%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: POLL0.dvi %%CreationDate: Fri Sep 27 15:30:52 2002 %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR9 CMR17 CMR10 CMTI9 CMBX9 CMBX10 CMMI10 CMMI8 CMSY10 %%+ CMSY8 CMR8 CMTI10 CMEX10 MSAM10 MSBM10 CMCSC10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe -P pdf -G0 POLL0 %DVIPSParameters: dpi=8000, compressed %DVIPSSource: TeX output 2001.03.27:0852 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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ada58f0c80555356dccaeeda426afa8d009882f28da75d347ffaa195b97a0fcf c20e27110d6dbdf49f856a5a23dc8ae5f727b7df4fec4df2723ce7c9fa57ba 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812b1188a10f6327c9e8714449de2ae636420f56a44cebd774f0b131c629 818455cc8dd8d40939f3ba8aa5abc54590c7286b172193c23adb1b4f9931a9f7 73b960b1f5b760438028478e4442dc93a567b07e20017c18fca2a1daa2649dee 5a6ec51fd6c3f4b27367c31e95a56ba4bbeda0493bc02306037e2ba69add9b94 373364db316691e73d6811cd76fbc92b0c67ca18dcdf05807f17d1b309456ea9 d113ea0fccd6eb73bd8dfdbd5905a5e38bbf61cfe58fb01ec95a4bdd9565433d 4a7abb8dca6f76c459484ad29c3480b588fae3d782340da9ccf5a3d1539e9455 8895bd7ded68c74fe985d580bc72d3560174719eeed44d242403a2d8381eb4c8 25777dcaf1bf951572358e6f168e5ef24fee9a5df907e633cbd4f9e6a3295836 582550af0c024ddcb85d976cb213480ee9c37ff58ef8fdcca0f3df3593b32e5f e79e58ad46d3dd5bc36921a67949145548376846a0bf6b243fab82910c0e4aa3 bde404ed68189230a3360490b2d26d9851fafccb616c1386aef74576ae99fd79 ee498a8b9fefc201352bd1f6f897f784d3c726ee6517b39ace1b2e16ac567d08 838ee3ab31f60c7cd0201bc59e103fb567478a0bba7b20a88b9c2e5ec1bea3de 2d5b5890cdb7b1174c4793dbe6b22d9ad84f70e581bf960dfb0ba96f72833065 22dd3c81ed3a86b0603c882cc98ae5979b180932ca821d8f8ddbf442f94ca01c 09914fd5ecdcdb971dd0a4e01f9990e980735cebabba897bab7076ce88c25aaf a38963b4df864aaf6661044d6b9288493d3dbfe90fd3175c6f6ec392fb6d64dd 1583d6cd5e97644542764f116db41b5dd09be7ad42f401073f6d6fac1357e78f 22510ac944a50c38489b000edf8718b67502556dd7b095e2d9628253536879ac 10c6c1580bf46d4b70aa3d50bd5d6c10bf3eeaa506c9578ed9fee0e10f9862b7 2c7c3fb600f9a3ca7fe6864fd0ec8428ecab5a0389386dbf8b2fd1128e4f502b 2091b8f2ed9c06dd1d088f387841a8735bf72033efb2e46ae1cab0f0c3e606c3 19dc2d04947c576ed6335a5c891e7f1a281db9af757b6114ee7e8183320fa9f4 c6c3e3bf6240b7f40411efe9bc1656e8551480aa0dae64245513d9824e6e2576 df312e6be6764290017e8e6822422bbaacb7ff5825cde4e8502f78a18dae6289 2f28d9b62035c93a999b221077f28a824b5bea168bfff8a7f902b627af0ddb0b 2be4974585ab88250ceb8c5533d817b0c5351ce1c760307b1cf6a093cd11233f a6a24caff50f66a52848aeda1a0017bc86444b16527b5f8570aacc1a976e4b8f 77061dbff4fd23433ac12528284fa66649060662b3360a1574df5ed2d374018f bd1f00e68e042e037903daacd1b65f9e5e9ef9a479b71beff554af3ff6a825f9 6e5bfe15e3164d920556a726fb9a753e176d01efc8434d77a18637cfef5696ce c681a539f89f67f8d535fa8ba10a6688d43ebb14985c9a9b9443ade26f22fdc4 ecc8299ac5bba6c2a08518542fdad9bba61e73825de93c778c2924571dca57e2 00d6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % 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 (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa4f3118e6b59bd7a2c35420557fc465c b2c852523436519025d7013ec029f4a3b529c171ec5c6d5a8a188b741f64cdfc f531dc0d5851f9d620c3d30c2d1c7f1b71b47acee7a580d5c2e7c58ab08d5af3 41b5710ac3169e524799e662da50cc19ff2eab91706fe0ed7a96b80e0c9c4353 21f163df55c261c2ee086bf79eb1d79fc8426a4e1fe3d54332c4144888d6ac9c df2ab5e45f95e1045b5b4b874020b7c38fe699eab188d354d805e511489d3f5f 4243c384bdcf642a5543716a9ccb7ecbfb696e6b1d6b627b777caf92364a37aa 19707462821e550c47dfbc4070c683272365d472d2282f33f1cdd2849fe8cea5 a149ba043b98b09a18fcc90a17847b8c98834495018b3dfe45f624cb2f3e40ac 5ec67585e507c59013e1a46beff701dbb789a9b817cb99d4927e1a6a4156b509 4e0253b7bebc5928d8c8c4aeddd276a6abc53b5270b3cd9eba342ac18abdd126 5608f1e9ead1ccc4a6c7fd465d10750cf96bc6658bba36212193779d7bf39a05 74806cdd1039ea780a18ea91c2c1dc99f622a59c3825e05ed4448e6126d2f470 d6b5496feb33e4118586bb19583111aee701 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 16 /parenleftBig put dup 17 /parenrightBig put dup 40 /braceleftBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 80 /summationtext put 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 83fd05010d6c0729362536d15d42df49c81b451a7a29952703b9b2def827658b e9c4706fa31764cf5e33ce2fec53bcd34431e6083c78d2953e8ba548a478e565 271d74fe9daf8246784bfb7d914164e5a7b1d43079385ebea35b28ef30833b33 8b8c85ddf1370e7c085357e77bf54b36f7a981c4ccef64b4871705d1e3149ec7 9f69fce7357e36bdc087de887bd802a899a9f22292051ef6152f5434f33c4e76 9eb52cf2a7a4a58af3b7d296ea908aedeec32dc771cdbf7e9e27fe20d669d412 058586f48e90345bcbe6604a7601ec2d754570e5b9b9888816b4dd2680425472 c7e0627063dd86b8fb9b676eed9c840c10da72739f3e1f88c8f9ac262a78d34b 0bceb2eff0a15f38a99bbd3200e9b24ca62e75ba1704f7f1e1dcf4075e340f3c df9dd2633b36743afa7c31b0e72d46d2b69f6cd2e532635f1ef4c55f98908518 109641877d6fdd45d14b2cc2ae93ec9ce0c63316279b6255402eb368bc9af9b8 fa989f8e8782d83476353baa5843623bda1689a883af06b3a22f656edfe799b2 dc59d7c03f70faf1678561bab4ae11b88fcc716b3ae2b4405060040ee8210263 2ccb8440b78748cb0a7e166709c987a8ee8598dbcef5a6e9d1ea33890175280b cedf25351db57a97a05f9e89e9fac089b436b7bc0edede61b9728687cca522a2 f68ee5338eb02d4848d5f5a5387749ba925b84a068febdaa3f8c787542522f67 61abbb6a2d10a67c69277913ec38bbc9b7f991b86f003821827f418b15c84ab2 9f174f9a963b088c5125d31ca395406a0b87bd9c83a82e8edcb3bc7b6bf5977d aeac1370bd302d2394bf05c8af41f174bd702012ad86903c0e74f357089cce0e 99ebd6a0b47782a3a6ab18932c53a23f578dac8d9c6ed7674231ceeddf26dc4a c105b6a477e954757f80efd9fa253816fa1d0616652a3d5d550f5fc0b7429957 f7fcf9980c51cd41a4e7192daa686f10f03f75b7abdf01d0d3b1b1f6c2ebde0b e7fa06be0ac77711ec41be0afb179721aca8bf0a3f0dcb312c75bf2b69df3841 de03a8e2b0e79f57992f93709ae16d956162f8f7882de24417c9b7f191a9953d 9c5eac9be4855110d680cddd88b42af6892953daf8d0fa83cac2b343cc21d406 32c0de8eae8df88f5eb64635851aaef10e0e4d09aae99f5d5c9f0966cc88d02f 2d62e5aa3d668a6630d5cc31d563cf6c60b2ef6525df4031ad86c17ac0cf6f3f 2a7cb1650154cf5f11781c61332db4c708c4dd1923d846b9ef996914b2c58cbd 8db8f65ec27f55f7c4a214efc52789c72a2682195f832d0bd985ae3a30dbd8bc f3a83670d7de8b2148abf5906fce5eb44976dff4eddbcb32752e2fe0faed3d2c ce210a4413bc497b68cab72c2a1115a08f1312091df996741034c326afb46562 18e26844cbe1315efaf862a0be1e4b978f2077a0c7f1c138cce0e6fd999a3427 d39593bb109fca0e03a7f09f1e0627e9a8cacdaf12cdee3364600fae36086df6 f78c625d1415cd245c13ae008fa7aa40b96a61c7b3941f1a9648193f4e706b83 62ca9ee7dc0d76294f9d37ec98a126cc3d287e35f4811711e585bbfa2334fff8 22aa1bb44fb78721435a677e645ef561ba508f07b6229418dedadf6985d0a2b8 ce22b28c5e98dfe9e72839c5cc06ed4c9d85a13b16bf14eb6ba8f7120d78622c 5c2058e900315c0b98b3f83ac102f053e0cbab72c8b4b796034a2ba06e68c4da 558f48842a5f8f15282f167e27849b03fc5c5dc0e01b86efecd88f8ee37dd519 a9bca4605e384e61454a575c4cbbf396449b07f653a5e4618fcac344ebfff0cd b1059761fbc52456d73cabcb26ceff6517cff976404dc90ea094d5afa91f6539 27157e823f7bb4fb70dc8e7e68d050402487cf65bdb31485e81a84a1b8e8890b eb2c448cc94ec8f2090ae1219f624b946a9a00467933cd058928281650b8afbc a10126e917fab3b9d37d94f743ed1ff68f3b0e7aa3a3ae3b88ded46bf4f48a6a e538b7fe6b49e4ee5645cbc8b759b51fad77398475ccb362dfee48559cbb4d34 604aeddf444721f38781457687771acb181c568cf56ad6150be50efafe6ad815 6e33af5331ba4445ee6c8e4623ee9ec254b433b3a9915e338a3ffdb83134cef7 344e92a8b03fef3b77c7542c041f811f992f8488c452b51e171649dff9a758b7 3e6d47f4c0cd08b5eedf205d08893d50bc9c3f17a59ea1ead7688ebe42f2bf6d 9a1c7ac15957f21f9d4d3990231b99a430fe45b0e8dc836a395110480ce16fc7 ec9640c8192e448293e78c169666022eda7fe7f63b456fea2642fccbaced3e72 03b4c445c03a0fc3e864371a5072834fe14db0cdc36f869bd3a27deaa8233fe2 be279da46a072f2fefab472fde3c4db9410008a3431f4fc2965f17acb2cd213d 381cc8323d296b897574aeac1424ea166797a596b273dd1cb02b347b371cabd0 893299560dcfa2aa1d8b0c2a663ca056ae0eff201b25c7a044c2f39ffaf4dbf1 d43c73dc0080af0672668ec4b1eaae7015a9ab8aae55adbacbc10335662550b3 a6312482f5191cd45bdeb326112215a850f21f69c4c197f12f1aa79a378c7c67 fab1bf46c38df58a5ad74aa28642c7142b52bfab1846f7c1 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 49 /one put dup 50 /two put dup 52 /four put dup 80 /P put dup 82 /R put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 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736d3aa7ce08e0bea8e769b127c5fede6d698f830b648ea9945ce11a72038d1f 197f46fe7bcf3f95460a69202b2cdc96199135e4b3b6908a86043f796c293d6d 5d844b923bafc8c6fc757ba7dc7635a9666f022d5e6d75c7e3585da813786538 2ee8e1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e125a42a237f8aa6c1 6fdcb0b5c8da4238991cd0193e4dd3aea198abf32a449ec1085b906fb406de98 b8d181ee02a346773e3b491158b881f3e94fa5110b2e8123d3e726c1f9ff14b0 85bc8aec42dc9be91d0627aa2df2b373dda3f1171f528406937aabbeb5d1357b d18946fa955dc011a572c7fecde23921a68607d008fca3677208775d28107cb6 c468c3333e9b3733b67170deba1fe165dfe61106ba1b8df26183b3bb2d877276 86b737900072dd58a2e3f27a7e8ba39e055ddd2639d5296f0c32b28b71fc76cd 647b7a6068c07e70f1a772c72320b2b1cc1e51b0f82b9e8881d069eefeb7b499 c97c8e896f55e1d952e10714d29fe2c4b43c6f449a1e8d608573f8147c716069 63c34e6a68344811394fa0a8c23444ff5833d98a9bbf25d1a1ebaccf5e84bca1 6ea2f0ab94cf3abdefe9fad8769845aa9c2ef6409d5ef54fafdd027b3ebd918d 829a6cf804ae96411433a188f74822eaae2c81dc9d1a2edb08e7a41c074dcc85 cded5b11144609c40bdeee9f53dde09170241e5886c4961ba7514e941b167e6d 48a2a96bcc2c098f027db43808de8871e4161632bca306b141b418a416e88160 d55950fa14c71b23612c0750e67c2d97c0343c2b8dcd488242aeab69047c3b3f 533addee1b578945accb347d51a46e8bc8ee43dab1a45a47549b5e06e5d79304 a6bf1802cb0ff6c81e31cd475a79c6976f724f0398930f5743b37026a0def1d7 01d523f94b4442c5ff01f2cba5c4673ad32260e7c4e5c4c2f2ed31a54f9fd979 bd3d8156c321ae4b8c03c522b9936a26fd3818f9565e15d67427ad0763a9d32d f4d12dad2ae40ebba16315455b58c9e1b178803a9d47dbbb210b3d730ce8a132 fa80becd01f896edba3dc07a1ed4abb8fedc67bf7f23063b3ec52993 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 33 /arrowright put dup 49 /infinity 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 b910bf03a0fd0ff582d7bf32eef7d0676dea7d3546c46d4eb62cc5f957c41086 7b839cc408660dec5f886c9f9a58ede1634780b7da0d8f10935518e756f1f21f 1e0e2534abe0ef6e0b849566e60b6487cf6710f0a76512c9378cb10c705a88ff 10bf1b4329bd9bb5978ececb15fde07c89c703f48e016526d84f14d559ceeed9 7180b3d624f013f79c7512e73af9846a8e6d2c5fe7b97b39e21af802250e4bc3 5a31451b09fbb3627a3a48113d2fd144d8e194cb7fff0554bc4adf47a6acf5a4 b78d0ebd72b08e83730786035a6101fcfd8f5c0afd20e79a1a27985cc70e535a 873f1c609ed2a4769e12a888740ddf5d65fec70b58a843ed3bb5ea18b1ded7f9 50caf2de411b3d6994ae6a4fbedc98c472b4e9387da5abc0d4c4ade478197116 e34bc2fc3f8b09e9973bca5f5dba0c67ffedd195b6ee1dc21ba25a277b09fb99 10109c9e2a99ea1e61545428fb39029a46d5c0cc7d1db8b9826a4da83e658e90 55befc5efc4e3f5c7d700aa6fcad88334497b785ba8a0c55c3f238c7c6d1a44f 796a805229182e28b809aa23f96bba8bc924c2378d62a9c921620235a33c85cf 588295d1c418d7c3a4e61f3f5c8db891c649dec4dc20657c49be55caf1946e6e cbdc2c83c9e94d5abe520b15e0694e5099a66979ba2f71e29295d015088f8fe6 d6079e756e9521b8c39b78198d81cabe0da31c73e45c8b1f2ace1fed84c0c677 fdbc2deebd66e67697a38cc0c542b64c10086390b0211d17c6ed34483647a007 e2c03b47eff76388f2fa78ceb406accd2471f4052521333fa5894e634c31086b 2dabddac5598dc81c38cb09c015220ec00944cfbc284d07c4143df6e6f17e937 069ae1bf619511cdbb0bcbec7f7ebad0b81e8ebebb2fe7b954001568134f945a de69cf09601397ac50a1d31853555ce4770da9bfbb29bcd52588d561434bce23 cdc3255e80355a19efeb8f34b59ff719a213437f7ed24a193b4e640c4f52bb56 4f3a9680d21e1f2c787d8fce009a921cf92a24103c87e297813e869a35138520 040e9469b200337b0fa85cf00ef968c4b3e7a0f79c3e 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 66 /B put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c430287cb233252ee604a481d21f6d474de7d8e00f4a323e006534d427c7e 009f7e849bc2a88531b276e08b5d6f6fde870470208d64d7aaaeab7a7a9815c0 97929f04ceffe9863d487ab4b7161b9f8492d6e8047aea0f3ee75fe940f9c7e2 c64dcb10bc579afa50808abe9ec980b4ddd51a3a1888d18940c1bfa339dd4a61 a13688a341a1995149b651a1384a57815e8e3cdb1e6496d2170647b249f646bc ae46a8d6ca42336db6d3990ede6cbded9b9b1555b2ab75df59263e22c8afeb10 cf67186ad27eb403d3714e1535fc250a173e142490d6eaa8054766fb764e0b8b 05e20f9864103acb8f0216d19a68d04ce4b6074148e9c4599df54aca9e59810a b65b7e69c89fee8d67062d4eecf8df563ba107c921a86df7276535f2ae4d76d9 0e00aeff33e2926c6c4868392dfa2d496b9647467b936685e224d3d3ab6a87ca ef7f80c8498f0a26dcb9f9f6e38b2c5d49a971dfe001a664e93212902f8d648e 5214a4a13d2ae266d96775f134d5cf99a03ff8130ddece4a904503c6c48da6da 437b2399fcf7104f865d234c654ecb1cd875f531cf6e8ffc230c57eb08b617d5 eecaedfdede28ad97b126138a1de1e5ca8d5b584618ffa5702a4d6d17ff61c3a fd033d92af604926010d6b1b6b8e830dc41dc8612436379633287061e5155a58 6219692bd1263e46464b14d959f75429abc023b0940f8333e69a94a5b708fa73 fee0179a6dff05f7d74f8ff05167ca7714415c2259f60694340fe6ea601a042f 1b8a25a9071d1cbdc0b82792c99a5eff1aab6317e3df1c2fd8f45a98fa63e050 ab0b92202e5fd787659e60f1cf29ca7df4ecb767a93bd04e41dc11e3d927db64 7ca725a608e4bf76b2e4b078ddaa4b0b600aa812cf04618f3d87624d8ffbacca 013f2fc05867fde48dc329085a21c97b07f3455e99b6283b245ccdf781dd6b5d 31b4f80704b33e0967c334d603eac82cf8c818e0d8af7cfb4bd00d8273ef6f0b aeb6a2fdcbb9b860f08cc0249185b1daaed6c0c3ea48e31db60dc6182768b899 936cf84f354bd393dd4d9208172fecddc9a56700ddd0f40415a258385bbf35e0 ffbb02060d5141c7794e6d1a39f12b41fea8b6c64ad092e4f7ef2c3d44058174 7e555355fdd62fce60f1c644293eb145da46b923d1fc2fa03f44536d485f182c c1fe41adce4d103b2f84c725bd9a9a86b55f9244672523acfc9a32bb6eee3e20 a93668365340617a3b11fcafef73ec1c53dbc5f0e006c4f3d0af3343adff3444 0ae56d286c970110757ed01923c1fe05119a0d9a54d24c364e381c56ceb7a312 1c5fe16414c0a89cf9f9f47b1383baf9d8c4c7cf59ea4d1c609269afbe65e687 38ce10b1b1c3e1e3999850996de02da94fd6cde6a7d534f52b3b99ffe60b0711 3438dfd3b53cd41e4de2d73735b1d7b2e80283ec692427b28619e35d4c1aaa94 645b2942706a8ec6fdecefc9186d3a34ef184c6b6be0052e99fa05b49e9d0175 ea94c5663b3b7c234d2314151291da19030e50a2be842edb767f9955270bae64 f0455c63c8f86164cc1e07176561d51d21ec56a9ead72947d59cc024baaa7d9b 291fa46e92439eb063774dcab9c667457dd751d9c19f0814e3bb559569174518 7531d43191e18136f99d4ea8d6d2ad0cd3c8bc6afc71edec8fcc48128e5d9aea f9b44d552da80278da6f045ae115a0662e80c2d48a755cedfda1bceba04a6546 80643dc037fec348286f995ca4b39514b729d534ce571e12c8aab93ba5eb2403 7afd8236b3e29763959a474610d0c6a115459b8f0ae2fc1b574dfa40c74937d1 0586beddb5d904dd02c5f3f5e96f77d4444412bd69948b4b021912a82a0c841b 50a2e51aeb321a3ed6fa222aaad6de187d89fd87efa5c52824b6cd2fbab63811 8ec837cdde8bf4bc2f8c1d0f59663b8aacad83b45c49510c9f821a805eab72c6 879b25611e1de2fccb4de4307e8826e1e52f56067b98ec1296281d987cc61fbc 1dd158e2ccd57e74a63106f1e0353ae4d014b3184335746f2d3908f0dca86427 3437d7af83dde54712c23a2729d064ecec0e6a02883dba5343ddb4e4d33ad7cc 8c6301d03a30b137e1a3931045c5e066d6adb645c4a22237a815c94277754c8c 33ffe73370ef3dc6f2b6e70b197bb66fbf63eba760bd7fb56b511915fd21a2b3 53931477d34b0dad01173583fdc8367db2eb28fb589da66fe55c2fcf473f2d39 113800501f087bcfb575059974fdac971b34f166b72c4b15734a83526374d6d0 0f4f0cf537c09f3df6696566c068e0f2b5e4d09d9e6ea62b5e3b194f0f863608 e72c4a0eaebf51f737a4ee170dd65099fb6c954ce2761024b211ae8e31adc5ee e3a7039c0e8583b18a67fd6bfe0cdfd1ac85831122de62a9773098d012086aa8 a33b11a46f59e72d67388bf70062cbd7aa0ee0b405c8540343dcc51f4a6fd555 5cd6fba93bbc510575610e79e4c2779e1b5416ab5130e0815e4a011c2ae608c8 f3d12fff099e24458682a5215a8ed32492f238c2a1eb25e5389c1eb6b37cbfbd ed4dadc17afdc8f11663c4299d9064480be242282f675ce88b79ec40567e0bf9 3aee03f7e9567508bcfd1b06ea1776bdba5dc189f1250b07966ac240715594e5 24eb06bfb68bc8edd35c42d4d99f24b9563d58b9b776203d9898e090cbd1a916 6ce21c54bff30166ab699cc892f41baa7d14149e7ef8471e3caab52f780b15f5 de054d7e74a254af076ba9b3ed2a3c31d39c446b012c14d8621fcd728ef258d5 0b75b2481423e8ef9106b6578c21d7ef8b1f4cbf89154c5a2beec65d0358e186 db1edf5eb0b1f6b5f1863a3a23432e8287f9f314697682e49b5c32bb13acb908 1c39ebc9c429786a6ca576f1a1568d4ff7884abd9bad2a1291f790c45a4c1cf9 5f8ad47810976ff8b59ce1056756ea25c6cc4841cd6004ae2351020342683094 b45e7794b880619e4bd6b65400911f2ecb1a0bfc038f98251059af179027a795 d64435160483 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 58 /period put dup 68 /D put dup 80 /P put dup 97 /a put dup 100 /d put dup 101 /e put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 110 /n put dup 115 /s put dup 116 /t put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 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aed61177f97ba80cb5e01b31b22f22585a72642da8bea5188bc26b16002aef59 c861b04ad3ae3c46b5da602a2f741dfe00dd02aa564c08ea86dbb51a0e9557f3 db1fecf53019b89b2888b5b5bfe4148733f3c5c89ec32533c052b07bbf9737dd dbb44328b2a5fca15bbbf33148341b5f31cc7c267ab1b8199ae497fd0d7dd5fb c0b8b483ef71007664a704f89522f6e8dc9ad7d3809a6c60d19de0459854067d 4ca55685d79f237bfb13132185223b019946f842540d56fdff739302c579a146 3ad24fb1d9934e734cb2b6813e472facade58772e813a7c8206f69cbd807bdd5 ffa0eb1181dc3c14ceee1cfb974301e249376a2e46820112ef403dd8b2311710 40bef38145f1bff300c451afa0768790a8cf7326bcac18259a95539da2c78bea 68c7d964704801402881384d7cf45d6dd1b8d35334c1d1963fc18b0eadf0504b 2c3b4e2038f630f2bea831e86874bfb91325f07653bbec197d4b8c76773bc641 83c68f8b67552aaab8f33d09041152e5cb65734d79838d86 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 14 /delta put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 28 /tau put dup 31 /chi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 66 /B put dup 68 /D put dup 69 /E put dup 73 /I put dup 78 /N put dup 80 /P put dup 81 /Q put dup 84 /T put dup 88 /X put dup 97 /a put dup 98 /b put dup 99 /c put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 110 /n put dup 112 /p put dup 113 /q put dup 116 /t put dup 118 /v 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 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 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aba7912f88c62840e9356ba9ecb6d571f85cbdf97997279025f846cb346175bb 53cfe36957c324643f5ff8f602abf309917ef0d6de86b6918f4c7e8675 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 12 /fi put dup 14 /ffi put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 65 /A put dup 68 /D put dup 71 /G put dup 73 /I put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 88 /X 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 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 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-301 -250 1164 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1189b9888940f92a866321a61df0cc8ac46ea69e79d2eb68961ea20e60f2c000 f1e391b35bb0cd754e1bee6ceacb4c652b476b1ba6e3dc0151f4141d69907452 1021f47f5530ae8c9cf00c15d7eba4d4f5695934b6e7f52c2b8597ee43a9645a c9a159e45d43ed0120b77223f7e625282f1fb96523054e83864249f8f02c47b3 fb43e64fbb47faa521ba6809d9dab0b41a4838bfcff504d90ec2070a9e39825d d58a584e5065949422 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 12 /fi 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 55 /seven put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 75 /K put dup 77 /M put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 105 /i put dup 106 /j put dup 108 /l put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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82df89cf9bf4b18022d0e5f3b02120a6d4949ecf0325a8d4254808e8c44a6d69 eb60d2f2a399aa86e1efe37f7fb2c6a1ca474fb1b749a48a01a7c5547edc5e65 90d35aec81919b99945c9cd56bf625792790c43f125ba56a0349c909216da728 56c343af276ace373eea541036771e91bd273e6c42fc5e9b1d5a5568eb9d351e f4e5005977358b3fecdb80687f6a9aeb6cb62e440a498bc743941fc2ff7aa0b4 c79554c8f3ac58d9961121958ac401ba8ea5da2ac89ad4619d2d29424eaf05e2 969242b286f5b40795e0eea5656f7c5f55f20183cfa2ae5b5313b5864ee29ccc 6a4936b85662ac4394070a43ef3fb24584ac0c00c610856f73428ae23d21dd1d 39bf67c5b4836a5e5786a2b153434133d479ba366beefc903c44775ed8dcbce2 7eddcb7f0aa46989f9255d18e4a5197ba0632f58680f1fef45ae0f0a0e93bab3 b3d0ce70f13344d8408ba8272ef4665f29cb32e02337dd86dbd7f8e48e5a455f 2b802f4a2db52d7d56a0d747bfdcaca9394491fc182b4b8fea4094d1d093112a fb6008c8728561b4765db7eba2256fc780c7e007f2cee3294843dbca82a71ffc 01bdad278900935960e2ea9801169cab3152390a7faecd0cf64b41e1ad9d5d5b 69566988b6adb2b034ee462c48cae241cb78d4d7b603970b1ab4a413e65057c2 798558c1bdd601c6d09b54a8de2ea2e08f0c55972c8d0db036359864e01101f8 ff24c3e3dfd82ca0a21a81396ed63ee42a94740ce8bb4d6e19dacc8c4dbe3875 12b9a1702c988780ccef9d7d898e23951fee088be093a18953c6c9b1f5aa8d2f 5bb2b5cd26ffb7b8e47f80ad81dd591c8b3582b01cfeede6 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 1 /Delta put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 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 122 /z put dup 123 /endash put dup 124 /emdash 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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%%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 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 51 /three put dup 52 /four put dup 55 /seven put dup 65 /A put dup 68 /D put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueXX 5000827 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3036f2ed7bb65d cc883aff8d6350d6e8af1a9c1d2d7fcddc4c554c7e350f2420586f43e2124611 487cdb176d453854b51cb8f9100bf241899bbef87d57f1135e589813995c4d86 ce91db2b3757948f365186c2a4f32d845f659a8e95028f9c0168851997135c67 ce7654f2de4f22f51311aa78f440e5fc2c58f6df901fd071b2d53b2697bfcebc 43fe4508828b4756ebbe1f3e8512514162b3bb44493a65f11ab56deaf152fd01 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39bb37d0f544587473daabc62301e132d3ec94ce32e49a7fb5a9d760698e875f 6d1b198f629f82c8864676d4895f00b6482cdbeb3dcebdb6e8437331a84592cf 1d346d9a811c15d7d2e46018302489eccb024358f3c3ea5b3f94f0461484d7ac 4d2d170f0afc846fdf914fe52536e7a55308c802b36f33eb6504c6b9ff8b38b4 98b7b1ec1e5cbc478f8f82e3163a797cf3b04fbb7b9f26b839b301e8e66b4f49 aea434e1eec54db862604188dae073deb33f711acac1e96237c2739e3ebe538c e972c4b474dc9196064c7f8c62cb73ca064b13eca385c5681189823ab9213116 822bc15ca5150a373d302fb26a1e5e7c4bafa47cd77eed916a6dbfcd3cf4bd2d ed89a84daf872477b2cec11bd4486efbaf3ae502dea75e3cc383cab8c9b426ef 07f85e4f6ea0cb060c5de071c5368da081cd5b57c85b5ab992548d3c18677148 507b17eecdfb056551d8baad80e1e56d646d0fadc205d2de4bf088962be7d613 b145eac1272d9a71922b4972abcec8d72aa064218eedc3c82b118ce8d238b9fc 36bf6df395e13c36c9a116c7bd68365bd6c24e578763cf4b0c2d7519c18952d5 cd409ba0277f57eb917e5be229f4e6485d2ee81b1fc37d5ac9b622458fb3f7e0 35301bdbb0c7cdf0a68ae7b5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 69 /E 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 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueXX 5000795 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be356c29c3aec91ef17f5d31183b1e489f1fa 559a6693fbdd04d4f7e99886d8cb7cca13d4aa9ceb34a708af22e69ccef0e504 c3997075243585edf60b6447c8d01cffb04b6e3ddbaa7da5891286861322a795 e9d990fd56af2f5c2b35801a0b07874e4ac3170481d232e150443253c92a8b05 513d4a4154a99d91f629ccd30376500f5d16aaa9b203bad6350e4b19424c0e33 75f2949bc1927a6f6221252f8a96618e646aa1b0810753c98becc26b37837775 24bca72b818d314074c1c91f4e1f4148d3d703d12d179ee6970bd55d04aa9a9d 97f63f2c7dbd129ec2ed3ba5f8080270ea5854ea165dbcc061e2f47f1aaf0997 2ac9a689a2a9620b91b53f6b5092884372f5f7afca495f331138d85a97c5bb83 d8072dc88010fc89108b60bc06d4f93c722e8908d7ce3c1ea3c70e9e65edd769 7db17ce0e012ad37d4030f33d30a73fd655b7a2e572f3378ac933dd75082f2f1 68702be19bc60cef6bd5f0ada180d21408c04b7f7db9b6dbaefe09e809a80ddf a5366d10930d3e68ca53e4721ff525853f4c784f2c2c3aa0129a34d9df00debc ae4037e4c0fbdce3989f35964b4c07e7817b805bfe8c15f0c0ebf226cff606b6 2954f0f42dff8c214a6537ab666d25389c44db7b5866440bbfc137712bcdcc89 c68cd1adfd85648b1ed29bfb45a564b02172137feef782d604e0d7e1f1737c96 719cca9e4b9dfdc87e5999b886a15ac572183dfafd8c4176cd98430c204d4e7c e989e1dea814d3088a21d9ae6c5fe7ab3d399b2982fd605e65509a8ed6790c21 a08a23e53dbe70f676d0e7b2e8261b092dc3415ac785635d133d309ac670c0c5 5868fd863ce42542ff1e83e1fa20a7a0e5d680dec3a22700f7f48d2582b8411d 757d17ab7530ceec0c6727c6a80f2493196b0b36e727bd665d27c9270c12f758 07e56e7190dd93b599443fd7d626998052d0f3c5a5a9de8fd3344f5f28ed0a6d ddc64258bdc11206c7c4888f097e36a8884638cc2414a32632796687b9929027 1cd549813461c5857965886b761467b55a5ed2961a7e2be79c57532a671b93e2 2ec95aec31c30ab2faa9799b10c1544f18a57798a8cee12d9bb244ed38167385 6156fc795c10280720bd18e753f2a3a74e4de29dbf22c2cf58f7daf5254cf27e 3a61a759c77512af95b7626db05efb9de1c139cc022038b1d9285f6238cdace5 6619a02b9214c87d9611588eb589dc689e77c8ab4ff585ca5c9d7e95fed098dd a72788ac8c2e48665fe0df6ce2f5e11179f4a2d7f8235e20ca69ccc7c282adfb 9bd99f6ac60ddc1be8c1da1e384be801c2bac28c36dd3f1ac65a58e61c29474e 68e9d6b9acb50e2557dad8149931b8087f22bb4b34e502aef8eef107f5be0d8f d2e07b5e4c98c86b3b393fd31a6a4eff3e531413d5164dff783bdac0193ea132 afebceb04b1d21439dd1c7bfe12bf9b17f1afb027f7d5b49b570f0f589f1930e 0ea3c419381ebe34d53c9620687c7e03af4a1b1ca09ef7e08080ba35be8f2ef0 10153b20ac601fd8a0abecc8ddcafa17ecc056aa530041990bea820bf42a24ee 296b137842d7f059f4bb9362b997bdea5974482c5e84258184bbd131a37f17eb 6eec6e661c6426f2d0c58319983e6f31b580097617cf7a05516ed66aa9592bbd 2240cdba67c46aedbf59def3c6835f7837e60e4f0feff8194bf55a8d39a05cd9 c8f82da2a5827fe4d4adf9b9dbb4aee6ea9554a59dea85c70520c4774bd1237a 448a057e6a984e87ca9c900dcf1b764c7066aa72cc327a7d97bc457e368dfc96 0b7576c1971e9b6b7ebebf8c4e691d080c8c5999da198b46e142a016264c9886 5e344eb61dc3075b4251d9186125ce5e5077b1f5edf6b3c0df177457dc5d87c0 c4a3f087d5853427322e2ecf1d68d33e6c67f8153f7feadd62e5685150cec690 21b975d70e781291813516ee32cac63e7a8074ef9a3f73a5d1e0ce9af3516c73 48b45bfc415f58f244c8deef4ce558f15315d328893f349c680d600c807e9a7f 18f263b9dab87cf51c67cc197c47224e5c1988b3d741186d53847011edf4167a 2d60324f22b35f453886c2bd935bed05825ffacd577a35bea5b41c43caf79256 f9bb171ae0f2171425a6645fce0083b69b2f595d2d0ba0afd9fd2d4fd05ce20d ce749e5ce2e68f1a1f549d52ea2fe7085fc2ec48021911c5406b73d761763c83 117e781b8eaeff34a9c397e25d2be84fdc3248b8953147ecd0441dac4f891df0 5126b9d064d0036a44927876fe349568b388b96a0374a1871d9d9c046d60b833 899b35e34e02d45b9834de7ec264ef39ab699e6200b8e6bf616c8208779576a4 720ea4eb2bf244c1ef9d614645e41ccb33ffb55ad501429ff40ae6f450d0a7b4 252a37708e7e5389b3d5597c05a87fb4d7865cd58b53f7925cb64c1c779d70ab 2d22c27dd40d2f08191478c56b2deec9d5e4e465c55452954e9842e8029d7869 b9850fea70bbcf40d034c32fc9b6cb753179701f47baefa5ad7dbefcf2c0966d 04277e62d81c0a2d62e6c5769d65f39c17e3aeea739946ec5f203fbcef7d9419 e8dfafda264fc1102bf4b8cc77012d962a2b44ad889dad53f0717e90d0b6c884 371895ebc4a49d4bba3a7726691919f2a8958fedde1594aeb2af17b7ab2b6bc0 ac5fb4b94a301c8da1f5cf683b300f2b8454ba89cc28c272e0aaa7de5a8d6d75 0bf8bbb199c1a22557d687889095b0d1b2cee8d7fd9be7dc1407c51fb6cde9de 48f22abe83d4d13ff3abf52ba7c0bd55771720b661267bd54fa79854d247ff77 8158ed2ef48ac3f0772e469e7c81bf8ad519be6a4f2999cfee6b8b9ff84b053d 0655893f534db1a8085c4ddc30c1757984618100febe220fa403f8209d7a0bf8 5cc5b9dfef4e2d7a83effe6f2f08ffa82c3537e18df4abfd44f95528dabee872 c9dc9655b8ff73801cb62a1ff329986184c6978b398532e359f9ce016c9df4f4 fa151c07b23f50c7026d693f9ac080e51d1822c9af243c1e9b0d6d365262dafc 6d70fd9c9b23400c36d8b30c8611a24a4e4f354d1464532ca2b0c602923e8b8d 198271f8adc4365a850696ea950e2570c7a3b6af6c11ffb897d4765da884e45c 9c38f74979e4b2c3c765d8413fe925d1542f76e61739f4aab7d22c54957be9e6 1294d43eba923e2982808effa6bacdac227b6b2ed73eb6a6aa72cb874c7e5bb3 ba9dea07f04538a38a0c77618fad7f459f05698a758c35c0c1bba50e5a311243 b473a326badf89bd1590fd52b840ec83fcc764692c9cafefa16b4a18aeb3c6a6 60a0e760654f737d9555392f0a7127d16d2c3b79adf20fdf3b5cf9cb76136afb facf9a2028f358d15df1b11ef8aca2bf77c442e4cf01fe6520c9ebb51dd86838 88a576cca1cc5f2ea30a63d9ffe3c149800137e800682ebc0178c45fc098952d e726a2c900be3aefcc9791b5d184df4fb3389cf5caa598178c92ba39f772dfe2 cc488cd874aea1f24fa4f8922b12632977c8158bcfe8bb90884de508cba00bdc 811ec067d3be62da8d711cf3d4941dd044b4b589848b7a39f1dcc9468f96f395 ffdcc7335167b6ffefa752d205dfc00aba7ac2d3fcaf07fc6b8b77030a45f380 b57a4e8ea0f6c839d20c8fdd0787bca48323ee73799f0651033ca69cf0c96add 1e2e1d3d65a5eb469ae03ae9d45999e2edbe84a37a35ff4c987d3d1366aa0a53 16dc3aa32d9b0b46f4f0ed84e092044b80ce38608c51c213e4d2278ca38f4139 a6de464d69c380ed95e5225777143382d62e1a4fb9a99cb47aafaa747614f93a d43e7712115a7771308db5d0d7f3d80e53bebed0bfea06baa7057e122805dc85 48286e0dd008d355953f7912dea58cdb7d32a66b8a83795a99ea33129f8c4c37 fd90a9ab47046682091212e6c3c4aeadfcdcb79d046a256373823f45c6230a0c f698eac5fde612c8f2c9dadc33c6fcd3d22969bd4b2ce9fad5bfbee8a3cd58a1 ff1c0bfc854c69d53e94fc413014d5b7314dddae3229d8cd859f1447faf7afc0 121636130bd0237deeab46ea79267d886ef13806d402b0487c58e5e006c17d21 8005714ac4a270d1b973a97b596909af613f929359bcfe312bfe3ca461b19b01 4cf9ca8ad84427b4ee3ce95c8e5121087e17d771150c4c8e8c854bf5bd256be3 c22292683c5bbd656828b57721b5970b1643081da0062cacdbf25db1b5183da1 f846ad81d061d2fe96173ef8a6c822bc45509a40b857f7591ef6f503a41e0850 a55a16b32aa2efc20523b50e581ac2647e7a862b1f76f85851c600b4c0d49665 583f40729c2683553513a8d0a09b3026f3345dbd15d1316fd95be51fd8cc5f3a 50141c81ffde47062a1b5ebc87ce02b2b8a28510e426d49348eef0fe8fe74c67 2d13c988e72509195fdca6ffd28ce29815ea5392813cca6eeec02e5025ad2b1e ddc14a655daf5655eaf0f35b3422cdf07ac307955588a26bd174b6a24f665ec5 92868a638c9302fd57ad10823ebebd6897d895e9cd59a4ada863bd48fbffb4c1 a157b5c8c256fb23bd1e71242923ad80931c8e7055e3a2f346e8f39b5c0f57bc a5ab078596290535e7d859284e5c217343d2201cd68e16350574d678bd244744 83ac26e2631bd75513fde4dd0058e508faa868675bae34237b4bd51c760c5032 fabdd1b88fb51cfdd72ccb56541dfb0b426c6a19a94ce2f049aa2a1d3a93ee23 87d67609da2930a44dedc652c903064eb35e09193e429cd7d9344af80ba9e85e 3aa00145e058b32157549c143b2cc9559ac552bcb33154fcb3f299220d8ea209 bf2b49b957e671fef87e9555e0e8cf429383a92323d5fd3da61cdb840442b814 d26c791d2d80f08e083b9d4b74e667c1a76a2262303cbab8332a5bd3b6d3928e 8a6d216556446e2525319eb84421645e978a60b0a9d966b19b05ccb83c8f0da1 00656cfb58af9e6b28292f8ae3be68894babf9fd98500029b1b8b56be901bcec dd2079a8bd962241b170dfad644adc9861a2472c4cfc736a246d4a5a31d52e4f 9dcf646d48aed0e9c2730f0ca7fd1c42e9a9da2112e8b5541bf7aaa9343d68c2 f9417d0bb81375e96c0d349834ca539b7a430598c146e160c2c025a3ff8d0bf2 07f56d6b6d9dcdc37d9b501de309c2ee3f983e1f65ca7a6f4c0bd7aa87104acc f77b2f2fa1f8c2b20c5b3a8c1f2afea6d78eb4766740c003a84799711d04a492 8a911c964762ce23fe05ebd006486fa58ec0b4689d38ed4c9ab58c0176b8ec62 72672f60857a0d4fbe3ac51061062141d2cb72f1593e70676dbfd3385caa0e9a 3a86813b95fca2a236a805a1e4850b85ee4a3603a1835c62558a0724e448ced9 e0ac99c2c281351a1450a46fd4853317b19525d02d81cd3edecc9387ddec5320 5c19c427ffed681b36ff8cd7ce93d7d07ae15bc7b5cc4937240f6e01ffde6dc3 94875766132a3c70bfdc516f485d01f710370f795c60bf1f113bcfc6a5c5ccc6 5c55b2747aa05eaacada1de25491e5633da4cdb16b5a7324e3d5239cc5aee15e 5c53deed3b9d592c257482fb25f6b383cbdcdb248e8037fa803b9a651f2d1fc0 766a284b9ef19e4df9248921df014a6a745012a388cd11349c7d303a4484b5c4 2660e111480b7e2a103860e562dc2fa7e4885865bda87d7538d59e90ee89082b 6b3dc841ac2c23a0a78c6aa8983ba57f8b7500845886453920da474b11177bcb 2a1032edcaa67da9fe6846aeef5794aed45b4f1d3fa4d38cdd87893d700754ca d0ead9658e8fe5ebe192f7ca09b380e8eb939253677982d0da04ab3d921b09ab ae6c5bff313f963c30a73afe35d92d403af5815cafebf8db03a65a57fff12d45 a9c164e52e8822c287897d1b71b3221306db346918a116d2f42ad55a66337bdb e897a778459b08544867a38a92600eb4abfbadc65f888ab8728c24174f171358 114949 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 14 /ffi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 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 63 /question put dup 64 /at put dup 65 /A put dup 66 /B put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W 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 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 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Fh(\025)g Fj(x)p Fh(g)1212 b(8)p Fj(t)336 b Fh(\025)h Fo(0)p Fj(:)-583 29758 y Fk(De\014nition)466 b(2.2.)606 b Fo(Sto)34 b(c)-34 b(hastic)379 b(pro)34 b(cess)377 b Fj(X)95 b Fo(\()p Fj(t)p Fo(\),)384 b Fj(t)336 b Fc(>)g Fo(0)378 b(de\014ned)h(on)f(the)g(measurable)g(space)-583 30230 y Fd(\020)78 31485 y Fk(X)p Fj(;)202 b Fh(B)2504 30562 y Fd(\000)3011 31485 y Fk(X)4065 30562 y Fd(\001)4572 30230 y(\021)5792 31485 y Fo(is)558 b(ergo)34 b(dic)558 b(i\013)g(for)h(all)f Fj(B)655 b Fh(2)595 b(B)20792 30562 y Fd(\000)21299 31485 y Fk(X)22353 30562 y Fd(\001)23419 31485 y Fo(and)560 b(all)e(its)g(initial)h(v)-67 b(alues)558 b Fj(X)95 b Fo(\(0\))559 b(the)-583 33212 y(follo)-34 b(wing)357 b(is)g(true:)784 b(lim)8669 33941 y Fi(t)p Fg(!1)11093 33212 y Fj(P)168 b Fh(f)p Fj(X)95 b Fo(\()p Fj(t)p Fo(\))338 b Fh(2)f Fj(B)61 b Fh(g)337 b Fo(=)f Fj(\026)p Fo(\()p Fj(B)61 b Fo(\))p Fj(;)358 b Fo(where)f Fj(\026)p Fo(\()p Fh(\001)p Fo(\))h(is)f(a)g(probabilit)-34 b(y)357 b(measure.)-583 37046 y Fk(De\014nition)466 b(2.3.)606 b Fo(Probabilit)-34 b(y)450 b(measure)g Fj(\026)p Fo(\()p Fh(\001)p Fo(\))h(on)f Fb(R)24930 37228 y Ff(+)26168 37046 y Fo(is)g(called)f(a)h(lattice)f(distribution)-583 38773 y(i\013)408 b(it)g(it)g(concen)-34 b(trated)409 b(in)g(the)f(no)34 b(des)409 b(of)f(a)h(lattice)f(with)h(step)f Fj(h)344 b(>)g Fo(0,)409 b(i.)550 b(e.)h(in)408 b(the)h(p)34 b(oin)-34 b(ts)-583 40499 y Fj(x)110 40681 y Fi(j)933 40499 y Fo(=)336 b Fj(x)2905 40681 y Ff(0)3700 40499 y Fo(+)269 b Fj(j)69 b(h;)1011 b(x)8219 40681 y Ff(0)9081 40499 y Fh(\025)337 b Fo(0)p Fj(;)1010 b Fh(8)p Fj(j)406 b Fh(2)337 b Fb(N)p Fj(:)2073 44201 y Fo(Later)586 b(on)g(supp)34 b(ose)587 b(that)h(the)e(random)h(v)-67 b(ariables)585 b Fj(\034)27561 44383 y Fi(i)28522 44201 y Fo(are)h(not)h(distributed)g (on)g(a)-583 45927 y(lattice)445 b(for)i(all)e Fj(i)406 b Fh(2)h Fb(N)p Fo(.)665 b(Let)446 b(us)g(denote)h(b)-34 b(y)20392 45261 y Fi(D)20185 45927 y Fh(!)446 b Fo(the)h(con)-34 b(v)g(ergence)446 b(in)g(distribution)h(\(w)-34 b(eak)-583 47654 y(con)g(v)g(ergence\).)1131 b(Let)602 b Fj(\020)10556 47836 y Fi(n)11784 47654 y Fo(b)34 b(e)601 b(the)i(instan)-34 b(t)603 b(of)f(time)g(when)h(the)f Fj(n)p Fo({th)g(customer)g(lea)-34 b(v)g(es)-583 49534 y(the)448 b(system,)460 b Fj(D)34 b Fo(\()p Fj(t)p Fo(\))8789 48794 y Fi(def)9053 49534 y Fo(=)674 b(max)201 b Fh(f)p Fj(n)337 b Fo(:)f Fj(\020)16001 49716 y Fi(n)16964 49534 y Fh(\024)h Fj(t)p Fh(g)p Fo(.)671 b(Denote)448 b(b)-34 b(y)449 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\))450 b(the)e(n)-34 b(um)g(b)34 b(er)450 b(of)f(customers)-583 51260 y(presen)-34 b(t)404 b(in)h(the)f(system)g(at)h(time)f Fj(t)p Fo(.)538 b(Let)11425 55312 y Fj(N)132 b Fo(\()p Fj(t)p Fo(\))338 b(=)e(max)202 b Fh(f)p Fj(n)336 b Fo(:)h Fj(\034)20860 55494 y Ff(1)21655 55312 y Fo(+)269 b Fj(:)202 b(:)g(:)268 b Fo(+)h Fj(\034)26292 55494 y Fi(n)27255 55312 y Fj(<)337 b(t)p Fh(g)o Fj(:)-583 59365 y Fo(Supp)34 b(ose)353 b Fj(q)43 b Fo(\(0\))6589 58698 y Fi(a:s:)6847 59365 y Fo(=)593 b(0)p Fj(:)352 b Fo(W)-101 b(e)352 b(shall)g(sa)-34 b(y)353 b(that)g(the)g(serv)-34 b(er)351 b(completed)i(the)f Fe(cycle)737 b Fo(of)352 b(mo)-34 b(ving)353 b(if)-583 61091 y(he)j(visited)h(\(at)g(least)f(once\))h(all)f(p)34 b(oin)-34 b(ts)358 b(of)f(the)g(circle)e(and)i(then)h(returned)f(to)g (0.)522 b(Th)-34 b(us)358 b(the)-583 62818 y(duration)447 b(of)f(the)g Fj(n)p Fo({th)h(cycle)d(is)i(a)g(random)g(v)-67 b(ariable)445 b Fj(T)25993 63000 y Fi(n)26620 62818 y Fo(,)456 b Fj(T)28121 63000 y Ff(1)29053 62818 y Fo(=)406 b(inf)95 b Fh(f)p Fj(k)445 b Fo(:)608 b Fh(j)p Fj(\032)35468 63015 y Fi(k)36036 62818 y Fh(j)406 b Fj(>)g Fo(1)p Fh(g)p Fo(.)664 b(All)-583 64545 y Fj(T)125 64727 y Fi(n)1165 64545 y Fo(are)414 b(indep)34 b(enden)-34 b(t)415 b(and)g(iden)-34 b(tically)414 b(distributed.)569 b(Let)414 b(us)g(denote)h(b)-34 b(y)414 b Fj(\032)p Fo(\()p Fj(t)p Fo(\))g(the)h(whole)-583 66272 y(distance)404 b(co)-34 b(v)g(ered)404 b(b)-34 b(y)404 b(the)h(serv)-34 b(er)403 b(up)i(to)g(a)f(momen)-34 b(t)405 b Fj(t)p Fo(.)p eop %%Page: 4 4 4 3 bop 2729 2295 a Fq(4)11422 b Fn(E.)365 b(Sp)-52 b(o)g(dar)g(ev)366 b(/)f(A)h(c)-52 b(ontinuous)365 b(p)-52 b(ol)52 b(ling)367 b(mo)-52 b(del)2729 5647 y Fk(3.)1573 b(Necessary)463 b(and)i(su\016cien)-39 b(t)465 b(conditions)g(of)g(ergo)39 b(dicit)-39 b(y)5386 8679 y Fo(Here)495 b(w)-34 b(e)497 b(shall)f(\014nd)h(the)f(conditions)i(under)e(whic)-34 b(h)497 b(the)g(pro)34 b(cess)495 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\))498 b(is)d(ergo)34 b(dic.)2729 10406 y(First)404 b(let)g(us)h(sho)-34 b(w)405 b(that)g(the)g(mean)f(cycle)f(duration)i (is)f(\014nite:)2729 13659 y Fk(Lemma)464 b(3.1.)606 b Fo(F)-101 b(or)409 b(all)g Fj(p)345 b(>)g Fo(0,)411 b Fj(q)389 b(>)345 b Fo(0)409 b(\()p Fj(p)346 b Fh(6)p Fo(=)f Fj(q)43 b Fo(,)411 b Fj(p)272 b Fo(+)h Fj(q)389 b Fo(=)345 b(1\),)411 b(and)f Fj(n)345 b Fh(2)g Fb(N)410 b Fo(the)f(follo)-34 b(wing)410 b(is)2729 15386 y(true:)21150 17920 y Fj(E)271 b(T)23024 18102 y Fi(n)23987 17920 y Fj(<)337 b Fh(1)p Fj(:)2729 21174 y Fe(Pr)-62 b(o)g(of.)1211 b Fo(W)-101 b(e)432 b(supp)34 b(ose)434 b Fj(p)385 b(>)g(q)476 b Fo(without)435 b(loss)e(of)g(generalit)-34 b(y)-101 b(.)625 b(Denote)433 b(\001)p Fj(\032)37333 21356 y Fi(n)38344 21174 y Fo(=)384 b Fj(\032)40298 21356 y Fi(n)41213 21174 y Fh(\000)288 b Fj(\032)43071 21356 y Fi(n)p Fg(\000)p Ff(1)44900 21174 y Fo(.)2729 22901 y(Then)715 b(one)f(gets)g(from)h(W) -101 b(ald's)713 b(equalit)-34 b(y)714 b(for)g(random)h(w)-34 b(alks)714 b(that)i Fj(E)271 b Fo(\001)p Fj(\032)40211 23083 y Ff(1)40939 22901 y Fj(E)h(T)42814 23083 y Fi(n)44294 22901 y Fo(=)2729 24628 y Fj(E)g(\032)p Fo(\()p Fj(T)5702 24810 y Fi(n)6328 24628 y Fo(\))607 b Fh(8)p Fj(n)336 b Fh(2)h Fb(N)p Fo(.)539 b(If)404 b Fj(p)337 b(>)f(q)448 b Fo(then)405 b Fj(E)271 b Fo(\001)p Fj(\032)22030 24810 y Ff(1)22893 24628 y Fj(>)336 b Fo(0,)404 b(whic)-34 b(h)405 b(implies)17164 27625 y Fj(E)271 b(T)19038 27807 y Fi(n)20001 27625 y Fh(\024)337 b Fo(1)269 b(+)25200 26805 y(1)p 23501 27345 4003 45 v 23501 28457 a Fh(j)p Fj(E)j Fo(\001)p Fj(\032)26642 28639 y Ff(1)27167 28457 y Fh(j)27973 27625 y Fj(<)337 b Fh(1)p Fj(:)44294 30672 y Fc(\003)2729 33925 y Fk(Lemma)464 b(3.2.)606 b Fo(If)404 b(pro)34 b(cess)404 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\))405 b(is)f(ergo)34 b(dic)403 b(then)i Fj(\025a)336 b(<)h Fo(1.)2729 37179 y Fe(Pr)-62 b(o)g(of.)1211 b Fo(Supp)34 b(ose)445 b(the)f(con)-34 b(trary)444 b(tak)-34 b(es)444 b(place:)617 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\))445 b(is)e(ergo)34 b(dic)443 b(and)h Fj(\025a)403 b Fc(>)f Fo(1.)657 b(Then)445 b(b)-34 b(y)2729 38906 y(the)405 b(existence)e(of)h(the)h(limiting)f (stationary)g(distribution)17686 41144 y Fj(D)34 b Fo(\()p Fj(t)p Fo(\))p 17652 41683 2487 45 v 17652 42796 a Fj(N)132 b Fo(\()p Fj(t)p Fo(\))20839 41298 y Fi(a:s:)20608 41964 y Fh(\000)-236 b(!)337 b Fo(1)808 b(as)1212 b Fj(t)337 b Fh(!)f(1)p Fj(:)2729 45762 y Fo(The)405 b(total)g(distance)f(up)h(to) g(the)g(momen)-34 b(t)405 b Fj(\020)23368 45944 y Fi(n)24399 45762 y Fo(is)f Fj(\032)p Fo(\()p Fj(\020)27246 45944 y Fi(n)27873 45762 y Fo(\))337 b(=)g(\()p Fj(\020)30962 45944 y Fi(n)31858 45762 y Fh(\000)33546 44684 y Fi(n)33247 44906 y Fd(P)33070 46782 y Fi(i)p Ff(=1)34795 45762 y Fj(a)35436 45944 y Fi(i)35811 45762 y Fo(\))p Fj(v)43 b(:)405 b Fo(Since)f Fj(D)34 b Fo(\()p Fj(\020)42859 45944 y Fi(n)43485 45762 y Fo(\))338 b Fh(\030)2729 47913 y Fj(N)132 b Fo(\()p Fj(\020)4836 48095 y Fi(n)5463 47913 y Fo(\))428 b(as)h Fj(n)376 b Fh(!)h(1)p Fj(;)427 b(D)34 b Fo(\()p Fj(\020)14583 48095 y Fi(n)15209 47913 y Fo(\))377 b(=)g Fj(n)427 b Fo(then)i(b)-34 b(y)429 b(the)f(la)-34 b(w)429 b(of)f(large)g(n)-34 b(um)g(b)34 b(ers)429 b(the)f(distance)h (p)34 b(er)2729 49640 y(unit)405 b(time)f(is)8811 53072 y Fj(\032)p Fo(\()p Fj(\020)10439 53254 y Fi(n)11065 53072 y Fo(\))p 8811 53611 2727 45 v 9596 54724 a Fj(\020)10126 54906 y Fi(n)12006 53892 y Fh(\030)13286 50977 y Fd(0)13286 52925 y(B)13286 53589 y(B)13286 54298 y(@)14254 53892 y Fo(1)270 b Fh(\000)16475 53072 y Fj(N)132 b Fo(\()p Fj(\020)18582 53254 y Fi(n)19209 53072 y Fo(\))p 16475 53611 3206 45 v 17499 54724 a Fj(\020)18029 54906 y Fi(n)20422 51225 y(n)20123 51447 y Fd(P)19946 53324 y Fi(i)p Ff(=1)21670 52303 y Fj(a)22311 52485 y Fi(i)p 19946 53611 2742 45 v 20953 54724 a Fj(n)22820 50977 y Fd(1)22820 52925 y(C)22820 53589 y(C)22820 54298 y(A)23990 53892 y Fj(v)25189 53226 y Fi(a:s:)24958 53892 y Fh(\000)-236 b(!)337 b Fo(\(1)270 b Fh(\000)f Fj(\025a)p Fo(\))202 b Fj(v)851 b Fo(as)808 b Fj(n)337 b Fh(!)g(1)p Fj(:)2729 58181 y Fo(Then)405 b(b)-34 b(y)405 b(Leb)34 b(esgue)403 b(theorem)12857 61240 y Fj(E)14157 60420 y(\032)p Fo(\()p Fj(\020)15785 60602 y Fi(n)16411 60420 y Fo(\))p 14157 60959 2727 45 v 14941 62071 a Fj(\020)15471 62253 y Fi(n)17352 61240 y Fh(\000)-236 b(!)337 b Fo(\(1)270 b Fh(\000)f Fj(\025a)p Fo(\))p Fj(\013)24765 60739 y Fg(\000)p Ff(1)26360 61240 y Fh(\024)337 b Fo(0)808 b(as)g Fj(n)336 b Fh(!)h(1)p Fj(;)2729 64242 y Fo(th)-34 b(us)352 b(w)-34 b(e)350 b(ha)-34 b(v)g(e)351 b(arriv)-34 b(ed)349 b(at)i(the)f(con)-34 b(tradiction,)362 b(since)349 b(in)i(ergo)34 b(dic)349 b(case)g(the)i(mean)f(v)-34 b(elo)34 b(cit)-34 b(y)2729 65969 y(of)404 b(the)h(serv)-34 b(er)403 b Fj(\032)p Fo(\(\001)p Fj(t)p Fo(\))p Fj(=)p Fo(\001)p Fj(t)h Fo(in)h(an)f(in)-34 b(terv)-67 b(al)403 b(\001)p Fj(t)h Fo(should)h(b)34 b(e)404 b(p)34 b(ositiv)-34 b(e.)9864 b Fc(\003)p eop %%Page: 5 5 5 4 bop 11351 2295 a Fn(E.)365 b(Sp)-52 b(o)g(dar)g(ev)365 b(/)h(A)g(c)-52 b(ontinuous)365 b(p)-52 b(ol)52 b(ling)366 b(mo)-52 b(del)11423 b Fq(5)-583 5647 y Fk(Theorem)464 b(3.3.)606 b Fo(Let)410 b Fh(f)p Fj(\034)11424 5829 y Fi(i)11800 5647 y Fh(g)12406 5207 y Fg(1)12406 5969 y Fi(i)p Ff(=1)13984 5647 y Fj(;)g Fh(f)p Fj(a)15978 5829 y Fi(i)16354 5647 y Fh(g)16960 5207 y Fg(1)16960 5969 y Fi(i)p Ff(=1)18948 5647 y Fo(b)34 b(e)411 b(the)g(sequences)f(of)h (indep)34 b(enden)-34 b(t)412 b(iden)-34 b(tically)-583 7373 y(distributed)413 b(random)f(v)-67 b(ariables)411 b(with)h Fj(E)70 b(a)19494 7555 y Fi(i)20219 7373 y Fo(=)349 b Fj(a)p Fo(,)413 b Fj(E)70 b(\034)24397 7555 y Fi(i)25122 7373 y Fo(=)349 b(1)p Fj(=\025)p Fo(.)561 b(Then)413 b(the)f(pro)34 b(cess)411 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\))413 b(is)-583 9100 y(ergo)34 b(dic)403 b(i\013)h Fj(\025a)336 b(<)h Fo(1.)-583 12315 y Fe(Pr)-62 b(o)g(of.)1211 b Fo(By)389 b(lemma)g(3.2)h(the)g(necessit)-34 b(y)390 b(is)f(pro)-34 b(v)g(ed.)534 b(Let)390 b(us)g(pro)-34 b(v)g(e)390 b(the)g(su\016ciency)-101 b(.)534 b(Sup-)-583 14042 y(p)34 b(ose)542 b Fj(q)43 b Fo(\(0\))4989 13376 y Fi(a:s:)5246 14042 y Fo(=)824 b(0.)952 b(First)543 b(w)-34 b(e)542 b(sho)-34 b(w)543 b(that)h Fj(q)43 b Fo(\()p Fj(t)p Fo(\))543 b(is)e(a)i(regenerativ)-34 b(e)541 b(pro)34 b(cess)541 b(\(see)h([1],)576 b(p.)-583 15769 y(87{90\).)805 b(Indeed,)515 b(when)494 b(the)g(next)f(customer)g(en) -34 b(ters)493 b(the)h(empt)-34 b(y)493 b(system,)515 b(the)494 b(past)f(of)-583 17496 y(the)400 b(pro)34 b(cess)399 b(is)h(erased,)g(b)34 b(ecause)399 b(one)h(can)g(supp)34 b(ose)401 b(without)g(loss)f(of)g(generalit)-34 b(y)399 b(that)i(at)-583 19412 y(this)396 b(instan)-34 b(t)398 b(the)f(serv)-34 b(er)395 b(is)i(placed)f(at)g(the)h(p)34 b(oin)-34 b(t)397 b(0.)536 b(Let)396 b Fj(c)27285 19594 y Fi(n)28248 19412 y Fo(=)30003 18334 y Fi(n)29704 18556 y Fd(P)29527 20433 y Fi(i)p Ff(=1)31252 19412 y Fj(\034)31782 19594 y Fi(i)32553 19412 y Fo(b)34 b(e)396 b(the)h(momen)-34 b(t)397 b(of)-583 21496 y(arriv)-67 b(al)319 b(of)i(the)h Fj(n)p Fo({th)f(service)e(request)i(to)h(the)f(system.)511 b(Let)321 b(us)g(\014x)g(regeneration)g(momen)-34 b(ts)3525 24089 y Fj(\037)4283 24271 y Ff(1)5146 24089 y Fo(=)336 b Fj(c)6950 24271 y Ff(1)7476 24089 y Fj(;)1009 b(\037)9580 24271 y Fi(n)10544 24089 y Fo(=)336 b(inf)95 b Fh(f)p Fj(c)14429 24271 y Fi(i)15141 24089 y Fj(>)337 b(\037)17179 24271 y Fi(n)p Fg(\000)p Ff(1)19007 24089 y Fj(;)606 b(i)337 b Fh(2)f Fb(N)h Fo(:)741 b Fj(q)43 b Fo(\()p Fj(c)25719 24271 y Fi(i)26364 24089 y Fh(\000)270 b Fo(0\))337 b(=)f(0)p Fj(;)1010 b(q)43 b Fo(\()p Fj(c)33803 24271 y Fi(i)34179 24089 y Fo(\))337 b Fj(>)g Fo(0)p Fh(g)p Fj(:)-583 26683 y Fo(Then)331 b(the)g Fj(n)p Fo({th)g(regeneration)f (cycle)f(is)h Fj(\022)18837 26865 y Fi(n)19800 26683 y Fo(=)337 b Fj(\037)21838 26865 y Fi(n)p Ff(+1)23789 26683 y Fh(\000)122 b Fj(\037)25612 26865 y Fi(n)26238 26683 y Fj(;)863 b(n)336 b Fh(\025)h Fo(1)p Fj(:)330 b Fo(Supp)34 b(ose)331 b Fj(\025a)337 b(<)f Fo(1.)514 b(Let)-583 28410 y(us)453 b(pro)-34 b(v)g(e)454 b(that)g Fj(q)43 b Fo(\()p Fj(t)p Fo(\))455 b(is)e(ergo)34 b(dic.)685 b(By)453 b(means)g(of)h(Smith's)g(theorem)f(\(cf.)687 b([1],)465 b(p.)453 b(92\))h Fj(q)43 b Fo(\()p Fj(t)p Fo(\))-583 30137 y(is)411 b(ergo)34 b(dic)411 b(if)h(it)g(is)g(ap)34 b(erio)g(dic,)412 b(i.e.)561 b(the)413 b(distribution)g(of)f Fj(\022)26812 30319 y Fi(i)27600 30137 y Fo(is)f(not)i(a)f(lattice)g (distribution)-583 31864 y(for)451 b(all)f Fj(i)414 b Fh(2)h Fb(N)p Fo(,)463 b(and)452 b Fj(E)70 b(\022)10717 32046 y Fi(i)11507 31864 y Fj(<)414 b Fh(1)p Fo(.)679 b(The)452 b(ap)34 b(erio)g(dicit)-34 b(y)450 b(of)h Fj(q)43 b Fo(\()p Fj(t)p Fo(\))452 b(follo)-34 b(ws)452 b(from)f(the)g(fact)h (that)-583 33591 y(the)442 b(input)i(stream)f Fh(f)p Fj(\034)9971 33773 y Fi(i)10346 33591 y Fh(g)10952 33151 y Fg(1)10952 33913 y Fi(i)p Ff(=1)12973 33591 y Fo(is)f(not)h (concetrated)g(on)f(a)h(lattice.)653 b(Let)442 b(us)h(sho)-34 b(w)443 b(then)h(that)-583 35317 y Fj(E)70 b(\022)951 35499 y Fi(i)1780 35317 y Fj(<)453 b Fh(1)475 b Fo(for)f(ev)-34 b(ery)473 b Fj(i)454 b Fh(2)g Fb(N)p Fo(.)749 b(Since)474 b(all)g Fj(\022)19713 35499 y Fi(i)20563 35317 y Fo(ha)-34 b(v)g(e)475 b(the)g(same)f(distribution)i(it)e(su\016ces)g(to)-583 37044 y(sho)-34 b(w)405 b(that)g(for)f Fj(i)337 b Fo(=)f(1.)2073 38771 y(Besides)290 b(the)h(system)g Fk(S)g Fo(describ)34 b(ed)290 b(in)h(section)f(2)h(in)-34 b(tro)34 b(duce)291 b(another)g(system)g Fk(S)38885 38331 y Fg(\003)39702 38771 y Fo(that)-583 40498 y(di\013ers)472 b(from)h Fk(S)g Fo(only)g(b)-34 b(y)473 b(the)g(fact)g(that)h(the)f(sev)-34 b(er)472 b(in)h(it)g(serv)-34 b(es)472 b(only)g(those)i(customers)-583 42225 y(that)405 b(arriv)-34 b(ed)404 b(to)h Fk(S)8414 41785 y Fg(\003)9344 42225 y Fo(during)g(the)g(last)g(cycle)e(.)539 b(It)404 b(is)g(supp)34 b(osed)406 b(that)g(the)e(serv)-34 b(er)404 b(do)34 b(es)404 b(not)-583 43952 y(p)34 b(erform)425 b(service)f(during)i(its)g(\014rst)g(cycle)e(in)i Fk(S)21321 43512 y Fg(\003)21847 43952 y Fo(.)603 b(Let)425 b Fj(X)25984 44134 y Fi(n)27036 43952 y Fo(b)34 b(e)426 b(the)g(n)-34 b(um)g(b)34 b(er)427 b(of)f(customers)-583 45679 y(in)d Fk(S)1624 45239 y Fg(\003)2573 45679 y Fo(at)g(the)h(end)f(of)h(the)f Fj(n)p Fo({th)h(cycle.)594 b(Then)424 b Fh(f)p Fj(X)23215 45861 y Fi(n)23841 45679 y Fh(g)24447 45120 y Fg(1)24447 46037 y Fi(n)p Ff(=1)26699 45679 y Fo(is)e(an)i(ap)34 b(erio)g(dic)422 b(homogeneous)-583 47405 y(Mark)-34 b(o)g(v)516 b(c)-34 b(hain.)877 b(This)517 b(means,)545 b(in)517 b(particular,)544 b(that)518 b Fh(f)p Fj(X)26968 47587 y Fi(n)27595 47405 y Fh(g)28201 46847 y Fg(1)28201 47764 y Fi(n)p Ff(=1)30546 47405 y Fo(is)e(regenerativ)-34 b(e,)544 b(while)-583 49132 y(the)501 b(momen)-34 b(ts)502 b(when)f(it)g(equals)f(to)h(0)g(are)f(its)h(regeneration)f(p)34 b(oin)-34 b(ts.)829 b(Let)501 b Fj(q)36087 48692 y Fg(\003)36613 49132 y Fo(\()p Fj(t)p Fo(\))g(b)34 b(e)500 b(the)-583 50859 y(n)-34 b(um)g(b)34 b(er)394 b(of)g(customers)f(in)g Fk(S)13029 50419 y Fg(\003)13949 50859 y Fo(at)g(the)h(momen)-34 b(t)394 b Fj(t)p Fo(,)h Fj(\022)23938 50419 y Fg(\003)23904 51167 y Ff(1)24857 50859 y Fo(|)e(the)h(\014rst)g(regeneration)f(cycle) e(of)-583 52586 y Fh(f)p Fj(X)1027 52768 y Fi(n)1653 52586 y Fh(g)2259 52027 y Fg(1)2259 52944 y Fi(n)p Ff(=1)4088 52586 y Fo(.)538 b(If)404 b(one)h(can)f(pro)-34 b(v)g(e)404 b(that)18167 55180 y Fj(\022)18736 55362 y Ff(1)19599 55180 y Fh(\024)20542 55362 y Fi(st)21708 55180 y Fj(\022)22311 54679 y Fg(\003)22277 55479 y Ff(1)22837 55180 y Fj(;)16258 b Fo(\(3.1\))18210 58542 y Fj(E)70 b(\022)19778 58042 y Fg(\003)19744 58842 y Ff(1)20639 58542 y Fj(<)337 b Fh(1)16301 b Fo(\(3.2\))-583 61037 y(then)456 b(w)-34 b(e)456 b(are)f(done.)693 b(Let)455 b(us)h(pro)-34 b(v)g(e)455 b(that)i(\(3.1\))f(holds.)693 b(W)-101 b(e)455 b(shall)g(sho)-34 b(w)457 b(that)f(the)g(c)-34 b(hain)-583 62764 y Fh(f)p Fj(X)1027 62946 y Fi(n)1653 62764 y Fh(g)2259 62206 y Fg(1)2259 63123 y Fi(n)p Ff(=1)4492 62764 y Fo(is)404 b(ergo)34 b(dic,)403 b(i.e.)537 b(that)405 b(there)f(exists)9025 65701 y(lim)8640 66366 y Fi(n)p Fg(!1)11295 65701 y Fj(P)168 b Fh(f)p Fj(X)13851 65883 y Fi(n)14815 65701 y Fo(=)336 b Fj(i)202 b Fh(j)p Fj(X)18055 65883 y Ff(0)18917 65701 y Fo(=)337 b(0)p Fh(g)g Fo(=)23388 64881 y(1)p 23158 65421 1067 45 v 23158 66533 a Fj(\031)23849 66715 y Fi(i)24694 65701 y Fj(>)g Fo(0)1616 b Fh(8)p Fj(i)336 b Fh(2)h Fb(Z)31576 65883 y Ff(+)32364 65701 y Fj(:)p eop %%Page: 6 6 6 5 bop 2729 2295 a Fq(6)11422 b Fn(E.)365 b(Sp)-52 b(o)g(dar)g(ev)366 b(/)f(A)h(c)-52 b(ontinuous)365 b(p)-52 b(ol)52 b(ling)367 b(mo)-52 b(del)2729 5647 y Fo(Supp)34 b(ose)405 b(the)f(con)-34 b(trary)404 b(is)g(true:)923 b(lim)18677 6311 y Fi(n)p Fg(!1)21332 5647 y Fj(P)168 b Fh(f)p Fj(X)23888 5829 y Fi(n)24852 5647 y Fo(=)336 b Fj(i)202 b Fh(j)p Fj(X)28092 5829 y Ff(0)28954 5647 y Fo(=)337 b(0)p Fh(g)g Fo(=)f(0)404 b(\(only)g(these)g(t)-34 b(w)g(o)406 b(cases)2729 7373 y(are)e(p)34 b(ossible)404 b(|)g(cf.)538 b([13],)403 b(p.)539 b(47\).)g(This)405 b(means)f(that)13844 9967 y Fj(P)168 b Fh(f)p Fj(X)16400 10149 y Fi(n)17364 9967 y Fj(>)336 b(y)43 b Fh(g)338 b(!)f Fo(1)808 b(as)1212 b Fj(n)336 b Fh(!)h(1)808 b(8)p Fj(y)381 b Fh(2)337 b Fb(N)p Fj(;)8624 b Fo(\(3.3\))2729 12561 y(or)499 b(in)g(other)g (terms,)522 b Fj(X)13917 12743 y Fi(n)15281 11895 y(P)15039 12561 y Fh(!)494 b(1)500 b Fo(as)f Fj(n)494 b Fh(!)h(1)p Fj(:)k Fo(Eviden)-34 b(tly)-101 b(,)522 b Fj(X)31880 12743 y Fi(n)p Ff(+1)34203 12561 y Fo(=)495 b Fj(\030)56 b Fo(\()p Fj(X)37702 12743 y Fi(n)38329 12561 y Fo(\))333 b(+)f Fj(\021)41010 12743 y Fi(n)42135 12561 y Fo(where)2729 14288 y Fj(\030)56 b Fo(\()p Fj(X)4790 14470 y Fi(n)5417 14288 y Fo(\))511 b(is)f(the)h(n)-34 b(um)g(b)34 b(er)512 b(of)e(customers)h(that)h(en)-34 b(tered)511 b Fk(S)29598 13848 y Fg(\003)30635 14288 y Fo(during)g(the)g Fj(n)p Fo({th)g(cycle.)856 b(W)-101 b(e)2729 16015 y(ha)-34 b(v)g(e)405 b Fj(E)70 b(\021)7091 16197 y Fi(n)8053 16015 y Fo(=)337 b Fj(\025\013)t(;)404 b(E)272 b Fo(\()p Fj(\030)56 b Fo(\()p Fj(X)15259 16197 y Fi(n)15886 16015 y Fo(\))202 b Fh(j)g Fj(X)18102 16197 y Fi(n)18729 16015 y Fo(\))337 b(=)f Fj(\025aX)23168 16197 y Fi(n)24199 16015 y Fo(for)404 b(su\016cien)-34 b(tly)404 b(large)g Fj(n)p Fo(.)537 b(Then)13406 18609 y Fj(E)70 b Fo(\()p Fj(X)15846 18791 y Fi(n)p Ff(+1)17944 18609 y Fh(\000)269 b Fj(X)20160 18791 y Fi(n)20989 18609 y Fh(j)202 b Fj(X)22532 18791 y Fi(n)23158 18609 y Fo(\))337 b(=)g(\()p Fj(\025a)269 b Fh(\000)g Fo(1\))p Fj(X)30627 18791 y Fi(n)31523 18609 y Fo(+)h Fj(\025\013)t(;)2729 21202 y Fo(hence)523 b Fj(E)70 b Fo(\()p Fj(X)8655 21384 y Fi(n)p Ff(+1)10832 21202 y Fh(\000)348 b Fj(X)13127 21384 y Fi(n)13754 21202 y Fo(\))535 b Fj(<)f Fo(0)523 b(if)f Fj(X)19599 21384 y Fi(n)20749 21202 y Fo(is)g(large)g(enough,)553 b(whic)-34 b(h)524 b(con)-34 b(tradicts)524 b Fj(X)40780 21384 y Fi(n)42183 20536 y(P)41941 21202 y Fh(!)534 b(1)p Fj(:)2729 22929 y Fo(Then)405 b(the)g(Mark)-34 b(o)g(v)404 b(c)-34 b(hain)404 b Fh(f)p Fj(X)17204 23111 y Fi(n)17831 22929 y Fh(g)18437 22371 y Fg(1)18437 23288 y Fi(n)p Ff(=1)20670 22929 y Fo(is)f(ergo)34 b(dic,)403 b(and)i(\(3.2\))g(is)f(pro)-34 b(v)g(ed.)5386 24656 y(Let)388 b(us)g(sho)-34 b(w)390 b(no)-34 b(w)390 b(that)f(\(3.1\))g(holds.)534 b(Let)388 b Fj(t)26301 24838 y Fi(n)27315 24656 y Fo(\()p Fj(t)28224 24216 y Fg(\003)28224 24956 y Fi(n)28850 24656 y Fo(\))h(b)34 b(e)388 b(the)h(momen)-34 b(t)389 b(of)g(completion)2729 26383 y(of)404 b(the)h Fj(n)p Fo({th)f(cycle)f(in)h Fk(S)h Fo(\()p Fk(S)15914 25943 y Fg(\003)16440 26383 y Fo(\))q(,)13231 28977 y Fj(T)13939 29159 y Fi(n)14902 28977 y Fo(=)337 b Fj(t)16620 29159 y Fi(n)17515 28977 y Fh(\000)269 b Fj(t)19165 29159 y Fi(n)p Fg(\000)p Ff(1)20993 28977 y Fj(;)1010 b(t)22778 28476 y Fg(\003)22778 29276 y Fi(n)23741 28977 y Fo(=)336 b Fj(t)25458 28476 y Fg(\003)25458 29276 y Fi(n)26353 28977 y Fh(\000)270 b Fj(t)28004 28476 y Fg(\003)28004 29276 y Fi(n)p Fg(\000)p Ff(1)30640 28977 y Fh(8)p Fj(n)337 b Fh(2)f Fb(N)p Fj(;)2729 31571 y Fo(let)436 b Fj(D)5550 31131 y Fg(\003)6075 31571 y Fo(\()p Fj(t)p Fo(\))h(b)34 b(e)436 b(the)h(n)-34 b(um)g(b)34 b(er)438 b(of)f(customers)g(that)g(left)g Fk(S)28846 31131 y Fg(\003)29809 31571 y Fo(up)g(to)g(the)g(momen)-34 b(t)437 b Fj(t)p Fo(.)636 b(Let)436 b(the)2729 33297 y(service)505 b(times)i(in)g(b)34 b(oth)508 b(systems)f(b)34 b(e)507 b(attributed)i(to)e(the)g(customers) h(according)e(to)i(the)2729 35024 y(order)404 b(of)g(their)g(service)f (in)h Fk(S)g Fo(\(without)i(loss)e(of)h(generalit)-34 b(y\).)538 b(Then)405 b(one)g(can)f(sho)-34 b(w)405 b(that)11011 37618 y Fj(D)12049 37118 y Fg(\003)12574 37618 y Fo(\()p Fj(t)13483 37118 y Fg(\003)13483 37918 y Fi(n)14109 37618 y Fo(\))270 b Fh(\000)f Fj(D)17100 37118 y Fg(\003)17625 37618 y Fo(\()p Fj(t)18534 37118 y Fg(\003)18534 37918 y Fi(n)p Fg(\000)p Ff(1)20363 37618 y Fo(\))337 b Fh(\024)22114 37800 y Fi(st)23280 37618 y Fj(D)34 b Fo(\()p Fj(t)25227 37800 y Fi(n)25853 37618 y Fo(\))270 b Fh(\000)f Fj(D)34 b Fo(\()p Fj(t)29753 37800 y Fi(n)p Fg(\000)p Ff(1)31581 37618 y Fo(\))808 b Fh(8)p Fj(n)337 b Fh(2)f Fb(N)p Fj(;)2729 40212 y Fo(that)405 b(follo)-34 b(ws)405 b(from)18704 42707 y Fj(T)19580 42207 y Fg(\003)19412 43007 y Fi(n)20443 42707 y Fh(\024)21386 42889 y Fi(st)22553 42707 y Fj(T)23261 42889 y Fi(n)25504 42707 y Fh(8)p Fj(n)336 b Fh(2)h Fb(N)13484 b Fo(\(3.4\))2729 45203 y(\(it)446 b(can)f(b)34 b(e)445 b(v)-34 b(eri\014ed)444 b(b)-34 b(y)446 b(induction)g(on)g Fj(n)p Fo(\).)661 b(If)445 b Fj(Q)25980 45385 y Fi(n)27254 45203 y Fo(\()p Fj(Q)28683 44763 y Fg(\003)28683 45503 y Fi(n)29310 45203 y Fo(\))g(is)g(the)g(n)-34 b(um)g(b)34 b(er)446 b(of)g(cycles)e(in)h Fk(S)2729 46930 y Fo(\()p Fk(S)3974 46490 y Fg(\003)4501 46930 y Fo(\))k(that)i(are)e(necessary)g (to)h(serv)-34 b(e)449 b Fj(n)g Fo(customers)h(in)f(one)h(regeneration) f(p)34 b(erio)g(d)449 b(then)h(it)2729 48657 y(folo)-34 b(ws)405 b(from)f(\(3.4\))h(that)g Fj(Q)15717 48839 y Fi(n)16681 48657 y Fh(\024)17624 48839 y Fi(st)18790 48657 y Fj(Q)19748 48217 y Fg(\003)19748 48956 y Fi(n)21183 48657 y Fh(8)p Fj(n)336 b Fh(2)h Fb(N)p Fo(,)404 b(and)h(th)-34 b(us)406 b(\(3.1\))f(is)e(pro)-34 b(v)g(ed.)5600 b Fc(\003)2729 52917 y Fk(4.)1573 b(Generalizations)464 b(and)h(op)39 b(en)465 b(questions)2729 55911 y Fe(R)-62 b(emark)433 b(4.1.)604 b Fo(The)460 b(metho)34 b(d)459 b(of)g(ma)67 b(jorizing)459 b(used)g(in)g(the)g(pro)34 b(of)459 b(of)g(theorem)g (3.3)f(is)g(not)2729 57638 y(the)452 b(only)g(one)f(p)34 b(ossible.)681 b(In)452 b(similar)f(problems)g(the)i(F)-101 b(oster)451 b({)h(Ly)-34 b(apuno)g(v)453 b(criterion)d(w)-34 b(as)2729 59365 y(often)452 b(used,)462 b(although)452 b(it)f(imp)34 b(oses)450 b(restrictions)h(on)g(the)g(con)-34 b(trol)451 b(sequences)f(and)i(yields)2729 61091 y(sometimes)540 b(sup)34 b(er\015ously)541 b(strong)h(su\016cien)-34 b(t)541 b(conditions)g(of)g(ergo)34 b(dicit)-34 b(y)-101 b(.)947 b(A)-34 b(t)541 b(the)g(same)2729 62818 y(time)356 b(the)h(sto)34 b(c)-34 b(hastic)357 b(ma)67 b(jorizing)356 b(allo)-34 b(ws)357 b(us)g(to)f(broaden)h(the)g(c)-34 b(hoice)356 b(of)h(p)34 b(ossible)356 b(con)-34 b(trol)2729 64545 y(sequences)330 b(and)g(to)h(get)f(the)g(follo)-34 b(wing)331 b(result)f(with)g(minimal)g(mo)34 b(di\014cations)331 b(in)f(the)g(ab)34 b(o)-34 b(v)g(e)2729 66272 y(pro)34 b(of:)p eop %%Page: 7 7 7 6 bop 11351 2295 a Fn(E.)365 b(Sp)-52 b(o)g(dar)g(ev)365 b(/)h(A)g(c)-52 b(ontinuous)365 b(p)-52 b(ol)52 b(ling)366 b(mo)-52 b(del)11423 b Fq(7)2073 5647 y Fo(Let)390 b Fh(f)p Fj(\034)5367 5829 y Fi(i)5742 5647 y Fh(g)6348 5207 y Fg(1)6348 5969 y Fi(i)p Ff(=1)7926 5647 y Fj(;)981 b Fh(f)p Fj(a)10491 5829 y Fi(i)10867 5647 y Fh(g)11473 5207 y Fg(1)11473 5969 y Fi(i)p Ff(=1)13440 5647 y Fo(b)34 b(e)390 b(stationary)g(metrically)e(transitiv)-34 b(e)390 b(sequences)f(indep)34 b(en-)-583 7373 y(den)-34 b(t)436 b(from)g(eac)-34 b(h)436 b(other,)443 b(let)870 b Fj(E)70 b(a)15198 7555 y Fi(i)15962 7373 y Fo(=)389 b Fj(a;)1072 b(E)70 b(\034)20839 7555 y Fi(i)21604 7373 y Fo(=)388 b(1)p Fj(=\025)871 b Fh(8)p Fj(i)389 b Fh(2)g Fb(N)p Fj(:)436 b Fo(Then)g(the)g(pro)34 b(cess)435 b Fj(q)43 b Fo(\()p Fj(t)p Fo(\),)-583 9100 y Fj(t)336 b Fh(\025)g Fo(0)405 b(is)e(sto)34 b(c)-34 b(hastically)404 b(b)34 b(ounded)406 b(i\013)e Fj(\025a)336 b(<)h Fo(1)p Fj(:)-583 12315 y Fe(R)-62 b(emark)433 b(4.2.)604 b Fo(There)297 b(could)h(b)34 b(e)297 b(further)g(generalizations)g(of)h(the)f(ab)34 b(o)-34 b(v)g(e)298 b(problem)f(in)g(order)-583 14042 y(to)498 b(approac)-34 b(h)499 b(the)g(question)f(of)g(ergo)34 b(dicit)-34 b(y)498 b(of)g(the)g(system)h(with)f("greedy")g(serv)-34 b(er,)520 b(i.e.)-583 15769 y(when)419 b(the)h(serv)-34 b(er)417 b(go)34 b(es)419 b(to)-34 b(w)g(ards)420 b(the)g(nearest)f (customer)g(on)g(the)g(circle.)581 b(Th)-34 b(us,)424 b(one)419 b(can)-583 17495 y(mak)-34 b(e)326 b(the)h(routing)g(random)g (w)-34 b(alk)326 b(on)h(the)g(circle)d(dep)34 b(enden)-34 b(t)328 b(on)f(the)g(presen)-34 b(t)327 b(state)g(of)f(the)-583 19222 y(system,)363 b(i.e.)520 b(on)354 b(the)g(n)-34 b(um)g(b)34 b(er)354 b(and)g(p)34 b(osition)354 b(of)f(the)h(customers) g(on)f(the)h(circle.)520 b(Then)354 b(one)-583 20949 y(can)368 b(supp)34 b(ose)370 b(the)f(serv)-34 b(er's)367 b(routing)j(to)f(b)34 b(e)368 b(a)h(semimartingale.)526 b(The)369 b(only)g(di\016cult)-34 b(y)369 b(that)-583 22676 y(arises)408 b(here)h(will)f(lie)g(in)h(the)g(pro)34 b(of)410 b(that)g(the)f(mean)g(cycle)f(duration)i(in)f(\014nite.)554 b(Once)408 b(this)-583 24403 y(obstacle)c(b)34 b(eing)404 b(o)-34 b(v)g(ercome,)403 b(the)i(rest)f(of)g(the)h(reasoning)f(in)g (section)g(3)g(do)34 b(es)404 b(not)h(c)-34 b(hange.)-583 28662 y Fk(Ac)-39 b(kno)g(wledgemen)g(ts)2073 31655 y Fo(The)514 b(ab)34 b(o)-34 b(v)g(e)514 b(researc)-34 b(h)513 b(is)h(a)f(part)h(of)g(the)g(author's)h(PhD)e(pro)67 b(ject)514 b(that)h(w)-34 b(as)515 b(made)-583 33382 y(during)574 b(his)g(sta)-34 b(y)575 b(at)f(the)h(Mosco)-34 b(w)575 b(State)f(Univ)-34 b(ersit)g(y)-101 b(,)616 b(F)-101 b(acult)-34 b(y)575 b(of)f(Mathematics)h(and)-583 35109 y(Mec)-34 b(hanics,)574 b(Chair)540 b(of)g(Probabilit)-34 b(y)541 b(Theory)f(under)g(the)h(sup)34 b(ervision)540 b(of)g(Prof.)947 b(L.)539 b(G.)-583 36836 y(Afanasiev)-67 b(a.)1072 b(The)582 b(author)h(w)-34 b(ould)583 b(lik)-34 b(e)581 b(to)i(thank)f(Prof.)1073 b(L.)581 b(G.)g(Afanasiev)-67 b(a)582 b(for)g(the)-583 38563 y(statemen)-34 b(t)351 b(of)e(problems,)361 b(constan)-34 b(t)351 b(discussions)f(and)g(man) -34 b(y)350 b(helpful)g(ideas)g(in)f(the)h(course)-583 40290 y(of)404 b(the)h(researc)-34 b(h.)-583 44549 y Fk(References)-71 47277 y Fq([1])606 b Fa(Af)-89 b(anasiev)g(a,)363 b(L.)358 b(and)h(Bulinska)-66 b(y)g(a,)362 b(E.)324 b Fq(\(1980\).)426 b Fn(Sto)-52 b(chastic)349 b(pr)-52 b(o)g(c)g(esses)351 b(in)e(queueing)i(and)e(inven-)1615 48738 y(tory)366 b(the)-52 b(ory)p Fq(.)453 b(Mosco)-28 b(w)341 b(State)h(Univ)-28 b(ersit)g(y)-85 b(,)342 b(Mosco)-28 b(w.)454 b(\(in)342 b(russian\).)-71 50199 y([2])606 b Fa(Al)-66 b(tman,)342 b(E.)332 b(and)h(F)-29 b(oss,)342 b(S.)298 b Fq(\(1993\).)385 b(P)-28 b(olling)299 b(on)f(a)g(graph)g (with)g(general)h(arriv)-57 b(al)299 b(and)f(service)i(time)1615 51660 y(distribution.)455 b(Rapp)28 b(ort)341 b(de)h(rec)-28 b(herc)g(he.)453 b(INRIA)340 b(Sophia{An)-28 b(tip)28 b(olis.)-71 53121 y([3])606 b Fa(Al)-66 b(tman,)351 b(E.)343 b(and)h(F)-29 b(oss,)351 b(S.)309 b Fq(\(1997\).)403 b(P)-28 b(olling)309 b(on)g(a)h(space)f(with)g(general)h(arriv)-57 b(al)310 b(and)f(service)i(time)1615 54582 y(distributions.)455 b Fn(Op)-52 b(er)g(ations)365 b(R)-52 b(ese)g(ar)g(ch)367 b(L)-52 b(etters)423 b Fl(20,)343 b Fq(187{194.)-71 56044 y([4])606 b Fa(Coffman,)360 b(E.)c(G.)h(and)f(Gilber)-66 b(t,)360 b(E.)c(N.)321 b Fq(\(1986\).)422 b(A)322 b(con)-28 b(tin)g(uous)320 b(p)28 b(olling)323 b(system)f(with)f(constan)-28 b(t)1615 57505 y(service)343 b(times.)456 b Fn(IEEE)365 b(T)-78 b(r)-52 b(an.)365 b(Inform.)g(The)-52 b(ory)430 b Fl(32,)343 b Fq(584{591.)-71 58966 y([5])606 b Fa(Coffman,)578 b(E.)538 b(G.)g(and)g(Gilber)-66 b(t,)577 b(E.)538 b(N.)499 b Fq(\(1987\).)925 b(P)-28 b(olling)500 b(and)f(greedy)g(serv)-28 b(ers)499 b(on)g(a)g(line.)1615 60427 y Fn(Queueing)367 b(Systems)423 b Fl(2,)343 b Fq(115{145.)-71 61888 y([6])606 b Fa(F)-29 b(oss,)286 b(S.)262 b(G.)g(and)g(Cherno)-22 b(v)-89 b(a,)285 b(N.)262 b(I.)230 b Fq(\(1995\).)272 b(Ergo)28 b(dic)229 b(prop)28 b(erties)230 b(of)f(p)28 b(olling)230 b(systems.)273 b(Preprin)-28 b(t)229 b(6.)1615 63350 y(Institute)342 b(of)g(Mathematics)h(SO)e(RAN)g(No)-28 b(v)g(osibirsk.)454 b(\(in)342 b(russian\).)-71 64811 y([7])606 b Fa(F)-29 b(oss,)377 b(S.)f(G.)g(and)g(Cherno)-22 b(v)-89 b(a,)377 b(N.)f(I.)341 b Fq(\(1996\).)454 b(On)341 b(stabilit)-28 b(y)342 b(of)f(p)28 b(olling)342 b(mo)28 b(dels)342 b(with)f(an)g(in\014nite)1615 66272 y(n)-28 b(um)g(b)28 b(er)341 b(of)g(queues.)456 b Fn(Sib)-52 b(erian)365 b(Math.)g(J.)341 b Fl(37,)i Fq(940{956.)p eop %%Page: 8 8 8 7 bop 2729 2295 a Fq(8)11422 b Fn(E.)365 b(Sp)-52 b(o)g(dar)g(ev)366 b(/)f(A)h(c)-52 b(ontinuous)365 b(p)-52 b(ol)52 b(ling)367 b(mo)-52 b(del)3241 5647 y Fq([8])607 b Fa(Kr)-22 b(oese,)426 b(D.)416 b(and)h(Schmidt,)426 b(V.)380 b Fq(\(1992\).)571 b(A)380 b(con)-28 b(tin)g(uous)380 b(p)28 b(olling)381 b(system)h(with)e(general)h(service)4928 7108 y(times.)455 b Fn(A)-26 b(nn.)366 b(Appl.)g(Pr)-52 b(ob)g(ab.)340 b Fl(2,)j Fq(906{927.)3241 8569 y([9])607 b Fa(Kr)-22 b(oese,)435 b(D.)424 b(and)g(Schmidt,)436 b(V.)388 b Fq(\(1993\).)593 b(Queueing)389 b(systems)g(on)e(a)h(circle.)594 b Fn(Z.)409 b(Op)-52 b(er.)408 b(R)-52 b(es.)388 b Fl(37,)4928 10030 y Fq(303{331.)2729 11491 y([10])607 b Fa(Kr)-22 b(oese,)541 b(D.)510 b(and)f(Schmidt,)542 b(V.)471 b Fq(\(1994\).)841 b(Single)472 b(serv)-28 b(er)470 b(queues)i(with)f (spatially)i(distributed)4928 12953 y(ariv)-57 b(als.)455 b Fn(Queueing)367 b(Systems)423 b Fl(17,)342 b Fq(317{345.)2729 14414 y([11])607 b Fa(Kr)-22 b(oese,)536 b(D.)506 b(P.)467 b Fq(\(1997\).)829 b(Hea)-28 b(vy)468 b(tra\016c)f(analysis)h(for)f (con)-28 b(tin)g(uous)466 b(p)28 b(olling)468 b(mo)28 b(dels.)831 b Fn(J.)481 b(Appl.)4928 15875 y(Pr)-52 b(ob)g(ab.)341 b Fl(34,)h Fq(720{732.)2729 17336 y([12])607 b Fa(Schassber)-22 b(ger,)355 b(R.)318 b Fq(\(1995\).)415 b(Stabilit)-28 b(y)319 b(of)e(p)28 b(olling)319 b(net)-28 b(w)g(orks)316 b(with)h(state-dep)28 b(enden)-28 b(t)319 b(serv)-28 b(er)317 b(rout-)4928 18797 y(ing.)454 b Fn(Pr)-52 b(ob.)366 b(in)f(Eng.)h(and)g(Inf.)f(Sci.)341 b Fl(9,)h Fq(539{550.)2729 20258 y([13])607 b Fa(Shir)-66 b(y)g(aev,)375 b(A.)i(N.)341 b Fq(\(1989\).)455 b Fn(Pr)-52 b(ob)g(ability)365 b(the)-52 b(ory)p Fq(.)453 b(Nauk)-57 b(a,)342 b(Mosco)-28 b(w.)454 b(\(in)342 b(russian\).)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF