Content-Type: multipart/mixed; boundary="-------------9910180938353" This is a multi-part message in MIME format. ---------------9910180938353 Content-Type: text/plain; name="99-387.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="99-387.comments" 5 pages ---------------9910180938353 Content-Type: text/plain; name="99-387.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="99-387.keywords" Stochastic Mechanics , Cosmology ---------------9910180938353 Content-Type: application/postscript; name="calodos.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="calodos.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: calodos.dvi %%Pages: 5 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMR12 CMTI12 CMBX9 CMR9 CMMI9 CMBX12 CMR10 CMTI10 %%+ CMMI10 CMSY10 CMR7 CMMI7 CMSY7 CMEX10 CMR5 CMBX10 %%EndComments %DVIPSCommandLine: dvips calodos %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 1999.10.18:1615 %%BeginProcSet: texc.pro %! 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All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 48 /zero put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4a71813d2ffb26 445026f89b4787516ecd1afc78f8bd19e91e9ccc9402e8c36d2449c1ff850a8a f61165aac3fe931332dd28e261b91b05edd18f44ea7d58a8f35fe88493b64aad 6bfac3a0136215fc2f4ca8e91d70c5010e6f4013e6d63b44f6fb00afdbd7cdb4 5ec5b1d9736f45cefc8a0124b815987cebd81bbe0d44dedb2d5ef37923b3d551 abb6a1cefca7868fc7bf3814ef7d7b6b1ae6e869cb77aa29e3d90b12b0dc3ff6 ec945922b5899bbf2f12e92731486d2ef1230c528bf8d7e0ae09ad7632a38966 5963de49d1ef3d65bc483e4a577b927c940f5e121169ba52f6576c85793e5fd7 7f5863c488e55bdefd5d8b2514795533aabbc12e7f51816c7e1484f1c441aa9a 66a5dc77158e79cd6692d299b95e8058b35e771a6972d2b5eb1cd6d2bb8e835d 361a6eac0c90c906aea1cd75c4412a1339dc1439f93e59917311bf20af4f2bc8 bba5a4626f75f28a47d4595c37f4019df480d9385975159142618e22e964f019 d88125210e2ef21d65baf500adf802297b24eebbf4e93c617a613f856bd0d45f e17a9480980ef83950bdb8ebf208c895ebc4a7132f0765b7c19a332ebbf8a3c9 ab65063a42e19ca9d43dec3de7aba46b9a5d24fb93d615c0a1726ab7e31c378e ab77150858535b91362ab0e2b968dee1c539964126d937f9d4980ccefa92bc81 b054996a65a13995c9c9d819ff05511cfc89cbfe67447c940405001d61be633b b771eff383fc6977ec06af30f981504260de7b9ec97359974734f495ac073935 fb30e3700679092ef5d971b6b2da0e15960f2391fa6b63c33e7f56b4a9b86951 1d3686a5e8e613a69a0add8b8c73b127ddcd397a48d785079e786d24b31bb502 0850037529377f7d1ed88ee66c914ca0969c9964657a4b2c3a0b788c4a330634 17e97a6dc53b44a2e5182bccd0ca71ec38d9a5ef4378a058b3acaf5e45677da6 b4dade0302f18b856b1f1fdbab7ad89f20835fb322b3b134fb399d9c8e2e3fb3 4d816a256f2862953fe111621e3cf6952d64719e8d0ddf71752279f5e2e5fa37 4227b4e7197985a2409739cfe4f9dafe0ae2e9a5378e9e1a0d2d42d2172f41fe 82390580a5793f867852599448ea194c4394bace73ce8fd9f890154aabb03342 b38112b5afd257bdd1459dd98578b1bc344ca75f591b6634d5fc6ccbe365b2f2 d2ec5106cdbc47a352f2e710146304dd83fb5a249bde87e1d5da5fb63ead418e cbd1c1f59aa27cb7aa26bece10b8a7ef2ce6415adbaf6613f04ec2c09512c82b 4ec54cb7018152ce9dcf87 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 90 /integraldisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fbb931da9ee6ade43de532d888f4d9aeca091a3d519db29d75b39638cef311 18b48922e370c79b2116c83f3ecb6246727017925aef0eab15a07d4edb4f5b2d 305c33c131e689249a309e8d36ac215efa2f8304cf8bccab0d996f85057ab377 ecd152a26df26887969eef8b255d02e96433461e098ac2d6914b4dabce4b5468 f5d983f7b8cde42c15febeaf2a35cca6b3abb0168b31e854738d575e1b48d556 f10897f6875bed99baaefa48e056afef774b4822e9c3d7e3a86de070c0b04b60 c6eaf195f487837339365cff950d9cdb765a0a85e62c384c931e81d3e26be712 421a0dc5f2ea3395697e7ea9887314a75b8a27b0a6427c2211be64862ff24241 58509c342beeca51c3be3b35208c45cf60a21b42fa67dfe3ace55b42f55eec02 78162046293e5700c2717ad61c9a9bba4272d5ff0ed5db9d68d77c00889e7bdc 663125dff688b01157beefc83f1bcdd88ae1e09f32e15f78d513e25590604553 65395690f351bba8d1db4f0139aac2b345978a2687f05fad99feb50b742ab1c6 127a43df55ae9e054499e729c34e3c97c716f69d2317f2541f8e5520cd125661 9fbcd729e46e596d4164d9dc6c9995c580339202d1dfff8a706c8d2fd61dc60b 5e4552dcf57487adcd25823f2f06697da91b20d49b95d9a7ae7adf994721fca3 68d37f757f5109a5e11f0b4a6f698aed2f3815d1ca22e6e425433077baabb280 ee7f80134985bb09e588b2bd87544ad996a078a4579f6a368feeb96d3ceae9c2 8a39844dbe8807855b40ec27ce7d914c7b1a97ace7f5b077910a355f35009ec0 a007e1b61d0a8eb742ad587bf75d61f03d1d307ee77353e9a454582c638b6da3 40fe66ffbb4189272f10759dbefa81e2537d29a71624329a59990b646cc2b811 f2754c922c92cba416f130ce68c9cc486ec89fb9ab0e26454275e19fd5f47eef 5992e809271722abe02b5f926c1bb76b557b23dbc6352a1e3cbc8f6ee1f76164 aa93ce94a7854275d181a87f4e167063c2b8c4c510e44bdd888cbf41da0d3ad9 226f0f147204b71a155ffc212a70df1bfbaaa83ed16eb088b8c6071e743b1252 f9503cc125e50e40a06e49e480c06c79bbbd0a3991242f2e8f02a5e35ed0c3ea 43abd8d0dcb114322fb82049b209aa5776ac5f8beddf07cbf542c8711b74d5fd 222cf41061afd051506318c0803202fcdef5fd4ac4406ef5e49cbe62b946d519 7711075f814322369c3a1797f6e8d1281c4289d72848220a1f3978e7a1566783 f72c6a22075e5a1e5ce0b9c14ad29775375fc7b85c865b03ef19e56a8deba23f 1d1a3b2297ab92a4cf32a34ab4c5b4ab1c254fb0b8a1eee7177fc2e7c6630bbe 31abec8fda6182387cd0344dd2b99fb91d9c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b873912be368f3f300b584a7c5dcdc5e3f796d62bd191959cd043bc0a0 108ac1860e97e05173d3b979ffeaa815405d9db68a72c102cca8b3becc60437a 946131e0670abd3348ce6dcbd3bdd4797f83472f944778fbeb0a0b93d8a4c1bb 95814c546dbc74544fd3216948863d6435fcbc33cb58a9ba7fec838875ef04fc ae4b62e7f80d98b25dcd109be87bc6aaac0ec53d1b9076b095980272f7a2a83a 4694d2844aa8fc4d7df0a6ae7ebda3217cbbaa6e1039d1aada1efcad0c46e0a9 c773609189ad3544cd020953d9ee8d664cde33fd01e2a23dbfb8c3064270a970 a72c95ce0abbd0e2e4bb6f14ceed933758f6408a0f5cee279b5681db6624b4be 056d56adf4694b9c67cf95921b0734161b42bc15c3764a35bfa34bad7b142f16 78dd87e12ed82ea54b94965ea23f1f6471c5fa0ec6e345cce35edff48834c014 4897c5fe2088292d14093b179e74f647807d4f7a4c2e94cadfd3e5a46e11e4e3 77cabe 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 28 /tau put dup 61 /slash put dup 105 /i put dup 116 /t put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82 ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96 0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0 24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772 0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2 364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba 0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279 617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a387b3 80db88cca083b06f5af70d768d1699826fb12ce12efc2b4c70923e052dbb964f 5fa957c3ce225c0fda64d9b5321ee1ade207c1cc93105096cc73118f4082594c 8ecddeb0d7bfde6f70bc62f10407c26a476ed88be7999d64a15912493829a9de 62c71f5a34fbf5a843e311873cd98817dc9f8a4aeb7e0738b5de10043f5cfea7 14784c4fe6a8366586afac2d60fa6428ed028beeba12c9e1eff4ae6601b7018b b88a67d5347bfe0bc239afbe0bdae0335f4ba056f28606c0071f1aa73d839c67 7cc6d7188aa0049c3f552001e29e6dfe69d81e717541cd0efaa52b9bb8361caa 250286ebf6a485d609d42470fe69b8805b0305f7f7e4ccf692efb8dcbf103671 e4fd13b8fdc88c824528f0a2c2bbb9eec0bddff84e4701613bdc65598cd3612e 1018763030961274319c660fc6d3d519bd3a4760882e3a4666eda9532f0fdc75 6e11c58398ad9a8cae0a678f3ff4ca9df6f4bfa433f77c98af1ac63e3d65b358 e0a09c7bfb49811a3e65fbed167ce9e15e7ef510e4b211f3f40a95773cc5fc76 192ddf85ac5e325086dcd03faf1c89fed4a3844f980046afc9b49c43d8e91fbd 06d363c55df5c96769812e2e708da7b4d35122aa2ab380a1c153ac86b80bd7c1 1dbab79e30827cb782ed485fa497c49a0cf984111330ea468d4291faefd8a5b3 420f8e81993ab6d4b4758bb001404f19b8a157790f3175232ac6807c17d90423 5f5947016e36bbf400f26d4d0f9fc3cf8b3f4a22a6f158dc13bdc6d55047dfea 3295b02bc36bdc825ee376f08c5ec53f75ba09fbbe5fe1f5eb6e0924193b1b8e 300c36b84c5c526882b98b3c8649f1f9c76852925283e26218051a8d6da28ac3 553f9e67b2a785206614acb7379f457af082daa0d75fba39276130b3777616c4 41d0b80ce96d88b9e5decb9290b1aa2361fd96ebe7ae0eec3b88b7414b54a917 c5716ef0045252f617912090c7644244a23914ea8bc9dc0c867ef3aae4f54a52 1964834f87acb312e1d246c0a95257d2bf95cc4cd0366992058fa633d70a14cd 58ab7593df5acfb141279f4e5e26892d88c19c68286097c1675c8ec1f9a6653b 91dd427c79b94c94dc441d44be674e44151bce81d2b328a1fecdf604debf61b2 3b17a331ae513ab0ce749525d5e0f9cb3808bcc6b01498b1de5b95af08b746bd 5e9138765bdae32db880be37 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 108 /l put dup 109 /m put dup 111 /o put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950 93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21 c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644 7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e 13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03 22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56 25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1 c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2 b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e 2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd 6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4 07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331 51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6 0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3 d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1 34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec 015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a 418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e 5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd 977f844d32b43b0e48caed5a4bdabcefe71695d69ca784df986fcee7058ce9dc d17edd3088b13d552d0bf8a20faf877ccd01440eba065cc8c49349a24173b615 aba11076bf84ce79599efebaae5cf7b50ec1d1d1015a3d07665714182f406b8b 790e52280d2cc345352aaf2bb87337494bebf5973f078293d119c2d0644ed1a8 284870d598b541f7e094eeedae2791cc24d47416d50e9cfe9743143ccaf0043b 3fcb3b079ffc1029b9173b920eeb4f2158652873e923cec260716687290c4dcd fd69c6dc79aefb0314fdf43aa6e6d978e5e2c4f4c3c0c36b16b5103e2ed3446a 66387d7b0401d41ef8ba6821a32fc70dd71935ad280ac0d4b1aad88dad249705 50916dfc6415095ed99dbaea487cf613f3ec49872b10bbd4c41911caa6fe69bd f50da2cc176d7205a54112f490a6733f8545c9c9ca8a3efd96cf14c9c08e7e47 e58a1ac77edb95df0b9fbc8416471a09c7a7c5ef361a099b8d348ef046050261 1445ad9eda60db92c9b0fe2dd3cbab01fca2ac0b5a38e24e91e2a5d014de08d1 0441c63e625139ed1f15b6f0c80ebfe82730c90170e37308784dc8b36acbce3f 25a7718bd860d127974e1cb369252fb4796b78bde61d8d4734e893e1dbc21a97 1d8510237c10d03172d84e4338a9cd6196e6f7cb74c66aaa6456ae770e8702d5 7b4c8b9a9c020f5c8b8cdaca096fbb843b6f9574df20eae01c203ac748683643 0736eed65d3925816417e89d5d7c22b9860da633704f24a2aae26f2799398ccf 7105466c75a8f0d77d29276db22d93e9436ddbb7e71e02f653e9a891df35c9dd afdb68e1e5691f693406d1d8c861ad1409a1afba4f831b76148d1da6c9ab8fba 6726bc7a385cfd0e44c19f6c9ab85c16a9ca104ec6f9306dccdd3c6311360b18 8815cc4afa1841b27b781c4740e3e5bc7a8ca1392a4e50995fc460d9ad1aabb2 6b5b0013cf1b98d4c65401c26ebfcd10da89082a4ba346578140b171ff9eb053 dee2a89bb2615b157eedc67ae62f0160fe3eedc207a8a1ee0111a759e7f32de6 c61facc4f6401c19fbaa810ccc8f8e665c20f8193a564c65f3ed0391730df8d6 b205f8f4635b2dbcaa38966ddf56bf9c1ba162c95744a16a51fba9abf6bc5739 f526cfb85051b30d2ca9abf47220310bb1b2d7d53ec836ff831e3883413a5aba 582b4a277b4bfb4e70c0010160c47185c85b896f34ec66024e50bec4dd29908f bafa91e80da9e01d50c8ab15a1530979d14a362890e46acc08f90aa8ec58ba11 886e871ca8b31107be6ff4fbf680474d07a6d419566e407339f10ad48697080b a38c49d5c6629685b022f09953190a6a26cc02ca70335c1536cef1a844e9f95a e1fb16193fcb2a64fcded62a8411b15de7ad62a920fe97021c6aedcde26a7322 c7a546ba615109b502220662cb0c50c7d8aa8a2e1689d2089f7765f08d74fd83 ca85d42f61482f00808def457f1ceb71b9fdb7a428f341a836573c12662d3f92 f24a5a8fdcd411ffbb4c32874a93bc5b26abb97d0d9b864bd142878472ddab44 e5a63bfd5283c72f7447898336eb2921394f373b328c4a32b33ce4685c6b34c8 3f58d5bb37a03e1ad01253d5f575777c798009ae1d806092340a0c61fca23a00 021c22e1e28610fa94c1b347394dfa9e88972af862db9b60ba50a5fe2ab8f348 172956be8a377c87cd784a7a14817dc1ecea19ddf919d347c577c9b380dbd8b3 4add9162faec7c0dcbdaba61c1541df178e864ff00d0621e77e67874f02ee74f 5b087ff1d955a834270c3ee7013bc45c7ae96e940a993a6897974c6e9485aad2 ba09c1550c410e6036a6230e48c47e310feb7d71e1a1dc67fe986f6752b032c2 9051c7615e0de8ee32e722f86cb07fb6cbb631447a04745ce28ee4c48f27d9b5 200fd694ac16d801ffbc282f29360981d275bb66c9780a768087d7f5c4e5652f fdedd244b10cc7c495ccad5def3181876f300bcef5767e6ca1501153410025b7 cdead4c04afd35f6e85e380b04d6a447cde568eb13502e3fed37eaa9b1e12978 74ceeecce94d79694051a557e26c747f6279c1a9267105ef9240d3814fc947d6 879198ac16646616e24c111ab0e42639fe21ab7d4586777c7c3207eb9c25de30 58b4e06233c554d626c122d41ae53f474f6a5ae7a4855a24bb75475bc24da895 15f74453c80ce89ee4e9df2f32732271db51c462646b87f6ca07e22cf58f231a 6107f9abb862cbbba73e0b5c34ae01f24971bc7881e24cf1550f40289910f6c4 72893984ef33f690ad01703e974adac618da1375cc90649134008a85908f2148 b92d6ea6d8963758d3ce2b3f4e05d27cb5f32cd5639edb021d499802d9e6b9b8 6b72c7aa8d456f5a01375762380d043732cc5ca497b82b905e3a01d76686c3f9 f6ac4b6fe50d2db0da0e26ef9f06f87d7efeb4ce085d4e3c6a5b03b86a67528b c62a0a56722ac2b8c797570632f4c4d195906f523c0ec6ac7d397234580cb82a b6ff0e33aad6430e26c23140b6fec41796f192c44d06cdc6c9fecb1360e83992 0e14ce6bcb946273b249f0af0c3d7ba81de349ebe97c1d822db99314a100925e 405d107c5b58ad9e8f854c21b190ebb13bca452c770ad7f044ddb3021856277e c6b58b328b42b78d703969f6cabadaf1bab2743008827179404b018dfc011797 e53e886e7d11c01954c48555290b8c55f249759a9aeaa8505fa46db2e6e62285 b7780fb689a9604474f62d8c7c0ee8598d2cdf0847968ca8ba76286322d735d8 3cf56799981b0399737e3286bad632a9e307546c93af78cbee23b822fa9aa6e2 f0c799e75aa4fc9d9192b01ac472abfdaedd4dd2afef508b66aea39bf98988e3 36cfd8416ddfd44c909eb2a9f2449a2da5d4086959e359ccb53ce7ae7b3ca7ee 3e584a22dc64f103ddfd8ee98471527eeaf126a40a0dea515f29b3490896badd 64f83e6f44f486e54b6effa0335447e5b3335f2156a79923703f31bcab81ba5f fdfdb15968360407d07f4368594f606b9bccb45832107bdbc6436614010eb7ae 58628665a2f4df8319ac3eb07a2790f08dd9717c6f1288517418213f2367cec4 611cd1532818a97c067e018ad556d52075ee8ae3429075413d6d3467dc6dee40 33ae9c4a2107570e04be8797794657064af5c44c408ee3fac0c732d6506ab7ec a5faf06d323a0f2d5a33c2caafbf78eb299ceb3c48718b8f04605b41ec8dd0fa a67181e6cb2b25f48395c91591af1213924610a74e3e6c5f80fb379a58221faf acafe6ab859e0ce2df3fa721fca6f1bcea47137f026231c5a2e7da2b71fd68aa a1b72e3bdda7ff27b6d652185e936c62ac70bc9426b3db43ff9ffea6aabe25c9 a3e7abeb1b550481a0e18cc43125d22f0ec99c1362a5baf7569576d36ac41484 eb8c250f97e76ee1333d227ecb52bdadb2ab9a5d6852fffc312f44aaf1b3f386 e03df2e981593ba4a0f4a94ae3e8da8e20e55b844e45b8cb2ac8b29ef1d52d34 1a834bb6adb428e23e15b20c9d845967404548334a8080ceaaed88440f7cba7c b114ef2aeaac29360ed9ff8c0b6af3acd10afb19b942d078874808e38f19ad0a c5413bd7ef0fcd74f7d65da1af2b6b98c7c234b72238ca5b40fe980bdc88cd8e ed9229f4e484131d3f48e531881801180d4a95d3b69aab5f28f7d96fe80c1bf2 ab3d32dfe5191a4251b0064280f754785d6eb8ef51f0d32fe3b53bc8c09f8ce1 245d38fcd271e189d7dbd48379922a6cc09cae6503011d7d6a8052f8fa84f15f 0e8d6631b493918615dfddcdcd99e7fcd03caa47663587936e5f4fd9587e928b 657c31334cd6156bb3ab311f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 17 /equivalence put dup 25 /approxequal put dup 39 /similarequal put dup 54 /negationslash put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c430bd45049e0e5328687f735c6b7e17a89e94cca971f78b83e3d108947a4 87ed95c40ebfbd0ebe6733ee7d9d44a18cd571d46f60c324914764632431af3e d51afe360bf4c8e35cdf6d373669c6390fe44674ea6cb433098f1b2f4557fd73 b821ad12d2190c24a6903c0c41055a7acd8fce0568139c5f851b2a80ff4d624a 38ff7138a122699fc05a8e04b6336e7ce34550f87e040c9acc0ddd395813b1a8 c01493d6f58b71707bb7c5279a82e96b0efa325d9f85f6d91986bb6d530dc592 f4070fec0ef87d2688b7e4ad628771aebc417d9aa4dbaa01156b6ee53a7a383c eeae16e869e5b698cf2ac025fbf8cc506310d12cbba09275290e4b0f610b5f79 db7dffb2907be797979f8c868527583be937e2ba54cc0e69fd19091a03d1e0aa fe98d8f27fe958a79d5bd0fb4fb83b393e366ee33e11f80a5ffed70846b75f24 1fd18090b9dd031d906c5f1aa11dd425777a153c613403b4388c40a84c90903f 73e0067395344b0ffea948447a6650e765532dc30dd84a543a567e4464cd5391 711ab480d1c3b3da5dab5de8ff204ebd94092f19eb1e9e276ec1fa5c07f6c7a0 342a0eb4f7edea73893ced5b9e1272c5f50eb2d70349b3c8b5a83b17163bd024 bfdd288ee4122569d13a3000f77eedacdc4e0a07738f1999c2f9b258e9ab065f 0bd3bf88a12c9823c7d0ed9229e9f22cff9b14549e1a46372e8a81f2634cdfba 323ecfdba096bd8762571e8d34e0536551ebbb591a9205b38b1c90a6173d51c3 1ebe0a965b0efebdb141734899b40246828c76e6c89a975bed52b2f2945d1e7a 816bd239f23c2bd7aadc5e09ee745b8e45fc11166e9b57cf51d5f09ca5d4a1e3 fea60f0446cc525da7947f0fc660fb58f60fd01a89fc1cf4b3095ade89222f28 6f094f31e7ff29b101fccc98f011a6e75da0713e79c8812d924964c2cc4c9ff2 b0d9969de0b1d25529555bdb3e5b2cc6db5e6ce67f44c92cd27f894aaa5dc34c 5405492e1c3260c8c253dc6bba27de7aa2972c65fe22910598376983697e8a3a 794d4cf833361f772e1bafaec37073cb20b2d7e7414869b4a2d2930d387709df adb1381ff0469efb8f1208ea996a293c74d295b838ad317a290a4fbf9987a2e8 f8f4b982db9d2af6c7117e253d1cf9ad3d898e9cc017f8ce04e8861c21cc7bd8 1dc26e70487f1d23b0d52303a83149b56dc485cb116a474e86f42fc1819b5e2d 455df04ff100e9b3efc4c819d5d417bdde7484f0638f6a441f1f2ece52411a5d a6d047ffa9e53b4dd3977710bbc75d238a3756a87baa03aafc2907e3bd018b45 64461e89cca4f468fc0089be74b3639a517dd986a75be48b5023b0ae9552d8a9 767072e3cf678cc9de1b947a3aaa17278f3006734a2a18288d4760fcd16163e7 2ccd3d81089c553cfb1eed71cca9a1876a9225e1623d7ea9d0dc7050780352ef 863f97893782f37621adc95355662c7d1bd8 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 28 /tau put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 65 /A put dup 66 /B put dup 68 /D put dup 71 /G put dup 72 /H put dup 77 /M put dup 82 /R put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 107 /k put dup 109 /m put dup 113 /q put dup 114 /r put dup 116 /t put dup 118 /v put dup 119 /w put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /fl put dup 46 /period put dup 65 /A put dup 71 /G put dup 76 /L put dup 80 /P put dup 81 /Q put dup 82 /R put dup 97 /a put dup 99 /c put dup 101 /e put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 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3be603f39589d4cf7678b55ed74a4cb7a2058d2548529a2ecb86e990c4210041 c86c8b28b931aa6cbb171403d2c21bfe85fe6544d71c2497d3e18b6da2449fb3 40353826cdca3d6324f66c38d22021b2274f9aac2ab247f798a374bbcad1c4e9 2876fa8a37be16b277a6a87c7d15f5a6edf10c449f8f61dbf91de9ef9e8d312c 59c254741611c299e8100011896fcea44151fb2f5450853bd45d870088c50e92 c50022671df7b282900d0c60897393dbcc894dc4b22cee1548fc7762367194c8 9ea07ecfa3e5a55bce653ae0baecb93978568a0afed4e531087dcfe7c6ca6132 e91e3f742e0b7aa9279cdf2c2dc8421f7ba9320ab01835806a1517e550377086 60d435a204efee34f5fba448b8a5bda18482b3a0ffa14d54df03b4400d7d539b c811ec0009badfee3a694451bea7f3da1d6314a20abc4beb944d2f59e89eee4a b6f925898d952ff35d2bf26bfcf20feec57dd76e0aa72b6abee506d705a5c678 db05396143575317d2dd0cfc7e069900019f4d95e3a8e734f0ad17d26c5f176c dd84237a649e5da918490d744aa2e6d206e690050b9fe47736cf7b37876ed3c4 bcb210fc509044b73930bc448c021ffb1012b86e5149b50cd84b1c8d2764e32f 54e6b365f17d88aa816565188a820c01a45b0015c6dc7c0dc97589175fc9024d cb557a30712fc707894b307db2a18b8d894473ece63f7b744b375930b33b5878 dc481e96eab1e2d0cfdd84480cce9f79d5119aa5a053f6fb64244a88 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 2 /Theta put dup 3 /Lambda put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 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 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 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 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a8d3825b32dfc5dc2393ab2a5aabadb01315ca207ce4f8f9d11efe0c75f5f33e a2331ca939b68c63ae8957466a1fe607ef39ef941eb41c08def3f1787b3bac89 db0bd988e82157bbeb56d83eaf425f4f31ba7b060d5d9c14acc645ebce6897b9 432ce9b472ae1df2df01098ee2c5ded76992528b01a2f11a01fa256bda565a89 fbebff03f473016ddd389ba1e70b78ef0f6ac336513c8f419f1bc8e6db8ded66 2c9e2944fc43e59369 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 13 /fl 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 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 82 /R put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 108 /l 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 /UniqueID 5000769 def currentdict end currentfile 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % 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 (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 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 104 /h put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a 757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4 ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821 f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89 02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4 30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c 61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f 1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42 483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693 f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68 f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84 ff7fbe77f6ddf9d06fa92b16ecebcbe0370b5cd9d450d0f2906a105cadf93ed0 0abc7fcf2c996e7c15e452006e35390d99b9cfc59925f1444c20d9c3e1fc2910 32cf9fa9d580eac1bc956334da391b870a757c3bee6aa3e005b20988d8587876 3ced20c6edf2ac2b22890e37ff7aedeb0986d85ae05bc84339bf2116df48c5d1 cc888bb33d409b06dd70ffd0618b2080442aac439aeb39c20a87ad74ef10629c f1604db8611e8e4224c5b21ab0c7ebddc77fe9a283b3a8c6a2a9508f6836e3fc 3eae1366b4da4f44cb7a77fd81d278c17775d56cb28b70f18d894bfd1ec1827f fb16b0d4c1a4ce155da066810170fea53e0d24874d641e89b4138ee09c0d9773 3cffbda704ad7e02253bba645663add10235bf3e6409c4ee1ff02f3b22a2b905 770dbdc0075ed2b43daec38c6933acc0f036969f9050db7b21aa259001890655 2281284ec4f19650869d334353174bbfd01938c3f57e0d720a112a7e6aeaf2e0 4d0c4ba46c5e28e9ba22a21c7559d8902ee68716b586bee15d647e379dd3903e f69b98f407228786550d423238f09f36b58e012b9e40fb34b1822fb68994dd33 0acbbb2434d83e2a0410c048cd36e5ea52b277d307db1fc8f3265de7012a5022 af330ef959b5b043c349e94d31e19112d5ae66f2724e76bb98470c948a67421b 7a2c2c67955fa47ab5fdd476d9caa38d88e108f51b36a3d76cf5fdc65c7698a8 6772f361b2f10a867841a54572d1a50d1c1d9440bf0c3b18f5c2672fa1008129 85ffeb6fc22932cd00260ab55a30055148f5eeda089786277e6a2a50053209d1 5b6119189723d27370a8584cd6ef58b950dba939e8a8c869fa105434 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 34 /quotedblright put dup 44 /comma put dup 46 /period put dup 49 /one put dup 67 /C put dup 68 /D put dup 87 /W put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def 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346c85cf820b42e7679cb27781dd2489a1c79112706b20fd6fe8c1de0d1df4e2 034133b0d03c94596cf8efff58bb23b514db103f9a4fbbf8e3a4ae3d87de6503 4a6a90279dace01a5b919a5f66a07cc4d792b903369664d189999f9f272a3441 085bfd6d9f107b00e127b6c0a29fb0d2268bcb2cc498959977fa015bc90aef1b 8c6169278f593f4ae6e59350b26e4a9d58a38e6eafaba6014ab23ca36807e2ad a4952111dcde61aed9352c35969ef202cba3231d679e8567f0b03da87ebea4ca 2ff6b7861927d342dbc5a54a2ea7bb0f5239c295d97314a3e31d9018f1698bd2 fc6506037ccb4f927aa5ec5fb14a7736ab653bb33691241cf3a6f02404e91879 daea7a73206b06afdd39829320c92463be5aa7c331c3c795a8e0432b92372eeb 25e8e1f18ccb302b8183ee761b035d1ceec2336c7d037f701e2b88bbd56cce97 5a16c218a4f342ec4b05922db5074c5eb0f827f776c932d5d2de7ed9d8693318 f0c52e1214e0ccc18d2f46753b34a2e6c75330d20b53ab5b04fcc2dd78d93829 0b6118172c7ff21e598b43c89e55179daf6fc79eba8eeb2ce9031afd7d542a45 75a9812ee053c7d5e579c049278be71ebbf0a2d77a6ee036e89b2136f37716b2 fd56636fb84fe3ce2781969d716bafc98404d48fc18dcfdaf7feff8e49a90907 d243f07b5d665c9a2ac3633e40b877ccd0217991d35bd9b2a3019676db5b6f94 749510c1b342261313eb2f66c7f426e4902b920db9e1713c0bd266d9b0cf11c8 1505a658e8c32c7d08435e5410e012a78a3efc0fc66df9b76c2e5ffe2bc39b0d e7f0600e0a0af8c0d341aba799a47004f0e008093410d95e0822e46789786bbf 501a8d433539f9d04cecfbc9ff0c684744a5d57eca183d707d056956a8bbab99 1bcf62affcf1f1d4c46e7e114d8bd92933ad92152cb42f72eaf58011b28ec970 776059a47f5d7607e28c209cf06b24c5ee7145aa13ad844d582f29c34f5b0986 84255274221cf3661e73c77a6f9d63b96a805061952f05121fdebc9055a6fb56 77f823384490ca1c836c1c7d65aabaeee88415bdfd9f237393cb5b1670d5fa72 fbbf3a4244eb6ad83ea55e0c1be9f24cc7820b62157b4bb1e9afe673b57ee39d e3406a815a6df305bbc66e07527eb96e9def0b65c616368157cf0cc106fb0673 84a3aa4e4d4924149f32e8e60edbc98c51212d8fb4cf4f04353b63c94eba8d65 696475e4779b65bd4978542d1c1ce04f7cfc232381a58e91fdc3bb929b85eeca efc17d0cab8d6150a599036d146fc6ea46cf934f70f0655cffa5ee6758bb6b95 825f14d191a13695d0450eae1da538902dde1758959455a297ccff8d54395ce8 99e12034519b8646ac714bf9221a7796a3ff8545dd7ad80a0fc51bd06efdbdc9 248dd8548b347e165a1634d6d69d055f1a57ecca35a31dd7f5ae9bc4dd4bb675 441707b2c721169c445df2aa78be2d5243504f64a036ef3054b342cf4c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d55fd4dda249cff0b56b9f3aff e9d0de215c02a52a6bc77155ff6b8cba5cd6646ba331254ac58ace650a967d3b 272331b87b6df06d5ab9d80fabe9f9ceac10139b61244814dd9fc295ed42d1b5 cd11c2e4beab318b20f51ca2c2930657e5343ab7bcf0e8870a0d12de4ffacb6c b3fdbdda481c2fcb84408d3d902e9a32070b2af6cd9317a33a42a43857c114b3 f4c3005cef9401f1c2bad3e69150d7145b79f95c9cfaf7a335b277e6435ab374 f6a3e78e124ac1e4615511f743ad65c5d778403a840310ac4902985f107fd33c 0049623e4c496cd353d2ae2a4804110c6a420a38ece5d5b235c5e35886a0987d 284e6110527b653b1b2c68c636ef423536180acadb954843eff4d9a82568a713 b682c574e30f793f093aef755c650e0e7175c2e3138695212d9fea7bd4b5805c a90985b134c6bc15a19afae0bfb3066363ca3e2568c2ac4559a69fc32feb443b 61243b4508b7524d974636855c83c8149d489b68fe18bd497116a953431251df bd09fa1d2ef66c85b997ab2f6b7c6d9d096cb43931379ff9782fa00c5f3cbd06 04265d16891ffc4f66e4a0307765d384c32aa83a4e4f89ac79ef8e76eed08450 e3466fbaf54f85324f0a4f04bd00ccc22d32e4132c51749bea28f112c2051857 423ea203df902ae80224d75efeb59094bdc5f4b6784ebeb01c38c34b695e681e 57a93ae18b657d13770300bde28833c732010ded4c8e79078d17acc3d4b521b1 6f2cac338c4f72e2e07c667227ef142d0273e5b501f24b02e9cad75fe9d18741 b36bbb29c9cd3d46964e00d8ba318912e69a6aa7ccf823c12a9f899264b172dc 4ba703f409dee59ff373e9e7ff2f5f56f29671216ef109b85314e1da17c9679c 2d7ffa3eada3f8b67f92d6dedf04502734e41017bed6852784631ee0b5ec8cff 984214283e540703e33b9c25a43b725e30fc70bd285571a564662d699adc5b3a a741da6ae9e90a0922bf02f690053fe14145e7bdb56a89c7be0563d321d2bb2c 9b50a920873013ba1a0e574d539a7b1d2e1b67492d71319bb807c341bb31c5e0 4d3a319385cc787860ce34c911e3a9ded3a059b8906c17cea75f0e4f2a094e41 35690d97ea76e79765eb9940bdda1791c9e99fb640269b0c2f380c63aeee568c 2e539e180af7d301c5aa085330bda242420a5fe528a9e6985789cd49d807f966 9b72145c59809c2a4495c470b7007d1751a45651033edddb55b484cad6254f1c 62a6c7e4ff123d6bc5683446d1d22cb4d95e94e8d51c90f8b03245c4471f2796 738ef5bc71c155a02d8f22fb937ad5e0859fba27465ba0bd41e06844010f6520 dfcbbe65acebf937f7099d1f5e62e666ed88886f674cf7d3bdd829db734e1351 c5d0dbae95c05d882faa8c6a290bef91d4defebccf65591e5bc4d79edfbd8f25 2261ce5f5b80a3d5b05dd71dd25011d2641c32e793dd1384483a3e297531e05a 5b7d7909b40b8a7b0a10fd9066c696df7cfdc39556da7fe10ca91652f048c399 945acee3e3453bf7ead5b3af2042175b239496f80d501f1b74a0a14cdbee6a87 4399b170911ed99b0a0b37d5c8e6688e78486976affcc8e74bfe52782f3fe838 0de0be783e217274095a39cd23999ff209da182ee2a846ba6843ef561135237f 34205db4e4bfc08f357f206aaa37175bd03c30c3dbb7f955109d225a93b4ae47 88ceede6a57e38371db28e19a163556d4afa3a0d5cdc029984dec1e4be531aec bcb6ffc0985a0e3491b438b1603c0e63b49ffd9e0c1bb1a7a6a5e1640baa2297 9fd7c136b1cba76e92be354c4df0682496c15bbdfa0296c99a18ba60a3aa3ad9 701071fe4990e15a230a23d456724d59966096c9b96c0e90e660157789c04675 314f2f098963e8f78aa888db00167a021af4a4b7243c1104b3a2480df077ecc5 7d41a49fa79d927709c777008adb58f5ed959f25ab6e125a2fb15af35eff32ad 42cc36ea6428cbcb074eb0d6c09de44f5dcd4baf74a680c3d1f26231bd956b20 385d23b2c68a1619fe2441af6eabbf203c339af755063771d42b4c9fcfdf1859 84b013ce91b074112a866b5a42a31a50a163940470d04cdd3239c3145e6953c4 a023ff958542a63cb6494edf4e8827113fd1835608aeda65faf500450eebd22f 19ec5c3032dd2161b6d92551d07fc4f104ad2a85e455da9032b156adf5bf74ee cb875b4d2e9e93400a24c4908539d8fccc0c2488a6f1fd9f38293d24d9c5d0bc 64f0d077fc97496444436cc5a53e7e396c16aeee0ed40a0652fbd7f3759904e0 6e80612d8cb804f9a72a3a76641173415dc07fc79bf8ced1eea521e0a1adeacc 939906f1a234e36c526e75261273c5b3ccac65480f8dfa9c35b8a6232f7ccdfb 073a8e6b113ad610c0419e9a57b5528ad42e2b578377fa4effbf855d553b7b2f f7cff7ebcb05925f8150930c42355e5124b8a8e20ebd0bdd2815e9966f03d143 5117c5a138e8287e1e2e5c07af239d2ed22d9913bc5d8e69af710d5612cec7fd 9c 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 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 56 /eight put dup 57 /nine put dup 64 /at put dup 65 /A put dup 67 /C put dup 68 /D put dup 73 /I put dup 76 /L put dup 77 /M put dup 83 /S put dup 85 /U put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36e555668d9578b338402f8c259f6813b0b71e6cbd95e19c20ced8495 2559e47577e612a4d94de3c1b4c6c41a6a3fa9e2313457242de74c7e4c0d722b 3e224d18baa726369542682e9459b951b2ac638494880c42be4e2175a3c067e5 945bfc1a05d3de8c3e8ab97f80ab6000e1f78fc258b85d3c84b038d7d0f5be85 0d43fe03e26cdfbb41c36d14cb552e8447ca678efea1d275e85503123a2263b1 4077587683de69a8f5a88d666172668411d0d0fed3e037ee468627207505dbb3 59cfdc5d7f526fca5416d741073284f5dd2471e09f5916f4bff1a90eea4d1283 7731f6a36e5ea695f4efc3bf5669b7f60ab606df5819149c0c8a4817f06dc172 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3970a575be883409157e229b33d27f707c7f17af4579b04e148c2b73831373be b2f869ef191537864b1d615cb1afc653f582b0df61e171d99cda67641b24ae8b c69b765446e721cbc0b3780b133f8efa46426936062e354641811a4321767698 c61e06a5f185b7848cb884df44b9069a169bad17acb225b6586f932af3bcb16d 9304bbfe65a08237b933c4b5b30520141afdb683574220e1f6e0cb7147b9234f 9792d4c1c69ab0408455d8cf787636c180ff3b2211548fd96425d7d7255f9012 6b7e9ba978ce7a5de77718ea3f6942cd3b5eeab10e353dcb84b345765e715d62 41dc82facef8a28d81c48088d973e38df400c4b475e62c8583a7a92b36759c44 c1c86c415e6086aae6702b2b78f51d9fb5ee52e723ed3bfec1124a98f5f200cc ff8e2dcfd4eaa4427e0cc7519ec2195a305f3a444e01731e5a986c67f0633974 8915851d8b9bf308ee38f905ad663ad11b3e7a353bd6542b958c7f313d7707ba 2467c11bd30f08782987cb3cccb4b0f1cb7a5c13676e06a5ba5470cdad2773cc 27842fca406ff97a04a8b7f7d3c6885e5a43eb82d8064c57ebc63634b5eb38e4 13c2cb1cc8880df9e6bcd16615eab1a4777c5a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 47 /slash put dup 48 /zero put dup 49 /one put dup 53 /five put dup 57 /nine put dup 71 /G put dup 97 /a put dup 101 /e put dup 105 /i put dup 112 /p put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204a520640fd7c4d05e35ea5486f a43d0e970787203855daccb1ed0b16325828b13b7c767a1a58c87902f0546ea5 404440fa6526975783c2d7a9572b8e5d5176bac598b8960609f49016aebf3763 89c1adfe6a1ffc0c53b3acd9d168ec3a278fd4f1d9b085dc2df701346c9d0887 3d230a161692b42a45bb5da343b4edd839dd60685a59aaa49fc65cd8e2ad2a9c 5cab953495172a1a9f40d5f38e922443a519dd96f667201a408bd1d89e35f4ab 98e2f68c3366efc14b5afe1018d9c845d808d4f8e07ea8168518a171ab4d6e21 70eeac099eb7ef46eb9781384da1fac3b3133bb718bc80082eaea88759745188 f266b31d0c7e791d633f16ed94e05517a32163e74cbd96dc5db066f2a5313d6d 7f09465608cb404613e0f058073af000e5bdfafbbf9da0c0d5c02a3447f2cdc1 f56481901e34265c26d331ac3f85bdcbc7c51ef9eddf2b9c189c5253f8e74282 d6f053d7d183ae17ea175e5ebc401e67d21a9fea139cbbf3bb1358c713a75843 b39a69aa2b1a7b975f53ff22d1dc3bdf7acd17afa1da21568310c68241b31d3d 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964e68df6be4e2fd8d03f8896d552725384f1fbc6156c840b8879eea4b1a031f b6d6a6c48365e30c64042bf855bcdf0060a3aca8561dc515b65927654bd69c20 f20e97e70702cee39c25c897c3bb86dd95d74166f705fe1872f6d552e7f937af 15e68c58f8d02faa05efe033a59f3c58cb13e1b80952ca84db5c0df5287a1ab8 3688286ec3adf91b03c9828651b3f87aba22f6241524ba555d5ac202a58999b6 d628e8bfec5a05ca127c1e038943806dc3050715892b57413db5c26cf444f41c e028ce29e1e9dbb5f54c807fa352c5b64b8b169e6c94fdffaeb978886a57c239 236635e4542e2352d11bc8f86ef2e1d3be23d6ef2adf618b1a6f73f584718f6d b0945434f77ed6e0b8102e53a1c7b15fa6689a8338ca29f015e68a20d315dc7e 6d17a72ba6b5a3a285072c1321b59c7a13489d8ee4564fb639a4cbf22c9ed9ab cffe7458a448fc33d280dd420b743471fcbfc700d2bc17f26097e5ec2dd8ff46 01c1d7e403c378bbd98f3ecbec06c89f5951c07dba8f2aee192fef6f284fb8b1 959852495588061d1bff1baf6dd7cfb53a3b1de1a205721b4bab73065a025688 b0f91ee071643f0e2a186a3fe147d349e59a053fc7fef107385cef038f4edaf2 bb03cc387b05aed95eecf35f611292e0843c35f777e1b9618fe929e0e7fd9af8 93d1b8d5a812b8f3228f48a5bfa6b34741d3b5884508949c99f221f273fadde0 c52bc2bb28cec179b11dace375ba8ab75c5f9da3cac16a57abe6dfd52e1317c5 bd3b62aa560ac354520ca637a583a43ebc62b2d94ead945bf32a6f2b8693f2e3 06952664c690456b95d28a998336dd066442853057a6cfa1de8b25dfaddc42dd 27d291b0aef3c191f311f5e84559e66282a58ff4416f2637b7dfdd25a980fbfe 06c92e0ef5660bb0ddce817583e3d3998af94999a09b7fb6b49ad0c05137f12c a14d7ea2a981a620d5a816c32f26d214f1743bf5ae1e45dcb572ec4be0a0fb51 14e70de0aadc8ff110c9fcd8ad550b393a30bfafc6f5f12ef13f20f027d0b1bd f2b7ea56d4f0a957561a54ffd5f2cb29cf6cc3aea4ff9fa17c75212bff0dab00 8f676852f1984a0694fb2b1e07d8520b838febe6fa2e936ab538223976639f87 fd9da679eb9e27b2a977f6ee64b0748037ea1b4751a7d82676077140c32f02b8 ab3523dae5390134339336a7fa483a033225f091c8cb37a10693ee4f8976e1bd 5de77fb84f7511ee129549c5b4e68d51ec0960a8571523d1c3a6f785594ece27 abef69d50dfaf723a6b41ae29a9e954a3f1e0cf04ea8c79f910121f43d224503 635ac2b7dcf178437765799aaeac24da6ffd28f7101e878796b09b52e2a5c652 4c9c6fc25e677b5c718cfd5b89c54dd5cb45686bb040248214064ee866428e44 8a5c638d3643b3226ac654293741e7104c7ce358d2ba9b25b0796417a001fbd8 a1d2d3a6ef7e9e1d45a2d6b23a2f149e265a764a1d6d6022f11adaf2d4f38e70 696008451812341abff50b455791c63d310a12a7305a589458ce9a1f86909b9b 9a37a0e181c252910ca1a199a73c40f7b747479542447311fccb2c466b39331c 12de774c110e56d06922115976b8f3441ed30aa32467aff94e3c973b01eb9bc9 fd86c26334eadde2ed4ca02de092d789b7322b27d7375ef4748349ada7d1d2c6 7e70dbc4f305bc1a48fdbd3d2a4d7157fa3a91f774770e1ddd13738f43c3a80e 91934ca7d06257139fe5656d31516da9abb8aa461c40ff56fe4765c800a44a50 2cdf0d1ffc39cc0a59af07534519ef8609fbf68d4e0e8a8171a7ab0d3f4e0abb 6d843e59549f7f39df13a333637d19047a4bfed228a8c8c0e94eddf79edc7fc8 245030d693edc89413f13cda21c3ff370c8b5643bc3387807b586adc9bc7f3df a3c8ec8532b87507fa3ca30a5e14a61f7f26f0c5054364d77cc63b9e5c3c1583 93a5ba1c7d7354298ca8bfc1fff7432ee3228bf9e0afacc399551acb03955e86 847537cdb16ac40bc6301b125adfb8e287fa90e2cf25567e9b1b5a56dc09ad19 10dc22f06d3f4377bcf1263064ba6cdbc29cc3122731e6e384e9aebab8f07b43 f8f8ac2adde9cfcac73f48a5b41d7f101b8a2bf6f7b665917d2f5757ac00a7ac 51b9cac6832278580485019fda89860f475a249c439752904a9dd61493c7e1e7 720b5d41a6f2ea4b026aeb24dea56adb0fd9d2cbcc0239ba3504f6654fb0c1f1 d6aee81e732bed48a35658210072e87a0d1982528f923b532c1b6ed484a7213c 71e3468d9bcdbf9a9066bdf65f2f133cd074186f012becb27a29f6e7890d1cd7 de55f3b2cafdd84ca637d4471fb5e03371737ed281ecaa32beb21c71edd0018b 2f762a592edf0c5b1b8583856996bd21d165de286b5226ea6cff58519323422b c89b39b8faa952207990270c3154db1b04e8f7f13155866ce996b9aed2034da1 2110416594ebc5df2234b462ccba149c3fc6f3a5461e0952a8a4e377ab0c2840 35e5ba4f1dad10389e2a2a59cadbde9830135160dca128782495bd34342b040a e778e33bda9accafd2c0fde8f35c6e6e488e6229c92b7f4b233582d02070d2dd 801f3f02036fbaf6265392e32837d21aecee6533dcf97ed5418d98a9f3c6c838 77fc6bed8d8612fb7259cb 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 79 /O put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be356c29c3aec91ef17f5d31183b1e489f1fa 559a6693fbdd04d4f7e99886d8cb7cca13d4aa9ceb34a708af22e69ccef0e504 c3997075243585edf60b6447c8d01cffb04b6e3ddbaa7da5891286861322a795 e9d990fd56af2f5c2b35801a0b07874e4ac3170481d232e150443253c92a8b05 513d4a4154a99d91f629ccd30376500f5d16aaa9b203bad6350e4b19424c0e33 75f2949bc1927a6f6221252f8a96618e646aa1b0810753c98becc26b37837775 24bca72b818d314074c1c91f4e1f4148d3d703d12d179ee6970bd55d04aa9a9d 97f63f2c7dbd129ec2ed3ba5f8080270ea5854ea165dbcc061e2f47f1aaf0997 2ac9a689a2a9620b91b53f6b5092884372f5f7afca495f331138d85a97c5bb83 d8072dc88010fc89108b60bc06d4f93c722e8908d7ce3c1ea3c70e9e65edd769 7db17ce0e012ad37d4030f33d30a73fd655b7a2e572f3378ac933dd75082f2f1 68702be19bc60cef6bd5f0ada180d21408c04b7f7db9b6dbaefe09e809a80ddf a5366d10930d3e68ca53e4721ff525853f4c784f2c2c3aa0129a34d9df00debc 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Ff(2)1897 2280 y(em)2003 2259 y Fj(+)g Fh(\027)2132 2231 y Ff(2)2127 2284 y(ob)2211 2085 y Fc(\023)2314 2202 y Fh(:)936 b Fj(\(4\))639 2395 y(Let)34 b(us)f(fo)r(cus,)i(for)e(the)g(sak)n(e)f(of) i(concreteness,)f(on)g(a)g(w)n(ell)g(sp)r(eci\014c)g(radiation,)h(i.e.) 515 2494 y(the)28 b(one)f(corresp)r(onding)f(to)h(th)h(\014rst)f(sp)r (ectral)g(line)h(of)g(h)n(ydrogen.)35 b(W)-7 b(e)28 b(kno)n(w)f(then)h (that)1747 2705 y Fh(\027)1788 2717 y Ff(em)1927 2705 y Fj(=)2061 2649 y Fh(B)p 2052 2686 86 4 v 2052 2762 a(h)2100 2738 y Ff(3)3273 2705 y Fj(\(5\))515 2911 y(where,)i(with)h (standard)f(notation,)g Fh(B)i Fj(=)c(\(3)p Fh(=)p Fj(8\))p Fh(m)2132 2923 y Ff(e)2164 2911 y Fh(e)2203 2881 y Ff(4)2240 2911 y Fh(\031)2290 2881 y Ff(2)2328 2911 y Fj(.)45 b(W)-7 b(e)31 b(denote)f(the)h(v)-5 b(alue)31 b(of)f(\(5\))515 3011 y(with)c(the)g(kno)n(wn)g(v)-5 b(alue)26 b(\(according)e(to)i (Calogero,)e(the)i(kno)n(wn)f(presen)n(t)h(v)-5 b(alue\))26 b(of)g Fh(h)f Fj(b)n(y)515 3111 y Fh(\027)556 3123 y Ff(0)593 3111 y Fj(.)37 b(W)-7 b(e)28 b(write)f Fh(\027)1049 3123 y Ff(ob)1146 3111 y Fj(=)c Fh(\014)t(\027)1326 3123 y Ff(0)1391 3111 y Fj(and)28 b Fh(\027)1594 3123 y Ff(em)1705 3111 y Fj(=)23 b Fh(\026\027)1884 3123 y Ff(0)1921 3111 y Fj(.)639 3210 y(According)28 b(to)i(standard)e(quan)n(tum)h(mec)n (hanics,)g Fh(\027)2300 3222 y Ff(em)2414 3210 y Fj(=)c Fh(\027)2545 3222 y Ff(0)2612 3210 y Fj(\(i.e.)42 b Fh(\026)26 b Fj(=)f(1\))k(and)g(th)n(us)515 3310 y(\(4\))e(reads)1682 3463 y Fh(w)53 b Fj(=)1920 3407 y(1)18 b Fg(\000)g Fh(\014)2114 3376 y Ff(2)p 1920 3444 232 4 v 1920 3520 a Fj(1)g(+)g Fh(\014)2114 3496 y Ff(2)2189 3463 y Fh(:)1061 b Fj(\(6\))639 3646 y(According)38 b(to)h(Calogero)e(conjecture,)k(due)e(to)g(the)h (radiation)d(b)r(eing)i(emitted)h(at)515 3746 y(di\013eren)n(t)35 b(time)g(and)f(th)n(us)h(with)g(a)f(di\013eren)n(t)h(v)-5 b(alue)35 b(of)f Fh(h)p Fj(\()p Fh(t)p Fj(\),)j(w)n(e)e(ha)n(v)n(e)e Fh(\027)2905 3758 y Ff(em)3028 3746 y Fg(6)p Fj(=)i Fh(\027)3169 3758 y Ff(0)3241 3746 y Fj(\(i.e.)515 3845 y Fh(\026)23 b Fg(6)p Fj(=)f(1\))28 b(and)f(th)n(us)h(\(4\))g(reads)1659 3998 y Fh(w)53 b Fj(=)1897 3942 y Fh(\026)1947 3912 y Ff(2)2002 3942 y Fg(\000)18 b Fh(\014)2136 3912 y Ff(2)p 1897 3979 278 4 v 1897 4055 a Fh(\026)1947 4031 y Ff(2)2002 4055 y Fj(+)g Fh(\014)2136 4031 y Ff(2)2212 3998 y Fh(:)1038 b Fj(\(7\))639 4186 y(F)-7 b(or)24 b(the)h(\014rst)f(h)n(ydrogen)f(sp)r (ectral)h(line)h(w)n(e)f(w)n(ould)g(ha)n(v)n(e)f(\(with)i Fh(t)2707 4198 y Ff(0)2769 4186 y Fj(the)g(presen)n(t)f(time,)515 4285 y Fh(t)545 4297 y Ff(em)661 4285 y Fj(the)k(emission)f(time\))1252 4525 y Fh(\027)1293 4537 y Ff(em)1432 4525 y Fj(=)1658 4469 y Fh(B)p 1558 4506 268 4 v 1558 4582 a(h)1606 4558 y Ff(3)1643 4582 y Fj(\()p Fh(t)1705 4594 y Ff(em)1793 4582 y Fj(\))1886 4525 y(=)2086 4469 y Fh(B)p 2011 4506 217 4 v 2011 4582 a(h)2059 4558 y Ff(3)2097 4582 y Fj(\()p Fh(t)2159 4594 y Ff(0)2196 4582 y Fj(\))2266 4408 y Fc(\024)2345 4469 y Fh(h)p Fj(\()p Fh(t)2455 4481 y Ff(0)2493 4469 y Fj(\))p 2320 4506 231 4 v 2320 4582 a Fh(h)p Fj(\()p Fh(t)2430 4594 y Ff(em)2518 4582 y Fj(\))2560 4408 y Fc(\025)2604 4425 y Ff(3)3273 4525 y Fj(\(8\))515 4744 y(and)g(therefore)1124 4969 y Fh(\026)50 b Fj(=)1350 4913 y Fh(\027)5 b Fj(em)p 1350 4950 153 4 v 1368 5026 a Fh(\027)1409 5038 y Ff(ob)1563 4969 y Fj(=)1678 4852 y Fc(\024)1757 4913 y Fh(h)p Fj(\()p Fh(t)1867 4925 y Ff(0)1905 4913 y Fj(\))p 1732 4950 231 4 v 1732 5026 a Fh(h)p Fj(\()p Fh(t)1842 5038 y Ff(em)1930 5026 y Fj(\))1972 4852 y Fc(\025)2016 4869 y Ff(3)2104 4969 y Fj(=)2219 4852 y Fc(\024)2299 4913 y Fh(R)q Fj(\()p Fh(t)2425 4925 y Ff(0)2462 4913 y Fj(\))p 2273 4950 247 4 v 2273 5026 a Fh(R)q Fj(\()p Fh(t)2399 5038 y Ff(em)2487 5026 y Fj(\))2530 4852 y Fc(\025)2573 4869 y Ff(3)p Fe(=)p Ff(2)2747 4969 y Fh(:)503 b Fj(\(9\))1926 5255 y(2)p eop %%Page: 3 3 3 2 bop 639 523 a Fj(In)40 b(the)h(follo)n(wing)e(w)n(e)g(write,)k(for) d(ease)f(of)h(notation,)j Fh(\034)53 b Fj(=)44 b Fh(t)2693 535 y Ff(0)2756 523 y Fg(\000)27 b Fh(t)2878 535 y Ff(em)2966 523 y Fj(,)43 b(and)d(\002)j(=)515 623 y([)p Fh(R)q Fj(\()p Fh(t)664 635 y Ff(0)719 623 y Fg(\000)17 b Fh(\034)9 b Fj(\))p Fh(=R)q Fj(\()p Fh(t)1046 635 y Ff(0)1083 623 y Fj(\)];)28 b(notice)f(that)h(for)e(a)h(uniformly)g(expanding)f(Univ)n (erse)h(\002)g(represen)n(ts)515 722 y(the)h(scale)f(factor)f Fh(a)p Fj(\()p Fh(t)1200 734 y Ff(em)1289 722 y Fj(\),)i(where)f(b)n(y) g(de\014nition)h Fh(a)p Fj(\()p Fh(t)2202 734 y Ff(0)2239 722 y Fj(\))c(=)e(1.)37 b(Th)n(us,)27 b Fh(\026)c Fj(=)g([)p Fh(a)p Fj(\()p Fh(t)3007 734 y Ff(em)3095 722 y Fj(\)])3150 692 y Fd(\000)p Ff(3)p Fe(=)p Ff(2)3307 722 y Fj(.)639 822 y(It)h(should)f(b)r(e)h(noted)f(that)h(the)f(Calogero)e(measuremen) n(t)i(\(7\))g(of)g(the)h(recession)e(sp)r(eed)515 922 y(do)r(es)j(therefore)f(also)g(dep)r(end)i(on)f Fh(\034)35 b Fj(\(whic)n(h)26 b(ob)n(viously)d(dep)r(ends)j(itself)g(on)f(the)g (distance)515 1021 y(of)i(the)h(ob)5 b(ject)28 b(whic)n(h)f(emitted)i 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y Ff(0)1533 1976 y Fj(;)k(the)h(\002)f(de\014ned)h(ab)r(o)n(v)n(e) f(is)g(just)h(\002)23 b(=)g([)p Fh(a)p Fj(\()p Fh(t)2892 1988 y Ff(em)2980 1976 y Fj(\)])3035 1946 y Fd(\000)p Ff(1)3125 1976 y Fj(.)639 2075 y(The)39 b(ev)n(olution)e(of)i Fh(a)p Fj(\()p Fh(t)p Fj(\))g(is)f(go)n(v)n(erned)e(b)n(y)j(the)f (Einstein)h(equations,)h(whic)n(h)f(for)e(a)515 2175 y(homogeneous)26 b(and)h(isotropic)f(matter-dominated)h(Univ)n(erse)g (are)1424 2303 y Fc(\022)1505 2364 y Fj(_)-33 b Fh(a)p 1495 2401 44 4 v 1495 2477 a(a)1549 2303 y Fc(\023)1610 2320 y Ff(2)1698 2420 y Fj(=)1823 2364 y(8)p Fh(\031)s(G\032)p 1823 2401 201 4 v 1902 2477 a Fj(3)2065 2420 y Fg(\000)2190 2364 y Fh(k)p 2172 2401 82 4 v 2172 2477 a(a)2216 2453 y Ff(2)2296 2420 y Fj(+)2402 2364 y(\003)p 2402 2401 58 4 v 2410 2477 a(3)3231 2420 y(\(10\))515 2648 y(where)30 b Fh(\032)g Fj(is)g(the)h(mass)e(densit)n(y)h(of)h(the)f(Univ)n(erse,)g (\003)g(the)h(cosmological)d(constan)n(t,)i(and)515 2747 y Fh(k)g Fj(a)d(parameter)g(equal)g(to)g(\(1,0,-1\))g(for)g(a)g (\(closed,)g(\015at,)h(op)r(en\))g(univ)n(erse.)639 2847 y(W)-7 b(e)30 b(will)g(assume)e(\003)e(=)g(0)j(and)g(consider)f(the)i (\015at)g(case)e Fh(k)h Fj(=)d(0.)42 b(Notice)29 b(that)h Fh(\032)p Fj(\()p Fh(t)p Fj(\))c(=)515 2946 y Fh(\032)558 2958 y Ff(0)595 2946 y Fh(=a)681 2916 y Ff(3)718 2946 y Fj(\()p Fh(t)p Fj(\))34 b([with)g Fh(\032)1107 2958 y Ff(0)1177 2946 y Fg(\021)f Fh(\032)p Fj(\()p Fh(t)1380 2958 y Ff(0)1417 2946 y Fj(\)].)55 b(W)-7 b(riting)34 b Fh(D)1932 2916 y Ff(2)1930 2967 y(0)2002 2946 y Fj(=)f(\(8)p Fh(=)p Fj(3\))p Fh(\031)s(G\032)2448 2958 y Ff(0)2485 2946 y Fj(,)i(\(10\))e(reads)g(then)44 b(_)-33 b Fh(a)p Fj(\()p Fh(t)p Fj(\))33 b(=)515 3046 y Fh(D)584 3058 y Ff(0)621 3046 y Fh(=)663 2975 y Fc(p)p 745 2975 139 4 v 745 3046 a Fh(a)p Fj(\()p Fh(t)p Fj(\))q(,)26 b(whic)n(h)g(is)f (readily)g(solv)n(ed)f(b)n(y)i(separation)e(of)h(v)-5 b(ariables)25 b(to)g(giv)n(e)g(\(the)i Fh(c)3197 3058 y Fe(i)3250 3046 y 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y Fj(=)i(1)24 b Fg(\000)f Fh(D)2400 3357 y Ff(1)2437 3345 y Fh(t)2467 3357 y Ff(0)2540 3345 y Fj(and)36 b(hence)g Fh(a)p Fj(\()p Fh(t)p Fj(\))h(=)g([1)23 b Fg(\000)515 3445 y Fh(D)584 3457 y Ff(1)621 3445 y Fj(\()p Fh(t)683 3457 y Ff(0)739 3445 y Fg(\000)18 b Fh(t)p Fj(\)])907 3414 y Ff(2)p Fe(=)p Ff(3)1011 3445 y Fj(.)37 b(W)-7 b(e)28 b(rewrite)f(this)h(\014nal)g(result)f(as)1438 3642 y Fh(a)p Fj(\()p Fh(t)1544 3654 y Ff(0)1600 3642 y Fg(\000)18 b Fh(\034)9 b Fj(\))52 b(=)e(\()q(1)17 b Fg(\000)i Fh(D)2172 3654 y Ff(1)2208 3642 y Fh(\034)9 b Fj(\))2286 3600 y Ff(2)p Fe(=)p Ff(3)2432 3642 y Fh(;)776 b Fj(\(12\))515 3825 y(with)29 b Fh(D)774 3837 y Ff(1)837 3825 y Fj(=)927 3762 y Fg(p)p 996 3762 238 4 v 63 x Fj(6)p Fh(\031)s(G\032)1196 3837 y Ff(0)1259 3825 y Fj(=)d(3)1392 3752 y Fc(p)p 1474 3752 468 4 v 1474 3825 a Fj(\()p Fh(GM)9 b Fj(\))p Fh(=)p Fj(\(2)p Fh(R)1873 3796 y Ff(3)1872 3847 y(0)1910 3825 y Fj(\),)30 b Fh(M)38 b Fj(the)29 b(total)g(mass)f(of)h(the)h(Univ)n(erse)e(and)515 3924 y Fh(R)578 3936 y Ff(0)643 3924 y Fj(its)f(presen)n(t)g(radius.)639 4024 y(Let)32 b(us)g(no)n(w)f(come)g(bac)n(k)g(to)h(the)g(relation)f(b) r(et)n(w)n(een)h Fh(r)i Fj(and)e(\()p Fh(t)2680 4036 y Ff(0)2739 4024 y Fg(\000)20 b Fh(t)p Fj(\))31 b Fg(\021)e Fh(\034)9 b Fj(.)50 b(This)32 b(is)515 4124 y(giv)n(en)27 b(b)n(y)1590 4163 y Fc(Z)1674 4184 y Fe(t)1699 4192 y Fb(0)1637 4352 y Fe(t)1662 4360 y Fb(0)1694 4352 y Fd(\000)p Fe(\034)1863 4220 y Fh(c)p 1811 4257 139 4 v 1811 4333 a(a)p Fj(\()p Fh(t)p Fj(\))1974 4276 y Fh(dt)50 b Fj(=)h Fh(r)30 b(:)928 b Fj(\(13\))515 4492 y(Using)28 b(\(12\),)h(an)f (elemen)n(tary)f(in)n(tegration)h(giv)n(es)f(\(3)p Fh(c=D)2339 4504 y Ff(1)2375 4492 y Fj(\)[1)19 b Fg(\000)g Fj(\(1)g Fg(\000)g Fh(D)2821 4504 y Ff(1)2857 4492 y Fh(\034)9 b Fj(\))2934 4462 y Ff(1)p Fe(=)p Ff(3)3040 4492 y Fj(])25 b(=)f Fh(r)31 b Fj(and)515 4592 y(therefore)1418 4737 y(\(1)18 b Fg(\000)g Fh(D)1662 4749 y Ff(1)1699 4737 y Fh(\034)9 b Fj(\))52 b(=)1943 4620 y Fc(\022)2004 4737 y Fj(1)18 b Fg(\000)2157 4681 y Fh(D)2226 4693 y Ff(1)p 2157 4718 106 4 v 2171 4794 a Fj(3)p Fh(c)2273 4737 y(r)2312 4620 y Fc(\023)2374 4637 y Ff(3)2453 4737 y Fh(:)755 b Fj(\(14\))1926 5255 y(3)p eop %%Page: 4 4 4 3 bop 515 523 a Fk(4.)60 b(Hubble-Calogero)47 b(relation.)515 705 y Fj(According)28 b(to)h(Hubble)h(la)n(w)e(\(and)i(exp)r(erimen)n (tal)e(observ)-5 b(ations\),)29 b(there)g(is)g(a)f(linear)h(re-)515 805 y(lation)e(b)r(et)n(w)n(een)h(distance)f(of)g(celestial)h(b)r(o)r (dies)f(and)h(their)f(recession)f(sp)r(eed,)1770 985 y Fh(v)1810 997 y Ff(0)1870 985 y Fj(=)d Fh(H)7 b(r)30 b(:)1107 b Fj(\(15\))515 1165 y(Here)33 b Fh(H)41 b Fj(is)34 b(the)h(Hubble)f(constan)n(t)g(\(notice)g(this)g(is)g(constan)n(t)f(in) i(space)e(but,)j(in)e(prin-)515 1265 y(ciple,)e(not)e(in)h(time\),)i Fh(r)g Fj(is)e(measured)f(b)n(y)h(v)-5 b(arious)29 b(means)h(including) h(direct)g(parallaxis)515 1365 y(measuremen)n(ts)38 b(\(as)h(of)g(no)n (w,)j(ev)n(en)d(for)f(quite)i(distan)n(t)f(ob)5 b(jects,)42 b(thanks)d(to)g(satellite)515 1464 y(observ)-5 b(ations\),)28 b(and)h Fh(v)1249 1476 y Ff(0)1316 1464 y Fj(is)g(obtained)h(from)f (red)f(shift)i(measuremen)n(ts)f(in)g(the)h(standard)515 1564 y(\()p Fh(\026)23 b Fj(=)g(1\))d(in)n(terpretation,)h(i.e.)34 b(from)20 b(\(6\).)35 b(Th)n(us,)22 b(in)e(our)g(notation,)h(Hubble)g (la)n(w)f(amoun)n(ts)515 1664 y(to)1514 1796 y Fh(w)1573 1808 y Ff(0)1661 1796 y Fj(=)1786 1739 y(1)e Fg(\000)g Fh(\014)1980 1709 y Ff(2)p 1786 1777 232 4 v 1786 1853 a Fj(1)g(+)g Fh(\014)1980 1829 y Ff(2)2079 1796 y Fj(=)2204 1739 y Fh(H)7 b(r)p 2204 1777 116 4 v 2244 1853 a(c)2357 1796 y(:)851 b Fj(\(16\))639 1988 y(W)-7 b(e)36 b(will)f(write)g Fh(\016)k Fj(=)c Fh(H)7 b(r)r(=c)p Fj(;)39 b(this)c(represen)n(ts)f(a)h (dimensionless)f(unit)i(of)f(distance,)515 2087 y(dep)r(ending)28 b(on)f Fh(t)h Fj(through)f Fh(H)7 b Fj(.)38 b(With)29 b(this)f(\(16\))f(reads)g(simply)h Fh(w)2633 2099 y Ff(0)2694 2087 y Fj(=)23 b Fh(\016)s Fj(.)38 b(Note)28 b(that)g(the)515 2187 y(last)c(relation)f(in)h(\(16\))g(represen)n(ts)f(the)h(actually)f (measured)h(relation.)34 b(F)-7 b(rom)24 b(this)h(w)n(e)e(get)1693 2411 y Fh(\014)1744 2377 y Ff(2)1832 2411 y Fj(=)1957 2355 y(1)18 b Fg(\000)g Fh(\016)p 1957 2392 184 4 v 1957 2468 a Fj(1)g(+)g Fh(\016)2178 2411 y(:)1030 b Fj(\(17\))515 2626 y(Inserting)31 b(this)i(in)n(to)f(\(7\),)i(using)e(\(9\),)i(and)e (recalling)f(that)i(\002)e(=)f Fh(a)p Fj(\()p Fh(t)2741 2638 y Ff(0)2800 2626 y Fg(\000)22 b Fh(\034)9 b Fj(\),)34 b(w)n(e)e(obtain)515 2726 y(the)c(mo)r(di\014cation)f(of)h(Hubble)g(la) n(w)f(implied)h(b)n(y)f(Calogero)e(conjecture:)1255 2955 y Fh(w)1314 2967 y Ff(cal)1450 2955 y Fj(=)1576 2899 y(\(1)18 b(+)g Fh(\016)s Fj(\))h Fg(\000)f Fj([)p Fh(a)p Fj(\()p Fh(t)2054 2911 y Ff(0)2110 2899 y Fg(\000)g Fh(\034)9 b Fj(\)])2293 2868 y Ff(3)2331 2899 y Fj(\(1)18 b Fg(\000)g Fh(\016)s Fj(\))p 1576 2936 1003 4 v 1576 3012 a(\(1)g(+)g Fh(\016)s Fj(\))h(+)f([)p Fh(a)p Fj(\()p Fh(t)2054 3024 y Ff(0)2110 3012 y Fg(\000)g Fh(\034)9 b Fj(\)])2293 2988 y Ff(3)2331 3012 y Fj(\(1)18 b Fg(\000)g Fh(\016)s Fj(\))2616 2955 y Fh(:)592 b Fj(\(18\))639 3179 y(This)28 b(is)g(indep)r(enden)n(t)h(of)g(the)f(mo)r(del)g(w)n(e)g(consider)f (for)h(the)g(ev)n(olution)g(of)g(Univ)n(erse.)515 3279 y(Adopting)c(the)g(mo)r(del)g(considered)f(in)i(the)f(previous)f (section,)h(w)n(e)g(can)f(mak)n(e)h(use)f(of)h(\(12\))515 3379 y(for)29 b Fh(a)p Fj(\()p Fh(t)p Fj(\),)i(and)e(of)h(the)g (relation)f(\(14\))h(in)g(order)e(to)i(express)e(this)i(in)g(terms)g (of)f Fh(\016)s Fj(.)44 b(In)30 b(this)515 3478 y(w)n(a)n(y)-7 b(,)26 b(and)i(with)g Fh(q)e Fj(=)d Fh(D)1270 3490 y Ff(1)1306 3478 y Fh(=)p Fj(\(3)p Fh(H)7 b Fj(\),)28 b(w)n(e)f(obtain) 1295 3712 y Fh(w)1354 3724 y Ff(cal)1491 3712 y Fj(=)1616 3656 y(\(1)18 b(+)h Fh(\016)s Fj(\))f Fg(\000)g Fj(\(1)h Fg(\000)f Fh(q)s(\016)s Fj(\))2253 3625 y Ff(6)2290 3656 y Fj(\(1)g(+)g Fh(\016)s Fj(\))p 1616 3693 922 4 v 1616 3769 a(\(1)g(+)h Fh(\016)s Fj(\))f(+)g(\(1)h Fg(\000)f Fh(q)s(\016)s Fj(\))2253 3745 y Ff(6)2290 3769 y Fj(\(1)g(+)g Fh(\016)s Fj(\))2575 3712 y Fh(:)633 b Fj(\(19\))639 3936 y(This)28 b(can)f(b)r(e)h(expanded)f(in)h Fh(\016)j Fj(around)26 b Fh(\016)h Fj(=)22 b(0)27 b(to)h(giv)n(e)1316 4151 y Fh(w)1375 4163 y Ff(cal)1512 4151 y Fg(\031)50 b Fj(\(1)18 b(+)g(3)p Fh(q)s Fj(\))c Fh(\016)35 b Fj(+)2109 4095 y(3)p 2109 4132 42 4 v 2109 4208 a(2)2160 4151 y Fh(q)2200 4117 y Ff(2)2252 4151 y Fh(\016)2292 4117 y Ff(2)2361 4151 y Fj(+)d Fh(:::)c(:)653 b Fj(\(20\))515 4360 y(In)28 b(terms)f(of)g Fh(v)k Fj(and)d Fh(r)r Fj(,)g(\(19\))f (reads)1240 4593 y Fh(v)54 b Fj(=)c Fh(H)7 b(r)49 b Fj(+)d(3)p Fh(q)s(H)7 b(r)48 b Fj(+)2086 4537 y(3)p Fh(q)2168 4507 y Ff(2)2204 4537 y Fh(H)2280 4507 y Ff(2)p 2086 4574 232 4 v 2163 4650 a Fj(2)p Fh(c)2327 4593 y(r)2366 4559 y Ff(2)2451 4593 y Fj(+)18 b Fh(:::)27 b(:)578 b Fj(\(21\))639 4807 y(With)35 b(the)g(rough)e(estimates)h Fh(M)43 b Fj(=)33 b(4)23 b Fg(\001)g Fj(10)2041 4777 y Ff(54)p Fd(\006)p Ff(8)2195 4807 y Fj(g)q(,)36 b Fh(R)2360 4819 y Ff(0)2431 4807 y Fj(=)e(10)2614 4777 y Ff(28)p Fd(\006)p Ff(2)2768 4807 y Fj(cm)g(\(also)g(used)g(in)515 4907 y([1)o(]\))39 b(w)n(e)g(get)f Fh(q)45 b Fg(\031)c Fj(1)p Fh(:)p Fj(5)25 b Fg(\001)h Fj(10)1409 4876 y Ff(2)p Fd(\006)p Ff(7)1530 4907 y Fj(.)70 b(This)39 b(h)n(uge)f(error)e(bar)i(only)g (allo)n(ws)g(for)g(qualitativ)n(e)515 5006 y(considerations.)1926 5255 y(4)p eop %%Page: 5 5 5 4 bop 515 523 a Fk(5.)60 b(Conclusions.)515 705 y Fj(If)32 b(w)n(e)f(assume)g(the)h(Calogero)d(conjecture)i(\(2\))h(to)f(hold,)i (then)f(radiation)e(from)h(distan)n(t)515 805 y(ob)5 b(jects)34 b(w)n(ould)g(ha)n(v)n(e)g(b)r(een)h(emitted)h(with)f(a)g (di\013eren)n(t)g(v)-5 b(alue)34 b(of)h Fh(h)g Fj(and)f(th)n(us)h(with) g(a)515 904 y(frequency)30 b(di\013eren)n(t)i(from)f(the)g(one)g (usually)g(assumed;)h(in)g(particular,)f(the)g(dominan)n(t)515 1004 y(radiation)e(corresp)r(onding)g(to)i(the)g(\014rst)f(sp)r(ectral) g(line)h(of)g(h)n(ydrogen)e(w)n(ould)h(ha)n(v)n(e)g(b)r(een)515 1103 y(emitted)24 b(with)g(a)f(frequency)g Fh(B)t(=h)1594 1073 y Ff(3)1630 1103 y Fj(\()p Fh(t)p Fj(\))h(higher)f(than)g(the)h (presen)n(t)f(one.)35 b(Therefore,)23 b(when)515 1203 y(w)n(e)32 b(compare)f(the)j(observ)n(ed)d(frequency)h(of)g(radiation)g (from)g(distan)n(t)h(ob)5 b(jects,)33 b(the)g(red)515 1303 y(shift)26 b(w)n(ould)e(b)r(e)i(higher)f(than)g(in)h(the)f (standard)f(in)n(terpretation.)36 b(This)25 b(e\013ect)h(increases,)515 1402 y(more)h(than)g(linearly)-7 b(,)27 b(for)g(greater)f(distances.) 639 1502 y(Th)n(us,)h(Calogero)c(conjecture)j(w)n(ould)g(imply)h(that)g (the)f(existing)g(observ)-5 b(ational)25 b(data)515 1602 y(of)20 b(the)h(relation)f(b)r(et)n(w)n(een)g(red)g(shift)h(and)g (distance,)g(ev)n(en)f(for)g(relativ)n(ely)f(small)i(distances,)515 1701 y(should)27 b(b)r(e)h(rein)n(terpreted)f(as)g(sho)n(wing)f(an)h (accelerating)f(expansion)h(of)g(the)h(Univ)n(erse.)639 1801 y(W)-7 b(e)22 b(stress)e(that)i(this)f(mo)r(di\014cation)g(of)g (Hubble)h(la)n(w)f(could)g(b)r(e)g(inferred)g(in)g(particular)515 1900 y(from)27 b(data)g(for)g(ob)5 b(jects)28 b(at)f(relativ)n(ely)g (small)g(distances,)g(i.e.)37 b(in)28 b(a)g(region)e(where)h(direct)515 2000 y(measuremen)n(t)21 b(of)h(distance)g(\(via)g(parallaxis\))e(is)i (p)r(ossible;)i(this)f(is)f(therefore)f(not)h(sub)5 b(ject)515 2100 y(to)29 b(exp)r(erimen)n(tal)f(uncertainities)h(of)g(the)g(same)g (nature)f(as)h(those)f(necessarily)g(en)n(tering)515 2199 y(the)g(discussion)f(of)g(data)g(referring)f(to)i(extremely)f(far) g(regions)f(of)h(the)h(Univ)n(erse.)639 2299 y(W)-7 b(e)28 b(ha)n(v)n(e)e(considered)g(the)i(simplest)g(mo)r(del)f(of)g(expansion) g(of)g(the)g(Univ)n(erse,)g(corre-)515 2399 y(sp)r(onding)f(to)h (Einstein)f(equations)g(with)h Fh(k)f Fj(=)d(\003)f(=)h(0,)k(and)f (discussed)g(the)h(mo)r(di\014cation)515 2498 y(of)g(Hubble)i(la)n(w)d (implied)j(b)n(y)e(the)h(Calogero)d(conjecture.)515 2773 y Fk(References)556 2955 y Fj([1])41 b(F.)35 b(Calogero,)g(\\Cosmic)e (origin)h(of)h(quan)n(tization",)g Fi(Phys.)j(L)l(ett.)e(A)e Fa(228)g Fj(\(1997\),)685 3054 y(335-346)556 3220 y([2])41 b(E.)35 b(Nelson,)h(\\Deriv)-5 b(ation)34 b(of)g(the)h(Sc)n(hr\177)-42 b(odinger)33 b(equation)h(from)h(Newtonian)f(me-)685 3320 y(c)n(hanics",)27 b Fi(Phys.)k(R)l(ev.)d Fa(150)f Fj(\(1966\),)f(1079-1085)556 3486 y([3])41 b(E.)28 b(Nelson,)f Fi(Quantum)h(\015uctuations)p Fj(,)f(Princeton)g(Univ)n(ersit)n(y)f (Press)g(1985)556 3652 y([4])41 b(F.)27 b(Guerra,)e(\\Structural)g(asp) r(ects)g(of)h(sto)r(c)n(hastic)f(mec)n(hanics)g(and)h(sto)r(c)n(hastic) f(\014eld)685 3752 y(theory",)i Fi(Phys.)k(R)l(ep.)d Fa(77)f Fj(\(1981\),)g(263-312)556 3918 y([5])41 b(G.)34 b(Gaeta,)f(\\Blac)n(k)e(b)r(o)r(dy)j(radiation)d(and)i(quan)n(tum)g (\015uctuations",)g Fi(Phys.)j(L)l(ett.)685 4017 y(A)28 b Fa(155)f Fj(\(1991\),)f(73-74)556 4183 y([6])41 b(C.W.)28 b(Misner,)g(K.S.)f(Thorne)g(and)g(J.A.)h(Wheeler,)g Fi(Gr)l(avitation)p Fj(,)h(F)-7 b(reeman)27 b(1973)1926 5255 y(5)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------9910180938353--