Content-Type: multipart/mixed; boundary="-------------0302110654501" This is a multi-part message in MIME format. ---------------0302110654501 Content-Type: text/plain; name="03-50.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-50.keywords" quantum information, ergodicity, von Neumann entropy ---------------0302110654501 Content-Type: application/postscript; name="r_siegmund_schultze_030205.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="r_siegmund_schultze_030205.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: breimanxx1.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold CMR8 CMMI8 CMR6 Times-Roman CMMI6 CMSY9 %%+ Courier CMMI10 CMR10 MSBM7 EUFM10 CMSY8 CMSY10 CMEX10 CMBX10 %%+ Times-Italic MSBM10 MSAM10 CMSY6 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips breimanxx1.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.02.05:2048 %%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: 8r.enc % @@psencodingfile@{ % author = "S. 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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 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 66a602a9f142a563fdae3c8d40de6a8aa581ff3172367ca325e6d23102c5c6a2 02cc995819e3cf8ba1deca8d0b8e75bb167d18fcc8fe48b040b39a2fdea4444b b3074f4c31e57cef6b463d8e7deaf58bb3d4162c9de18792de834b87b8720323 c01a537d6ac479819cece5bfad6e498a402aaff52a5e322125084bbacffb7a7e 34b0dae164452a73bb9e6d7aa32ec4fb5b4306adc025d7f2a391a7622d374889 f5a721791b49e84dee4bc5884e8d9fec9b236dffc09fc6029cf15f25028fdf6e dcd6594738dcdf795b921a633a8ba8eb5c4dbd19fff5b63b65b0594e9e24d6df 1c79f275b9f94561ae97ed3d7af26b084888a86173b7777983281765e31d20f3 c2 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 69 /E put 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 4a7abb8dca6f76c459484ad29c3480b588fae3d782340da9ccf5a3d158e68bf0 efe444399382e030884b4b1eb1465a78fa1afde244588004940122efab06a71f 7e71a839054b0f1c9c495035b9e969359c337521b2e95f6d958c8a2ca31c8335 34e01e455692727ce235eb7f8427e5bad38b25dfd4ccae42cad98cad37f640c3 754e128c0a88779977b3c7aae31089ad21671af398302d581e3089d445935e55 4c98f09ed609fd6db5db4e982d91f085109c3327226eb8016d64f21ec8f8a202 bc05423a81dd4920920079a33e081012896d3d78699d7a9f1fab782d011f4370 46be073541d03992d2165460d05ff68037a499c1b28038f3f0461fb882b4eb24 3bfa5cb9677276d5d8581ff5a609c05e01baec34d5ac4a4c26606cd6fc583757 e48dcc80ee7465c9d17d7f5e1eef0664966e6568b89c60aacbbeeadd9c1e082d 65b88dbad4b3e282f692106300143eb72b2a95ba64b774402f1e173d991ab4d7 fc5fb57ba1f9db8685d7eb9f062abb561f04c81a5521f1de620c8195ee40df49 3439b0ddccad847070ec5a4829c83496d17172a231600a533ff1b188bcf059d3 bb20aeb2bdeb8e2b960d7762f6efb4bafa9fa5f447e5df665c1197b923635296 1518df8265b08e45baa75862a8f65f5354f95d588c5254694ca2a80f6a05c18a f679a18860f00e19d3c066415894ca2daf6dcfe4a61e4b70e2d251534d2c6219 905dd9eb3ae9b10f3c12850aac334282557125e14e03cfce95c6530e18f08de4 69e6902e4ecd3e61c64fad93c1dbf4afaa5980dd8851b9754e6fd966f5c8dec1 08459ff130bbb77297f6caeec7a0fd03e0064161397b0e3090ea18c4eba3e379 e9561b19a61c61ed9a26105830d737dd39348960663fcb9c4fbb198e5b562e5a ff556325b413e24817c442bc244fe532fb9808060cca0997a0d97f84a96e740a 9eabfe65ae5ef9c73ae39532dd6ed7d9e5513062d9f5f52c0207388141dd4d85 b19fcf0e4019dc315e4f6f950a9cedabdfe5177e3047fc99eb88f20d138ab813 517398008f545e15d3138de507719a9a2df3d4a914685c7fdd6921706b950177 181c3875c4ac4cfbe84a44a3230652d2b734d895384a541334eb288b4cc50778 edb35e820a5ce5af7eda7355c0fe04dcb1edc540f83f481f5ad032b5ab7f27bc 98f28ad8bb3a7d38825d6a068f2ea770088e031a09ea8cf1f7d9969b78f03041 9df604e7e26ba937d54b6f12aa5b8e06bac9c4497c0729d8e44a350dfb0f61b8 d56eeef617c6114bddeb6bec460442c9 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 49 /one put dup 119 /w put dup 120 /x put dup 121 /y 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 34ef6b441871c6993da3a81afc9bf70ff3842a21a29c0e49da1ccba37dd6b920 2702db510b8b1109acf4c27ee8d676bdbd16abe189f34a9b61532eb777457698 cee0561838eaab2d3939c5093afbb215bac433d1918c739b62566906bb2187f3 378521fb52e70c18886e1aa15f53a1f8a169528cf2ddd54c203613ff88e619f2 6c9c50c2c3b8b8c868a88afab1dc8472e7b6f3f992a161723a3c0904865a7c42 3281601eee91f35222c4a71f343739f102eb43145a47e4fac3bd666e4c114a90 5950618ecb1bdc29f90f6ebed1d8325fe6b52e14a8870e9b4bb088e585c71b91 493c12845a101937e3473ac5e9ae24f7c358f7d9e8e9b20ec9e6ce4429b55ae8 aa69952af43d57f7451969ccac33dafe647bbc3ea5e0682fbfb59a389ae2391e 4609fd282e9a80eff3e96c2127cf5db56c6e9ea66aefdbe92e688671555403b8 10033d58cc39146c1a8508b3d5edfa25f24d78b1419264f16ae7aa81d8a8fcb5 e12e301e15ff1254590f50b94eb38efe5ce0e77ab149905b11ba173ce62e68fb 1896e6f8a2fbdf9d56e5edee9cbfe8f89c97439a6a2670b366de800c383701d7 4d2fbbd0037d982d98844a8f150f82e49409f8cc72e8a1f9cc5d6fd8b03899ee 5dcf699ed14c3ff8b4e6a4a730bafa4cb3a7eade2eeef64f72bbf1c23d0ff258 1516481933270b3fe179b88d6deca8d069c7f94fd1883020462d1200b9ef614b 5c5069b059aebe5d104b9fba37c7ec3fbaf628caab93d5eb0f4e03f302a74918 569744fde92875a669b44ad9b27901cdc0b6551825c09bee4853c7e3dfb26206 8c37a2b67ca6bec5365034508e1cc0254f650062054572d8746a6f79c83d997e 6d73d3606c7fcc387159521adc7aecc25d28c73065dc9a4f7fdd7a6140d939dd ee5518cec48ba3356d46cf9f54774ea814544f3e2286d7ec0f0e7adfff6ea869 c81a49ae0b6f7a39a221b7a5cd79d8961fe71e9448af419228af97898fd00191 c08056ae8ec0ea903f35e8612f98b63ced63305d8652cbc85414a0da004093b9 1476ddc3ec9aed5215496688ec503b33179d2eaf3325c0c126a62a538a10525f 06830b9c48b5d8fbd3d551f0a1ddeeb7404a25edbfee840d401062cec9fa8ccd b012bc9725ba723972f318aef9f6ecb116f5bf242217d6c2368d1eaac150f918 9ff794a5fb4d510b4142b01604eea9823ff5b5bfc2f976354bddcb62d6b8681b 659c5b14190942f280e9e884ba548ffc72c50f19266fcde443255b1cc7999100 2589183c542e9a70714f5c6b877853c92a92907bf9df5bcb345efd01219fd97e 20dccd29adb22ac2b9f8c8383f8a452a896f02fc0f19d4347fbd1f0ec4a91494 f339115896450bcae277de73e6228b2c09f7d357b66a33dd500f00592cc3db07 434acf453b50448b4a70a58eaa41ca5856951a17341d13ebb65212c5dc23a2aa ced0e7ce97876a95aa4f29ac2771f43cb5ee60129486c5d426788dacf2bfe017 5edd9ca81d90ce7270ddd09dbcebd266b0d31d8a58c4160e8710fea51b3ca4dd 5b79c397dc54447c34c8e8df909dbe179319d3fe2a3afbce66a4069c502e89e4 088a50d1c913ca87fc65ad901c651745f604a21f3906d8d05d59164e09b1da0f 7f19425d2653e2a9da0dfebd00909bf59ec1be50c4a35237526fbccc17f913c3 311253a848d477229d8485f78d017f72a0a20a64db71bcde7a3678b8068c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 76 /circleplustext put dup 80 /summationtext put dup 81 /producttext put dup 83 /uniontext put dup 84 /intersectiontext put dup 88 /summationdisplay put dup 91 /uniondisplay put dup 101 /tildewide put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a 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7cd310b30757fbc5d46bb7195f7241111a2a 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 3 /asteriskmath put dup 10 /circlemultiply 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 50 /element put dup 56 /universal put dup 57 /existential put dup 65 /A put dup 66 /B put dup 67 /C put dup 72 /H put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put dup 116 /unionsq put dup 117 /intersectionsq put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 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df701abdb0abad6b60fb40fd029c83a80e26544deb890dc4b3019ffaa1816a66 aee290fba4bb20dd34b2e6bdff04a70962c67ff516f55e7bca54425aca076bd5 d595054024522d131dd2f26e31e5daa62f9b28fd42c56d1a5a3095dce9ecbe26 b45324b1aed2985f9fe75df467dc78a57b7e30e883eec087fb2534d345d6ff83 b3678ff60495c48355728813f1398728cd7a54ce4068993cdb59c7353737f9dc c7feba6ea926f9f4c95d9f6e30484ef1b2d8f663c1f6eaa3d4f9b1a8ea3296cd 30381e1c9040bd25d0014122c26790f88aab1ad53f92df5f826e04a2ca3d3fc1 d2defb00b988d8711832e6905a2aef733a05e1c59904d3c0895957542a97be73 57195e6d8e40eb936480a9ed329ca3fdb3e61327aefb1d7a63e59043137269e7 51e78539aaa5420acf3a9a073ce568a8a7603fefb7d12e2a5b352aac0ded28f0 a5f48aa85fa5c612f70f08fecb0142fb50503ef0556dafea46d0dc19e89f160d d4fa1ce16fe252afc23f4dd0154bcacbaeeb7f5c617f18a89b2ffc234b7272f0 aac7aeccde838f5e735ff47ade00b42086a28233ee9e1219fae28544de771438 df424cdccc01b3cb75905144d877c241bb03aa37aa443be09f9984c36080f745 0cafeb5b52dc6c0ede6646148cb4d9a6465d75f5ea45e65710872c98501230c9 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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 21 /greaterequal put dup 33 /arrowright put dup 49 /infinity put dup 50 /element put dup 65 /A put dup 66 /B put dup 67 /C put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a4261be7bd48981fe5d74f36597276d570bdc1ca4d7a29ec280a13e7 cf740be69a5d79aff1ac325360e35ace9b7338a0d639d1a12ea484c43a1ae98c 3b6388532dbf33a3d9d0269db68b7a40451f68e14ea905164d8cfdf7e01d1a3d 7d97a280fd7b1664708aa91fdec822b75cbca7e846cc17cf2c03e485367838a8 44339ad3194ef665a11f1e1a246d1b7d6e005d5fbe263fc4b151e730ab3dc8f3 1b19da178175dbbfacb789821ab7c3fa6d28c9cd518bd5874253ec2a04729533 a3d4cacd2e697e38807d1245e753873a16e5254326c439e988498e60fe374897 d383c6ffa145fd7617fe093cf56c9552dd4dc003ced67336a1e10389b649144d 962a3cf7c16f4a43338bcf35cfc5b54f87cc0caa974179179c34ed5eee919f83 df67b2c7d175a6c3075eb5f57a9aa1bc2bb17ae2dafde96fc499e8bf2c97247f d4fa569ea30b3445fdb8fff3bc7da9c1f04010a60c7f56d59164fc50a46ed50d 86ee4057e91a012794c76482d4aae60e04c6ef1ff8c5ae2edfb17ecef898ad76 2d921990c5ef8f76b51e3af4f2fe0301018fcdc593f694dc295e64ce5f20fcaf 2924de5d2a35953ddbac1b4cea729d93ac067792ddac5853bf9e314e735a506e 3811cd2c3d6b79b691da4a6de3dc8284667eb675c2d831eb9450e553651c2a93 44c0761a321331fc05fa9b0cd0993282a4bfedc8b3d2177d9a27b0187cb1f442 2c218556a45a5673531ff85c25036a3ba8159f3c833baa7c4e785c10ad5bb742 e2c31a6fef5e1b93ae7fbd7158f86009ffcc18c31e5cb9cb2d75a300da848fa3 fa2e7b00589547fff69d12dcc3dfe7d9a64ca003f0490ffea361f8cf3977810b 8fde4514df8b68b1645d14a624ca15c3b5cc72cc2d7c7ca9e5212d9525b1e33a 8cc94b86dfd52a1200ec0c0c0af39069b4371f7eab88bf86f4bae9366e0bef99 3d5ff6a1a25e9c903e4378be468d99f8dbbee8a05e6218288bdff459f74756e7 613767608454ab9c28c9c13fda255882d2b2ab38b2da82f3b2055a0b4aa7af76 601593e57b6f65b302965762bd425eef7ad2b2d7477230579ff7065a6e9a822a 6d6206c2982be55fd1952649f15a9718ced5af0bd5b2bb3a6f14f948a59e22f5 7be99d86fa048bc41517e16120fa57c0bd83098e2b2fe2dbd214a3aa940ac751 3cc543684457c0eb4adcff37cb53045f8d713a29c0e227caf4373612594cfaed 047701da531c9c27d6e6128fd4407dc884483e29494c0ce4ef1379fa79a525c0 a05f8eba3710515f3c8fdf48f682b0ab8f2c5386a0bf44393b36b6fdebdb15fb 43bdda62f4c507482ef139f9da90556780a901281ebe4fd2355d3239c5681f54 579f441e429f98df96cb54cd15c0bb05f95349da3d1abad2e3ec302e3dc327bf 764b7fce66c28f2c69b75187444ba37fe85bb7e3039a748dd7aaab43bcea4f1c f5232bc0ad78d670d34c4ef22cb37ff6dfedc8d7b591425817062382048c8627 291058fb35af2d920ba284edab63fafeeb997538231c31e085b269670ce0ae8a d6f2592348df7f3c7ddbc15cb1061e41e4aabf378f8caa97c8d55ea1ca344e96 b24ef4f18cd13ddfd1e7430208b601ec5214cfef6ffeaae46480a9ffdcec6c3a fc4065f59b8ea501975aef574ad66c20ebe2d711871ebc9c0b653910ea5bb4c7 508896895149824731660e2aa51c08646a3bcb188a76377b662bc19320d79622 fab88d5b6d298a88889c17b69002842e0d68a8c1af0f884b16b2ed3d63e364df 981e8fab6de894d083c0a5189ada2c043ac4065174324044fd3a98b414f61f3c a3bce338cdd13c187547ba22dba6bc28b69c1e519cc3d68426dd63e7258b1268 294d070858c2a1585c4df2ad01310ccf71469ad323f7a7595be521c3b2cd39b6 fdb5c1b75167ec2df28011ef6bb1730bff2449a90bac71c7696adc3da09df8c5 e66f397f0ba3056e60c7b8ca3d2da89cbd9936fbee47a51e9c3f3a806b401296 244886d9fbde709c3d2f3a13c61b09566fe52977d8b015c632a2b0683cb26965 46ac4b742b78a21a0fa5e147d4e9c137350f71a478225f6c88cc600acf0f7b74 593a1fe912920710fab85159006820515be27ac1b38c0d859bdf0a8e50bdf3d5 fc962ed118bea8ab28dad3bfc0aa725d02ef9d646a44f294454126bbb0fa1e5b f81ea4a22b8138dcf559114bb36e3ab83573d319cab6034cb1aea070e8e598ae 748a103419672d0ed71ab3fb09e1589c5ef6fd7acff0f5df2f34174a02d61b30 a71092e20a40326b8eceddce2d9822bb7d89e43a4033437c80a1493ad2af71fb 94663c7765a74fda6dc23a933fd0a69dd138fa21f85562b674f1aac60cbc65cc 44ed4bae91bc0c40084d36a777a3c524b69ca590341402001fb553317d532e29 4fca88a4cf2a3474bb7849ba44c243eab1612816a4db7714d12a4825c3d8d5c9 4b0f2905500b0d3ede4b08d7b2602e499d46ac77fef97ed59d0e96c7a5e7daf7 86ca93e9cc0cde73953b516da236712aee90a20626ff9d83d4e5e251ba531362 ccb1e2cb31f92c6ba30cc9b81a3cab1d4a47addf550e3b730b988fe579eaa2f2 cdabc2e545e14bea4ce8a83a4d5e21c4d36dc65f57c7907ab7b4b70b0d338b0e 62e43da29125f9356685996bddffa4e11a30453d840f8f 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: 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 35 /numbersign 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 58 /colon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 103 /g put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 120 /x put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12 cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e 4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618 99b8ea06b092c3c1e503e6e436e0a9fa22576c8930ab3dc8c20f5d82b69cddf8 ff4dacfa9c54bed5a3aa3ea5b129fe96be632843b9b6bc91b615581a985db56b 1e01ca60ee69ca92cf5c0882ece62edad3e106d835348822400f0b66af658f2a e56ed08f8b0010571807009b73ab12a8cf14ca6c71f03c2a48c500f9d62266af 154a6375ff600d9bac3f05ce34142d6867a79581c533176bb2f3117336671e2e 44638a97167e2ea9644e31ea16c2ad2990ea33c54001e0c8156e6de8ab6a4d40 a7137ba275f39589fea2e2db8256adc103d6f9cc038037a47e8fd469c5f98a5e 3c15bd4ace40d340018b1cff7d1ed8abb0ac57b5b5a2c20a51957b96c453edb7 dae5affd91a46d938fe0a13363001d844ded4323f1ee6d30012aea19b024a552 315505535c85dc26bad31e09c50e6512802976d298c4e90d0044c362e6bf3ab3 62a454ee93de25ce54411090c29e9d75c80ce26a84404bd9de3aee0e3f921ac5 87f907572b8354a5c3165eea7e8b2ba4e33e5f268e289f7a845011ad57106785 1f85979be5b201b9c656ae57e895071eee3f1a7d49bf6ba81772eeee8ca214eb b3edb380024fb17e0b2ccc9742479a3c226cbdc1c6f261117abb5223d156b519 b8ff0450c06ea01e5a9ba079f660c4dd1befc22046b4497c229e80e98f5a1873 82294488d85aafc0e85daf152de85b745a039cba8c877695d5145638b3f09589 fead427bb4218063e8c5858ad8d8b51d508028044856e2706f3d284e13079cdd a1b6393d622163b28d0e61a293df2f3dc3f1025340ced7342fc1c2787c7614a7 3941a162243c9f505c6534e331946c9ef909f645ac6aaa31ac87bbe23cab9f3f ef2ea0671983b84c15067cc3b382147315dc00e6772b134964ba6acfd727f00c c0b91d4bb0ce6e2ad17ec164824b0db88d7445bc6978215881dbc6f52ed8c408 902faa266d7334bb66526031cfc7e42d9d1ef88a4b57fc92db0444946ffa1cbb 4e751daec7b2d7d3c818947a90a2ec5f7a222d156e9f128c41e016ab1a140f7c efb56bdb234622c129b950b1ec1082da5360f0629a26c85877c5766dce015844 82e1f0bd015ed9e32c4aab5c3ce387476db7da151ca41669a62e62db01b526a2 8758b85370f302efd6f223dec015571d3814fb3da6e08d5563815f70e3b77f33 2e1738d46e8c0186a476d1ca39b299ca1ae10e56a65ac621b48850f1a462253f 2fe5c82285c5b74d3d828e13990f63c95c4c60d8bb2567adaf6f384defbcf72d d46302303292629e6e1db5c9972553cd3115f0bc5411189693d82e0308e03cef 6aec293f45d41f655b479238a49d3f05e1a0467fbcef6ba117717969ea55786a 2a9f73cb629432a5c605eb5cd312b69d66dfa73f9d25090d50ad73a5aa7e6dc3 c60cb8aa10b06a6638b131bfda11ea32a7b42b68bf72f2c56395a9773e6e1682 dc5b6aa5c4f93aa6b9a2d96660be65765de3a9e15a5805a42c23fd590198642d 638edec3569e3600d26dc540f3866f89b871a0d216ffbe970278941f5b4c144e 285c2c8c153690912031c52317b4fb2c7bf20480828f57d355d4c4b5560f4517 ec72f28fa398d38fa9a75047fd52b30fb1cd8fe3639448e5120306cc21a6ed30 44059d21abb6f165210e760026e5a7166e6e205e6fee39461ef33dce4a153457 607a8c9c894db36fe67db39006cd0a3a115a75a8b949defe69199086a900b2b8 9ac0f5fa6ccc28fd58fc9add6964b7e6d9aa80d8970bef69b62e6f1283db175a 2dbcc52e2f7a3458807f24a5cbc16f2ad5f70c62397bb9b7a7b5d534d434f3aa 602a43f2e36d32ee5c44c5b9d3eda6fef93499871fa3bc35c027efc963927d59 8e6b8b7373bc3b55ac13ed00edfa07934e0f6ed080ee84b85cfbe65f95d30c9a 915ad543496052c4d8cbb63b2bb68384b67fec25e0e218b1569e444bca0ce971 0c7db1816b4b5def691c238edd28f48e36b1b61451865e870a3895fc4e7315cc b03b327615adc3aefe8d2114c772d494711b9a086a06df37da2518193307459a 4177443910b0fa9a6a086fda894d2e8724dfba3709a3682558f8c5707cdbeabe 11e8f819edfac844de2da362f3924e1c1708a51981bad61f4488755c23eb875f 02fc6a8513d9ba41853297f865f5e363dc547ef060699c90e3108161768f2ffb b6cdc6479acdef08b4e06beaf83ceed41caaea7e879e8b4ecb39952f394953ce 6092792c81079dc8d5350a3fa7182c2d4f6f3b6eba31b8bdd3d879143a6bee1d a1555ed5f14c58438e03d97629d870c9eeaf253a25371d46ec045883b367bc13 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23c62d736bd0011009199ff916797f5d73b5d5be1d0b692494337c14ffdc6007 5f81dfd5b65c5a66ab5eaac7eba842d70b6e5032d8519075f1dd3985b1b77282 aa8e847780bfaffd9a624367b691e1cf3003d1ec71581fd0a95dce3eb54401da c24a30d244deb50cabdbc50765aa3e772225bb184ae4734083e2fa25b4b04840 95846980ec53a3f7a533c171f1ee6e0b608e270bfc7fa8be5a359c038b8049fa 742006ccbfb16f8fb74c1fd6b59a9d6d37c2f1845f2689243597e4a3997ad9bb 4c89e8 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 9 /Psi put dup 24 /xi put dup 27 /sigma put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 67 /C put dup 68 /D put dup 73 /I put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 86 /V put dup 87 /W put dup 99 /c put dup 101 /e put dup 104 /h put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end 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39b365e5ead2dea6cc5b6a0a96ca943a960533e90b94cc0c76bfd5197dd01b07 b326b87d9e8bf65efb36f2882fd8150a8e8857dadf2e9d7d734145f4c8e2d219 6e3a76fcde245efad4ec752c276b24965dbfe794e233f590176ab03f9edefe73 cb38dd49c888b4195f3dc07be4fe295457964f18f4e4612adacc92c9b0fd3877 79d52db20c1862b9c1878c0ab5ff58ac8d89eb03e6408815ab3ed45bc2718844 efa6fb3ebf02237892072d45188324e35a6b99c0ecfbdc9335e71818b966f415 a1d0c5ff76527a722d765222b81963d206483468887d8cad997b7f9014612e1c f30b480e4c93568bbfb613fa2b8c0f2688af89a01bf73bbad76d832c25bbbf03 f2a7c45ddad6296523908c77e44845e4b9ecf77ac3706312385afdad0094888e 323cac69056e732a8ece0a9d0039a8381f6ad6e93a9020c1930d06b2d6d315ca 64cd2b7bc2902166fd544c3ea9905f4b1b413cf0fdfe18c703a7ab5b14b9c169 47f03d745cfb5d95210cd60afc09f55b6a40a4e3f2de3efae2cdaf97b28892b3 a0b21cf82984 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: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 34 /epsilon put dup 59 /comma put dup 63 /star put dup 73 /I put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 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4741e5bf794edb76107ac0d044e4e43ca9ce737b4ee5caeabab2b13be912a2fc 81086397005fca28268effebf0e2258cf098223cc63b5dc29cf78166e8c914c6 a947b657a790252493fe91ba021105ac8fed3032fea2219cd995f453823ccebb 8ccdfe865b60f2ee2edbc74e22a35cc8138e2b56b06599bb3cbb260e1dc428ce 6d40bb2b96f169d4fd68cb4fa556f22b1f2ab43315f6228a2c00b27ba9688374 a97717b6f482609f826b6f2ee5e63f959eb46733d1a56158bf93fad9e58bf70f 395d21bb76bb4b3fd64bf576d6623fa280b829dbc5b7f7f8726079e96fef6e31 8eacb7296b335395de291d0173df3543b87da41da690a4327af034238c955647 130bd10052092247f20eb81821dfbbc48c91dea7996acf5ac51078f8d033e3a3 04facc12cf832d779fd85a9efe35c89c526a54a9337c516e5c7c271207924f4e 7c3d8b37df9f807b7453a25bc9f3764b1d01d41ce06505647da53a80787b245a e72d5bd77e6527470e55a1f60e2955062c34907eb6a29b0e4776b704b7c4fde5 28fe4d9db426e818913ab99c7d38939d61a9991cb523e4b470d6677e84e5bcd9 01040b5dda544d673720e27a0dd22ec43a5b91e2525465ec344cf94e12b7cd9c 447c35d08e9dc28109759c3982eccbc7dd4ce7dbf970366c0871f31539908914 cf88e340d4f7d77f7e2ffceaefcf64ab6b95232d139acf0868d4d19fceede852 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % 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 (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 40 /parenleft put dup 41 /parenright put dup 49 /one put dup 50 /two put dup 61 /equal 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523db6c2aa8118208aa 5a699c8678888b3be71c4979985d484db3daf3f1e55911db10ce126e2f6e68c3 6528c9c5d66ec46f30482314a9d5b8c1f45464121458e0bbec9c9d55628b8b7b 879534834b1f0349fdfaf0386cc0e83d75c9c3dab51bdc3b097ed9f1f7b7bb65 b53f88436f48fb86d4f2712f642e721e9c541dc9c880d01b39acc9df3e305ded 3d8c40c4843cabd873c013d431d216f9a684602f4b4b8ca99205f12ad913ffaa 89e4708a61183a32cb67825e635d4d558d0d72f38277fd43ef46ed6c62aa9229 dac6b67e6339ad772af8bad8d0239b21e7169903d4505c97b00a3a9eef2eeb3c e1d9f8be3ecd39597200ea9212868299da8a84c84f6a34b2553c4b1cc9802e92 cffbe20c8818a65f9426c665e87218654894960ed99aabf2bdfd3b1bc2779d82 719cc7b9948fb22174d914a37c9c43d623db3d7ff862648f3ced5ff9a5f379b6 6b85f89d5e750ec719557011931fa39582043efa9da752711b6f3cb0c8b67dd4 8b5a152d947aef63b9c0dbd14bbe6c50e92271884932c865e6e753bcda06269b 08786e3d8d01d0c79b72ca27190dcb78653edd76483c1bddadd712f9071edec3 08afadf7240a3cf2b9c6aa8e81f36bb7fd97e2d25b569fe29e221851e6a5d66e 39d5638a6faf49b34e62024abbee6c3e3e345736c59d56479c749754d326dc8b 8c776e9c660702e510c5fe7388adfdf2202f4b3b8baa512ce917c751964d8b4a f0e463e7e876db7bb9183f3759f4db8aad0e1ee1f49b4daa32fb36c5face875e 3ce8ea5e346a3ac941be1aae669ca1fd600a8ac5260f98a7e0342aea9ea236b5 294fbdaf793ee9a01f60da8b3fb471b785afceb9ed7592213e87a8e09cc99181 813507da7be0ab9566f8177ddb711d1709d072f5f7a2c4b052db87d62a1b38b1 785bd233a9c50562d3aaf98ba9e5effd451a018c4cdd46eb94c48ab1b8026bbf 7586f38ab0d14f4872abf6f6551746ea8e0e278b1f5012bb5bf4e8fc6c3c56e5 b40a96c428d858b6189595436970b3a135f59f609600393b25f961fe7564cb4e 34a03c2e584a 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 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 67 /C put dup 73 /I put dup 77 /M put dup 78 /N put dup 87 /W put dup 91 /flat 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 112 /p put dup 114 /r put dup 115 /s put dup 118 /v put dup 119 /w 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 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 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Fo(\))26 b Fp(>)f Fo(1)c Fk(\000)e Fp(")125 4744 y Fh(\(typical)25 b(sets\).)p eop %%Page: 3 3 3 2 bop 0 17 a Fu(Chained)20 b(T)-6 b(ypical)19 b(Subspaces)h(-)e(a)h (Quantum)h(V)-8 b(ersion)19 b(of)g(Breiman')l(s)g(Theorem)523 b(3)0 248 y Fq(Except)32 b(for)g(the)g(concatenation)k(condition)e (\(1\))e(these)h(are)f(kno)n(wn)g(properties)i(of)0 348 y(the)e(typical)i(sets)e(for)h(the)f(case)g(of)g(a)g(stationary)j(er)n (godic)f Fp(P)13 b Fq(.)31 b(Condition)i(\(3\))g(is)e(a)0 448 y(weak)o(ened)38 b(v)o(ersion)g(of)f(the)g(well-kno)n(wn)g (Asymptotic)h(Equipartition)i(Property)0 547 y(\(AEP\),)31 b(particularly)37 b(it)c(ensures)i(that)e Fp(h)g Fq(is)g(an)g (asymptotic)j(entrop)o(y)f(rate)f(in)f(the)0 647 y(general)25 b(\(possibly)h(non-stationary\))j(situation.)0 746 y(W)-7 b(e)23 b(obtain)i(the)e(equi)n(v)n(alence)k(assertion)0 904 y Fy(Lemma)c(2.1.)i Fh(A)17 b(pr)l(obability)k(measur)m(e)e Fp(P)30 b Fh(on)18 b Fo([)p Fp(A)1583 871 y Fn(Z)1632 904 y Fp(;)d Fm(A)1737 871 y Fn(Z)1786 904 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Fq(be)36 b(the)f(subset)i(of)f(those)g(trajectories,)i(for)e (which)g(the)0 871 y(relation)306 836 y Fx(1)p 306 851 36 4 v 313 903 a Fw(l)351 871 y Fp(h)p Fo(\(\()p Fp(v)517 885 y Fw(i)547 871 y Fo(\))582 885 y Fw(i)p Fl(2)p Fn(Z)701 871 y Fo(\))26 b Fp(>)f(s)t Fo(+)t Fp(")18 b Fq(holds.)i(By)e(2.)h(and) g(by)g(the)h(relation)h Fg(E)p Fp(h)p Fo(\(\()p Fp(v)2400 885 y Fw(i)2429 871 y Fo(\))2464 885 y Fw(i)p Fl(2)p Fn(Z)2584 871 y Fo(\))k(=)0 971 y Fp(h)52 986 y Fw(l)101 971 y Fq(we)e(obtain)409 1156 y Fp(h)461 1171 y Fw(l)512 1156 y Fp(>)i(l)r Fo(\()p Fp(s)20 b Fk(\000)g Fp(")868 1118 y Fx(2)908 1156 y Fo(\)\(1)h Fk(\000)f Fp(P)1193 1171 y Fw(l)1220 1156 y Fo(\()p Fp(V)1328 1111 y Fw(";)p Fx(+)1308 1185 y Fw(l)1439 1156 y Fo(\)\))h(+)f Fp(l)r Fo(\()p Fp(s)g Fo(+)g Fp(")p Fo(\))p Fp(P)1974 1171 y Fw(l)2001 1156 y Fo(\()p Fp(V)2110 1111 y Fw(";)p Fx(+)2089 1185 y Fw(l)2221 1156 y Fo(\))0 1363 y Fq(resulting)26 b(in)d Fp(P)492 1378 y Fw(l)519 1363 y Fo(\()p Fp(V)627 1319 y Fw(";)p Fx(+)607 1392 y Fw(l)739 1363 y Fo(\))i Fp(<)g Fo(2)p Fp(")p Fq(.)125 1465 y(4.)19 b(Combining)j(the)f (preceeding)i(results)f(we)e(can)h(easily)h(deri)n(v)o(e)f(for)g(each)g Fp(")k(>)g Fo(0)0 1581 y Fq(the)e(e)o(xistence)h(of)e(an)g Fp(l)i Fq(and)e(of)h(some)f Fp(N)10 b Fo(\()p Fp(")p Fo(\))23 b Fq(such)g(that)f(there)i(is)e(a)g(subset)2380 1558 y Fj(e)2368 1581 y Fp(V)2442 1548 y Fl(\003)2421 1609 y Fw(l)2506 1581 y Fk(\032)j Fp(V)2675 1548 y Fl(\003)2655 1609 y Fw(l)0 1681 y Fq(with)e(the)h(properties)-22 1855 y(\(a\))47 b Fp(P)183 1870 y Fw(l)209 1855 y Fo(\()255 1832 y Fj(e)244 1855 y Fp(V)317 1822 y Fl(\003)297 1882 y Fw(l)357 1855 y Fo(\))26 b Fp(>)e Fo(1)d Fk(\000)f Fp(")j Fq(,)-27 1988 y(\(b\))47 b Fp(e)167 1955 y Fl(\000)p Fw(nl)q Fx(\()p Fw(s)p Fx(+)p Fw(")p Fx(\))491 1988 y Fp(<)25 b(P)658 1940 y Fx(\()p Fw(n)p Fx(\))645 2018 y Fw(l)760 1988 y Fo(\(\()p Fp(v)874 2002 y Fw(i)903 1988 y Fo(\))938 1955 y Fw(n)938 2014 y(i)p Fx(=1)1056 1988 y Fo(\))h Fp(<)f(e)1255 1955 y Fl(\000)p 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Fq(such)j(that)f Fp(P)1466 3070 y Fw(l)1493 3055 y Fo(\()1528 2987 y Fj(T)1604 3082 y Fw(k)r Fl(\025)p Fw(N)7 b Fx(\()p Fw(")p Fx(\))1867 3055 y Fp(A)1935 3007 y Fx(\()p Fw(k)r Fx(\))1935 3085 y Fw(l)q(;")2033 3055 y Fo(\))29 b Fp(>)h Fo(1)22 b Fk(\000)f Fp(")p Fq(.)k(The)h(set)11 3182 y Fj(e)0 3205 y Fp(V)73 3172 y Fl(\003)53 3233 y Fw(l)138 3205 y Fo(:=)259 3137 y Fj(T)335 3232 y Fw(k)r Fl(\025)p Fw(N)7 b Fx(\()p Fw(")p Fx(\))598 3205 y Fp(A)666 3157 y Fx(\()p Fw(k)r Fx(\))666 3234 y Fw(l)q(;")787 3205 y Fq(ful\002lls)24 b(both)g(conditions)j(abo) o(v)o(e.)0 3354 y(Ob)o(viously)421 3331 y Fj(e)410 3354 y Fp(V)483 3321 y Fl(\003)463 3382 y Fw(l)555 3354 y Fq(generates)36 b(a)d(sequence)j(of)d(chained)j(sets)e Fk(f)p Fp(C)2080 3306 y Fx(\()p Fw(n)p Fx(\))2073 3366 y Fw(")2181 3354 y Fk(g)2226 3321 y Fl(1)2226 3379 y Fw(n)p Fx(=1)2397 3354 y Fq(ful\002lling)0 3454 y(1-4)h(gi)n(v)o(en)g (in)f(section)j(2.)c(In)i(the)g(gi)n(v)o(en)g(situation,)h(we)e(may)g (reformulate)j(these)0 3554 y(properties)26 b(as)e(follo)n(ws:)-22 3736 y(\(a\))47 b Fp(C)197 3688 y Fx(\()p Fw(n)p Fx(\))190 3748 y Fw(")323 3736 y Fo(=)25 b(\()p Fp(C)526 3688 y Fx(\()p Fw(n)p Fx(+1\))519 3748 y Fw(")718 3736 y Fo(\))753 3755 y Fw([)830 3736 y Fq(for)f Fp(n)h Fk(\025)g Fo(1)-27 3865 y Fq(\(b\))72 b Fo(#)p Fp(C)298 3817 y Fx(\()p Fw(n)p Fx(\))291 3877 y Fw(")424 3865 y Fk(2)25 b Fo(\()p Fp(e)587 3832 y Fw(nl)q Fx(\()p Fw(s)p Fl(\000)p Fw(")p Fx(\))831 3865 y Fp(;)15 b(e)913 3832 y Fw(nl)q Fx(\()p Fw(s)p Fx(+)p Fw(")p Fx(\))1158 3865 y Fo(\))23 b Fq(for)h Fp(n)h Fk(\025)g Fp(N)10 b Fo(\()p Fp(")p Fo(\))-22 3979 y Fq(\(c\))47 b Fp(\011)191 3946 y Fx(\()p Fw(nl)q Fx(\))314 3979 y Fo(\()p Fp(p)p Fo(\))52 b Fp(<)g(e)647 3946 y Fl(\000)p Fw(nl)q Fx(\()p Fw(s)p Fl(\000)p Fw(")p Fx(\))983 3979 y Fq(for)38 b Fp(n)51 b Fk(\025)g Fp(N)10 b Fo(\()p Fp(")p Fo(\))38 b Fq(and)h(an)o(y)f Fp(p)51 b Fo(=)h Fk(\012)2214 3946 y Fw(n)2214 4007 y(k)r Fx(=1)2346 3979 y Fp(v)2390 3994 y Fw(k)2433 3979 y Fq(,)37 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Fk(\012)1629 4596 y Fw(n)1629 4657 y(k)r Fx(=1)1761 4633 y Fp(v)1805 4648 y Fw(k)1848 4633 y Fp(;)p eop %%Page: 7 7 7 6 bop 0 17 a Fu(Chained)20 b(T)-6 b(ypical)19 b(Subspaces)h(-)e(a)h (Quantum)h(V)-8 b(ersion)19 b(of)g(Breiman')l(s)g(Theorem)523 b(7)0 248 y Fq(and)24 b(then)g(for)g(general)h Fp(n)g Fo(=)g Fp(ml)d Fo(+)e Fp(r)m(;)15 b(r)29 b(<)c(l)f Fq(by)g(the)g (set-up)534 461 y Fp(p)580 423 y Fx(\()p Fw(n)p Fx(\))580 483 y Fw(")707 461 y Fo(:=)h Fp(R)913 360 y Fj(\020)967 461 y Fq(tr)1023 479 y Fx([)p Fw(ml)q Fx(+)p Fw(r)r Fx(+1)p Fw(;)p Fx(\()p Fw(m)p Fx(+1\))p Fw(l)q Fx(])1593 360 y Fj(\020)1648 461 y Fp(p)1694 423 y Fx(\(\()p Fw(m)p Fx(+1\))p Fw(l)q Fx(\))1694 483 y Fw(")1982 360 y Fj(\021\021)2106 461 y Fp(:)0 670 y Fq(Observ)o(e)k(that)g(both)g(de\002nitions)i(are)e (compatible.)h(Ob)o(viously)-6 b(,)30 b(by)f(de\002nition)h(the)0 770 y(property)24 b(\(q1\))e(is)g(ful\002lled)g(by)g(the)g(de\002ned)h (system)f(of)f(projectors.)k(Ne)o(xt,)c(we)f(ha)n(v)o(e)0 869 y(with)j Fp(n)i Fo(=)g Fp(ml)d Fo(+)e Fp(r)m(;)15 b(r)29 b(<)c(l)257 1063 y(e)299 1025 y Fw(n)p Fx(\()p Fw(s)p Fl(\000)p Fx(2)p Fw(")p Fx(\))582 1063 y Fp(<)g Fo(#)p Fp(C)826 1025 y Fx(\()p Fw(m)p Fx(\))819 1085 y Fw(")971 1063 y Fk(\024)g Fq(tr)q Fo(\()p Fp(p)1204 1025 y Fx(\()p Fw(n)p Fx(\))1204 1085 y Fw(")1306 1063 y Fo(\))g Fk(\024)g Fo(#)p Fp(C)1610 1025 y Fx(\()p Fw(m)p Fx(\))1603 1085 y Fw(")1730 1063 y Fq(tr)q Fo(\()p Fi(1)1873 1088 y Fl(A)1929 1069 y Fv(\()p Ft(l)p Fv(\))2006 1063 y Fo(\))1366 1209 y Fp(<)g Fq(tr)p Fo(\()p Fi(1)1604 1234 y Fl(A)1660 1215 y Fv(\()p Ft(l)p Fv(\))1738 1209 y Fo(\))p Fp(e)1815 1171 y Fw(n)p Fx(\()p Fw(s)p Fx(+)p Fw(")p Fx(\))2063 1209 y Fp(<)g(e)2201 1171 y Fw(n)p Fx(\()p Fw(s)p Fx(+2)p Fw(")p Fx(\))2541 1209 y Fq(\(3.2\))0 1388 y(for)h Fp(n)f Fq(suf)n(\002ciently)j(lar)n(ge.)e(In)g(f)o(act,)g (the)h(\002rst)e(inequality)k(in)c(this)i(chain)g(is)f(ob)o(vious.)0 1488 y(By)d(de\002nition)i(we)e(ha)n(v)o(e)958 1800 y Fp(p)1004 1762 y Fx(\()p Fw(ml)q Fx(\))1004 1822 y Fw(")1173 1800 y Fo(=)1269 1678 y Ff(tr)p Fx(\()p Fw(p)1372 1642 y Fv(\()p Ft(ml)p Fv(\))1372 1688 y Ft(")1499 1678 y Fx(\))1332 1713 y Fj(X)1340 1909 y Fw(i)p Fx(=1)1541 1800 y Fp(q)1585 1752 y Fx(\()p Fw(m)p Fx(\))1582 1827 y Fw(i)0 2104 y Fq(for)h(certain)h(minimal)f(projectors)i Fp(q)1155 2056 y Fx(\()p Fw(m)p Fx(\))1152 2131 y Fw(i)1299 2104 y Fq(from)d Fo(\()p Fk(B)1593 2122 y Fx(\()p Fw(l)q Fx(\))1674 2104 y Fo(\))1709 2071 y Fx(\()p Fw(m)p Fx(\))1831 2104 y Fq(,)g(and)688 2431 y Fp(p)734 2394 y Fx(\(\()p Fw(m)p Fx(+1\))p Fw(l)q Fx(\))734 2454 y Fw(")1048 2431 y Fo(=)1144 2309 y Ff(tr)17 b Fx(\()p Fw(p)1264 2274 y Fv(\()p Ft(ml)p Fv(\))1264 2319 y Ft(")1390 2309 y Fx(\))1215 2345 y Fj(X)1224 2540 y Fw(i)p Fx(=1)1467 2315 y Fw(k)1504 2325 y Ft(i)1433 2345 y Fj(X)1437 2540 y Fw(j)t Fx(=1)1580 2431 y Fp(q)1624 2383 y Fx(\()p Fw(m)p Fx(\))1621 2458 y Fw(i)1765 2431 y Fk(\012)j Fp(q)1897 2445 y Fw(i;j)0 2712 y Fq(for)25 b(some)g(minimal)h(projectors)h Fp(q)1102 2726 y Fw(i;j)1206 2712 y Fq(from)e Fk(B)1467 2731 y Fx([)p Fw(m)p Fx(+1])1663 2712 y Fq(.)f(In)h(order)h(to)f (simplify)h(our)g(no-)0 2812 y(tation)f(let)707 2921 y Fp(I)7 b Fo(\()p Fp(m;)15 b(r)s Fo(\))26 b(:=)f([)p Fp(ml)e Fo(+)c Fp(r)k Fo(+)d(1)p Fp(;)15 b Fo(\()p Fp(m)21 b Fo(+)f(1\))p Fp(l)r Fo(])p Fp(:)0 3074 y Fq(W)-7 b(e)23 b(obtain)309 3367 y(tr)q Fo(\()p Fp(p)446 3329 y Fx(\()p Fw(ml)q Fx(+)p Fw(r)r Fx(\))446 3389 y Fw(")678 3367 y Fo(\))i(=)g Fq(tr)905 3184 y Fj(0)905 3348 y(@)984 3367 y Fp(R)1069 3184 y Fj(0)1069 3348 y(@)1149 3245 y Ff(tr)p Fx(\()p Fw(p)1252 3209 y Fv(\()p Ft(ml)p Fv(\))1252 3255 y Ft(")1379 3245 y Fx(\))1212 3280 y Fj(X)1220 3476 y Fw(i)p Fx(=1)1455 3251 y Fw(k)1492 3261 y Ft(i)1421 3280 y Fj(X)1426 3476 y Fw(j)t Fx(=1)1568 3367 y Fp(q)1612 3319 y Fx(\()p Fw(m)p Fx(\))1609 3394 y Fw(i)1753 3367 y Fk(\012)20 b Fq(tr)1900 3385 y Fw(I)5 b Fx(\()p Fw(m;r)r Fx(\))2110 3367 y Fp(q)2151 3381 y Fw(i;j)2231 3184 y Fj(1)2231 3348 y(A)2311 3184 y(1)2311 3348 y(A)738 3745 y Fo(=)25 b 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Fw(m;r)r Fx(\))2110 4123 y Fp(q)2151 4137 y Fw(i;j)2231 3940 y Fj(1)2231 4104 y(A)2311 3940 y(1)2311 4104 y(A)738 4501 y Fo(=)834 4379 y Ff(tr)q Fx(\()p Fw(p)938 4344 y Fv(\()p Ft(ml)p Fv(\))938 4389 y Ft(")1064 4379 y Fx(\))897 4415 y Fj(X)906 4610 y Fw(i)p Fx(=1)1107 4501 y Fq(tr)1177 4318 y Fj(0)1177 4482 y(@)1257 4501 y Fp(R)1342 4318 y Fj(0)1342 4482 y(@)1455 4385 y Fw(k)1492 4395 y Ft(i)1421 4415 y Fj(X)1426 4610 y Fw(j)t Fx(=1)1568 4501 y Fq(tr)1623 4520 y Fw(I)g Fx(\()p Fw(m;r)r Fx(\))1834 4501 y Fp(q)1875 4515 y Fw(i;j)1955 4318 y Fj(1)1955 4482 y(A)2034 4318 y(1)2034 4482 y(A)738 4762 y Fk(\025)25 b Fq(tr)p Fo(\()p Fp(p)970 4725 y Fx(\()p Fw(ml)q Fx(\))970 4785 y Fw(")1114 4762 y Fo(\))g(=)g(#)p Fp(C)1418 4725 y Fx(\()p Fw(m)p Fx(\))1411 4785 y Fw(")1539 4762 y Fp(:)p eop %%Page: 8 8 8 7 bop 0 17 a Fu(8)2130 b(I.)18 b(Bjelak)o(o)o(vi)t(\264)-29 b(c)20 b(et)e(al.)0 248 y Fq(Here)33 b(in)g(the)g(second)h(step)g(we)e (made)h(use)g(of)g(the)g(mutual)h(orthogonality)j(of)c(the)0 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Fj(0)783 4318 y(@)862 4338 y Fp(q)906 4290 y Fx(\()p Fw(m)p Fx(\))903 4365 y Fw(i)1048 4338 y Fk(\012)1173 4222 y Fw(k)1210 4232 y Ft(i)1139 4251 y Fj(X)1143 4447 y Fw(j)t Fx(=1)1285 4338 y Fp(q)1326 4352 y Fw(i;j)1406 4155 y Fj(1)1406 4318 y(A)1511 4338 y Fo(=)25 b Fp(\011)1673 4300 y Fx(\(\()p Fw(m)p Fx(+1\))p Fw(l)q Fx(\))1961 4338 y Fo(\()p Fp(p)2042 4300 y Fx(\(\()p Fw(m)p Fx(+1\))p Fw(l)q Fx(\))2042 4360 y Fw(")2330 4338 y Fo(\))h Fp(>)f Fo(1)20 b Fk(\000)g Fp(";)0 4643 y Fq(where)31 b(we)f(used)i(the)f(Schmidt)g (representation)j(and)e(\(d\))f(to)f(obtain)j(the)e(last)g(line.)0 4743 y(This)23 b(pro)o(v)o(es)i(\(q4\).)183 b Fk(u)-61 b(t)p eop %%Page: 9 9 9 8 bop 0 17 a Fu(Chained)20 b(T)-6 b(ypical)19 b(Subspaces)h(-)e(a)h (Quantum)h(V)-8 b(ersion)19 b(of)g(Breiman')l(s)g(Theorem)523 b(9)0 248 y Fa(Ac)o(knowledg)o(ements.)47 b Fu(W)-6 b(e)23 b(are)h(deeply)h(grateful)f(to)f(Ruedi)i(Seiler)e(for)g(his)h (continuous)i(support)f(of)0 331 y(our)19 b(w)o(ork)h(on)f(a)g(quantum) 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(The)i(Proper)f(F)o(ormula)g(for)h(Relati)n(v)o(e)f(Entrop)o(y)h(and)g (its)f(Asymptotics)h(in)f(Quan-)139 1458 y(tum)k(Probability)-5 b(,)18 b(Commun.)i(Math.)f(Phys.)f(143,)i(99-114)g(\(1991\))37 1541 y(4.)46 b(G.)14 b(K)n(eller)m(,)g(Equilibrium)h(States)e(in)i(Er)o (godic)g(Theory)-5 b(,)15 b(London)h(Mathematical)f(Society)f(Student) 139 1624 y(T)-5 b(e)o(xts)18 b(42,)h(Cambridge)h(\(1998\))p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0302110654501--