Content-Type: multipart/mixed; boundary="-------------0303300708631" This is a multi-part message in MIME format. ---------------0303300708631 Content-Type: text/plain; name="03-143.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-143.comments" Future versions may be found at http:www.ma.utexas.edu/users/radin/papers.html ---------------0303300708631 Content-Type: text/plain; name="03-143.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-143.keywords" aperiodic, symmetry, packings, tilings, densest packings ---------------0303300708631 Content-Type: application/postscript; name="18.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="18.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: text12.dvi %%Pages: 22 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX10 CMR10 CMMI10 MSBM10 CMMI7 CMSY10 CMR7 CMTI10 %%+ CMSY7 CMMI5 CMEX10 CMSY5 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips text12.dvi -o text12.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.03.28:1707 %%BeginProcSet: texc.pro %! 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put dup 100 /d put dup 110 /n put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueXX 5087380 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311e252234d51741e18db3a68e8ad10242 29e5817a10e796a78d2c7f7c1f50961b9a57aa604c9f821dbf5a9295197bc666 31678d7d2c7e1f8f2151ce0c29efce46270570f4301c5dad1b38884732e53dad 05dfc36b020e726ca575f71f04abf2b49e1f1d6d2a08a477658ca9a48f1c8cce 14382f0a42201de56e2821ee2b0e91a818b1b753d810ec2428dae5153b66af66 9442192024becf743a8f6264a58a0b3aa823510a4957d1bab3e1b83135362888 3e392f49926471a8021fdb48637baf0abcf31204b1b214f48c99f44af7782323 69d772ae4f49be53a1bf584747bf29b94f530d59a5be5370b8dd0691e32a21ba 9d0d592cf3bb50a99a3ecd18d6c4114cb4cfecc49705da90d7edb10e3a28f9eb a49347a09d31eec896f2a28e9607d99d42914aea16545c16e136bdd0b75fe486 61e24c7a9e9b233a76754c760822d0a88c575e08ae3e3f081d7bfb80ec4c03ac a08b65fb6474f71fc95c7c2462f2eb3754e647c29498288f2ced0bd3a2bca5c3 2f80a61fa667802d376cacd34de1f9572d1b3ab09d6f352750db4a768f869638 a87457889aa502850427b40e1294c5ba33e6b17532b2d13b5f50e71582f93daa 231e86597872a2a968127afb0f36257a76ce1eb24e6c4f29fce2aaf6532fb5cf df84da03f03a45b915209f67d398c7c4f7a3b0623750259087a478dca684b29e a8b7f52060bae9394369ed1cecc645d113cca3772a8dc36c6d916b5c5e65454c 0a188a33395fd3da67ad0a31ddab6a8434dd80f0bd0ea1a2a62eecc331d88b3e 369552daa1c575a98fe84383548626b65be7c24ae7eb61159f149872cfd87cf7 6c1a7c155c7186c7600e58cb61b8cb0c5dea98268a39e928bf6fc53985eaa763 2b28c1eb3d82e4d3fe225223f4266d2b6147e344aad2d4884a9308aadc7801af a606838925e3e50ee7aaf73f090baefcfd4e34b795cd92d83c944d91a4940f2f c955d727ea5bd76f0c8057b12621eceb0947b0a5dd10dbcbc52957dd978d7db0 c794660afdd4e946b3d7fc1ba60907fb3f756aab0406c0e7bce5a2238fb3e12e 07e2c0a7f465e90057642d704434ae0b57bd46c8ea91ab2a386e24c6deaf9cb0 8cdaa8fc4ec3fadc06bf28659cb878453db16f4b03925b2127b83be8fc240f33 23ea950b51d70c8fe861e30c346efa0a0125137598caca5478991e35f5bbbc19 4c787488ba339830bca15f8333431902e82b66a514a41c0bff92719a6a0d9587 4cff62c622fc61a0308a69f9fb7ef51bb274ce9e059c04b64e817abdbd105999 25a64183d9b3f2b3a0804d7da0a4804edf681b05cb69464d94ddbf91d22bb919 efb1a4580cd94be376000f6fe30dbbc654b555ba5a12aacc9d9da87ce23ab836 cef2be2e9c63a4fa2cc30f6409e88bfb619b97fe2abf29a54de079565b87d380 3c44742ef2522a418841bf38c505bfe076f76954ea8391e8b8bd4f91fc70f191 53ac4a3e5ab0e2f85451ca69db6661319aa1d9198d41d126b182d2aaeb8ba237 15299c1417dfbf7604c300e661775269f0f967e7525c0cf7156d5d988e3ee454 70b96074214b4bfba71d74fedc0a73da6486da2c2018775b70e7edff44949328 e691de1d234a6b99f5e7ea269d8fa49a1245042ae19c6bc5be91e15ebc539e88 a0a42671b37c8819b62c89d74c03533f9f5dbda8222d99bc19ed55673ff3a16a 663d3ba0e4996c06b31eae59266f25a8e0cf3f6fb9527c76bcb2c69955eb3b66 227553a36d8302c4e38521488d50aa144450a14f96093d2c568305eccc9644e6 eb4bbdbcbf93147a688ed55ae1cd6b47af6acd4dea8fac56cb83c1d169ced288 321c93c63f997d6ba8cfa6a2a0d41593be537d032f7a9a410c53a68be184e52d 1b8b99869673b720a5ead5934621f3e8ea6c6930382713b473501001fc852779 04fd8b6795d9ded508f671f5973c37e01a892917d29c0cf86b12b5e6ac494f6f 9248e94f863a8c98f261bc95e299cbfd25526cad98300bae34f756e52a38be53 8a2e6020433252c3c71ed7043688ed9edc2f4506aebdb330ec8176ef160f615d fc94fb25b9bb54827f532024e9ab33b6fc5f42416e73d6c62d19ac8a3caa6d78 e2b8c48e5d514e495d39eb4c236988cbcf4d40e91508eda40b8d983b578a4208 1d99fb2375a9af5b2deb06c8a0a6ea2f14cb4ad3f4590d2851a18a8e081b46cb f4d6cc71d3f67326bff33450bf4c731c9fef2ccdd0d61afd7f02179e3e0abe9a 42540441d32c162ae4154f0731b5aa43f938a202c239855fa943a3e315b9a642 377b77d512223b84f8a2cdcda450bdd6fc4f84afb229d88b13c4752dc4d95113 a259787e4c42d6c564ac849d5f9780d8ef59ce68268d052563c19581b06f7789 ab1dec3feac624cf6ddd2a821ed46b01f14a668f7abe74a5529c94f086db03c7 1ef817caad815c4d3588f99ab3a90b53ec855dda69d299ca7c6efcd2 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 66 /B put dup 71 /G put dup 80 /P put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b87899a29a3248b54f680006ce3ecd78acab44b6ec55f8c6ff120d406e f0729a5a5f6550949e4ba2c55873629c93943a86a43dab50c9a937617cb338df e5b0a4af48d1b1d9f1845cb5eedf5187ee8a95786d730d8c8a195888a2dc71ce 10810f27547441bfe0cfe7e6d29711b675df22766cf8ab489977f660ca498a1d 9e0f081187bf7f210104d3f3183e10cc76c50f5e969ba0e4c2f6d6ad2e17b43d 7b7524509f35e1d8bf4334c1d1fa9bca139230fcbc8b818e4dccacda56a84f8d 04d11125b6661fcb3144c5ac1180548ebbab4ac8e33092972b3085fed0080efd 90bbb124bac1457bcd99640bf1d7f063ec2866e609cd2f9007c995cc1ec7bfce fc749df7d46f8eab6318dac059bd2df1ddcc173094e867deff28dd120b4fc9fc 48619588cc12281dee5878bdca9f8930d5f429b58e167f16cb73fac679bb7775 87cf5ded9ad7f12bcbd0eb279923b996f5a0421f43fd904bf83214412e253e77 cc1c7efdff4a5a32ed7cef1b54afb4c3ce95a41954fbaf9b7083dadd3e4b7d08 967f86e85cf394005ca91a23b05c4ceb67f51146753f70f3c35c0e36ecea486c 4d4a464c218d1b93fc48b1f3a51fe63b383c8ed426d0966a34aa514d9727a56c 58fdf26f45d7b7cd80f2cced9e632fd795ca09e56d7df0df223107f7c3bc151c b702cc97309626494bf14b7862dc1f2f7aee60b9e759e13cd2ecf4850fa7b1d6 fdcc7d6c0bce4afbaf5a1c6e2e9dec40422c284a6293f125dfaa9547ff093c2f 5a05d530d0ce5bb1bfbb13830f31638af38d29ed490c00b6317c38cb44fcd7da 8b8e3d339d4a67f22a3da0e0d99ba4ef28600dca5468b35bd2fca73bd094490a 296859763e3828039397393564d3e7501149586f46084aa68aab4c5be06042e9 7303e3a2a93ab394c3a55ab9e56e0afb4d59e8408a987dee3f0f6bd078a89b46 a2006e8219490a54ab0522bf4f2e0b2e9dfc47eb621f1fd867d68420832cc3a1 5981ac5ded33f691aab3c23df015c89212c83252212aa983878d6482c64d8cff 1f13661eb6156cdfd1d307b41a59283f060ca8f4564c088c28853e477a0622a4 933a3afd0c091f9226b6b48fd1b4e8559d5e2700ffaf4d650ffbf5bc81d4a2cb 15eb2f505af29dfc09cd0f4183ef997257ca7170e00c97b426b828c90a7aff69 3e7ff5503cb94674db4e9da6d50097af8c7c6d8c30937924a7f89ebb6c03df5a 9a9a4361c5f8e0e8152267f12b9bb49932dbaca4cde745db1a60eb5d5dc181fa b1a04e6482015c38869f6927653d8a1e8f5b853fc9ceb72a0a1cdbe001dbdf27 2107a859d3c6b01f043ca49b8d23b4cbc8e867afe7d1fc8228875a8ad876d480 81bfacdf40367751344e2b47a6fe5b6b15ccfcd299416dfe5e898f356b87b907 7d02ad9c56a9595945385dd14f45a68729664c0bf385b59c7f52f6c6f1c768c8 05000f4d3ef09ab9877ce4e5b96873369db2b45ac8962141570af3f1575752da 580e5a2e73398892d70882a0e860596d4a5d3f480c95b9561ec5355582a1095d ef84221a7aff9c7063680897f39d5f79ed5cbfd77fb718d95da5962673e8d913 6b819a986faab1a1d97e7bfa5da292c8af35ffee39edb8647ab000396407c328 99a8c1c5188175fb6ce6a331dedf5e6560452c5c7cea1f5840e99947a8e08956 5db9b2ebc5f6fda37ce6f68ee6b218e05d64cc577d00d423481aa66b1b47d04b 810d57d7a7cbc91d04c1189b3cf17fe62508cbf76eae73480667989a3c5a45e8 27634cce62 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 46 /period 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 76 /L put dup 77 /M 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 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueXX 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950 93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21 c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644 7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e 13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03 22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56 25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1 c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2 b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e 2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd 6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4 07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331 51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6 0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3 d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1 34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec 015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a 418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e 5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd 977f844d32b43b0e48caed5a4bdabcefe71695d69ca784db55ff8fd5c5c42e30 40097ef70580328190679608cd0486b30d04adf83d6f1ffd90a24c58edddc0ac c7c71c959152eb3fac9e629b5504e8aadc162d7e118b9f2f5efa7ad72c4fbf6f af48e11940e268445d7bc7215603fb1902aaebda29e644945bfd0aa8acda7f77 9a65ed558a690ecf9ec616fface456178cd64143512ab0a042417eaa00218d85 97e330319b8c689da459e52e72d0ea6edc748d88bb588a8ad4ad70047bef13da 964cb4a45fb1f4834a12a72defb60729df354cc14b0f2919f54072cd5f33d698 08007cd33f18ef00c24215358ea7ebcd243442bea1d1f71ded4b97090716fc55 a9909be7f913fb248d4a9d26334057b337c01c290ef9ca63c52544f9a4ee6a51 ed8381535bcb9ffd3cd6be1e0a2fe048027cba988448fe8f286ab16cde42cd3a 34c05cde079f8a5820120f92cf4789d5be49fad0a1cbeb98df17a935d48971dd 37d262770aa0c8b76a39ada38f8ad93fe340e1aa51146c8661567b92190e5494 3a043cfa76ae70e9acf56fe6ca3f9c490f5d365fae9b665d745ed9d313970804 9cb5fe530be9a10f2551c07755a6f6215c90f5cc685780ce2ce2be362a17fece adebf2437b943afaff89c123d3d4b9d331e3b81f18d703d1ccabcbed1b3250d2 296f27a3162b7d6dca04882baf730a210286fdae713c23d9596120db130cb88a f0d7380dfdf20e97a0e6c68e9b47f7ee26c2205f4c72ebf14d3421a566d8ee37 6eeb76e514810a80af52cc36a60cd2823a6f15976059fc13941ebc1dc3b66523 8118bde1004e3099054f5d89cfab0c167dd5220fbfb9d9606aad288b0f0e41c1 ea775bfbac527580078834d5484261662f5e666d3deedd4696b4efcc6f1df2c9 00f8310891cafbcb95b2e4c8807e914c5f4d2037eb1a405b2219e9b39e60d627 b8397a40ea1fe2daa36b77dfa3919068e25917099c62766ec6c62ed2156d9331 8af80ac66106a4ac0484954bd6ef743ee77c5b6a5c8d93dbc8f0fa1003e90a3d 08c5c4747bc68da89469d81e 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 1 /periodcentered put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 33 /arrowright put dup 36 /arrowboth put dup 44 /arrowdblboth put dup 50 /element put dup 66 /B put dup 71 /G put dup 79 /O put dup 80 /P put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c43028b05e52e64e13948d004710ad07edf9d82d5649cfcbc6e22d7a1a6ac 89ac000978333df923022e75f54864c075e634c2fa4bfd368a73e7105bed34ba f30a8c6ae60d4bc793917514ff586e2e615ed194c40e17421e53aaa7f814dcef 10aa842a47d6d13df61bef49ba603c28b7794af8bddf21aabbef874b63368819 055709d59530eb32ca7f8274c2099190f1ac99268e331209e5b870257c11bef6 b39f2c12d30901217ffa454aeb48ed62535c03e08e6a416539aba58fbad15102 b19d38bf0ef432f1ec86461d867194214ff9a5bc4c7b53b6b19cb50b644d5a5c 1691726ae0e33518152d921e0044873f0b9f262fff1f9a0203f5b6553ac52961 d67c7bff246217178e79cb308afb4cd481810877aa1c4e3abbb556efda7a0fe2 9821d5b78ed7e4686ea99dbc74b6e411c88630ef4533e8bdd76633c64227f794 5a9daed66994eb4e3bda915186826445e70737a675b84adc87ec93d42221b74d 974fc81cfec4f4f9f1e530f88b653e9b0dd2208515924bc8dee72b30db052abf c4c9a44754864acde43592a94057af0098f9aba8c3656e0c22a32ff03f17175d ea16ba0c3a2f95bfa3a33c40600aba84b6f65a1d0ede21b7576f6825fcc36759 15e6653c49396e1651a83403da6244ca697a71c6518aec352badb4e5371b2bae 03a2370b7e1656dbf7f3b29b3d32198d1c52fed4c97e00e23404d13431e41fb6 77b0b859b570320e97b7f50549561b096b9489e027467022623bb90764aae41e 07633507a94255427851649183f3a1f9734c7cd0ea9d69db1aa39071c9179137 67da81c900f903b1b78ea413f10a502dede7bc0f34080d9b51d56cb4dde8f279 14f38a3f70a5f393c2b8a0d4879612a067c1bab0074a39ce4f106a13395c0821 5ee8d35d7cf8f212770837b545da11c37eef0daffd78a98158159f9a64cb6b32 c60ccd756fda40e0cf3a77df8f79335fed10a2a8a55a1f63fec86ef7fdc2cbb8 4943bbe328170705af1ece686103491c008264b2d72e91796bb59ec74d232a90 d804c63ec36e31c6dff94d195feb2c442686b93b91d86ea6d52bed54617ee76b 9aafc66feaf66b8139496a9c26815939b7d540a328fa1381096296df97c0375c b84f7a1811405b11520f2cf7262ef6aaaa97e6d66619af042c55e2050a19bd7a aa3164d9492306a0d3ccd57db4405e5694ca506780dac173dd2fb928f85b2fa2 9fe2a6f11baad39ca150227d2c421cf595a87c15ec11654c962f02848e00e99c ac53c11e469ad6877e9e514fc9c85bd4f00e9a098a6f48b31ebdaf88f3eba527 49bf7164ce787a9015cb1f9ba679cfdd54a322a038882b397ca9c8aaa776589f 2ff3dc2ba64e5bfe523e38664e49bb0e65e58361f03f7819862628f30dcf9931 b6530966c40ab2611ad6233ba0aa46200e04e297de4ad27cd4bf34626e70a724 f0d468e145f101b6e02c6b657021ed19ab77bf8757ab4758a58d2644bf2eb454 e2c012ce86a4641b44e27e41beb62b40f1b3514ba6a8ab504284ed5a6f19fe87 e2ae24e108387a5eae5e8c76f9d0b6738fb0cd3b3c46b8c172fcf631b1c5fa9f 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4f325dae022f1c61e548a1ae84de791da49c10314d8c3f10ac19ee9d733b2ef9 8f9b9f39c1b7f872d0ee91bb4412a6e6b38ef15d939d70a002ff131236780e48 29f2c94db4cdd4320ee31793b5a7351ed1c19b3067b5c04b4f9c1633335b7f0a 15c8d52897b14951998c88e9999f9ab96969962128cac94ae244c79888b164d8 180155cf3f89fe51741946cdff9f3e0f1e5be60987025982ade9cf222a9255f6 66acad1c929b0704909090588c4b0373143c5520709adf1a0767c8c53288669b a152a290b66477f05f05f96951d6eade77198a73d20f267241c8b5ce5bfbb609 573d7a26c823ff79a45daf8802de392080577efbcaceeb6ac2343d7b03733683 85dc993edcdc518a187d9b087fd8ba15b99eb7ed8507bcd5079dc44d71e0373c 9d6bf26471152b059d47e1887abf80a1a75528e9142990bf1e85c7eeaa2cdb6e 91a7ea46bac2c3ae5885d926acbcbbd7eea6d6f816ee691698b387a8a249c1a4 293b6cad3344276aff81fd9369011d1f929292d192e3c361ec88078a6c373b51 e8e97e0f758dc8c946f8e69f500432ac0cf44244be5939509a29993f5a14aa93 58962f4be4d2e5d773aa4c19b5780894cd0b7b1d4e31de4ed51f2cb0ebbe7912 511684ed04666c556293e14f7818d0436a412ac84d2d9a1deabbfe3fcbead920 54e91e17b0a693e4c43181c663cf0d4be45544ae38c346412da01ce469167d88 3c5ed6fb0b0b9e7bcaf0a28dc528c64b4d4c158c4a83bfc1c186990c54f2f276 b8d0bd9073f3baa52da9e7a8d4b84ec95532e3184e9d04ad41ee273ec584b81d c7ac77c8ef715e055ea24b40e5a0cc9ffc9513efac1f9ca66bbf73474468217a 3f3354d6d2326fcfdd014dfd5401237fd9fbc8f53c6c431ed6531f9dfbda32d9 9ac75c37070e17a22f2bf568dd5d74abc3e0ba253c6d2181e70764598a3b716b 5ba9f374836b3597ef29b9d21970925fcfacceb83870a126fb5efe4679771c90 949b17328ee0584dbee0d74f00ca8c61ebc589782242aa93c5e615df91487928 a29f79e03698227fc2d503ea84e83b519cb8681eece2b2a0453063bd7597c4f3 a7c72d1041968e82ae6fe2e60959062cbbf29285ec3c826097d052486edaf76b 509623110d58d3b22a9b854648f961c1e5c814d8f7c8260b6d863a3cee37c4ab db11957182b10da433a753a8ca9ff2321e689344b955a66d4e1f068c90367c6f f14ea8eac550caef6c3de3396244910c678edb356440a6bb13c0ab1f98da2765 1ca6842ddcacc061179d94b11d7e517a51d862226659bb16e39b95faf785063b d90819b0616e72c08a62ae37c9b7f998955f98787be979d4681baea85b7c91b6 190e7fccccadb2542dd0c8c642473e48f5422b67657984aa81edaf5ecbdb397f 7e6d8223a9b8d3750aef0cd1de87c26c76e72869559bc4cfc05defdcf70dd9e8 62ed02bc956e658e9cb0855d83ba915c16a5a331091594c849279449e07c5e77 8ce3f4996446cd9dba411fde3b801a4c6bd45400b1382f3651f882985249d01a 7eac219c7c65e68c2d8571fbbfa918649ebdd587f57c377f2571efb411daa204 cd5590a3b065d19ee6a05cd2ba31b16df53f41d98e5a1f73ac51a08de7e1f5bb feb3c798530ddb19ef11678b8033c0b70c4c2f00f794d8e3125a4c437db7253f f18ef76ca46680d77923b401a9756d7903928a1ac1c92fd1e04a38dec11d2678 24b377375140b244db81b6fc570dcb7d409a1b032eea9be12c41bff2db37e68d ea36f6625e1477cf6f04a92e3a417ff1fc320bc75fec28d51721ffffe30c975b 6d07ac70d289cbc4a21b15e108ee5a2680d46c3261a777524f1ad4c65d9215e7 353f0e48bc14ce8d11cbdf6e98436fc2514353474827e1b236dd8584d8ed2300 a17ccf06e7b3c59907d108791851c8112be4fdb65431700c5a25 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /mu put dup 100 /d put dup 106 /j put dup 110 /n put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82 ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96 0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0 24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772 0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2 364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba 0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279 617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a387b3 80db88cca083b06f5af70d768d1699826fb12ce12efc2b4c70923e052dbb964f 5fa957c3ce225c0fda64d9b5321ee1ade207c1cc93105096cc73118f4082594c 8ecddeb0d7bfde6f70bc62f10407c26a476ed88be7999d64a15912493829a9de 62c71f5a34fbf5a843e311873cd98817dc9f8a4aeb7e0738b5de10043f5cfea7 14784c4fe6a8366586afac2d60fa6428ed028beeba0b764ebf0c24518b480463 059076fce400dcddd0f2e7d5b8edd8607f820dde31951b08e7d92faf6285c40f da0792b827df768d1590f5d68156e4fc26e9be3f42186b48b0e9a457326d0e62 966dad92cdbae92f3339ac4d17ea35acd94f8f2e6d40e9040ee5463b7671e281 32c50e0ab66994c3827e6a3da26c7db3e608cf2eb0aba846b85ddcb1d7d9d17a f604898d89956603f72f8902f15f054d17595a3e3552922746375c589463efd3 6b06f96f4098d36cc4a6906531f03ae1427df49dd2489150dfc6288ff715e9e3 cb0bd78ce1cc933b162f406e9e5a8dd0b18da1485d668e16117a74b4298a0949 f3beabf11e8cc0d13c9fe10a0e5e01cd099c91ecfc134bf66eeb9676f28c9894 cebaa0c3ce502038e4fe53b8a9f3f33f8e19b6dd9ff3553fa722b75ac50fbbb2 8cf26ebfd62c0108b6b8ee1e8fd7b471097eb464b6b4c9991a65e45ebd814771 26b806a476d9119abd5c1f927a20f287708010ec8c5cb095f81003bfae1d309a e96ddeb2900997b763cce6f13afabf617fbf239725029b1239c23562ba6a64bc c1a75de0efd3eab1ba490294f27a59757b42b2d1cab240c8817da430c12dc8ac 5bb9745a1f9671eacb6e8e43a0b66ea774b32a2b016debb3a5e80b1ed1ba716d 03496ec3fd56e42c462ea8501a04482edf00cfdfb8eb1ca452408f7133a7dd36 482ac0226f2ecd11aee71f6e54d7fe91dab35f2a132faef25e52b42b339956f7 02bc23f6e5e9762dbcf228820555e3553c154674bbe6f625b437a7fb80f6422c ec0b34fe1589f04baea51ce70d7af3684fbcb4d872ea28a330f976c513922c1a 4ee77f6c4d77f2318ddc7167ef0393f8f952f9280c6f029d988c2cf8fc663137 39b1d4c1a9727b6438605a957c8e082ccc0b02d03eb1b582f183c6108997f845 bafec1326032e7901bca52396a6234111e19f74d66dd6c5f138cffc0dd6a7aba eec802120f1d96573247af4afa2a498797024d221a489c5cf362d0f388e0adaf 0fa324265496085d09ae518cf0381cc231752996d6b9ec9c0e7937353de3801b 1164a1fa0d6bef6bc3a7976a230578f780a32e215ca2e68a38270ec8d75679d6 9ad7158aca8473a360229913abac70583632fdd2179d79e9cc8d36747bf39d08 74ed739af7ca1bfd209e3e145574c8cfbdc6fec0a863ade3577b8e069b22a5c6 61d05894bd3fd524229c6063c43cb82fb6650ce31ffb6754b988770e20172bd4 861e9660423879cef3275ca5db459a56b873ae7f8f43a2b8102bdc88f33561d9 90b148c861c250b5c07a88ecfa69a7a2141a92376abbc98b7be1b14c30a3289e 3220e21d01411b75bef0668a4f16e70e136574da783b4e1a678ef0d23ea752a4 a57b892df58bfbabdd6202ef1bc39d74a162ca9a0ae41327c232c3f42f3852a2 c487d730c93936021d4df849d3c803 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 72 /H put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812eae30521c3c775adf1959595a43d8a9c4e12d9f9ece27a0c9b5f45e38 8e26a39cb0ad4e25ab8f21b25ad1b106ed22af7947ea8ae4dc17b9facbc5e22e 89a91b046ba4cddde69c1997fa7f4cd949ba3ac4b6e001475daf165b9432dc70 6e30aeead8cc342d94b20a4045a331175655d6aa279627efc0fb53a4ce66b68f a45b5765f0c1368c056ed96db40d15cac38d09732d6cb16a42bcb747f46389d6 3813a2d88cda3fed9babd6b8303b0f5e485d54cafb36b8071c93f258f636f639 b7c616c50abfdf63d2269f968bb4dfd2133dab639de3bc2882f86c5668063926 b6d866f15818b2acc7cad29b4a1d573431eb2117f58dc289bb199106018828ab 85e75a4f8d71f30fc4372ad9983b5a9014d06368c64ba38a3ecc3b1e4c7f9bd5 facd66c8e959ef3971c9ed95d3a71db3829148734e540aecbf0db2bd202f765d 0f51697f6058ae2d7757601ffc686e2b28aab7a25d691fcc1900ab7addcc89e2 50931b34df6b0b01710a30710d74022c0ff2016f5bd033e222a1837be9b951b0 db69b136bf6bb4aacc7b0310c8f102a874374295611e19ce302a70fa753ba1cb 087d8b81f56bdcacfd85cbe6421d4b9f6392e5665db1bb3e3efcafba3f02d1e4 733d21ed73fb21217822d36b6b0bef8573300101e399892f16ca615cfca06cc1 b8818335d34721b5075c7ca358e8826284128e07683f0a5f32a06fea597b450a 3dd8898704a4339cef82faa883b21ada73956718b023b9f32c7bc980eb76e04d fe88d6c2fc91fc71c1026b77c2f6534c42f1853091271ae682a2e3fbff891577 2b017acc33aee84725389f589f683529c0b1a0a8fbd91ec6aeb2b2785c22111d 264eddd445c02c516f87dd9c53c5f730abacbb68fe25adf42fe3ffced1826e68 03f73161e35d90a2bcf3f77b6ff98f3a85b06ee93ec91288f54de9d348fb57d5 b7a02f8e902faf339a6a1f34a30e96ede77d5f60915cdc2e0e586748a6fec6b0 53411aa00158c2417b4a9df1fc3644a85ba3feb85aae4fd14987b01d63663b2d d5d6384144eb99d9b821b390f58129eedd8e5a9a5caf7be04143d09c37110f49 6ad884071bb2502a02d6ffbc20fca2e02c0740c39ced7db89f1c778e3a8d96d2 de83094f3d315d2c5bb689caca74c573765a58b0f68a5cfa6259dcd1e1d2bfec d436cdd604e3e64b7ed2714babbfe35124bc696fefaf1c090d2ede54c41cb18b 0fe44af1dea1ccec5453567e73394a6946bfda1f11dd7c2e1d1088fdb95354f3 7418e4e565e2ba9d94b08e0ff44d4ebd2ad93ed2a5c06a4e722e48687b1073e3 f394f70a55f7ab79cb1d802ad39d0a8823868ac75b22353af2bb2d46e5b5416c 9a17c6516baeb9ba078da9150276c1da55fe896b066385c0ca08532c7a32e67d b73f7660151072ce89d20bc14f60add94da269ec54ad386f332e7b2b83ab386c 30d3a336c475a5f530ccb33fbe58152b3038e2aa4d5f734d0edb7d2528378b86 db96acda8f74eb02ea307ca149f36d13af7d1d0981cc78dccb7dcf0e14841985 c15d033803b58ce797e67bba694560c322ac4be3db83dffd6d3cbed0c47f9afa fc0d560ca3f8226061fed9acee03a9ba5397ec6b887a51fbf5463e2ee123ab53 a4ce4a1aaeb0b8571ee17982077b27102f33609c3ec3aaae034e9e2affe214c0 d6d0aef7e7daa2eecbe5a8513262b548ec69afec652754aa42881365c7095512 dd65d1a3f2dc2b66c94ceaabcc5bc6d66ec34f5b36641074c20d84a516161c43 48f660ac99159f9d444e495d7b49a105a8c03e3e40280ebad8639440ec0133dc 92fb901a46d77c9b452ecc6f8ca6acc56830656dda2f8349ff1ba489b1ddb6cd e784c3c564bec17c0443cb16bfb2bfa591c5ec245d198b5cf4a9ebc658c8e3a2 005dd0f98d0aae46d714379a38ff866c0e9c3a4118bf32733b0b119fca93cbf9 6719ef185b037936f936b7a7eb00f693b4c4ab947126aa4df6fdad0960258155 a97798a061c61207b472001c2f06da58880837baa7f2f9ba029a0363bb 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 30 /phi 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 66 /B put dup 71 /G put dup 72 /H put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 88 /X 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 109 /m put dup 110 /n put dup 112 /p put dup 115 /s put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 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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 0 /Gamma put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 33 /exclam put dup 34 /quotedblright put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 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 90 /Z 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 123 /endash put dup 125 /hungarumlaut put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 58 /colon put dup 65 /A put dup 66 /B put dup 68 /D put dup 70 /F put dup 73 /I put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S 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 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 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b(b)m(y)g(an)m(y)f(of)h (the)g(disks)g(in)g(Figure)f(3.)49 b(F)-10 b(or)31 b(the)g(disks)g(in)g (that)g(pac)m(king)g(the)f(relativ)m(e)-150 4262 y(fraction,)h Fj(\031)t(=)p Fk(2)491 4165 y Fg(p)p 589 4165 59 5 v 589 4262 a Fk(3,)h(is)e(th)m(us)f(the)g(highest)h(p)s(ossible)f(densit) m(y)g(of)h(an)m(y)g(pac)m(king)f(b)m(y)h(equal)g(disks)g(in)-150 4401 y Fi(E)-73 4359 y Ff(2)-20 4401 y Fk(:)51 b(in)m(tuitiv)m(ely)-10 b(,)40 b(the)d(densit)m(y)g(has)h(b)s(een)e(maximized)i(sim)m (ultaneously)f(in)h(all)h(lo)s(cal)g(regions.)-150 4541 y(The)i(argumen)m(ts)f(b)m(y)h(Hsiang)h([Hsia])h(and)e(b)m(y)h(Hales)g ([Hale])g(for)f(ball)h(pac)m(kings)f(in)h Fi(E)3690 4498 y Ff(3)3784 4541 y Fk(share)-150 4680 y(this)k(approac)m(h)e(of)i(sim)m (ultaneous)e(lo)s(cal)j(optima,)h(though)e(the)f(quan)m(tit)m(y)h(b)s (eing)g(optimized)-150 4819 y(is)d(no)g(longer)f(simply)h(the)f (relativ)m(e)h(v)m(olume)g(of)f(the)h(V)-10 b(oronoi)43 b(region;)h(see)e([Laga].)65 b(And)43 b(w)m(e)-150 4959 y(note)35 b(that)g(the)g(other)f(solv)m(ed)h(problems)f(listed)h(ab)s (o)m(v)m(e,)g(b)s(eing)g(tilings,)i(share)d(this)h(feature)e(of)-150 5098 y(sim)m(ultaneous)k(lo)s(cal)j(optimization.)82 5238 y(Although)g(densest)e(pac)m(king)h(problems)g(are)g(at)h(the)f (heart)g(of)h(our)f(discussion,)g(w)m(e)g(will)1921 5559 y(1)p eop %%Page: 2 3 2 2 bop -150 116 a Fk(not)45 b(b)s(e)g(concerned)d(with)j(issues)f(of)h (actually)h(solving)f(suc)m(h)f(problems,)h(but)g(with)g(broader)-150 256 y(questions)28 b(suc)m(h)f(as)h(the)g(existence,)i(and)e(esp)s (ecially)g(the)g(qualitativ)m(e)i(features)c(\(symmetries\),)-150 395 y(of)36 b(their)g(solutions.)51 b(The)36 b(reason)f(is)i(that)f (although)g(there)f(are)h(signi\014can)m(t)g(applications)g(for)-150 535 y(the)42 b(solution)g(of)h(a)f(densest)f(pac)m(king)h(problem,)g (esp)s(ecially)h(for)e(ball)i(pac)m(kings,)g(the)f(deep)s(er)-150 674 y(in)m(terest)32 b(for)h(mathematics)g(is)h(the)f(in)m(v)m (estigation)g(suc)m(h)f(in)m(v)m(estigation)i(spa)m(wns,)g 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b(it)f(the)g(case)g(that)g(for)g(ev)m(ery)f(p)s(olyhedron)g(whic)m(h)g (can)h(tile)h Fi(E)2934 1668 y Fh(d)3027 1710 y Fk(or)f Fi(H)3259 1668 y Fh(d)3352 1710 y Fk(there)f(is)h(\(also\))82 1850 y(a)f(tiling)g(consisting)f(precisely)f(of)h(the)g(images)h(of)f (the)f(p)s(olyhedron)g(b)m(y)i(the)e(elemen)m(ts)g(of)82 1989 y(a)k(subgroup)e(of)h(rigid)h(motions?)-118 2129 y(iii\))59 b(What)d(are)f(the)g(di\013eren)m(t)f(structures)f(\(in)i (particular)g(symmetries\))g(of)g(the)g(densest)82 2268 y(pac)m(kings)38 b(b)m(y)h(b)s(o)s(dies)f(of)h Fi(E)1288 2226 y Fh(d)1381 2268 y Fk(or)f Fi(H)1613 2226 y Fh(d)1668 2268 y Fk(?)82 2468 y(The)33 b(history)h(of)f(researc)m(h)e(on)i(Hilb)s (ert's)h(18th)f(problem)f(is)i(erratic.)49 b(Bieb)s(erbac)m(h)32 b(ga)m(v)m(e)h(a)-150 2607 y(celebrated)d(solution)h(of)h(i\))g(in)g (1910)g([Bieb].)50 b(Ho)m(w)m(ev)m(er)30 b(a)i(simple)g(coun)m (terexample)d(w)m(as)i(giv)m(en)-150 2747 y(for)44 b(ii\))i(in)f(1928)g 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b(circle)f(in)i(a)g(p)s(en)m(tagonal)f(pac)m(king)1892 5559 y(12)p eop %%Page: 13 14 13 13 bop 79 3749 a @beginspecial -46 @llx 175 @lly 389 @urx 646 @ury 3240 @rwi @setspecial %%BeginDocument: k-dtiling.ps %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 3.0.1. %%For: () () %%Title: (/d1/grad/strauss/Penrose6.ai) %%CreationDate: (6/15/94) (16:04) %%BoundingBox: -46 175 389 646 %%DocumentProcessColors: Black %%DocumentSuppliedResources: procset Adobe_packedarray 2.0 0 %%+ procset Adobe_cmykcolor 1.1 0 %%+ procset Adobe_cshow 1.1 0 %%+ procset Adobe_customcolor 1.0 0 %%+ procset Adobe_IllustratorA_AI3 1.0 1 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 30 31 582 761 %AI3_DocumentPreview: Header %%Template: %%PageOrigin:30 31 %%AI3_PaperRect:0 792 612 0 %%AI3_Margin:30 31 30 31 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_packedarray 2.0 0 %%Title: (Packed Array Operators) %%Version: 2.0 %%CreationDate: (8/2/90) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_packedarray 5 dict dup begin put /initialize % - initialize - { /packedarray where { pop } { Adobe_packedarray begin Adobe_packedarray { dup xcheck { bind } if userdict 3 1 roll put } forall end } ifelse } def /terminate % - terminate - { } def /packedarray % arguments count packedarray array { array astore readonly } def /setpacking % boolean setpacking - { pop } def /currentpacking % - setpacking boolean { false } def currentdict readonly pop end %%EndResource Adobe_packedarray /initialize get exec %%BeginResource: procset Adobe_cmykcolor 1.1 0 %%Title: (CMYK Color Operators) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cmykcolor 4 dict dup begin put /initialize % - initialize - { /setcmykcolor where { pop } { userdict /Adobe_cmykcolor_vars 2 dict dup begin put /_setrgbcolor /setrgbcolor load def /_currentrgbcolor /currentrgbcolor load def Adobe_cmykcolor begin Adobe_cmykcolor { dup xcheck { bind } if pop pop } forall end end Adobe_cmykcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_cmykcolor eq { end } if } def /setcmykcolor % cyan magenta yellow black setcmykcolor - { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat Adobe_cmykcolor_vars /_setrgbcolor get exec pop } def /currentcmykcolor % - currentcmykcolor cyan magenta yellow black { Adobe_cmykcolor_vars /_currentrgbcolor get exec 3 { 1 sub neg 3 1 roll } repeat 0 } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 1.1 0 %%Title: (cshow Operator) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 3 dict dup begin put /initialize % - initialize - { /cshow where { pop } { userdict /Adobe_cshow_vars 1 dict dup begin put /_cshow % - _cshow proc {} def Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if userdict 3 1 roll put } forall end end } ifelse } def /terminate % - terminate - { } def /cshow % proc string cshow - { exch Adobe_cshow_vars exch /_cshow exch put { 0 0 Adobe_cshow_vars /_cshow get exec } forall } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_customcolor 1.0 0 %%Title: (Custom Color Operators) %%Version: 1.0 %%CreationDate: (5/9/88) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_customcolor 5 dict dup begin put /initialize % - initialize - { /setcustomcolor where { pop } { Adobe_customcolor begin Adobe_customcolor { dup xcheck { bind } if pop pop } forall end Adobe_customcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_customcolor eq { end } if } def /findcmykcustomcolor % cyan magenta yellow black name findcmykcustomcolor object { 5 packedarray } def /setcustomcolor % object tint setcustomcolor - { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def /setoverprint % boolean setoverprint - { pop } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI3 1.0 1 %%Title: (Adobe Illustrator (R) Version 3.0 Abbreviated Prolog) %%Version: 1.0 %%CreationDate: (7/22/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI3 61 dict dup begin put % initialization /initialize % - initialize - { % 47 vars, but leave slack of 10 entries for custom Postscript fragments userdict /Adobe_IllustratorA_AI3_vars 57 dict dup begin put % paint operands /_lp /none def /_pf {} def /_ps {} def /_psf {} def /_pss {} def /_pjsf {} def /_pjss {} def /_pola 0 def /_doClip 0 def % paint operators /cf currentflat def % - cf flatness % typography operands /_tm matrix def /_renderStart [/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0] def /_renderEnd [null null null null /i1 /i1 /i1 /i1] def /_render -1 def /_rise 0 def /_ax 0 def % x character spacing (_ax, _ay, _cx, _cy follows awidthshow naming convention) /_ay 0 def % y character spacing /_cx 0 def % x word spacing /_cy 0 def % y word spacing /_leading [0 0] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def % typography operators /Tx {} def /Tj {} def % compound path operators /CRender {} def % printing /_AI3_savepage {} def % color operands /_gf null def /_cf 4 array def /_if null def /_of false def /_fc {} def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc {} def /_i null def Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3 { dup xcheck { bind } if pop pop } forall end end Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3_vars begin newpath } def /terminate % - terminate - { end end } def % definition operators /_ % - _ null null def /ddef % key value ddef - { Adobe_IllustratorA_AI3_vars 3 1 roll put } def /xput % key value literal xput - { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop % integer npop - { { pop } repeat } def % marking operators /sw % ax ay string sw x y { dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add } def /swj % cx cy fillchar ax ay string swj x y { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add 6 2 roll /_cnt 0 ddef {1 index eq {/_cnt _cnt 1 add ddef} if} forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss % ax ay string matrix ss - { 4 1 roll { % matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss % cx cy fillchar ax ay string matrix jss - { 4 1 roll { % cx cy fillchar matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke }ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def % path operators /sp % ax ay string sp - { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp % cx cy fillchar ax ay string jsp - { { % cx cy fillchar ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath }ifelse 2 copy rmoveto } exch cshow 5 npop } def % path construction operators /pl % x y pl x y { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c % x1 y1 x2 y2 x3 y3 c - { curveto } def /C /c load def /v % x2 y2 x3 y3 v - { currentpoint 6 2 roll curveto } def /V /v load def /y % x1 y1 x2 y2 y - { 2 copy curveto } def /Y /y load def /l % x y l - { lineto } def /L /l load def /m % x y m - { moveto } def } {%else /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def }ifelse % graphic state operators /d % array phase d - { setdash } def /cf {} def % - cf flatness /i % flatness i - { dup 0 eq { pop cf } if setflat } def /j % linejoin j - { setlinejoin } def /J % linecap J - { setlinecap } def /M % miterlimit M - { setmiterlimit } def /w % linewidth w - { setlinewidth } def % path painting operators /H % - H - {} def /h % - h - { closepath } def /N % - N - { _pola 0 eq { _doClip 1 eq {clip /_doClip 0 ddef} if newpath } { /CRender {N} ddef }ifelse } def /n % - n - {N} def /F % - F - { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf }ifelse } { /CRender {F} ddef }ifelse } def /f % - f - { closepath F } def /S % - S - { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps }ifelse } { /CRender {S} ddef }ifelse } def /s % - s - { closepath S } def /B % - B - { _pola 0 eq { _doClip 1 eq % F clears _doClip gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S }ifelse } { /CRender {B} ddef }ifelse } def /b % - b - { closepath B } def /W % - W - { /_doClip 1 ddef } def /* % - [string] * - { count 0 ne { dup type (stringtype) eq {pop} if } if _pola 0 eq {newpath} if } def % group operators /u % - u - {} def /U % - U - {} def /q % - q - { _pola 0 eq {gsave} if } def /Q % - Q - { _pola 0 eq {grestore} if } def /*u % - *u - { _pola 1 add /_pola exch ddef } def /*U % - *U - { _pola 1 sub /_pola exch ddef _pola 0 eq {CRender} if } def /D % polarized D - {pop} def /*w % - *w - {} def /*W % - *W - {} def % place operators /` % matrix llx lly urx ury string ` - { /_i save ddef 6 1 roll 4 npop concat userdict begin /showpage {} def false setoverprint pop } def /~ % - ~ - { end _i restore } def % color operators /O % flag O - { 0 ne /_of exch ddef /_lp /none ddef } def /R % flag R - { 0 ne /_os exch ddef /_lp /none ddef } def /g % gray g - { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G % gray G - { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k % cyan magenta yellow black k - { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K % cyan magenta yellow black K - { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x % cyan magenta yellow black name gray x - { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X % cyan magenta yellow black name gray X - { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def % locked object operator /A % value A - { pop } def currentdict readonly pop end setpacking % annotate page operator /annotatepage { } def %%EndResource %AI3-Grid.0 18 18 3 0 0 0 3 %%EndProlog %%BeginSetup Adobe_cmykcolor /initialize get exec Adobe_cshow /initialize get exec Adobe_customcolor /initialize get exec Adobe_IllustratorA_AI3 /initialize get exec %%EndSetup 0 A u u u u 0 R 0 G 0 i 0 J 0 j 1 w 4 M []0 d %AI3_Note: 0 D 103.8711 412.8662 m 134.8572 390.3529 L 103.8706 367.8406 L 111.1857 390.3537 L 103.8706 412.8666 L 103.8711 412.8662 L s U u 65.5686 367.8405 m 34.5839 390.3542 L 22.7471 353.9286 L 46.4184 353.9279 L 65.5689 367.8411 L 65.5686 367.8405 L s U u 84.7177 308.9012 m 115.7044 331.4135 L 84.7182 353.9268 L 77.4031 331.4137 L 84.7181 308.9008 L 84.7177 308.9012 L s U u 84.7197 353.9272 m 115.7044 331.4135 L 127.5412 367.8391 L 103.8699 367.8398 L 84.7194 353.9266 L 84.7197 353.9272 L s U u 46.4183 353.9272 m 84.7197 353.9272 L 72.8838 390.3536 L 65.5686 367.8405 L 46.4178 353.9271 L 46.4183 353.9272 L s U u 111.1856 390.3527 m 72.8849 390.3538 L 84.7197 353.9272 L 103.8706 367.8406 L 111.1855 390.3533 L 111.1856 390.3527 L s U u 84.7197 353.9272 m 46.4189 353.9283 L 58.2537 317.5017 L 77.4046 331.4151 L 84.7196 353.9278 L 84.7197 353.9272 L s U u 103.8685 294.9884 m 65.5678 294.9895 L 77.4046 331.4151 L 84.7189 308.9021 L 103.8691 294.9883 L 103.8685 294.9884 L s U U u s U U u u u 1 w 127.5397 367.8398 m 115.7026 331.4149 L 154.0028 331.4132 L 146.6889 353.926 L 127.5391 367.8399 L 127.5397 367.8398 L s U u 103.8682 367.8407 m 134.8548 390.3523 L 146.6889 353.926 L 127.5388 367.8401 L 103.8677 367.8404 L 103.8682 367.8407 L s U u 158.5257 390.3513 m 196.8266 390.3507 L 184.9913 426.7769 L 177.676 404.2642 L 158.5251 390.3512 L 158.5257 390.3513 L s U u 134.8548 390.3523 m 146.6889 353.926 L 177.6755 376.4375 L 158.5253 390.3517 L 134.8543 390.352 L 134.8548 390.3523 L s U u 177.6759 404.2634 m 146.692 426.7772 L 134.8548 390.3523 L 158.5257 390.3513 L 177.6762 404.264 L 177.6759 404.2634 L s U U u s U U u u u 1 w 77.4019 258.5626 m 65.5666 294.989 L 103.8672 294.9884 L 84.7166 281.0748 L 77.402 258.562 L 77.4019 258.5626 L s U u 134.8538 272.4756 m 146.6877 236.0498 L 177.6739 258.561 L 158.524 272.475 L 134.8533 272.4753 L 134.8538 272.4756 L s U u 154.0052 331.4132 m 115.7046 331.4138 L 127.5398 294.9875 L 146.6905 308.9011 L 154.0051 331.4139 L 154.0052 331.4132 L s U u 127.5384 294.9881 m 115.7046 331.4138 L 84.7184 308.9027 L 103.8683 294.9887 L 127.539 294.9883 L 127.5384 294.9881 L s U u 158.5245 272.4755 m 127.5384 294.9881 L 115.7032 258.5619 L 134.8538 272.4756 L 158.525 272.4752 L 158.5245 272.4755 L s U u 84.7173 281.0756 m 115.7022 258.5624 L 127.5384 294.9881 L 103.8672 294.9884 L 84.717 281.0751 L 84.7173 281.0756 L s U u 127.5384 294.9881 m 158.5234 272.4749 L 170.3596 308.9005 L 146.6884 308.9009 L 127.5382 294.9875 L 127.5384 294.9881 L s U u 146.6896 353.9252 m 177.6745 331.4121 L 146.6884 308.9009 L 154.0037 331.4133 L 146.6892 353.9256 L 146.6896 353.9252 L s U U u s U U u u u 1 w 77.4017 213.5386 m 84.7163 191.0258 L S U u 108.388 236.0515 m 146.6877 236.0498 L 134.8538 272.4755 L 115.7032 258.5628 L 108.3881 236.0509 L 108.388 236.0515 L s U u 58.2536 272.4783 m 46.4173 236.0527 L 84.7179 236.0521 L 77.4033 258.565 L 58.2529 272.4785 L 58.2536 272.4783 L s U u 84.7169 236.051 m 46.4173 236.0527 L 58.2512 199.6269 L 77.4017 213.5397 L 84.7168 236.0516 L 84.7169 236.051 L s U u 115.7028 258.5634 m 84.7169 236.051 L 115.7027 213.5386 L 108.388 236.0515 L 115.7033 258.5638 L 115.7028 258.5634 L s U u 84.7157 191.0267 m 115.7019 213.5378 L 84.7169 236.051 L 77.4017 213.5386 L 84.7162 191.0263 L 84.7157 191.0267 L s U u 84.7169 236.051 m 115.7031 258.5622 L 84.7181 281.0753 L 77.4029 258.5629 L 84.7174 236.0506 L 84.7169 236.051 L s U u 34.5829 272.4776 m 65.569 294.9887 L 77.4029 258.5629 L 58.253 272.4769 L 34.5823 272.4772 L 34.5829 272.4776 L s U U u S U U u u u 1 w 34.5837 317.4952 m 65.5698 294.9819 L 34.5832 272.4696 L 41.8983 294.9827 L 34.5832 317.4956 L 34.5837 317.4952 L s U u 15.4303 213.5302 m 46.417 236.0425 L 15.4308 258.5558 L 8.1157 236.0427 L 15.4307 213.5298 L 15.4303 213.5302 L s U u 15.4323 258.5561 m 46.417 236.0425 L 58.2538 272.468 L 34.5825 272.4687 L 15.432 258.5556 L 15.4323 258.5561 L s U u -22.8691 258.5561 m 15.4323 258.5561 L 3.5963 294.9826 L -3.7188 272.4695 L -22.8697 258.5561 L -22.8691 258.5561 L s U u 41.8982 294.9817 m 3.5975 294.9828 L 15.4323 258.5561 L 34.5832 272.4696 L 41.8981 294.9822 L 41.8982 294.9817 L s U u 15.4323 258.5561 m -22.8685 258.5573 L -11.0337 222.1306 L 8.1172 236.0441 L 15.4322 258.5567 L 15.4323 258.5561 L s U u 34.5811 199.6174 m -3.7196 199.6185 L 8.1172 236.0441 L 15.4315 213.5311 L 34.5817 199.6173 L 34.5811 199.6174 L s U U u s U U u u u 1 w -3.7193 317.4988 m -34.7058 294.9879 L -3.7211 272.4744 L 3.5944 294.9867 L -3.7198 317.4992 L -3.7193 317.4988 L s U u -22.8695 331.4133 m 15.4312 331.4122 L 3.5944 294.9867 L -3.7199 317.4996 L -22.8701 331.4134 L -22.8695 331.4133 L s U u 34.5809 317.498 m 65.5667 294.985 L 77.4025 331.4111 L 58.2516 317.4977 L 34.5804 317.4983 L 34.5809 317.498 L s U u 15.4312 331.4122 m 3.5944 294.9867 L 41.8952 294.9856 L 34.5808 317.4986 L 15.4306 331.4123 L 15.4312 331.4122 L s U u 58.2511 317.4971 m 46.4177 353.9231 L 15.4312 331.4122 L 34.5809 317.498 L 58.2517 317.4974 L 58.2511 317.4971 L s U U u s U U u u u 1 w 3.5987 367.8332 m 15.4341 331.4065 L -22.867 331.4071 L -3.7161 345.3209 L 3.5985 367.8338 L 3.5987 367.8332 L s U U u S U U u u u 1 w 58.2529 199.6267 m 46.4195 236.0527 L 15.433 213.5419 L 34.5827 199.6276 L 58.2535 199.627 L 58.2529 199.6267 L s U u 34.5827 199.6276 m 58.2539 199.627 L 77.4044 213.5401 L 77.4042 213.5396 L S U u 34.5827 199.6276 m S U U u S U U U u u u u u 1 w 34.5812 463.2072 m 65.5678 485.7195 L 77.4026 449.2929 L 58.252 463.207 L 34.5807 463.2069 L 34.5812 463.2072 L s U u 65.5666 412.8658 m 34.5801 390.355 L 65.5648 367.8414 L 72.8804 390.3537 L 65.5662 412.8662 L 65.5666 412.8658 L s U u 127.5383 412.8641 m 115.7035 449.2907 L 84.7168 426.7784 L 103.8674 412.8643 L 127.5388 412.8643 L 127.5383 412.8641 L s U u 84.717 426.7799 m 115.7035 449.2907 L 84.7188 471.8044 L 77.4032 449.292 L 84.7174 426.7795 L 84.717 426.7799 L s U u 72.881 390.3534 m 84.717 426.7799 L 46.416 426.7799 L 65.5666 412.8658 L 72.8809 390.3528 L 72.881 390.3534 L s U u 58.253 463.2066 m 46.4162 426.781 L 84.717 426.7799 L 77.4026 449.2929 L 58.2524 463.2067 L 58.253 463.2066 L s U u 84.717 426.7799 m 72.8802 390.3543 L 111.1809 390.3532 L 103.8666 412.8662 L 84.7164 426.78 L 84.717 426.7799 L s U u 146.6881 426.7781 m 134.8513 390.3525 L 103.8666 412.8662 L 127.5378 412.8655 L 146.6883 426.7786 L 146.6881 426.7781 L s U U u s U U u u u 1 w 189.5108 485.7145 m 177.6749 449.2882 L 146.6893 471.8011 L 170.3608 471.8011 L 189.511 485.715 L 189.5108 485.7145 L s U u 134.8531 508.2279 m 146.6898 544.653 L 108.3896 544.6541 L 115.7038 522.1414 L 134.8537 508.2279 L 134.8531 508.2279 L s U u 84.7166 471.803 m 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