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88c2565897fb3f3cf8cb71051b7157a6ad41979f61444717d420da558616abda 6874b3e9f75f7eba48b9fc90d48053fda59f5048e1a17806b5e1bf3244954c19 dc2eeff9a8955d81b3a71078a3b858707a1aa9fa10f8b563959f2308ee9713f8 3215408f46513898ad1292c9c3d04f96c718f30786bc1869737ed8cc3ed6db8d 8f86f5a50e30c425038b35e9df199d05bb22fef54b961e9e2a8e0b0ff5375648 237df92942aa43762c75a50b1d56492deabc7d13b0d4875ab96c4b4d58b42aa8 ce8506378f7f3b2078005ff4b0631cd56802a6653dbfb5d00e9497249b0766c5 572dc723d6a220160b6b1a9a2450c521b14863744c66aa993f2f11492fd714d6 a82971298794fdc0dcab6008277db0ee66508b7a5f24ab8615d40b8becfe0220 b19bb923c430b69b3d84c96976dcd594d70838dad6b0a9a501fd0e89fa9b91d1 c16606f2723d88125197ce5164f153bd87f06cd85e04d681c1f577b78b345b2c 72de6d68f5968f1ad8eae7 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 110 /n 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 84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2 b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc 55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7 8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316 ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325 e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd45416d f3459365434123a76ccf883a4973bab19807e1f0c4bab03a45f7ed69ff2660ff 3963e4def11001eec4238c368a39d874fd30b3c14f4186ec7700fbce22abe468 eb32baf7b0164f8f21a9b5e706b91411faaa44467cb2180ab03de375c1ab93e9 76e11ab92fdd4a7280a6d1a8dc65c4c89d04c8ed6988045a2a3de9a4c7b1efd3 75b79ee3d49569213fcb818f6f1cf250f5e595c4b2ce78148497f5323c48692f 54f30fc48142c886c22b5da3373585156267c6f5b4072348a72b5b868dc7da64 b15554e348e7a712389c1a17a64dc7a8953d6f023ea3171a7dbdbb71e23d6048 893d76686c6bf567058e02bb2b5b28b46ffb96cd76f61d79d11e59662b305ee8 fe6dda348cce7cbbc161a192ced2759fad12e42972d5c410f004fe73373a3284 36e506f3d79938a71dccf4003b0ffe7f26127bd6e34641aa4f67f13e7a57bfbe afec952f32d00a378cbfeddd288517c3f94d4ead346ff17362b4627ff5d6ed8e cb464adced528abc737f60757126141d8bbfff88b34903f63859a31fec7cd0aa 8c7c2faf82dfa6a0f244113c19a69e4048b5841e56fe2b598cfb74cbaf068b0d 419d3fc96bf6432034b0116b56751d560596a0fc49f11d3bec72a72e79a78826 561018f0c18cf917d435766e819608fa07dc31aec59875feb076d6658170c09a a789b6e755ee6f373620cb8677bb48c9db725746983bf71fdffb0149828e0dfd 77 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: LINE10 %!PS-AdobeFont-1.1: LINE10 1.00 %%CreationDate: 1992 Oct 23 20:22:05 % 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 (LINE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LINE10 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 24 /a24 put dup 27 /a27 put dup 45 /a45 put dup 58 /a58 put readonly def /FontBBox{-150 -150 1020 1020}readonly def /UniqueXX 5011940 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d75c99a46517d00d55f57d7d06eae02 ce42bc6f02479dd2b017bee2b4b2093511b992b19e8e014150ad177269b3adf0 23af9203c2683b5609d89e5aa47fe696911727fcf0abc3e1dfc253326900dd94 846b641ebfba6b841c0cd25c4007ed9c66cc327c6abaf2f0383b50af8cf8ed88 2862a220211a24d4b3dd653090fe7fac59306b7135abb21d197f619eced07cbd 4d124b4312e6473000e14bb6c54247a1f7f994aa26ebf9caf9d5716ac43905f5 b94fca61ce218c06224b3ec1acdd20bd9c8327753e2ca1e695c68eccf4e111dd 3934185e507dcb0a6437c282d50b4bb6a31395c0cb4045eca17f8d8b1ab660f2 7b2b5ab0905667ae7c16c3e708a1f648dea18a27d00c0983381266645de25ecd 98644decfaf2dd16f582ade8140a1ac7a45e5013d7bd740370d25dd5c5976bce 6e4923c284c9c25b69f6b8a623cbf8414f4195cf8caf2dc1e744ec0d5c074534 c726d4f52e2d4d977b2771b51c778fbfec37dab729199fb6429be2b3290829c4 e99ecc0a0d0b2ff51d4ecaba6c404bba73068ddfe292c2afb6c1bbef138d32fd d3d7149c12808919798cc06e9d2aea273930ad09596f6356651c02e493590c5d 8764970c475e0c9b1b01b1a033a63bda9da68e386365dcb5f41ba24de0b7bae8 5c472b8ecb947c7c24fe4b91e55b37745cfc098059466df03f6ff06c84a67ec7 585856d6d084b4d59eb4841ba5bbc81c03a3d2c4925127207125a3b703a2546a 45623f45738bbcce796a0d23ef110ace8de25bfcbf7c85b380840909f82f494a 32c2bbcad3e17315e1b939a58aa8ba020d47575de5bf75a7b540b19ee3fbd787 4a9451346e148cbf9e134460f977b140d9e1da3080d213bca6fea156640152c0 930e471d873355ed27610737cb42966ea1061f27d2da45fa860c3d975c8f6234 206587991f29dc2910066935cd33926ec02902b1e0a1536eb15434ae05c680f3 1dadd8ed5d203224105b6d1cc732e53ddb6a046ab43cf1b625a7ee4baa40e5a1 cbf83782feb8628e9034ec76a3f07b67617e24c7336d98598ed7c8ac33fccf47 704939a11e7fad08dbd3467f61704f34f08829097006c7af1eefcd139d423e14 46aeecad0e1c629b6246ae6b598e10ff00bd3ebd34df85f907dbaffd89b7dbc6 2b050985ab52fcc4f791d501ccd5438f43e3ee9c0bc3ab38e6b55b19dc32df3b e3d833b1bde678d018d842b60bd239c145f8447636278988f63180a5ff6d8168 fd8d744dff4d53e9e9539c3c274263d8c343d8c51752521e52a2aa156b277345 7a71dfa41ea9169eb811e4e3b6a0dc188486999b07025f83785b0789586d0fc6 27c8d8ac3dfcfae50e9eb9a8fb292b14c2457019a06c4ad64b98b3a307d0fdfa 00aca3dcdc696c732ffae052e29665e819b885ed0690ed76c040d5f227cd4c08 5483f030cdc034dafd84fb01388ca168334095bbab6675e198e8f0aa45e8f9be cf7d2eaab38aa33a7241a6634f935ff19fa467b81e41c7a5dbc9a9f0b9dfbcb4 a3c942e80428369ab4d91c6cf4716d297d6094eab9994f98ed3dcc7d3952e482 48 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 49 /one put dup 50 /two put dup 51 /three put dup 52 /four 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 87f907572b8354a5c3165eea7e8b2ba4e15b8cf59f19f384a2b127700dfe72b8 411f4d84943c80435f0a92346002b0730dd79cf579e431431c3c81b051c44591 232a971a09394620296b2ab3924d7e55b37866ae5d870fefe6720ed44d115e1a 93a4801b7747bb654df8541370a37d0f0765239adb5d3e0343a2c8107d5c67d0 cbd21cd3a62bcbe03887cec69cbe43a2f6353e9aa653ffdedcab3f2e98d7effc d47739501cca1b3fc8797192df8dbf1f65ae6f74d79625794879736b346e2187 d4ef95df8c15a807fcfb98cf195745171169d8669c51b69353a865295ae53617 fe751a5da4a5bb80e02106a25747e98aaa8a8a222a1f714bf914d833ffbe81a4 254c7133d22eac4042fe662ffca41c229153ebd7d1040e98a7769a88c7b59f16 e1c8aba377bc25d54e4ba7be43cb8103ece5c475d5371afda7561306b0ee5fc9 91943e6f4a7361887ee691713b6e9ad0963d2b8954cb71ed3b3e37bb220bcc49 ce0207f9b5c69caebe33140d00777320f3d43a5745c9e79fb8043e38ec48b174 c2e897748571596c69e4b67967c2930fbdaabf254f7781dfa43de92e47528e66 7395ab75aaa6aca8160d04786151fbe2bf7788220e6becff36ce8dc03ea5b42e 42d4e0e8cf5d65d1dfe37ef3410498732cc5ff58ae85b9dd7372998d19c5afd2 7d1ed9c5fb6ce7baca1af7e14127472aad001a6481495e317b04aebd676e36fd 8e505eaa56bd1fb991c67ed2f06c02d836a341442aea6b6ad99a688bb3156da0 9262bbd40d3bcf778717413c427ebfe128aef51e68b10b9b815f1dbecbdde6ec e0ccd08716f330a685877a297e37d2b80c18f2a1b3a1b9ad85134939920758b5 ae2e5e99e2adc455ed54b6b3a0c082e8ab653050e62104d59a58e9425e5e2723 100a0d5f59dd2276a1768292b00397531bafcb69b30d3cba894b4e5a248d7e88 c9d597043b4e9d9a37bf7c40912f2ba2226881f960d4944ea676720abd89d96f 23ab486e93922d12f2d460c8e31a95f174c17c4e340bae7f12af1daf96342828 afa1b7583c614a91d39e7cc872a70539291bf427602d9e40e43b51d9d41f595d 7bf267e941f582532d8f99ba3a442f7a58a9100d15fffb5f717961423daa761d cc439b31c6a31b39cfbf97b6168a56cb09993119223d390385c953ab1cf05caf 50fe48f3ed4b165fb315eb12005ed6cab1064d4e0fb8c5fcd936da5bdd3051ea 1e2602d852e4544d80cdce2796845d18acdf1aae326d0e05ba88cf08c8d009a3 93036354a656e991764c30d2dc6811ce6b5f47889644560ef13a6bca7a5dd37e fba16c9fea6a7dde8269006437780956d54ef45e8f96db4e4369aca8d400aed3 4584a5a59df91356fd3e74b2b42872ee0a26c5a3d4930a57e719798cc067ed85 f205680360e4242ddcdf606f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 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 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 18 /theta put dup 23 /nu put dup 25 /pi put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 69 /E put dup 72 /H put dup 73 /I put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 85 /U put dup 87 /W put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g 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 113 /q put dup 116 /t put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueXX 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 3c3346a1093e6b1036902c1bf42fc317c80abf04020a47b344c36de42f05c490 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 51 /three put dup 52 /four put dup 71 /G put dup 97 /a put dup 101 /e put dup 110 /n put dup 116 /t put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueXX 5000772 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3037a112066957 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094a5f9559023c9671b432de8ce26dea7d2df616c389b5b604ebe4b1f38e4e2b 8e6b79553f7817a000cdc8801e5cb4528888d30e36e69b3f43335222507c7025 42fc863e51f676506fbb896d091c0a67012884cd0dc5cbd9713871d4750cc1aa 409a21436b69fbd72947661b0f1c7c33109ab985b6151dfb352427ab49caef5f e8d49329284e85967594819fed373f43b0a5ed6d9001f242873ff1770e31230b 503e9f944e414a0c770834bb2f6909a73310ef85aeec193445f9adfe6f2b4886 bbcbb7c09b0c92ab9141d80bb5686335c21d620ae7fd29c841fa591e17712ccd b89b993a3c67d3578ba06000a9811e2da46a0cae91f133066981f8ea89ddfde1 c58fc53914e14e59771ef31801570baaf47ef0b33a09dc0b4478b8ab21da1ec5 206d4755cfbd3ba63324baa32476745d675daad37f3ab28bd6cf99fec4b3ec5f 994eb436ac4d302a7240da54e3c732f532c2cff1561d9d618480591bddc25106 85ec864f760b6c16c6604ecdd03f197385c07c480c4f20ca0f015bd3f5bb661b e4da79472349968de3031a5e247d5a0e942842d76166b13127754694b38d8a4f f354e6fcfd5fd416478a7a56366f6c110ba25045b0349234bc7209ceac5b7636 eecc9cf4061af05166ba9f9d0ab0bcba0e93172460848136544d9f6c66f61e95 0fac6fce084a8d668e5512db2d42f6c0bb9468f43b3ead2dc3a243211357277f 41986401cfc0896fc5d663aaced5bf90b127960d235a7fa051ed9f6d3347d5e5 1275731662cad3e461a9929aa3880c3988c811549e4794d3f23e7efc06a4601a 25515d31c0073a6b3eeb638f8ecdfd772c841884e27a9e074e5af121b95c8a46 7f4b1da9369f0768cdd7f4a07b51fe0f5050cebe49ed5cb538239f0eb10d7cf6 0d6355d1bb93bbfe7f821e4a789efc5b4cca822ffbe9ba25622019f1d8110de2 215134572f978d2c3131dbf928e5a622c73ff8d6548d8157e9ff8142f434d64c 7fa783a7668d098d25a2a07c187408320d9a03ac518d916342707dea3cebbcec 827c0985b71020f0f5cb9b67ea8583bbb1cb1ed92f9b9c6ee5e0bac254453f57 d781efc6050a7e87425f502e634dcf61340bd704033f7bae638cdea18459f533 0c3ea26825922a64cdf58124f51dfa95cbcfbe4ce1e4d387e19c8d686a06911b 80ea2ac10e9ae6a58d682c55d52aba9212cfb749bd4e616d2a67e893921a9661 7dff4dfdad91fe3756a79fdd55155ad86294f26d76c6c2952a33c1f987acd084 fdb901bcdc74f053762cb7ee916162c79d88af99a695a5d3d55ce7e79632db3e 6572a360e69c643529a00ee5e88c132287eda25c42a34b25a3a1a7cb3dab6292 9d199a9a782f0e6aa3c4501ec3f982ef83326850a84a61733038ac138a665bd3 e47c077d949f9d837ae07f9eaab91792b5e692faf9327451de12415986615fcf aac987f232ab978d32250c3e640ebdc363017bb072d5efc5fe2d03a650483a47 7b3a10e64058c0c492c260b2147f093d144ebb7284e56a38f679f4b4629521d6 7816c24ce3b6ba5286a1e5cfe0b39a8747dccefc7cbe25534ac3befbc9aa658f e74b91623992e4c5086d1fa54c30ad401133d2e99e338cf819122d9ec5155ceb da4e4364d6f8a31a85406982d42fb5aa93e85afb13e814f6a0cc117366185867 4ac8c1d0be5c5eca911c47910b73cbaacbdceb9ee044111ef24324ba87178b61 7e919ed7c6e3e9a195f84ade27f2f99c31e120cc5351f5947e1cba443126175c 060829b7a58207f040c84686e965209db2c3457dfa12bb937b29be46ff8fa943 ee89287785c8a68aef1618d5d8060a6616813ed6e6de8e4beda620f7931f7289 e1a372ebe5ec11c28d8ffcbd1c74f169e15e0a185da072ceb5b5641a1dba1d81 f991a78deab7dd7f0f4b9f0a13001fbe022b17a7d1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 28 /arrowparrleftright put dup 62 /greaterorequalslant put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa4f3118e6b59bd7a2c35420557fc465c b2c85252268f045892b701e8055efad14768ef1151af1c425c94965124aff763 8101cefddab9b4757811116e4e0afa423adc2ef80d89b0338421554a2e4d8dec b1a295b6aeeafec51e83098d8c7d623c04e668d8496e1bf1e1319673f03f3201 c4d6c96025f343831894d9b7d5f9918d9f5941399627ae3109787555e2240e0b 4a56b5c6d98fc93eaaa7b41a67be7c80422344692922b17917a63b02bcbfae4a 5ceb83e59f5de7eed3cf517d0eea86e8546c0f7e16aa5ea21defa716e83954c7 e1cef78e3cd6f7be1909e29e5c04fe2a04dfe315a9d9a57782ca5a292b61f5b4 923d9c063df7472c3d3fcf54803cb1ea70c5b4be7b83b20517b70493cf5edd8a 76ef9009f25cf7e7a4cf886599d7873e5b09b027409afc4719955fbe61d3719f d152363bf06effac575666f718f98fc93087b4fe2c9074916cb06a506c7b3107 7612bbb3d64ca9074fb63f2ae579c887ef46eb95ed3b9cea95a64e782e9d6804 573657b01ed1a90dd0857bd2df9c9c8b5db93c733ee43cd38154c263c48059dc 0c8a63ad84d6de4681feb40fe21b30ba776b023d61ad450f5c1692a767b39cbc 0f150ad12e759891b41d10a263ff985ba399d18f2a53dd64aaca63044d6e2217 04a54e115f75fba78ee522e55e93e4 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 49 /one put dup 50 /two 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523de97a57cbed59a39 c235a135d115ebd4abbd5c9600b26694d650c64477d24d3e668cf2f77c682069 8a49e801bc835101d0380ff234ffc28ff2f6fe6f1ad59d35142a82e252b03506 4eefbe506595eee4c52ed8c9e252fe3a9894b250b5a8765bd0a3ccec511fc398 f294b9ef281f87d76802eced7414297358d29f12e1d246c0f39f9ec4536c3f4f 0549474956b5667672941778cd589fde416abb9915c030ac96e1b70221c9b072 04f75663bcb1dc96dbafd3ddde72bd6af74b96324b707d58c89ca136d07c38f1 bd08201d21d46b9067a4c1ec2857c203487a9237cfbf1dbef5af4c59fc1e726d f49161e746feae8bab48ec220e62fc4437ae29ddff8582dfeb1afa3531a3f86a 22606ab4a62e2107e4569716d1b12297b276035d91ee77babb02b1a5a9428528 b13475a731a58f734f2640f57946f21fd852f775db7637444b84f2dcf1a530e5 964667948960b901dcee0d45e7fbe71331faf54efa7462dd3d6c0e88334556a5 b1418fab410355d9856668d76d6943ca25da0ea62be33599f490997674a9eb45 5f94c730ca6580cdc3a7bd5f362d0ecffecb99b24d7301bca4a0fe45 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueXX 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e28519671e8def84a1526a8b89450ef2bd624857da91e7a4a832f89e4f9cc 36f6027a64831992e98b1707ddc56e562de9ad0278d89f3416dfab55ea0e5b25 9cfdc4787442890a5a8986bd394cfd87942f66b3712745aa18e52c6bd1d44d48 3f75ca3a5d39391f2bb9441314fbb25ed2b6813e66bbdec80f12a88c2f94f601 fdb6b48613c26c3ac738dcd4ab05a16c34aac07eb789901b095230281fc71f04 5ac83d60c6b82255c6276398134634a8135902a31a52e84b55aece4be46e9d93 72e8c2738a3ae29ce61298d5c2e792bc098a143f3f08614489 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 106 /j put dup 107 /k put dup 110 /n put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f bcea9907a04cf93c12727ec40db3f2f77596dca477862747435bdedacd9b2311 6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a 84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711 de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e 93971def6fc0aed1bcd3e15825f528f4afa81d6438300c6fe46e2dd64d12aff2 a02cee37df0964a05519a52f4b6ea9e715790a595017d3ad2ac42d6795cbb8d7 924c74cc1ebb2b1a427f522035e8146f451fbac602f1aba0597334f53c359e1a 63b7f1a43b87a79e9ef138b5c13ca3dd521b86cd6c30ab50fde190f2135de5cb af7bc320e67f43c7bd685f1f063cf06f1120bfc404c8666a1d4c85a40476bd4b cdee143e7e4248ee4a0f1e72e2184215c8ffb7a349520ef48e99d37cd52231a8 a38ea66a16eb8e4f5f7e8b7721be5bb64b708540613206a1e11df62b355bfbcb d78bc3ae7feed11b7d0b06776b9ab30384e4b9199fc55cb3b979ca2390efcf14 5cfab320dc4f159a172d160cc91674d7cbd368ff4b99c0c1c965c75bb4d046da d3816a9acd530eebb65e441b80dad62239255bac86248bcbb4ec875952e232c6 fd8b018958c479152c353ab9a46cba5b4427e3114e6796cb904fd8151056cbfc 08e7a10b29119540e08457857c8734460e069f2053776a4c49006f2286afd11e d7f5bb9240c8e7ea0a73c4942cb0d736e0ddb4dca9bbe3ad7ea8839da861ab9b 8798e25f2b9887031f73e83836b48c8b7add5b1a7778a8b4e2b1483ba972895a 2dab9cbd14fefba93cba0982a5989b0e523985a0f7647fec9f3dcfe69e6094a9 8f29ac8b57869c3b7ce218cabad3c95160b738d675601fe035a0cbc370b8e26a 01efcb7d360ef67aa3e284441e698c6fecdf6e92f28cd1b78fb3cce7f18fe8d8 ba648973ee40b181289096db35a7b53d97a929154394b7011c3bf23fd6229ecd 6fb2f1d29afb1764526a674c1266ede8de37f8ea41a08dc2581baf369b1bdd64 c03fa750fc6cb69e86f167c7fd745933a001faef768a82f4d4d54c8fdeb2e11d b208a071dbb9deb368820d33b85736e67351c88216536568c06208fdc3efab9c a04cfc23857e02533b8527972c65c88756d0d4c52f2c8e9fd5cfd1a4332eec55 e243c6200c3978ffc8f53d1e3954920070775c05409bbfb96aae65f815f17e9f df6f9662d742fe5458c6d12c0f0a871fe2c00ca95ebd25ec5f603c0349d3cb18 f9cd4542c4bb85583c47451535ca126022fb92800cb4c0e5d88eb20b369aa6e1 5b65138b16838444fa183418ee0acd65595205f3e4208f372b756fec07b3cd3e 980af97239f03598db9ffee0f1e81bc3f8196fd1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % 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 (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 26 /rho put dup 28 /tau put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueXX 5087392 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d78041490e364babe4b85935b8c9c7758c2dbe253653c 892b1fc2c6a01103e0b8553f847bb38d8e4fcd563ebe51cb7d5f0877af29249d b61636618fb31eeb6cbb4ea4db687fd77ed1574da8c9f9d33b592ec0e38d798c 498a205cab252f7e2f1ddb82a38f331f917b8452af11b2b93e34c1ef55ee005c e8418dbcd0fb9d4d3fa8cb388ec91f16c8864913ad3fc8960d3c424650bdd12c 4db4049367faae97c660f00021f712e9eb6366b7ce74255ff62b72396ca43287 7c77fecdc53883427c90c1c3ff7bd46e472cea9bd72eef0e1be36abb3a50a7bf 6f5d460fa2fc81466014df9ee1e15365642c2de78706dfa740e035b4f28f290d 79b8ba16e5bca13fd9c3eb7eb54006ac2c1cf0bf363b3b69e923797a95b76515 073892c75cf733da7c07da8ed1a8d1ded902f784764c6df6fcd0fd28083d88c8 4c41aeaa6c2c2c1bb10219f4feaab75ee904f4314fc0b9de5e96054f2472ad86 42140315385400686cb07a0585d922ae4b1b25ae722edc6b4afe053560fc9ac9 20a1d2fb8d0921c52c9468d34dba9bed42e3a8308742d36186ed0a3b43f690a4 dca6bb2af8bd698fb303fd68df53edc5e01912cf007dd31ca7481ce844be1258 7002d4aafb204a8075fc6df86f22249d61dd840e7ef87362d72e35f4e8ece044 95ae41ee5c02d6aafaad37141935867a8770fbd9e9e894ea6cc5cf3770f35d98 09be73c56fb053ebb622cd4a3826bc95c192bc2248e1a30e641799994debd48f c5a0ca09be0b2831672271e6a087154d1541899171bc12c8ae00dac586f5c0dc a9c8f4bc7910fe68531c2adf25f29002b74151ec41cfe904b25dc975f97ca163 59d6ea5787a3b0529b3a7a7f8b5b8606cf11dfa1029106881e531349e8317d6d 256ecbe471ffe359862eb09635446dda8dfb9f884b8377f6c24c63394b05e988 667a1290c15a457dc7d484a161ef35b538ad0f94e13caef2976260b04977d7e9 5598f218ceb2709c1200e0fdea4b0415bd0d0d0d815dc99a8636e4ae99b70d71 9e303e0b3bf17deb3ceb96d31ff60080c93ecd7e5fff6a336e45e3ef09421f9e 33de8f78ad6cfa4538e54a082c91458c0ec85924d234b8dda59681bfbb31a5ad a3a86217e1e4bc64b8a943c421c29c2c5631acde1735c58553cfa0b8a099e38b 0ef4c29a93a874fe5d4ff49cd34001e69e745f673cbae9c0475dc5b86e69d0b1 3c984de4a4d023c5fd71cc7beb8d37c25fd44d2c3d28c9c475938ef5a4b526d6 9afa56e2ec186a2a60dc899f2eb2d858665e7313158a57d08040188c4e8f47a8 33dccdaa34fc7b75a14331bc646fb53116f29e20b6baac56e95f88d6a8c98ed0 aa759590483a7f41ed6d5e3edfab80f60635d673a90faaf1309f086fb92d3d73 88529ec0984edd70303fe3cbbce010e5be6de87806323dba1eec1b462fb1716b fb3154848c774e44d69349e9435beaf1c82b28b8a5c28d25193de65b2edfe45e b43c4d81a1f75109e6e2e53db510f0038d3a40ee84241c98 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 45 /hyphen put dup 46 /period 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 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 73 /I put dup 76 /L put dup 77 /M put dup 82 /R put dup 83 /S put dup 84 /T 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 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 readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueXX 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea a29b69d1b622b1f0cffc58291248759607d91150cb0651120970dc9f743bebef 44f6ae92facec57658999c8bf01f60611560043962c0695e1bb87d090e0fdaab 659d6557208a660be9aeef8ae55f71b8bc76394d792967e41bd8023b6e7f8c3d 9987d5e54c53bf2bbb32855b946473b44833bd78873df8e4c7e668ffff25aabb 8da4148f744b9d0524d6cb8281247b3052cc5d66f3f1bcf8a56a3fb446ea587b d8be30257652cee035628aeddfd8283b5ad21b8b1480ad24d898970ac8a1e33e 543ce4e3c48f9ee621c5ce3e8ae930f890011b630866c988606068d9e92396eb f51bb3db204505fc3d09d4701ac703a14d92bbfe27bd7411b363a88e33a8e9a8 025ac31f21e73dc52b333b918d0b1270c54873a490222d041a66e0192612be6d 2c88958a8f70c10390146ee5091df020ab97675e8e6acf98b28b539cd0a20d24 a42f535ae44b8f5e9290b38fc6b02e1bbbdf1aca96558c2dd5afbec53f03ab51 fbce958ed4a65b17fbc03f9defd4aea4a15229f3c320876235f2d8b69bda5f48 03a2798790d35b394c63295997dd487bc603cdd10d18f3e3fcc7f17d2a6afc77 f1d7f6cf69d2a86b104b9d3b260e4a78716927a485ad8a650d610e68378f4514 3610b087981f0a0655090163dd2dd4d0030faf6a953896a9cb2cd033ec99b921 2305b4f3abda8ed56490ec5ae8e12fc42abba4b1dcdb68d2cff2a3526a453395 ebc2549aba1e63a27ad8f80d247c052ae774c5d3f92f881a4a1f782731fd0a84 9b7cea9cafb404d498105698b6ae9c1340f7830ad6b281434ecdc960efdc2bff d263e69e025e091054ad957815d225744704c5d49867794860fb81167e7ae7d8 198131d6bbdd4aeb2fd88fc00f9ce5f9b832e53c8022f5955a2338092b3545ee eeb9fdd9ca0ade12643691c6fcf38c5698950d18e12fe8d92c67033a1a0e135e 23223bab5e8fa1cab2953a126b931815946ddb3db5b5d35a6f68aa004fed2fee 11f2211a881f7c5d058e35ec6bba31dff5a40f0afbdb7ee1d0ae834a5a13475f fa1b42706bac90db4f6ee925ba2cbfc07e2c5e8244ba08f2dd359eeffd2c847c 41cfc6fb704a6f0b3967daaaef8a8efcc83b9cec5b8881b6ae5ca0afbc7ad6de 51042b1ea69ef54241256e4e31cb46ff162f549887e767ada8bcbfbe5709a295 1a8a7d3401e22cf146b1746ff67172b3649a3a0a1a884da9063392259d9e9cf2 2a56d8cfd07657dcc2fc78cd1e87bbaafc7f8a45c719bf1678253e5927bf47df dc9764954ad40dec6c47b1fad5086add5634298fe75775b44d2d6ba1eb06f80a e5755deb6699e3b1ba7739b3eef514581a2041d7cd05c83a529ca10f895a4a71 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3e3dc525cc93369004d701330423bd5bf2757f96c4bfa4d86b9f5f09ae895a9a 2b08b9a9bae9c6cfec8e90831d5a76acfda13c744ef967f5ae4b4ee18933f298 e63237e7970463421b42670cbfc60a603a8f556f889b43bbcaff4b4a3cef8b24 27b7498a3f8804ad5c8c9023e6f17a8504bf03e5f52e5444881cdc1245657466 26eb353453e23bbcec6fd960d8adf4c4edab9346a63eb47a105db77d385e7864 ddff0e86803b48d464640417f60fa93e2ee4553fa4436d 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 123 /kappa put dup 126 /planckover2pi1 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 be30812b1b98cebe66cfb9d98e4ea24e4c0d4d77ed282661248dddb6b5506928 91e6557b1f6238bca064ddb13b68d37ccc74ea8110f7e0bc4c4f903c8e43c772 eb210276cdb3b1df2815060a0d29c94fb764b5bf40377af52248d706e117de49 7b5426761f4d1431e38cf3f9e386d35f95636ec78db4fab1ce3cf70644582561 e1595ee6f32fe27c6a759857eef72f2d107b7c68594fea131dc16fc924756634 1be9a51c45a37e81d3692bc04e4ef6dccdfd8519baf7a014c74251c12c0edc03 b37158fcd4409ef066ec97ef1d5dd4a46c35854e965385e7412414795e7fe33c 80ec0e4eddd97b9166745b625fa8c9cd999bf044f34af040bf1993df711af6ce 8aa76ff01e1b43bd006ed1a138186386b721b61ae7bb6441af1e91d4f878da5b 7cb66bdcdf2bc98ffdede4c807a12b234fdba373d711402bca4d4db43fef6eec 4a82ba4197c5a930036e91dcccf1a587b7feb93c31cd6494d70f8686cbd0a866 594193ba921d8ba69d759022e73628f011f52e622cb13060729db1c56ce41486 640e983baf721d4c39a929d04bf855cb7c5ea1b6e5bee59cd9bef078de944eae 83786199708ce082cc85f384d6dba6c03272715527c8dd86a0349b886313cc87 5c71a2b970eaba2761153da553de99b2dc9cad25bbe03beae0c172c134e74d0d f160b6cc4b63dadb5556cdc815156ded2ef04d664868dacec13cd5eb27d16a69 70002fc4ad8a8ae2bea1a25ff9a91d51a9f079ae9373f2f43ef641b027bb1457 5f0420ccf291bdf6722f33e9de870eda7b7556623fe6e628550be64673498855 c21bed72b9e166df9890a07fac4fef737f766160dcfb663516c81b0016ceddf4 e9e6a11d7b84957d3b6fd62c6de51b0e76dbf188e6ebb08502d73b5ff98843c7 9221ade463a4ea79958493f40958d270e8c3d30fedad10a510134833a2dd4f0e de9f3c27d26b4575dfa41bab0df32088abdd03bc8dc8f36a115c8e9e6e5fdfd4 bc32ef92f8e60db82c386733da4e86a3d6d7b783070fb99df2198d5791fc5e24 5777b86e4d9225610091d8c157235406afd4d7723aa256e9c51012500f6ca572 673403c0bcec01298cff9423b0dc269297b0f87d786cb1f95915ddd74acb6737 8c056115786f4b8eb4e517e7fe3d9de55d352c9c8599a0ffed6a4c2dd6c84c7c ce33068001a5258fb4873f10c7038c12b03513acdb01caffd3d2 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 23 /nu put dup 28 /tau put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 105 /i put dup 106 /j put dup 107 /k put dup 110 /n put dup 111 /o put dup 114 /r put dup 116 /t put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31 aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638 12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c 366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6 472e98856850b4538383e2bbafd08cbc620aa262fd8cee9f0727845c6313bb79 0cb57cd3cbab270b030bd7f643ee644b01279f75e809ffea5a60f3636b311145 fe6d31b0dfd931218174f08cb884a188cba4e7c570674424e2b4f7593f7251c3 5b8b10350758d9f3e7b1ea76b196e3dda3a5fa204aca9ed5b95ecc38dfbf2e76 996a1a6411fd322e3c3ba5ba395526c1a0a385420e3cd3fea8fa1758f8ddf539 2dcbae76816377231d5af956f56eeccb49f081129dedd64fd2b3aaa32d5d1049 c1b8dd4ce18b2d88d0093ef02b39169f7123b922217fd43e5618db76a062fee5 d3fd8153fba8e166830a7b3824618e320ae2e53df4a9df97f453386ba9f4bbe8 f4591e4b9ea9de69f7ca154dc693150c02373751ddec1be223deae31adf06b08 6f775a97e3d335729017d3af56b89ebe42092ebd9c33a98f5ada3c27441e3a67 4fd8cfc540305a501d82d4a598b7e78d9e3c035bf0550d4c60ebd384a4123d3d fd73787bf56a2a58e3f42e2d20420c6313072949229da6cecd476653e7f96228 06ec89f7495cfe6c2b83adb1dbdf859e03d88ec7c02e3dbf0b9dc800906611e3 2808072d78a582f3c5a8bdeb2ab1ee96788ebb55f4b02cf406032bbfefa27b21 de45dbe20e033c9deb3c5a714b87a93ae87cc68c3e0d42bc6e4a75d5b478499d 608ad3d41aecdf800d59fd97a8946a3e28b3d94b9b4188bb1a07ba1426efaec6 bcd6c1f014cd5abf617d6e701a57b31e8562ef41dc099733a32b758141e94377 eca93a880036c4392ac7470a4a4eeadde096637b966b96dea1b24f6d6931612c a4e18a782f3a9cd6d9f0f88b2c1e443112b48b5cada9528f9d0d452f1970e7a9 e751df927fab238db0d5025409f705b18f0ff5610e55d404d01c632e3f96acf9 60c22306bb28ef3cb6a7dd9338289cbea1a1fc29bea3d501ee299ab1c601d0d7 0e614ed4f456c3e3d8229ce9b4bf5de123865893a6236b692e856fdfd525aaae 0ac55e08b4fca8c4e4c3b7bd3ea6fb7213d34171a36bb74e1700c73c52702837 c73e999ab3772ceff5b752327161eb0aff1bf535209446827812d2f9506eeaa6 abc45380d4fc377ca95d4d91f1ce4fececa50d10c63c4d506e814fd6e0d40847 99413ede619a62239455722dbe97717168c1a61738cc1591e68757e286028f03 09867ef250e6dce7208b849c88020a3d5aab8c1354677222ef7539c6e6e6477e d3231301327ce8381de13c30a907ab896b1db3454c92dfb07faeff94ce659ac2 6b8c63a2442d895be0e84f1207108f443445bebf1a68cba19241f94442c2931c 37a6b91c7ab9e7b78f01983fb1992b19a8def330866fe5904ea0a7e3db16f915 f717932eea7079f633532894c2a9d0e6830192d09c4a084db39fd8cd555735dc 938db52a900aa2bd8738b282def68a9a3055fe9f51a49ce89af9257af9118bf5 6eb89d392d526829fab92bff9b1592c1694ec8fca453958a5905e86b7ec2053f 35c045e4c9887fbec994315171510b8705b19d18b807c14c0e7a90391cd79857 272646d5fe0f1472f3486241596f838315dad3ae1b132b7a7b07fc3788ddfb1b badb81cd1704877943cb68ff8df54c78df721897186a0317b2265e7d09d40d9a 240498fe1e4a0148bf3974cb20e6af4034f225e0b864a08be2e2a0445ca0840e 10700180bc87abcdfffb194399e98e580fe9d0acd992780beef7bad3629dbd03 186eb51bc9bed780f8267d64d41d250a7443e28c3417282372d136e4c693190f 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 49 /infinity put dup 63 /perpendicular put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a0fd0ff582d7bf32eef7d0676dea7d3546c46d4eb62cc5f957c41086 7b839cc408660dec5f886c9f9a58ede1634780b7da0d8f10935518e756f1f21f 1e0e2534abe0ef6e0b849566e60b6487cf6710f0a76512c9378cb10c705a88ff 10bf1b4329bd9bb5978ececb15fde07c89c703f48e016526d84f14d559ceeed9 7180b3d624f013f79c7512e73af9846a8e6d2c5fe7b97b39e21af802250e4bc3 5a31451b09fbb3627a3a48113d2fd144d8e194cb7fff0554bc4adf47a6acf5a4 b78d0ebd72b08e83730786035a6101fcfd8f5c0afd20e79a1a27985cc70e535a 873f1c609ed2a4769e12a888740ddf5d65fec70b58a843ed3bb5ea18b1ded7f9 50caf2de411b3d6994ae6a4fbedc98c472b4e9387da5abc0d4c4ade478197116 e34bc2fc3f8b09e11fd4d47a1abddbef10103bf7e557d129c5c1219bc1df1885 ef3aadf12d397a8c27fe3f209aa24a83820d03aea6b1a1d9e549dd02159098f1 67ec7dc3b1d3290a40bd87c4d22366c7c4668628240aa47792c53dd24aaecc76 d391e2bcb749e8f27b0199b89b84c3033c77e545388a6369bae2c89fb8659a88 a7e0fa4146a14b60ea181b746972589abe734ec18c9ce6becae63e36811b62ff 6a0b69e9de13df7105c45b9742a1d654f891805d6f516335b3628b20a98a2873 8d1e24fea22cbca553c620e0bf2ba61cf66accd9eac100c17f7f5302a4a96717 a5f2a267fb3422cfd5e1646ca1c4b1c8d8c9fa52aa9193d89133979b0d6c75a6 905f7c01c144c23eb11d1d74bb257b140a9e7bb42b9f97f6e073e5cfe2f22d82 365dc1dbe334e90a88da87b0d12cf1595c69b90e15c4e1231dcca2a76efab70d 457505ad6e8383e0e128c9f3780aef35c07d34c31c9eeb3c745e4dd20a478f06 a834cbd5f575d487755e2fd86f1edb0e88ef5d2f7d57aa12f83f13d8bfcb12e6 5b72b77be1ca921496b284b6e53b65ac8394854296e157d8831252a6f80f52f6 fa98996e39 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e50f1040e0b79f4bd6 363db28ab690a45da1b6b3b7266446da08d1e9a5245a35aef973e3f48494f783 224244de14fabde13417ebf1956b06cf8cab943bb1192072c25095f82bbf91e3 d252e5ec09a2b7126587bee21ad890f1030bb39e74690e2c5184901b30b99e3e 810ccba1c36ed55c07e85351ef98155f3d299d3e963c58dcf340e08f0f85dc1b 130f2b52042209fa8e1e6377147b041596ded156fb4af2908630f65e8575d1f9 8ea8f9030ad977519be4bfafdf7378399b0a403f01dc2928fdaa2f771c760459 f4a72a0a2410e020e6e3a7719341585ab889fa5be3fa5d5872f7bb90c283ea04 19856c3f5ea11e1868634c54bef1263939e6e1d45fbf5c5448ff348d82a50048 a63c5595783d9aa3dc06e8c3e84dc45c6efb3b24e9caa86a6f7a74d9a50b09e7 99f274b00ab7a9fc9537c3c594d96c4021e712595b6f8a2a1cd3800ac30ca63f dbfa811d7ed09092ff6d2c419164b8b4460619c33bcb360fbf9e30db0515e0db ab5a8d396c66b284ba7e554eb021b7a79f35ff555af586caba0c3bc2d1ad2997 34961c7a9b5a37fc4b28cb814e44f694f647b072821875685ba923b444a1bc51 f266f65601075fdb32d1e01d1bcafb9d574283f78022e0f07b8e075e9748275f f91cc4b3109e729833a8f709d68713f8b1366104fda994fce09b2ab60170fe1a 5e50b061cf484e3dae3eb4baed23a64d0203de53565c6b0206968276723077d9 1c6289f0596ebbf69426ccb1c6154c74077212ab59f46e846179e7b9634ea973 7c36a7c57455533140662efb95a2173a5a0dd54a4bd23c612d0984e283ca98d6 66ed78bc5936c5579454962a7e051cef52b8f638af79a636bc9d6f4aeae864c6 46e81ec82b1068cd94cda6eb062649b81263dba56732937377b3fc33640d8fc1 e10c567fc2a293e866c5605b4812d75d4b2910f9fa5d38f91e34d69056e50be4 6a887c2100c60115ed43e67ffde939c59dfdf68a9e9824346c42018297e903af 087af454f9d67fe7c9480e2b6870840401b85a197d4f8af30cff3ae5a4849be2 5332dd8e8f7186406a129b657338bcfbc9adc3ee588209500dbe5e724cefe502 ff2208c88f47eb0217270f4888f4d0246ad79fac966d5c1cc437be910ca78146 0ab55471f1ea6152d6b6b1f9e590c9228b405ee23641589e8b965881c634427b 24f0e9cff429d8af44d105e1f4e0e6d2475aeeb5df4d08ff529919e467ebc0c6 3ce25caf11ba56ea08fb680638f93d3c02cbeb12be741ed1d0baa18374286e81 81e8c8ec5490b6d09fdaee7fad9966e4f9e12021b5e2a9aa97a35fab3dbd2a54 501e057fbcecb0d9444804a7a04284ed9c576372f05ae9f84c7c2357529bdb3e be2677ca9d0fd2b9b3b512f7292cd52a243a3aa0f0e0fe9e2321be33267de923 332252c4d98f06879afd77db33e980223a73e863e8735f63cce4d4db31a39056 f4994bf8e32842446662b182e444ea7d9cfd9dfc859be4d1553ca8938e1ee258 548d97ab98970b6b68b7abe835a051c7c71c68e0c66b32594b59b0b5d8f050e9 4f196505bd1ecaa6f5a1c1d9aaeb53c2bd92199276eb18d39fe376b5b2ce48f4 0cea3126b7550c234599557a627b130e569474e7d859c9885e10660ed5fb133b a7ee930fe7b8855629ebce30111abd96777eb420b42d3bfc059a4186bd5cfa0a b424a65b3d775f998d27a90ee14a6b12d654c3b23bb6f4143b0486da95210461 df27475413db61400647f3d5540464c6270f667aa4607dddf2726c8d5d025ebf f32e0e58e5863db9969ef713927b9dddb37db5821ffb5cd7021800b7b0a95bbb 28b4f0f96eb6f9915008dba41f92782a6aaff3ebde0d90ee76a4c90a3a154569 48a5840ed08d0b031b555f28e4510a705df81f06b74358b3317913109dede117 f67bbee5d7df0fa0b7986893ae3eba6f61a87434f195fa 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % 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 (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 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 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E 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 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 88 /X put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueXX 5000829 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36e555668d9578b338402f8c259f6813b0b71e6cbd95e19c20ced8495 2559e47577e612a4d94de3c1b4c6c41a6a3fa9e2313457242de74c7e4c0d722b 3e224d18baa726369542682e9459b951b2ac638494880c42be4e2175a3c067e5 945bfc1a05d3de8c3e8ab97f80ab6000e1f78fc258b85d3c84b038d7d0f5be85 0d43fe03e26cdfbb41c36d14cb552e8447ca678efea1d275e85503123a2263b1 4077587683de69a8f5a88d666172668411d0d0fed3e037ee468627207505dbb3 59cfdc5d7f526fca5416d741073284f5dd2471e09f5916f4bff1a90eea4d1283 7731f6a36e5ea695f4efc3bf5669b7f60ab606df5819149c0c8a4817f06dc172 0543467645daeffe4457293e0c0407c4ec7857558d0452de2ac773f141783edf 81b30215ae8d2d062aeb3cb69eb0d62bf04780997c9c027a22896f456b784378 7f2ccdd4804375321e7946d3d254521249a4d28a360f4d3163912a688c16e807 15d0440bd27bb78fcbc89bc28028aab2f594f8b641e45b9c599180b69663eef0 03465a2425aa4f8b29dade493002fb335b23eb145108ef3ab828755d3753ea8d f0683265497b1cb5cb484c13f7a4e003fa6ab3ed5e24fcc6125cee4e33936122 3cc907af3c64e5aaad882c356e673e6ca2509a71920e99549d8797e9af709e51 4ebefe61aa0478a60f3a2b7b3d47542fbd126303e31718e6b9c711d202dff7af eb7c19098c9e2a52aa57844eb07e1bfe9067dbe7d0bcd87c86f4ea099deb2373 edf149ab7955979e26ad415a5c29c1dfd02b5f0678dc863d3d6e537ad3b40da7 6529df395597aad7f22d53ed7e16573ce620e179f10fc8e66d1eef855b5427e2 9a7aee650c79f4ee340b1bcc4aef263bba31c829effbd9df68ce46b8fd90d280 0c6578962434e58b2a1c8ae85c4654718c99105befa5d23dad4fe1966b21f5f6 31929755011244a3849081a219b46d033c401902b78253bec6141a6ddb478579 4150eff18c3986bbd7e7f0830360b7656bba7289d51acfaf88a2b06f3fac8bdd 403104fb9335db5b4b2a433b5909af075a55ba0498187a9d21b3e6cec2acafbd 2f4d1515335df504d1ac6bde1744ab4768d0f15d1a245782a3475edf07a2a740 f6e8a35d90f3eb0b17377648475743c8749c7cd9c2eb0d2c7e291fd545663afa 3b4e8750576d9483006d4a2147c1c8eda6c1c432ccb0f69c2ee0b3962e1518e8 1bd0ebc7040ed985086fa8fa08267047626b0d6a6b9f3fc9539314d349392502 6e91a726065db6ecd4ed2cceb32ba3a86257e5ddfdd92223f533dcacd8edb96c 883473b6622da17abd93e6278318aff0b5f3f9921618832d0acd3b0af983e487 a2e32a6c79dc50e06187cb0a9c6d01067952a73b376cc2425f0ccedeff16545d f46166c504f6f8633abd6b72f45f2d783bb121ef398143451ac424a5d3dffd6e c6c7b0e261007d537c9f20dc55e7aa8b7b7256fa09d2b78e5cf5a33061712bd8 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CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 22 /macron put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /tilde put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 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b(of)e(the)h(macroscopic)h(mass)f(renormalisation.)43 b(T)-8 b(o)31 b(do)f(that)g(w)m(e)i(consider)g(the)257 5554 y(energy)g(loss)g(when)g(the)g(c)m(harge)f(crosses)i(the)e(in)m (tersection)i(b)s(et)m(w)m(een)g(the)f(second)g(and)1852 5848 y(1)p eop %%Page: 2 3 2 2 bop 257 265 a Fz(the)33 b(\014rst)g(media:)1488 458 y(\026)1472 483 y(\001)1553 432 y Fu(\(21\))1553 511 y Ft(?)1710 483 y Fz(=)28 b Fw(\016)t(W)1953 498 y Fu(21)2050 483 y Fz(+)22 b Fw(U)2214 498 y Fu(1)2254 483 y Fw(:)1090 b Fz(\(2\))257 702 y(It)36 b(is)h(w)m(ell)g(kno)m(wn)g(that)e Fw(\016)t(W)1334 717 y Fu(12)1434 702 y Fz(+)24 b Fw(\016)t(W)1673 717 y Fu(21)1781 702 y Fz(=)33 b(0)i([2,)h(4])g(and)g(in)g(the)g(X-ra)m (y)g(region)g Fw(U)3345 717 y Fu(1)3418 702 y Fs(\030)257 822 y Fw(U)323 837 y Fu(2)391 822 y Fs(\030)28 b Fw(U)10 b Fz(,)33 b(since)h Fw(\017)910 837 y Fu(1)978 822 y Fs(\030)28 b Fw(\017)1122 837 y Fu(2)1189 822 y Fs(\030)g Fz(1.)44 b(As)33 b(a)f(result,)i(w)m(e)f(obtain:)1478 1116 y Fw(U)38 b Fz(=)1712 1023 y(\026)1696 1048 y(\001)1777 997 y Fu(\(12\))1777 1076 y Ft(?)1929 1048 y Fz(+)2043 1023 y(\026)2027 1048 y(\001)2108 997 y Fu(\(21\))2108 1076 y Ft(?)p 1696 1093 542 4 v 1942 1184 a Fz(2)2248 1116 y Fw(:)1096 b Fz(\(3\))257 1359 y(F)-8 b(or)39 b(the)h (de\014nition)h(of)e(the)h(energy-angle)g(distribution)h(of)e(the)h (XTR)g(photons)g(w)m(e)257 1480 y(expand)34 b(the)f(electric)h(\014eld) f(in)g(the)g(F)-8 b(ourier)33 b(in)m(tegral:)430 1741 y Fv(E)504 1756 y Ft(?)562 1741 y Fz(\()p Fv(r)p Fw(;)17 b(t)p Fz(\))27 b(=)894 1605 y Fr(Z)11 b(Z)1077 1741 y Fw(d!)19 b(d)p Fv(k)e(E)1409 1756 y Ft(?)1467 1741 y Fz(\()p Fv(k)p Fw(;)g(!)t Fz(\))g(exp)g([)p Fw(i)p Fz(\()p Fv(kr)22 b Fs(\000)h Fw(!)t(t)p Fz(\)])16 b Fw(;)114 b Fv(E)2614 1756 y Ft(?)2673 1741 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))p Fv(k)26 b Fz(=)i(0)p Fw(;)189 b Fz(\(4\))257 2002 y(where)39 b Fv(k)e Fz(and)g Fw(!)k Fz(are)c(the)h(w)m(a)m(v)m(e)h (v)m(ector)f(and)f(the)h(frequency)h(of)e(the)h(XTR)f(photon,)257 2123 y(resp)s(ectiv)m(ely)-8 b(.)47 b(Then)34 b(relation)e(\(1\))g (will)i(b)s(e:)562 2366 y(\026)546 2392 y(\001)627 2341 y Fu(\(12\))627 2419 y Ft(?)840 2392 y Fz(=)83 b Fs(\000)p Fw(ev)1189 2256 y Fr(Z)1289 2282 y Ft(1)1244 2481 y(\0001)1391 2392 y Fw(d!)1522 2256 y Fr(Z)1638 2392 y Fw(d)p Fv(k)p Fw(E)1826 2341 y Fu(\(12\))1820 2419 y Fq(n)12 b Ft(?)1956 2392 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))2217 2256 y Fr(Z)2315 2282 y Ft(1)2271 2481 y(\0001)2417 2392 y Fw(dt)g Fz(exp)g([)p Fw(it)p Fz(\()p Fv(kv)25 b Fs(\000)d Fw(!)t Fz(\)])840 2660 y(=)83 b Fs(\000)p Fz(2)p Fw(\031)t(ev)1297 2524 y Fr(Z)1396 2550 y Ft(1)1352 2749 y(\0001)1498 2660 y Fw(d!)1630 2524 y Fr(Z)1746 2660 y Fw(d)p Fv(k)p Fw(E)1934 2609 y Fu(\(12\))1928 2687 y Fq(n)12 b Ft(?)2064 2660 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))p Fw(\016)t Fz(\()p Fw(!)24 b Fs(\000)f Fv(kv)r Fz(\))p Fw(;)608 b Fz(\(5\))257 2963 y(where)41 b Fw(E)624 2912 y Fu(\(12\))618 2991 y Fq(n)11 b Ft(?)753 2963 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))38 b(is)i(the)f(comp)s(onen)m(t)h(of)e Fv(E)2010 2978 y Ft(?)2069 2963 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))38 b(parallel)h(to)g(the)g(direction)h(of)257 3084 y(the)f(c)m(harge)h(motion)e Fv(n)p Fz(,)i(and)f Fw(\016)k Fz(is)c(the)g(Dirac)f(delta)h(function.)62 b(The)39 b(latter)g(will)g (b)s(e)257 3204 y(used)34 b(to)e(\014nd)h(the)g(in)m(tegral)g(with)h (resp)s(ect)f(to)g(the)g(mo)s(dule)g(of)f(the)h(w)m(a)m(v)m(e)h(v)m (ector)g Fw(k)s Fz(:)852 3346 y Fr(Z)969 3482 y Fw(d)p Fv(k)27 b Fz(=)h(2)p Fw(\031)1334 3346 y Fr(Z)1434 3372 y Ft(1)1389 3572 y Fu(0)1525 3482 y Fw(k)1579 3441 y Fu(2)1618 3482 y Fw(dk)1740 3341 y Fr(\032)1814 3346 y(Z)1914 3372 y Fu(0)1870 3572 y Ft(\000)p Fu(1)1981 3482 y Fw(d)17 b Fz(cos)f Fw(\022)26 b Fz(+)2364 3346 y Fr(Z)2463 3372 y Fu(1)2419 3572 y(0)2519 3482 y Fw(d)17 b Fz(cos)g Fw(\022)2782 3341 y Fr(\033)2873 3482 y Fw(;)257 3754 y Fz(where)37 b Fw(\022)i Fz(is)d(the)f(angle)h(b)s(et)m(w)m(een)h Fv(n)f Fz(and)g Fv(k)p Fz(.)52 b(One)36 b(can)f(see)i(that)e(the)h (delta)g(function)257 3874 y(in)31 b(\(5\))f(connects)i(the)f(signs)g (of)f Fw(!)k Fz(and)c(cos)17 b Fw(\022)s Fz(.)43 b(Therefore)32 b(the)f(in)m(tegrals)g(with)g(resp)s(ect)257 3995 y(to)44 b Fw(!)k Fz(and)d(cos)17 b Fw(\022)47 b Fz(are)e(divided)h(in)m(to)e(t) m(w)m(o)h(regions)g(where)h(b)s(oth)e Fw(!)k Fz(and)c(cos)17 b Fw(\022)48 b Fz(ha)m(v)m(e)257 4115 y(the)35 b(same)g(sign.)48 b(After)35 b(reducing)g(the)f(in)m(tegration)h(with)f(resp)s(ect)i(to)e (the)g(frequency)257 4236 y(to)44 b(the)h(ph)m(ysical)h(region,)i Fw(!)j Fs(\025)d Fz(0)c(and)g(with)h(resp)s(ect)g(to)f(cos)18 b Fw(\022)47 b Fz(o)m(v)m(er)e(the)g(forw)m(ard)257 4356 y(hemisphere,)35 b(relation)e(\(5\))f(b)s(ecomes:)375 4614 y(\026)359 4639 y(\001)440 4588 y Fu(\(12\))440 4667 y Ft(?)653 4639 y Fz(=)83 b Fs(\000)p Fz(4)p Fw(\031)997 4598 y Fu(2)1036 4639 y Fw(e)17 b(v)1165 4504 y Fr(Z)1265 4530 y Ft(1)1221 4729 y Fu(0)1356 4639 y Fw(d!)1488 4504 y Fr(Z)1588 4530 y Fu(1)1543 4729 y(0)1644 4639 y Fw(d)g Fz(cos)f Fw(\022)1923 4504 y Fr(Z)2023 4530 y Ft(1)1978 4729 y Fu(0)2114 4639 y Fw(k)2168 4598 y Fu(2)2207 4639 y Fw(d)h(k)2345 4529 y Fr(n)2412 4639 y Fw(E)2490 4588 y Fu(\(12\))2484 4667 y Fq(n)12 b Ft(?)2619 4639 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))p Fw(\016)t Fz(\()p Fw(!)25 b Fs(\000)d Fv(kv)r Fz(\)+)822 4877 y(+)p Fw(E)976 4826 y Fu(\(12\))970 4905 y Fq(n)11 b Ft(?)1105 4877 y Fz(\()p Fv(k)p Fw(;)17 b Fs(\000)p Fv(kv)r Fw(;)g Fs(\000)p Fw(!)t Fz(\))p Fw(\016)t Fz(\()p Fs(\000)p Fw(!)26 b Fz(+)c Fv(kv)r Fz(\))2172 4766 y Fr(o)2254 4877 y Fw(:)1090 b Fz(\(6\))257 5117 y(In)26 b(the)f(X-ra)m(y)g(region)g(the)h(main)f (con)m(tribution)h(to)f(the)g(in)m(tegral)g(with)h(resp)s(ect)g(to)f (cos)17 b Fw(\022)257 5237 y Fz(will)30 b(b)s(e)f(from)f Fw(\022)j Fs(\030)d Fz(0.)42 b(Therefore)30 b(w)m(e)g(can)f(mak)m(e)h (the)f(substitution)i(2\(1)14 b Fs(\000)g Fz(cos)k Fw(\022)s Fz(\))27 b Fs(\030)i Fw(\022)3456 5201 y Fu(2)257 5358 y Fz(and)23 b(c)m(hange)h(the)f(upp)s(er)g(limit)h(for)e(the)h(in)m (tegration)g(with)h(resp)s(ect)g(to)e Fw(\022)2878 5322 y Fu(2)2940 5358 y Fz(to)h(b)s(e)g(in\014nit)m(y)-8 b(,)257 5478 y(since)24 b(the)e(main)g(con)m(tribution)h(to)f(the)g(in)m (tegral)h(will)f(b)s(e)g(from)g(the)g(region)h(of)e Fw(\022)31 b Fs(\034)c Fz(1.)40 b(In)257 5599 y(addition,)28 b(the)f(in)m (tegration)f(with)h(resp)s(ect)h(to)e Fw(k)j Fz(results)e(in)g Fw(k)k Fz(=)c Fw(!)t(=v)20 b Fz(cos)d Fw(\022)31 b Fs(\030)d Fw(!)t(=c)d Fz(and)1852 5848 y(2)p eop %%Page: 3 4 3 3 bop 257 265 a Fz(app)s(earance)37 b(of)f(a)g(factor)g(from)g(the)h (delta)f(function,)i(1)p Fw(=v)20 b Fz(cos)d Fw(\022)37 b Fs(\030)e Fz(1)p Fw(=v)t Fz(.)54 b(Therefore,)257 385 y(the)33 b(energy-angle)h(distribution)f(of)f(the)h(energy)h(loss)f (will)h(b)s(e:)410 574 y Fw(d)461 538 y Fu(2)517 549 y Fz(\026)500 574 y(\001)581 523 y Fu(\(12\))581 602 y Ft(?)p 399 619 324 4 v 399 710 a Fp(~)p Fw(d!)19 b(d\022)683 681 y Fu(2)760 641 y Fz(=)28 b Fs(\000)951 574 y Fz(2)p Fw(\031)1059 538 y Fu(2)1098 574 y Fw(e)p 951 619 193 4 v 1020 710 a Fp(~)1170 531 y Fr(\020)1240 574 y Fw(!)p 1240 619 65 4 v 1251 710 a(c)1314 531 y Fr(\021)1373 553 y Fu(2)1429 531 y Fr(n)1496 641 y Fw(E)1574 591 y Fu(\(12\))1568 669 y Fq(n)12 b Ft(?)1703 641 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))22 b(+)g Fw(E)2145 591 y Fu(\(12\))2139 669 y Fq(n)11 b Ft(?)2274 641 y Fz(\()p Fs(\000)p Fv(k)p Fw(;)17 b Fs(\000)p Fw(!)t Fz(\))2672 531 y Fr(o)2755 641 y Fw(;)115 b Fv(kv)29 b Fz(=)f Fw(!)t(:)131 b Fz(\(7\))257 847 y(Here)23 b(w)m(e)h(in)m(tro)s(duced)f(the)g(XTR)f(photon)h(energy) -8 b(,)25 b Fp(~)p Fw(!)t Fz(,)f(where)f Fp(~)f Fz(is)h(Planc)m(k's)h (constan)m(t.)257 968 y(It)i(will)f(b)s(e)h(sho)m(wn)g(b)s(elo)m(w)g (\(see)g(relations)g(\(17\),)g(\(18\))e(and)h(\(23\))g(in)g(section)h (2.1\))f(that)g(in)257 1102 y(the)37 b(X-ra)m(y)f(region)g Fw(E)1080 1051 y Fu(\(12\))1074 1130 y Fq(n)p Ft(?)1210 1102 y Fz(\()p Fs(\000)p Fv(k)p Fw(;)17 b Fs(\000)p Fw(!)t Fz(\))33 b(=)h Fw(E)1829 1051 y Fu(\(12\))p Ft(\003)1823 1130 y Fq(n)p Ft(?)1994 1102 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\),)36 b(where)h Fs(\003)f Fz(means)h(the)g(complex)257 1222 y(conjugation)e(op)s(eration.)49 b(The)36 b(energy-angle)f (distribution)h(of)e(the)h(emitted)h(energy)257 1343 y(of)c(the)h(XTR)g(photons)g(is)h(then:)780 1509 y Fw(d)831 1473 y Fu(2)870 1509 y Fw(U)p 701 1554 324 4 v 701 1645 a Fp(~)p Fw(d!)20 b(d\022)986 1616 y Fu(2)1062 1577 y Fz(=)28 b Fs(\000)1253 1509 y Fz(2)p Fw(\031)1361 1473 y Fu(2)1401 1509 y Fw(e)p 1253 1554 193 4 v 1323 1645 a Fp(~)1472 1466 y Fr(\020)1542 1509 y Fw(!)p 1542 1554 65 4 v 1553 1645 a(c)1616 1466 y Fr(\021)1676 1488 y Fu(2)1732 1577 y Fz(Re)1863 1466 y Fr(n)1930 1577 y Fw(E)2008 1526 y Fu(\(12\))2002 1605 y Fq(n)12 b Ft(?)2137 1577 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))22 b(+)g Fw(E)2579 1526 y Fu(\(21\))2573 1605 y Fq(n)11 b Ft(?)2708 1577 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))2952 1466 y Fr(o)3034 1577 y Fw(:)310 b Fz(\(8\))257 1788 y(Av)m(eraging)31 b(o)m(v)m(er)g(the)f(forw)m(ard)g(and)h(bac)m(kw)m(ard)g(directions)g (of)f(motion)g(used)h(in)f(\(8\))g(is)257 1909 y(needed)39 b(for)d(an)g(o)s(dd)h(n)m(um)m(b)s(er)h(of)e(in)m(terfaces)i(only)-8 b(.)56 b(If)36 b(the)h(n)m(um)m(b)s(er)h(of)f(in)m(terfaces)h(is)257 2029 y(ev)m(en,)j(as,)e(for)d(example,)k(for)d(a)g(n)m(um)m(b)s(er)i (of)e(plates)h(of)f(the)h(second)h(medium)f(placed)257 2149 y(in)e(di\013eren)m(t)g(p)s(ositions)f(in)g(the)h(\014rst)f (medium,)i(it)e(is)g(enough)h(to)e(consider)j(the)e(XTR)257 2270 y(energy)40 b(loss)f(for)e(the)i(forw)m(ard)f(direction)h(of)f (motion)g(only)-8 b(.)61 b(In)38 b(particular,)i(for)e(one)257 2390 y(plate)26 b(the)f(energy-angle)h(distribution)g(of)e(the)i (emitted)g(energy)g(of)e(the)h(XTR)h(photons)257 2511 y(reads:)1047 2658 y Fw(d)1098 2622 y Fu(2)1137 2658 y Fw(U)p 969 2703 324 4 v 969 2794 a Fp(~)p Fw(d!)19 b(d\022)1253 2765 y Fu(2)1330 2725 y Fz(=)28 b Fs(\000)1521 2658 y Fz(4)p Fw(\031)1629 2622 y Fu(2)1668 2658 y Fw(e)p 1521 2703 193 4 v 1590 2794 a Fp(~)1740 2615 y Fr(\020)1810 2658 y Fw(!)p 1810 2703 65 4 v 1821 2794 a(c)1884 2615 y Fr(\021)1943 2637 y Fu(2)1999 2725 y Fz(Re)2131 2615 y Fr(n)2198 2725 y Fw(E)2276 2675 y Fu(\(121\))2270 2753 y Fq(n)11 b Ft(?)2441 2725 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\))2685 2615 y Fr(o)2767 2725 y Fw(:)577 b Fz(\(9\))257 2937 y(Relations)37 b(\(8\))e(and)i(\(9\))e(will)i(b)s(e)f(used)h(in)g (the)f(next)h(section)g(for)f(the)g(calculation)h(of)257 3057 y(the)c(XTR)g(energy)h(loss)f(for)f(di\013eren)m(t)i(geometries)g (of)e(the)h(medium)h(in)m(terfaces.)257 3384 y Fx(2)161 b(Calculations)54 b(of)i(the)f(X-ra)l(y)g(transition)f(radia-)499 3567 y(tion)f(energy)g(loss)f(for)i(di\013eren)l(t)e(geometries)257 3815 y Fo(2.1)136 b(Single)45 b(in)l(terface)i(b)t(et)l(w)l(een)f (absorbing)f(media)257 4000 y Fz(F)-8 b(or)45 b(simplicit)m(y)-8 b(,)51 b(w)m(e)46 b(consider)h(the)e(case)h(when)h(the)f(\014rst)f(and) h(second)g(media)g(are)257 4120 y(lo)s(cated)34 b(in)f(semi)i(spaces)f Fw(z)g(<)28 b Fz(0)33 b(and)h Fw(z)f(>)c Fz(0,)k(resp)s(ectiv)m(ely)j (\(\014g.)d(1\),)h(and)f(the)h(c)m(harge)257 4241 y(mo)m(v)m(es)28 b(along)d(the)h Fw(z)k Fz(axis)c(\()p Fv(r)p Fz(\()p Fw(t)p Fz(\))h(=)h Fv(v)r Fw(t)g Fz(=)f Fs(f)p Fz(0)p Fw(;)17 b Fz(0)p Fw(;)g(v)t(t)p Fs(g)p Fz(\).)40 b(Since)26 b(the)g(dielectric)h(prop)s(erties)257 4361 y(dep)s(end)33 b(on)f Fw(z)t Fz(,)g(w)m(e)h(will)f(\014rst)g(de\014ne)h(the)f(in)m (termediate)h(F)-8 b(ourier)32 b(comp)s(onen)m(ts)h(of)e(the)257 4481 y(electric)j(\014eld:)704 4688 y Fv(E)p Fz(\()p Fv(q)p Fw(;)17 b(!)t(;)g(z)t Fz(\))26 b(=)1245 4552 y Fr(Z)1427 4620 y Fw(d)p Fn(\032)p 1371 4665 223 4 v 1371 4756 a Fz(\(2)p Fw(\031)t Fz(\))1555 4727 y Fu(2)1621 4552 y Fr(Z)1720 4578 y Ft(1)1676 4778 y(\0001)1843 4620 y Fw(dt)p 1832 4665 108 4 v 1832 4756 a Fz(2)p Fw(\031)1950 4688 y Fv(E)p Fz(\()p Fv(r)p Fw(;)17 b(t)p Fz(\))g(exp)f([)p Fs(\000)p Fw(i)p Fz(\()p Fn(\032)p Fv(q)23 b Fs(\000)g Fw(!)t(t)p Fz(\)])16 b 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Fs(\000)23 b Fw(\020)2143 1945 y Fu(2)2135 2011 y Fq(j)2191 1851 y Fw(:)257 2235 y Fz(Here)h Fv(E)552 2199 y Fu(\()p Fq(j)t Fu(\))666 2235 y Fz(are)f(the)h(amplitudes)h(of)d(the)i(transv)m (erse)h(electromagnetic)g(radiation)e(\014elds)257 2355 y(expanding)35 b(from)e(the)g(plane)h Fw(z)g Fz(=)28 b(0.)45 b(These)35 b(amplitudes)g(can)e(b)s(e)h(deriv)m(ed)h(from)e (the)257 2476 y(b)s(oundary)g(conditions)h(for)e(the)h(total)f (electric)i(\014elds)g Fv(E)2373 2440 y Fu(\()p Fq(j)t Fu(\))p Fq(tot)2549 2476 y Fz(:)837 2683 y Fw(\017)876 2698 y Fu(1)916 2683 y Fw(E)994 2642 y Fu(\(1\))p Fq(tot)988 2707 y(n)1201 2683 y Fz(=)27 b Fw(\017)1343 2698 y Fu(2)1383 2683 y Fw(E)1461 2642 y Fu(\(2\))p Fq(tot)1455 2707 y(n)1641 2683 y Fw(;)114 b(E)1860 2642 y Fu(\(1\))p Fq(tot)1854 2707 y(\034)2067 2683 y Fz(=)28 b Fw(E)2249 2642 y Fu(\(2\))p Fq(tot)2243 2707 y(\034)2428 2683 y Fw(;)114 b Fv(q)28 b Fz(=)g Fw(q)t Fn(\034)13 b Fw(;)423 b Fz(\(14\))257 2890 y(where)33 b Fn(\034)45 b Fz(is)32 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b(b)s(e)f(from)f Fw(E)895 3744 y Fu(\(2\))889 3805 y Fq(n)989 3795 y Fz(.)56 b(Note)37 b(that)f(the)h(terms)h(prop)s (ortional)e(to)g Fv(B)2743 3759 y Fu(\()p Fq(j)t Fu(\))2871 3795 y Fz(will)h(con)m(tribute)257 3915 y(to)31 b(Cerenk)m(o)m(v)j (radiation)d(in)h(the)f(sp)s(ectral)h(ranges)g(where)g Fw(R)q(e)p Fs(f)p Fw(\017)2654 3930 y Fq(j)2691 3915 y Fs(g)c Fw(>)f Fz(1,)32 b(whic)m(h)h(is)e(not)257 4035 y(the)f(case)h(for)e(the)h(X-ra)m(y)f(region.)43 b(W)-8 b(e)30 b(will)g(use)h(the)e(standard)h(represen)m(tation)i(of)d(the)257 4156 y(dielectric)35 b(p)s(ermittivities:)1452 4425 y Fw(\017)1491 4440 y Fq(j)1556 4425 y Fz(=)27 b(1)22 b Fs(\000)1840 4349 y Fw(!)1905 4313 y Fu(2)1901 4374 y Fq(j)p 1840 4402 V 1840 4494 a Fw(!)1905 4465 y Fu(2)1976 4425 y Fz(+)g Fw(i)2161 4358 y(c)p 2117 4402 130 4 v 2117 4494 a(!)t(l)2211 4509 y Fq(j)2257 4425 y Fw(;)1038 b Fz(\(16\))257 4686 y(where)34 b Fw(!)600 4701 y Fq(j)669 4686 y Fz(and)e Fw(l)887 4701 y Fq(j)956 4686 y Fz(are)h(the)g(plasma)g 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5529 153 4 v 2421 5620 a(2)p Fw(Z)2537 5635 y Fq(j)2584 5552 y Fw(;)1852 5848 y Fz(4)p eop %%Page: 5 6 5 5 bop 974 310 a Fv(A)1059 269 y Fu(\()p Fq(j)t Fu(\))1178 310 y Fs(')28 b Fw(A)1373 169 y Fr(\032)1457 243 y Fw(!)p 1457 287 65 4 v 1468 378 a(c)1532 310 y(\022)s Fn(\034)13 b Fw(;)1726 243 y Fz(1)p 1699 287 104 4 v 1699 378 a Fw(Z)1766 393 y Fq(j)1834 310 y Fs(\000)1944 243 y Fw(!)p 1944 287 65 4 v 1955 378 a(c)2018 310 y(\022)2066 269 y Fu(2)2106 169 y Fr(\033)2197 310 y Fw(;)114 b(A)28 b Fz(=)2608 243 y Fw(ie)p 2552 287 190 4 v 2552 378 a Fz(2)p Fw(\031)2660 349 y Fu(2)2700 378 y Fw(c)2752 310 y(;)257 569 y Fz(where)37 b(w)m(e)f(in)m(tro)s(duce)g(the)g Fy(c)-5 b(omplex)36 b(formation)g(zone)p Fz(,)f Fw(Z)2439 584 y Fq(j)2476 569 y Fz(,)h(of)e(X-ra)m(y)h(transition)h(ra-)257 689 y(diation)d(in)g(the)g Fw(j)6 b Fz(-th)32 b(medium:)1572 937 y Fw(Z)1639 952 y Fq(j)1703 937 y Fz(=)1929 870 y Fw(L)1995 885 y Fq(j)p 1817 914 327 4 v 1817 1062 a Fz(1)22 b Fs(\000)g Fw(i)2030 994 y(L)2096 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387 y(the)h(\014nal)g(result)h(for)e(the)h (energy-angle)g(distribution)h(of)e(emitted)h(XTR)g(energy:)1125 568 y Fw(d)1176 532 y Fu(2)1215 568 y Fw(U)p 1047 613 324 4 v 1047 704 a Fp(~)p Fw(d!)19 b(d\022)1331 675 y Fu(2)1408 636 y Fz(=)1522 568 y Fw(\013)p 1522 613 63 4 v 1524 704 a(\031)1611 525 y Fr(\020)1680 568 y Fw(!)p 1680 613 65 4 v 1691 704 a(c)1755 525 y Fr(\021)1814 547 y Fu(2)1870 636 y Fw(\022)1918 594 y Fu(2)1958 636 y Fz(Re)2090 555 y Fr(\010)2148 636 y Fz(\()p Fw(Z)2253 651 y Fu(1)2314 636 y Fs(\000)k Fw(Z)2481 651 y Fu(2)2520 636 y Fz(\))2558 594 y Fu(2)2597 555 y Fr(\011)2672 636 y Fw(;)623 b Fz(\(25\))257 862 y(where)31 b Fw(\013)e Fz(is)g(the)h(\014ne)f(structure)i(constan)m(t)e(\(w)m(e)h(consider)g (for)f(simplicit)m(y)i(the)e(particle)257 982 y(c)m(harge)35 b Fw(e)g Fz(to)f(b)s(e)g(equal)h(to)f(the)h(electron)g(c)m(harge\).)49 b(One)34 b(can)h(see)g(that)f(in)h(absorbing)257 1103 y(media)j(the)g(emitted)g(XTR)f(energy)h(is)g(de\014ned)g(b)m(y)g(the)f 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Fw(i)2982 5513 y(!)p 2982 5557 V 2989 5648 a(v)3057 5580 y(z)3102 5595 y Fu(1)3141 5469 y Fr(\021)3217 5580 y Fw(;)78 b Fz(\(32\))1852 5848 y(6)p eop %%Page: 7 8 7 7 bop 471 280 a Fw(\034)39 b Fz(:)264 b Fw(E)921 239 y Fu(\(1\))915 305 y Fq(n)1032 280 y Fz(exp)q(\()p Fs(\000)p Fw(i\020)1372 295 y Fu(1)1412 280 y Fw(z)1457 295 y Fu(1)1496 280 y Fz(\))22 b Fs(\000)h Fw(A\022)1777 239 y Fu(2)1817 280 y Fw(Z)1884 295 y Fu(1)1939 280 y Fz(exp)2105 169 y Fr(\020)2165 280 y Fw(i)2208 213 y(!)p 2208 257 65 4 v 2215 348 a(v)2282 280 y(z)2327 295 y Fu(1)2367 169 y Fr(\021)2454 280 y Fz(=)843 496 y Fs(\000)p Fw(E)998 455 y Fu(\(2\))992 521 y Fq(n)1109 496 y Fz(exp)q(\()p Fw(i\020)1372 511 y Fu(2)1412 496 y Fw(z)1457 511 y Fu(1)1496 496 y Fz(\))f(+)g Fw(E)1732 455 y Fu(\(3\))1726 521 y Fq(n)1843 496 y Fz(exp)q(\()p Fs(\000)p Fw(i\020)2183 511 y Fu(2)2223 496 y Fw(z)2268 511 y Fu(1)2308 496 y Fz(\))g Fs(\000)h Fw(A\022)2589 455 y Fu(2)2628 496 y Fw(Z)2695 511 y Fu(2)2751 496 y Fz(exp)2917 386 y 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5332 y Fz(\()p Fw(Z)2499 5347 y Fq(i)2549 5332 y Fs(\000)h Fw(Z)2716 5347 y Fq(i)p Fu(+1)2834 5332 y Fz(\))2925 5207 y Fq(k)r Ft(\000)p Fu(1)2925 5237 y Fr(Y)2889 5447 y Fq(j)t Fu(=)p Fq(i)p Fu(+1)3106 5332 y Fw(H)3187 5347 y Fq(j)3224 5332 y Fz(\()p Fw(a)3313 5347 y Fq(j)3349 5332 y Fz(\))3387 5161 y Fr(#)3462 5332 y Fw(;)3332 5562 y Fz(\(40\))1852 5848 y(7)p eop %%Page: 8 9 8 8 bop 257 265 a Fz(where)30 b Fw(a)586 280 y Fq(k)657 265 y Fz(=)d Fw(z)805 280 y Fq(k)862 265 y Fs(\000)14 b Fw(z)998 280 y Fq(k)r Ft(\000)p Fu(1)1131 265 y Fw(;)33 b Fz(\()p Fw(k)e Fz(=)d(2)p Fw(;)17 b(:)g(:)g(:)32 b(;)17 b(n)d Fs(\000)g Fz(1\))28 b(is)h(the)g(thic)m(kness)i(of)d(the)h Fw(k)s Fz(-th)f(medium.)257 385 y(The)48 b(F)-8 b(ourier)46 b(image)g(of)g(the)h Fw(n)p Fz(-comp)s(onen)m(t)g(of)e(the)i(radiation) f(\014elds,)51 b(expanding)257 506 y(along)33 b(the)g Fw(z)t Fz(-axis,)g(reads:)423 762 y Fw(E)501 721 y Fu(\(1)p Fq(;:::)11 b(;n)p Fu(\))495 787 y Fq(n)748 762 y Fz(\()p Fv(k)p Fw(;)17 b(!)t 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1119 y Fq(k)1221 1104 y Fz(\()p Fw(a)1310 1119 y Fq(k)1353 1104 y Fz(\))22 b Fs(\000)h Fz(1])16 b Fw(Z)1672 1119 y Fq(k)1731 933 y Fr(")1790 1104 y Fz(\()p Fw(Z)1895 1119 y Fq(k)r Ft(\000)p Fu(1)2049 1104 y Fs(\000)23 b Fw(Z)2216 1119 y Fq(k)2258 1104 y Fz(\))f(+)2424 979 y Fq(k)r Ft(\000)p Fu(2)2416 1009 y Fr(X)2431 1219 y Fq(i)p Fu(=1)2560 1104 y Fz(\()p Fw(Z)2665 1119 y Fq(i)2715 1104 y Fs(\000)h Fw(Z)2882 1119 y Fq(i)p Fu(+1)3000 1104 y Fz(\))3091 979 y Fq(k)r Ft(\000)p Fu(1)3092 1009 y Fr(Y)3055 1219 y Fq(j)t Fu(=)p Fq(i)p Fu(+1)3273 1104 y Fw(H)3354 1119 y Fq(j)3390 1104 y Fz(\()p Fw(a)3479 1119 y Fq(j)3516 1104 y Fz(\))3554 933 y Fr(#)3628 1104 y Fs(\000)433 1452 y(\000)p Fw(Z)577 1467 y Fq(n)641 1282 y Fr(")699 1452 y Fz(\()p Fw(Z)804 1467 y Fq(n)p Ft(\000)p Fu(1)963 1452 y Fs(\000)g Fw(Z)1130 1467 y Fq(n)1177 1452 y Fz(\))f(+)1340 1328 y Fq(n)p Ft(\000)p Fu(2)1335 1358 y Fr(X)1350 1568 y Fq(i)p Fu(=1)1479 1452 y Fz(\()p Fw(Z)1584 1467 y Fq(i)1634 1452 y Fs(\000)g Fw(Z)1800 1467 y Fq(i)p Fu(+1)1918 1452 y Fz(\))2007 1328 y Fq(n)p Ft(\000)p Fu(1)2010 1358 y Fr(Y)1973 1568 y Fq(j)t Fu(=)p Fq(i)p Fu(+1)2191 1452 y Fw(H)2272 1467 y Fq(j)2308 1452 y Fz(\()p Fw(a)2397 1467 y Fq(j)2434 1452 y Fz(\))2472 1282 y Fr(#\))2627 1452 y Fw(:)1013 b Fz(\(41\))257 1751 y(T)-8 b(aking)45 b(half)e(of)h(the)g(sum)h(of)e (the)h(latter)g(relation)g(with)h Fw(E)2576 1700 y Fu(\()p Fq(n;:::)10 b(;)p Fu(1\))2570 1761 y Fq(n)2823 1751 y Fz(\()p Fv(k)p Fw(;)17 b(!)t Fz(\),)45 b(whic)m(h)h(is)257 1871 y(describ)s(ed)31 b(b)m(y)f(\(41\),)e(with)i(the)f(substitution)h Fw(k)h Fj(\034)c Fw(n)14 b Fs(\000)g Fw(k)19 b Fz(+)14 b(1)p Fw(;)114 b Fz(\()p Fw(k)31 b Fz(=)c(1)p Fw(;)17 b(:)g(:)g(:)32 b(;)17 b(n)p Fz(\))p Fw(;)29 b Fz(one)257 1992 y(gets,)34 b(for)e(the)h(energy-angle)g(distribution)h(of)e(the)h (emitted)g(XTR)g(energy)-8 b(,)1066 2157 y Fw(d)1117 2121 y Fu(2)1156 2157 y Fw(U)1232 2121 y Fu(\(1)p Fq(;:::)11 b(;n)p Fu(\))p 1066 2201 414 4 v 1111 2293 a Fp(~)p Fw(d!)19 b(d\022)1395 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Fr(X)1343 3253 y Fq(k)r Fu(=2)1479 3135 y Fz(\()p Fw(Z)1584 3150 y Fq(k)1649 3135 y Fs(\000)22 b Fw(Z)1815 3150 y Fq(k)r Fu(+1)1948 3135 y Fz(\))2010 3011 y Fq(k)r Ft(\000)p Fu(1)2002 3040 y Fr(X)2017 3250 y Fq(i)p Fu(=1)2146 3135 y Fz(\()p Fw(Z)2251 3150 y Fq(i)2301 3135 y Fs(\000)h Fw(Z)2468 3150 y Fq(i)p Fu(+1)2586 3135 y Fz(\))2722 3011 y Fq(k)2678 3040 y Fr(Y)2641 3250 y Fq(j)t Fu(=)p Fq(i)p Fu(+1)2859 3135 y Fw(H)2940 3150 y Fq(j)2976 3135 y Fz(\()p Fw(a)3065 3150 y Fq(j)3102 3135 y Fz(\))p Fw(:)155 b Fz(\(43\))257 3402 y(These)31 b(relations)e(describ)s(e)i(the)e(energy-angle)g(distribution)h(of)f (XTR)g(photons)g(emit-)257 3523 y(ted)47 b(inside)h(the)f Fy(most)g(gener)-5 b(al)47 b(XTR)h(r)-5 b(adiator)46 b Fz(consisting)h(of)f(arbitrary)h(n)m(um)m(b)s(er)257 3643 y Fw(n)41 b(>)f Fz(2)f(of)h(di\013eren)m(t)h(media)f(with)h (arbitrary)f(thic)m(knesses.)69 b(One)40 b(can)g(see)h(that)f(the)257 3763 y(functions)h Fw(H)766 3778 y Fq(j)842 3763 y Fz(ha)m(v)m(e)f(the) 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b(4)p Fs(j)p Fw(L)1679 5519 y Fu(1)1741 5504 y Fs(\000)22 b Fw(L)1906 5519 y Fu(2)1946 5504 y Fs(j)1974 5463 y Fu(2)2030 5504 y Fz(sin)2150 5463 y Fu(2)2206 5363 y Fr(\022)2321 5436 y Fw(a)2372 5451 y Fu(2)p 2289 5481 V 2289 5572 a Fz(4)p Fw(L)2404 5587 y Fu(2)2454 5363 y Fr(\023)2544 5504 y Fw(;)751 b Fz(\(45\))1852 5848 y(8)p eop %%Page: 9 10 9 9 bop 257 265 a Fz(in)33 b(accordance)h(with)f(the)g(standard)g (theory)g([12].)257 551 y Fo(2.3)136 b(Mo)t(dels)45 b(of)g(random)g (stac)l(k)257 736 y Fz(In)h(radiators)g(based)h(on)e(foam)h(or)f(a)h (\014bre)g(stac)m(k)h(with)g(inserted)g(XTR)f(detectors)257 856 y(\(stra)m(w)35 b(tub)s(es\),)g(XTR)f(is)h(measured)g(from)f (particles)h(crossing)g(di\013eren)m(t)g(sets)g(of)f(the)257 977 y(gap)26 b(thic)m(knesses.)45 b(Since,)28 b(according)e(to)g (\(43\),)g(eac)m(h)h(gap)e(con)m(tributes)j(to)d(the)i(energy-)257 1097 y(angle)f(distribution)h(of)e(the)h(emitted)h(XTR)f(energy)h(as)e (not)h(more)g(than)g(one)g Fw(H)8 b Fz(-factor,)257 1218 y(a)m(v)m(eraging)36 b(o)m(v)m(er)h(indep)s(enden)m(tly)h (\015uctuating)d(gap)g(thic)m(knesses)k(\(for)c(simplicit)m(y)-8 b(,)38 b(w)m(e)257 1338 y(do)49 b(not)g(consider)h(constrains)f(due)h (to)e(\014nite)i(radiator)e(thic)m(kness\))j(results)f(in)f(an)257 1458 y(expression)35 b(for)d Fs(h)p Fw(R)990 1422 y Fu(\(1)p Fq(;:::)11 b(;n)p Fu(\))1237 1458 y Fs(i)32 b Fz(whic)m(h)i(is)f (similar)h(to)e(\(43\):)637 1751 y Fs(h)p Fw(R)751 1710 y Fu(\(1)p Fq(;:::)11 b(;n)p Fu(\))998 1751 y Fs(i)27 b Fz(=)1312 1626 y Fq(n)p Ft(\000)p Fu(1)1306 1656 y Fr(X)1321 1866 y Fq(i)p Fu(=1)1450 1751 y Fz(\()p Fw(Z)1555 1766 y Fq(i)1605 1751 y Fs(\000)c Fw(Z)1772 1766 y Fq(i)p Fu(+1)1890 1751 y Fz(\))1928 1710 y Fu(2)1989 1751 y Fz(+)1306 2090 y(+2)1453 1965 y Fq(n)p Ft(\000)p Fu(1)1448 1995 y Fr(X)1455 2207 y Fq(k)r Fu(=2)1591 2090 y Fz(\()p Fw(Z)1696 2105 y Fq(k)1761 2090 y Fs(\000)g Fw(Z)1928 2105 y Fq(k)r Fu(+1)2060 2090 y Fz(\))2122 1965 y Fq(k)r Ft(\000)p Fu(1)2115 1995 y Fr(X)2130 2205 y Fq(i)p Fu(=1)2259 2090 y Fz(\()p Fw(Z)2364 2105 y Fq(i)2414 2090 y Fs(\000)f Fw(Z)2580 2105 y Fq(i)p Fu(+1)2698 2090 y Fz(\))2834 1965 y Fq(k)2790 1995 y Fr(Y)2753 2205 y Fq(j)t Fu(=)p Fq(i)p Fu(+1)2971 2090 y Fw(H)3052 2105 y Fq(j)3088 2090 y Fw(;)207 b Fz(\(46\))257 2393 y(where)38 b Fw(H)624 2408 y Fq(j)697 2393 y Fz(\()p Fw(j)i Fz(=)34 b(2)p Fw(;)17 b(:)g(:)g(:)32 b(;)17 b(n)25 b Fs(\000)g Fz(1\))36 b(are)g(functions)i (\(35\))d(a)m(v)m(eraged)j(o)m(v)m(er)g(the)e(thic)m(kness)257 2513 y(distributions)e Fw(p)876 2528 y Fq(j)913 2513 y Fz(\()p Fw(z)t Fz(\):)388 2776 y Fw(H)469 2791 y Fq(j)533 2776 y Fz(=)27 b Fs(h)p Fw(H)756 2791 y Fq(j)792 2776 y Fz(\()p Fw(z)t Fz(\))p Fs(i)i Fz(=)1088 2640 y Fr(Z)1188 2666 y Ft(1)1143 2866 y Fu(0)1279 2776 y Fw(dz)21 b(p)1445 2791 y Fq(j)1482 2776 y Fz(\()p Fw(z)t Fz(\))c(exp)1789 2635 y Fr(\024)1842 2776 y Fs(\000)1964 2708 y Fw(iz)p 1929 2753 153 4 v 1929 2844 a Fz(2)p Fw(Z)2045 2859 y Fq(j)2091 2635 y Fr(\025)2161 2776 y Fw(;)2302 2635 y Fr(\022)2375 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Fq(j)2000 3602 y Fz(\))2065 3534 y(exp)2230 3393 y Fr(\024)2283 3534 y Fs(\000)2370 3466 y Fw(\027)2418 3481 y Fq(j)2455 3466 y Fw(z)p 2370 3511 135 4 v 2403 3602 a Fz(\026)g Fw(z)2442 3617 y Fq(j)2515 3393 y Fr(\025)2584 3534 y Fw(;)711 b Fz(\(48\))257 3789 y(where)36 b(\000)f(is)g(the)g (Euler)h(gamma)f(function,)41 b(\026)-55 b Fw(z)1971 3804 y Fq(j)2043 3789 y Fz(is)35 b(the)g(mean)h(thic)m(kness)h(of)d (the)i Fw(j)6 b Fs(\000)p Fz(th)257 3910 y(medium)38 b(in)f(the)g(radiator)f(and)h Fw(\027)1545 3925 y Fq(j)1616 3910 y Fw(>)e Fz(0)h(is)h(a)g(parameter)g(whic)m(h)h(roughly)f(describ) s(es)257 4030 y(the)c(relativ)m(e)h(thic)m(kness)i(\015uctuations.)44 b(In)33 b(fact,)f(the)h(relativ)m(e)h(thic)m(kness)i(\015uctuation)257 4150 y Fw(\016)300 4165 y Fq(j)370 4150 y Fz(is,)d(according)g(to)f (equation)h(\(48\),)1015 4431 y Fw(\016)1058 4446 y Fq(j)1123 4431 y Fz(=)1236 4276 y Fr(p)p 1336 4276 479 4 v 84 x Fs(h)p Fz(\()p Fw(z)1458 4375 y Fq(j)1516 4360 y Fs(\000)c Fz(\026)-55 b Fw(z)1661 4375 y Fq(j)1698 4360 y Fz(\))1736 4331 y Fu(2)1775 4360 y Fs(i)p 1236 4408 578 4 v 1490 4499 a Fz(\026)g Fw(z)1529 4514 y Fq(j)1852 4431 y Fz(=)27 b Fw(\027)2009 4380 y Ft(\000)p Fu(1)p Fq(=)p Fu(2)2003 4456 y Fq(j)2175 4431 y Fw(;)114 b Fz(\()p Fw(j)33 b Fz(=)28 b(1)p Fw(;)17 b Fz(2\))p Fw(:)257 4692 y Fz(Then,)34 b(substituting)h(\(48\))d(in)m(to)h(\(47\),)f(one)h(can)g(deriv)m(e)i (analytically)f(the)f(v)-5 b(alues)34 b Fw(H)3432 4707 y Fq(j)3468 4692 y Fz(.)257 4812 y(F)-8 b(or)25 b(example,)k(in)d(the)g (general)h(case)f(of)g(a)f(gamma-distributed)i(radiator,)g(calculating) 257 4933 y(\(47\))32 b(with)i(the)f(help)g(of)f(\(48\))g(one)h(gets:) 1385 5206 y Fw(H)1466 5221 y Fq(j)1530 5206 y Fz(=)1634 5065 y Fr(\024)1686 5206 y Fz(1)22 b(+)g Fw(i)1982 5138 y Fz(\026)-55 b Fw(z)2021 5153 y Fq(j)p 1898 5183 237 4 v 1898 5274 a Fz(2)p Fw(Z)2014 5289 y Fq(j)2050 5274 y Fw(\027)2098 5289 y Fq(j)2145 5065 y Fr(\025)2198 5088 y Ft(\000)p Fq(\027)2288 5098 y Fm(j)2340 5206 y Fw(:)955 b Fz(\(49\))257 5478 y(This)27 b(equation)f(allo)m(ws)g(us)g(to)f (calculate)h(the)g(factor)f Fw(R)2284 5442 y Fu(\(1)p Fq(;:::)11 b(;n)p Fu(\))2556 5478 y Fz(analytically)26 b(and)g(hence)257 5599 y(ev)-5 b(aluate)30 b(the)f(energy-angle)h (distribution)g(of)f(emitted)h(XTR)g(photons)f(in)h(a)e(wide)i(set)1852 5848 y(9)p eop %%Page: 10 11 10 10 bop 257 265 a Fz(of)31 b(radiators)g(with)g(\015uctuating)h(gap)e (thic)m(knesses.)47 b(F)-8 b(or)30 b(radiators)h(with)g(small)h(irreg-) 257 385 y(ularities,)40 b(when)e Fw(\027)972 400 y Fq(j)1045 385 y Fw(>)e Fz(100,)i(the)f(direct)i(calculation)f(of)f(\(49\))f (results)j(in)f(n)m(umerical)257 506 y(instabilities)j(and)f(is)g(time) g(consuming.)65 b(In)39 b(this)h(case)h(the)e(Gaussian)h(distribution) 257 626 y(can)33 b(b)s(e)g(used)h(for)e(the)h(a)m(v)m(eraging)g(of)f (the)h(functions)h(\(35\):)1147 905 y Fw(p)1196 920 y Fq(j)1232 905 y Fz(\()p Fw(z)t Fz(\))29 b(=)1616 838 y(1)p 1499 882 283 4 v 1499 985 a Fw(\033)1554 1000 y Fq(j)1591 902 y Fs(p)p 1674 902 108 4 v 83 x Fz(2)p Fw(\031)1808 905 y Fz(exp)1974 765 y Fr(\024)2027 905 y Fs(\000)2114 838 y Fz(\()p Fw(z)e Fs(\000)i Fz(\026)-55 b Fw(z)2369 853 y Fq(j)2405 838 y Fz(\))2443 802 y Fu(2)p 2114 882 369 4 v 2225 974 a Fz(2)p Fw(\033)2333 939 y Fu(2)2329 999 y Fq(j)2493 765 y Fr(\025)2562 905 y Fw(;)733 b Fz(\(50\))257 1190 y(where)33 b Fw(\033)593 1205 y Fq(j)662 1190 y Fz(are)e(the)i(ro)s(ot-mean-squared)e(\015uctuations)i(of)e(the)h(thic) m(kness)j(in)d(the)g Fw(j)6 b Fz(-th)257 1310 y(medium.)45 b(Then)34 b(for)e Fw(\033)1128 1325 y Fq(j)1193 1310 y Fs(\034)h Fz(\026)-55 b Fw(z)1365 1325 y Fq(j)1402 1310 y Fz(:)833 1601 y Fw(H)914 1616 y Fq(j)978 1601 y Fz(=)28 b(exp)1247 1461 y Fr(\024)1300 1601 y Fs(\000)1406 1534 y Fw(i)6 b Fz(\026)-55 b Fw(z)1484 1549 y Fq(j)p 1387 1578 153 4 v 1387 1670 a Fz(2)p Fw(Z)1503 1685 y Fq(j)1572 1601 y Fs(\000)1713 1525 y Fw(\033)1772 1489 y Fu(2)1768 1550 y Fq(j)p 1681 1578 163 4 v 1681 1670 a Fz(8)p Fw(Z)1804 1635 y Fu(2)1797 1695 y Fq(j)1853 1461 y Fr(\025)1934 1601 y Fz(=)27 b Fw(H)2118 1616 y Fq(j)2154 1601 y Fz(\()6 b(\026)-55 b Fw(z)2237 1616 y Fq(j)2274 1601 y Fz(\))17 b(exp)2494 1461 y Fr(\024)2547 1601 y Fs(\000)2666 1525 y Fw(\033)2725 1489 y Fu(2)2721 1550 y Fq(j)p 2634 1578 V 2634 1670 a Fz(8)p Fw(Z)2757 1635 y Fu(2)2750 1695 y Fq(j)2807 1461 y Fr(\025)2876 1601 y Fw(;)419 b Fz(\(51\))257 1891 y(where)36 b Fw(H)622 1906 y Fq(j)658 1891 y Fz(\()6 b(\026)-55 b Fw(z)741 1906 y Fq(j)778 1891 y Fz(\))34 b(corresp)s(onds)h(to)f(the)h(case)g (of)e(the)i(regular)f(radiator)f(\()p Fw(p)2961 1906 y Fq(j)2998 1891 y Fz(\()p Fw(z)t Fz(\))e(=)f Fw(\016)t Fz(\()p Fw(z)e Fs(\000)263 2011 y Fz(\026)-55 b Fw(z)302 2026 y Fq(j)339 2011 y Fz(\))38 b(\).)58 b(In)38 b(transparen)m(t)h (media)f(the)g(second)h(factor,)g(exp)q(\()p Fs(\000)p Fw(\033)2615 1975 y Fu(2)2611 2036 y Fq(j)2655 2011 y Fw(=)p Fz(8)p Fw(Z)2827 1975 y Fu(2)2820 2036 y Fq(j)2865 2011 y Fz(\),)g(pro)m(vides)h(the)257 2132 y(n)m(umerical)34 b(stabilit)m(y)g(of)e(the)h(calculations)h(\(see,)g(e.g.,)f(relations)g (\(56\))f(and)h(\(58\)\).)257 2420 y Fo(2.4)136 b(Multiple)45 b(stac)l(ks)h(of)f(plates)257 2605 y Fz(In)c(practice,)i(XTR)d(is)h (generated)g(b)m(y)g(sp)s(ecial)g(radiators)f(consisting)i(of)d(a)h (stac)m(k)i(of)257 2725 y(foils)36 b(\(plastics)h(lik)m(e)g(p)s (olyprop)m(ylene)g(or)e(m)m(ylar\))h(with)h(gas)e(gaps)h(or)f(a)g(foam) g(\(\014g.)g(3\).)257 2846 y(Supp)s(ose)40 b(w)m(e)f(ha)m(v)m(e)h Fw(n)e Fz(foils)h(of)f(the)g(\014rst)h(medium)h(\(index)f(1\))f(with)h (thic)m(knesses)j Fw(a)3425 2861 y Fq(k)3468 2846 y Fz(,)257 2966 y Fw(k)32 b Fz(=)d(1)p Fw(;)17 b(:::;)g(n)33 b Fz(in)m(tersp)s (ersed)j(with)e(gas)f(gaps)g(of)g(the)h(second)g(medium)h(\(index)g (2\))e(with)257 3087 y(thic)m(knesses)k Fw(b)799 3102 y Fq(k)842 3087 y Fz(,)c Fw(k)e Fz(=)d(1)p Fw(;)17 b(:::;)g(n)22 b Fs(\000)h Fz(1.)44 b(The)34 b(relativistic)g(c)m(harge)f(serially)i (in)m(tersects)g(the)257 3207 y(sequence)h(of)c(gaps:)1010 3427 y Fw(a)1061 3442 y Fu(1)1101 3427 y Fw(;)17 b(b)1186 3442 y Fu(1)1226 3427 y Fw(;)g(a)1321 3442 y Fu(2)1360 3427 y Fw(;)g(b)1445 3442 y Fu(2)1485 3427 y Fw(;)g(:)g(:)g(:)32 b(;)17 b(b)1761 3442 y Fq(k)r Ft(\000)p Fu(1)1894 3427 y Fw(;)g(a)1989 3442 y Fq(k)2032 3427 y Fw(;)g(b)2117 3442 y Fq(k)2159 3427 y Fw(;)g(:)g(:)g(:)33 b(;)17 b(b)2436 3442 y Fq(n)p Ft(\000)p Fu(1)2573 3427 y Fw(;)g(a)2668 3442 y Fq(n)2715 3427 y Fw(:)580 b Fz(\(52\))257 3647 y(Calculations)30 b(similar)f(to)f(those)g(considered)j(in)d(the)h (previous)g(sections)h(result)f(in)g(the)257 3767 y(follo)m(wing)43 b(expression)i(for)d(the)h(energy-angle)g(distribution)g(of)f(the)h (emitted)h(XTR)257 3888 y(energy:)962 4101 y Fw(d)1013 4065 y Fu(2)1052 4101 y Fw(U)1128 4065 y Fu(\()p Fq(n)p Fu(\))p 934 4146 324 4 v 934 4237 a Fp(~)p Fw(d!)19 b(d\022)1218 4208 y Fu(2)1295 4168 y Fz(=)1409 4101 y Fw(\013)p 1409 4146 63 4 v 1411 4237 a(\031)1498 4058 y Fr(\020)1568 4101 y Fw(!)p 1568 4146 65 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4071 y(particle)37 b(tra)5 b(jectory)37 b(\(p)s(oin)m(t)f Fw(g)1415 4086 y Fu(1)1454 4071 y Fz(\))71 b Fy(inside)i Fz(the)37 b(radiator)e(\(G4En)m(v)m(elop) s(e\))i(with)g(ener-)257 4192 y(gies)30 b(and)f(p)s(olar)g(angles)g (relativ)m(e)i(to)d Fv(v)j Fz(randomly)f(selected)h(from)e(the)g (corresp)s(onding)257 4312 y(tables)j(of)e(the)g(in)m(tegral)h(energy)h (and)e(angular)g(distributions.)45 b(Note)30 b(that)h(eac)m(h)g(XTR)257 4433 y(photon)36 b(is)h(not)e(mo)m(v)m(ed)j(to)e(the)g(radiator)f (output,)i(but)f(instead)h(is)g(considered)h(then)257 4553 y(as)c(a)g(secondary)h(particle)f(under)h(general)68 b Fi(Geant4)k Fz(trac)m(king)35 b(and)e(hence)j(will)e(b)s(e)257 4673 y(in)m(v)m(olv)m(ed)44 b(in)e(the)f(radiator)g(in)g(its)h (particular)f(pro)s(cesses)j(lik)m(e)e(photoabsorption)g(or)257 4794 y(Compton)34 b(scattering.)404 4914 y(The)45 b(implemen)m(tation)h (describ)s(ed)g(ab)s(o)m(v)m(e)g(w)m(as)f(compared)g(with)g(exp)s (erimen)m(tal)257 5034 y(data.)e(Histograms)30 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(Giani,)i(V.)e(Gric)m(hine)h(et)f(al.,)i Fy(Comput.)g(Phys.)f(Commun.) 458 1681 y(132)34 b(\(2000\))g(241.)257 1884 y Fz([17])49 b(J.)27 b(Ap)s(ostolakis,)j(S.)d(Giani,)h(V.)g(Gric)m(hine)g(et)f(al.,) i Fy(Nucl.)h(Instr.)g(and)f(Meth.)h(A453)458 2004 y(\(2000\))k(597.)257 2208 y Fz([18])49 b(Y.)34 b(W)-8 b(atase,)34 b(Y.)g(Suzuki,)h(Y.)f (Kurihara)f(et)h(al.,)g Fy(Nucl.)i(Instr.)f(and)g(Meth.)h(A248)458 2328 y(\(1986\))e(379.)257 2532 y Fz([19])49 b(G.D.)35 b(Barr,)h(R.)f(Carosi,)i(L.)f(Gatignon)f(et)h(al.,)g Fy(Nucl.)i(Instr.)f(and)g(Meth.)h(A294)458 2652 y(\(1990\))c(465.)257 2985 y Fx(Figure)53 b(Captions)127 3204 y Fv(Fig.)d(1.)f Fz(Diagram)28 b(of)f(a)h(c)m(harged)h(particle)g(crossing)g(the)g (single)g(in)m(terface)g(b)s(et)m(w)m(een)h(t)m(w)m(o)501 3324 y(absorbing)j(media.)127 3528 y Fv(Fig.)50 b(2.)f Fz(Diagram)c(of)g(a)g(c)m(harged)h(particle)g(crossing)h(the)e(most)h (general)g(XTR)g(radi-)501 3648 y(ator)c(consisting)i(of)e Fw(n)g Fz(media)h(and)g Fw(n)29 b Fs(\000)g 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V 1037 3245 V 1084 3008 a Fa(q)30 b(q)h(q)p 1202 3245 V 1249 3245 V 1297 3245 V 1344 3245 V 1391 3245 V 1438 3245 V 1486 3245 V 1533 3245 V 1580 3245 V 1627 3245 V 1816 1898 a FA(2)1772 1919 y Fa(\016\015)1772 1787 y(\017)o(\014)1823 3262 y FA(~)1793 3292 y Fg(H)1890 3310 y Ff(2)2218 1898 y FA(3)2173 1919 y Fa(\016\015)2173 1787 y(\017\014)2194 3292 y Fg(H)2291 3310 y Ff(3)2501 1898 y FA(4)2457 1919 y Fa(\016\015)2457 1787 y(\017)o(\014)2478 3292 y Fg(H)2575 3310 y Ff(4)2832 1898 y FA(3)2787 1919 y Fa(\016\015)2787 1787 y(\017\014)2809 3292 y Fg(H)2906 3310 y Ff(3)3116 1898 y FA(2)3071 1919 y Fa(\016\015)3071 1787 y(\017\014)p 2100 3245 8 1418 v 2383 3245 V 2714 3245 V 2998 3245 V 1729 4091 a Fv(Fig.)51 b(4)1828 5848 y Fz(20)p eop %%Page: 21 22 21 21 bop 963 1827 1897 4 v 963 3245 4 1418 v 2856 3245 V 963 3248 1897 4 v 1557 1709 a Fo(G4En)l(v)l(elop)t(e)p 494 2538 2835 4 v 3246 2536 a Fe(-)375 2489 y FA(Inciden)m(t)375 2630 y(particle)87 b Fg(p)907 2648 y Ff(1)2903 2630 y Fg(p)2962 2648 y Ff(2)3210 2489 y Fo(v)1675 2536 y Fe(\030)1733 2521 y(\030)-83 b(:)1675 2536 y Fa(r)1651 2630 y Fg(g)1707 2648 y Ff(1)p 1084 3008 12 945 v 1131 3008 V 1179 3008 V 1226 3008 V 1273 3008 V 1061 1993 a FA(F)-10 b(oils)1557 2182 y(XTR)38 b(radiator)1793 3008 y Fa(q)30 b(q)g(q)h(q)f(q)p 2501 3008 V 2549 3008 V 2596 3008 V 2643 3008 V 2690 3008 V 1729 4091 a Fv(Fig.)51 b(5)1828 5848 y Fz(21)p eop %%Page: 22 23 22 22 bop 257 4998 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 4252 @rwi 4252 @rhi @setspecial %%BeginDocument: fig6.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1849 1837 306 261 bl 1849 1837 306 261 C 2268 2268 0 0 C /xs 0 def (dE/dx and X-ray TR \(Li/He 300 folis\): 0.9 Xe + 0.1 CH) /Times-Bold 70 stwn (4) /Times-Bold 49 stwn ( , 3 cm \(STP\)) /Times-Bold 70 stwn gsave 1134 2164 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (dE/dx and X-ray TR \(Li/He 300 foils\): 0.9 Xe + 0.1 CH) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 -23 m (4) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( , 3 cm \(STP\)) show gr 1849 1837 306 261 C NC 306 261 m 1837 Y s 340 261 m -34 X s 323 302 m -17 X s 323 342 m -17 X s 323 383 m -17 X s 323 424 m -17 X s 340 465 m -34 X s 323 506 m -17 X s 323 547 m -17 X s 323 587 m -17 X s 323 628 m -17 X s 340 669 m -34 X s 323 710 m -17 X s 323 751 m -17 X s 323 792 m -17 X s 323 832 m -17 X s 340 873 m -34 X s 323 914 m -17 X s 323 955 m -17 X s 323 996 m -17 X s 323 1036 m -17 X s 340 1077 m -34 X s 323 1118 m -17 X s 323 1159 m -17 X s 323 1200 m -17 X s 323 1241 m -17 X s 340 1281 m -34 X s 323 1322 m -17 X s 323 1363 m -17 X s 323 1404 m -17 X s 323 1445 m -17 X s 340 1486 m -34 X s 323 1526 m -17 X s 323 1567 m -17 X s 323 1608 m -17 X s 323 1649 m -17 X s 340 1690 m -34 X s 323 1730 m -17 X s 323 1771 m -17 X s 323 1812 m -17 X s 323 1853 m -17 X s 340 1894 m -34 X s 323 1935 m -17 X s 323 1975 m -17 X s 323 2016 m -17 X s 323 2057 m -17 X s 340 2098 m -34 X s /xs 0 def (0) /Times-Bold 70 stwn gsave 261 237 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (0) show gr /xs 0 def (10) /Times-Bold 70 stwn gsave 261 441 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (10) show gr /xs 0 def (20) /Times-Bold 70 stwn gsave 261 645 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (20) show gr /xs 0 def (30) /Times-Bold 70 stwn gsave 261 849 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (30) show gr /xs 0 def (40) /Times-Bold 70 stwn gsave 261 1053 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (40) show gr /xs 0 def (50) /Times-Bold 70 stwn gsave 261 1258 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (50) show gr /xs 0 def (60) /Times-Bold 70 stwn gsave 261 1462 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (60) show gr /xs 0 def (70) /Times-Bold 70 stwn gsave 261 1666 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (70) show gr /xs 0 def (80) /Times-Bold 70 stwn gsave 261 1870 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (80) show gr /xs 0 def (90) /Times-Bold 70 stwn gsave 261 2074 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (90) show gr 306 261 m 1849 X s 306 295 m -34 Y s 366 278 m -17 Y s 425 278 m -17 Y s 485 278 m -17 Y s 545 278 m -17 Y s 604 295 m -34 Y s 664 278 m -17 Y s 724 278 m -17 Y s 783 278 m -17 Y s 843 278 m -17 Y s 902 295 m -34 Y s 962 278 m -17 Y s 1022 278 m -17 Y s 1081 278 m -17 Y s 1141 278 m -17 Y s 1201 295 m -34 Y s 1260 278 m -17 Y s 1320 278 m -17 Y s 1379 278 m -17 Y s 1439 278 m -17 Y s 1499 295 m -34 Y s 1558 278 m -17 Y s 1618 278 m -17 Y s 1678 278 m -17 Y s 1737 278 m -17 Y s 1797 295 m -34 Y s 1856 278 m -17 Y s 1916 278 m -17 Y s 1976 278 m -17 Y s 2035 278 m -17 Y s 2095 295 m -34 Y s 2095 295 m -34 Y s 2155 278 m -17 Y s /xs 0 def (0) /Times-Bold 70 stwn gsave 306 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (0) show gr /xs 0 def (10) /Times-Bold 70 stwn gsave 604 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (10) show gr /xs 0 def (20) /Times-Bold 70 stwn gsave 902 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (20) show gr /xs 0 def (30) /Times-Bold 70 stwn gsave 1201 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (30) show gr /xs 0 def (40) /Times-Bold 70 stwn gsave 1499 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (40) show gr /xs 0 def (50) /Times-Bold 70 stwn gsave 1797 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (50) show gr /xs 0 def (60) /Times-Bold 70 stwn gsave 2095 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (60) show gr 1849 1837 306 261 C 2268 2268 0 0 C 1849 1837 306 261 C 2268 2268 0 0 C /w 48 def /w2 {w 2 div} def /w3 {w 3 div} def 902 1996 m24 gsave 998 1972 t 0 r 0 0 m /Symbol findfont 70 sf 0 0 m (g) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( = 4x10) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 35 m (3) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( , PAI+TR: 10) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 35 m (3) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( events) show gr 1849 1837 306 261 C 2268 2268 0 0 C 1849 1837 306 261 C 2268 2268 0 0 C 902 1894 m25 gsave 998 1870 t 0 r 0 0 m /Times-Bold findfont 70 sf 0 0 m ( experiment: electron , p = 2 GeV/c) show gr 1849 1837 306 261 C 2268 2268 0 0 C /xs 0 def (Energy Loss \(keV\)) /Times-Bold 70 stwn gsave 2155 100 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (Energy Loss \(keV\)) show gr /xs 0 def (Arbitrary Units) /Times-Bold 70 stwn gsave 102 2098 t 90 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (Arbitrary Units) show gr 1849 1837 306 261 C /w 24 def /w2 {w 2 div} def /w3 {w 3 div} def 306 261 366 261 425 261 485 261 545 261 604 322 664 587 724 812 783 975 843 1098 902 1486 962 1526 1022 1547 1081 1669 1141 1730 1201 1710 1260 1445 1320 1486 1379 996 1439 1322 1499 1179 1558 832 1618 730 1678 771 1737 812 1797 506 1856 649 1916 547 1976 506 2035 424 30 { m24} R 306 261 m 60 X 17 Y 59 X 50 Y 60 X 50 Y 60 X 50 Y 59 X 17 Y 60 X 234 Y 60 X 267 Y 59 X -33 Y 60 X 435 Y 59 X 134 Y 60 X 200 Y 60 X -67 Y 59 X -16 Y 60 X -51 Y 60 X -217 Y 59 X 134 Y 60 X -335 Y 59 X -33 Y 60 X 100 Y 60 X -100 Y 59 X -100 Y 60 X -318 Y 60 X 33 Y 59 X -67 Y 60 X 51 Y 59 X -117 Y 60 X -134 Y 60 X 100 Y 59 X -117 Y 60 X -167 Y s gr gr showpage end %%EndDocument @endspecial 1729 5201 a Fv(Fig.)51 b(6)1828 5848 y Fz(22)p eop %%Page: 23 24 23 23 bop 257 4998 a @beginspecial 0 @llx 0 @lly 567 @urx 567 @ury 4252 @rwi 4252 @rhi @setspecial %%BeginDocument: fig7.eps 80 dict begin /s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def /sw {stringwidth} def /r {rotate} def /rl {roll} def /R {repeat} def /d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def /c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def /cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def /box {m dup 0 exch d exch 0 d 0 exch neg d cl} def /NC{systemdict begin initclip end}def/C{NC box clip newpath}def /bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def /mp {newpath /y exch def /x exch def} def /side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def /mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def /mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def /mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def /m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def /m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 4 {side} repeat cl fill gr} def /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d x w2 sub y w2 add m w w neg d x w2 sub y w2 sub m w w d s} def /m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def /m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def /reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def /nfnam exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne {dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont /FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont /Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def /accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex 201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute 212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex 217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex 221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex 228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex 237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis 244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def /Times-Roman /Times-Roman accvec ReEncode /Times-Italic /Times-Italic accvec ReEncode /Times-Bold /Times-Bold accvec ReEncode /Times-BoldItalic /Times-BoldItalic accvec ReEncode /Helvetica /Helvetica accvec ReEncode /Helvetica-Oblique /Helvetica-Oblique accvec ReEncode /Helvetica-Bold /Helvetica-Bold accvec ReEncode /Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode /Courier /Courier accvec ReEncode /Courier-Oblique /Courier-Oblique accvec ReEncode /Courier-Bold /Courier-Bold accvec ReEncode /Courier-BoldOblique /Courier-BoldOblique accvec ReEncode /oshow {gsave [] 0 sd true charpath stroke gr} def /stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf text sw pop xs add /xs exch def} def /stwb { /fs exch def /fn exch def /nbas exch def /textf exch def textf length /tlen exch def nbas tlen gt {/nbas tlen def} if fn findfont fs sf textf dup length nbas sub nbas getinterval sw pop neg xs add /xs exch def} def /accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal 69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral 74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright 79 /greaterequal 80 /braceleft 81 /braceright 82 /radical 83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal 88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus 50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup 55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def /Symbol /Special accspe ReEncode gsave .25 .25 scale gsave 0 0 t black [] 0 sd 1 lw 1849 1837 306 261 bl 1849 1837 306 261 C 2268 2268 0 0 C /xs 0 def (Energy Loss and X-ray TR: 0.3 Xe + 0.55 He + 0.15 CH) /Times-Bold 70 stwn (4) /Times-Bold 49 stwn ( , 5 cm \(STP\)) /Times-Bold 70 stwn gsave 1134 2164 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (Energy Loss and X-ray TR: 0.3 Xe + 0.55 He + 0.15 CH) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 -23 m (4) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( , 5 cm \(STP\)) show gr 1849 1837 306 261 C NC 306 261 m 1837 Y s 340 261 m -34 X s 323 307 m -17 X s 323 353 m -17 X s 323 399 m -17 X s 340 445 m -34 X s 323 490 m -17 X s 323 536 m -17 X s 323 582 m -17 X s 340 628 m -34 X s 323 674 m -17 X s 323 720 m -17 X s 323 766 m -17 X s 340 812 m -34 X s 323 858 m -17 X s 323 904 m -17 X s 323 950 m -17 X s 340 996 m -34 X s 323 1042 m -17 X s 323 1088 m -17 X s 323 1133 m -17 X s 340 1179 m -34 X s 323 1225 m -17 X s 323 1271 m -17 X s 323 1317 m -17 X s 340 1363 m -34 X s 323 1409 m -17 X s 323 1455 m -17 X s 323 1501 m -17 X s 340 1547 m -34 X s 323 1593 m -17 X s 323 1639 m -17 X s 323 1685 m -17 X s 340 1730 m -34 X s 323 1776 m -17 X s 323 1822 m -17 X s 323 1868 m -17 X s 340 1914 m -34 X s 323 1960 m -17 X s 323 2006 m -17 X s 323 2052 m -17 X s 340 2098 m -34 X s /xs 0 def (0) /Times-Bold 70 stwn gsave 261 237 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (0) show gr /xs 0 def (20) /Times-Bold 70 stwn gsave 261 421 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (20) show gr /xs 0 def (40) /Times-Bold 70 stwn gsave 261 604 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (40) show gr /xs 0 def (60) /Times-Bold 70 stwn gsave 261 788 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (60) show gr /xs 0 def (80) /Times-Bold 70 stwn gsave 261 972 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (80) show gr /xs 0 def (100) /Times-Bold 70 stwn gsave 261 1156 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (100) show gr /xs 0 def (120) /Times-Bold 70 stwn gsave 261 1339 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (120) show gr /xs 0 def (140) /Times-Bold 70 stwn gsave 261 1523 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (140) show gr /xs 0 def (160) /Times-Bold 70 stwn gsave 261 1707 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (160) show gr /xs 0 def (180) /Times-Bold 70 stwn gsave 261 1890 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (180) show gr /xs 0 def (200) /Times-Bold 70 stwn gsave 261 2074 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (200) show gr 306 261 m 1849 X s 306 295 m -34 Y s 399 278 m -17 Y s 491 278 m -17 Y s 583 278 m -17 Y s 676 295 m -34 Y s 768 278 m -17 Y s 861 278 m -17 Y s 953 278 m -17 Y s 1046 295 m -34 Y s 1138 278 m -17 Y s 1230 278 m -17 Y s 1323 278 m -17 Y s 1415 295 m -34 Y s 1508 278 m -17 Y s 1600 278 m -17 Y s 1692 278 m -17 Y s 1785 295 m -34 Y s 1877 278 m -17 Y s 1970 278 m -17 Y s 2062 278 m -17 Y s 2155 295 m -34 Y s /xs 0 def (0) /Times-Bold 70 stwn gsave 306 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (0) show gr /xs 0 def (20) /Times-Bold 70 stwn gsave 676 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (20) show gr /xs 0 def (40) /Times-Bold 70 stwn gsave 1046 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (40) show gr /xs 0 def (60) /Times-Bold 70 stwn gsave 1415 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (60) show gr /xs 0 def (80) /Times-Bold 70 stwn gsave 1785 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (80) show gr /xs 0 def (100) /Times-Bold 70 stwn gsave 2155 191 t 0 r xs 2 div neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (100) show gr 1849 1837 306 261 C 2268 2268 0 0 C 1849 1837 306 261 C 2268 2268 0 0 C /w 48 def /w2 {w 2 div} def /w3 {w 3 div} def 676 2006 m24 gsave 771 1982 t 0 r 0 0 m /Symbol findfont 70 sf 0 0 m (g) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( = 6.0x10) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 35 m (4) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( , PAI+TR: 5x10) show currentpoint pop 0 t /Times-Bold findfont 49 sf 0 35 m (3) show currentpoint pop 0 t /Times-Bold findfont 70 sf 0 0 m ( events) show gr 1849 1837 306 261 C 2268 2268 0 0 C 1849 1837 306 261 C 2268 2268 0 0 C 676 1914 m25 gsave 771 1890 t 0 r 0 0 m /Times-Bold findfont 70 sf 0 0 m ( experiment: electron , p = 30 GeV/c) show gr 1849 1837 306 261 C 2268 2268 0 0 C /xs 0 def (Energy Loss \(keV\)) /Times-Bold 70 stwn gsave 2155 100 t 0 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (Energy Loss \(keV\)) show gr /xs 0 def (Arbitrary Units) /Times-Bold 70 stwn gsave 102 2098 t 90 r xs neg 0 t 0 0 m /Times-Bold findfont 70 sf 0 0 m (Arbitrary Units) show gr 1849 1837 306 261 C /w 24 def /w2 {w 2 div} def /w3 {w 3 div} def 306 261 335 261 363 261 391 261 420 307 448 490 477 527 505 794 534 858 562 876 591 867 619 977 647 1032 676 1161 704 1170 733 1372 761 1336 790 1391 818 1547 846 1501 875 1629 903 1482 932 1685 960 1584 989 1345 1017 1437 1046 1547 1074 1354 1102 1455 1131 1574 1159 1602 1188 1106 1216 1308 1245 1345 1273 1152 1301 1161 1330 1115 1358 968 1387 1023 1415 986 1444 941 1472 885 1501 1032 1529 858 1557 766 1586 931 1614 794 1643 748 1671 656 1700 720 1728 757 1756 702 1785 601 1813 573 1842 693 1870 619 1899 490 1927 490 1956 619 1984 490 2012 481 2041 500 2069 500 2098 362 2126 380 65 { m24} R 306 261 m 10 Y 29 X 10 Y 28 X 31 Y 28 X -10 Y 29 X 20 Y 28 X 123 Y 29 X 123 Y 28 X 164 Y 29 X 31 Y 28 X 41 Y 57 X 184 Y 28 X 41 Y 29 X 103 Y 28 X 184 Y 29 X 11 Y 28 X 102 Y 29 X 113 Y 28 X 133 Y 28 X -72 Y 29 X 82 Y 28 X -20 Y 29 X 113 Y 28 X -113 Y 29 X 41 Y 28 X 72 Y 29 X -328 Y 28 X 164 Y 28 X -93 Y 29 X 41 Y 28 X -41 Y 29 X -133 Y 28 X -92 Y 29 X 41 Y 28 X -297 Y 28 X 184 Y 29 X -20 Y 28 X -93 Y 29 X -92 Y 28 X -41 Y 29 X 123 Y 28 X -164 Y 29 X -123 Y 28 X 41 Y 28 X -41 Y 29 X -82 Y 28 X -92 Y 29 X -31 Y 28 X 31 Y 29 X -72 Y 28 X -41 Y 57 X 62 Y 28 X -82 Y 29 X -21 Y 28 X 21 Y 29 X -51 Y 28 X -21 Y 29 X 21 Y 28 X -31 Y 28 X 10 Y 29 X -72 Y 28 X 21 Y 29 X -31 Y 28 X -10 Y 29 X -82 Y s gr gr showpage end %%EndDocument @endspecial 1729 5201 a Fv(Fig.)51 b(7)1828 5848 y Fz(23)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF