524.5 4.5 @i 867.5 1524.5 4 @e 869.5 1834.5 4.5 @i 869.5 1834.5 4 @e 869.5 1574.5 4.5 @i 869.5 1574.5 4 @e 869.5 1811.5 4.5 @i 869.5 1811.5 4 @e 869.5 1597.5 4.5 @i 869.5 1597.5 4 @e 878.5 1914.5 4.5 @i 878.5 1914.5 4 @e 878.5 1494.5 4.5 @i 878.5 1494.5 4 @e 880.5 1830.5 4.5 @i 880.5 1830.5 4 @e 880.5 1578.5 4.5 @i 880.5 1578.5 4 @e 888.5 1828.5 4.5 @i 888.5 1828.5 4 @e 888.5 1580.5 4.5 @i 888.5 1580.5 4 @e 891.5 1937.5 4.5 @i 891.5 1937.5 4 @e 891.5 1471.5 4.5 @i 891.5 1471.5 4 @e 894.5 1826.5 4.5 @i 894.5 1826.5 4 @e 894.5 1582.5 4.5 @i 894.5 1582.5 4 @e 898.5 1824.5 4.5 @i 898.5 1824.5 4 @e 898.5 1584.5 4.5 @i 898.5 1584.5 4 @e 902.5 1823.5 4.5 @i 902.5 1823.5 4 @e 902.5 1585.5 4.5 @i 902.5 1585.5 4 @e 906.5 1822.5 4.5 @i 906.5 1822.5 4 @e 906.5 1586.5 4.5 @i 906.5 1586.5 4 @e 906.5 1961.5 4.5 @i 906.5 1961.5 4 @e 906.5 1447.5 4.5 @i 906.5 1447.5 4 @e 909.5 1821.5 4.5 @i 909.5 1821.5 4 @e 909.5 1587.5 4.5 @i 909.5 1587.5 4 @e 911.5 1820.5 4.5 @i 911.5 1820.5 4 @e 911.5 1588.5 4.5 @i 911.5 1588.5 4 @e 913.5 1819.5 4.5 @i 913.5 1819.5 4 @e 913.5 1589.5 4.5 @i 913.5 1589.5 4 @e 913.5 1950.5 4.5 @i 913.5 1950.5 4 @e 913.5 1458.5 4.5 @i 913.5 1458.5 4 @e 915.5 1819.5 4.5 @i 915.5 1819.5 4 @e 915.5 1590.5 4.5 @i 915.5 1590.5 4 @e 916.5 1818.5 4.5 @i 916.5 1818.5 4 @e 916.5 1590.5 4.5 @i 916.5 1590.5 4 @e 917.5 1818.5 4.5 @i 917.5 1818.5 4 @e 917.5 1591.5 4.5 @i 917.5 1591.5 4 @e 918.5 1817.5 4.5 @i 918.5 1817.5 4 @e 918.5 1591.5 4.5 @i 918.5 1591.5 4 @e 919.5 1817.5 4.5 @i 919.5 1817.5 4 @e 919.5 1591.5 4.5 @i 919.5 1591.5 4 @e 919.5 1817.5 4.5 @i 919.5 1817.5 4 @e 919.5 1591.5 4.5 @i 919.5 1591.5 4 @e 923.5 1980.5 4.5 @i 923.5 1980.5 4 @e 923.5 1429.5 4.5 @i 923.5 1429.5 4 @e 934.5 1974.5 4.5 @i 934.5 1974.5 4 @e 934.5 1434.5 4.5 @i 934.5 1434.5 4 @e 946.5 1997.5 4.5 @i 946.5 1997.5 4 @e 946.5 1411.5 4.5 @i 946.5 1411.5 4 @e 958.5 2104.5 4.5 @i 958.5 2104.5 4 @e 958.5 1304.5 4.5 @i 958.5 1304.5 4 @e 967.5 2011.5 4.5 @i 967.5 2011.5 4 @e 967.5 1397.5 4.5 @i 967.5 1397.5 4 @e 996.5 2025.5 4.5 @i 996.5 2025.5 4 @e 996.5 1383.5 4.5 @i 996.5 1383.5 4 @e 1028.5 2049.5 4.5 @i 1028.5 2049.5 4 @e 1028.5 1359.5 4.5 @i 1028.5 1359.5 4 @e 1041.5 2033.5 4.5 @i 1041.5 2033.5 4 @e 1041.5 1375.5 4.5 @i 1041.5 1375.5 4 @e 1053.5 2026.5 4.5 @i 1053.5 2026.5 4 @e 1053.5 1382.5 4.5 @i 1053.5 1382.5 4 @e 1060.5 2017.5 4.5 @i 1060.5 2017.5 4 @e 1060.5 1391.5 4.5 @i 1060.5 1391.5 4 @e 1064.5 2010.5 4.5 @i 1064.5 2010.5 4 @e 1064.5 1399.5 4.5 @i 1064.5 1399.5 4 @e 1067.5 2004.5 4.5 @i 1067.5 2004.5 4 @e 1067.5 1404.5 4.5 @i 1067.5 1404.5 4 @e 1069.5 1999.5 4.5 @i 1069.5 1999.5 4 @e 1069.5 1409.5 4.5 @i 1069.5 1409.5 4 @e 1071.5 1995.5 4.5 @i 1071.5 1995.5 4 @e 1071.5 1413.5 4.5 @i 1071.5 1413.5 4 @e 1073.5 1992.5 4.5 @i 1073.5 1992.5 4 @e 1073.5 1416.5 4.5 @i 1073.5 1416.5 4 @e 1074.5 1989.5 4.5 @i 1074.5 1989.5 4 @e 1074.5 1419.5 4.5 @i 1074.5 1419.5 4 @e 1075.5 1987.5 4.5 @i 1075.5 1987.5 4 @e 1075.5 1422.5 4.5 @i 1075.5 1422.5 4 @e 1076.5 1985.5 4.5 @i 1076.5 1985.5 4 @e 1076.5 1424.5 4.5 @i 1076.5 1424.5 4 @e 1077.5 1983.5 4.5 @i 1077.5 1983.5 4 @e 1077.5 1425.5 4.5 @i 1077.5 1425.5 4 @e 1077.5 1981.5 4.5 @i 1077.5 1981.5 4 @e 1077.5 1427.5 4.5 @i 1077.5 1427.5 4 @e 1078.5 1980.5 4.5 @i 1078.5 1980.5 4 @e 1078.5 1428.5 4.5 @i 1078.5 1428.5 4 @e 1078.5 1979.5 4.5 @i 1078.5 1979.5 4 @e 1078.5 1429.5 4.5 @i 1078.5 1429.5 4 @e 1078.5 1979.5 4.5 @i 1078.5 1979.5 4 @e 1078.5 1429.5 4.5 @i 1078.5 1429.5 4 @e 1078.5 1978.5 4.5 @i 1078.5 1978.5 4 @e 1078.5 1430.5 4.5 @i 1078.5 1430.5 4 @e 1099.5 2064.5 4.5 @i 1099.5 2064.5 4 @e 1099.5 1344.5 4.5 @i 1099.5 1344.5 4 @e 1125.5 2060.5 4.5 @i 1125.5 2060.5 4 @e 1125.5 1349.5 4.5 @i 1125.5 1349.5 4 @e 1127.5 2074.5 4.5 @i 1127.5 2074.5 4 @e 1127.5 1334.5 4.5 @i 1127.5 1334.5 4 @e 1153.5 2081.5 4.5 @i 1153.5 2081.5 4 @e 1153.5 1327.5 4.5 @i 1153.5 1327.5 4 @e 1180.5 2084.5 4.5 @i 1180.5 2084.5 4 @e 1180.5 1324.5 4.5 @i 1180.5 1324.5 4 @e 1206.5 2084.5 4.5 @i 1206.5 2084.5 4 @e 1206.5 1324.5 4.5 @i 1206.5 1324.5 4 @e 1217.5 2093.5 4.5 @i 1217.5 2093.5 4 @e 1217.5 1315.5 4.5 @i 1217.5 1315.5 4 @e 1231.5 2081.5 4.5 @i 1231.5 2081.5 4 @e 1231.5 1327.5 4.5 @i 1231.5 1327.5 4 @e 1259.5 2075.5 4.5 @i 1259.5 2075.5 4 @e 1259.5 1333.5 4.5 @i 1259.5 1333.5 4 @e 1283.5 2064.5 4.5 @i 1283.5 2064.5 4 @e 1283.5 1344.5 4.5 @i 1283.5 1344.5 4 @e 1307.5 1978.5 4.5 @i 1307.5 1978.5 4 @e 1307.5 1430.5 4.5 @i 1307.5 1430.5 4 @e 1308.5 1979.5 4.5 @i 1308.5 1979.5 4 @e 1308.5 1429.5 4.5 @i 1308.5 1429.5 4 @e 1308.5 1979.5 4.5 @i 1308.5 1979.5 4 @e 1308.5 1429.5 4.5 @i 1308.5 1429.5 4 @e 1308.5 1980.5 4.5 @i 1308.5 1980.5 4 @e 1308.5 1428.5 4.5 @i 1308.5 1428.5 4 @e 1309.5 1981.5 4.5 @i 1309.5 1981.5 4 @e 1309.5 1427.5 4.5 @i 1309.5 1427.5 4 @e 1309.5 1983.5 4.5 @i 1309.5 1983.5 4 @e 1309.5 1425.5 4.5 @i 1309.5 1425.5 4 @e 1310.5 1985.5 4.5 @i 1310.5 1985.5 4 @e 1310.5 1424.5 4.5 @i 1310.5 1424.5 4 @e 1311.5 1987.5 4.5 @i 1311.5 1987.5 4 @e 1311.5 1421.5 4.5 @i 1311.5 1421.5 4 @e 1312.5 1989.5 4.5 @i 1312.5 1989.5 4 @e 1312.5 1419.5 4.5 @i 1312.5 1419.5 4 @e 1313.5 1992.5 4.5 @i 1313.5 1992.5 4 @e 1313.5 1416.5 4.5 @i 1313.5 1416.5 4 @e 1314.5 1996.5 4.5 @i 1314.5 1996.5 4 @e 1314.5 1413.5 4.5 @i 1314.5 1413.5 4 @e 1316.5 2000.5 4.5 @i 1316.5 2000.5 4 @e 1316.5 1408.5 4.5 @i 1316.5 1408.5 4 @e 1318.5 2004.5 4.5 @i 1318.5 2004.5 4 @e 1318.5 1404.5 4.5 @i 1318.5 1404.5 4 @e 1319.5 2010.5 4.5 @i 1319.5 2010.5 4 @e 1319.5 1398.5 4.5 @i 1319.5 1398.5 4 @e 1322.5 2017.5 4.5 @i 1322.5 2017.5 4 @e 1322.5 1391.5 4.5 @i 1322.5 1391.5 4 @e 1326.5 2025.5 4.5 @i 1326.5 2025.5 4 @e 1326.5 1384.5 4.5 @i 1326.5 1384.5 4 @e 1336.5 2036.5 4.5 @i 1336.5 2036.5 4 @e 1336.5 1372.5 4.5 @i 1336.5 1372.5 4 @e 1358.5 2043.5 4.5 @i 1358.5 2043.5 4 @e 1358.5 1366.5 4.5 @i 1358.5 1366.5 4 @e 1384.5 2070.5 4.5 @i 1384.5 2070.5 4 @e 1384.5 1338.5 4.5 @i 1384.5 1338.5 4 @e 1392.5 2024.5 4.5 @i 1392.5 2024.5 4 @e 1392.5 1385.5 4.5 @i 1392.5 1385.5 4 @e 1416.5 2013.5 4.5 @i 1416.5 2013.5 4 @e 1416.5 1396.5 4.5 @i 1416.5 1396.5 4 @e 1441.5 1996.5 4.5 @i 1441.5 1996.5 4 @e 1441.5 1413.5 4.5 @i 1441.5 1413.5 4 @e 1460.5 1978.5 4.5 @i 1460.5 1978.5 4 @e 1460.5 1430.5 4.5 @i 1460.5 1430.5 4 @e 1467.5 1817.5 4.5 @i 1467.5 1817.5 4 @e 1467.5 1591.5 4.5 @i 1467.5 1591.5 4 @e 1467.5 1817.5 4.5 @i 1467.5 1817.5 4 @e 1467.5 1591.5 4.5 @i 1467.5 1591.5 4 @e 1468.5 1817.5 4.5 @i 1468.5 1817.5 4 @e 1468.5 1591.5 4.5 @i 1468.5 1591.5 4 @e 1468.5 1818.5 4.5 @i 1468.5 1818.5 4 @e 1468.5 1590.5 4.5 @i 1468.5 1590.5 4 @e 1470.5 1818.5 4.5 @i 1470.5 1818.5 4 @e 1470.5 1590.5 4.5 @i 1470.5 1590.5 4 @e 1471.5 1819.5 4.5 @i 1471.5 1819.5 4 @e 1471.5 1589.5 4.5 @i 1471.5 1589.5 4 @e 1473.5 1820.5 4.5 @i 1473.5 1820.5 4 @e 1473.5 1589.5 4.5 @i 1473.5 1589.5 4 @e 1475.5 1821.5 4.5 @i 1475.5 1821.5 4 @e 1475.5 1588.5 4.5 @i 1475.5 1588.5 4 @e 1476.5 1982.5 4.5 @i 1476.5 1982.5 4 @e 1476.5 1426.5 4.5 @i 1476.5 1426.5 4 @e 1477.5 1821.5 4.5 @i 1477.5 1821.5 4 @e 1477.5 1587.5 4.5 @i 1477.5 1587.5 4 @e 1479.5 1958.5 4.5 @i 1479.5 1958.5 4 @e 1479.5 1450.5 4.5 @i 1479.5 1450.5 4 @e 1480.5 1823.5 4.5 @i 1480.5 1823.5 4 @e 1480.5 1586.5 4.5 @i 1480.5 1586.5 4 @e 1484.5 1824.5 4.5 @i 1484.5 1824.5 4 @e 1484.5 1584.5 4.5 @i 1484.5 1584.5 4 @e 1488.5 1826.5 4.5 @i 1488.5 1826.5 4 @e 1488.5 1582.5 4.5 @i 1488.5 1582.5 4 @e 1492.5 1828.5 4.5 @i 1492.5 1828.5 4 @e 1492.5 1580.5 4.5 @i 1492.5 1580.5 4 @e 1494.5 1938.5 4.5 @i 1494.5 1938.5 4 @e 1494.5 1470.5 4.5 @i 1494.5 1470.5 4 @e 1498.5 1831.5 4.5 @i 1498.5 1831.5 4 @e 1498.5 1577.5 4.5 @i 1498.5 1577.5 4 @e 1506.5 1835.5 4.5 @i 1506.5 1835.5 4 @e 1506.5 1574.5 4.5 @i 1506.5 1574.5 4 @e 1509.5 1911.5 4.5 @i 1509.5 1911.5 4 @e 1509.5 1497.5 4.5 @i 1509.5 1497.5 4 @e 1515.5 1840.5 4.5 @i 1515.5 1840.5 4 @e 1515.5 1568.5 4.5 @i 1515.5 1568.5 4 @e 1516.5 1884.5 4.5 @i 1516.5 1884.5 4 @e 1516.5 1524.5 4.5 @i 1516.5 1524.5 4 @e 1528.5 1850.5 4.5 @i 1528.5 1850.5 4 @e 1528.5 1558.5 4.5 @i 1528.5 1558.5 4 @e 1542.5 1806.5 4.5 @i 1542.5 1806.5 4 @e 1542.5 1602.5 4.5 @i 1542.5 1602.5 4 @e 1549.5 1880.5 4.5 @i 1549.5 1880.5 4 @e 1549.5 1528.5 4.5 @i 1549.5 1528.5 4 @e 1556.5 1780.5 4.5 @i 1556.5 1780.5 4 @e 1556.5 1629.5 4.5 @i 1556.5 1629.5 4 @e 1564.5 1756.5 4.5 @i 1564.5 1756.5 4 @e 1564.5 1652.5 4.5 @i 1564.5 1652.5 4 @e 1568.5 1729.5 4.5 @i 1568.5 1729.5 4 @e 1568.5 1679.5 4.5 @i 1568.5 1679.5 4 @e 1570.5 1704.5 4.5 @i 1570.5 1704.5 4 @e 1593.5 2012.5 4.5 @i 1593.5 2012.5 4 @e 1593.5 1396.5 4.5 @i 1593.5 1396.5 4 @e 1608.5 1704.5 4.5 @i 1608.5 1704.5 4 @e 630 2169 :M f151 sf 1.336(-0.8)A 630 2056 :M 1.336(-0.6)A 630 1944 :M 1.336(-0.4)A 630 1831 :M 1.336(-0.2)A 680 1718 :M (0)S 642 1606 :M 3.748(0.2)A 642 1493 :M 3.748(0.4)A 642 1381 :M 3.748(0.6)A 642 1268 :M 3.748(0.8)A 706 2234 :M 1.336(-0.8)A 818 2234 :M 1.336(-0.6)A 931 2234 :M 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currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix makepattern gR }bd /:u { 14 dict begin /$d 8 dict def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PaintData xdf /PatHeight xdf /PatWidth xdf /PatternMtx[PatWidth 0 0 PatHeight 0 0]def $d begin /ImageType 1 def /MultipleDataSource F def /Height PatHeight def /Width PatWidth def /Decode patDecode def /ImageMatrix PatternMtx def /DataSource PaintData def /BitsPerComponent 8 def end /PaintProc { begin $d image end }def currentdict PatternMtx end gS $c setcolorspace pmtx setmatrix makepattern gR }bd /bk[1 1 1]def /fg[0 0 0]def /:b{ :t setpattern pop pop }bd /:d{ :t setpattern 10{pop}repeat }bd /:c{ :u setpattern 10{pop}repeat }bd %%EndFile level2 not endnoload %%BeginFile: lw8_uniform_graphics-2.0 /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /@c { moveto 0 rlineto stroke }bd /@w { moveto 0 exch rlineto stroke }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: lw8_basic_text-2.0 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe 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endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld /mT[.24 0 0 -.24 10.56 830.179]def initQDpatterns /sD 16 dict def %%IncludeFont: Helvetica /f135/Helvetica :mre /f151 f135 42 scf /Courier findfont[10 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y([2)p Fn(;)15 b Fo(2)p Fn(;)g Fo(12)p Fn(;)g Fo(1)1059 4933 y Fi(1)1137 4966 y Fo(],)31 b Fn(\013)26 b Fo(=)f(1.)41 b(Greene's)31 b(metho)s(d)f(giv)m(es)i Fn(")2475 4980 y Fm(c)2510 4966 y Fo(\()p Fn(!)s Fo(\))25 b(=)g(0)p Fn(:)p Fo(8160.)p eop %%Page: 7 7 7 6 bop 1188 66 a Fh(SHAPE)31 b(OF)f(ANAL)-6 b(YTICITY)31 b(DOMAINS)883 b(7)569 246 y Fd(T)-8 b(able)30 b(1.)45 b Fo(Radius)27 b(of)f(con)m(v)m(ergence)j(for)e(some)g(v)-5 b(alues)27 b(of)g(the)g(rotation)569 375 y(n)m(um)m(b)s(er)h Fn(!)s Fo(:)40 b Fn(\032)1071 389 y Fh(1)1111 375 y Fo(\()p Fn(!)s Fo(\))30 b(is)g(the)g(v)-5 b(alue)30 b(giv)m(en)h(b)m(y)e(form)m (ula)h(\(4\))q(,)g(while)g Fn(\032)2902 389 y Fm(P)2961 375 y Fo(\()p Fn(!)s Fo(\))569 505 y(is)g(the)h(v)-5 b(alue)31 b(obtained)f(n)m(umerically)i(b)m(y)e(using)g(P)m(ad)m(\023) -43 b(e)32 b(appro)m(ximan)m(ts.)p 919 634 1822 4 v 961 783 a Fn(!)499 b(p=q)179 b(C)1893 802 y Fm(p=q)2163 783 y Fn(\032)2210 797 y Fh(1)2250 783 y Fo(\()p Fn(!)s Fo(\))83 b Fn(\032)2510 797 y Fm(P)2569 783 y Fo(\()p Fn(!)s Fo(\))p 919 864 V 961 1013 a([2)p Fn(;)15 b Fo(10)p Fn(;)g Fo(1)1246 980 y Fi(1)1323 1013 y Fo(])169 b(1/2)85 b(0.125000)h(0.514)95 b(0.510)961 1195 y([3)p Fn(;)15 b Fo(12)p Fn(;)g Fo(1)1246 1162 y Fi(1)1323 1195 y Fo(])169 b(1/3)85 b(0.041667)h(0.557)95 b(0.555)961 1376 y([4)p Fn(;)15 b Fo(15)p Fn(;)g Fo(1)1246 1343 y Fi(1)1323 1376 y Fo(])169 b(1/4)85 b(0.026042)h(0.528)95 b(0.526)961 1557 y([10)1076 1524 y Fi(1)1151 1557 y Fo(])341 b(0/1)85 b(1.000000)h(0.320)95 b(0.313)961 1739 y([10)p Fn(;)15 b Fo(1)1161 1706 y Fi(1)1237 1739 y Fo(])255 b(0/1)85 b(1.000000)h(0.290)95 b(0.284)961 1920 y([2)p Fn(;)15 b Fo(2)p Fn(;)g Fo(12)p Fn(;)g Fo(1)1331 1887 y Fi(1)1409 1920 y Fo(])83 b(2/5)i(0.008713)h(0.707)95 b(0.704)p 919 1978 V 270 2204 a(with)34 b(the)g(limit)h(sup)s(erior)e ([8],)j(so)e(that)h(\(3\))g(can)f(b)s(e)f(written)i(also)g(for)e(the)i (v)-5 b(alues)34 b(of)g Fn(!)270 2334 y Fo(w)m(e)d(are)g(considering,)f (then)g(w)m(e)h(obtain)g(that)g Fn(\032)p Fo(\()p Fn(!)s Fo(\))g(can)g(b)s(e)e(appro)m(ximated)i(as)1313 2538 y Fn(\032)p Fo(\()p Fn(!)s Fo(\))26 b Fk(\031)f Fn(\021)1660 2500 y Fh(2)p Fm(=q)1784 2437 y Fj(\020)1838 2538 y Fn(q)s(C)1954 2500 y Fi(\000)p Fh(1)1947 2571 y Fm(p=q)2056 2538 y Fn(\025)2109 2552 y Fm(c)2144 2437 y Fj(\021)2198 2460 y Fh(1)p Fm(=q)2322 2538 y Fn(;)927 b Fo(\(4\))270 2727 y(where)24 b Fn(C)592 2745 y Fm(p=q)725 2727 y Fo(is)g(the)h(same)g (constan)m(t)g(as)g(de\014ned)e(in)h([14)q(],)i(and)e Fn(\025)2472 2741 y Fm(c)2532 2727 y Fk(\031)h Fo(4)p Fn(\031)2728 2694 y Fh(2)2776 2727 y Fk(\001)8 b Fo(0)p Fn(:)p Fo(828)28 b Fk(\031)c Fo(32)p Fn(:)p Fo(669)270 2856 y(\(see)31 b([13)q(]\).)370 2986 y(Then)43 b(for)h(the)h(radius)f (of)g(con)m(v)m(ergence)j Fn(\032)p Fo(\()p Fn(!)s Fo(\),)i(b)m(y)c (comparing)f(the)h(v)-5 b(alues)45 b Fn(\032)3220 3000 y Fh(1)3259 2986 y Fo(\()p Fn(!)s Fo(\))270 3115 y(obtained)30 b(through)g(form)m(ula)g(\(4\))i(and)d(the)h(v)-5 b(alues)31 b Fn(\032)2117 3129 y Fm(P)2176 3115 y Fo(\()p Fn(!)s Fo(\))f(obtained)h(b)m(y)f(P)m(ad)m(\023)-43 b(e)31 b(appro)m(xi-)270 3245 y(man)m(ts,)g(w)m(e)g(\014nd)e(the)h(results)g(listed)h(in)f (table)i(1.)370 3374 y(In)h(all)i(cases)g Fn(\032)p Fo(\()p Fn(!)s Fo(\))d Fn(<)f(")1202 3388 y Fh(c)1238 3374 y Fo(\()p Fn(!)s Fo(\))k(strictly;)i(furthermore)c(the)h(discrepancy)g(b) s(et)m(w)m(een)h(the)270 3504 y(t)m(w)m(o)k(v)-5 b(alues)37 b(increases)h(as)g Fn(!)i Fo(gets)e(close)h(to)f Fn(p=q)s Fo(.)61 b(In)36 b(a)i(forthcoming)g(publication)f(w)m(e)270 3633 y(shall)g(turn)e(this)i(remark)f(in)m(to)i(a)f(quan)m(titativ)m(e) i(statemen)m(t)f(and)e(compare)h(the)g(results)270 3763 y(from)30 b(P)m(ad)m(\023)-43 b(e)32 b(appro)m(ximan)m(ts)f(and)f(from) g(Greene's)h(metho)s(d)e(for)i Fn(")2554 3777 y Fh(c)2589 3763 y Fo(\()p Fn(!)s Fo(\).)370 3892 y(A)42 b(few)h(w)m(ords)f(are)h (necessary)g(to)h(explain)f(what)g(w)m(e)g(mean)g(b)m(y)f(\\close":)68 b(strictly)270 4022 y(sp)s(eaking,)24 b(in)d(fact,)k(an)c(irrational)i (n)m(um)m(b)s(er)e(is)g(close)i(to)g(in\014nitely)f(man)m(y)f(rational) i(v)-5 b(alues.)270 4151 y(F)d(or)33 b(example,)g([2)p Fn(;)15 b Fo(10)p Fn(;)g Fo(1)1103 4118 y Fi(1)1181 4151 y Fo(])32 b(is)h(close)g(to)g(1)p Fn(=)p Fo(2)h(b)s(ecause)e(its)g(con) m(tin)m(ued)h(fraction)g(starts)g(as)270 4281 y(the)f(expansion)g(of)h (1)p Fn(=)p Fo(2)c(=)f([2])33 b(and)f(then)g(is)g(follo)m(w)m(ed)i(b)m (y)e(a)h(larger)f(in)m(teger)i(\(10,)g(in)e(this)270 4410 y(case\);)f(the)d(next)g(b)s(est)g(appro)m(ximan)m(t)h(of)f([2)p Fn(;)15 b Fo(10)p Fn(;)g Fo(1)1988 4377 y Fi(1)2066 4410 y Fo(])28 b(is)g([2)p Fn(;)15 b Fo(10])28 b(=)d(10)p Fn(=)p Fo(21,)31 b(but)c([2)p Fn(;)15 b Fo(10)p Fn(;)g Fo(1)3287 4377 y Fi(1)3365 4410 y Fo(])270 4540 y(is)25 b Fg(not)35 b Fo(close)26 b(to)g(10)p Fn(=)p Fo(21)i(as)d(the)g(follo)m (wing)i(partial)f(quotien)m(t)h(in)d(its)i(con)m(tin)m(ued)g(fraction)g (is)270 4669 y(a)e(small)h(in)m(teger)g(\(1,)i(in)c(this)h(case\).)40 b(Instead,)26 b(consider)e Fn(!)2275 4683 y Fh(1)2339 4669 y Fo(=)h([10)p Fn(;)15 b Fo(1)2635 4636 y Fi(1)2712 4669 y Fo(])24 b(and)f Fn(!)2988 4683 y Fh(2)3053 4669 y Fo(=)i([10)3264 4636 y Fi(1)3339 4669 y Fo(];)270 4799 y(the)e(sequence)h(of)f(rational)h(appro)m(ximan)m(ts)f(obtained)h(b)m (y)f(truncation)g(of)g(their)g(con)m(tin)m(ued)270 4928 y(fractions)31 b(is)g(0)p Fn(=)p Fo(1,)i(1)p Fn(=)p Fo(10,)f(1)p Fn(=)p Fo(11,)h(.)16 b(.)f(.)g(for)31 b Fn(!)1720 4942 y Fh(1)1759 4928 y Fo(,)g(and)f(0)p Fn(=)p Fo(1,)j(1)p Fn(=)p Fo(10,)f(10)p Fn(=)p Fo(101,)i(.)16 b(.)f(.)g(for)31 b Fn(!)3069 4942 y Fh(2)3108 4928 y Fo(:)41 b(so)31 b(w)m(e)270 5058 y(can)j(sa)m(y)g(that)g(b)s(oth)f(are)h(close)h(to)f(0,)h(but)e Fn(!)1840 5072 y Fh(2)1912 5058 y Fo(is)h(also)g(close)h(to)g(1)p Fn(=)p Fo(10,)h(while)d Fn(!)3066 5072 y Fh(1)3139 5058 y Fo(is)g(not.)270 5187 y(It)45 b(follo)m(ws)g(that)g(the)g(natural)f (b)s(oundary)e(corresp)s(onding)i(to)h(the)f(rotation)i(n)m(um)m(b)s (er)p eop %%Page: 8 8 8 7 bop 390 66 a Fh(8)330 b(ALBER)-6 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lw8_basic-2.3 %%Copyright: Copyright 1990-1997 Adobe Systems Incorporated and Apple Computer Incorporated. All Rights Reserved. /bd{bind def}bind def /xdf{exch def}bd /xs{exch store}bd /ld{load def}bd /Z{0 def}bd /T/true /F/false /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 14{ld}repeat /framewidth -1 def /QDframwid -1 def /numframes Z /mTS matrix def /$m matrix def /av 85 def /por T def /normland F def /psb-nosave{}def /pse-nosave{}def /us Z /psb{/us save store}bd /pse{us restore}bd /level2 /languagelevel where { pop languagelevel 2 ge }{ F }ifelse def /level3 /languagelevel where { pop languagelevel 3 ge }{ F }ifelse def /odictstk Z /oopstk Z /fcl { count oopstk sub dup 0 gt { {pop}repeat }{ pop }ifelse countdictstack odictstk sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /sfcl2 { /odictstk countdictstack store count/oopstk xs }bd /efcl2 { stopped{$error/newerror F put}if fcl }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /setcopies { userdict/#copies 3 -1 roll put }bd /devg/DeviceGray def /devr/DeviceRGB def /devc/DeviceCMYK def /ststpgdev{}def /dopgdev{}def /stpgdev{}def /buf Z /didstop T def /sfcl { /didstop T store /odictstk countdictstack store count/oopstk xs currentfile cvx stopped { $error/newerror F put didstop { save/didstop xs /buf vmstatus exch sub exch pop dup 0 lt{pop 0}if dup 64000 gt{pop 64000}if string store { currentfile buf readline { (}efcl)eq{exit}if }{ /UnexpectedEOF errordict/rangecheck get exec }ifelse }loop didstop restore }if }if fcl }bd /efcl { /didstop F store exec stop }bd level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /setcopies { 1 dict begin/NumCopies xdf currentdict end setpagedevice }bd /devg[/DeviceGray]def /devr[/DeviceRGB]def /devc[/DeviceCMYK]def /setpagedevice where{pop/realstpgdev/setpagedevice ld}if /SC_topddict Z /SC_spdict Z /dopgdev { md/setpagedevice undef SC_topddict realstpgdev }bd /stpgdev { SC_topddict dup 3 -1 roll { SC_spdict 2 index known { SC_spdict 2 index get dup 3 -1 roll { put dup }forall pop put dup }{ put dup }ifelse }forall pop pop }bd /ststpgdev { md/setpagedevice/stpgdev load put /SC_topddict 0 dict store /SC_spdict 3 dict begin /InputAttributes 0 dict def /Policies 0 dict def /OutputAttributes 0 dict def currentdict end store }def /sfcl/sfcl2 ld /efcl/efcl2 ld level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { mT $m currentmatrix mTS concatmatrix pop /pm save store mT concat }bd /endp { pm restore }bd /adjRect { dup 2 mul 6 2 roll 4 index sub exch 5 -1 roll sub exch 4 2 roll 4 index add exch 5 -1 roll add exch 4 2 roll }bd /frame1up { gS mTS setmatrix QDframwid lw /setstrokeadjust where{pop T setstrokeadjust}if clippath pathbbox 2 index sub exch 3 index sub exch currentlinewidth framewidth mul adjRect numframes dup 0 lt{pop 0}if { 4 copy rS currentlinewidth framewidth mul 4 mul adjRect }repeat pop pop pop pop gR }bd /$c devr def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile level3 startnoload %%BeginFile: lw8_safeclipL12-1.0 /rectclip where { pop/rCa/rectclip ld }{ /rCa { np 0 1 index length 4 idiv { 2 copy 4 getinterval aload pop 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K 4 add }repeat clip np pop pop }bd }ifelse /savedstack Z /subsavedstack Z /execstring Z /saferCa { /execstring xs /odictstk countdictstack store /oopstk 0 store count 0 ne { savedstack 0 eq{ count 100 gt{count}{100}ifelse array/savedstack xs }{ count savedstack length gt { count array/savedstack xs }if }ifelse count savedstack 0 3 -1 roll getinterval astore/subsavedstack xs }{ /subsavedstack 0 store }ifelse execstring cvx stopped { $error/newerror F put newpath }if fcl subsavedstack 0 ne{ subsavedstack aload pop }if }bd %%EndFile level3 endnoload level3 not startnoload %%BeginFile: lw8_safeclipL3-1.0 /saferCa/pop ld %%EndFile level3 not endnoload %%BeginFile: lw8_level1_colorspace-2.0 /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /$cs Z /:rg{devr :ss}bd /:sc{$cs :ss}bd /:dc { dup type/arraytype eq{0 get}if dup/DeviceCMYK eq { pop devc }{ /DeviceGray eq { devg }{ devr }ifelse }ifelse /$cs xdf }bd /:sgl{}def /:dr{}bd /:fCRD{pop}bd /:ckcs{}bd /:ss{/$c xdf}bd %%EndFile level2 startnoload %%BeginFile: lw8_level1_patterns-2.0 /patfreq Z /patangle Z /bk Z /fg Z /docolorscreen Z /graystring Z /pattransf{}def /initQDpatterns { /patfreq 9.375 store /patangle 1 0 $m defaultmatrix dtransform exch atan por not {90 add}if normland{180 add}if store :a }def /docolorscreen /setcolorscreen where { pop/currentcolorscreen where { pop/setcmykcolor where { pop T }{ F }ifelse }{ F }ifelse }{ F }ifelse def /setgraypattern { /graystring xs patfreq patangle { 1 add 4 mul cvi graystring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and }setscreen 64 div setgray }bd /:b { /pattransf load settransfer pop pop pop setgraypattern }bd docolorscreen startnoload /screensave 5 array def /:a{currentgray currentscreen currenttransfer screensave astore pop}bd /:e{screensave aload pop settransfer setscreen setgray}bd /:d { pop pop pop /pattransf load settransfer setgraypattern 8{pop}repeat }bd /:c /:d ld docolorscreen endnoload docolorscreen not startnoload /screensave 20 array def /:a{currentcmykcolor currentcolorscreen currentcolortransfer screensave astore pop}bd /:e{screensave aload pop setcolortransfer setcolorscreen setcmykcolor}bd /rstring Z /grstring Z /blstring Z /convroll{64 div 4 -1 roll}bd /setcolorpattern { /graystring xs /blstring xs /grstring xs /rstring xs patfreq patangle { 1 add 4 mul cvi rstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi grstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi blstring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } patfreq patangle { 1 add 4 mul cvi graystring exch get exch 1 add 4 mul cvi 7 sub bitshift 1 and } setcolorscreen convroll convroll convroll convroll setcmykcolor }bd /:d { pop pop pop /pattransf load settransfer pop pop setcolorpattern }bd /:c /:d ld docolorscreen not endnoload %%EndFile level2 endnoload level2 not startnoload %%BeginFile: lw8_level2_patterns-2.0 /pmtx Z /BGnd Z /FGnd Z /PaintData Z /PatternMtx Z /PatHeight Z /PatWidth Z /$d Z /savecolor 4 array def /savecolorspace Z /patDecode Z /:a{ mark 0 0 0 currentcolor savecolor astore pop cleartomark /savecolorspace currentcolorspace store $c setcolorspace /patDecode [currentcolor counttomark dup 2 add 1 roll cleartomark[exch {0 1}repeat] def }bd /:e{ savecolorspace setcolorspace mark savecolor aload pop setcolor cleartomark }bd /initQDpatterns { gS initmatrix mT dup 4 get exch 5 get :T 1 0 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt 0 1 dtransform round exch round exch idtransform dup mul exch dup mul exch add sqrt neg scale 0 por not{90 add}if normland{180 add}if rotate matrix currentmatrix gR /pmtx xs :a }bd /:t { 14 dict begin /BGnd xdf /FGnd xdf /PaintData xdf /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PatternMtx[24 0 0 24 0 0]def /PaintProc BGnd null ne { { begin BGnd aload pop :F 0 0 1 1 rF FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }{ { begin FGnd aload pop :F 24 24 T PatternMtx PaintData imagemask end } }ifelse def currentdict PatternMtx end $c setcolorspace gS pmtx setmatrix makepattern gR }bd /:u { 14 dict begin /$d 8 dict def /PatternType 1 def /PaintType 1 def /BBox[0 0 1 1]def /TilingType 1 def /XStep 1 def /YStep 1 def /PaintData xdf /PatHeight xdf /PatWidth xdf /PatternMtx[PatWidth 0 0 PatHeight 0 0]def $d begin /ImageType 1 def /MultipleDataSource F def /Height PatHeight def /Width PatWidth def /Decode patDecode def /ImageMatrix PatternMtx def /DataSource PaintData def /BitsPerComponent 8 def end /PaintProc { begin $d image end }def currentdict PatternMtx end gS $c setcolorspace pmtx setmatrix makepattern gR }bd /bk[1 1 1]def /fg[0 0 0]def /:b{ :t setpattern pop pop }bd /:d{ :t setpattern 10{pop}repeat }bd /:c{ :u setpattern 10{pop}repeat }bd %%EndFile level2 not endnoload %%BeginFile: lw8_uniform_graphics-2.0 /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /@c { moveto 0 rlineto stroke }bd /@w { moveto 0 exch rlineto stroke }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: lw8_basic_text-2.0 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld /mT[.24 0 0 -.24 10.56 830.179]def initQDpatterns /sD 16 dict def %%IncludeFont: Helvetica /f135/Helvetica :mre /f151 f135 42 scf /Courier findfont[10 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780.5 2142 @w 13 818.5 2142 @w 13 855.5 2142 @w 13 930.5 2142 @w 13 968.5 2142 @w 13 1005.5 2142 @w 13 1080.5 2142 @w 13 1118.5 2142 @w 13 1155.5 2142 @w 13 1230.5 2142 @w 13 1268.5 2142 @w 13 1306.5 2142 @w 13 1380.5 2142 @w 13 1418.5 2142 @w 13 1456.5 2142 @w 13 1530.5 2142 @w 13 1568.5 2142 @w 13 1606.5 2142 @w 26 743.5 1254 @w 26 893.5 1254 @w 26 1043.5 1254 @w 26 1193.5 1254 @w 26 1343.5 1254 @w 26 1493.5 1254 @w 26 1643.5 1254 @w 13 780.5 1254 @w 13 818.5 1254 @w 13 855.5 1254 @w 13 930.5 1254 @w 13 968.5 1254 @w 13 1005.5 1254 @w 13 1080.5 1254 @w 13 1118.5 1254 @w 13 1155.5 1254 @w 13 1230.5 1254 @w 13 1268.5 1254 @w 13 1306.5 1254 @w 13 1380.5 1254 @w 13 1418.5 1254 @w 13 1456.5 1254 @w 13 1530.5 1254 @w 13 1568.5 1254 @w 13 1606.5 1254 @w 901 743.5 1254 @w 901 1643.5 1254 @w 901 743 2154.5 @c 901 743 1254.5 @c 0 G 852.5 1707.5 4.5 @i 852.5 1707.5 4 @e 852.5 1701.5 4.5 @i 852.5 1701.5 4 @e 855.5 1724.5 4.5 @i 855.5 1724.5 4 @e 855.5 1684.5 4.5 @i 855.5 1684.5 4 @e 855.5 1761.5 4.5 @i 855.5 1761.5 4 @e 855.5 1647.5 4.5 @i 855.5 1647.5 4 @e 860.5 1739.5 4.5 @i 860.5 1739.5 4 @e 860.5 1669.5 4.5 @i 860.5 1669.5 4 @e 867.5 1749.5 4.5 @i 867.5 1749.5 4 @e 867.5 1659.5 4.5 @i 867.5 1659.5 4 @e 867.5 1766.5 4.5 @i 867.5 1766.5 4 @e 867.5 1642.5 4.5 @i 867.5 1642.5 4 @e 869.5 1791.5 4.5 @i 869.5 1791.5 4 @e 869.5 1617.5 4.5 @i 869.5 1617.5 4 @e 869.5 1777.5 4.5 @i 869.5 1777.5 4 @e 869.5 1632.5 4.5 @i 869.5 1632.5 4 @e 870.5 1802.5 4.5 @i 870.5 1802.5 4 @e 870.5 1606.5 4.5 @i 870.5 1606.5 4 @e 871.5 1763.5 4.5 @i 871.5 1763.5 4 @e 871.5 1645.5 4.5 @i 871.5 1645.5 4 @e 875.5 1816.5 4.5 @i 875.5 1816.5 4 @e 875.5 1592.5 4.5 @i 875.5 1592.5 4 @e 881.5 1829.5 4.5 @i 881.5 1829.5 4 @e 881.5 1579.5 4.5 @i 881.5 1579.5 4 @e 888.5 1842.5 4.5 @i 888.5 1842.5 4 @e 888.5 1566.5 4.5 @i 888.5 1566.5 4 @e 888.5 1896.5 4.5 @i 888.5 1896.5 4 @e 888.5 1512.5 4.5 @i 888.5 1512.5 4 @e 896.5 1851.5 4.5 @i 896.5 1851.5 4 @e 896.5 1558.5 4.5 @i 896.5 1558.5 4 @e 907.5 1860.5 4.5 @i 907.5 1860.5 4 @e 907.5 1549.5 4.5 @i 907.5 1549.5 4 @e 909.5 1869.5 4.5 @i 909.5 1869.5 4 @e 909.5 1539.5 4.5 @i 909.5 1539.5 4 @e 918.5 1869.5 4.5 @i 918.5 1869.5 4 @e 918.5 1539.5 4.5 @i 918.5 1539.5 4 @e 920.5 1882.5 4.5 @i 920.5 1882.5 4 @e 920.5 1526.5 4.5 @i 920.5 1526.5 4 @e 926.5 1894.5 4.5 @i 926.5 1894.5 4 @e 926.5 1514.5 4.5 @i 926.5 1514.5 4 @e 932.5 1904.5 4.5 @i 932.5 1904.5 4 @e 932.5 1505.5 4.5 @i 932.5 1505.5 4 @e 942.5 1915.5 4.5 @i 942.5 1915.5 4 @e 942.5 1493.5 4.5 @i 942.5 1493.5 4 @e 951.5 1922.5 4.5 @i 951.5 1922.5 4 @e 951.5 1486.5 4.5 @i 951.5 1486.5 4 @e 963.5 1931.5 4.5 @i 963.5 1931.5 4 @e 963.5 1478.5 4.5 @i 963.5 1478.5 4 @e 975.5 1936.5 4.5 @i 975.5 1936.5 4 @e 975.5 1472.5 4.5 @i 975.5 1472.5 4 @e 987.5 1940.5 4.5 @i 987.5 1940.5 4 @e 987.5 1469.5 4.5 @i 987.5 1469.5 4 @e 992.5 1954.5 4.5 @i 992.5 1954.5 4 @e 992.5 1454.5 4.5 @i 992.5 1454.5 4 @e 999.5 1946.5 4.5 @i 999.5 1946.5 4 @e 999.5 1462.5 4.5 @i 999.5 1462.5 4 @e 1000.5 1943.5 4.5 @i 1000.5 1943.5 4 @e 1000.5 1465.5 4.5 @i 1000.5 1465.5 4 @e 1007.5 1953.5 4.5 @i 1007.5 1953.5 4 @e 1007.5 1455.5 4.5 @i 1007.5 1455.5 4 @e 1017.5 1961.5 4.5 @i 1017.5 1961.5 4 @e 1017.5 1447.5 4.5 @i 1017.5 1447.5 4 @e 1025.5 1966.5 4.5 @i 1025.5 1966.5 4 @e 1025.5 1443.5 4.5 @i 1025.5 1443.5 4 @e 1038.5 1971.5 4.5 @i 1038.5 1971.5 4 @e 1038.5 1437.5 4.5 @i 1038.5 1437.5 4 @e 1049.5 1974.5 4.5 @i 1049.5 1974.5 4 @e 1049.5 1434.5 4.5 @i 1049.5 1434.5 4 @e 1062.5 1977.5 4.5 @i 1062.5 1977.5 4 @e 1062.5 1431.5 4.5 @i 1062.5 1431.5 4 @e 1072.5 1976.5 4.5 @i 1072.5 1976.5 4 @e 1072.5 1432.5 4.5 @i 1072.5 1432.5 4 @e 1083.5 2130.5 4.5 @i 1083.5 2130.5 4 @e 1083.5 1278.5 4.5 @i 1083.5 1278.5 4 @e 1085.5 1975.5 4.5 @i 1085.5 1975.5 4 @e 1085.5 1434.5 4.5 @i 1085.5 1434.5 4 @e 1089.5 1976.5 4.5 @i 1089.5 1976.5 4 @e 1089.5 1433.5 4.5 @i 1089.5 1433.5 4 @e 1095.5 1972.5 4.5 @i 1095.5 1972.5 4 @e 1095.5 1436.5 4.5 @i 1095.5 1436.5 4 @e 1098.5 1989.5 4.5 @i 1098.5 1989.5 4 @e 1098.5 1419.5 4.5 @i 1098.5 1419.5 4 @e 1103.5 1973.5 4.5 @i 1103.5 1973.5 4 @e 1103.5 1435.5 4.5 @i 1103.5 1435.5 4 @e 1111.5 1976.5 4.5 @i 1111.5 1976.5 4 @e 1111.5 1432.5 4.5 @i 1111.5 1432.5 4 @e 1126.5 1977.5 4.5 @i 1126.5 1977.5 4 @e 1126.5 1431.5 4.5 @i 1126.5 1431.5 4 @e 1137.5 1970.5 4.5 @i 1137.5 1970.5 4 @e 1137.5 1438.5 4.5 @i 1137.5 1438.5 4 @e 1138.5 1986.5 4.5 @i 1138.5 1986.5 4 @e 1138.5 1422.5 4.5 @i 1138.5 1422.5 4 @e 1148.5 1972.5 4.5 @i 1148.5 1972.5 4 @e 1148.5 1437.5 4.5 @i 1148.5 1437.5 4 @e 1161.5 1966.5 4.5 @i 1161.5 1966.5 4 @e 1161.5 1442.5 4.5 @i 1161.5 1442.5 4 @e 1167.5 1970.5 4.5 @i 1167.5 1970.5 4 @e 1167.5 1438.5 4.5 @i 1167.5 1438.5 4 @e 1169.5 1960.5 4.5 @i 1169.5 1960.5 4 @e 1169.5 1449.5 4.5 @i 1169.5 1449.5 4 @e 1173.5 1963.5 4.5 @i 1173.5 1963.5 4 @e 1173.5 1445.5 4.5 @i 1173.5 1445.5 4 @e 1178.5 1958.5 4.5 @i 1178.5 1958.5 4 @e 1178.5 1450.5 4.5 @i 1178.5 1450.5 4 @e 1184.5 1960.5 4.5 @i 1184.5 1960.5 4 @e 1184.5 1448.5 4.5 @i 1184.5 1448.5 4 @e 1187.5 1975.5 4.5 @i 1187.5 1975.5 4 @e 1187.5 1433.5 4.5 @i 1187.5 1433.5 4 @e 1193.5 1939.5 4.5 @i 1193.5 1939.5 4 @e 1193.5 1469.5 4.5 @i 1193.5 1469.5 4 @e 1193.5 1940.5 4.5 @i 1193.5 1940.5 4 @e 1193.5 1468.5 4.5 @i 1193.5 1468.5 4 @e 1193.5 1941.5 4.5 @i 1193.5 1941.5 4 @e 1193.5 1467.5 4.5 @i 1193.5 1467.5 4 @e 1193.5 1942.5 4.5 @i 1193.5 1942.5 4 @e 1193.5 1466.5 4.5 @i 1193.5 1466.5 4 @e 1193.5 1944.5 4.5 @i 1193.5 1944.5 4 @e 1193.5 1464.5 4.5 @i 1193.5 1464.5 4 @e 1193.5 1946.5 4.5 @i 1193.5 1946.5 4 @e 1193.5 1463.5 4.5 @i 1193.5 1463.5 4 @e 1193.5 1948.5 4.5 @i 1193.5 1948.5 4 @e 1193.5 1460.5 4.5 @i 1193.5 1460.5 4 @e 1194.5 1951.5 4.5 @i 1194.5 1951.5 4 @e 1194.5 1457.5 4.5 @i 1194.5 1457.5 4 @e 1194.5 1957.5 4.5 @i 1194.5 1957.5 4 @e 1194.5 1451.5 4.5 @i 1194.5 1451.5 4 @e 1206.5 1960.5 4.5 @i 1206.5 1960.5 4 @e 1206.5 1448.5 4.5 @i 1206.5 1448.5 4 @e 1215.5 1958.5 4.5 @i 1215.5 1958.5 4 @e 1215.5 1450.5 4.5 @i 1215.5 1450.5 4 @e 1215.5 1961.5 4.5 @i 1215.5 1961.5 4 @e 1215.5 1447.5 4.5 @i 1215.5 1447.5 4 @e 1222.5 1971.5 4.5 @i 1222.5 1971.5 4 @e 1222.5 1438.5 4.5 @i 1222.5 1438.5 4 @e 1224.5 1961.5 4.5 @i 1224.5 1961.5 4 @e 1224.5 1447.5 4.5 @i 1224.5 1447.5 4 @e 1233.5 1970.5 4.5 @i 1233.5 1970.5 4 @e 1233.5 1439.5 4.5 @i 1233.5 1439.5 4 @e 1245.5 1990.5 4.5 @i 1245.5 1990.5 4 @e 1245.5 1419.5 4.5 @i 1245.5 1419.5 4 @e 1248.5 1975.5 4.5 @i 1248.5 1975.5 4 @e 1248.5 1433.5 4.5 @i 1248.5 1433.5 4 @e 1262.5 1969.5 4.5 @i 1262.5 1969.5 4 @e 1262.5 1440.5 4.5 @i 1262.5 1440.5 4 @e 1269.5 1976.5 4.5 @i 1269.5 1976.5 4 @e 1269.5 1433.5 4.5 @i 1269.5 1433.5 4 @e 1275.5 1997.5 4.5 @i 1275.5 1997.5 4 @e 1275.5 1411.5 4.5 @i 1275.5 1411.5 4 @e 1284.5 1973.5 4.5 @i 1284.5 1973.5 4 @e 1284.5 1435.5 4.5 @i 1284.5 1435.5 4 @e 1292.5 1974.5 4.5 @i 1292.5 1974.5 4 @e 1292.5 1435.5 4.5 @i 1292.5 1435.5 4 @e 1296.5 1985.5 4.5 @i 1296.5 1985.5 4 @e 1296.5 1424.5 4.5 @i 1296.5 1424.5 4 @e 1301.5 1975.5 4.5 @i 1301.5 1975.5 4 @e 1301.5 1433.5 4.5 @i 1301.5 1433.5 4 @e 1313.5 1977.5 4.5 @i 1313.5 1977.5 4 @e 1313.5 1431.5 4.5 @i 1313.5 1431.5 4 @e 1325.5 1977.5 4.5 @i 1325.5 1977.5 4 @e 1325.5 1431.5 4.5 @i 1325.5 1431.5 4 @e 1335.5 1974.5 4.5 @i 1335.5 1974.5 4 @e 1335.5 1434.5 4.5 @i 1335.5 1434.5 4 @e 1349.5 1970.5 4.5 @i 1349.5 1970.5 4 @e 1349.5 1438.5 4.5 @i 1349.5 1438.5 4 @e 1359.5 1967.5 4.5 @i 1359.5 1967.5 4 @e 1359.5 1441.5 4.5 @i 1359.5 1441.5 4 @e 1369.5 1961.5 4.5 @i 1369.5 1961.5 4 @e 1369.5 1448.5 4.5 @i 1369.5 1448.5 4 @e 1378.5 1951.5 4.5 @i 1378.5 1951.5 4 @e 1378.5 1457.5 4.5 @i 1378.5 1457.5 4 @e 1385.5 1964.5 4.5 @i 1385.5 1964.5 4 @e 1385.5 1444.5 4.5 @i 1385.5 1444.5 4 @e 1386.5 1943.5 4.5 @i 1386.5 1943.5 4 @e 1386.5 1465.5 4.5 @i 1386.5 1465.5 4 @e 1388.5 1944.5 4.5 @i 1388.5 1944.5 4 @e 1388.5 1464.5 4.5 @i 1388.5 1464.5 4 @e 1401.5 1941.5 4.5 @i 1401.5 1941.5 4 @e 1401.5 1467.5 4.5 @i 1401.5 1467.5 4 @e 1411.5 1938.5 4.5 @i 1411.5 1938.5 4 @e 1411.5 1470.5 4.5 @i 1411.5 1470.5 4 @e 1423.5 1931.5 4.5 @i 1423.5 1931.5 4 @e 1423.5 1477.5 4.5 @i 1423.5 1477.5 4 @e 1433.5 1923.5 4.5 @i 1433.5 1923.5 4 @e 1433.5 1485.5 4.5 @i 1433.5 1485.5 4 @e 1444.5 1913.5 4.5 @i 1444.5 1913.5 4 @e 1444.5 1495.5 4.5 @i 1444.5 1495.5 4 @e 1453.5 1905.5 4.5 @i 1453.5 1905.5 4 @e 1453.5 1504.5 4.5 @i 1453.5 1504.5 4 @e 1461.5 1893.5 4.5 @i 1461.5 1893.5 4 @e 1461.5 1515.5 4.5 @i 1461.5 1515.5 4 @e 1465.5 1881.5 4.5 @i 1465.5 1881.5 4 @e 1465.5 1527.5 4.5 @i 1465.5 1527.5 4 @e 1466.5 1868.5 4.5 @i 1466.5 1868.5 4 @e 1466.5 1540.5 4.5 @i 1466.5 1540.5 4 @e 1470.5 1869.5 4.5 @i 1470.5 1869.5 4 @e 1470.5 1539.5 4.5 @i 1470.5 1539.5 4 @e 1479.5 1862.5 4.5 @i 1479.5 1862.5 4 @e 1479.5 1547.5 4.5 @i 1479.5 1547.5 4 @e 1489.5 1851.5 4.5 @i 1489.5 1851.5 4 @e 1489.5 1557.5 4.5 @i 1489.5 1557.5 4 @e 1491.5 1866.5 4.5 @i 1491.5 1866.5 4 @e 1491.5 1542.5 4.5 @i 1491.5 1542.5 4 @e 1498.5 1839.5 4.5 @i 1498.5 1839.5 4 @e 1498.5 1569.5 4.5 @i 1498.5 1569.5 4 @e 1506.5 1830.5 4.5 @i 1506.5 1830.5 4 @e 1506.5 1578.5 4.5 @i 1506.5 1578.5 4 @e 1512.5 1817.5 4.5 @i 1512.5 1817.5 4 @e 1512.5 1591.5 4.5 @i 1512.5 1591.5 4 @e 1513.5 1803.5 4.5 @i 1513.5 1803.5 4 @e 1513.5 1605.5 4.5 @i 1513.5 1605.5 4 @e 1515.5 1762.5 4.5 @i 1515.5 1762.5 4 @e 1515.5 1646.5 4.5 @i 1515.5 1646.5 4 @e 1516.5 1789.5 4.5 @i 1516.5 1789.5 4 @e 1516.5 1619.5 4.5 @i 1516.5 1619.5 4 @e 1516.5 1763.5 4.5 @i 1516.5 1763.5 4 @e 1516.5 1645.5 4.5 @i 1516.5 1645.5 4 @e 1517.5 1774.5 4.5 @i 1517.5 1774.5 4 @e 1517.5 1634.5 4.5 @i 1517.5 1634.5 4 @e 1523.5 1751.5 4.5 @i 1523.5 1751.5 4 @e 1523.5 1658.5 4.5 @i 1523.5 1658.5 4 @e 1527.5 1781.5 4.5 @i 1527.5 1781.5 4 @e 1527.5 1627.5 4.5 @i 1527.5 1627.5 4 @e 1528.5 1739.5 4.5 @i 1528.5 1739.5 4 @e 1528.5 1669.5 4.5 @i 1528.5 1669.5 4 @e 1532.5 1725.5 4.5 @i 1532.5 1725.5 4 @e 1532.5 1683.5 4.5 @i 1532.5 1683.5 4 @e 1532.5 1825.5 4.5 @i 1532.5 1825.5 4 @e 1532.5 1583.5 4.5 @i 1532.5 1583.5 4 @e 1532.5 1712.5 4.5 @i 1532.5 1712.5 4 @e 1532.5 1696.5 4.5 @i 1532.5 1696.5 4 @e 630 2169 :M f151 sf 1.336(-0.6)A 630 2019 :M 1.336(-0.4)A 630 1869 :M 1.336(-0.2)A 680 1718 :M (0)S 642 1569 :M 3.748(0.2)A 642 1418 :M 3.748(0.4)A 642 1268 :M 3.748(0.6)A 706 2234 :M 1.336(-0.6)A 856 2234 :M 1.336(-0.4)A 1006 2234 :M 1.336(-0.2)A 1181 2234 :M (0)S 1312 2234 :M 3.748(0.2)A 1462 2234 :M 3.748(0.4)A 1612 2234 :M 3.748(0.6)A endp showpage %%Trailer end %%EOF %%EndDocument @endspecial 689 2400 a Fd(Figure)i(6.)46 b Fo(P)m(oles)24 b(of)f(the)g(P)m(ad)m(\023)-43 b(e)25 b(appro)m(ximan)m(t)e([240)p Fn(=)p Fo(240],)29 b Fn(!)f Fo(=)d([10)3085 2367 y Fi(1)3161 2400 y Fo(],)689 2530 y Fn(\013)h Fo(=)f(1.)390 2737 y Fn(!)447 2751 y Fh(2)519 2737 y Fo(should)32 b(b)s(e)g(visibly)h (in\015uenced)f(b)s(oth)g(b)m(y)h(the)g(singularities)h(corresp)s (onding)e(to)i(0)p Fn(=)p Fo(1)390 2867 y(and)d(b)m(y)g(those)g (corresp)s(onding)g(to)g(1)p Fn(=)p Fo(10,)j(whic)m(h)d(w)m(e)g(could)h (call)g Fg(sub)-5 b(dominant)p Fo(.)45 b(This)31 b(is)390 2997 y(indeed)j(the)g(case,)j(as)e(w)m(e)g(can)f(see)h(from)f(\014gure) g(6;)j(note)e(that)g(only)g(the)f(sub)s(dominan)m(t)390 3126 y(singularities)27 b(near)g(the)f(real)h(axis)g(are)g(really)g (detectable)h(as)f(those)g(near)f(the)g(imaginary)390 3256 y(axis)31 b(giv)m(e)h(a)e(negligeable)j(e\013ect)f(with)e(resp)s (ect)g(to)i(the)e(dominan)m(t)h(ones.)490 3385 y(F)-8 b(ollo)m(wing)28 b(ideas)f(\014rst)e(in)m(tro)s(duced)h(in)f([16)r(],)i (w)m(e)g(b)s(eliev)m(e)g(that)f(the)h(natural)f(b)s(oundary)390 3515 y(is)i(created)h(b)m(y)f(accum)m(ulation)i(of)e(lines)h(of)f (singularities)h(due)e(to)i(resonances,)g(so)g Fg(al)5 b(l)38 b Fo(the)390 3644 y(rational)k(appro)m(ximan)m(ts)g Fn(p)1365 3659 y Fm(k)1407 3644 y Fn(=q)1493 3659 y Fm(k)1577 3644 y Fo(of)f(the)g(rotation)h(n)m(um)m(b)s(er)e(should)g(con)m (tribute,)k(with)390 3774 y(2)p Fn(q)476 3789 y Fm(k)553 3774 y Fo(of)34 b(lines)g(of)g(singularities)h(to)f(the)g(build-up)e (of)j(the)f(natural)g(b)s(oundary;)f(therefore)390 3903 y(it)44 b(acquires)f(a)h(fractal)g(shap)s(e,)i(as)d(eac)m(h)i(lob)s(e)e (is)g(actually)i(decomp)s(osed)e(in)g(a)g(larger)390 4033 y(n)m(um)m(b)s(er)25 b(of)i(lob)s(es)g(on)f(a)h(smaller)g(scale)h (and)e(so)h(on;)h(these)f(smaller)g(lob)s(es)g(are)g(ev)m(en)m(tually) 390 4162 y(not)43 b(detectable)h(with)f(P)m(ad)m(\023)-43 b(e)44 b(appro)m(ximan)m(ts)f(of)g(feasible)g(order)f(with)g(the)h (computer)390 4292 y(tec)m(hnology)f(a)m(v)-5 b(ailable)42 b(to)f(us,)g Fg(exc)-5 b(ept)42 b(when)g(the)g(ne)-5 b(arness)42 b(to)g(two)h(distinct)e(r)-5 b(ational)390 4421 y(values)33 b(is)f(str)-5 b(ong)p Fo(,)32 b(lik)m(e)g(in)e(the)h (case)g(of)g Fn(!)1838 4435 y Fh(2)1907 4421 y Fo(ab)s(o)m(v)m(e.)490 4551 y(What)41 b(o)s(ccurs)f(practically)i(b)m(y)f(increasing)g(the)g (v)-5 b(alues)40 b(of)h(a)g(partial)g(quotien)m(t)h Fn(a)3442 4566 y Fm(k)3485 4551 y Fo(,)390 4680 y(for)37 b(some)g Fn(k)s Fo(,)i(in)d(the)h(con)m(tin)m(ued)h(fraction)f(expansion)g(for)g (the)g(rotation)h(n)m(um)m(b)s(er)d Fn(!)40 b Fo(is)390 4810 y(that)33 b(the)g(latter)i(b)s(ecomes)e(closer)h(to)f(the)g(con)m (v)m(ergen)m(t)i Fn(p)2394 4825 y Fm(k)r Fi(\000)p Fh(1)2527 4810 y Fn(=q)2613 4825 y Fm(k)r Fi(\000)p Fh(1)2746 4810 y Fo(,)f(so)f(that)g(for)g Fn(k)f Fo(=)d(2,)390 4939 y(the)40 b(e\013ect)g(of)g(the)f(singularit)m(y)i(corresp)s(onding)d (to)i(suc)m(h)f(a)h(rational)g(v)-5 b(alue)40 b(is)f(sort)h(of)390 5069 y(ampli\014ed:)57 b(then)38 b(the)h(singularities)h(detected)g(b)m (y)e(the)h(P)m(ad)m(\023)-43 b(e)41 b(appro)m(ximan)m(ts)e(tend)f(to) 390 5198 y(accum)m(ulate)d(near)e(suc)m(h)f(a)i(dominan)m(t)f (singularit)m(y)-8 b(,)35 b(and)d(the)h(rest)h(of)f(the)g(b)s(oundary)e (of)p eop %%Page: 9 9 9 8 bop 1188 66 a Fh(SHAPE)31 b(OF)f(ANAL)-6 b(YTICITY)31 b(DOMAINS)883 b(9)270 266 y Fo(the)28 b(analyticit)m(y)i(domain)e(app)s (ears)f(as)h(a)g(set)g(of)g(a)g(few)g(scattered)h(p)s(oin)m(ts)e (without)h(m)m(uc)m(h)270 395 y(visible)35 b(structure:)48 b(to)35 b(obtain)f(a)h(more)f(meaningful)g(picture)g(one)h(should)e (increase)i(b)m(y)270 525 y(far)25 b(the)g(order)f(of)h(the)g(P)m(ad)m (\023)-43 b(e)26 b(appro)m(ximan)m(ts,)h(whic)m(h)e(is)f(not)i(so)f (easy)g(from)f(the)h(n)m(umerical)270 654 y(p)s(oin)m(t)30 b(of)h(view.)270 838 y Fs(Ac)m(kno)m(wledgmen)m(ts.)47 b Fo(W)-8 b(e)25 b(thank)f(S.)g(D'Angelo)i(\(INFN)g(T)-8 b(or)24 b(V)-8 b(ergata\))27 b(for)d(pro)m(viding)270 967 y(us)44 b(computing)g(resources.)83 b(Calculations)46 b(ha)m(v)m(e)g(b)s(een)d(p)s(erformed)g(on)i(DEC)f(Alpha)270 1097 y(computers,)30 b(using)g(DEC)h(F)-8 b(ortran)31 b(90)g(and)f(Mathematica.)1565 1302 y Fd(References)308 1465 y Fr([1])40 b(Chirik)n(o)n(v,)26 b(B.)g(V.,)g(Ph)n(ys.)g(Rep.)f Fc(52)h Fr(\(1979\),)h(264{379)308 1575 y([2])40 b(Fishman,)24 b(S.,)f(Gremp)r(el,)h(D.)e(R.,)i(Prange,)g(R.)e(E.,)i(Ph)n(ys.)e(Rev.)g (Lett.)h Fc(49)g Fr(\(1982\),)h(509{512;)j(Grem-)428 1685 y(p)r(el,)f(D.)g(R.,)f(Prange,)i(R.)f(E.,)g(Fishman,)h(S.,)f(Ph)n (ys.)f(Rev.)g(A)g Fc(29)p Fr(,)i(\(1984\),)g(1639-1647)308 1794 y([3])40 b(Casati,)28 b(G.,)e(Guarneri,)h(I.,)f(F)-6 b(ord,)25 b(J.,)i(Viv)l(aldi,)f(F.,)g(Ph)n(ys.)g(Rev.)f(A)g Fc(34)h Fr(\(1986\),)h(1413-1419)308 1904 y([4])40 b(Aubry)-6 b(,)24 b(S.,)i(Ph)n(ys.)f(D)h Fc(7)f Fr(\(1983\),)j(240{258)308 2013 y([5])40 b(Sinclair,)22 b(R.)f(M.,)h(Hosea,)g(J.)g(C.,)g (She\016eld,)f(G.)g(V.,)h(Rev.)e(Sci.)g(Instrumen)n(ts)g Fc(41)g Fr(\(1970\),)j(1552{1559)308 2123 y([6])40 b(MacKa)n(y)-6 b(,)34 b(R.)e(S.,)j(Lecture)d(Notes)g(in)h(Ph)n(ysics)f(247,)k (Springer,)e(Berlin-New)f(Y)-6 b(ork,)34 b(p.)e(390{454,)428 2232 y(1986)308 2342 y([7])40 b(Da)n(vie,)26 b(A.)f(M.,)i(Nonlinearit)n (y)g Fc(7)f Fr(\(1994\),)h(219{229)308 2452 y([8])40 b(Berretti,)29 b(A.,)f(Gen)n(tile,)g(G.,)h Fb(Bryuno)h(function)f(and)h (the)g(standar)l(d)h(map)p Fr(,)d(Preprin)n(t)f(I)r(I)g(Univ)n (ersit\022)-38 b(a)428 2561 y(di)25 b(Roma)h({)g(T)-6 b(or)26 b(V)-6 b(ergata)26 b(\(1998\))308 2671 y([9])40 b(Eliasson,)33 b(L.)d(H.,)i(Univ)n(ersit)n(y)d(of)h(Sto)r(c)n(kholm)g (Preprin)n(t)g(\(1988\),)j(and)c(Math.)i(Ph)n(ys.)f(Elect.)h(J.)f Fc(2)p Fr(,)428 2780 y(No.)c(4)g(\(1996\),)h Fa ()270 2890 y Fr([10])40 b(Berretti,)27 b(A.,)e(Chierc)n(hia,)i(L.,)g(Nonlinearit)n (y)g Fc(3)e Fr(\(1990\),)j(39{44)270 3000 y([11])40 b(Berretti,)30 b(A.,)f(Celletti,)h(A.,)f(Chierc)n(hia,)h(L.,)g(F)-6 b(alcolini,)31 b(C.,)e(J.)g(Statist.)g(Ph)n(ys.)f Fc(66)h Fr(\(1992\),)h(1613{)428 3109 y(1630)270 3219 y([12])40 b(F)-6 b(alcolini,)27 b(C.,)g(de)f(la)g(Lla)n(v)n(e,)g(R.,)g(J.)g (Statist.)g(Ph)n(ys.)g Fc(67)g Fr(\(1992\),)h(645{666)270 3328 y([13])40 b(Berretti,)27 b(A.,)e(Marmi,)j(S.,)d(Nonlinearit)n(y)i Fc(7)f Fr(\(1994\),)h(603{321)270 3438 y([14])40 b(Berretti,)27 b(A.,)e(Gen)n(tile,)i(G.,)g(J.)f(Math.)g(Pures)g(Appl.)f Fc(78)h Fr(\(1999\),)i(159{176)270 3548 y([15])40 b(Da)n(vie,)26 b(A.)f(M.,)i Fb(R)l(enormalisation)h(for)g(analytic)g(ar)l(e)l(a-pr)l (eserving)j(maps)p Fr(,)c(unpublished)270 3657 y([16])40 b(Berretti,)27 b(A.,)e(Marmi,)j(S.,)d(Ph)n(ys.)h(Rev.)f(Lett.)h Fc(68)g Fr(\(1992\),)h(1443{1446)370 3863 y Fq(Alber)-5 b(to)39 b(Berretti,)h(Dip)-5 b(ar)g(timento)37 b(di)h(Ma)-5 b(tema)g(tica,)40 b(I)r(I)f(Universit)2772 3857 y(\022)2770 3863 y(a)e(di)h(R)n(oma)g(\(Tor)270 3972 y(Ver)n(ga)-5 b(t)g(a\),)27 b(Via)h(della)g(Ricer)n(ca)g(Scientifica,)e(00133)k(R)n (oma,)d(It)-5 b(al)g(y)370 4082 y Fb(E-mail)27 b(addr)l(ess)6 b Fr(:)36 b Fa(berretti@mat.uniroma2.it)370 4268 y Fq(Corrado)f(F)-9 b(alcolini,)38 b(Dip)-5 b(ar)g(timento)35 b(di)f(Ma)-5 b(tema)g(tica,)37 b(I)r(I)f(Universit)2781 4262 y(\022)2779 4268 y(a)e(di)h(R)n(oma)g(\(Tor)270 4378 y(Ver)n(ga)-5 b(t)g(a\),)27 b(Via)h(della)g(Ricer)n(ca)g(Scientifica,)e(00133)k(R)n (oma,)d(It)-5 b(al)g(y)370 4487 y Fb(E-mail)27 b(addr)l(ess)6 b Fr(:)36 b Fa(falcolin@mat.uniroma2.it)370 4674 y Fq(Guido)f(Gentile,) h(Dip)-5 b(ar)g(timento)34 b(di)h(Ma)-5 b(tema)g(tica,)37 b(Universit)2522 4668 y(\022)2520 4674 y(a)d(di)h(R)n(oma)g(Tre,)i(Lar) n(go)270 4783 y(San)28 b(Leonardo)g(Murialdo)g(1,)g(00146)i(R)n(oma,)e (It)-5 b(al)g(y)370 4893 y Fb(E-mail)27 b(addr)l(ess)6 b Fr(:)36 b Fa(gentile@matrm3.mat.uniroma3.)q(it)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0009210745249--