Content-Type: multipart/mixed; boundary="-------------0302110651985" This is a multi-part message in MIME format. ---------------0302110651985 Content-Type: text/plain; name="03-49.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-49.keywords" quantum data compression, quantum coding, von Neumann entropy rate ---------------0302110651985 Content-Type: application/postscript; name="A_Szkola_030121.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="A_Szkola_030121.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: data_compression.dvi %%Pages: 14 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMSY8 CMR9 CMBX10 CMR10 CMBX12 CMMI10 %%+ CMTI10 CMSY10 CMSY6 CMSY9 CMMI8 MSBM7 EUFM10 MSBM10 CMR8 CMEX10 %%+ MSAM10 CMBX8 CMR6 CMMI6 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips data_compression.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.01.21:1632 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 40 /parenleft put dup 41 /parenright put dup 101 /e put dup 110 /n put dup 118 /v put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523da5d7776ec0bb452 fc23761a3e881b097d783e662b66d6be1dbe632b82bf88dcefa360fc48e76b08 05c18fc9da16bb1bbf03edaa89c9eeaac7c929377fe0e4089decd64a32b91c44 cb5392461310af2a5af1e8b43926b6d849c09656daeaf64d686fd6a1349fde83 b354c1dc1ce8fe772cebdabd47fee5cf482ffe026916da019c3d23d0468c67f5 a59c6d31fce59c89f463187909933cb058da372428f10fabfa0346ebe2b3d65f bbac1a259ce30934f63a38c87d389ecbaf4707f0cbf916fafdde9810e4bf8e56 4144639df9e457852ae3f40a6186491aee722a2006333218abb3ea8aae25f377 1f637f1154852cc8dad8324d450e51a665e773f63fe8b49e0e30ff1d4ffd1ec2 e7e3dbd8a7a8678e9ef8914a6e6c7824d068fd2a3019594894fd336897b0fb30 a1298620e5352c2e0126772cfaa5a4f17c33358624e36d0b87138973fc0eff74 a03c2b964a5065fa11b3451f00a7cefea6dbdbfc720fb1c231dfd78a14653d1c e229480ea9810b240a74d389420df4e33f9a283535319cf41795e519e56c40e6 be9e36f10819660979f29c865d7c3bb7459ec429e1809e9cf247c626f841a91e 57dc0d95926011ca16789306b04cd6a67ae8ce994eb88e45b7a3bcb9425be2bc 386b7afad4924489ceca031a394410b1fb49ae710cc30a24b3f841a613a1c25e ba3e53f5f36b40e91039823339b49288e5e9c007406214ea100e23c6875715e9 39c9a914740ad6529a8910e15e3c384b0168455571c66c9306d1ff343c943e55 7c2a8b266a81be89b2ae6dd514090d573ff0b46212091fbde01d70220c69d489 425f1687fff8f668e27315901f3075319f0e4591ae3116c23a5ae1f918c0455d 8149883b0041709502b6d06063d54267374b037d927a3e9259d5f0c830d7dd7f 70268a18fe02179ecae3cc38f766d1718e5d41cd41dd4e0ee43f40685496cca0 7032a77700611b685e6c5bd7e6553ce73be76abfb8da3e6069cf08605d6cd409 36ee1f5be94303ce48634344173cafb6035cdb6f378c1cdbd5fed7457a862445 81fd7a4c6a9802d600c2c1f739580871b0d3afe452c23b60c0c8f09b9f802021 4c22af3d624a1b3b18b41ce5a0802a9a9296c7b27d81b02e095426ca77be228b 1c4ad7f72b58f3c4bf59e448051b0226a724baacd44217d3979b27bb2fc8d1ed 327b6931190b4fe69807d342cefec552d704ca7af0610478fbc5b95164af7331 739b9037aa1d7697f3b58793e7601adaf79df8ad1707a689ef953639dd188598 153b3546f04a0b9f3ce2e578399b13247167c8caa0929f218e49e5815a7199cd 7762303bbd2366c1821e64ce1a1ac6655f50d61cdcc87240ef15d9de6bd7c853 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % 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 (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 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 105 /i put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueXX 5000766 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be1f91da738298311c1360c8158d61cb73427 3c21bce59b0f2e1d38c2fbc0984ce6a04f5d3bc84e2601397499a981b200b307 771141805f1f5cd7b12befe020f7121ec103dc2baf17f0aca1d0740c92a8dd61 12fa9c0d30cdae4f2af757b9f713c127d6ca02ef315205b81eff629104b21462 17d2b0f823133bccc80c9e400d6840db5fdf828f845313290fedee040d34f309 8f1b5a6b8941c81d1e607dcb310b14169cb433329994b4d1ac1b491e7422d518 2a8faf7ed3cbc2e23c58a2e310b56da54f51360556d27d58783694c51aaf62a3 a2db91ac8df80303c35cfd503341005020a5cf501fc0b64ff4f497951df6cd50 f00fafb04725d23bdd36616c7c06cd9052305682f6b6e521882922377b4979a2 e6f031b91b2a86d8631e81de17f90158ca05045c3b823da8b2d2aefd37a32728 45bace7594ceaafaecbf6140212789b3937a24cdd8dee327c934a9b0e328fd83 a1b535d9bbea6f0204ce5ee74cc30769734d4fa3dd0cac3986510c99ba062868 9285146cbe64caa89cc2f18a61d924e7f312fa189e0ae4deb913ed1cdfeae61b 4e0fe25f2775a8b2edabadebab4eb2ecf47258c1a77101c810cccd3b06633907 f765fc80bb1a2527f8a59c52760fffabbbac1d65a11708a3bea4557f24536773 d17dfd0eeee4e22f406e04765cf582d6ca4414f2441b6ff463c56018e44aa2fd c9af3f0480da99856aaa97e56b4bc28d9a74e6d74e5ee199932ba9548c9f5a24 4ad6d8509e006d51a96e77cf6decfe21ff0391441c8b95ace9dcb2d93694eb75 e76e0ef6fcdfb8a73c860e09dc49dcfea499450162b7373cccfe5e771eb05086 9552a2ff03a1c1c6a08405ec3ad93fa9c951b4aa746b4c4bf3f98a916ba7134e 93d777c339423c4fad91e1968b981744bda6f085de1cc197203a9c445611f874 04f536e7380673d2182990e967ba536ac1d0a712e35b18a7a72ab6d07fc759e7 2b70a3ebae0d559d6cdc0ac3e945d1c4042fec07456806262a0fe0ae906b06ae 34681d3864d092900f6eec466aa165710673f5e872cae65558a5e15965d70414 6bbea095c7d7aac93a4a590e8077bfec29e453d9fb3d005e02560c4bac687eab b752e7cbc3303a0e1dd626364d814b38c3a00609ff483593b868658c60d869aa 06819fffbbea588431ff9bf945a246c2fb7d99f884dc25f8954de82f05b0d738 383587c43dcc557bd4eebf2d2123e45f42693eee1ad44eb95807657858b51bb5 09acacd053870df3cc4baba387f348d0eb44391666b2a0e06b320667d446cc9a 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 22 /harpoonupright 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 21f163df55cd905d6378ed3727210df9236bae33a8707ea32222638258fce5e8 1ee9d3a461f391f5d538dc1e12517da01ecf683034d503b2b868d08817cfbf56 20e1c3612b7f732b9b0dba389bbae32e467f9e7704599a8130ef87d406580cc3 f0cb9a60dda91c10a7fff64c1c53af1867f2903c02899cf8da9cb403c5f830a5 c50194042597dd36c6292552deac9c3e014a79bd8954518cc0697d591c1bf905 195b2ee491c5b7641df3f19df3d2224bd03b8f55fabe60d956661eac7403007c 919fbf78f742ca0df9e0d55a34ea44fcca5eb7229e18a45401d771a3f8766814 d315 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 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 80 /P put dup 81 /Q put dup 82 /R put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 80f59351e84bfc88c87b3a4a1d25e168b9d134554f6a581378c7d2d6eca8ac09 045cc3a5e0ed86f147133f094029e3483bebc81cfde69942cf645ea20d0a2b64 5140ccc2f9cb4a3d969f4b0a79cd3329b440dfcff5285494406f3dd08d804c86 df191e57232f6f1f83df6430f214e03fa5412b1e13d83c60c52a698bc9a38159 19a64162af7b83a9468fae9507c6cb55ea80df8c696dfbc3296c663902d77e89 a181502627281181ac8624f65be9de5fb32f056cc7dd7cbc7366a91717b5892a 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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 32 /parenleftBigg put dup 33 /parenrightBigg put dup 78 /circlemultiplytext put dup 80 /summationtext put dup 83 /uniontext put dup 88 /summationdisplay put dup 112 /radicalbig put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83f5e3715ef7b431f1a45424456653074011de9e5981647b1540523b5832b2b5 217e227f78f6c0c7a0c802d9dbd9ad07a950750f4a7fa8b4f1823c8722120ad4 359a5c881389897fa4845ed67f117232717d0b94740158cf35d3310fe0d1eb5e d4d87b1aa7c7d86e27dd915f63084346525a60100eb1b059e58c7105c4a7fc27 6ad3d53093890901ac2a6c44e021d1f70554247eef02753b3999961cf4947d0b c37a264641ea7e49b33af99d58ad05371e5a8382681fc55691997726cf0aa9de 60e67e6a33571eb34d4f3603648f20b8f9f3c6a1ac5e4752528083edbb0df9f3 3418d3ee9d666c71e2ff57b17c59042e321cef2e713897bedcf43d776287fcc4 73fe0083f38076fe53fd9bba1044409abd171b14361ea4fcdd47eade4512a20a a789963073bc41460ee0b7122e70bd529f8ed759ffdc6b3e027512cd0c861309 2e590f481df2475447735d4805a63ee8eac03edff01b653a99f8de9c2105082a 2a939192a3e2c7a6f0707146fe3abfd5e8c3b1b40e9244eae60e0b2b55f83f05 2b323a09637141a69882c55ec354495c942e7591c1a4a90dc4bc6802a4b7fe32 6df95c30e662b429da52edf0064467550b2f290e8f6321f9f74fb68034def4e4 15f521cef40b550fed679b416b2b2cf87b6549d05b73171b8f414e3dc4e36e1b 8fe6aef03bdc735650c851e8d7be196e429429beb86a057d75ac329258f3a080 581442642cb0512aa9922f9cefe6d38648217e5d4b9a1d70bd895cb556f79d8d 8646ca337c3e80fccaf26cfdeb603690d3f25108315a32de6aba311efd348404 83b4d3762da86d9a222fb3f1d996955c9d92c6d3d0e1a2dbe777a84ba7c82edc 2559a16560e6c7b63c2bd414ebd1cc054281fd59c55523c3ff1d15de8575ddb1 7ebf92a59b74359f6449c77d29d6757a9bf2e7a8c7d07cf7da75735d16ce3a2b 2ae993c50731251d74c19ae7a2989e1df2ee0746f96c2f83fdc7eb11169c1529 24c8c35eb6d7116679767cee8425be3c81a863c9f1e43e8d58ecdb08df5f2b24 041c89288798e20c672c7d89c0d77099690b10c3f86259e519cfb1e0d153daba 37cdf85e970cc74a8dae72d67945f1522eb11763856993a1ace2d4c44df403b8 8a4cf18151e72519a9c67d76ae7387560e6a55dba80719486020fb7a8a7177c4 16d8b92e1c0c5a01cd119136641d7635620892d2705f86609d4cbb377404a096 706df145c4ed93c5d45d004198d16b9d98e333e8f5dcb96b7cb1cd2f209d0f1f aabaeac41aaafddbc0f11eba4986aad5bcd257ef3d2a5b57fcbf14707e07c7c8 19d9bfc349261115ed785b6d11e47c3472e2bc0cc9d7b074de1e8cd9ebbad800 5c70b0a87f75ba85a06b621adee74c8212b561703e4cedd955d290679e42c770 6b78e824eeac2530480aa500767e1675b25ee36e1f4ef6560714f16c2f8233bb 9a2cfa0022ed3f11a6ad68a8d6b338fe1ecc9102c6336f2bf9e051d0b69b263f 4a33b8337401c9b3c80c1d6a2a36b21f5a3ccd8c3db14a9699992f03a1999a95 95e19a2fcb521b9f6dde4b0947e5caffc62024660b61f6c5559610f39f3850c4 b0cd139bdbc254159f34a76e7d7adba34af1d48e655af14779966505424e2fd3 b2d9d40097ebbdc30ddb5af8cbaec90f2da6b0810ea9bc21e5712eb19c6cb122 299dfd76926a38f2e13ea3f2ad32c7ee71c7d7f0982e304494dfd1d79f31263e 4729329ac9f9798636855de43a7da51ae44c01f356f54316e591e7d831dad090 3967f11e427d9dc6fb757fe0cdd2c29239458c45f588bc90bc7109b6d8c4f12a 6353fbbd0e79ace55382e85a9b390b0fc320db8b79f1ebbf04684985ca167d94 d20540875e720a165d72c65bfd09797ab686b34286aa7bb9a8b0ebde547ee531 528c8f6e1dec692b1dc79b6da3469656cda6cd685a5ec4ecd452f9d7868cc498 16cc9b56dcabcf443da9f2da7583e2e0cce0f3845c1617541fe9eb3a99966c22 a581a0 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 3 /Lambda put dup 9 /Psi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 61 /equal put dup 99 /c put dup 101 /e put dup 108 /l put dup 110 /n put dup 111 /o put dup 118 /v put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e5097a1b55c863d0b8 20331d09750bb867d77af81bfaf6a91b652e183f99266f540648a72af0c878a0 462f0430feadc8748dccc3f768c6770240d3cab7d00895f33c8a5eea54014329 d1030b28f2186f0437a515063dcef54688bf9652a036881e25bbeec02bc64a33 0bad2a3f573fbbdea0729f09f1ffee631003f34f5f49952f44ab165cda7e9bec 7dd663979ed116da614778117b72cc9787af5a6be91549e28b53bc168a21e5bf 88fe530ad412acce210374cef8e42b9d961c2e89c49a606ce0d5dc6e56457391 fa60c541522f3a1ee500de51abcb9799ab2d0d4e0a1a25dd04f1ff992754b92f cbf376301bcaddad6faaceff46ad0a54e2b93b6323d18c5422e0f1542b185bf6 f32b0f22dd9e3611b2eab2ab4d77c3cd3ac693e13953888da2946df180a26eb6 a40a8c203938303eeeca326777314b73e8390ac5c3f27e7f2b05eb7fd63fbddf f388155ef279b48e672c4e078a3aa2d6564b08953b0ecf85d4032544d5d664a7 c38c23e6d56d0b5ad727689c8aacb65b1fc14b6018e64777d5cb51139b9e3704 3847de91f21938c31aef4fe9ea2783dcea90cda1476228541f4b1c3c068bc355 d386af4133e84d434ace065730095acb3dee95f74d4cc75f0ca5a263cda9a33e e25d30ccd2f39d21255a907e8d89c84529c098ed9069444bf7368da3c440fdc3 fae1ae8de3fc9801b5d83791d7a817e63dd8d4ebd5ea5df0d99e49ef321c9a6a e118cc183a83847f66ddac3f548d85adf68a491272b6bff38125840d7d22da7a 9711ca1f8ac914a21e682bf831509ae6eea3f5d4298e7c01d3cb574234766a10 4bfae3ceace89a00c29c955266433e1995df4d4ec109a531fcf36ede311db9e4 189a74136c0c989ad69c5ffeb167a72b995f6ab30f5e30a3c05685d163e48347 cd9aa45469361e897f9f2dc1a9d32b80b6a16d9b493d3aec14c4dcc2acb4bd2d 35f7192c3edf2f28baaafc5d7e461381526afba43a0fbe3f27ccf410e24daa6c 7b157bc4eb9a1f5be0d35089fbf50af13893910f10b6ff18b1ffd0a9324eb7cd 89edb1daf976c9ce25d509f2c7182a9a63b6483dead06301b8a2ce267241f7cb bb0a87d3ae9795a10f7c10fa39e9c404b646a73eb27ddb6a07349b2720602015 aa2a7afa20efff7a7c006f8079d8427134f76ac73b156f6eb6d9b3a5cc1c63d2 2a3ca35e7bfccc2efa078c2740de3cc8973180feda0b3acb39b28f2f60b4935e 67308dd4b6cd760049330b3c6aa83de447222bb90616b3a7aa2b930bda3e0c58 bf375047222a11b3c650784b5259691ff6a94c97bc9171c329230976dff4f582 201d1ab3a82bf6813928b666f7b5ecbd561732f6a37e1ecf37552b26ddec7c4e 5980bcd30f5127a1fc4c46371bc24ce311102319891a9d7dcf21d469fc79ff44 12bc6186f68352b33a996b3663c4a38a2454e3515a509980584397aeb37a13b6 d14d79411507169318581f03bbb8d6c1928dd599e662567ed409e4aae6b23c02 ee2834d029acb72d361a83be31826b44f7335d1e4f21dfa56b6125ccd7e0f535 6fe28147dce30a9063dd7f6e13bed2c6ffefeca684f8f8b2d2bf8e4eefe067c2 7582ba9e01d46b0749bc1390b50f4e5f6d4ee549012169ace5b6cba278ed7cc3 d4c878878336ffbc5bc65533e52721f219bc2d9ca0e7aebe9cedd95d9846b8d7 46eec7e3c309f903c5ffd3e510de99db28755a2f3209bb2ff9d643180adf64fe 8a7b444977c7d0434076120c9eb379303a8a6a9a893b4907bf0e361b50c5da82 d5a168ecadda9724a2d99d22bab4b077d05cfeb699b9cdcfa4ea1ca612e5a930 2045f4afeac8092951042414fa04e3d66c36cefef54e723417b0a67790e9ab66 f4c32cdd661f24894eb8eed70d17fe480e73ae8864546f90aae302533e245bfd 4a6797ce1c788a0419415bf7618b903dbe97ae763c54d4939cdd45149b460235 a5223678c867da4cdc73d8afd737f45879489ced6b8d5161562163fdfa786ec6 d4d88ecbea94a44802e8bbb835ae12708314ee40a8804b6e205cbe160de83cae b2e0d6b846f512f2aba6f0d141288ed31c9ef24a8e448f5a01998905e18e1296 2dd1b79afc6e5cb84c8194b99a302a0d93f14df014eee3f01b99b20ec5858803 c2900aebaa4664ed9a7a5a4c9ae33b3005a0a9da97258747cb376a13de6011b0 3a4927b0b815978f44a536e0906945f005cfa5b6797603260c9f595b6037b962 732c70a2eb3748c812bd262956a890de1799adad510640c3047044a22986af91 51ce0ac7c2e4918aba16ddfc67a6420e7ce4025925ca41b7ef1b5da09c8a1bcf e9b9d729d0ad88a7601b95b51847a4175d7be22db733b047dca3167cd400ac85 da0c78ad66fc4c01d089748fd88f1f4c62fefdb965d27cd0a2402388570175db d61a58978896f909ed5350425d8e4ab6ab218f703f70c9faf6cf2438b88935f0 4cbe822db33a4aaa34b6207a044690c359b84b0df7ad26cd74db62b378454ee4 550f56dc767c539ef4d9687162f30821d044e1a1874cd75634bb6bf32e40feea 00e63cfe3ed62e93680dca8fbb0860f3c257276a063b65b204ffb3f55c058408 1a0cb504517a8b0210b8dfb6b04caa40bfd43e1201d1b6ff65525499ace67aab 4e6611a4fa75c2b09ba54026beddae24837c23c79317c311226959d6ee6ef19c 51b781c79d3ef45356b52e24631e1fd436838f513a1f6a5ec94cbabdb25a0772 453538b52a97cfbb3cb3fd4e4def3719fefa2f533c802a85f84c2d4b4ee8721a 5a3e6ab79d0e9b0a0278e281daf0604db0818dccb0a5a2506d76c709c8866264 64c9d5b4a7eb19581690053a89aaf124d0d0068af91919ef5a74f9cf9db19cf8 787e37c122126c0028df46282ec73e35cabe8f5ae7e0a36cd7c05d4576475ef0 0e9c6de1a91a2c3bfc086816edbe8c4e6586487807c5c6e07faab1d25e0ee6a4 68fc050eebe65962951dba972ed19756ba715292a7622d3ce610c064f93adb44 ff8ba1ec56204891279f79d2c13e9dd4dc27d0cea69f26176747fe0c8e72dfe5 040574c700f7ddbf75a7c7fcc74c8a8d8f5c31bb688635be43f8b91f6d48e8c6 1e69e9947802b01b0c0297d289ffef1752127e82b4cda5d52ff093ecb9cb86ca d3d19309cfab4b1c09a152ffdcd7f047f92987 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 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 4a7abb8dca6f76c45e50c1c9ba538078a5b7b67307730c84cfc5f62677924a48 28a9bb5be0b65603fd59e525ee6d0fdbef578ed48c15b1a344bd3e748631dc30 08992697b3543551e2a8740b14bdcc1df5780e9b12aed9da00183a46d0f2c727 ba64ce49e2dc7ae49ddec532db0ff9043ad3307040d1c84f4f7904c6250e4190 3f3cc5b97aa240986d464d116eb09e28c4a357bfc705238f21d179c1e8efa07a e338e737da2d04db865b77e9a539e9499aef03ebf58dce169a522fe6d2b43aff 0d806a114cf5af8368256694185c39f8eb6f61376624e3fa5572e82b68906652 e42d01549282e0bed67ed3692a53d6089395fa4e372a719e5b5e0224d57006cd f9736a43baf17b1991ae1d3e369c421fe0303d1c99fc9a131f48f07b54ed6e03 677f59d7599c753759e1b2e70a1c8781495a47d1d1ecc959d1fffd02d90ef97e d64051366bd579214b3a765d141bf635bb8f5e37e8ac4ca526cabcc4952f6d96 00f48de74285669150e7573b96739e8070aa8345003a001eb68af57ac4a9fdbf e39c159f52aea9d039c6649a8658950d75bacbfc078edf61ce692ea376694e7b 3b6c69f74cc753e0ee2c984c2495fa75c58028513718d676376add5a49c8f69b 2fdf21d07a0fb882bb9187709918da7840e1b40411532b9a5a2358b5cdf1de91 01c6b8ae55b866b2c6bd35cf9c3b48ec213929100b9ce305126f7795f8493a17 7ae5e1d525c518141e6464360ee250ae8c35f41820ffaee87bb999a091a86b96 96816c80ef31d1072b1fa4e55369c97fe3bdc3424bde0fa8591ed9433868a9f3 ab2cb902e6ce 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: EUFM10 %!PS-AdobeFont-1.1: EUFM10 2.1 %%CreationDate: 1992 Nov 20 17:36:20 % Euler fonts were designed by Hermann Zapf. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueXX 5031986 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e320fe93acc64a4016412366d1ad2 8776cfdce37d3a89b95e5bb9373a99730cba9c11192589e22438b44f4ecc6a8d 1f72a7ea6a698d9580bcafcc2366c5964e5d3094b67d86eec82e16761e4b6f4d fd245d3c0b4188a0543ee88fa787fb10793268e415e389ff071cdd46bf6b260e 1e9c9ac037edba327c6379836655308ddf35e4a4488ad32d3ab301c67a2fa71e 8ae00daeead4271df276f5ce395a57e414f85237cf8f1be070309ed5c3078506 c9d38c2adeeac618d04c0be2ff891dcfc9ada7588efb91f739188a933e1d37bf 632cf042106df1bae0cdfb79c578e565014cead123bf856cc0c14983f5548a20 c0d45446e0dd2b017f528e46d394a88a2d5f86fc669ac7d489f1851c100b29a0 ee3ec82faf87eba944a57dc14ebc94f2445a8a21ee68eef1848d534bdd192ea1 181220351ff93c51e53fcd5ee6ec92bd644d121eac52bc163acb6948a7a4c256 7243c7113b1b5650aeeedb14ffd9b6ce33605907595230a06db01bfb510a460e 76598fb2bb67498f79f0f5b5c5fdb5515cf2257aad324ef1a877a296e2851d38 f8995123e527c4956247fc8ab910206a9ce8736563ff0d4cd5d00579d60bca51 650af348ac4d6422c4cd74d924b532d4a28ba95eff24aca4b3cd1d28e207c7f8 906f8dd99aa04c135fe46c1dc8ee89bd768df17240a70f1a96382defcc180b9a f1b6fa57a9b0a2440bae0797790f91733970b16e742e6341d95faa40c583dac5 13a84eb181d2946b5d0075f71db8a991dc1a809cd3cfec573514392567a82e75 946ccf6e14f4a968313b3b6d727c83018ed58b882b96db208ebd27f7d30ffbc8 ab11e10a0f81425a62bdf7eed9f618c746103dc2d1c3e1f37d27083f4068a30e 099c92685e320266ff8047e81140658a63a6b52e4cd63e95d1b83fde2655d8b5 7dc0c494c0f8ff83dcb158003fceb26057e00e9956478aa7c7ff7d6ab5410885 a8065f3bb52a1e5a3f5cdd7383fad86053a1fe64c470c8156c68b9583b2875f9 6c760be65705bb8bb203c8d260aa583676b8db3976b46167c8cab1a04ff58280 b7776ea0b394408eb1b8cb9018045ffdfd6ab95a78e383549036eb2e1800f86f 664350e741912af6490c3003eb00323d773ab37fa3d06466390252f009a7d041 d12d605a465db01b611bb2da6ad7ad1bf90f09eebe743eabc41c3056dec59f75 f8e8f40c4ef5ca4bc392ce2d078f9c092bc70bf5015c85708e2849e419de8491 2246c8dcda4d1b4971323278b8578ff21927eda4af9ed5a90269c3ebb384bce6 07e822dbcd9b90e1bfb8071b933f90ac82027b383409797f084b13f7b004f5d6 f84238ef4ff4446c872e016f72dc7dc3e1cc6f320347e045f6a888145a9408ff e6dfef43b1c3b4c556133b18aaf701cbef6ada7d0ae1e914f04534b1a704b39d 886c0a350ca7d83beb2bdbbe4c175591bed7e150817a5a1d03d95c91a120645d 60eab857a931d4c38341b0a2d33c706a8703ace63950fba26323cc4911f0e8c0 d19598d827ba42e5df321fb75fe471ad8c372cdc07d96dddcc28409b9a78f577 2d98dcd6b26f228f9bc7e267f667630443046fbcbb211c518d48ebccdbcbc513 00af92723c33 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 90 /Z put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b4dcf3fe48b07398eec882c325567e28b9eb4d699111343b1910da9117d 74d6e9de75247ad908f8ce2cfc49e0faa22dbf4d1abe2c035b8f8eee2d1967e0 7cb9b5d8de5e0b1c3a86c7a08a580e51be75a8afdaba2cda08f87d352652a3c7 9bda6bcd32fd59e8079fee3fe7fa161ff626461e85ff8b9b60e2e6bc72884c6f dbaa5e8ad5912206cdd26b204cb34a5403c4fe9cc6d0a2e6805a98624c56baf0 3e673abaa926e941739ba23126dd78ca82499f376d15bfc7cc70f1586f5f10a1 fe99eed1a1f44ace1fc2bb8017599cf6ff3def1dcd7c683d21b5652c6c93b8fd f9fc70c3d5ade5f3509e03de2b93dc0c472061d17beec5a88b851b793206ce75 b32359f056a3c5e76af7a9627a6b2b293cd072e4904b8ea1ee2d0f2cee2175ca 61159ca39298a4f6af8a0ebb1b58b27e885e5708431c42838394cd45ffac06b8 154636f0b299cfec94493715c60025f42809234a89f13b3e1fbceadecd031fab 6a6283d5240402df432ecdc150513a5f917cc45341849958fe523cfb4f12c69b 2e88beef9104f76fd48daf72a990c050b4e5c2d83a06ea0d371d7c1af50e2d67 40cb2c9abc6d77dd70772fc9278e6d49da30c0212c2f94b8982c5712e4371957 2ba955ff6c60656c47616dc710c883796ac55106bf68c080194622842b1ad038 52341556036b02a3f7eb6f38b2309d6b6e99045f5bd4174518ba63d83666766c 93132f0f05f1f0fe8c7474a85a586aa3cd51ef9224707a0708a9966f537d0894 dcf9c38a780a51ba59a43c90bd24f1d6a2050e126c5fc34584ad719d39cbe7e1 143ef5e04ce291fabd56ec617cef4fdae6985b1b9578a354a47004f11f22070f 73ea58d77c881753362b0eba27d7ba8844f5f61ebe2db5bbeb5393a0ed2fa354 6983c159dd941027ea44d54767355c6ed7b16c94627eb33e2096be435cc31619 8a18f365e4150c0163b423490f452a5d417fa9ed181b136c268f5815afb45eb9 4e058d13a0627c4987680c1bc8330dbb569320979a83eed5cad9f45d88d50516 de0e929e0da1466cfcd7538a8d2ba843bafb1409a1b5cb2f705701e887c39ece 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 26 /rho put dup 34 /epsilon put dup 59 /comma put dup 65 /A put dup 83 /S put dup 99 /c put dup 100 /d put dup 101 /e put dup 105 /i put dup 107 /k put dup 110 /n put dup 115 /s put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31 aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638 12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c 366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6 472e944b3a49d5dc688432bff673249b16f7028176be3887f82cd6aceefb4785 1a5e19f0cef93a799de55ae8707f3c54fa37edf8a0332721f50c4d5d9092de05 e26413903122ef3fb9b7659dea448a06b931429dd62a086db45f6431f63c0030 664c3e100e86a7a736e8a139e2e5833b16428ceb59121fd1cf29e41648e79260 3a60fa20164e5ffc4a88abc9c9cd9292b0744318ce263430b10b8242eb8047a1 284a87fc6ffcbf9ae369a47fdcc5cb37cc424e0fe6ec7480ca0d7eaa3272e11e fbe9672936ae5678ade441adb402b478dcab7dd38a0cc817140ee33490fbfeb5 4e556817092ea1c06fd00a1348e5f61f465d441ae2e55c7935a2e18bb8ad11ea 1127b72556d0d867567f2c0f43ae74fa033f0fa012e8bd9c56df1f6d28e27dd1 9183119834029788ec1693a9e738c847af6e89ff144c0c35dad4647f2e97dd79 828b8e99f4b65277e3a5a283e4c2da5596012daaafa470fb1dba9a941cc44d37 9972f04118073a922acc5cdb50db7a9a54eeaaa7d769c0fee0fbbed199c10ed4 66f3bc57a9cab49c23ada4f74527ceb5203db37f337e4e51267216c6090a3d93 148c4271e7dac6d75d01ccf6f40bd8ab6e9743af4a71602a8a9f5459d9ab59ea 3e9e78f7b9418145069cc765fb862157982fc5900b40936da4a8930e8d3a016e dfc55554301b586e1669cde141ef969895e885c519fafac89720dd55837bfd79 609f81bf7718ee081b7b933140da61002931207f2e7c459a2a0d1521c6cf81e2 752d24a495fdf4c5124dfd6f0ad46825adb75b773a67868eee39a8fc70719d11 9b3d76cd04cee0b54799173dddd23852fec884393f50e26002f37c9f36eb4915 48f8d8dd0fba9428ea40690d8fe3731541ede7aea4b17f6cd183b3e4b5faf594 a48cb63464623c356445e0bbf488e61e7475d49973107e73658aa2b566894a78 1e0a961c99f26c6e247168b656cb76b6775992dbb6cc709ce9bd9a1a272c9f9f c263b6fdb830e65cc2412a7a309320e1facdf453bd461335d2bc9c4b09f829d2 6b31dc74eaec74512c2aa6f7225313bf35b146b42fafd6613c42e8f4491c3b80 860d62190d6c169a5120ac4656757662d8db032bc7f0726d265cf030fdfa4900 7cdeb8ebf9097017b34595ffa1d6de3959b274cc5afb1107eee098ab8429b8a6 73bb582b8f79f3a7010f8e657630d1e9dee634578ba0a288f4bdf268fc423252 1273a574d279a3c80fd2e0d785b3e43ed3c6e877a4f7b989eda2c0a4e3513db4 b0b05b9494dafafb3c05b9f35df75560d7e1ca889c081898bfab2b13386c8402 f962b3f9dd2ef5527d65e14f5bd316343ac4c7330e277dd3e63eb318d6a317b1 d697d6d5a66769bb022deec31a033778a1ec1e9a94341d621501933581e26e2b d703efd115c129ae0b3f9dadc3232f0f1a72a76c85dc300fde95a3aba91425ad 49c3d5a5d0aa2b7b4defea9760c5626649b3cb66c48520a5a73451475cf96c62 2f1e80d365b71486616b4bab484a46cc259fdede31cf81f80ae244481b884faa 8d813030a941c82f74246b7560a69b7cde0cdc567744d1a5678f2964c9f1937d cac43d2b46cb5c7758e85775f9e5d86aa21d525b8473584d4a99e0e95ee1bc7a 3f074a05a6431c7fe58d3945362a86d4009a64c125a9de60dc79af76df59f0fa 3ef749c9299574add5724c9581582f5f9ca11248bf3cd8d943bc5fa58726160a a211b80bdd23671009650b51d1c337cd7764c36806f391cd977bfa0cb2ca3635 6c9c4f54620004ab8498af3da051aa55aff149660e460b7c1fe1d9d24d2c1f88 a61eef835f4ecb7e87d1553f8be704b388c94ef0541e79114fe997a6cae025d7 6d164e5438da8fd4f9885e76e1b92eb0caaab7ff29c8663358dbe47bec432f22 967a9fba4e436d911b75d7ec4518f134f99335e4822ead7b8b155eed31ca70d3 ee2c770bde231c759466d358ebd865098406b5cbb6818680ed03dcd1d8ba64d4 f2e1973e6e37e2b11421e9149eec961fda0c2d8c302e8cc1e626dbf7fb585717 5717f8d61d4883bb50ef8fc344b7ade2b2514035a5c3dc0b5679fcd76e4e0b29 f671fd554eab9b5b13400556b458f7f5b9be6e917e971f3e80766a6aec98b3d4 a69cb290cd440cad7de252c9b987a63c3ee844ec980a5f9fd140f9205660ba97 01b306c782c109c8965e47134d5275e3042ab1858357a2ddd90b38f1773ecee4 197ac82c5aa87e6e03b46899b9c7e8b00754e0b302790f2d71d3ba391f86a054 376f01ff314632cfb4334da57189418c3960e1c432c578db74e8d11f88c0e38e 65f4a7d934767cd7ffba1751cf3ff6fbf1fb7e4fe686d177b39b4b226b6d2ebd a779f8c292139ae3f8a4957b18abbcf0eee03ec4514604c67ff3e94b3c576f97 4a7ef1e6545b74beaae5236d421ad212c5579100cc0d9df27f273489080b06a8 c09f731e7a974e4ded39fcc1c4528cfd12b4e7c9b2022fa67266487946453b29 fae53f7ac4429c7d092867431b94413d5931287563d0d284f1ad4d66f23c887f 58d78afbbbaa89799c8e8e23731fe622aa892c33a33fa5f53c403b27d7a5ff97 27f3bebd1d322c724fbdcbb206eaf8b853ee3d23582a6f8a4b7ee9f2af7454dc b839e26179d379aeca9892adc11780b07db32531cc4b8f2aff39f2ad9bab0cf4 3dcabb7cbe52f4caf7e3ff88d589add294983c17b559bbb16ae134eeeaff79b2 49ea8a49f1dcfd215f0e78abb3a395e399a77a6e1eb6565ff72f67fb9122313d 1194e38621abdd9ac07f49cb8be95e69945806e35ec1f9edb16ff16fc4df2375 9c594963bd2d4035fd57f3aa9298e666a92fe17eb70dc862bda17b0b0cbba3c7 cd187cfa8be28d55a9ccfa99619f1fc072b0b72406863eca5419c467c967b72c 6d9fdc15450762c1ed54b32751ff7e8def35e3c8d97e7b8433fb0dd70a23adf6 129817dff7d2b0f8330c1e16920044bc85bb856dcad522264297bc7435c7be57 deb60095f4c1d6ad723ad9e798048baaff52da6b5ded35bd9b3869585c17a77c dc8fd2a89beab9977b262d7b9be9e8e75d11bd2ee8a08df250c8043635e91f0e bf0b0ee06dd58f07c811d7875d7e3da9a2ecbdefe6ee38e4b32d8d6b69e69514 cdc88226e39f0479679e837747226e73a6cafecded14077392f78f16087ce1da ce6d4c4c70c9445c7fa7565ec1941a8d8a36968ae08339bf8a279a855fda1ad6 30b9bce7182178648a8ec93d7930aadc150e2f323a1073f654b726f401939b88 ad9839c49b7f29ed13caa3a1b4af051418ab9f34fe6c2863e237d35773e2f8bf b1ea1b6f685ff68b57a6be4b7136ec44596939644cfb85e11957042ce7c5af3e 2c07623502b0b4d089c6aa54a033d6f3c4f7ae905cf4774665b5345a735b7247 585a51a399a284d8b9e251d562064b56501594c786674b7c6096faa29ea26b43 6945dbcb55cab8b2a1c7c26e340483488cc16a7af46e640982b269ee790b5472 3ff6bdb0f6d3991659be52b1a60f88518347ead5d06992887b795d577d485c47 93627a9cfa86254a852a589c87a250094b9a95c03a9b1eeea1e39dc31ac5a081 69213e23184a225f01a2ddbc79426164f2c39abb53d6d8e3b090f5486c4e16b6 58335e08048e7e86dd1c709b036e2cace3ff5e0b3bb1bc5c87fc0f677619ed46 f3169a671ea70a91e72d4fa8880eb4384cb197ec54c595bbcc1e23eaf0fb5979 ef3aaba9fa2f97dea3306baffbb84d65ca60d05f2c3d06439840103921c8ad33 94ece9b3b5fa7aedc92fde36a5169333718b6634fe1b22467f0a039b0c980393 92ce72a541be46ef4fe497da632752c8bf0b527f2773c39ad4bc0b665f279604 4214314986909c315832f52698a3893197cc77 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % 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 (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 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 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueXX 5000819 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddc63eb43f34fa90ea73a234af35fd9b24eb7 4f19626e9124df7acb92629cc87b2cf81c4a89b27447806db34393ddf0402958 e2daee0b4bf315f9aa0a2650d2e11ee289ffaec940d0af160fe7f29411c1c458 69d1ac3bcfe2ae4da72422549095f1fc9fec606289316f106e719a4ae2fd45ee 868fddf07a80e9a626bb43cdfdaa9dcd208b88fd99af20b27f9d6b5cda6a3fa8 8d5acfce8b5eebb38854378cecc3bfdac526514f1be9fb28ae628918ba942a3e 05b78c3aff808cf416a5ed01be280231b75a7aee0c66b0549713bef6b3cbc188 e625ba8091f481ffd2b7a47220a8ad34d58daa96e5249e4f0706f1d535a25c6f 06cf9e2ff58fac111fadba4bd9095019791eada3119a041682c621b0e1831c3a f432fbe9d742963d816a1692e1010b567e2ae4d40d61f8a54b0401377c4b13fb 4fe1cf1aa15a3083562f28c7372e6479154306f1edee2664c2e9ae3a06f2c7f2 0dbba0d0d18e6c51c5090d4e888bd6ff50f9886b327dfe843b14c432b1c7ecfe f5a88cf8aabbc7cfcd35557663beee65e1d4ee72b329014e72b21350d36304c8 d9440a569c79eaeac097fcaf616f64f4ad6761a5cc902258bed6e689d5f82f1f 176fd5faff805c7590a821283fc148b5a020f24070d304a6867ae385ed6f6198 726d78540234ae574ae384a45bba776c084b94decf657985f4bac7c6a5b0cf8c 6ef5103d9c8f116ba6b100224a223b497ed5a1e8cbdfb23133e0e4a5f54e8b2c 1e21d829fb064945bf3c21290d4e3fd41494f15b1187b99f042af42e01429edd 83c9ef1aeae04d89cdf86aedd9c7cc9cded0d2dceff5612ba22c36d4ed921d7e e7a0e0520c92da27df2665bac00c1e9a6a00801182727134a52b5d54c4d882ce b948a97f4ff72598df13e7f0685ffd7e5b0d130673d686357ae147424314475a a5e927759ccac76ffa01ab6d16d0a325aace0d9ce0cc13eabb2b9eefbf3dc196 dc45e847dd7717e417f6767320127aeae1394e3392476d0761bd587c60a78883 531c073d45135fb89e1263a5f6027994ae37ec3ae8d553ecc1867060542d90f1 dd273f59 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueXX 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e2851973f31a3280c08220536dd2c2de1ffd15fc7390913427ab78eb6d43b 8063223d65fd28ff3d1247f681b2b45681509b57ddc243e6cb03cc2ca12bab7a e851b881f9bdd89fcffa4f8091bd827649a5b36353db09f98c8c02ce4d952a03 b627a8e3a463bbab6dd9b6d37bef0d0b80a8eccadd52569152625253d39d9d51 a7d9f6b731bed1f2b2446ed069bc913fdf127bb1f1ead88b0e31d4b96c31d371 5135ef273e1f19fde6a48695c0ec0dc75a9be460b057704adf3d59cf65ed666b 0cfac98391d5df064100a0afe65339786504e6475faa102489d0cf4e53b6e7db 2f1d9adf662bcea1d4e141c924a2f2ee310ca66093ccb6347d0840ae8b030a21 82facba07ef5a923af56e83d97c9cfcb7724fa7641c8f2be11cbcbf8a1a7e462 0a1a66d5c637a77a4baf72927075ef06eb322320b1af562b6ad0b8c1e8dffc1a eaa86807bd77a2521e49fa2f74d1f2f63530f7329b5ea704c4537aab8678d43f 86d533aac7625741c4f0f9b5d049f1bf74da5cdda609059287332a25dc8d5daf c2b1eb627ac98cb7a091e53190a301545fa7ca36e98315992cc8f3a52a41d7b5 7e317bcf96fa7d46e00b7d4141774c6c8b3d9b709e122ec775aa33b5e6c1cfe9 d450d6c61a5ed3f79167aed7e5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 10 /circlemultiply put dup 14 /openbullet put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 55 /mapsto put dup 56 /universal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 72 /H put dup 80 /P put dup 83 /S put dup 84 /T put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c4300265fd2347a3a851a9cb00aa30bbb57598cca6485e51c30bb78bf8307 1bcb3fea6ce14383cb382f324afa02d18cff3ac22b494d3d02302ee13ec9ffff 860b0bdac4c968e9168d001095bafd61afec9a5a23e727abaf5b193f527df2af 10123a3aad31cf3d8b4bb2e32a699afcfdd2612aa694bbd53a6ea0bf3ec61b47 ff905e5e898717c40328643d610218c2fee0b1ab6bea10870a7acf2b59d179b5 d0d0643d73bd771d34e998f2a43766fb826480f5c00a787818e8ed460612c5d2 86c799428a405262e066668b2c1070989d5c6828e0ebd20259d1535c76dbf996 7bee994ca9546d3a52fed6cad0ddeaeafc4b4ddaaf8b0c8298f72ff9ff37111b 5c7f64e20651fab5c678d2dc91977aef35de0e5b949f9361320a425125932193 d6281f91ce97ac30c72c4bb921c6e820e4a68a18121577d7c5179c01872582a7 5244018a589b04c718e7a244fa3b7740d38fb387070ca3239eb976b717a8fd7a 9df0472f8a261ea6748879c812fd3a8702ebd48f80e74da386b978c36b513e50 383f5f58dd744a97bd5181b818167db01c7d2cc00c6f136a4e1d96eb254de0ff 299ed39e76704545fe7fb523d98deb09cd68bdfa23598bdbb178bfad9095cf62 3610aea84b94426464e1c8d44e35ddcc657443f9baab5b66c8ce8a13e71deb3c 1eab8cd381ef62ff2b3a44f9edfd71a7383e9dd302ab6780700d15da46d5e560 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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 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 65 /A put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T 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 readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 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fd67df929ad214a734a27acf495208a27685b42bba5a8ffcca90ef4f35810b71 0b3a6c323240d5a3fb4b7723a6ef03a4c31f0e99de01599d84586f0404bb5bf5 b3921df8ebc731b2d3b0629a787005d78af6b64b6bb7e51110438df2b22e2930 398ecfe6808e6db5239ee2d35c78570179f8062ef0d454e49364061c0c801d09 8a655287f7d6ae2bd6fc5c3c993cb0b27d26e9d625949c2bbd1303fee6ebdb80 f3cc36366a382cd5efc23283abd29d5ed89a9b51eb7e0626aaf11da8ea7e4edd 4e99316b2400d17762d3fb595ab4d671d1ddac38a3ca5db3759e20d6d2762f6a 29144213ec3841c728d57e73cb76998a8a15d4be15477f135f8e9e03fa932c72 6c66ac421539e7cd7e7456804dbf82bd8a3f269145fb543ae7a9215cedbd137c 93a5a7db136be33250d15dc539f4bc3ab65330246d556cb459635a1c2cbf102b 182c47a0e4841b86535ee1a8a891c69108e12cc1d05c13581e325ba655c52b1f c41207cf43a7fc9f6a15c10e7bbb3e6b9555976814d271036c5a602ea6ec2317 11d39f00cc611d1084c5b194a6186510e001ff3bff677520fd8aaf6c80c88ffc 3f804115918b0713011069740863179ce4fd4ff006e2b11548fd1db70cdfb11f 731def67c8917d6b091094deaeff5302edf857ff7df487bd70fef1c515b48efe 4df3615ef5e27dc62e39ada6938f1bcccec96746635c29dc8771104ed7f38c72 28034788d755faa966f9d2a9677595133197b913d8bbe9f3f31524f7c041a295 b3439dffb796761f57229a862c934c479f4efa496bb867a7cb7e7d370924bd4b 9053fe78d60973945b2b257b8d5e57a85cca0ce7ef97d6dfc6bea6004f1eed0f cb6f5f99b96053092e791d0e 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 12 /beta put dup 17 /eta put dup 21 /lambda put dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 30 /phi put dup 32 /psi put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 62 /greater put dup 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 88 /X put dup 97 /a put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 107 /k put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict 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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 3 /Lambda put dup 9 /Psi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 22 /macron put dup 32 /suppress put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 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 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 67 /C put dup 68 /D put dup 70 /F put dup 73 /I put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueXX 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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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 25 /germandbls 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 54 /six put dup 55 /seven put dup 58 /colon put dup 64 /at put dup 65 /A put dup 66 /B put dup 70 /F put dup 71 /G put dup 73 /I put dup 74 /J put dup 77 /M put dup 78 /N put dup 83 /S put dup 84 /T put dup 85 /U 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 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 127 /dieresis put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 dcf4871a5d023c9ef57d3362d9f2d7a440bb69bf653364105f16f4d0f03582f9 aced3d05cc76489b16e3fa8a446094d30038b06ecceda269f2eab9d19a99c7f9 39f9548f206c5a457a19270b2b82c43b091dfc5573468eaa3e7a4a32f8042891 d85e4b180fcbcb3091d2800e54c87d84ce9cad6869b5aabbbe47f40c68799893 d22b765295e1e69e33aa048b7ed98ba480ceca91f3ebf8ef85fe9a3976909626 b95ac5940d53f9b02215d84a44837ba25ed15cce0d504f1d335065594f3bc824 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1030f8a03809dadffb0edc742d3f4007b5186c6733bcbe0d14ff05d982641fc2 a912e7300c478a53f33a3636f761cc8230e113cc3e7e275a9e2fcfc2601ec804 92fe120330 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 10 /circlemultiply put dup 26 /propersubset put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 69 /E put dup 72 /H put dup 80 /P put dup 84 /T put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % 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 (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 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 19 /acute put dup 32 /suppress put dup 44 /comma put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 65 /A put dup 66 /B put dup 73 /I put dup 74 /J put dup 83 /S put dup 97 /a put dup 99 /c put dup 101 /e put dup 103 /g put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 122 /z put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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aac3a0060211514af9ce34e888bf846ca6cf1d7c5767779b5e5dec809be8463c 1a9a8667e4e51156b6d4986ad8603be84e3b3ca665d17132a5ff00f537d7f6b2 edb14b03ccafa073a25b9be7f0a53fa38e29568cf4bb0d2d0065d9d478b2588c 25814fb68bdba9132afdbbaf676bb70d4b6090507c32e11fddb88c747fe754fd f6420c7dd4078e09404f7e23f65091180b86944c1c112015e64b5a0e48d489b9 cf268aaaf5a79b18a3a6faf7f405a7a12f673d368d65f8f6b4c2 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 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 81 /Q put dup 83 /S put dup 84 /T 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 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueXX 5000795 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 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1564 y Fp(;)g(\027)q(;)g(T)e Fq(\))32 b(on)382 1677 y(a)h(doubly)f (in\014nite)h(pro)s(duct)f(space)h Fp(A)1731 1644 y Fv(1)1836 1677 y Fq(:=)d Fp(:)15 b(:)g(:)23 b Fn(\002)e Fp(A)h Fn(\002)g Fp(A)g Fn(\002)g Fp(:)15 b(:)g(:)q Fq(,)33 b(where)g Fi(A)3043 1644 y Fv(1)3150 1677 y Fq(is)g(the)382 1790 y Fp(\033)s Fq(-\014eld)d(generated)i(b)m(y)e(cylinder)g(sets,)h Fp(T)43 b Fq(is)31 b(the)f(shift)g(on)g Fp(A)2497 1757 y Fv(1)2603 1790 y Fq(and)f Fp(\027)36 b Fq(a)31 b(probabilit)m(y)382 1903 y(measure)j(on)f(\()p Fp(A)972 1870 y Fv(1)1047 1903 y Fp(;)15 b Fi(A)1152 1870 y Fv(1)1228 1903 y Fq(\))34 b(uniquely)f(determined)g(b)m(y)h(the)g(probabilit)m(y)g(distribution) 382 2016 y Fp(P)43 b Fq(of)31 b(the)f(sto)s(c)m(hastic)i(pro)s(cess.) 382 2129 y(A)g(discrete)g(QIS)f(can)h(b)s(e)e(view)m(ed)j(as)f(a)g (quan)m(tum)f(spin)f(c)m(hain)j(p)s(ossibly)d(coupled)i(to)382 2242 y(an)38 b(external)g(en)m(vironmen)m(t)h(where)e(one)h(fo)s(cuses) g(on)g(the)g(information)g(carried)g(b)m(y)382 2355 y(the)g(quan)m(tum) f(state.)j(Alternativ)m(ely)-8 b(,)41 b(w)m(e)d(can)h(think)e(of)h(a)h (QIS)e(as)h(a)g(device)h(that)382 2467 y(sends)22 b(quan)m(tum)h(ph)m (ysical)h(systems)g(of)f(a)h(\014xed)f(t)m(yp)s(e,)h(prepared)e(in)h(a) h(join)m(t)g(generally)382 2580 y(mixed)i(and)f(en)m(tangled)i(state.)g (In)f(b)s(oth)f(cases,)i(a)f(QIS)f(pro)m(vides)h(input)f(for)g(quan)m (tum)382 2693 y(c)m(hannels.)382 2806 y(Before)46 b(w)m(e)g(presen)m(t) f(a)h(mathematical)h(mo)s(del)e(for)h(QIS,)e(whic)m(h)h(corresp)s(onds) f(to)382 2919 y(the)35 b(Kolmogoro)m(v)h(represen)m(tation)f(of)g (classical)i(IS,)c(w)m(e)i(in)m(tro)s(duce)g(quasilo)s(cal)g Fp(C)3301 2886 y Fv(\003)3340 2919 y Fq(-)382 3032 y(algebras)28 b(as)g(the)g(non-comm)m(utativ)m(e)i(coun)m(terpart)e(of)f(the)h (doubly)f(in\014nite)g(pro)s(duct)382 3145 y(space)41 b Fp(A)703 3112 y Fv(1)778 3145 y Fq(.)g(This)f(standard)g (mathematical)j(formalism)d(is)h(in)m(tro)s(duced)f(in)g(detail)382 3258 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Fp(;)15 b Fi(A)665 2494 y Fv(1)741 2527 y Fq(\))32 b Fo(uniquely)f(determine)-5 b(d)33 b(by)f Fq(\011\()p Fp(a)p Fq(\))26 b(=)2063 2459 y Ff(P)2159 2554 y Fc(i)p Fv(2)p Fk(A)2282 2535 y Fb(\003)2346 2527 y Fp(a)p Fq(\()p Fe(i)p Fq(\))p Fp(\027)2544 2494 y Fg(\(\003\))2653 2527 y Fq(\()p Fe(i)p Fq(\))p Fo(,)32 b(for)g(al)5 b(l)33 b Fp(a)25 b Fn(2)g(A)3318 2541 y Fg(\003)382 2640 y Fo(and)37 b(arbitr)-5 b(ary)39 b Fq(\003)33 b Fn(\032)f Fh(Z)p Fo(,)k(wher)-5 b(e)37 b Fp(a)p Fq(\()p Fn(\001)p Fq(\))d Fn(2)e Fp(C)7 b Fq(\()p Fp(A)1975 2607 y Fg(\003)2028 2640 y Fq(\))37 b Fo(is)f(the)h(Gelfand)h(r)-5 b(epr)g(esentation)39 b(of)382 2753 y Fp(a)44 b Fn(2)g(A)652 2767 y Fg(\003)704 2753 y Fo(.)f(Then)g(the)h(IS)f(given)f(by)h Fq(\()p Fn(A)1797 2720 y Fv(1)1872 2753 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\))43 b Fo(has)h(the)g(Kolmo)-5 b(gor)g(ov)46 b(r)-5 b(epr)g(esen-)382 2866 y(tation)27 b Fq(\()p Fp(A)743 2833 y Fv(1)818 2866 y Fp(;)15 b Fi(A)923 2833 y Fv(1)999 2866 y Fp(;)g(\027)q(;)g(T)e 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Fg(\()p Fk(n)p Fg(\))1732 3941 y Fq(instead)g(of)h Fp(\032)2196 3908 y Fg(\(\003\))2334 3941 y Fq(and)f(\011)2582 3908 y Fg(\()p Fk(n)p Fg(\))2714 3941 y Fq(instead)g(of)h(\011)3202 3908 y Fg(\(\003\))3309 3941 y Fq(.)382 4054 y(A)f(stationary)i(QIS)d (\()p Fn(A)1205 4021 y Fv(1)1280 4054 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\))31 b(is)f Fo(er)-5 b(go)g(dic)37 b Fq(if)1152 4337 y(lim)1123 4391 y Fk(n)p Fv(!1)1323 4337 y Fq(\011)1409 4181 y Ff( )1480 4337 y Fq(\()1530 4275 y(1)p 1525 4316 55 4 v 1525 4399 a Fp(n)1605 4223 y Fk(n)p Fv(\000)p Fg(1)1606 4251 y Ff(X)1615 4446 y Fk(i)p Fg(=0)1754 4337 y Fp(T)1820 4299 y Fk(i)1847 4337 y Fq(\()p Fp(a)p Fq(\)\))2000 4299 y Fg(2)2041 4181 y Ff(!)2138 4337 y Fq(=)25 b(\011\()p Fp(a)p Fq(\))2423 4299 y Fg(2)382 4613 y Fq(holds)34 b(for)h(all)h(self-adjoin)m(t)h Fp(a)c Fn(2)f(A)1619 4580 y Fv(1)1694 4613 y Fq(.)j(It)g(is)g(imp)s(ortan)m(t)g(to)h (realize)h(that)e(for)g(a)h(QIS)382 4726 y(as)27 b(a)g(dynamical)g (system)g(on)f(a)h(quasilo)s(cal)h(algebra)g(this)e(de\014nition)h(of)f (ergo)s(dicit)m(y)j(is)382 4839 y(equiv)-5 b(alen)m(t)32 b(to)g(the)g(de\014nition)e(used)h(in)f([2)q(])h(\(cf.)h(Prop)s (osition)f(6.3.5)i(in)e([15)q(]\),)h(where)382 4951 y(\()p Fn(A)490 4918 y Fv(1)565 4951 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\))36 b(is)h(said)f(to)h(b)s(e)e(ergo)s(dic)i(if)f(\011)g(is)g(an)g (extremal)i(p)s(oin)m(t)e(in)g(the)g(compact)382 5064 y(con)m(v)m(ex)27 b(set)e(of)h(stationary)g(states)h(on)e Fn(A)1785 5031 y Fv(1)1859 5064 y Fq(,)g(\(cf.)h([10)r(]\).)g(Th)m(us)e (the)h(results)g(for)g(ergo)s(dic)382 5177 y(quan)m(tum)d(dynamical)g (systems)h(presen)m(ted)f(in)g([2])h(hold)f(for)g(the)g(ergo)s(dic)h (QIS)e(de\014ned)382 5290 y(ab)s(o)m(v)m(e.)382 5403 y(Finally)38 b(in)f(this)h(section)g(w)m(e)g(in)m(tro)s(duce)f(the)h (en)m(trop)m(y)g(rate)g Fp(s)p Fq(\(\011\))f(of)h(a)f(stationary)1854 5652 y(4)p eop %%Page: 5 5 5 4 bop 382 548 a Fq(QIS)33 b(\()p Fn(A)678 515 y Fv(1)753 548 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\),)35 b(whic)m(h)g(is)f(the)h (crucial)g(quan)m(tit)m(y)h(in)e(the)h(presen)m(t)f(pap)s(er.)g(Recall) 382 661 y(the)h(one-to-one)i(corresp)s(ondence)d(of)h(a)g(stationary)h (\011)e(on)g Fn(A)2564 628 y Fv(1)2673 661 y Fq(and)g(the)h(family)g (of)382 774 y(densit)m(y)c(op)s(erators)f Fn(f)p Fp(\032)1190 741 y Fg(\()p Fk(n)p Fg(\))1292 774 y Fn(g)p Fp(n)c Fn(2)f Fh(N)p Fq(.)30 b(The)g Fo(entr)-5 b(opy)34 b(r)-5 b(ate)38 b Fp(s)p Fq(\(\011\))31 b(is)f(then)g(de\014ned)f(b)m(y)1338 1002 y Fp(s)p Fq(\(\011\))d(:=)54 b(lim)1669 1056 y Fk(n)p Fv(!1)1882 940 y Fq(1)p 1878 981 55 4 v 1878 1064 a Fp(n)1942 1002 y(S)5 b Fq(\()p Fp(\032)2085 964 y Fg(\()p Fk(n)p Fg(\))2188 1002 y Fq(\))p Fp(;)1007 b Fq(\(2\))382 1234 y(where)23 b Fp(S)5 b Fq(\()p Fp(\032)781 1201 y Fg(\()p Fk(n)p Fg(\))883 1234 y Fq(\))25 b(:=)h Fn(\000)p Fq(tr)o Fp(\032)1253 1201 y Fg(\()p Fk(n)p Fg(\))1370 1234 y Fq(log)1488 1255 y Fg(2)1542 1234 y Fp(\032)1589 1201 y Fg(\()p Fk(n)p Fg(\))1714 1234 y Fq(is)e(the)f(v)m(on)h(Neumann)e(en) m(trop)m(y)i(of)g(the)f(densit)m(y)382 1346 y(op)s(erator)31 b Fp(\032)796 1313 y Fg(\()p Fk(n)p Fg(\))897 1346 y Fq(.)382 1631 y Fr(3)135 b(Data)46 b(Compression)f(Sc)l(hemes)382 1834 y Fq(In)31 b(order)g(to)i(de\014ne)e(lossless)h(data)h (compression)f(sc)m(hemes)g(for)f(enco)s(ding)h(quan)m(tum)382 1946 y(signals)27 b(w)m(e)f(need)g(the)h(concept)g(of)f Fo(tr)-5 b(ac)g(e)30 b(pr)-5 b(eserving)30 b(quantum)f(op)-5 b(er)g(ations)p Fq(.)30 b(A)c(ph)m(ys-)382 2059 y(ical)40 b(approac)m(h)f(to)g(trace)h(preserving)e(quan)m(tum)g(op)s(erations)h (can)g(b)s(e)e(obtained)i(as)382 2172 y(follo)m(ws.)d(Consider)e(a)h (quan)m(tum)f(system)h Fp(S)k Fq(prepared)34 b(in)g(some)h(state)h Fp(\032)f Fq(acting)h(on)382 2285 y(the)h(Hilb)s(ert)f(space)h Fn(H)q Fq(.)g(W)-8 b(e)37 b(imagine)h(that)f(this)g(system)f(in)m (teracts)j(with)d(its)h(en)m(vi-)382 2398 y(romen)m(t,)k(a)f(quan)m (tum)g(system)g Fp(S)1574 2412 y Fg(en)n(v)1725 2398 y Fq(in)f(a)i(state)g 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y(quan)m(tum)f(op)s(eration)h Fn(E)8 b Fq(:)1184 3265 y Fn(E)g Fq(\()p Fp(\032)p Fq(\))26 b(:=)g(tr)1576 3279 y Fv(H)1636 3287 y Fb(en)n(v)1736 3265 y Fq(\()p Fp(U)10 b Fq(\()p Fp(\032)21 b Fn(\012)f Fp(\032)2084 3279 y Fg(en)n(v)2195 3265 y Fq(\))p Fp(U)2302 3228 y Fv(\003)2342 3265 y Fq(\))p Fp(:)853 b Fq(\(3\))382 3455 y(It)36 b(can)f(b)s(e)g(sho)m(wn)g(that)i(eac)m(h)f(trace)h (preserving)e(quan)m(tum)g(op)s(eration)h Fn(E)44 b Fq(p)s(osseses)382 3568 y(the)31 b(follo)m(wing)i(represen)m(tation)f(kno)m(wn)f(as)g (Kraus)f(or)h(sum)f(represen)m(tation)j(\(cf.)e([6)q(],)382 3681 y([7)q(],)f([13)r(]\))1433 3884 y Fn(E)8 b Fq(\()p Fp(\032)p Fq(\))26 b(=)1728 3798 y Ff(X)1782 3994 y Fk(i)1874 3884 y Fp(E)1941 3898 y Fk(i)1970 3884 y Fp(\032E)2089 3847 y Fv(\003)2084 3907 y Fk(i)2128 3884 y Fp(;)382 4156 y Fq(where)h Fp(E)709 4170 y Fk(i)763 4156 y Fn(2)e(B)s Fq(\()p Fn(H)q Fq(\))j(and)1262 4088 y Ff(P)1358 4183 y Fk(i)1401 4156 y Fp(E)1473 4123 y Fv(\003)1468 4182 y Fk(i)1513 4156 y 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Fn(C)1308 5099 y Fg(\()p Fk(n)p Fg(\))1435 5136 y Fq(:)25 b Fn(S)7 b Fq(\()p Fn(H)1660 5099 y Fv(\012)p Fk(n)1762 5136 y Fq(\))26 b Fn(\000)-16 b(!)26 b(S)7 b Fq(\()p Fn(H)2170 5099 y Fg(\()p Fk(n)p Fg(\))2271 5136 y Fq(\))p Fp(;)924 b Fq(\(4\))1258 5403 y Fn(D)1331 5366 y Fg(\()p Fk(n)p Fg(\))1457 5403 y Fq(:)26 b Fn(S)7 b Fq(\()p Fn(H)1683 5366 y Fg(\()p Fk(n)p Fg(\))1785 5403 y Fq(\))25 b Fn(\000)-15 b(!)25 b(S)7 b Fq(\()p Fn(H)2192 5366 y Fv(\012)p Fk(n)2294 5403 y Fq(\))1854 5652 y(5)p eop %%Page: 6 6 6 5 bop 382 548 a Fq(where)35 b Fn(H)728 515 y Fg(\()p Fk(n)p Fg(\))863 548 y Fn(\022)e(H)1045 515 y Fv(\012)p Fk(n)1181 548 y Fq(for)i(all)h Fp(n)d Fn(2)g Fh(N)i Fq(and)g Fn(S)7 b Fq(\()p Fn(H)2096 515 y Fv(\012)p Fk(n)2197 548 y Fq(\))p Fp(;)51 b Fn(S)7 b Fq(\()p Fn(H)2483 515 y Fg(\()p Fk(n)p Fg(\))2585 548 y Fq(\))36 b(denote)f(the)h(sets)f(of) 382 661 y(densit)m(y)30 b(op)s(erators)h(on)f Fn(H)1302 628 y Fv(\012)p Fk(n)1433 661 y Fq(resp.)g Fn(H)1729 628 y Fg(\()p Fk(n)p Fg(\))1831 661 y Fq(.)g(W)-8 b(e)31 b(refer)f(to)h Fn(C)2416 628 y Fg(\()p Fk(n)p Fg(\))2518 661 y Fq(,)g Fn(D)2647 628 y Fg(\()p Fk(n)p Fg(\))2778 661 y Fq(as)g(compression)382 774 y(resp.)f(decompression)g(map.)382 887 y(The)g Fo(r)-5 b(ate)38 b Fp(R)q Fq(\()p Fn(C)5 b Fq(\))31 b(of)g(a)f(compression)h(sc)m(heme)g(\()p Fn(C)5 b Fp(;)15 b Fn(D)s Fq(\))31 b(is)f(de\014ned)g(b)m(y)1195 1153 y Fp(R)q Fq(\()p Fn(C)5 b Fq(\))26 b(:=)f(lim)15 b(sup)1582 1226 y Fk(n)p Fv(!1)1838 1092 y Fq(log)1956 1114 y Fg(2)2010 1092 y Fq(dim)g Fn(H)2255 1059 y Fg(\()p Fk(n)p Fg(\))p 1838 1132 519 4 v 2070 1216 a Fp(n)2366 1153 y(:)864 b Fq(\(5\))382 1463 y Fr(4)135 b(Fidelities)382 1666 y Fq(In)26 b(this)h(section)i(w)m(e)e(review)h(the)f(basic)g (notions)h(and)e(prop)s(erties)h(of)g(the)g(\014delit)m(y)h(and)382 1779 y(deriv)m(ed)41 b(quan)m(tities)h(needed)f(to)h(measure)e(the)i (distance)f(b)s(et)m(w)m(een)h(t)m(w)m(o)g(quan)m(tum)382 1892 y(states.)27 b(The)e(\014delit)m(y)h Fp(F)39 b Fq(b)s(et)m(w)m (een)26 b(t)m(w)m(o)h(densit)m(y)f(op)s(erators)g Fp(\032)g Fq(and)f Fp(\033)k Fq(acting)e(on)e(some)382 2005 y(\014nite)30 b(dimensional)h(Hilb)s(ert)f(space)h Fn(H)g Fq(is)f(de\014ned)g(b)m(y) 1417 2237 y Fp(F)13 b Fq(\()p Fp(\032;)i(\033)s Fq(\))27 b(:=)e(tr)1919 2129 y Ff(q)p 2010 2129 301 4 v 47 x Fn(p)p 2085 2176 48 4 v 2085 2237 a Fp(\032\033)2187 2176 y Fn(p)p 2263 2176 V 61 x Fp(\032:)920 b Fq(\(6\))382 2452 y(The)23 b(\014delit)m(y)h(is)g(symmetric)g(in)f(its)h(en)m(tries)g (and)f(tak)m(es)i(v)-5 b(alues)24 b(b)s(et)m(w)m(een)g(0)g(and)f(1)h (with)382 2565 y Fp(F)13 b Fq(\()p Fp(\032;)i(\033)s Fq(\))27 b(=)f(0)31 b(i\013)g Fp(\032)g Fq(and)f Fp(\033)k Fq(are)d(supp)s(orted)e(on)i(orthogonal)h(subspaces.)e Fp(F)13 b Fq(\()p Fp(\032;)i(\033)s Fq(\))28 b(=)d(1)382 2678 y(app)s(ears)32 b(only)g(in)g(the)h(case)g Fp(\032)c Fq(=)g Fp(\033)s Fq(.)k(In)e(ligh)m(t)j(of)f(these)f(prop)s(erties)g (it)h(is)g(reasonable)382 2791 y(to)42 b(in)m(terpret)g(the)g 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(represen)m(ted)f(b)m(y)g Fp(P)47 b Fq(\(resp.)35 b Fe(1)23 b Fn(\000)f Fp(P)13 b Fq(\).)382 4629 y(The)36 b(trace)i(distance)f (quan)m(ti\014es)g(the)g(largest)h(di\013erence)g(of)f(probabilities)g (for)f(ob-)382 4742 y(taining)31 b(outcome)h(\\y)m(es")g(if)e(w)m(e)h (p)s(erform)e(measuremen)m(ts)h(on)h(quan)m(tum)f(systems)g(in)382 4855 y(the)e(states)i Fp(\032)e Fq(and)g Fp(\033)s Fq(.)g(This)g (relation)h(b)s(et)m(w)m(een)g(the)g(\014delit)m(y)f(and)g(the)h(trace) g(distance)382 4968 y(giv)m(es)j(us)d(an)i(idea)f(ab)s(out)h(the)f(op)s (erational)i(in)m(terpretation)f(of)g(the)g(\014delit)m(y)-8 b(.)523 5081 y(The)23 b(question)g(ho)m(w)h(w)m(ell)g(is)f(the)h(state) g(of)g(the)f(op)s(en)g(quan)m(tum)g(system)g(preserv)m(ed)382 5194 y(b)m(y)i(a)h(time)g(ev)m(olution,)i(a)d(measuremen)m(t)h(or)g (more)f(generally)i(b)m(y)e(an)h(arbitrary)f(quan-)382 5307 y(tum)41 b(pro)s(cesses)h(de\014ned)f(b)m(y)h(a)g(Kraus)f (represen)m(tation)i(leads)f(to)h(sev)m(eral)g(\014delit)m(y)1854 5652 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Fn(\022)25 b(H)1448 4799 y Fv(\012)p Fk(n)1582 4832 y Fo(such)33 b(that)480 5044 y(1\))46 b Fq(tr\()p Fp(\032)762 5011 y Fg(\()p Fk(n)p Fg(\))864 5044 y Fp(P)922 5086 y Fv(T)979 5051 y Fb(\()p Fa(n)p Fb(\))961 5096 y Fa(")1073 5044 y Fq(\))35 b Fn(\025)f Fq(1)24 b Fn(\000)f Fp(")p Fo(,)38 b(wher)-5 b(e)38 b Fp(P)1838 5086 y Fv(T)1895 5051 y Fb(\()p Fa(n)p Fb(\))1877 5096 y Fa(")2027 5044 y Fo(is)f(the)h(pr)-5 b(oje)g(ctor)40 b(onto)f(the)e(subsp)-5 b(ac)g(e)609 5202 y Fn(T)682 5154 y Fg(\()p Fk(n)p Fg(\))659 5214 y Fk(")784 5202 y Fo(,)480 5390 y(2\))46 b Fq(2)654 5357 y Fk(n)p Fg(\()p Fk(s)p Fg(\(\011\))p Fv(\000)p Fk(")p Fg(\))1012 5390 y Fn(\024)25 b Fq(tr\()p Fp(P)1272 5431 y Fv(T)1328 5396 y Fb(\()p Fa(n)p Fb(\))1311 5442 y Fa(")1423 5390 y Fq(\))h Fn(\024)f Fq(2)1625 5357 y Fk(n)p Fg(\()p Fk(s)p Fg(\(\011\)+)p Fk(")p Fg(\))1957 5390 y Fo(.)1854 5652 y Fq(8)p eop %%Page: 9 9 9 8 bop 382 548 a Fo(Mor)-5 b(e)g(over,)34 b(these)f(subsp)-5 b(ac)g(es)33 b(c)-5 b(an)34 b(b)-5 b(e)32 b(chosen)i(as)510 747 y Fn(T)583 709 y Fg(\()p Fk(n)p Fg(\))560 769 y Fk(")710 747 y Fq(:=)83 b(span)o Fn(f)p Fp(e)1158 699 y Fg(\()p Fk(n)p Fg(\))1158 774 y Fk(i)1286 747 y Fn(2)25 b(H)1450 714 y Fv(\012)p Fk(n)1551 747 y Fn(j)84 b Fq(tr\()p Fp(\032)1813 709 y Fg(\()p Fk(n)p Fg(\))1915 747 y Fp(P)1973 788 y Fk(e)2006 753 y Fb(\()p Fa(n)p Fb(\))2006 810 y Fa(i)2101 747 y Fq(\))25 b Fn(2)g Fq([2)2317 709 y Fv(\000)p Fk(n)p Fg(\()p Fk(s)p Fg(\(\011\)+)p Fk(")p Fg(\))2704 747 y Fp(;)15 b Fq(2)2789 709 y Fv(\000)p Fk(n)p Fg(\()p Fk(s)p Fg(\(\011\))p Fv(\000)p Fk(")p Fg(\))3177 747 y Fq(])p Fp(;)1660 941 y(e)1702 893 y Fg(\()p Fk(n)p Fg(\))1702 968 y Fk(i)1804 941 y Fo(eigenve)-5 b(ctor)33 b(of)f Fp(\032)2430 904 y Fg(\()p Fk(n)p Fg(\))2532 941 y Fn(g)p Fp(:)607 b Fq(\(13\))382 1129 y Fe(Remark:)34 b Fo(The)j(ab)-5 b(ove)36 b(the)-5 b(or)g(em)39 b(r)-5 b(epr)g(esents)37 b(a)g(simpli\014e)-5 b(d)38 b(form)f(of)f(the)g(Quantum)382 1242 y(Shannon-McMil)5 b(lan)40 b(The)-5 b(or)g(em)42 b(pr)-5 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b(b)m(y)h(\(13\))i(represen)m(ts)e(a)g(subspace) f(of)382 2145 y(probabilit)m(y)26 b(close)h(to)f(1)g(for)g(large)g Fp(n)f Fq(in)h(the)f(case)i(of)f(an)f(ergo)s(dic)h(source)g(\()p Fn(A)3018 2112 y Fv(1)3093 2145 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\).)382 2258 y(In)41 b(analogy)h(to)h(the)e(classical)j (theory)d(w)m(e)h(will)g(call)h(suc)m(h)e(a)h(space)g(the)f Fp(")p Fq(-t)m(ypical)382 2371 y(subspace)30 b(of)g Fn(H)943 2338 y Fv(\012)p Fk(n)1075 2371 y Fq(with)g(resp)s(ect)g(to)i Fp(\032)1752 2338 y Fg(\()p Fk(n)p Fg(\))1853 2371 y Fq(.)382 2597 y(The)54 b(next)h(prop)s(osition)g(is)f(strongly)i (related)f(to)h(the)f(Quan)m(tum)f(AEP)g(Theo-)382 2710 y(rem.)34 b(In)f([2)q(])h(it)g(is)g(pro)m(v)m(en)g(for)g(the)g(higher)f (dimensional)h(case.)i(The)d(prop)s(osition)h(is)382 2823 y(crucial)e(for)g(the)f(pro)s(of)g(of)h(the)f(second)h(and)f (third)f(part)i(of)g(the)f(Data)i(Compression)382 2936 y(Theorem)h(presen)m(ted)h(b)s(elo)m(w.)g(These)f(parts)h(sa)m(y)g (that)g(an)g(asymptotically)i(reliable)382 3048 y(compression)50 b(to)h(the)f(v)m(on)h(Neumann)f(en)m(trop)m(y)g(rate)h(is)g(ac)m(hiev) -5 b(able)52 b(and)d(is)i(an)382 3161 y(optimal)44 b(one.)f(The)g (relev)-5 b(an)m(t)44 b(quan)m(tit)m(y)g(for)f(compression)g(is)g(the)g (minimal)g(loga-)382 3274 y(rithmic)31 b(dimension)g(of)g(subspaces)g (of)g Fn(H)1835 3241 y Fv(\012)p Fk(n)1968 3274 y Fq(dep)s(ending)f(on) h(the)g(minimal)g(required)382 3387 y(probabilit)m(y)g(of)f(the)h (subspaces.)382 3575 y Fp(\014)433 3589 y Fk(";n)532 3575 y Fq(\(\011\))26 b(:=)f(min)p Fn(f)p Fq(log)1135 3597 y Fg(2)1174 3575 y Fq(\(tr)q Fp(q)s Fq(\))p Fn(j)30 b Fp(q)e Fn(2)d(B)s Fq(\()p Fn(H)1746 3538 y Fv(\012)p Fk(n)1848 3575 y Fq(\))30 b(pro)5 b(jector)q Fp(;)46 b Fq(tr)o Fp(\032)2463 3538 y Fg(\()p Fk(n)p Fg(\))2565 3575 y Fp(q)28 b Fn(\025)d Fq(1)c Fn(\000)f Fp(")p Fn(g)p Fp(;)47 b(")25 b Fn(2)g Fq(\(0)p Fp(;)15 b Fq(1\))p Fp(:)382 3783 y Fq(W)-8 b(e)62 b(refer)f(to)h(subspaces)e Fn(P)1468 3735 y Fg(\()p Fk(n)p Fg(\))1461 3795 y Fk(")1647 3783 y Fn(\032)76 b(H)1872 3750 y Fv(\012)p Fk(n)2035 3783 y Fq(with)60 b(tr)p Fp(\032)2390 3750 y Fg(\()p Fk(n)p Fg(\))2492 3783 y Fp(P)2550 3824 y Fv(P)2605 3789 y Fb(\()p Fa(n)p Fb(\))2599 3835 y Fa(")2776 3783 y Fn(\025)76 b Fq(1)42 b Fn(\000)e Fp(")61 b Fq(and)382 3926 y(log)r(\(tr)q Fp(P)664 3967 y Fv(P)719 3932 y Fb(\()p Fa(n)p Fb(\))713 3978 y Fa(")814 3926 y Fq(\))44 b(=)g Fp(\014)1059 3940 y Fk(";n)1158 3926 y Fq(\(\011\))e(as)g(high)g(probabilit)m(y)g (subspaces)f(\(with)h(resp.)f(to)h Fp(\032)3233 3893 y Fg(\()p Fk(n)p Fg(\))3335 3926 y Fq(\))382 4054 y(corresp)s(onding)29 b(to)i(the)g(lev)m(el)h Fp(")p Fq(,)f(cf.)g([14)q(].)382 4167 y(It)c(turns)e(out)i(that)g(the)g(asymptotic)g(rate)h(of)e Fp(\014)2012 4181 y Fk(";n)2112 4167 y Fq(\(\011\))h(do)s(es)f(not)h (dep)s(end)e(on)h Fp(")h Fq(in)f(the)382 4280 y(case)31 b(of)g(an)f(ergo)s(dic)h(state)h(\011)e(and)g(is)g(equal)h(to)g(the)g (en)m(trop)m(y)g(rate)g Fp(s)p Fq(\(\011\).)382 4454 y Fe(Prop)s(osition)36 b(5.2)46 b Fo(L)-5 b(et)26 b Fq(\()p Fn(A)1384 4421 y Fv(1)1459 4454 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\))26 b Fo(b)-5 b(e)25 b(an)h(er)-5 b(go)g(dic)27 b(quantum)f(information)i(sour)-5 b(c)g(e)382 4567 y(with)33 b(the)g(entr)-5 b(opy)35 b(r)-5 b(ate)33 b Fp(s)p Fq(\(\011\))p Fo(.)g(Then)g(for)g(every)g Fp(")25 b Fn(2)g Fq(\(0)p Fp(;)15 b Fq(1\))1374 4793 y(lim)1345 4848 y Fk(n)p Fv(!1)1559 4732 y Fq(1)p 1554 4772 55 4 v 1554 4855 a Fp(n)1619 4793 y(\014)1670 4807 y Fk(";n)1769 4793 y Fq(\(\011\))26 b(=)f Fp(s)p Fq(\(\011\))p Fp(:)968 b Fq(\(14\))382 5003 y(No)m(w,)37 b(disp)s(osing)d(of)i(the)g(ab)s(o)m(v)m(e)h(prop)s (osition)f(w)m(e)g(can)g(extend)g(results)f(concerning)382 5116 y(compressibilit)m(y)c(of)g(information)g(to)g(the)f(case)i(of)e (correlated)i(\(ergo)s(dic\))g(QIS.)382 5290 y Fe(Theorem)j(5.3)g (\(Data)f(Compression)i(Theorem\))45 b Fo(L)-5 b(et)29 b Fq(\()p Fn(A)2669 5257 y Fv(1)2744 5290 y Fp(;)15 b Fq(\011)p Fp(;)g(T)e Fq(\))29 b 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3155 y(quence)63 b Fn(f)p Fp(P)831 3122 y Fg(\()p Fk(n)p Fg(\))933 3155 y Fn(g)978 3169 y Fk(n)p Fv(2)p Fj(N)1183 3155 y Fq(of)f(pro)5 b(jectors)63 b(in)g Fn(H)1995 3122 y Fv(\012)p Fk(n)2096 3155 y Fq(,)g(resp)s(ectiv)m(ely)-8 b(,)64 b(with)f(asymptot-)382 3268 y(ically)68 b(not)f(v)-5 b(anishing)66 b(exp)s(ectation)i(v)-5 b(alues)67 b(tr)p Fp(P)2269 3235 y Fg(\()p Fk(n)p Fg(\))2371 3268 y Fp(\032)2418 3235 y Fg(\()p Fk(n)p Fg(\))2606 3268 y Fq(=)85 b Fp(\021)2807 3294 y Fk(d)2843 3274 y Fb(\()p Fa(n)p Fb(\))2938 3268 y Fq(\()p Fp(\032)3020 3235 y Fg(\()p Fk(n)p Fg(\))3122 3268 y Fq(\))67 b(and)382 3381 y(lim)508 3395 y Fk(n)p Fv(!1)725 3345 y Fg(1)p 721 3360 V 721 3412 a Fk(n)789 3381 y Fq(log)907 3403 y Fg(2)961 3381 y Fq(tr)p Fp(P)1103 3348 y Fg(\()p Fk(n)p Fg(\))1255 3381 y Fq(=)49 b Fp(R)q Fq(\()p Fn(C)5 b Fq(\))50 b Fp(<)f(s)p Fq(\(\011\).)c(This)f(w)m(ould)h (b)s(e)f(a)h(con)m(tradiction)i(to)382 3494 y(Prop)s(osition)30 b(5.2.)214 b Fd(\003)382 3720 y Fo(A)-5 b(cknow)5 b(le)-5 b(dgement.)71 b Fq(The)f(authors)f(are)i(grateful)f(to)h(Ruedi)f (Seiler,)h(Rainer)382 3833 y(Siegm)m(und-Sc)m(h)m(ultze)48 b(and)e(T)m(yll)i(Kr)s(\177)-48 b(uger)46 b(for)g(helpful)g (discussions)h(and)f(v)-5 b(aluable)382 3946 y(commen)m(ts)31 b(on)f(this)h(pap)s(er.)382 4171 y(This)41 b(w)m(ork)h(w)m(as)g(supp)s (orted)e(b)m(y)i(the)g(DF)m(G)i(via)e(the)g(SFB)h(288)g(\\Quan)m(tenph) m(ysik)382 4284 y(und)29 b(Di\013eren)m(tialgeometrie")35 b(at)c(the)g(TU)f(Berlin.)382 4571 y Fr(References)427 4774 y Fq([1])47 b(H.)27 b(Barn)m(um,)g(C.)f(F)-8 b(uc)m(hs,)28 b(R.)f(Jozsa,)h(B.)f(Sc)m(h)m(umac)m(her,)h(General)g(Fidelit)m(y)g (Limit)569 4887 y(for)i(Quan)m(tum)f(Channels,)h(Ph)m(ys.)g(Rev.)h(A)g (54,)g(No)g(6,)g(4707-4711)j(\(1996\))427 5074 y([2])47 b(I.)60 b(Bjelak)m(o)m(vi)m(\023)-43 b(c,)65 b(T.)c(Kr)s(\177)-48 b(uger,)59 b(Ra.)j(Siegm)m(und-Sc)m(h)m(ultze,)f(A.)g(Szk)m(o )-25 b(la,)62 b(The)569 5187 y(Shannon-McMillan)47 b(Theorem)f(for)g(Ergo)s (dic)g(Quan)m(tum)f(Lattice)k(Systems,)569 5300 y(math.DS/0207121)1831 5652 y(13)p eop %%Page: 14 14 14 13 bop 427 548 a Fq([3])47 b(N.)k(Datta,)h(Y)-8 b(u.)51 b(Suho)m(v,)f(Data)i(Compression)e(Limit)g(for)g(an)h(Information)569 661 y(Source)24 b(of)g(In)m(teracting)h(Qubits,)f(Quan)m(t.)g(Inf.)f (Pro)s(cess.)h(V)-8 b(ol.)26 b(1,)e(No.)h(4,)g(257-281)569 774 y(\(2002\))427 961 y([4])47 b(E.)24 b(B.)g(Da)m(vies,)i(Quan)m(tum) d(Theory)g(of)h(Op)s(en)e(Systems,)i(Academic)h(Press,)f(Lon-)569 1074 y(don)30 b(1976)427 1262 y([5])47 b(M.)d(F)-8 b(annes,)45 b(A)f(Con)m(tin)m(uit)m(y)h(Prop)s(ert)m(y)f(of)g(the)g(En)m(trop)m(y)g (Densit)m(y)h(for)f(Spin)569 1375 y(Lattice)32 b(Systems,)e(Comm)m(un.) g(Math.)h(Ph)m(ys.)f(31,)i(291-294)h(\(1973\))427 1562 y([6])47 b(K.-E.)23 b(Hellwig,)h(K.Kraus,)e(Pure)g(Op)s(erations)g(and) g(Measuremen)m(ts,)h(Comm)m(un.)569 1675 y(Math.)31 b(Ph)m(ys.)f(11,)i (214-220)h(\(1969\))427 1863 y([7])47 b(K.-E.)40 b(Hellwig,)h(K.Kraus,) e(Op)s(erations)h(and)f(Measuremen)m(ts)h(I)s(I,)f(Comm)m(un.)569 1976 y(Math.)31 b(Ph)m(ys.)f(16,)i(142-147)h(\(1970\))427 2164 y([8])47 b(F.)d(Hiai,)h(D.)f(P)m(etz,)h(The)e(Prop)s(er)g(F)-8 b(orm)m(ula)44 b(for)g(Relativ)m(e)i(En)m(trop)m(y)d(and)g(its)569 2276 y(Asymptotics)34 b(in)e(Quan)m(tum)g(Probabilit)m(y)-8 b(,)35 b(Comm)m(un.)d(Math.)h(Ph)m(ys.)g(143,)h(99-)569 2389 y(114)d(\(1991\))427 2577 y([9])47 b(M.)27 b(Horo)s(dec)m(ki,)h (Limits)g(for)e(Compression)g(of)h(Quan)m(tum)f(Information)h(b)m(y)g (En-)569 2690 y(sem)m(bles)k(of)f(Mixed)h(States,)g(Ph)m(ys.)g(Rev.)f (A)h(57,)g(3364-3369)k(\(1998\))382 2878 y([10])47 b(R.B.)31 b(Israel,)g(Con)m(v)m(exit)m(y)h(in)e(the)g(Theory)g(of)g(Lattice)i (Gases,)g(Princeton,)e(New)569 2990 y(Jersey)g(1979)382 3178 y([11])47 b(R.)23 b(Jozsa,)g(B.)h(Sc)m(h)m(umac)m(her,)f(A)g(New)g (Pro)s(of)f(of)h(the)g(Quan)m(tum)f(Noisless)h(Co)s(ding)569 3291 y(theorem,)31 b(Journal)f(of)g(Mo)s(dern)g(Optics,)g(V)-8 b(ol.41,)33 b(No.12,)g(2343-2349,)h(\(1994\))382 3479 y([12])47 b(K.)j(Kraus,)f(States,)i(E\013ects)g(and)f(Op)s(erations.)f (F)-8 b(undamen)m(tal)51 b(Notions)g(of)569 3592 y(Quan)m(tum)22 b(Theory)-8 b(,)23 b(Lecture)g(Notes)h(in)e(Ph)m(ysics)h(190,)h (Springer-V)-8 b(erlag,)24 b(Berlin)569 3704 y(1983)382 3892 y([13])47 b(M.)d(A.)g(Nielsen,)h(I.)f(L.)g(Ch)m(uang,)f(Quan)m (tum)g(Computation)h(and)f(Quan)m(tum)569 4005 y(Information,)30 b(Cam)m(bridge)h(Univ)m(ersit)m(y)g(Press,)f(Cam)m(bridge)h(2000)382 4193 y([14])47 b(D.)41 b(P)m(etz,)h(M.)f(Moson)m(yi,)h(Stationary)f (Quan)m(tum)e(Source)i(Co)s(ding,)f(J.)g(Math.)569 4306 y(Ph)m(ys.)30 b(42,)h(4857-4864)k(\(2001\))382 4493 y([15])47 b(D.)31 b(Ruelle,)g(Statistical)i(Mec)m(hanics,)f(W.A.)f(Benjamin,)g (New)g(Y)-8 b(ork)31 b(1969)382 4681 y([16])47 b(P)-8 b(.C.)29 b(Shields,)g(The)f(Ergo)s(dic)i(Theory)e(of)i(Discrete)g (Sample)f(P)m(aths,)h(American)569 4794 y(Mathematical)j(So)s(ciet)m(y) f(1996)382 4981 y([17])47 b(A.)53 b(Uhlmann,)f(Relativ)m(e)j(En)m(trop) m(y)e(and)f(the)h(Wigner-Y)-8 b(anase-Dyson-Lieb)569 5094 y(Conca)m(vit)m(y)28 b(in)e(an)g(In)m(terp)s(olation)i(Theory)-8 b(,)26 b(Comm)m(un.)g(Math.)h(Ph)m(ys.)f(54,)i(21-32)569 5207 y(\(1977\))1831 5652 y(14)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0302110651985--