Content-Type: multipart/mixed; boundary="-------------0608200130467" This is a multi-part message in MIME format. ---------------0608200130467 Content-Type: text/plain; name="06-227.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-227.keywords" semiclassical analysis, Aharonov-Bohm effect, magnetic scattering, ---------------0608200130467 Content-Type: application/postscript; name="06tamura.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="06tamura.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.78 p1.4c Copyright 1996-99 ASCII Corp.(www-ptex@ascii.co.jp) %%based on dvipsk 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: 06tamura.dvi %%Pages: 26 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMMI12 CMMIB10 CMR8 CMSY10 CMEX10 CMMI8 %%+ CMSY8 CMSY6 CMR6 CMMI6 CMTI12 LASY10 %%EndComments %DVIPSCommandLine: dvipsk -D600 -t a4size -P dl 06tamura.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.08.18:1200 %%BeginProcSet: texc.pro %! 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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 109 /m put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 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 2dab9cbd14fefba93cba0982a5989b0e523985a0f7647fec9f3dcfe69e633fd3 3a09b82747c4100b2085ac6bf480c5faae5beb0bb312d5b7b6dd2584c51ad5c5 8e0cb9e3f298060cdad0b197c8bfa295d0bf6e90f74cdfab995b43bb9a9e6114 a63a144002e94dcc20087f5f6481a4e6096e384e96b524cc83505af6abeaa6dc 8391a22d3c4b938638b9d722ace9eaf0a31c1454c77c817d11e6a05377a59090 8c1b8fab8be718469cc151faa24b2b96675a3d6043a09090b8d4f7911f0f670e 1f30c042b5887e3c3a8f74837d9cd148ed8de7ae3befc38513f2e3abb464f1ac 5822d90a64659dfae119b0b9d420091739b32dc2673e2f77584d6a7ec60977f3 3a9a6572336aa317a4cf70e7567973bf0a5adc64efb516da6f5a80c5fb2d28b1 bdf132f00c04574ce303e4f2ce8f306157e6c066ec767837d7aedc466f141dde 2ab84715a761cb7ccdf4408fc1180c439c80213d9acf6a840b4ca669f0c0cef6 283c77a68034e80569215896068275e4c87c7a54ddf7d2f683296da26887f615 faf33a221910cc965faea425d5b2d531c5cae4d3bb3be0041e2f391e0354d55d 5cec03bb2fed2a399c7c4223c5ea25518d9b3fed11c1b0885a69f9286e1adcfe 61148fbe8b7788a8622331811f4103bdce931d0942f3f506561574d9a1ac69f0 b936d5 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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 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 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523d8c1e5c02115408a 277a0db93878d14fcdfef599913c0cd614d43dc6a08bb4db21730e0c454740fb 6efc542a3a65c0080b19eb0787edb1b37a32e81102ec944c67e6712ba229a7b0 f9e92271d62dad21f274948d3b192dac77c79729bf891b3baa4f1d47ba7b900e e71b90feb7bf7fcfe223a9a69bc9bd354545708209e94c9684039464f9c333ba 8aa21460a6f38d76a2818e68e399eeacc9b2e5398442d0c0b8098632193a25ca e74eaf66e72fe08cacbb33d3408326fbc47285c7adb308c36f722193b9b79923 6f261acab89287167758fa79e14e17e0c3f3b22bc9ee837b6b18e9ea24b188ee 918fc4e70deddf636926d49802a979db9e1295707f9597f7ebb40e217ba3e96d e0d10a489a4aebdc49ce09dfd486bdaad0f3289eff0e71b7be769a1179b173bb a14a84151fc069850c130ba6ecaa1689a36022ed87031431c8429ce07c43075f 3f05465b2b640034eae993b30fa5686b7a624c6860f65de70469d17302f19922 b4b7f96b22c6561c32e3f723ab82b00ebd9b773d6fcf2c0ff63f1f8c749c7c25 524b08b58bb82e74a0a5fded3ac97701bd3172fca204ada3199c90db6f590f08 ae1b58578550316b02d92cef0f5eaeecc647dfd4dd484ac02853fd98fb9a3d83 6806660a02e3cae87f40e233afa8713aa9653d6edcc650a180f092b72c8d0633 99939f85d8824275004ef023c9b72a1c4ce2a360ab6e276eb4a8300d9dbd6d31 732f3a5d95fa19345d0538a0fa83701431bf816a31add1f09832e26885a79cc6 772858c31cbbb2873786c844bc9a68d67aca310535718ab9764af97e11780ee4 8548cbb6d7a86b952b548e2f29fc4e6c612bd88057bb8d6c143198bb149c68aa c1159a67dd766610d4bc2b5aa0d4b385a285ce947e54cdfe8d941e679dae43ab af8e44d114db80eac854a5b1963081dca7c9b986183f22d51f88efe0 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 /UniqueID 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: 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 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 20 /lessequal put dup 33 /arrowright put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 54 /negationslash put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a424be22b2705a8cb19faec2280d0b32d4cc53b3cb3eac086e8b5692 18a84a317a7fe4b86c9d9946a2673084ca7d8a7be223a2668570c4de07d69b71 dc331ab74e496fdcaf15d803b9f79880522aced10e0fdcfa9680ef375cc28f27 d05be261ffb0153bd79939bbffba536b65a064156a955a6a8a9e8987986bab91 1f10559d195d9a926052283c2d0ea70ed716d1ba208d70291470e35d93181614 632bc22b4ad6415127bf89ee1eae4f1e2b2c9d03df3a741089430846e1069b4c 01040a0407f3a4e97cc27db6c91a1c15b8e99000653bda10df292a50ce4d9dda 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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 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 61 /slash put dup 69 /E put dup 76 /L put dup 78 /N put dup 99 /c put dup 100 /d put dup 101 /e 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 112 /p put dup 115 /s put dup 116 /t put dup 119 /w put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def 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5599df1748c1b3809e22f112366ac1500b9bf273e1d89fe5dc7ea6444a255f17 6f6663e959fb8d27575a743560c5e51c80368e3c92a21b5d12a12acb03be2963 f8903b217d9dbc3a4a78fbab670271a8d2417a424726c57fd46ab4ac2b3d0c2a 29b93222cb3e2ade03da3e8e6256c734464a2bc8b33f4eaf64e9cf3dd37d2c32 6e2a548081a9f326d53e03ea93b954a8976404da281206eecd9274243bf52bdb bfc90a0aa8c24ea6324020afd044014804c84b669767d33ecc9314b9f5090c4a 0b2d6a11e6a5c7177abcc0da8d309b1b45363f5c31d35ea3a51029ddfaf995b2 9b10e036aa7f4c8cbdf8dea600cc76e9b2a38e412b9b850b671f4844c43e2b9c 08164be29b585f158ae402788701e9c4e95ae6444a79aaf2fcd3da55761ccca9 700c822ec0ad8ebc8ba49d6555e2346265ea474b73bea229e7539087ac8bc4b1 a45606c477276b82d244a6bf6846ff163a36d42b30ba65a68cadc1612ca4f135 5e782d9115f3b3b824bc081a0a25e38102c1a220b647e17cb64d169d87d28181 1a9db07adb1c459e18538431d4d4dcc596797b2a9578bd361340678e6bc60bbb a927af85a4fd0d3587c049ae8ab7fc10ea2e6ffd5651941b2f0b9734c9549309 90794b72cd5e5852539ce5d438aa2ece8388f3b447e88a03b9acef4375ab1ada 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a2c55ef1894b484ff446e01daf1cb52bc903c56b7999d11a1ff063b3751d08a0 cef5fd4f4a25c86aafa01cce267d9ee1cd13dce0ba897de829a337e3c5d5054e d537bedb7e24f2177f506acdcbe4d435f8cd03cfa3e131b5190ab25ac1d3f92c 4c00c4b9b175fbf0d5f3b9aa7c00d18befb9cf4a3fe96c9af04a5ab1d21a5d45 2ef34069b52337082950bc5cb7b4a080a9ec695a1e2bdd57463dc422d7977e25 400ed6c4aaf68558502202440ad44143d76009297f8bb80ea6ec702ea4d0c22c a0e9389b0cda142a80673c5b23ea8b1a72f290fd8fc197d0403f9a79dccb0576 d205728ef35e8bb134c0e54057bc43bbcc90c51d11962192a8996149625f947c 75059ce7cc626cb8c5b260d87e33df2c114f0129db0bd2fa95451151dde40243 a54bb1df9cf6dbbf33629b2f94 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 98 /hatwide 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 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c85f7ca0e5c7210206d0a81af268b52fcefca2a6a1a326d3e6a4ee4b83f185b3 e320e38ccabe2deec68463498d1d6db83f17fd42879bd0215bd9e5542023a7e9 a0e9aa06bff422bbe45fa1455cc9ffc0d52f39e948f10fad8b3f6fe2d7f5a3b3 2efb4593778f84ef26004ed4421719701b9ec71976b434c0ea6a707fca43613b 132906b5ca538132d8022e17d4a5fc93c7e957560c7ae271c6b14ea1f7c66756 ba2134f8a370cf4a64794a250e423694876f273306fa91d84691759e97ac8877 2e7218d8e22e258e58e84444a35fce76c36092d3b8067deb5fc5efb388255ff5 931f66d881d19199cc9263249ca34149a6ace889749876fb15250b21a3f97b6a 000960360deb03f7da707d4fee2729c7e54724b8f59e59d42d513155359e1506 3896ae1db35974ac471630a27d02ae525e6008f0c9e2606503903d26bcc55ee8 3d7408baabc7e1d9a747aa18ccb5745e75e680a41106203e0f64f1501a89c2a3 69cad519e0c421e80cbe4b1b8f304a2639ff381741434c728fd9125c306f2c8f b353ccf0a73cef583e28a0b13622c44d33d560ef29669b375a0e91821b633242 7acd1d73cbbc55fd831679b02cde160ce012eeeed971819a852d20e4517a5ab4 4d6db450dbbc50d1bb8fcac863598d8dc6d982c219109b83f409791dbe5f9fce 44f6831f30d4f47a68698137a283b59c14a3fb6208a15ce2a127a59a98bc9030 8ec0f0bbca30482af37bba6ff312da914ce57a2b727e6186349155ecdbe0c051 aa52e7434fa43a2e4a28c8b83753c6a5c2ad3be842e763d97dd22f3ec62ea1fe 4afd6101a50b37553a24db257260e66051a4b3d1b1310c1e9312ef7b464de01e 8197441d1e7fb6239c52a554d7468c8193ce353395d5ecaa5f6f3b2040d1f03a 790d589011cd69fcf2a851914f60a62d715960106a1fc6ee9a2ae8530b662ac6 24f8a5e6701d77926fbf449339f9059999aaaa094b172f13db83476a118c8bfa 113777182a7ac4d6e1bb2be120817d6a6a63b9d9325040b9652942ee3ca55262 75feb20181dcd86d1b85240e052dec7398ecc05e0b9bccaceada6f0b8e464ed2 34ea26b7257e936e684b653f955d01b15b6e5430099047feabd940aec39dc381 12c51bee272c0d63da18f530d9dcfdf159ec2b6c61af6356ee7a8e7faf6b555e 06ea649c2d4c25657975e2c3dd7fb5469aa790c0c2490636f32f73469a72cc1b 3e2b8af7d7f57d15b067628c0a49d100642ebf04031a296d718531d9651a728a eef1097b14b1213b876e5de55129dab00a732b61a63ae2bd3d424d7e67279ebf 42f66ddae4c8c6fce651d8ebfd1a223dde335437b486de02ffdf0b55bd429c44 c76df23102b273175faaaaa64bb3915cef9cdafcb15d58232865dcb774cefb21 704d7f48c990f147dd863735a0469fda4c2c806b1e20eb2c9ed2c1fc9c61e279 8c4f85de16243fc978d77b51350ce5868ff7f2724e1403c22a8f15952c7c74ec 06f4168fad102b04185f36e08e0369416cc1941a498b25d073193b598ccbc0f2 8e9098f69a3b63e8046c79420783880422a4b652b6761f2eb949e7a51bfee296 41f08c430a72ab6b508e5637d7d18ea0f061deb8c84b2d7b02b50f4c4159a8dd b749ccf4509ad2cae64e93ae0881aa3d89db3c4924864a7ecf030f9d01ebb621 1c8c8933728d5bf3a113430dc3c347218d2187d54dc079add83a6a290db33b20 88d9c44319552fbf80fbcdd75d27019686452bac767d588567af9c1fdd814624 0cdecff3c8d166fd984a3789c26429b11c37e2f7d19790945d8b5931c510a7ee b416b471bd88a9b02e3bac798b276dd265c22bb74ac3036667880b5f600b7710 9ecb9680c2510c67dc38d2ccbc6a2b63dcbeaa2ddf5eb0cb48636093a210ae30 4ee73ecd007ab7f77a9d684d112115ebd5a937781a9f15e1ca2b4b88c20792fa ba0490814e6c03317fa2229b108ab90c850a2cc297a575a66c892dd0d9ebe817 f6c618bdfa57567040e4e300dc544608cd2d785a87557e067c4ff0c85fe238b8 f05c9435cbca78b9c94d1c41c4388cfa8b04bb671482fc7dbdb838a5c74fc044 4b85157320674671fe2a588ff734d4f6d5e113ed903dab5e6e4e09b851df2797 0b40d2df7c11a16d711270bd666280fb8a9ca5a65790239e636011d592f4705d 250c18e2e0ee3434584e93edeb36427976b719df0c32d7888b40ef3c43d2ba76 542417e69e5d9e5395343a212ac691e7f53fd1ce5803769d9abcd21b1be2da17 dfc426563212b2ea42196353c7de77c428ce3f02ff43912236c8e1695a432ff3 e6fb3842a22911fa6153308b2fd7a852370e08edd880bed5793f617db097f9ef 8b4fea2d4e8dbb2941cd4bb0cae3e677d4ab3ad5710f23f1ef095f60e3497b77 6d1419550a12e7fa7cbff505857a098996544f05df2941560291 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 10 /circlemultiply put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 27 /propersuperset put dup 28 /lessmuch put dup 29 /greatermuch put dup 33 /arrowright put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 59 /emptyset put dup 68 /D put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put dup 114 /nabla 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 b64c4300276df7b05bc5105fdf3c2d2569e28b3a1e8323541e56e0a3e974ec21 2797bba533bee34d71cce28e4bbdfbfe1b29ebe072da13f89c279845e370ea49 ee3c2aff89a3660d6593c93784c2b9cea8250ee0c653131a25135049351750f4 840fe058c2b4a88c4883bdb30e0f1bb4572426941ae2a9669b6345efca2bcae2 0cee49dc41ee97068ea57ccec63dc7e6f9b49a3c16cdf0cbaa17b5ce26ffedf4 7eed957cb68f3d2f88efce1afe6e5eee48e1035e0d6a88b32d9b6100af8b8d3d 51d9cc24f63b65403640334a3a4b475ab94bee25502920c45a1905434ff91b47 fe997d2a08a37625f3c6d44386ab07c92e84013a574df7fdc11ede5baa8b51af e4781aa9430522a6cfa6adf0eac0102f78f273be9c538ff4ce7228ee444200eb 78550131f6edf6c8e0f1449a40abbfecaef1f43a233ee324e9c9049f98bcb604 2ff7524f3f66df98798a9fc2e471404dde69642eb305588fb582751870207fb5 d19cf8eae4fe8d101d5b133203313eabb94b42284e093d5e50c7a70918b317af 0288dbd0934f008ae64f0bf71f57834332a53502e09b83d96ea0652a7ec549fc a94f269eaa744cdf21e77d2e6bfab8326722c09ee2cf3200a83a25831db6ddf3 262371ee52ab16d85ac2934e18227cccc1d8834387112f067a1eb984e7e0c0da bee859a035ef0199b6f7a9bb7f96c9cf15d77684d393cffc632a50dc2c5e5033 2687cd330f2891b4fc0c0ab14fc9f3949df03000b1637852d8b56ad49d05931f b24883be4804487fa89daea2bb954dd83180cffd6eaa321e4351b15cb2980c28 baf8c2e0543b7de0cfd6c8209f04260c2120a5c7adb9a44aa15176b5984826c1 2cedf632175ade10047541f548f20c785a6506fcaa85fe15ce1fa6c35ebff2b2 dbb8a573b6ae24229beb9f7ed2ceeb2c7c32a5d24f8c8d13212c11d555e8ebe5 c0ec198d809e10809ea7e2073f2437402e58f03f4a06ac159b49278fa7b3f755 b0daff1fe31885b04d131f6235d578ea3b6bb8ea10cbd87105923fe78b221261 e3b0e7587356404dc2e718eed3fdacc3808101540da157f58caf6e2352d63dde df95d2f551636d843e2ee3a1066660c2c4aa01097204711f13ef9e61adc778a9 956e9bbcdd788c534aeb248b5e92015e5e3e317398d52bcb56b8c177f3e62c68 8fa71c111ab137b9866ef89c9f7d7bf785e9ddb11787c448e00cc226da1cf554 52344914b57bca0edd22f14abe272e44a8433938d8d3059f443bfed1a8c16798 fb53709e8320ae2c812f42453d6e5f4517067aec23e251d10bc4aaa887f94491 4278718ac687554f8f5a7f0c0970db255827ce600ecde73a509780ef1626ac2a 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29f2e8bfcd5b9166c92bd8621bba061f84559d8579a4802d6505559d52d4cf73 45ec43344f9526f334c5923f202f5e67a80c16e705f9898751353f497dc19317 d72b468fe97d244ab2d19f7226d483d8a49ba6a0c76ea4309207140b738e9fd2 ca28474e2b1c6be2d550aa2b0e017eee30e126e0aa48c54f4ef3fdedeabf1475 33573daa1184b774675981b89fa4d1d95fa35edca11d02688ed5f7af0d3ceb8a 15fb8019fa2429a0549281e1f12f31b681c233de98709509b1db08962c74cba5 4908777a8c5b4e6e910650afe780fcb69549933b5a923605171bce00d7c47c2b 59bfa29120b37f556b488521176bed95622c63fc24607314258e062d5bc4eeaa eeb1213429a7c2205489f5ca1f45546a8a9fa6e9fd9b165383e8038c5ed3bbe8 ffe3ac9a2358828cde6f60011a1828b754080fc4e00e636d04f374ebb51d0de1 c60043d68962db3cf21eb026a88e76bc64378464b019924009aff11c2589ee85 20e00543dc103489598f7b470163f753e390322a3a6c0dcd5fa6b095e0f40693 c9541402c0cfd4f5b345b1b325118533e263ad6491af052cb883258e2f0e42d6 5c21baba15d4c1e0a93cc676d527b4580c19b9fe6612c7832e1005c09bb3bff8 36492e9f9eb6b9d4c205c656827b5e3fc5347094e3845a9dd6477feca74e5e94 b7a8fc01ef58915c5ccd49b4f5aa9c879fe910374a32451e171736b88ed99fd8 b11d14131238bb5cce4f3c857ffd87ddfcdf7d316173b4f307a186d248a23b32 b13df451a29a470ee6bf8f469f9d703a6f49ded2f30f0d41eaa7c3c6ef4aae1d 114ecd9dd8fe78897cfef6e6222b14af9b7746bd4badafb35bbd323abad961c8 e8cf7f58992f3ed2ffbdc88dc998db6bd68ca4c65afa53809125acab9b7da715 748227e53d7e381a46952a1d23318f6165fea0d1d87003339573a6ac6bce750f 8e538802f465f052 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 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 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0c715fdc87663b6b0b616cf91483d6a0af3fe740c9797345f7a17e884bb84802 85bf2b80763da843e420cb56420327630e6a368546700f378976f0fb9123846e 1d21079491d2d9cc960543f9d6c72df4e37f2758a0968ba337bd1827ef3a3f32 74f865177f459c397f4257d0b13b8d28add50789506ff8ecfec1fb25b9f94153 ea9e2413afd09224d08dd8d23edef93c1cbf59353836cb8b2f0eba72099b12e2 d3ec0c15a000a4385f964dd55aa8eceb3fc83a94f148fd42b5cc5d74948ef095 032adf7c1fc23ad9237642a8366b6cf498b7e969f6d8cfd5dd6ffefe04c0ba9b 08084f74a71d10a38c52fccb6e34df48c35fe7a7d88029c94fe97924b66e4dcb f37419dac39a782174bce8ac854cc1cbdbf626e3098690d0c4cdb71eefb1db56 4d1687a9d428175744ae40819ee7e2f600c255c51f0c3b236f37af8efa4ba478 aa7f2cbc2a8d98ef3a42ef215c8244745bee36e1111f7ccadd45b7ef243c220d f0be03548a81ef5d1e7d181e2f1eae7b4ab627a115f68ff3e50c74fa3e69f057 16804d9b10e058cb759515ccfac880ad301a41c9a524a703833ed2f31785366b c0ef712e17ed8d567a1862a2118c9648c6c69ce024ee53474cc3b6857595a433 8a2ffa848178efd06b203e5a30a8995153cfe3136d6aca83827f29eb114f5085 9ba535be90b27a72331588bcb8a2d3f243b2409221d08b3bf16a3bd05e3000c2 d89b8c21e32f4d29ecf7ea5ec2d0e122411aa1e5b44e6c6796029f2591969993 f3f50037fe8c09f043b2ed83117690af9eba3bb2286aa2d9f43552ab1c5da018 b81260ac9dbe2a601f46ca3e6438aa670e1fe8836e7a1882f130d9e9fc97b19b c41337700c67fdfb443a121e0315c8fa80447c1140b72cb36d7947ed3f51c2fb 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 82 /R put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 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 95ae41ee5c02d6aafaad37141935867a8770fbd9e9ea71e77d3c935c53100566 039eb96ba3821b284b42a0e2ac4ad3181ff029ce1394c31e7694b2e7f47d34c4 190a2ec05ecb43774baeceb345230f68a967b91883e3b184d030c1183d707d1f 2cda85d6de979350243ede31995d77233c2ee1e2b00c53ee0c0fea0c527c706e 114259f991939e5a79d0eb4ef82df7fb0f7434be3b242b840f1c0dee6aa1a98c 20f395e9b93d121bb1e0e420aaaf34ecc31289bea097a288ffbc9dc85f95b752 f4561d817fa7ad9921e00b0ec4cb9ef1385d0cedcd674a9138118ad7a9e02b87 8e71ef2710a5fb847b900e2c917660d161606700958f72c0fcf42ce0752b209f e00ba3aeaf22b19a27480e0e6797cf37b07de77db58375f6c8f45d6755c15e45 eb0be8b1514781b038bfc8d4c0892015ef53dab93e4a2ef508bba2036e30fbda 1dc0803e90cd463d9eeae68b8d3fabdf0b6706f973d20bd3fa27640ef9c15c4d 081e1c458e386fc66c4a21b47b5b447cca02c179b6d9d406f26759fda215e4d2 387a1b6641d6f5454b27be1eee70ef8fb564c06a9df1c191231e30ad5bba8ff3 d22ef750bf75673e9eea30b5175d9670145d5bcd82750ca66d3a9a8290668c7c 658877a6dd0377c31f627de8f23aecc930b7a771437e72ebb36defad48d80524 b63d052d862a83b34e4857135476717d9a53bad61f9ab5a36e530dda5d5cde4c e8cf725c9bfe976d662056b6cf199cfc3ff19b2ccaba7638c2d7bb2e0d5cdf82 eceae11701d69f57da89589869d22f3b3bbfa9be4a1a579421101bf8e867c5ee 318990b8deda6e8fae2be98aff1513db3c512efc4f79bfb789c6a157009c375f d2a2dcb905a15de14202e8309cab410ce78ee34c1e7b76c6237309a7218929fe d30e9c2064ea79b07045404a4f3f7025fd95a80c13 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 16 /zeta put dup 17 /eta put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 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 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 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 90 /Z 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 106 /j put dup 107 /k 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 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 3c3346a1093e6b1036902c1bf42fc317c80abf04020a47b344c36de42f05c490 a0ff44ab6d5249e9f552a8707bb7661e242644814001c8430ebd5e5f0b944ceb 666ee64359d663e355b2f17093a964139d17287f6ca6a024767eba4fe4873855 babe2f07b91560f68300b06dfe27264c163195d446980c35bca0b48f7806626a e72636593a05ba403ce1c0f8b2cea3ecd586e90ac17d034ba4af708304f23131 3459fbbbfb97d4834d0395754ab3f22d6495d2144087d448616fa1ce27bc50d3 46543287e3860d99b433624119bb9920a2113604c0e260fd275ba55e0fd19c83 e19addc3baa1f32f6b7284038845ccee71a3311ddb17b84975f7a984bed7c6ec 2a06e5b335a763d081c6273f86a46632fd9141a27902074fc860df3a2eb59b89 774c767022dbb577e30da128bd7706a43af886d0c256b50fa968ef06776aac0b a5387e9011eb2334c1f42c090f06a1125c207ea6324e87f46414050d88004e87 79bd39f94399c3f1de84b8aae5edc6c3611e8ac49460509e672000d0afd94568 4ab67ff5c6bf2301522775398e192532677826b8cc7821a3a6a2765ee6edd840 b30d07f445681d61f0af1154c46147dfea6f3500f327b50eb05b5007e9e2a5e1 50be9f8fb62b781a609cfc01a10c69b3c05cb9368d5080db5967cb19b03aeb8a 38d5229ecec9a0453df594e38df4004c27fbd2230371a01fa865070b1de53b95 3c9422ec87ff72882f150c22a5d364ca8c1f2723231101b6ac7f8506f5d25825 91b9aa77d893bfea886d0dc93a91c7fccb621382bd048902b63c0591b53cbd3d 2b95364c62b73012b107ad5a263511c3b10e763b41474928dac7821e52611748 8934e12a5defe06e7a9a1a1dbd4b9a988c17c456a6ca96c904d51418fc3ecfe1 a22a641b52fc6f4ebd5e29521062f295ea948b80540962c56970d4e8f943b252 744b117309fbe54cf3bb1b98b596018ccb25adb0e9bf871537218f0e68a0b8ed f44d7a9945756de6af2fefbe4ee8c4b10969bac63044aaf278e8afb2f62b5e29 14314b59065512b2a3d732a0a794ca21f416266ea0642d7089a71125506e607c d97cd1f27841af5559d7e368c67d7c4256bccfa77e1506f8a5c86f10ce5a5bd7 60d3ae386610de29a8b8017680901728c9d6d332105f143750bbfecda2eb9871 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3bbb86ebc9db17ea3a7c132831718428a2b2b1e596dc796fc6f04482765135a1 a8cc45138a53eaa5cdff0195a85fbe87bf10f6d7f0d6f9d9b08d9813efaf6b7d df6695f8f1f754b6965d79296cd38cc6572e0d58077de5912cbdc6cbc93d641a 30b61c38cbf9c8f4f81ec55a9548b0f16a192b5fc4319645198570c062a7574b b841c7503ab1b2658af11ec7d147ec091f8a50c1d85b07a95c5bb1deac5c2ff1 5689598c3f87dda21630097160660a3627b8ed31c20103665ea11fd7b6e338df 89241475baeb5f9515d9 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 12 /fi put dup 46 /period 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 65 /A put dup 70 /F put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 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 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea a29b69d1b622b1f0cffc58291248759607d91150cb0651120970dc9f743bebef 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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 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 6 /Sigma put dup 8 /Phi put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 22 /macron 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 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 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c4f779c8a8f8126eb8d7db952dc353ff234294eb43006d58c31a5734d41e1d61 53fdd5b78f4834c9da038cc5922c0891de1e263d091c99408653aa149f8c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (06tamura.dvi) @start /Fa 205[ 74 50[{ } 1 99.6264 /LASY10 rf /Fb 134[ 47 45 65 45 52 32 40 41 45 50 50 55 80 25 45 1[ 30 50 45 30 45 50 45 45 50 11[ 72 70 55 71 75 66 1[ 72 87 61 75 51 38 72 2[ 66 74 70 1[ 72 6[ 30 4[ 50 50 50 50 50 2[ 30 1[ 30 2[ 40 40 20[ 50 6[ 55 60 11[{ } 54 99.6264 /CMTI12 rf /Fc 146[ 54 1[ 33 25 106[{ } 3 49.8132 /CMMI6 rf /Fd 205[ 30 30 30 4[ 47 43[{ } 4 49.8132 /CMR6 rf /Fe 255[ 48{ } 1 49.8132 /CMSY6 rf /Ff 143[ 59 5[ 20 51[ 0 4[ 71 19 12[ 35 1[ 71 12[ 55 13[ 55 2[ 35 1[ 20 55{ } 12 66.4176 /CMSY8 rf /Fg 135[ 40 51 2[ 25 33 2[ 36 2[ 62 21 37 29 24 41 2[ 33 36 31 20[ 56 1[ 48 6[ 52 7[ 35 1[ 20 24[ 33 44 4[ 31 40 36 41 31 35 42 41 2[ 33 35 31 2[ 36 40 45 11[{ } 35 66.4176 /CMMI8 rf /Fh 157[ 46 7[ 46 106 120 22[ 73 73 14[ 73 73 28[ 61 61 50 50 16[{ } 12 83.022 /CMEX10 rf /Fi 141[ 83 1[ 83 1[ 50 2[ 50 28 39 39 50 50 9[ 66 23[ 77 8[ 50 4[ 0 3[ 66 100 9[ 77 5[ 100 3[ 100 100 77 77 1[ 77 2[ 77 77 9[ 77 1[ 77 77 77 3[ 77 28 77{ } 31 99.6264 /CMSY10 rf /Fj 129[ 35 31[ 35 20 1[ 20 29[ 55 1[ 20 6[ 35 35 35 35 35 4[ 55 1[ 27 27 40[{ } 14 66.4176 /CMR8 rf /Fk 173[ 87 82[{ } 1 99.6264 /CMMIB10 rf /Fl 133[ 45 48 55 70 1[ 56 35 46 44 43 49 47 3[ 51 40 33 56 47 48 45 51 42 1[ 51 6[ 67 1[ 81 92 57 66 57 60 74 77 1[ 75 78 94 66 83 54 1[ 81 77 63 72 81 70 74 73 51 1[ 76 49 76 27 27 18[ 64 4[ 46 61 63 61 2[ 42 55 50 55 43 1[ 59 57 56 1[ 45 48 43 1[ 43 51 55 62 11[{ } 70 99.6264 /CMMI12 rf /Fm 134[ 59 1[ 81 59 62 44 44 46 1[ 62 56 62 93 31 59 1[ 31 62 56 34 51 62 50 62 54 12[ 78 62 84 1[ 77 3[ 67 2[ 42 7[ 85 7[ 56 56 56 56 56 56 56 56 56 56 1[ 31 33[ 62 12[{ } 41 99.6264 /CMBX12 rf /Fn 128[ 49 49 2[ 49 43 51 51 70 51 54 38 38 38 51 54 49 54 81 27 51 30 27 54 49 30 43 54 43 54 49 2[ 49 27 1[ 27 1[ 73 73 100 73 73 70 54 72 1[ 66 76 73 89 61 76 50 35 73 77 64 66 75 70 69 73 3[ 76 1[ 27 27 49 49 49 49 49 49 49 49 49 49 1[ 27 33 27 76 1[ 38 38 17[ 49 7[ 81 54 54 57 2[ 70 1[ 70 2[ 68 1[ 81 61{ } 85 99.6264 /CMR12 rf /Fo 138[ 65 46 46 46 2[ 59 65 98 3[ 33 65 2[ 52 65 2[ 59 12[ 85 10[ 42 88 25[ 33 46[{ } 16 119.552 /CMR12 rf /Fp 134[ 85 1[ 117 2[ 63 64 66 2[ 81 90 134 45 2[ 45 1[ 81 49 74 90 72 90 78 12[ 112 90 5[ 153 6[ 101 4[ 122 65[{ } 22 143.462 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin 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a(\() p Fl(x) p Fi 1963 1818 a(\000) p Fl 2062 1818 a(d) p Fj 2113 1833 a(2) p Fn 2152 1818 a(\)) p Fl(;) p 2332 1818 a(d) p Fg 2383 1833 a(j) p Fn 2446 1818 a(=) p Fl 2550 1818 a(e) p Fg 2595 1833 a(j) p Fl 2632 1818 a(=h;) p Fn 3343 1818 a(\(1.9\)) 0 1990 y(with) p Fl 231 1990 a(\032) p Fj 281 2005 a(1) p Fn 362 1990 a(=) p 480 1990 a([) p Fl(\013) p Fj 569 2005 a(1) p Fl 609 1990 a(=h) p Fn(]) p 782 1990 a(and) p Fl 980 1990 a(\032) p Fj 1030 2005 a(2) p Fn 1112 1990 a(=) p 1230 1990 a([) p Fl(\013) p Fj 1319 2005 a(2) p Fl 1358 1990 a(=h) p Fn(].) p 1586 1990 a(The) p 1795 1990 a(function) p 2185 1990 a(exp) r(\() p Fl(i\020) p Fn 2457 1990 a(\() p Fl(x) p Fn(\)\)) p 2666 1990 a(is) p 2773 1990 a(single) p 3053 1990 a(v) p 3099 1990 a(alued) p 3367 1990 a(o) m(v) m(er) p Fk 0 2111 a(R) p Fj 87 2068 a(2) p Fi 158 2111 a(n) p 238 2111 a(f) p Fl(d) p Fj 339 2126 a(1) p Fl 378 2111 a(;) p 422 2111 a(d) p Fj 473 2126 a(2) p Fi 512 2111 a(g) p Fn(,) p 637 2111 a(and) p Fl 840 2111 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p Fn 1733 2879 a(\() p Fl(h) p Fn(\)) p 1893 2879 a(=) p 1997 2879 a(\() p Fi(\000) p Fl(i) p Fi(r) p 2251 2879 a(\000) p Fl 2350 2879 a(B) p Fg 2424 2894 a(d) p Fn 2465 2879 a(\)) p Fj 2503 2830 a(2) p Fn 3294 2879 a(\(1.10\)) 0 3095 y(with) p Fl 222 3095 a(B) p Fg 296 3110 a(d) p Fn 364 3095 a(=) p Fl 468 3095 a(\014) p Fj 523 3110 a(1) p Fn 562 3095 a(\003\() p Fl(x) p Fi 746 3095 a(\000) p Fl 845 3095 a(d) p Fj 896 3110 a(1) p Fn 935 3095 a(\)) p 996 3095 a(+) p Fl 1094 3095 a(\014) p Fj 1149 3110 a(2) p Fn 1188 3095 a(\003\() p Fl(x) p Fi 1371 3095 a(\000) p Fl 1471 3095 a(d) p Fj 1522 3110 a(2) p Fn 1561 3095 a(\),) p 1659 3095 a(where) p Fl 1940 3095 a(U) p Fn 2016 3095 a(\() p Fl(h) p Fn(\)) p 2177 3095 a(=) p Fl 2280 3095 a(U) p Fj 2346 3110 a(1) p Fn 2386 3095 a(\() p Fl(h) p Fn(\)) p Fl(U) p Fj 2584 3110 a(2) p Fn 2624 3095 a(\() p Fl(h) p Fn(\)) p 2788 3095 a(and) p Fl 522 3311 a(\014) p Fg 577 3326 a(j) p Fn 641 3311 a(=) p Fl 745 3311 a(\014) p Fg 800 3326 a(j) p Fn 837 3311 a(\() p Fl(h) p Fn(\)) p 996 3311 a(=) p Fl 1100 3311 a(\013) p Fg 1162 3326 a(j) p Fl 1198 3311 a(=h) p Fi 1325 3311 a(\000) p Fl 1425 3311 a(\032) p Fg 1475 3326 a(j) p Fn 1540 3311 a(=) p Fl 1643 3311 a(\013) p Fg 1705 3326 a(j) p Fl 1742 3311 a(=h) p Fi 1869 3311 a(\000) p Fn 1968 3311 a([) p Fl(\013) p Fg 2057 3326 a(j) p Fl 2094 3311 a(=h) p Fn(]) p Fl(;) p Fn 2367 3311 a(0) p Fi 2444 3311 a(\024) p Fl 2549 3311 a(\014) p Fj 2604 3326 a(1) p Fl 2643 3311 a(;) p 2720 3311 a(\014) p Fj 2775 3326 a(2) p Fl 2842 3311 a(<) p Fn 2945 3311 a(1) p Fl(:) p Fn 3294 3311 a(\(1.11\)) 0 3527 y(W) p 92 3527 a(e) p 187 3527 a(denote) p 521 3527 a(b) m(y) p Fl 675 3527 a(g) p Fg 722 3542 a(d) p Fn 762 3527 a(\() p Fl(!) p Ff 861 3542 a(\000) p Fi 981 3527 a(!) p Fl 1140 3527 a(!) p Fj 1201 3542 a(+) p Fn 1260 3527 a(;) p Fl 1304 3527 a(E) p Fn 1382 3527 a(\)) p 1472 3527 a(the) p 1659 3527 a(scattering) p 2128 3527 a(amplitude) p 2608 3527 a(at) p 2747 3527 a(energy) p Fl 3077 3527 a(E) p 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a(the) p 303 3397 a(resolv) m(en) m(t) p 713 3397 a(estimate) p Fi 608 3617 a(k) p Fl(s) p Fg 704 3632 a(j) p Fl 740 3617 a(R) p Fn 815 3617 a(\() p Fl(E) p Fn 953 3617 a(+) p Fl 1051 3617 a(i) p Fn(0;) p Fl 1177 3617 a(K) p Fg 1260 3632 a(d) p Fn 1301 3617 a(\)) p Fl(s) p Fg 1385 3632 a(k) p Fi 1427 3617 a(k) p 1505 3617 a(\030) p Fl 1610 3617 a(O) p Fn 1688 3617 a(\() p Fi(j) p Fl(d) p Fi(j) p Ff 1833 3575 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fn 1996 3617 a(\)) p Fl(;) p 2175 3617 a(j) p Fi 2249 3617 a(6) p Fn(=) p Fl 2352 3617 a(k) s(;) p Fi 2548 3617 a(j) p Fl(d) p Fi(j) p 2681 3617 a(!) p 2809 3617 a(1) p Fl(;) p Fn 0 3837 a(established) p 506 3837 a(in) p 626 3837 a(the) p 800 3837 a(previous) p 1195 3837 a(w) m(orks) p 1478 3837 a([8,) p 1619 3837 a(9],) p 1763 3837 a(where) p Fi 2051 3837 a(k) p 2177 3837 a(k) p Fn 2266 3837 a(denotes) p 2625 3837 a(the) p 2799 3837 a(norm) p 3060 3837 a(of) p 3177 3837 a(b) s(ounded) 0 3957 y(op) s(erators) p 431 3957 a(acting) p 724 3957 a(on) p Fl 860 3957 a(L) p Fj 926 3921 a(2) p Fn 998 3957 a(and) p Fl 1188 3957 a(s) p Fg 1234 3972 a(j) p Fn 1270 3957 a(\() p Fl(x) p Fn(\)) p 1434 3957 a(is) p 1532 3957 a(the) p 1700 3957 a(c) m(haracteristic) p 2299 3957 a(function) p 2681 3957 a(of) p Fl 2792 3957 a(S) p Fg 2852 3972 a(j) p Fn 2889 3957 a(.) 146 4127 y(W) p 238 4127 a(e) p 316 4127 a(further) p 645 4127 a(add) p 836 4127 a(three) p 1086 4127 a(remarks) p 1460 4127 a(to) p 1580 4127 a(the) p 1749 4127 a(theorem) p 2130 4127 a(in) p 2245 4127 a(the) p 2415 4127 a(last) p 2601 4127 a(section) p 2928 4127 a(\(section) p 3293 4127 a(6\).) p 3454 4127 a(In) 0 4247 y(Remark) p 376 4247 a(6.1) p 543 4247 a(w) m(e) p 695 4247 a(discuss) p 1031 4247 a(the) p 1208 4247 a(case) p 1424 4247 a(when) p Fl 1688 4247 a(!) p Ff 1749 4262 a(\000) p Fn 1851 4247 a(=) p Fi 1970 4247 a(\006) p Fn 2051 4247 a(^) p Fl 2047 4247 a(e) p Fn 2134 4247 a(or) p Fl 2263 4247 a(!) p Fj 2324 4262 a(+) p Fn 2426 4247 a(=) p Fi 2545 4247 a(\006) p Fn 2626 4247 a(^) p Fl 2622 4247 a(e) p Fn 2668 4247 a(.) p 2766 4247 a(Ev) m(en) p 3020 4247 a(in) p 3143 4247 a(this) p 3342 4247 a(case,) 0 4368 y(w) m(e) p 151 4368 a(can) p 337 4368 a(deriv) m(e) p 631 4368 a(the) p 806 4368 a(asymptotic) p 1315 4368 a(form) m(ula) p 1680 4368 a(with) p 1909 4368 a(only) p 2131 4368 a(the) p 2306 4368 a(leading) p 2649 4368 a(terms,) p 2956 4368 a(pro) m(vided) p 3364 4368 a(that) p Fl 0 4488 a(!) p Ff 61 4503 a(\000) p Fi 151 4488 a(6) p Fn(=) p Fl 259 4488 a(!) p Fj 320 4503 a(+) p Fn 379 4488 a(.) p 456 4488 a(The) p 659 4488 a(obtained) p 1063 4488 a(form) m(ula) p 1423 4488 a(tak) m(es) p 1675 4488 a(a) p 1759 4488 a(di\013eren) m(t) p 2146 4488 a(form.) p 2421 4488 a(The) p 2624 4488 a(second) p 2941 4488 a(term) p 3177 4488 a(seems) p 3457 4488 a(to) 0 4609 y(b) s(e) p 139 4609 a(di\016cult) p 504 4609 a(to) p 630 4609 a(calculate.) p 1094 4609 a(In) p 1223 4609 a(fact,) p 1451 4609 a(the) p 1625 4609 a(second) p 1947 4609 a(term) p 2187 4609 a(con) m(tains) p 2576 4609 a(the) p 2751 4609 a(forw) m(ard) p 3115 4609 a(amplitude) 0 4729 y(suc) m(h) p 220 4729 a(as) p Fl 339 4729 a(f) p Fg 387 4744 a(h) p Fn 432 4729 a(\() t(^) p Fl 470 4729 a(e) p Fi 543 4729 a(!) p Fn 674 4729 a(^) p Fl 670 4729 a(e) q(;) p 760 4729 a(E) p Fn 838 4729 a(;) p Fl 882 4729 a(\013) p Fj 944 4744 a(1) p Fl 983 4729 a(;) p 1027 4729 a(e) p Fj 1072 4744 a(1) p Fn 1111 4729 a(\)) p 1181 4729 a(or) p Fl 1300 4729 a(f) p Fg 1348 4744 a(h) p Fn 1393 4729 a(\() p Fi(\000) p Fn 1512 4729 a(^) p Fl 1508 4729 a(e) p Fi 1581 4729 a(!) p 1709 4729 a(\000) p Fn 1790 4729 a(^) p Fl 1786 4729 a(e;) p 1875 4729 a(E) p Fn 1953 4729 a(;) p Fl 1997 4729 a(\013) p Fj 2059 4744 a(2) p Fl 2098 4729 a(;) p 2142 4729 a(e) p Fj 2187 4744 a(2) p Fn 2227 4729 a(\)) p 2297 4729 a(whic) m(h) p 2576 4729 a(is) p 2674 4729 a(div) m(ergen) m(t) p 3099 4729 a(in) p 3213 4729 a(general.) 0 4849 y(The) p 206 4849 a(other) p 467 4849 a(t) m(w) m(o) p 656 4849 a(remarks) p 1034 4849 a(are) p 1202 4849 a(dev) m(oted) p 1571 4849 a(to) p 1696 4849 a(the) p 1869 4849 a(generalization) p 2498 4849 a(to) p 2623 4849 a(the) p 2797 4849 a(case) p 3009 4849 a(of) p 3125 4849 a(scattering) 0 4970 y(b) m(y) p 140 4970 a(man) m(y) p 411 4970 a(solenoidal) p 866 4970 a(\014elds.) p 1168 4970 a(The) p 1373 4970 a(results) p 1688 4970 a(obtained) p 2094 4970 a(hea) m(vily) p 2432 4970 a(dep) s(end) p 2776 4970 a(on) p 2916 4970 a(the) p 3089 4970 a(lo) s(cation) p 3465 4970 a(of) 0 5090 y(cen) m(ters.) p 385 5090 a(In) p 513 5090 a(particular,) p 998 5090 a(the) p 1172 5090 a(Aharono) m(v{Bohm) p 1927 5090 a(e\013ect) p 2191 5090 a(is) p 2295 5090 a(strongly) p 2679 5090 a(re\015ected) p 3075 5090 a(in) p 3195 5090 a(the) p 3369 5090 a(case) 0 5211 y(that) p 221 5211 a(cen) m(ters) p 560 5211 a(of) p 681 5211 a(solenoidal) p 1141 5211 a(\014elds) p 1401 5211 a(are) p 1574 5211 a(on) p 1719 5211 a(an) p 1864 5211 a(ev) m(en) p 2097 5211 a(line.) p 2349 5211 a(The) p 2559 5211 a(Aharono) m(v{Bohm) p 3318 5211 a(e\013ect) 0 5331 y(problem) p 377 5331 a(in) p 488 5331 a(man) m(y) p 751 5331 a(solenoidal) p 1199 5331 a(\014elds) p 1446 5331 a(has) p 1618 5331 a(also) p 1811 5331 a(b) s(een) p 2039 5331 a(discussed) p 2460 5331 a(in) p 2572 5331 a(the) p 2737 5331 a(ph) m(ysical) p 3109 5331 a(literatures) 0 5451 y(\(see) p 196 5451 a(for) p 345 5451 a(example) p 727 5451 a([2,) p 862 5451 a(12,) p 1019 5451 a(15,) p 1176 5451 a(16]) p 1333 5451 a(and) p 1523 5451 a(references) p 1971 5451 a(there\).) p 2296 5451 a(Among) p 2635 5451 a(these) p 2884 5451 a(w) m(orks,) p 3188 5451 a(Sto) m(vicek) 1747 5753 y(5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop Fn 0 407 a([15,) p 186 407 a(16]) p 345 407 a(has) p 520 407 a(studied) p 864 407 a(a) p 947 407 a(problem) p 1328 407 a(similar) p 1649 407 a(to) p 1770 407 a(that) p 1983 407 a(in) p 2099 407 a(the) p 2268 407 a(presen) m(t) p 2609 407 a(w) m(ork) p 2849 407 a(and) p 3040 407 a(dev) m(elop) s(ed) p 3495 407 a(a) 0 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p Fn 2316 3061 a(exp) q(\() p Fi(\000) p Fl(itK) p Fn 2738 3061 a(\)) p 3343 3061 a(\(2.1\)) 0 3303 y(for) p 149 3303 a(a) p 230 3303 a(b) s(ounded) p 629 3303 a(op) s(erator) p Fl 1022 3303 a(J) p Fn 1117 3303 a(on) p Fl 1253 3303 a(L) p Fj 1319 3267 a(2) p Fn 1359 3303 a(.) 146 3469 y(Let) p Fl 310 3469 a(K) p Fg 393 3484 a(d) p Fn 461 3469 a(=) p 565 3469 a(\() p Fi(\000) p Fl(i) p Fi(r\000) p Fl(B) p Fg 947 3484 a(d) p Fn 989 3469 a(\)) p Fj 1027 3433 a(2) p Fn 1088 3469 a(b) s(e) p 1210 3469 a(de\014ned) p 1535 3469 a(b) m(y) p 1660 3469 a(\(1.10\).) p 1976 3469 a(The) p 2166 3469 a(op) s(erator) p 2548 3469 a(is) p 2635 3469 a(self{adjoin) m(t) p 3142 3469 a(under) p 3408 3469 a(the) 0 3589 y(b) s(oundary) p 438 3589 a(conditions) p 903 3589 a(lim) p Ff 1039 3605 a(j) p Fg(x) p Ff(\000) p Fg(d) p Fc 1190 3615 a(j) p Ff 1222 3605 a(j!) p Fj(0) p Fi 1368 3589 a(j) p Fl(u) p Fn(\() p Fl(x) p Fn(\)) p Fi(j) p Fl 1638 3589 a(<) p Fi 1741 3589 a(1) p Fn(.) p 1911 3589 a(W) p 2003 3589 a(e) p 2078 3589 a(ha) m(v) m(e) p 2301 3589 a(established) p 2800 3589 a(the) p 2966 3589 a(basic) p 3209 3589 a(sp) s(ectral) 0 3710 y(prop) s(erties) p 455 3710 a(of) p Fl 562 3710 a(K) p Fg 645 3725 a(d) p Fn 714 3710 a(in) p 824 3710 a(section) p 1146 3710 a(7) p 1223 3710 a(of) p 1331 3710 a([8].) p 1503 3710 a(According) p 1962 3710 a(to) p 2078 3710 a(the) p 2242 3710 a(results) p 2548 3710 a(there,) p Fl 2821 3710 a(K) p Fg 2904 3725 a(d) p Fn 2973 3710 a(has) p 3143 3710 a(no) p 3275 3710 a(b) s(ound) 0 3830 y(states,) p 306 3830 a(and) p 496 3830 a(there) p 746 3830 a(exists) p 1016 3830 a(the) p 1185 3830 a(b) s(oundary) p 1625 3830 a(v) p 1671 3830 a(alue) p Fl 1878 3830 a(R) p Fn 1953 3830 a(\() p Fl(E) p Fn 2091 3830 a(+) p Fl 2190 3830 a(i) p Fn(0;) p Fl 2316 3830 a(K) p Fg 2399 3845 a(d) p Fn 2439 3830 a(\)) p 2510 3830 a(in) p 2625 3830 a(\(1.14\).) p 2947 3830 a(This) p 3171 3830 a(has) p 3345 3830 a(b) s(een) 0 3951 y(v) m(eri\014ed) p 331 3951 a(b) m(y) p 456 3951 a(use) p 615 3951 a(of) p 715 3951 a(the) p 873 3951 a(comm) m(utator) p 1413 3951 a(metho) s(d) p 1758 3951 a(due) p 1932 3951 a(to) p 2041 3951 a(Mourre) p 2374 3951 a([11].) p 2593 3951 a(Moreo) m(v) m(er) p 3011 3951 a(w) m(e) p 3144 3951 a(can) p 3313 3951 a(pro) m(v) m(e) 0 4071 y(that) p Fl 222 4071 a(W) p Ff 314 4086 a(\006) p Fn 373 4071 a(\() p Fl(K) p Fg 494 4086 a(d) p Fl 535 4071 a(;) p 579 4071 a(H) p Fj 660 4086 a(0) p Fn 699 4071 a(\)) p 780 4071 a(exists) p 1060 4071 a(and) p 1261 4071 a(is) p 1370 4071 a(asymptotically) p 2037 4071 a(complete) p 2460 4071 a(\(Ran) p Fl 2690 4071 a(W) p Ff 2782 4086 a(\006) p Fn 2841 4071 a(\() p Fl(K) p Fg 2962 4086 a(d) p Fl 3002 4071 a(;) p 3046 4071 a(H) p Fj 3127 4086 a(0) p Fn 3166 4071 a(\)) p 3250 4071 a(=) p Fl 3372 4071 a(L) p Fj 3438 4035 a(2) p Fn 3478 4071 a(\).) 0 4191 y(Hence) p Fl 290 4191 a(S) p Fn 356 4191 a(\() p Fl(K) p Fg 477 4206 a(d) p Fl 517 4191 a(;) p 561 4191 a(H) p Fj 642 4206 a(0) p Fn 681 4191 a(\)) p 752 4191 a(can) p 930 4191 a(b) s(e) p 1063 4191 a(de\014ned) p 1399 4191 a(as) p 1519 4191 a(a) p 1600 4191 a(unitary) p 1944 4191 a(op) s(erator.) 146 4357 y(Let) p Fl 320 4357 a(U) p Fj 386 4372 a(1) p Fn 426 4357 a(\() p Fl(h) p Fn(\)) p 589 4357 a(and) p Fl 778 4357 a(U) p Fj 844 4372 a(2) p Fn 883 4357 a(\() p Fl(h) p Fn(\)) p 1047 4357 a(b) s(e) p 1179 4357 a(de\014ned) p 1514 4357 a(b) m(y) p 1648 4357 a(\(1.8\).) p 1919 4357 a(Then) p Fl 2172 4357 a(H) p Fj 2253 4372 a(0) p Fn 2320 4357 a(=) p Fl 2424 4357 a(U) p Fj 2490 4372 a(1) p Fn 2529 4357 a(\() p Fl(h) p Fn(\)) p Ff 2661 4321 a(\003) p Fl 2701 4357 a(H) p Fj 2782 4372 a(0) p Fg(h) p Fl 2862 4357 a(U) p Fj 2928 4372 a(1) p Fn 2967 4357 a(\() p Fl(h) p Fn(\)) p 3131 4357 a(for) p Fl 3279 4357 a(H) p Fj 3360 4372 a(0) p Fg(h) p Fn 3467 4357 a(=) p Fi 0 4478 a(\000) p Fl(h) p Fj 133 4442 a(2) p Fn 173 4478 a(\001,) p 314 4478 a(and) p 504 4478 a(hence) 915 4683 y(exp) q(\() p Fi(\000) p Fl(itH) p Fj 1328 4698 a(0) p Fn 1368 4683 a(\)) p 1434 4683 a(=) p Fl 1538 4683 a(U) p Fj 1604 4698 a(1) p Fn 1643 4683 a(\() p Fl(h) p Fn(\)) p Ff 1775 4642 a(\003) p Fn 1831 4683 a(exp) q(\() p Fi(\000) p Fl(itH) p Fj 2244 4698 a(0) p Fg(h) p Fn 2325 4683 a(\)) p Fl(U) p Fj 2429 4698 a(1) p Fn 2469 4683 a(\() p Fl(h) p Fn(\)) p Fl(:) p Fn 0 4888 a(W) p 92 4888 a(e) p 168 4888 a(use) p 337 4888 a(the) p 505 4888 a(notation) p 895 4888 a(\(2.1\)) p 1128 4888 a(to) p 1247 4888 a(set) p Fl 461 5093 a(W) p Fj 553 5108 a(+) p Fn 612 5093 a(\() p Fl(h) p Fn(\)) p 772 5093 a(=) p Fl 875 5093 a(W) p Fj 967 5108 a(+) p Fn 1026 5093 a(\() p Fl(H) p Fj 1145 5108 a(0) p Fl 1184 5093 a(;) p 1228 5093 a(H) p Fj 1309 5108 a(0) p Fn 1348 5093 a(;) p Fl 1392 5093 a(U) p Fj 1458 5108 a(2) p Fn 1498 5093 a(\() p Fl(h) p Fn(\)\)) p Fl(;) p 1809 5093 a(W) p Ff 1901 5108 a(\000) p Fn 1960 5093 a(\() p Fl(h) p Fn(\)) p 2120 5093 a(=) p Fl 2223 5093 a(W) p Ff 2315 5108 a(\000) p Fn 2375 5093 a(\() p Fl(H) p Fj 2494 5108 a(0) p Fl 2533 5093 a(;) p 2577 5093 a(H) p Fj 2658 5108 a(0) p Fn 2697 5093 a(;) p Fl 2741 5093 a(U) p Fj 2807 5108 a(2) p Fn 2846 5093 a(\() p Fl(h) p Fn(\)) p Ff 2978 5052 a(\003) p Fn 3018 5093 a(\)) p Fl(:) p Fn 3343 5093 a(\(2.2\)) 0 5299 y(Then) p Fl 255 5299 a(S) p Fn 321 5299 a(\() p Fl(H) p Fg 440 5314 a(h) p Fl 484 5299 a(;) p 528 5299 a(H) p Fj 609 5314 a(0) p Fg(h) p Fn 689 5299 a(\)) p 759 5299 a(admits) p 1079 5299 a(the) p 1247 5299 a(decomp) s(osition) p Fl 701 5504 a(S) p Fn 767 5504 a(\() p Fl(H) p Fg 886 5519 a(h) p Fl 931 5504 a(;) p 975 5504 a(H) p Fj 1056 5519 a(0) p Fg(h) p Fn 1135 5504 a(\)) p 1201 5504 a(=) p Fl 1305 5504 a(U) p Fj 1371 5519 a(1) p Fn 1410 5504 a(\() p Fl(h) p Fn(\)) p Fl(W) p Fj 1634 5519 a(+) p Fn 1693 5504 a(\() p Fl(h) p Fn(\)) p Fl(S) p Fn 1891 5504 a(\() p Fl(K) p Fg 2012 5519 a(d) p Fl 2053 5504 a(;) p 2097 5504 a(H) p Fj 2178 5519 a(0) p Fn 2217 5504 a(\)) p Fl(W) p Ff 2347 5519 a(\000) p Fn 2406 5504 a(\() p Fl(h) p Fn(\)) p Fl(U) p Fj 2604 5519 a(1) p Fn 2643 5504 a(\() p Fl(h) p Fn(\)) p Ff 2775 5463 a(\003) p Fl 2815 5504 a(:) p Fn 3343 5504 a(\(2.3\)) 1747 5753 y(6) p 90 rotate dyy eop %%Page: 7 7 7 6 bop Fn 0 407 a(The) p 201 407 a(existence) p 616 407 a(of) p Fl 727 407 a(W) p Ff 819 422 a(\006) p Fn 878 407 a(\() p Fl(h) p Fn(\)) p 1042 407 a(follo) m(ws) p 1363 407 a(as) p 1482 407 a(a) p 1564 407 a(consequence) p 2114 407 a(of) p 2225 407 a(Lemma) p 2574 407 a(2.1) p 2731 407 a(b) s(elo) m(w.) 146 577 y(W) p 238 577 a(e) p 322 577 a(use) p 498 577 a(the) p 673 577 a(abbreviation) p 1247 577 a(that) p 1466 577 a(in) m(tegrations) p 2008 577 a(with) p 2237 577 a(no) p 2380 577 a(domain) p 2734 577 a(attac) m(hed) p 3140 577 a(are) p 3310 577 a(tak) m(en) 0 697 y(o) m(v) m(er) p 209 697 a(the) p 377 697 a(whole) p 653 697 a(space.) p 952 697 a(Let) p Fl 762 917 a(') p Fj 826 932 a(0) p Fn 866 917 a(\() p Fl(x) p Fn(;) p Fl 1003 917 a(\025;) p 1104 917 a(!) p Fn 1169 917 a(\)) p 1233 917 a(=) p 1337 917 a(exp) q(\() p Fl(i) p Fi 1557 828 a(p) p 1640 828 57 4 v Fl 1640 917 a(\025) p 1714 917 a(x) p Fi 1791 917 a(\001) p Fl 1841 917 a(!) p Fn 1906 917 a(\)) p Fl(;) p 2084 917 a(\025) p 2169 917 a(>) p Fn 2273 917 a(0) p Fl(;) p 2463 917 a(!) p Fi 2555 917 a(2) p Fl 2649 917 a(S) p Fj 2715 876 a(1) p Fl 2754 917 a(;) p Fn 0 1137 a(b) s(e) p 132 1137 a(the) p 299 1137 a(generalized) p 803 1137 a(eigenfunction) p 1401 1137 a(of) p 1511 1137 a(the) p 1679 1137 a(free) p 1865 1137 a(Hamiltonian) p Fl 2425 1137 a(H) p Fj 2506 1152 a(0) p Fn 2546 1137 a(.) p 2616 1137 a(W) p 2708 1137 a(e) p 2783 1137 a(de\014ne) p 3064 1137 a(the) p 3232 1137 a(unitary) 0 1258 y(mapping) p Fl 401 1258 a(F) p Fn 505 1258 a(:) p Fl 560 1258 a(L) p Fj 626 1222 a(2) p Fi 694 1258 a(!) p Fl 821 1258 a(L) p Fj 887 1222 a(2) p Fn 927 1258 a(\(\(0) p Fl(;) p Fi 1096 1258 a(1) p Fn(\);) p Fl 1278 1258 a(d\025) p Fn(\)) p Fi 1444 1258 a(\012) p Fl 1544 1258 a(L) p Fj 1610 1222 a(2) p Fn 1649 1258 a(\() p Fl(S) p Fj 1753 1222 a(1) p Fn 1793 1258 a(\)) p 1863 1258 a(b) m(y) 453 1508 y(\() p Fl(F) p 568 1508 a(u) p Fn(\)) p 677 1508 a(\() p Fl(\025;) p 816 1508 a(!) p Fn 881 1508 a(\)) p 946 1508 a(=) p 1049 1508 a(2) p Ff 1098 1467 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fn 1263 1508 a(\(2) p Fl(\031) p Fn 1409 1508 a(\)) p Ff 1447 1467 a(\000) p Fj(1) p Fh 1558 1391 a(Z) p Fn 1673 1508 a(\026) p Fl 1657 1508 a(') p Fj 1721 1523 a(0) p Fn 1761 1508 a(\() p Fl(x) p Fn(;) p Fl 1898 1508 a(\025;) p 1999 1508 a(!) p Fn 2064 1508 a(\)) p Fl(u) p Fn(\() p Fl(x) p Fn(\)) p Fl 2306 1508 a(dx) p Fn 2438 1508 a(=) p 2541 1508 a(2) p Ff 2590 1467 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fh 2762 1501 a(b) p Fl 2755 1508 a(u) p Fn 2810 1508 a(\() p Fi 2848 1418 a(p) p 2931 1418 V Fl 2931 1508 a(\025!) p Fn 3053 1508 a(\)) p 3343 1508 a(\(2.4\)) 0 1758 y(and) p Fl 190 1758 a(F) p Fn 267 1758 a(\() p Fl(h) p Fn(\)) p 431 1758 a(b) m(y) 633 2008 y(\() p Fl(F) p Fn 748 2008 a(\() p Fl(h) p Fn(\)) p Fl(u) p Fn(\)) p 990 2008 a(\() p Fl(\025;) p 1129 2008 a(!) p Fn 1194 2008 a(\)) p 1258 2008 a(=) p 1362 2008 a(2) p Ff 1411 1967 a(\000) p Fj(1) p Fg(=) p Fj(2) p Fn 1575 2008 a(\(2) p Fl(\031) t(h) p Fn(\)) p Ff 1815 1967 a(\000) p Fj(1) p Fh 1926 1891 a(Z) p Fn 2041 2008 a(\026) p Fl 2026 2008 a(') p Fj 2090 2023 a(0) p Fn 2129 2008 a(\() p Fl(x=h) p Fn(;) p Fl 2371 2008 a(\025;) p 2472 2008 a(!) p Fn 2537 2008 a(\)) p Fl(u) p Fn(\() p Fl(x) p Fn(\)) p Fl 2779 2008 a(dx;) p Fn 0 2258 a(where) p Fh 289 2251 a(b) p Fl 282 2258 a(u) p Fn 337 2258 a(\() p Fl(\030) p Fn 423 2258 a(\)) p 493 2258 a(is) p 591 2258 a(the) p 759 2258 a(F) p 815 2258 a(ourier) p 1097 2258 a(transform) p 1544 2258 a(of) p Fl 1655 2258 a(u) p Fn(.) p 1781 2258 a(Then) p 2036 2258 a(a) p 2117 2258 a(simple) p 2421 2258 a(computation) p 2990 2258 a(sho) m(ws) p 3271 2258 a(that) p Fl 1431 2478 a(F) p Fn 1535 2478 a(=) p Fl 1639 2478 a(F) p Fn 1716 2478 a(\() p Fl(h) p Fn(\)) p Fl(U) p Fj 1914 2493 a(1) p Fn 1953 2478 a(\() p Fl(h) p Fn(\)) p Fl(:) p Fn 3343 2478 a(\(2.5\)) 0 2698 y(The) p 201 2698 a(mapping) p Fl 602 2698 a(F) p Fn 679 2698 a(\() p Fl(h) p Fn(\)) p 843 2698 a(decomp) s(oses) p Fl 1372 2698 a(S) p Fn 1438 2698 a(\() p Fl(H) p Fg 1557 2713 a(h) p Fl 1602 2698 a(;) p 1646 2698 a(H) p Fj 1727 2713 a(0) p Fg(h) p Fn 1806 2698 a(\)) p 1877 2698 a(in) m(to) p 2075 2698 a(the) p 2243 2698 a(direct) p 2519 2698 a(in) m(tegral) p Fl 442 2950 a(S) p Fn 508 2950 a(\() p Fl(H) p Fg 627 2965 a(h) p Fl 672 2950 a(;) p 716 2950 a(H) p Fj 797 2965 a(0) p Fg(h) p Fn 876 2950 a(\)) p Fi 942 2950 a(') p Fl 1047 2950 a(F) p Fn 1124 2950 a(\() p Fl(h) p Fn(\)) p Fl(S) p Fn 1322 2950 a(\() p Fl(H) p Fg 1441 2965 a(h) p Fl 1485 2950 a(;) p 1529 2950 a(H) p Fj 1610 2965 a(0) p Fg(h) p Fn 1690 2950 a(\)) p Fl(F) p Fn 1805 2950 a(\() p Fl(h) p Fn(\)) p Ff 1937 2909 a(\003) p Fi 2004 2950 a(') p Fh 2109 2833 a(Z) p Ff 2192 2859 a(1) p Fj 2155 3022 a(0) p Fi 2283 2950 a(\010) p Fl 2377 2950 a(S) p Fn 2443 2950 a(\() p Fl(\025) p Fn(;) p Fl 2582 2950 a(H) p Fg 2663 2965 a(h) p Fl 2707 2950 a(;) p 2751 2950 a(H) p Fj 2832 2965 a(0) p Fg(h) p Fn 2912 2950 a(\)) p Fl 2967 2950 a(d\025;) p Fn 0 3213 a(where) p 288 3213 a(the) p 463 3213 a(\014bre) p Fl 691 3213 a(S) p Fn 757 3213 a(\() p Fl(\025) p Fn(;) p Fl 896 3213 a(H) p Fg 977 3228 a(h) p Fl 1021 3213 a(;) p 1065 3213 a(H) p Fj 1146 3228 a(0) p Fg(h) p Fn 1226 3213 a(\)) p 1292 3213 a(:) p Fl 1346 3213 a(L) p Fj 1412 3172 a(2) p Fn 1452 3213 a(\() p Fl(S) p Fj 1556 3172 a(1) p Fn 1595 3213 a(\)) p Fi 1661 3213 a(!) p Fl 1788 3213 a(L) p Fj 1854 3172 a(2) p Fn 1894 3213 a(\() p Fl(S) p Fj 1998 3172 a(1) p Fn 2037 3213 a(\)) p 2114 3213 a(is) p 2219 3213 a(called) p 2502 3213 a(the) p 2676 3213 a(scattering) p 3133 3213 a(matrix) p 3457 3213 a(at) 0 3334 y(energy) p Fl 312 3334 a(\025) p 396 3334 a(>) p Fn 500 3334 a(0) p 581 3334 a(and) p 771 3334 a(it) p 868 3334 a(acts) p 1069 3334 a(as) 480 3554 y(\() p Fl(S) p Fn 584 3554 a(\() p Fl(\025) p Fn(;) p Fl 723 3554 a(H) p Fg 804 3569 a(h) p Fl 848 3554 a(;) p 892 3554 a(H) p Fj 973 3569 a(0) p Fg(h) p Fn 1053 3554 a(\)\() p Fl(F) p Fn 1206 3554 a(\() p Fl(h) p Fn(\)) p Fl(u) p Fn(\)\() p Fl(\025;) p Fi 1586 3554 a(\001) p Fn 1631 3554 a(\)\)) p 1722 3554 a(\() p Fl(!) p Fn 1825 3554 a(\)) p 1890 3554 a(=) p 1994 3554 a(\() p Fl(F) p Fn 2109 3554 a(\() p Fl(h) p Fn(\)) p Fl(S) p Fn 2307 3554 a(\() p Fl(H) p Fg 2426 3569 a(h) p Fl 2470 3554 a(;) p 2514 3554 a(H) p Fj 2595 3569 a(0) p Fg(h) p Fn 2675 3554 a(\)) p Fl(u) p Fn(\)) p 2823 3554 a(\() p Fl(\025;) p 2962 3554 a(!) p Fn 3027 3554 a(\)) 0 3774 y(for) p Fl 149 3774 a(u) p Fi 232 3774 a(2) p Fl 326 3774 a(L) p Fj 392 3738 a(2) p Fn 432 3774 a(.) p 503 3774 a(Similarly) p 917 3774 a(w) m(e) p 1061 3774 a(ha) m(v) m(e) p Fl 639 4021 a(S) p Fn 705 4021 a(\() p Fl(K) p Fg 826 4036 a(d) p Fl 866 4021 a(;) p 910 4021 a(H) p Fj 991 4036 a(0) p Fn 1030 4021 a(\)) p Fi 1095 4021 a(') p Fl 1201 4021 a(F) p 1278 4021 a(S) p Fn 1344 4021 a(\() p Fl(K) p Fg 1465 4036 a(d) p Fl 1504 4021 a(;) p 1548 4021 a(H) p Fj 1629 4036 a(0) p Fn 1668 4021 a(\)) p Fl(F) p Ff 1783 3979 a(\003) p Fi 1850 4021 a(') p Fh 1955 3903 a(Z) p Ff 2038 3930 a(1) p Fj 2001 4092 a(0) p Fi 2130 4021 a(\010) p Fl 2224 4021 a(S) p Fn 2290 4021 a(\() p Fl(\025) p Fn(;) p Fl 2429 4021 a(K) p Fg 2512 4036 a(d) p Fl 2552 4021 a(;) p 2596 4021 a(H) p Fj 2677 4036 a(0) p Fn 2715 4021 a(\)) p Fl 2770 4021 a(d\025:) p Fn 0 4275 a(The) p 201 4275 a(next) p 420 4275 a(lemma) p 734 4275 a(is) p 832 4275 a(w) m(ell) p 1030 4275 a(kno) m(wn) p 1339 4275 a(\(see) p 1535 4275 a([13,) p 1719 4275 a(Theorem) p 2131 4275 a(IX.) p 2299 4275 a(31]) p 2456 4275 a(for) p 2605 4275 a(example\).) p Fm 0 4553 a(Lemma) p 397 4553 a(2.1) p Fb 589 4553 a(The) p 788 4553 a(fr) p 854 4553 a(e) p 894 4553 a(e) p 974 4553 a(solution) p Fn 1343 4553 a(exp) q(\() p Fi(\000) p Fl(itH) p Fj 1756 4568 a(0) p Fn 1796 4553 a(\)) p Fl(f) p Fb 1927 4553 a(with) p 2139 4553 a(initial) p 2425 4553 a(state) p Fl 2660 4553 a(f) p Fi 2746 4553 a(2) p Fl 2840 4553 a(L) p Fj 2906 4517 a(2) p Fb 2981 4553 a(b) p 3021 4553 a(ehaves) p 3329 4553 a(like) p Fn 340 4773 a(\(exp) q(\() p Fi(\000) p Fl(itH) p Fj 791 4788 a(0) p Fn 831 4773 a(\)) p Fl(f) p Fn 928 4773 a(\)\() p Fl(x) p Fn(\)) p 1125 4773 a(=) p 1228 4773 a(\(2) p Fl(it) p Fn(\)) p Ff 1421 4732 a(\000) p Fj(1) p Fn 1532 4773 a(exp) q(\() p Fl(i) p Fi(j) p Fl(x) p Fi(j) p Fj 1863 4732 a(2) p Fl 1903 4773 a(=) p Fn(4) p Fl(t) p Fn(\)) p Fh 2096 4739 a(b) p Fl 2074 4773 a(f) p Fn 2132 4773 a(\() p Fl(x=) p Fn(2) p Fl(t) p Fn(\)) p 2418 4773 a(+) p Fl 2516 4773 a(o) p Fn(\(1\)) p Fl(;) p Fi 2831 4773 a(j) p Fl(t) p Fi(j) p 2949 4773 a(!) p 3077 4773 a(1) p Fl(;) p Fb 0 4993 a(on) p Fl 139 4993 a(L) p Fj 205 4957 a(2) p Fb 245 4993 a(.) p Fn 146 5271 a(W) p 238 5271 a(e) p 313 5271 a(recall) p 572 5271 a(that) p Fl 783 5271 a(\015) p Fn 839 5271 a(\() p Fl(x) p Fn(\)) p 998 5271 a(=) p Fl 1101 5271 a(\015) p Fn 1157 5271 a(\() p 1201 5271 a(^) p Fl 1195 5271 a(x) p Fn 1251 5271 a(\)) p 1320 5271 a(denotes) p 1672 5271 a(the) p 1839 5271 a(azim) m(uth) p 2214 5271 a(angle) p 2468 5271 a(from) p 2697 5271 a(the) p 2864 5271 a(p) s(ositiv) m(e) p Fl 3224 5271 a(x) p Fj 3279 5286 a(1) p Fn 3350 5271 a(axis.) 0 5391 y(Let) p Fl 178 5391 a(\020) p Fn 229 5391 a(\() p Fl(x) p Fn(\)) p 395 5391 a(b) s(e) p 531 5391 a(de\014ned) p 870 5391 a(b) m(y) p 1009 5391 a(\(1.9\).) p 1289 5391 a(It) p 1398 5391 a(b) s(eha) m(v) m(es) p 1764 5391 a(lik) m(e) p Fl 1946 5391 a(\020) p Fn 1997 5391 a(\() p Fl(x) p Fn(\)) p Fi 2161 5391 a(\030) p Fl 2271 5391 a(\032\015) p Fn 2377 5391 a(\() p 2421 5391 a(^) p Fl 2415 5391 a(x) p Fn 2471 5391 a(\)) p 2544 5391 a(as) p Fi 2667 5391 a(j) p Fl(x) p Fi(j) p 2811 5391 a(!) p 2944 5391 a(1) p Fn(,) p 3107 5391 a(where) p Fl 3392 5391 a(\032) p Fn 3478 5391 a(is) 1747 5753 y(7) p 90 rotate dyy eop %%Page: 8 8 8 7 bop Fn 0 407 a(the) p 172 407 a(in) m(teger) p 498 407 a(de\014ned) p 837 407 a(b) m(y) p 977 407 a(\(1.13\).) p 1307 407 a(Hence) p 1601 407 a(the) p 1773 407 a(lemma) p 2091 407 a(ab) s(o) m(v) m(e) p 2371 407 a(implies) p 2705 407 a(that) p Fl 2920 407 a(W) p Fj 3012 422 a(+) p Fn 3072 407 a(\() p Fl(h) p Fn(\)) p 3240 407 a(de\014ned) 0 527 y(b) m(y) p 135 527 a(\(2.2\)) p 369 527 a(acts) p 570 527 a(as) p 689 527 a(the) p 857 527 a(m) m(ultiplication) p Fl 886 741 a(F) p 963 741 a(W) p Fj 1055 756 a(+) p Fn 1114 741 a(\() p Fl(h) p Fn(\)) p Fl(F) p Ff 1323 700 a(\003) p Fn 1390 741 a(=) p 1493 741 a(exp) q(\() p Fl(i\032\015) p Fn 1819 741 a(\() p Fl(!) p Fn 1922 741 a(\)\)) p Fi(\002) p Fn 2103 741 a(=) p 2207 741 a(exp) q(\() p Fl(i\032!) p Fn 2542 741 a(\)) p Fi(\002) p Fn 0 954 a(on) p Fl 138 954 a(L) p Fj 204 918 a(2) p Fn 244 954 a(\(\(0) p Fl(;) p Fi 413 954 a(1) p Fn(\);) p Fl 595 954 a(d\025) p Fn(\)) p Fi 763 954 a(\012) p Fl 865 954 a(L) p Fj 931 918 a(2) p Fn 971 954 a(\() p Fl(S) p Fj 1075 918 a(1) p Fn 1114 954 a(\).) p 1231 954 a(If) p 1331 954 a(w) m(e) p 1477 954 a(note) p 1697 954 a(that) p Fl 1911 954 a(\015) p Fn 1967 954 a(\() p Fi(\000) p Fl(!) p Fn 2147 954 a(\)) p 2217 954 a(=) p Fl 2326 954 a(!) p Fn 2414 954 a(+) p Fl 2514 954 a(\031) p Fn 2608 954 a(or) p Fl 2730 954 a(!) p Fi 2819 954 a(\000) p Fl 2920 954 a(\031) p Fn 3014 954 a(according) p 3456 954 a(as) 0 1075 y(0) p Fi 76 1075 a(\024) p Fl 182 1075 a(!) p 274 1075 a(<) p 377 1075 a(\031) p Fn 469 1075 a(or) p Fl 588 1075 a(\031) p Fi 674 1075 a(\024) p Fl 780 1075 a(!) p 872 1075 a(<) p Fn 975 1075 a(2) p Fl(\031) p Fn 1083 1075 a(,) p 1142 1075 a(then) p Fl 567 1288 a(F) p 644 1288 a(W) p Ff 736 1303 a(\000) p Fn 795 1288 a(\() p Fl(h) p Fn(\)) p Fl(F) p Ff 1004 1247 a(\003) p Fn 1070 1288 a(=) p 1174 1288 a(exp) q(\() p Fi(\000) p Fl(i\032) p Fn(\() p Fl(\015) p Fn 1615 1288 a(\() p Fi(\000) p Fl(!) p Fn 1795 1288 a(\)\)\)) p Fi(\002) p Fn 2015 1288 a(=) p 2118 1288 a(\() p Fi(\000) p Fn(1\)) p Fg 2320 1247 a(\032) p Fn 2377 1288 a(exp) q(\() p Fi(\000) p Fl(i\032!) p Fn 2789 1288 a(\)) p Fi 2850 1288 a(\002) p Fl 2949 1288 a(:) p Fn 0 1502 a(W) p 92 1502 a(e) p 182 1502 a(denote) p 510 1502 a(b) m(y) p Fl 660 1502 a(S) p Fn 726 1502 a(\() p Fl(\022) s(;) p 856 1502 a(!) p Fn 921 1502 a(;) p Fl 965 1502 a(\025;) p 1066 1502 a(H) p Fg 1147 1517 a(h) p Fl 1190 1502 a(;) p 1234 1502 a(H) p Fj 1315 1517 a(0) p Fg(;h) p Fn 1414 1502 a(\)) p 1499 1502 a(and) p Fl 1702 1502 a(S) p Fn 1768 1502 a(\() p Fl(\022) s(;) p 1898 1502 a(!) p Fn 1963 1502 a(;) p Fl 2007 1502 a(\025;) p 2108 1502 a(K) p Fg 2191 1517 a(d) p Fl 2230 1502 a(;) p 2274 1502 a(H) p Fj 2355 1517 a(0) p Fn 2394 1502 a(\)) p 2478 1502 a(the) p 2661 1502 a(k) m(ernels) p 3000 1502 a(of) p 3125 1502 a(scattering) 0 1622 y(matrices) p Fl 403 1622 a(S) p Fn 469 1622 a(\() p Fl(\025) p Fn(;) p Fl 608 1622 a(H) p Fg 689 1637 a(h) p Fl 733 1622 a(;) p 777 1622 a(H) p Fj 858 1637 a(0) p Fg(h) p Fn 937 1622 a(\)) p 1020 1622 a(and) p Fl 1221 1622 a(S) p Fn 1287 1622 a(\() p Fl(\025) p Fn(;) p Fl 1426 1622 a(K) p Fg 1509 1637 a(d) p Fl 1549 1622 a(;) p 1593 1622 a(H) p Fj 1674 1637 a(0) p Fn 1713 1622 a(\)) p 1795 1622 a(resp) s(ectiv) m (ely) p 2283 1622 a(.) p 2392 1622 a(Then) p 2659 1622 a(it) p 2768 1622 a(follo) m(ws) p 3101 1622 a(from) p 3343 1622 a(\(2.3\)) 0 1742 y(and) p 190 1742 a(\(2.5\)) p 423 1742 a(that) p Fl 482 1956 a(S) p Fn 548 1956 a(\() p Fl(\022) s(;) p 678 1956 a(!) p Fn 743 1956 a(;) p Fl 787 1956 a(E) p 865 1956 a(;) p 909 1956 a(H) p Fg 990 1971 a(h) p Fl 1033 1956 a(;) p 1077 1956 a(H) p Fj 1158 1971 a(0) p Fg(h) p Fn 1237 1956 a(\)) p 1303 1956 a(=) p 1406 1956 a(\() p Fi(\000) p Fn(1\)) p Fg 1608 1915 a(\032) p Fn 1665 1956 a(exp) q(\() p Fl(i\032) p Fn(\() p Fl(\022) p Fi 2044 1956 a(\000) p Fl 2144 1956 a(!) p Fn 2209 1956 a(\)\)) p Fl(S) p Fn 2351 1956 a(\() p Fl(\022) s(;) p 2481 1956 a(!) t(;) p 2590 1956 a(E) p Fn 2668 1956 a(;) p Fl 2712 1956 a(K) p Fg 2795 1971 a(d) p Fl 2833 1956 a(;) p 2877 1956 a(H) p Fj 2958 1971 a(0) p Fn 2997 1956 a(\)) p Fl(:) p Fn 0 2170 a(The) p 201 2170 a(scattering) p 651 2170 a(amplitude) p Fl 1112 2170 a(f) p Fg 1160 2185 a(h) p Fn 1204 2170 a(\() p Fl(!) p Ff 1303 2185 a(\000) p Fi 1390 2170 a(!) p Fl 1517 2170 a(!) p Fj 1578 2185 a(+) p Fn 1637 2170 a(\)) p 1707 2170 a(is) p 1805 2170 a(de\014ned) p 2141 2170 a(b) m(y) p Fl 794 2383 a(f) p Fg 842 2398 a(h) p Fn 887 2383 a(\() p Fl(!) p Ff 986 2398 a(\000) p Fi 1072 2383 a(!) p Fl 1200 2383 a(!) p Fj 1261 2398 a(+) p Fn 1319 2383 a(\)) p 1385 2383 a(=) p Fl 1488 2383 a(c) p Fn(\() p Fl(E) p 1646 2383 a(=h) p Fj 1751 2342 a(2) p Fn 1791 2383 a(\)) p Fl(S) p Fn 1895 2383 a(\() p Fl(!) p Fj 1994 2398 a(+) p Fl 2052 2383 a(;) p 2096 2383 a(!) p Ff 2157 2398 a(\000) p Fn 2216 2383 a(;) p Fl 2260 2383 a(E) p 2338 2383 a(;) p 2382 2383 a(H) p Fg 2463 2398 a(h) p Fl 2507 2383 a(;) p 2551 2383 a(H) p Fj 2632 2398 a(0) p Fg(h) p Fn 2711 2383 a(\)) 0 2597 y(through) p 369 2597 a(the) p 537 2597 a(scattering) p 987 2597 a(k) m(ernel) p 1274 2597 a(and) p 1464 2597 a(also) p 1659 2597 a(w) m(e) p 1803 2597 a(ha) m(v) m(e) p Fl 830 2810 a(g) p Fg 877 2825 a(d) p Fn 917 2810 a(\() p Fl(!) p Ff 1016 2825 a(\000) p Fi 1102 2810 a(!) p Fl 1229 2810 a(!) p Fj 1290 2825 a(+) p Fn 1349 2810 a(;) p Fl 1393 2810 a(E) p Fn 1471 2810 a(\)) p 1537 2810 a(=) p Fl 1640 2810 a(c) p Fn(\() p Fl(E) p Fn 1798 2810 a(\)) p Fl(S) p Fn 1902 2810 a(\() p Fl(!) p Fj 2001 2825 a(+) p Fl 2059 2810 a(;) p 2103 2810 a(!) p Ff 2164 2825 a(\000) p Fn 2223 2810 a(;) p Fl 2267 2810 a(E) p 2345 2810 a(;) p 2389 2810 a(K) p Fg 2472 2825 a(d) p Fl 2512 2810 a(;) p 2556 2810 a(H) p Fj 2637 2825 a(0) p Fn 2676 2810 a(\)) 0 3024 y(as) p 129 3024 a(the) p 306 3024 a(sp) s(ecial) p 633 3024 a(case) p 848 3024 a(with) p Fl 1080 3024 a(h) p Fn 1179 3024 a(=) p 1298 3024 a(1,) p 1418 3024 a(where) p Fl 1709 3024 a(c) p Fn(\() p Fl(E) p Fn 1867 3024 a(\)) p 1946 3024 a(is) p 2054 3024 a(de\014ned) p 2399 3024 a(in) p 2522 3024 a(\(1.3\).) p 2820 3024 a(Since) p Fl 3084 3024 a(c) p Fn(\() p Fl(E) p 3242 3024 a(=h) p Fj 3347 2987 a(2) p Fn 3386 3024 a(\)) p 3467 3024 a(=) p Fl 0 3144 a(h) p Fj 56 3108 a(1) p Fg(=) p Fj(2) p Fl 166 3144 a(c) p Fn(\() p Fl(E) p Fn 324 3144 a(\),) p 427 3144 a(w) m(e) p 576 3144 a(obtain) p 884 3144 a(the) p 1056 3144 a(follo) m(wing) p 1473 3144 a(prop) s(osition) p 1990 3144 a(as) p 2114 3144 a(the) p 2287 3144 a(\014rst) p 2492 3144 a(step) p 2703 3144 a(to) m(w) m(ard) p 3033 3144 a(the) p 3205 3144 a(pro) s(of) p 3465 3144 a(of) 0 3264 y(Theorem) p 412 3264 a(1.1.) p Fm 0 3533 a(Prop) s(osition) p 606 3533 a(2.1) p Fb 798 3533 a(L) p 854 3533 a(et) p Fl 968 3533 a(g) p Fg 1015 3548 a(d) p Fn 1055 3533 a(\() p Fl(!) p Ff 1154 3548 a(\000) p Fi 1245 3533 a(!) p Fl 1377 3533 a(!) p Fj 1438 3548 a(+) p Fn 1497 3533 a(;) p Fl 1541 3533 a(E) p Fn 1619 3533 a(\)) p Fb 1694 3533 a(b) p 1734 3533 a(e) p 1816 3533 a(the) p 1980 3533 a(sc) p 2060 3533 a(attering) p 2427 3533 a(amplitude) p 2878 3533 a(at) p 2997 3533 a(ener) p 3178 3533 a(gy) p Fl 3307 3533 a(E) p Fb 3423 3533 a(for) 0 3654 y(p) p 45 3654 a(air) p Fn 200 3654 a(\() p Fl(K) p Fg 321 3669 a(d) p Fl 362 3654 a(;) p 406 3654 a(H) p Fj 487 3669 a(0) p Fn 526 3654 a(\)) p Fb 599 3654 a(and) p 788 3654 a(let) p Fl 925 3654 a(\032) p Fb 1010 3654 a(b) p 1050 3654 a(e) p 1130 3654 a(as) p 1254 3654 a(in) p 1374 3654 a(\(1.13\).) p 1708 3654 a(Then) p Fl 486 3867 a(f) p Fg 534 3882 a(h) p Fn 579 3867 a(\() p Fl(!) p Ff 678 3882 a(\000) p Fi 764 3867 a(!) p Fl 891 3867 a(!) p Fj 952 3882 a(+) p Fn 1011 3867 a(\)) p 1077 3867 a(=) p 1180 3867 a(\() p Fi(\000) p Fn(1\)) p Fg 1382 3826 a(\032) p Fn 1439 3867 a(exp) q(\() p Fl(i\032) p Fn(\() p Fl(!) p Fj 1808 3882 a(+) p Fi 1890 3867 a(\000) p Fl 1989 3867 a(!) p Ff 2050 3882 a(\000) p Fn 2109 3867 a(\)\)) p Fl(h) p Fj 2241 3826 a(1) p Fg(=) p Fj(2) p Fl 2351 3867 a(g) p Fg 2398 3882 a(d) p Fn 2438 3867 a(\() p Fl(!) p Ff 2537 3882 a(\000) p Fi 2624 3867 a(!) p Fl 2751 3867 a(!) p Fj 2812 3882 a(+) p Fn 2871 3867 a(;) p Fl 2915 3867 a(E) p Fn 2993 3867 a(\)) p Fl(:) p Fn 146 4136 a(W) p 238 4136 a(e) p 317 4136 a(end) p 505 4136 a(the) p 676 4136 a(section) p 1004 4136 a(b) m(y) p 1143 4136 a(making) p 1490 4136 a(a) p 1574 4136 a(commen) m(t) p 1997 4136 a(on) p 2136 4136 a(the) p 2307 4136 a(amplitude) p Fl 2771 4136 a(f) p Fg 2819 4151 a(h) p Fn 2864 4136 a(\() p Fl(!) p Ff 2963 4151 a(\000) p Fi 3054 4136 a(!) p Fl 3187 4136 a(!) p Fj 3248 4151 a(+) p Fn 3306 4136 a(;) p Fl 3350 4136 a(\013) q(;) p 3457 4136 a(p) p Fn(\)) 0 4256 y(in) p 126 4256 a(\(1.5\)) p 371 4256 a(for) p 531 4256 a(later) p 771 4256 a(reference.) p 1254 4256 a(Let) p Fl 1440 4256 a(H) p Fg 1521 4271 a(\014) p Fn 1616 4256 a(=) p 1740 4256 a(\() p Fi(\000) p Fl(i) p Fi(r) p 2002 4256 a(\000) p Fl 2109 4256 a(A) p Fg 2182 4271 a(\014) p Fn 2230 4256 a(\)) p Fj 2268 4220 a(2) p Fn 2352 4256 a(with) p Fl 2586 4256 a(A) p Fg 2659 4271 a(\014) p Fn 2754 4256 a(=) p Fl 2877 4256 a(\014) p Fn 2938 4256 a(\003\() p Fl(x) p Fn(\).) p 3243 4256 a(This) p 3478 4256 a(is) 0 4377 y(self{adjoin) m(t) p 514 4377 a(under) p 787 4377 a(the) p 951 4377 a(same) p 1191 4377 a(b) s(oundary) p 1626 4377 a(condition) p 2050 4377 a(at) p 2166 4377 a(the) p 2330 4377 a(origin) p 2602 4377 a(as) p 2718 4377 a(in) p 2828 4377 a(\(1.2\).) p 3097 4377 a(W) p 3189 4377 a(e) p 3261 4377 a(denote) 0 4497 y(b) m(y) p Fl 133 4497 a(g) p Fn 184 4497 a(\() p Fl(!) p Ff 283 4512 a(\000) p Fi 368 4497 a(!) p Fl 496 4497 a(!) p Fj 557 4512 a(+) p Fn 615 4497 a(;) p Fl 659 4497 a(E) p 737 4497 a(;) p 781 4497 a(\014) p Fn 842 4497 a(\)) p 909 4497 a(the) p 1074 4497 a(scattering) p 1522 4497 a(amplitude) p 1979 4497 a(at) p 2096 4497 a(energy) p Fl 2405 4497 a(E) p Fn 2512 4497 a(for) p 2658 4497 a(pair) p 2856 4497 a(\() p Fl(H) p Fg 2975 4512 a(\014) p Fl 3022 4497 a(;) p 3066 4497 a(H) p Fj 3147 4512 a(0) p Fn 3186 4497 a(\)) p 3254 4497 a(and) p 3440 4497 a(b) m(y) p Fl 0 4618 a(g) p Fn 51 4618 a(\() p Fl(!) p Ff 150 4633 a(\000) p Fi 236 4618 a(!) p Fl 363 4618 a(!) p Fj 424 4633 a(+) p Fn 483 4618 a(;) p Fl 527 4618 a(E) p 605 4618 a(;) p 649 4618 a(\014) p 710 4618 a(;) p 754 4618 a(p) p Fn(\)) p 868 4618 a(the) p 1033 4618 a(amplitude) p 1490 4618 a(for) p 1635 4618 a(the) p 1799 4618 a(scattering) p 2246 4618 a(b) m(y) p 2378 4618 a(the) p 2542 4618 a(\014eld) p 2750 4618 a(2) p Fl(\031) t(\014) p 2919 4618 a(\016) p Fn 2966 4618 a(\() p Fl(x) p Fi 3074 4618 a(\000) p Fl 3166 4618 a(p) p Fn(\).) p 3321 4618 a(Then) 0 4738 y(w) m(e) p 144 4738 a(can) p 322 4738 a(sho) m(w) p Fl 215 4951 a(f) p Fg 263 4966 a(h) p Fn 308 4951 a(\() p Fl(!) p Ff 407 4966 a(\000) p Fi 494 4951 a(!) p Fl 621 4951 a(!) p Fj 682 4966 a(+) p Fn 741 4951 a(;) p Fl 785 4951 a(\013) q(;) p 892 4951 a(p) p Fn(\)) p 1005 4951 a(=) p 1109 4951 a(\() p Fi(\000) p Fn(1\)) p Fj 1311 4910 a([) p Fg(\013=h) p Fj(]) p Fl 1476 4951 a(e) p Fg 1521 4910 a(i) p Fj([) p Fg(\013=h) p Fj(]\() p Fg(!) p Fd 1777 4919 a(+) p Ff 1828 4910 a(\000) p Fg(w) p Fe 1934 4919 a(\000) p Fj 1985 4910 a(\)) p Fl 2017 4951 a(h) p Fj 2073 4910 a(1) p Fg(=) p Fj(2) p Fl 2183 4951 a(g) p Fn 2234 4951 a(\() p Fl(!) p Ff 2333 4966 a(\000) p Fi 2419 4951 a(!) p Fl 2546 4951 a(!) p Fj 2607 4966 a(+) p Fn 2666 4951 a(;) p Fl 2710 4951 a(E) p 2788 4951 a(;) p 2832 4951 a(\014) p 2893 4951 a(;) p 2937 4951 a(p=h) p Fn(\)) p 3343 4951 a(\(2.6\)) 0 5165 y(in) p 114 5165 a(exactly) p 450 5165 a(the) p 618 5165 a(same) p 862 5165 a(w) m(a) m(y) p 1060 5165 a(as) p 1180 5165 a(ab) s(o) m(v) m(e,) p 1483 5165 a(where) p Fl 1765 5165 a(\014) p Fn 1853 5165 a(=) p Fl 1957 5165 a(\013) q(=h) p Fi 2147 5165 a(\000) p Fn 2246 5165 a([) p Fl(\013) q(=h) p Fn(].) p Fm 707 5504 a(3.) p 831 5504 a(Represen) m(tation) p 1608 5504 a(for) p 1781 5504 a(scattering) p 2301 5504 a(amplitudes) p Fn 1747 5753 a(8) p 90 rotate dyy eop %%Page: 9 9 9 8 bop Fn 146 407 a(As) p 297 407 a(already) p 648 407 a(stated) p 947 407 a(in) p 1068 407 a(section) p 1400 407 a(1,) p 1517 407 a(the) p 1691 407 a(k) m(ernel) p 1985 407 a(of) p 2103 407 a(scattering) p 2560 407 a(matrix) p Fl 2883 407 a(S) p Fn 2949 407 a(\() p Fl(\025) p Fn(;) p Fl 3088 407 a(H) p Fg 3169 422 a(\014) p Fl 3216 407 a(;) p 3260 407 a(H) p Fj 3341 422 a(0) p Fn 3380 407 a(\)) p 3457 407 a(at) 0 527 y(energy) p Fl 312 527 a(\025) p 396 527 a(>) p Fn 500 527 a(0) p 581 527 a(is) p 679 527 a(explicitly) p 1102 527 a(calculated) p 1562 527 a(\(see) p 1758 527 a([2,) p 1894 527 a(3,) p 2002 527 a(14]) p 2159 527 a(for) p 2308 527 a(example\).) p 2766 527 a(It) p 2872 527 a(tak) m(es) p 3122 527 a(the) p 3290 527 a(form) p Fl 706 729 a(S) p Fn 772 729 a(\() p Fl(\022) s(;) p 902 729 a(!) p Fn 967 729 a(;) p Fl 1011 729 a(\025;) p 1112 729 a(H) p Fg 1193 744 a(\014) p Fl 1239 729 a(;) p 1283 729 a(H) p Fj 1364 744 a(0) p Fn 1403 729 a(\)) p 1468 729 a(=) p 1572 729 a(\() p Fl(i=\031) p Fn 1751 729 a(\)) p 1806 729 a(sin) p Fl 1942 729 a(\014) p 2003 729 a(\031) p 2078 729 a(e) p Fg 2123 688 a(i) p Fj([) p Fg(\014) p Fj 2210 688 a(]\() p Fg(!) p Ff 2303 688 a(\000) p Fg(\022) p Fj 2393 688 a(\)) p Fl 2424 729 a(F) p Fj 2487 744 a(0) p Fn 2527 729 a(\() p Fl(!) p Fi 2651 729 a(\000) p Fl 2751 729 a(\022) p Fn 2799 729 a(\)) p 3343 729 a(\(3.1\)) 0 931 y(for) p Fl 145 931 a(\022) p Fi 221 931 a(6) p Fn(=) p Fl 325 931 a(!) p Fn 390 931 a(,) p 445 931 a(where) p Fl 723 931 a(F) p Fj 786 946 a(0) p Fn 826 931 a(\() p Fl(\022) p Fn 912 931 a(\)) p 979 931 a(is) p 1073 931 a(as) p 1189 931 a(in) p 1299 931 a(\(1.3\).) p 1569 931 a(By) p 1718 931 a(de\014nition,) p 2176 931 a(the) p 2340 931 a(amplitude) p Fl 2797 931 a(g) p Fn 2848 931 a(\() p Fl(!) p Ff 2947 946 a(\000) p Fi 3032 931 a(!) p Fl 3160 931 a(!) p Fj 3221 946 a(+) p Fn 3279 931 a(;) p Fl 3323 931 a(E) p 3401 931 a(;) p 3445 931 a(\014) p Fn 3506 931 a(\)) 0 1052 y(is) p 98 1052 a(related) p 423 1052 a(to) p Fl 542 1052 a(S) p Fn 608 1052 a(\() p Fl(!) p Fj 707 1067 a(+) p Fl 766 1052 a(;) p 810 1052 a(!) p Ff 871 1067 a(\000) p Fn 929 1052 a(;) p Fl 973 1052 a(E) p 1051 1052 a(;) p 1095 1052 a(H) p Fg 1176 1067 a(\014) p Fl 1223 1052 a(;) p 1267 1052 a(H) p Fj 1348 1067 a(0) p Fn 1387 1052 a(\)) p 1457 1052 a(through) p 1826 1052 a(the) p 1994 1052 a(relation) p Fl 214 1253 a(g) p Fn 292 1253 a(=) p Fl 395 1253 a(c) p Fn(\() p Fl(E) p Fn 553 1253 a(\)) p Fl(S) p Fn 657 1253 a(\() p Fl(!) p Fj 756 1268 a(+) p Fl 815 1253 a(;) p 859 1253 a(!) p Ff 920 1268 a(\000) p Fn 978 1253 a(;) p Fl 1022 1253 a(E) p 1100 1253 a(;) p 1144 1253 a(H) p Fg 1225 1268 a(\014) p Fl 1272 1253 a(;) p 1316 1253 a(H) p Fj 1397 1268 a(0) p Fn 1436 1253 a(\)) p 1501 1253 a(=) p 1605 1253 a(\() p Fl(ic) p Fn(\() p Fl(E) p Fn 1834 1253 a(\)) p Fl(=\031) p Fn 1980 1253 a(\)) p 2035 1253 a(sin) p Fl 2171 1253 a(\014) p 2232 1253 a(\031) p 2307 1253 a(e) p Fg 2352 1212 a(i) p Fj([) p Fg(\014) p Fj 2439 1212 a(]\() p Fg(!) p Fd 2530 1221 a(+) p Ff 2580 1212 a(\000) p Fg(!) p Fe 2679 1221 a(\000) p Fj 2731 1212 a(\)) p Fl 2763 1253 a(F) p Fj 2826 1268 a(0) p Fn 2865 1253 a(\() p Fl(!) p Fj 2964 1268 a(+) p Fi 3045 1253 a(\000) p Fl 3145 1253 a(!) p Ff 3206 1268 a(\000) p Fn 3264 1253 a(\)) p Fl(;) p Fn 0 1455 a(so) p 111 1455 a(that) p 314 1455 a(\(1.3\)) p 539 1455 a(follo) m(ws) p 850 1455 a(from) p 1072 1455 a(\(2.6\)) p 1297 1455 a(with) p Fl 1510 1455 a(p) p Fn 1587 1455 a(=) p 1690 1455 a(0.) p 1807 1455 a(In) p 1920 1455 a(this) p 2102 1455 a(section) p 2419 1455 a(w) m(e) p 2554 1455 a(represen) m(t) p 2966 1455 a(the) p 3125 1455 a(scattering) 0 1576 y(amplitude) p Fl 452 1576 a(g) p Fn 503 1576 a(\() p Fl(!) p Ff 602 1591 a(\000) p Fi 688 1576 a(!) p Fl 815 1576 a(!) p Fj 876 1591 a(+) p Fn 935 1576 a(;) p Fl 979 1576 a(E) p 1057 1576 a(;) p 1101 1576 a(\014) p Fn 1162 1576 a(\)) p 1223 1576 a(in) p 1328 1576 a(terms) p 1591 1576 a(of) p 1694 1576 a(resolv) m(en) m(t) p Fl 2095 1576 a(R) p Fn 2170 1576 a(\() p Fl(E) p Fn 2291 1576 a(+) p Fl 2372 1576 a(i) p Fn(0;) p Fl 2498 1576 a(H) p Fg 2579 1591 a(\014) p Fn 2625 1576 a(\).) p 2731 1576 a(A) p 2828 1576 a(similar) p 3140 1576 a(argumen) m(t) 0 1696 y(applies) p 324 1696 a(to) p 441 1696 a(the) p 606 1696 a(amplitude) p Fl 1065 1696 a(g) p Fg 1112 1711 a(d) p Fn 1152 1696 a(\() p Fl(!) p Ff 1251 1711 a(\000) p Fi 1337 1696 a(!) p Fl 1465 1696 a(!) p Fj 1526 1711 a(+) p Fn 1584 1696 a(;) p Fl 1628 1696 a(E) p Fn 1706 1696 a(\)) p 1775 1696 a(for) p 1921 1696 a(the) p 2087 1696 a(scattering) p 2535 1696 a(b) m(y) p 2669 1696 a(t) m(w) m(o) p 2851 1696 a(solenoidal) p 3299 1696 a(\014elds.) 0 1817 y(W) p 92 1817 a(e) p 168 1817 a(form) m(ulate) p 607 1817 a(the) p 775 1817 a(result) p 1046 1817 a(as) p 1166 1817 a(Prop) s(osition) p 1691 1817 a(3.1) p 1848 1817 a(at) p 1967 1817 a(the) p 2135 1817 a(end) p 2320 1817 a(of) p 2431 1817 a(the) p 2599 1817 a(section.) 146 1982 y(W) p 238 1982 a(e) p 314 1982 a(in) m(tro) s(duce) p 748 1982 a(a) p 829 1982 a(cut{o\013) p 1152 1982 a(function) p Fl 1534 1982 a(\037) p Fi 1622 1982 a(2) 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5504 a(\006\() p Fl(R) q(;) p Fi 1454 5504 a(\000) p Fl(!) p Fj 1592 5519 a(+) p Fl 1651 5504 a(;) p 1695 5504 a(\016) t(=) p Fn(2\)) p Fl(;) p 2018 5504 a(q) p Fj 2061 5519 a(+) p Fn 2148 5504 a(=) p 2252 5504 a(1) p 2347 5504 a(on) p 2497 5504 a(\006\(2) p Fl(R) q(;) p Fi 2773 5504 a(\000) p Fl(!) p Fj 2911 5519 a(+) p Fl 2970 5504 a(;) p 3014 5504 a(\016) p Fn 3061 5504 a(\)) p Fl(:) p Fn 3343 5504 a(\(3.6\)) 1747 5753 y(9) p 90 rotate dyy eop %%Page: 10 10 10 9 bop Fn 0 407 a(W) p 92 407 a(e) p 168 407 a(set) p Fl 395 615 a(J) p Fj 449 630 a(+0) p Fn 571 615 a(=) p Fl 675 615 a(q) p Fj 718 630 a(+) p Fn 794 615 a(exp) q(\() p Fl(i\014) p 1075 615 a(\015) p Fn 1131 615 a(\() p Fl(x) p Fn(;) p Fi 1268 615 a(\000) p Fl(!) p Fj 1406 630 a(+) p Fn 1465 615 a(\)\)) p Fl(p) p Fj 1590 630 a(+) p Fl 1649 615 a(;) p 1790 615 a(J) p Fj 1844 630 a(+1) p Fn 1966 615 a(=) p Fl 2069 615 a(q) p Fj 2112 630 a(+) p Fn 2188 615 a(exp) q(\() p Fi(\000) p Fl(i\014) p 2546 615 a(\015) p Fn 2602 615 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Fl(H) p Fj 2672 1463 a(0) p Fl 2711 1448 a(;) p 2755 1448 a(H) p Fj 2836 1463 a(0) p Fn 2875 1448 a(;) p Fl 2919 1448 a(J) p Ff 2973 1463 a(\000) p Fj(1) p Fn 3067 1448 a(\)) p Fl(;) p Fn 3343 1448 a(\(3.8\)) 0 1656 y(where) p Fl 728 1776 a(S) p Fj 788 1791 a(0) p Fn 828 1776 a(\() p Fl(H) p Fg 947 1791 a(\014) p Fl 994 1776 a(;) p 1038 1776 a(H) p Fj 1119 1791 a(0) p Fn 1158 1776 a(\)) p 1223 1776 a(=) p Fl 1327 1776 a(W) p Fj 1419 1791 a(+) p Fn 1478 1776 a(\() p Fl(H) p Fg 1597 1791 a(\014) p Fl 1644 1776 a(;) p 1688 1776 a(H) p Fj 1769 1791 a(0) p Fn 1808 1776 a(;) p Fl 1852 1776 a(J) p Fj 1906 1791 a(+0) p Fn 2000 1776 a(\)) p Ff 2038 1735 a(\003) p Fl 2077 1776 a(W) p Ff 2169 1791 a(\000) p Fn 2228 1776 a(\() p Fl(H) p Fg 2347 1791 a(\014) p Fl 2394 1776 a(;) p 2438 1776 a(H) p Fj 2519 1791 a(0) p Fn 2558 1776 a(;) p Fl 2602 1776 a(J) p Ff 2656 1791 a(\000) p Fj(0) p Fn 2750 1776 a(\)) p Fl(:) p Fn 0 1945 a(The) p 196 1945 a(op) s(erator) p Fl 584 1945 a(S) p Fj 644 1960 a(0) p Fn 683 1945 a(\() p Fl(H) p Fg 802 1960 a(\014) p Fl 849 1945 a(;) p 893 1945 a(H) p Fj 974 1960 a(0) p Fn 1013 1945 a(\)) p 1078 1945 a(also) p 1269 1945 a(has) p 1438 1945 a(the) p 1601 1945 a(direct) p 1873 1945 a(in) m(tegral) p 2223 1945 a(decomp) s(osition,) p 2889 1945 a(b) s(ecause) p 3245 1945 a(it) p 3337 1945 a(com-) 0 2066 y(m) m(utes) p 292 2066 a(with) p Fl 521 2066 a(H) p Fj 602 2081 a(0) p Fn 642 2066 a(.) p 733 2066 a(W) p 825 2066 a(e) p 908 2066 a(denote) p 1230 2066 a(the) p 1405 2066 a(\014bre) p 1634 2066 a(b) m(y) p Fl 1776 2066 a(S) p Fj 1836 2081 a(0) p Fn 1876 2066 a(\() p Fl(\025) p Fn(;) p Fl 2015 2066 a(H) p Fg 2096 2081 a(\014) p Fl 2142 2066 a(;) p 2186 2066 a(H) p Fj 2267 2081 a(0) p Fn 2306 2066 a(\)) p 2384 2066 a(:) p Fl 2451 2066 a(L) p Fj 2517 2030 a(2) p Fn 2557 2066 a(\() p Fl(S) p Fj 2661 2030 a(1) p Fn 2700 2066 a(\)) p Fi 2777 2066 a(!) p Fl 2917 2066 a(L) p Fj 2983 2030 a(2) p Fn 3022 2066 a(\() p Fl(S) p Fj 3126 2030 a(1) p Fn 3166 2066 a(\)) p 3243 2066 a(and) p 3440 2066 a(its) 0 2186 y(k) m(ernel) p 293 2186 a(b) m(y) p Fl 435 2186 a(S) p Fj 495 2201 a(0) p Fn 535 2186 a(\() p Fl(\022) s(;) p 665 2186 a(!) p Fn 730 2186 a(;) p Fl 774 2186 a(\025;) p 875 2186 a(H) p Fg 956 2201 a(\014) p Fl 1001 2186 a(;) p 1045 2186 a(H) p Fj 1126 2201 a(0) p Fn 1165 2186 a(\).) p 1292 2186 a(W) p 1384 2186 a(e) p 1466 2186 a(see) p 1630 2186 a(b) m(y) p 1772 2186 a(Lemma) p 2126 2186 a(2.1) p 2289 2186 a(that) p Fl 2507 2186 a(W) p Ff 2599 2201 a(\000) p Fn 2658 2186 a(\() p Fl(H) p Fj 2777 2201 a(0) p Fl 2816 2186 a(;) p 2860 2186 a(H) p Fj 2941 2201 a(0) p Fn 2980 2186 a(;) p Fl 3024 2186 a(J) p Ff 3078 2201 a(\000) p Fj(1) p Fn 3172 2186 a(\)) p 3249 2186 a(acts) p 3456 2186 a(as) 0 2306 y(the) p 168 2306 a(m) m(ultiplication) p Fl 625 2515 a(F) p 702 2515 a(W) p Ff 794 2530 a(\000) p Fn 852 2515 a(\() p Fl(H) p Fj 971 2530 a(0) p Fl 1011 2515 a(;) p 1055 2515 a(H) p Fj 1136 2530 a(0) p Fn 1175 2515 a(;) p Fl 1219 2515 a(J) p Ff 1273 2530 a(\000) p Fj(1) p Fn 1367 2515 a(\)) p Fl(F) p Ff 1482 2473 a(\003) p Fn 1548 2515 a(=) p 1652 2515 a(exp) q(\() p Fi(\000) p Fl(i\014) p 2010 2515 a(\015) p Fn 2066 2515 a(\() p Fi(\000) p Fl(\022) p Fn 2229 2515 a(;) p Fl 2273 2515 a(!) p Ff 2334 2530 a(\000) p Fn 2393 2515 a(\)\)) p Fl(p) p Ff 2518 2530 a(\000) p Fn 2577 2515 a(\() p Fi 2615 2425 a(p) p 2698 2425 57 4 v Fl 2698 2515 a(\025\022) p Fn 2803 2515 a(\)) p Fi(\002) p Fn 0 2723 a(on) p Fl 135 2723 a(L) p Fj 201 2687 a(2) p Fn 241 2723 a(\(\(0) p Fl(;) p Fi 410 2723 a(1) p Fn(\);) p Fl 592 2723 a(d\025) p Fn(\)) p Fi 759 2723 a(\012) p Fl 858 2723 a(L) p Fj 924 2687 a(2) p Fn 964 2723 a(\() p Fl(S) p Fj 1068 2687 a(1) p Fn 1107 2723 a(\),) p 1205 2723 a(where) p Fl 1487 2723 a(F) p Fn 1596 2723 a(is) p 1694 2723 a(de\014ned) p 2030 2723 a(b) m(y) p 2165 2723 a(\(2.4\).) p 2436 2723 a(Similarly) p Fl 589 2941 a(F) p 666 2941 a(W) p Fj 758 2956 a(+) p Fn 817 2941 a(\() p Fl(H) p Fj 936 2956 a(0) p Fl 975 2941 a(;) p 1019 2941 a(H) p Fj 1100 2956 a(0) p Fn 1139 2941 a(;) p Fl 1183 2941 a(J) p Fj 1237 2956 a(+1) p Fn 1331 2941 a(\)) p Fl(F) p Ff 1446 2900 a(\003) p Fn 1513 2941 a(=) p 1616 2941 a(exp) q(\() p Fi(\000) p Fl(i\014) p 1974 2941 a(\015) p Fn 2030 2941 a(\() p Fl(\022) p Fn 2116 2941 a(;) p Fi 2160 2941 a(\000) p Fl(!) p Fj 2298 2956 a(+) p Fn 2358 2941 a(\)\)) p Fl(p) p Fj 2483 2956 a(+) p Fn 2541 2941 a(\() p Fi 2579 2852 a(p) p 2662 2852 V Fl 2662 2941 a(\025\022) p Fn 2767 2941 a(\)) p Fi 2828 2941 a(\002) p Fl 2927 2941 a(:) p Fn 0 3149 a(Hence) p 290 3149 a(it) p 387 3149 a(follo) m(ws) p 708 3149 a(from) p 938 3149 a(\(3.8\)) p 1171 3149 a(that) p Fl 793 3357 a(S) p Fn 859 3357 a(\() p Fl(!) p Fj 958 3372 a(+) p Fl 1017 3357 a(;) p 1061 3357 a(!) p Ff 1122 3372 a(\000) p Fn 1180 3357 a(;) p Fl 1224 3357 a(E) p 1302 3357 a(;) p 1346 3357 a(H) p Fg 1427 3372 a(\014) p Fl 1474 3357 a(;) p 1518 3357 a(H) p Fj 1599 3372 a(0) p Fn 1638 3357 a(\)) p 1703 3357 a(=) p Fl 1807 3357 a(S) p Fj 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1652 3853 a(the) p 1832 3853 a(idea) p 2049 3853 a(due) p 2245 3853 a(to) p 2376 3853 a([6,) p 2524 3853 a(7].) p 2705 3853 a(W) p 2797 3853 a(e) p 2885 3853 a(calculate) p Fl 3303 3853 a(T) p Ff 3360 3868 a(\000) p Fn 3467 3853 a(=) p Fl 0 3973 a(H) p Fg 81 3988 a(\014) p Fl 128 3973 a(J) p Ff 182 3988 a(\000) p Fj(0) p Fi 298 3973 a(\000) p Fl 398 3973 a(J) p Ff 452 3988 a(\000) p Fj(0) p Fl 546 3973 a(H) p Fj 627 3988 a(0) p Fn 699 3973 a(as) p Fl 307 4181 a(T) p Ff 364 4196 a(\000) p Fn 450 4181 a(=) p 554 4181 a(exp) q(\() p Fl(i\014) p 835 4181 a(\015) p Fn 891 4181 a(\() p Fl(x) p Fn(;) p Fl 1028 4181 a(!) p Ff 1089 4196 a(\000) p Fn 1148 4181 a(\)\)) p 1241 4181 a(\() p Fl 1278 4181 a(H) p Fj 1359 4196 a(0) p Fl 1398 4181 a(q) p Ff 1441 4196 a(\000) p Fi 1523 4181 a(\000) p Fl 1622 4181 a(q) p Ff 1665 4196 a(\000) p Fl 1725 4181 a(H) p Fj 1806 4196 a(0) p Fn 1845 4181 a(\)) p Fl 1900 4181 a(p) p Ff 1949 4196 a(\000) p Fn 2035 4181 a(=) p 2139 4181 a(exp) q(\() p Fl(i\014) p 2420 4181 a(\015) p Fn 2476 4181 a(\() p Fl(x) p Fn(;) p Fl 2613 4181 a(!) p Ff 2674 4196 a(\000) p Fn 2732 4181 a(\)\)[) p Fl(H) p Fj 2916 4196 a(0) p Fl 2956 4181 a(;) p 3000 4181 a(q) p Ff 3043 4196 a(\000) p Fn 3102 4181 a(]) p Fl(p) p Ff 3178 4196 a(\000) p Fn 0 4389 a(b) m(y) p 135 4389 a(use) p 304 4389 a(of) p 415 4389 a(\(3.4\).) p 686 4389 a(Similarly) p 1101 4389 a(w) m(e) p 1244 4389 a(ha) m(v) m(e) p Fl 648 4597 a(T) p Fj 705 4612 a(+) p Fn 792 4597 a(=) p Fl 895 4597 a(H) p Fg 976 4612 a(\014) p Fl 1023 4597 a(J) p Fj 1077 4612 a(+0) p Fi 1194 4597 a(\000) p Fl 1293 4597 a(J) p Fj 1347 4612 a(+0) p Fl 1441 4597 a(H) p Fj 1522 4612 a(0) p Fn 1589 4597 a(=) p 1693 4597 a(exp) q(\() p Fl(i\014) p 1974 4597 a(\015) p Fn 2030 4597 a(\() p Fl(x) p Fn(;) p Fi 2167 4597 a(\000) p Fl(!) p Fj 2305 4612 a(+) p Fn 2364 4597 a(\)\)[) p Fl(H) p Fj 2548 4612 a(0) p Fl 2587 4597 a(;) p 2631 4597 a(q) p Fj 2674 4612 a(+) p Fn 2733 4597 a(]) p Fl(p) p Fj 2809 4612 a(+) p Fl 2868 4597 a(:) p Fn 0 4806 a(Since) p Fl 255 4806 a(W) p Fj 347 4821 a(+) p Fn 406 4806 a(\() p Fl(H) p Fg 525 4821 a(\014) p Fl 572 4806 a(;) p 616 4806 a(H) p Fj 697 4821 a(0) p Fn 736 4806 a(;) p Fl 780 4806 a(J) p Ff 834 4821 a(\000) p Fj(0) p Fn 928 4806 a(\)) p 993 4806 a(=) p 1097 4806 a(0) p 1178 4806 a(b) m(y) p 1314 4806 a(Lemma) p 1662 4806 a(2.1,) p 1846 4806 a(it) p 1944 4806 a(follo) m(ws) p 2264 4806 a(that) p Fl 641 5047 a(W) p Ff 733 5062 a(\000) p Fn 792 5047 a(\() p Fl(H) p Fg 911 5062 a(\014) p Fl 958 5047 a(;) p 1002 5047 a(H) p Fj 1083 5062 a(0) p Fn 1122 5047 a(;) p Fl 1166 5047 a(J) p Ff 1220 5062 a(\000) p Fj(0) p Fn 1314 5047 a(\)) p 1380 5047 a(=) p Fi 1483 5047 a(\000) p Fl(i) p Fh 1627 4930 a(Z) p Fn 1727 5047 a(exp) q(\() p Fl(itH) p Fg 2063 5062 a(\014) p Fn 2110 5047 a(\)) p Fl(T) p Ff 2205 5062 a(\000) p Fn 2281 5047 a(exp) q(\() p Fi(\000) p Fl(itH) p Fj 2694 5062 a(0) p Fn 2734 5047 a(\)) p Fl 2789 5047 a(dt:) p Fn 0 5279 a(If) p 98 5279 a(w) m(e) p 241 5279 a(use) p 410 5279 a(this) p 600 5279 a(relation,) p 985 5279 a(then) p 1207 5279 a(w) m(e) p 1350 5279 a(get) p Fl 434 5487 a(S) p Fj 494 5502 a(0) p Fn 533 5487 a(\() p Fl(\025) p Fn(;) p Fl 672 5487 a(H) p Fg 753 5502 a(\014) p Fl 800 5487 a(;) p 844 5487 a(H) p Fj 925 5502 a(0) p Fn 964 5487 a(\)) p 1029 5487 a(=) p 1133 5487 a(2) p Fl(\031) t(i) p Fn(\000\() p Fl(\025) p Fn(\)) p Fh 1485 5391 a(\020) p Fi 1534 5487 a(\000) p Fl(J) p Ff 1674 5446 a(\003) p Fj 1665 5512 a(+0) p Fl 1760 5487 a(T) p Ff 1817 5502 a(\000) p Fn 1898 5487 a(+) p Fl 1996 5487 a(T) p Ff 2067 5446 a(\003) p Fj 2053 5512 a(+) p Fl 2112 5487 a(R) p Fn 2187 5487 a(\() p Fl(\025) p Fn 2304 5487 a(+) p Fl 2402 5487 a(i) p Fn(0;) p Fl 2528 5487 a(H) p Fg 2609 5502 a(\014) p Fn 2656 5487 a(\)) p Fl(T) p Ff 2751 5502 a(\000) p Fh 2810 5391 a(\021) p Fn 2876 5487 a(\000\() p Fl(\025) p Fn(\)) p Ff 3070 5446 a(\003) p Fn 1723 5753 a(10) p 90 rotate dyy eop %%Page: 11 11 11 10 bop Fn 0 407 a(in) p 120 407 a(exactly) p 462 407 a(the) p 636 407 a(same) p 886 407 a(w) m(a) m(y) p 1090 407 a(as) p 1216 407 a([7,) p 1357 407 a(Theorem) p 1775 407 a(3.3]) p 1965 407 a(\(see) p 2167 407 a([17,) p 2357 407 a(subsection) p 2836 407 a(7.3]) p 3026 407 a(also\),) p 3294 407 a(where) 0 527 y(\000\() p Fl(\025) p Fn(\)) p 221 527 a(:) p Fl 276 527 a(L) p Fj 342 491 a(2) p Fg 342 552 a(s) p Fn 382 527 a(\() p Fk(R) p Fj 507 485 a(2) p Fn 547 527 a(\)) p Fi 612 527 a(!) p Fl 740 527 a(L) p Fj 806 491 a(2) p Fn 845 527 a(\() p Fl(S) p Fj 949 491 a(1) p Fn 989 527 a(\)) p 1059 527 a(is) p 1157 527 a(the) p 1325 527 a(trace) p 1569 527 a(op) s(erator) p 1962 527 a(de\014ned) p 2298 527 a(b) m(y) 1162 732 y(\(\000\() p Fl(\025) p Fn(\)) p Fl(u) p Fn(\)) p 1504 732 a(\() p Fl(\022) p Fn 1590 732 a(\)) p 1656 732 a(=) p 1759 732 a(\() p Fl(F) p 1874 732 a(u) p Fn(\)) p 1984 732 a(\() p Fl(\026;) p 2125 732 a(\022) p Fn 2173 732 a(\)) p Fi(j) p Fg 2239 747 a(\026) p Fj(=) p Fg(\025) p Fn 0 937 a(for) p Fl 153 937 a(s) p 233 937 a(>) p Fn 344 937 a(1) p Fl(=) p Fn(2.) p 573 937 a(This) p 799 937 a(relation) p 1161 937 a(yields) p 1439 937 a(the) p 1611 937 a(represen) m(tation) p 2253 937 a(for) p Fl 2406 937 a(S) p Fj 2466 952 a(0) p Fn 2505 937 a(\() p Fl(!) p Fj 2604 952 a(+) p Fl 2663 937 a(;) p 2707 937 a(!) p Ff 2768 952 a(\000) p Fn 2826 937 a(;) p Fl 2870 937 a(E) p 2948 937 a(;) p 2992 937 a(H) p Fg 3073 952 a(\014) p Fl 3120 937 a(;) p 3164 937 a(H) p Fj 3245 952 a(0) p Fn 3284 937 a(\),) p 3386 937 a(and) 0 1058 y(the) p 168 1058 a(lemma) p 482 1058 a(b) s(elo) m(w) p 759 1058 a(is) p 857 1058 a(obtained) p 1258 1058 a(from) p 1488 1058 a(\(3.9\).) p Fm 0 1314 a(Lemma) p 397 1314 a(3.1) p Fb 589 1314 a(Assume) p 953 1314 a(that) p Fl 1152 1314 a(!) p Ff 1213 1329 a(\000) p Fi 1300 1314 a(6) p Fn(=) p Fl 1403 1314 a(!) p Fj 1464 1329 a(+) p Fb 1523 1314 a(.) p 1598 1314 a(Then) p Fl 1852 1314 a(g) p Fn 1930 1314 a(=) p Fl 2033 1314 a(g) p Fn 2084 1314 a(\() p Fl(!) p Ff 2183 1329 a(\000) p Fi 2269 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3838 a(\() p Fi(j) p Fl(\030) p Fi 1806 3838 a(j) p Fn 1855 3838 a(+) p 1953 3838 a(1\)) p Ff 2039 3790 a(\000j) p Fg(m) p Ff(j) p Fn 2217 3838 a(\() p Fi 2254 3838 a(j) p Fl(x) p Fi(j) p Fn 2387 3838 a(+) p Fl 2485 3838 a(d) p Fg 2536 3797 a(\033) p Fn 2583 3838 a(\)) p Ff 2621 3790 a(\000j) p Fg(l) p Ff 2718 3790 a(j) p Fl 2758 3838 a(:) p Fn 0 4043 a(W) p 92 4043 a(e) p 168 4043 a(no) m(w) p 371 4043 a(assert) p 649 4043 a(that) p Fi 898 4248 a(k) p Fl(r) p Ff 992 4263 a(\000) p Fg(L) p Fl 1099 4248 a(w) p Ff 1169 4263 a(1) p Fl 1243 4248 a(R) p Fn 1318 4248 a(\() p Fl(E) p Fn 1456 4248 a(+) p Fl 1554 4248 a(i) p Fn(0;) p Fl 1680 4248 a(L) p Fj 1746 4263 a(1) p Fg(d) p Fn 1822 4248 a(\)) p Fl(s) p Fj 1906 4263 a(1) p Fi 1945 4248 a(k) p Fn 2078 4248 a(=) p Fl 2237 4248 a(O) p Fn 2315 4248 a(\() p Fi(j) p Fl(d) p Fi(j) p Ff 2460 4207 a(\000) p Fg(N) p Fn 2581 4248 a(\)) p 3343 4248 a(\(4.4\)) p Fi 932 4393 a(k) p Fl(s) p Fj 1028 4408 a(1) p Fl 1067 4393 a(R) p Fn 1142 4393 a(\() p 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a(\033) p Fn 1992 5150 a(and) p Fi 2183 5150 a(j) p Fn 2217 5150 a(^) p Fl 2211 5150 a(x) p Fi 2290 5150 a(\000) p Fn 2395 5150 a(^) p Fl 2391 5150 a(e) p Fi(j) p Fl 2495 5150 a(<) p 2602 5150 a(\016) p Fn 2683 5150 a(and) p 2875 5150 a(if) p Fi 2966 5150 a(j) p Fl(\030) p Fi 3042 5150 a(j) p Fj 3070 5114 a(2) p Fl 3140 5150 a(<) p 3246 5150 a(E) p 3324 5150 a(=) p Fn(2) p 3457 5150 a(or) p Fi 0 5270 a(j) p Fl(\030) p Fi 76 5270 a(j) p Fj 104 5234 a(2) p Fl 170 5270 a(>) p Fn 273 5270 a(2) p Fl(E) p Fn 400 5270 a(,) p 460 5270 a(then) p 682 5270 a(the) p 850 5270 a(sym) m(b) s(ol) p Fl 1184 5270 a(L) p Fj 1250 5285 a(1) p Fg(d) p Fn 1326 5270 a(\() p Fl(x;) p 1463 5270 a(\030) p Fn 1511 5270 a(\)) p Fi 1571 5270 a(\000) p Fl 1670 5270 a(E) p Fn 1781 5270 a(of) p 1892 5270 a(op) s(erator) p Fl 220 5487 a(L) p Fj 286 5502 a(1) p Fg(d) p Fi 384 5487 a(\000) p Fl 484 5487 a(E) p Fn 589 5487 a(=) p Fl 693 5487 a(e) p Fg 738 5446 a(i\020) p Fd 793 5455 a(2) p Fn 849 5487 a(\() p Fl(K) p Fj 970 5502 a(1) p Fg(d) p Fi 1067 5487 a(\000) p Fl 1167 5487 a(E) p Fn 1245 5487 a(\)) p Fl 1300 5487 a(e) p Ff 1345 5446 a(\000) p Fg(i\020) p Fd 1455 5455 a(2) p Fn 1521 5487 a(=) p Fl 1625 5487 a(e) p Fg 1670 5446 a(i\020) p Fd 1725 5455 a(2) p Fh 1780 5391 a(\020) p Fn 1830 5487 a(\() p Fi(\000) p Fl(i) p Fi(r) p 2084 5487 a(\000) p Fl 2183 5487 a(B) p Fj 2257 5502 a(1) p Fg(d) p Fn 2333 5487 a(\)) p Fj 2371 5446 a(2) p Fi 2433 5487 a(\000) p Fl 2532 5487 a(E) p Fh 2610 5391 a(\021) p Fl 2677 5487 a(e) p Ff 2722 5446 a(\000) p Fg(i\020) p Fd 2832 5455 a(2) p Fi 2898 5487 a(\030) p Fl 3003 5487 a(H) p Fj 3084 5502 a(0) p Fi 3146 5487 a(\000) p Fl 3245 5487 a(E) p Fn 1723 5753 a(16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fn 0 407 a(has) p 170 407 a(a) p 248 407 a(b) s(ounded) p 643 407 a(in) m(v) m(erse.) p 1003 407 a(This) p 1222 407 a(enables) p 1560 407 a(us) p 1682 407 a(to) p 1798 407 a(construct) p 2223 407 a(an) p 2355 407 a(appro) m(ximation) p 3001 407 a(to) p Fl 3117 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1822 2249 a(\() p Fl(x) p Fn(\)) p 1981 2249 a(=) p Fl 2084 2249 a(\020) p Fj 2127 2264 a(1) p Fn 2166 2249 a(\() p Fl(x) p Fn(\)) p 2320 2249 a(+) 2427 2223 y(~) p Fl 2418 2249 a(\020) p Fj 2461 2264 a(2) p Fn 2500 2249 a(\() p Fl(x) p Fn(\)) p Fl(;) p Fn 3343 2249 a(\(4.7\)) 0 2448 y(on) p 143 2448 a(\006,) p 281 2448 a(\006) p 392 2448 a(b) s(eing) p 661 2448 a(as) p 788 2448 a(in) p 909 2448 a(\(4.2\).) p 1201 2448 a(Let) p 1392 2448 a(~) p Fl 1383 2448 a(\032) p Fj 1433 2463 a(+) p Fn 1493 2448 a(\() p Fl(\030) p Fn 1579 2448 a(\)) p 1655 2448 a(b) s(e) p 1795 2448 a(a) p 1884 2448 a(smo) s(oth) p 2235 2448 a(real) p 2432 2448 a(sym) m(b) s(ol) p 2773 2448 a(with) p 3002 2448 a(the) p 3177 2448 a(prop) s(ert) m(y) 0 2568 y(that) p 219 2568 a(~) p Fl 210 2568 a(\032) p Fj 260 2583 a(+) p Fn 350 2568 a(has) p 522 2568 a(a) p 602 2568 a(sligh) m(tly) p 942 2568 a(larger) p 1217 2568 a(supp) s(ort) p 1576 2568 a(than) p Fl 1802 2568 a(\032) p Fj 1852 2583 a(+) p Fn 1942 2568 a(and) p 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3085 y(and) p Fl 186 3085 a(q) p Fn 261 3085 a(has) p 431 3085 a(supp) s(ort) p 788 3085 a(in) p 898 3085 a(\006) p Fj 968 3100 a(2) p Fn 1035 3085 a(=) p Fi 1139 3085 a(fj) p Fl(x) p Fi(j) p Fl 1327 3085 a(>) p 1431 3085 a(M) p Fi 1535 3085 a(j) p Fl(d) p Fi(j) p Fg 1642 3049 a(\033) p Fl 1688 3085 a(=) p Fn(3) p Fl(;) p Fi 1876 3085 a(j) p Fn 1910 3085 a(^) p Fl 1904 3085 a(x) p Fn 1973 3085 a(+) p 2067 3085 a(^) p Fl 2063 3085 a(e) p Fi(j) p Fl 2164 3085 a(>) p 2267 3085 a(\016) p Fi 2314 3085 a(g) p Fn(.) p 2433 3085 a(The) p 2629 3085 a(relation) p 2983 3085 a(\(4.7\)) p 3212 3085 a(remains) 0 3206 y(true) p 206 3206 a(o) m(v) m(er) p 415 3206 a(\006) p Fj 485 3221 a(2) p Fn 524 3206 a(.) p 595 3206 a(Hence) p 885 3206 a(w) m(e) p 1028 3206 a(ha) m(v) m(e) 551 3404 y(\() p Fl(K) p Fg 672 3419 a(d) p Fi 734 3404 a(\000) p Fl 834 3404 a(E) p Fn 912 3404 a(\)) p Fl(e) p Fg 995 3363 a(i) p Fj 1025 3345 a(~) p Fg 1019 3363 a(\020) p Fl 1059 3404 a(q) p Fn 1133 3404 a(=) p Fl 1237 3404 a(e) p Fg 1282 3363 a(i) p Fj 1312 3345 a(~) p Fg 1306 3363 a(\020) p Fn 1346 3404 a(\() p Fl(H) p Fj 1465 3419 a(0) p Fi 1526 3404 a(\000) p Fl 1626 3404 a(E) p Fn 1704 3404 a(\)) p Fl(q) p Fn 1816 3404 a(=) p Fl 1920 3404 a(e) p Fg 1965 3363 a(i) p Fj 1995 3345 a(~) p Fg 1989 3363 a(\020) p Fn 2045 3404 a(\() p Fl(q) p Fn 2130 3404 a(\() p Fl(H) p Fj 2249 3419 a(0) p Fi 2310 3404 a(\000) p Fl 2410 3404 a(E) p Fn 2488 3404 a(\)) p 2548 3404 a(+) p 2646 3404 a([) p Fl(H) p Fj 2754 3419 a(0) p Fl 2793 3404 a(;) p 2837 3404 a(q) p Fn 2884 3404 a(]\)) p Fl 2966 3404 a(:) p Fn 0 3602 a(W) p 92 3602 a(e) p 176 3602 a(denote) p 499 3602 a(b) m(y) p 647 3602 a(~) p Fl 643 3602 a(r) p Fg 687 3617 a(N) p Fn 795 3602 a(b) s(ounded) p 1201 3602 a(op) s(erators) p 1641 3602 a(suc) m(h) p 1869 3602 a(that) p 2089 3602 a(\() p Fi(j) p Fl(x) p Fi(j) p Fn 2260 3602 a(+) p Fi 2358 3602 a(j) p Fl(d) p Fi(j) p Fn(\)) p Fg 2502 3554 a(N) p Fn 2590 3602 a(~) p Fl 2585 3602 a(r) p Fg 2629 3617 a(N) p Fn 2737 3602 a(and) p 2940 3602 a(~) p Fl 2935 3602 a(r) p Fg 2979 3617 a(N) p Fn 3063 3602 a(\() p Fi(j) p Fl(x) p Fi(j) p Fn 3234 3602 a(+) p Fi 3332 3602 a(j) p Fl(d) p Fi(j) p Fn(\)) p Fg 3476 3554 a(N) p Fn 0 3723 a(are) p 163 3723 a(b) s(oth) p 393 3723 a(b) s(ounded) p 791 3723 a(uniformly) p 1236 3723 a(in) p Fl 1349 3723 a(d) p Fn(.) p 1471 3723 a(Since) p Fl 1725 3723 a(q) t(w) p Fj 1842 3738 a(+) p Fn 1901 3723 a(\() p Fl(x;) p 2038 3723 a(D) p Fg 2119 3738 a(x) p Fn 2163 3723 a(\)) p 2228 3723 a(=) p Fl 2332 3723 a(w) p Fj 2402 3738 a(+) p Fn 2461 3723 a(\() p Fl(x;) p 2598 3723 a(D) p Fg 2679 3738 a(x) p Fn 2723 3723 a(\)) p 2793 3723 a(and) p 2983 3723 a(since) 967 3937 y(\(1) p Fi 1076 3937 a(\000) p Fn 1184 3937 a(~) p Fl 1175 3937 a(\032) p Fj 1225 3952 a(+) p Fn 1285 3937 a(\)) p Fl(e) p Ff 1368 3896 a(\000) p Fg(i) p Fj 1453 3878 a(~) p Fg 1447 3896 a(\020) p Fl 1486 3937 a(w) p Fj 1556 3952 a(+) p Fn 1643 3937 a(=) p 1751 3937 a(~) p Fl 1746 3937 a(r) p Fg 1790 3952 a(N) p Fl 1858 3937 a(;) p Fn 2008 3937 a(~) p Fl 1999 3937 a(\032) p Fj 2049 3952 a(+) p Fn 2136 3937 a(=) p 2248 3937 a(~) p Fl 2239 3937 a(\032) p Fj 2289 3952 a(+) p Fn 2349 3937 a(\() p Fl(D) p Fg 2468 3952 a(x) p Fn 2512 3937 a(\)) p Fl(;) p Fn 0 4135 a(for) p 149 4135 a(an) m(y) p Fl 333 4135 a(N) p Fi 449 4135 a(\035) p Fn 577 4135 a(1,) p 685 4135 a(w) m(e) p 829 4135 a(ha) m(v) m(e) 620 4344 y(\() p Fl(K) p Fg 741 4359 a(d) p Fi 803 4344 a(\000) p Fl 903 4344 a(E) p Fn 981 4344 a(\)) p Fl(e) p Fg 1064 4303 a(i) p Fj 1094 4286 a(~) p Fg 1088 4303 a(\020) p Fl 1128 4344 a(q) t(R) p Fn 1250 4344 a(\() p Fl(E) p Fn 1388 4344 a(+) p Fl 1486 4344 a(i) p Fn(0;) p Fl 1612 4344 a(H) p Fj 1693 4359 a(0) p Fn 1732 4344 a(\)) p 1779 4344 a(~) p Fl 1770 4344 a(\032) p Fj 1820 4359 a(+) p Fl 1879 4344 a(e) p Ff 1924 4303 a(\000) p Fg(i) p Fj 2009 4286 a(~) p Fg 2003 4303 a(\020) p Fl 2043 4344 a(w) p Fj 2113 4359 a(+) p Fn 1108 4506 a(=) p Fl 1211 4506 a(w) p Fj 1281 4521 a(+) p Fn 1362 4506 a(+) p 1464 4506 a(~) p Fl 1460 4506 a(r) p Fg 1504 4521 a(N) p Fn 1593 4506 a(+) p Fl 1691 4506 a(e) p Fg 1736 4464 a(i) p Fj 1766 4447 a(~) p Fg 1760 4464 a(\020) p Fn 1800 4506 a([) p Fl(H) p Fj 1908 4521 a(0) p Fl 1948 4506 a(;) p 1992 4506 a(q) p Fn 2039 4506 a(]) p Fl(R) p Fn 2141 4506 a(\() p Fl(E) p Fn 2279 4506 a(+) p Fl 2377 4506 a(i) p Fn(0;) p Fl 2503 4506 a(H) p Fj 2584 4521 a(0) p Fn 2623 4506 a(\)) p 2670 4506 a(~) p Fl 2661 4506 a(\032) p Fj 2711 4521 a(+) p Fl 2770 4506 a(e) p Ff 2815 4464 a(\000) p Fg(i) p Fj 2900 4447 a(~) p Fg 2894 4464 a(\020) p Fl 2934 4506 a(w) p Fj 3004 4521 a(+) p Fl 3062 4506 a(:) p Fn 0 4704 a(W) p 92 4704 a(e) p 174 4704 a(can) p 359 4704 a(tak) m(e) p 577 4704 a(0) p Fl 664 4704 a(<) p 778 4704 a(\016) p Fi 863 4704 a(\034) p Fn 1001 4704 a(1) p 1088 4704 a(so) p 1214 4704 a(small) p 1476 4704 a(and) p Fl 1671 4704 a(M) p Fi 1814 4704 a(\035) p Fn 1952 4704 a(1) p 2040 4704 a(so) p 2166 4704 a(large) p 2410 4704 a(that) p 2628 4704 a(the) p 2802 4704 a(free) p 2995 4704 a(particle) p 3354 4704 a(with) 0 4824 y(initial) p 283 4824 a(state) p 522 4824 a(in) p Fl 637 4824 a(G) p Fj 714 4839 a(+) p Fn 806 4824 a(at) p Fl 926 4824 a(t) p Fn 991 4824 a(=) p 1095 4824 a(0) p 1178 4824 a(nev) m(er) p 1438 4824 a(passes) p 1734 4824 a(o) m(v) m(er) p 1943 4824 a(supp) p Fi 2161 4824 a(r) p Fl(q) p Fn 2324 4824 a(for) p Fl 2474 4824 a(t) p 2538 4824 a(>) p Fn 2643 4824 a(0.) p 2764 4824 a(This) p 2988 4824 a(enables) p 3331 4824 a(us) p 3457 4824 a(to) 0 4945 y(put) 1006 5076 y([) p Fl(H) p Fj 1114 5091 a(0) p Fl 1153 5076 a(;) p 1197 5076 a(q) p Fn 1244 5076 a(]) p Fl(R) p Fn 1346 5076 a(\() p Fl(E) p Fn 1484 5076 a(+) p Fl 1582 5076 a(i) p Fn(0;) p Fl 1708 5076 a(H) p Fj 1789 5091 a(0) p Fn 1828 5076 a(\)) p 1875 5076 a(~) p Fl 1866 5076 a(\032) p Fj 1916 5091 a(+) p Fl 1975 5076 a(e) p Ff 2020 5034 a(\000) p Fg(i) p Fj 2105 5017 a(~) p Fg 2099 5034 a(\020) p Fl 2139 5076 a(w) p Fj 2209 5091 a(+) p Fn 2296 5076 a(=) p 2404 5076 a(~) p Fl 2399 5076 a(r) p Fg 2443 5091 a(N) p Fl 2510 5076 a(:) p Fn 3343 5076 a(\(4.8\)) 0 5241 y(T) p 62 5241 a(o) p 144 5241 a(see) p 301 5241 a(it,) p 426 5241 a(w) m(e) p 570 5241 a(represen) m(t) p 990 5241 a(the) p 1158 5241 a(resolv) m(en) m(t) p Fl 906 5466 a(R) p Fn 981 5466 a(\() p Fl(E) p Fn 1119 5466 a(+) p Fl 1217 5466 a(i) p Fn(0;) p Fl 1343 5466 a(H) p Fj 1424 5481 a(0) p Fn 1463 5466 a(\)) p 1529 5466 a(=) p Fl 1632 5466 a(i) p Fh 1699 5349 a(Z) p Ff 1782 5375 a(1) p Fj 1745 5537 a(0) p Fl 1873 5466 a(e) p Fg 1918 5425 a(itE) p Fn 2044 5466 a(exp) q(\() p Fi(\000) p Fl(itH) p Fj 2457 5481 a(0) p Fn 2497 5466 a(\)) p Fl 2552 5466 a(dt) p Fn 1723 5753 a(17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fn 0 407 a(in) p 117 407 a(the) p 288 407 a(in) m(tegral) p 647 407 a(form) p 880 407 a(of) p 994 407 a(propagator) p 1496 407 a(exp) q(\() p Fi(\000) p Fl(itH) p Fj 1909 422 a(0) p Fn 1950 407 a(\).) p 2068 407 a(If) p Fl 2168 407 a(x) p Fn 2260 407 a(is) p 2361 407 a(in) p 2478 407 a(the) p 2649 407 a(supp) s(ort) p 3014 407 a(of) p Fi 3128 407 a(r) p Fl(q) p Fn 3293 407 a(and) p 3486 407 a(if) 0 527 y(\() p Fl(y) t(;) p 134 527 a(\030) p Fn 182 527 a(\)) p Fi 246 527 a(2) p Fl 340 527 a(G) p Fj 417 542 a(+) p Fn 476 527 a(,) p 535 527 a(then) p Fi 987 648 a(j) p Fl(x) p Fi 1092 648 a(\000) p Fl 1192 648 a(y) p Fi 1265 648 a(\000) p Fn 1364 648 a(2) p Fl(t\030) p Fi 1496 648 a(j) p 1551 648 a(\025) p Fl 1656 648 a(c) p Fn 1715 648 a(\() p Fl(t) p Fn 1810 648 a(+) p Fi 1908 648 a(j) p Fl(x) p Fi(j) p Fn 2041 648 a(+) p Fi 2139 648 a(j) p Fl(y) p Fi 2219 648 a(j) p Fn 2268 648 a(+) p Fi 2366 648 a(j) p Fl(d) p Fi(j) p Fg 2473 606 a(\033) p Fn 2519 648 a(\)) 0 821 y(for) p Fl 149 821 a(t) p Fi 212 821 a(\025) p Fn 317 821 a(0,) p 425 821 a(and) p 615 821 a(hence) p Fi 380 1049 a(k) p Fn(\() p Fi(j) p Fl(x) p Fi(j) p Fn 600 1049 a(+) p Fi 699 1049 a(j) p Fl(d) p Fi(j) p Fn(\)) p Fg 844 1008 a(N) p Fn 910 1049 a([) p Fl(H) p Fj 1018 1064 a(0) p Fl 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a(anishes) p 756 1717 a(on) p 891 1717 a(\006) p Fj 961 1732 a(2) p Fn 1001 1717 a(,) p 1061 1717 a(\(4.5\)) p 1294 1717 a(follo) m(ws) p 1614 1717 a(from) p 1844 1717 a(Lemma) p 2193 1717 a(4.1.) 146 1886 y(W) p 238 1886 a(e) p 311 1886 a(conclude) p 709 1886 a(the) p 874 1886 a(pro) s(of) p 1126 1886 a(b) m(y) p 1258 1886 a(sho) m(wing) p 1627 1886 a(\(4.6\).) p 1897 1886 a(This) p 2116 1886 a(is) p 2211 1886 a(v) m(eri\014ed) p 2549 1886 a(in) p 2660 1886 a(almost) p 2972 1886 a(the) p 3137 1886 a(same) p 3378 1886 a(w) m(a) m(y) 0 2007 y(as) p 120 2007 a(\(4.5\).) p 391 2007 a(But) p 584 2007 a(w) m(e) p 728 2007 a(require) p 1056 2007 a(a) p 1137 2007 a(sligh) m(t) p 1401 2007 a(mo) s(di\014cation) p 1962 2007 a(to) p 2081 2007 a(construct) p 2509 2007 a(an) p 2645 2007 a(appro) m(ximation) p 3295 2007 a(to) p Fl 868 2241 a(w) p Ff 938 2256 a(\000) p Fl 997 2241 a(R) p Fn 1072 2241 a(\() p Fl(E) p Fn 1210 2241 a(+) p Fl 1308 2241 a(i) p Fn(0;) p Fl 1434 2241 a(L) p Fj 1500 2256 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4954 a(i) p Fn(0;) p Fl 1935 4954 a(L) p Fj 2001 4969 a(2) p Fg(d) p Fn 2077 4954 a(\)\)) p 2170 4954 a([) 2217 4928 y(~) p Fl 2197 4954 a( ) p Fj 2260 4969 a(2) p Fl 2300 4954 a(;) p 2344 4954 a(L) p Fj 2410 4969 a(1) p Fg(d) p Fn 2486 4954 a(]) p 2540 4954 a(=) p Fl 2644 4954 a(O) p Fg 2719 4969 a(p) p Fn 2758 4954 a(\() p Fi(j) p Fl(d) p Fi(j) p Ff 2903 4913 a(\000) p Fj(1+) p Fg(c\033) p Fn 3125 4954 a(\)) 0 5157 y(for) p 149 5157 a(some) p Fl 393 5157 a(c) p 463 5157 a(>) p Fn 567 5157 a(0,) p 675 5157 a(and) p 865 5157 a(also) p 1060 5157 a(it) p 1158 5157 a(follo) m(ws) p 1478 5157 a(from) p 1709 5157 a(Lemma) p 2057 5157 a(5.1) p 2214 5157 a(that) 843 5359 y([) 890 5332 y(~) p Fl 870 5359 a( ) p Fj 933 5374 a(3) p Fl 973 5359 a(;) p 1017 5359 a(L) p Fj 1083 5374 a(0) p Fg(d) p Fn 1159 5359 a(]) p Fl(R) p Fn 1261 5359 a(\() p Fl(E) p Fn 1399 5359 a(+) p Fl 1497 5359 a(i) p Fn(0;) p Fl 1623 5359 a(L) p Fj 1689 5374 a(0) p Fg(d) p Fn 1765 5359 a(\)[) p Fl(L) p Fj 1896 5374 a(1) p 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1635 a(2) p Fn 2956 1620 a(\)) 257 1765 y(+) p Fl 416 1765 a(\034) p Fj 458 1780 a(3) p Fn 498 1765 a(\() p Fl(h) p Fn(\)) p 647 1765 a(\() p Fl 684 1765 a(\022) p Fj 729 1780 a(+) p Fn 806 1765 a(cos\() p Fl(\013) p Fj 1036 1780 a(1) p Fl 1076 1765 a(=h) p Fn 1203 1765 a(+) p Fl 1301 1765 a(\013) p Fj 1363 1780 a(2) p Fl 1402 1765 a(=h) p Fn(\)) p Fl(\031) p Fn 1626 1765 a(+) p Fl 1724 1765 a(\022) p Ff 1769 1780 a(\000) p Fn 1845 1765 a(cos) q(\() p Fl(\013) p Fj 2076 1780 a(1) p Fl 2115 1765 a(=h) p Fi 2242 1765 a(\000) p Fl 2342 1765 a(\013) p Fj 2404 1780 a(2) p Fl 2443 1765 a(=h) p Fn(\)) p Fl(\031) p Fn 2645 1765 a(\)) p Fl 2700 1765 a(f) p Fg 2748 1780 a(h) p Fn 2793 1765 a(\() t(^) p Fl 2831 1765 a(e) p Fi 2903 1765 a(!) p Fl 3031 1765 a(!) p Fj 3092 1780 a(+) p Fn 3151 1765 a(;) p Fl 3195 1765 a(\013) p Fj 3257 1780 a(3) p Fl 3296 1765 a(;) p 3340 1765 a(e) p Fj 3385 1780 a(3) p Fn 3424 1765 a(\)) 257 1910 y(+) p Fl 416 1910 a(o) p Fn(\() p Fl(h) p Fj 557 1869 a(1) p Fg(=) p Fj(2) p Fn 667 1910 a(\)) p Fl(;) p 944 1910 a(h) p Fi 1028 1910 a(!) p Fn 1155 1910 a(0) p Fl(;) p Fn 0 2115 a(where) p Fl 491 2319 a(\034) p Fj 533 2334 a(1) p Fn 572 2319 a(\() p Fl(h) p Fn(\)) p 787 2319 a(=) p 946 2319 a(exp) q(\() p Fl(i) p Fn(\() p Fl(\013) p Fj 1266 2334 a(2) p Fl 1306 2319 a(=h) p Fn(\)) p Fl(\034) p Fn 1502 2319 a(\() p Fi(\000) p Fn 1621 2319 a(^) p Fl 1617 2319 a(e) p Fn 1663 2319 a(;) p 1710 2319 a(^) p Fl 1707 2319 a(e;) p 1796 2319 a(!) p Fj 1857 2334 a(+) p Fn 1915 2319 a(\)\)) p 2008 2319 a(exp) q(\() p Fl(i) p Fn(\() p Fl(\013) p Fj 2328 2334 a(3) p Fl 2367 2319 a(=h) p Fn(\)) p Fl(\034) p Fn 2563 2319 a(\() p Fi(\000) p Fn 2682 2319 a(^) p Fl 2678 2319 a(e) p Fn 2724 2319 a(;) p 2772 2319 a(^) p Fl 2768 2319 a(e;) p 2857 2319 a(!) p Fj 2918 2334 a(+) p Fn 2977 2319 a(\)\)) p Fl 491 2465 a(\034) p Fj 533 2480 a(2) p Fn 572 2465 a(\() p Fl(h) p Fn(\)) p 787 2465 a(=) p 946 2465 a(exp) q(\() p Fl(i) p Fn(\() p Fl(\013) p Fj 1266 2480 a(1) p Fl 1306 2465 a(=h) p Fn(\)) p Fl(\034) p Fn 1502 2465 a(\() t(^) p Fl 1540 2465 a(e) p Fn(;) p 1633 2465 a(^) p Fl 1629 2465 a(e;) p 1718 2465 a(!) p Fj 1779 2480 a(+) p Fn 1838 2465 a(\)\)) p 1931 2465 a(exp\() p Fl(i) p Fn(\() p Fl(\013) p Fj 2250 2480 a(3) p Fl 2290 2465 a(=h) p Fn(\)) p Fl(\034) p Fn 2486 2465 a(\() p Fi(\000) p Fn 2605 2465 a(^) p Fl 2601 2465 a(e) p Fn 2647 2465 a(;) p 2694 2465 a(^) p Fl 2691 2465 a(e;) p 2780 2465 a(!) p Fj 2841 2480 a(+) p Fn 2899 2465 a(\)\)) p Fl 491 2610 a(\034) p Fj 533 2625 a(3) p Fn 572 2610 a(\() p Fl(h) p Fn(\)) p 787 2610 a(=) p 946 2610 a(exp) q(\() p Fl(i) p Fn(\() p Fl(\013) p Fj 1266 2625 a(1) p Fl 1306 2610 a(=h) p Fn(\)) p Fl(\034) p Fn 1502 2610 a(\() t(^) p Fl 1540 2610 a(e) p Fn(;) p 1633 2610 a(^) p Fl 1629 2610 a(e;) p 1718 2610 a(!) p Fj 1779 2625 a(+) p Fn 1838 2610 a(\)\)) p 1931 2610 a(exp\() p Fl(i) p Fn(\() p Fl(\013) p Fj 2250 2625 a(2) p Fl 2290 2610 a(=h) p Fn(\)) p Fl(\034) p Fn 2486 2610 a(\() t(^) p Fl 2524 2610 a(e) p Fn 2570 2610 a(;) p 2617 2610 a(^) p Fl 2614 2610 a(e) o(;) p 2702 2610 a(!) p Fj 2763 2625 a(+) p Fn 2822 2610 a(\)\)) p Fl(:) p Fn 0 2815 a(W) p 92 2815 a(e) p 168 2815 a(can) p 347 2815 a(also) p 542 2815 a(sho) m(w) p 784 2815 a(that) p 996 2815 a(the) p 1164 2815 a(bac) m(kw) m(ard) p 1600 2815 a(amplitude) p Fl 2060 2815 a(f) p Fg 2108 2830 a(h) p Fn 2181 2815 a(=) p Fl 2285 2815 a(f) p Fg 2333 2830 a(h) p Fn 2377 2815 a(\() t(^) p Fl 2415 2815 a(e) p Fi 2488 2815 a(!) p 2616 2815 a(\000) p Fn 2697 2815 a(^) p Fl 2693 2815 a(e) p Fn(\)) p 2809 2815 a(ob) s(eys) p Fl 97 3019 a(f) p Fg 145 3034 a(h) p Fi 217 3019 a(\030) p Fl 322 3019 a(f) p Fj 370 3034 a(1) p Fn 432 3019 a(+) p 530 3019 a(\(cos) q(\() p Fl(\013) p Fj 799 3034 a(1) p Fl 838 3019 a(=h) p Fn(\)) p Fl(\031) p Fn 1040 3019 a(\)) p Fj 1078 2978 a(2) p Fl 1117 3019 a(f) p Fj 1165 3034 a(2) p Fn 1227 3019 a(+) p 1325 3019 a(\() p Fl(\022) p Fj 1408 3034 a(+) p Fn 1484 3019 a(cos\(\() p Fl(\013) p Fj 1752 3034 a(1) p Fn 1814 3019 a(+) p Fl 1912 3019 a(\013) p Fj 1974 3034 a(2) p Fn 2013 3019 a(\)) p Fl(\031) t(=h) p Fn(\)) p 2275 3019 a(+) p Fl 2373 3019 a(\022) p Ff 2418 3034 a(\000) p Fn 2494 3019 a(cos) q(\(\() p Fl(\013) p Fj 2763 3034 a(1) p Fi 2824 3019 a(\000) p Fl 2924 3019 a(\013) p Fj 2986 3034 a(2) p Fn 3026 3019 a(\)) p Fl(\031) t(=h) p Fn(\)\)) p Fj 3303 2971 a(2) p Fl 3359 3019 a(f) p Fj 3407 3034 a(3) p Fn 0 3224 a(as) p Fl 120 3224 a(h) p Fi 204 3224 a(!) p Fn 331 3224 a(0,) p 439 3224 a(where) p Fl 721 3224 a(f) p Fg 769 3239 a(j) p Fn 833 3224 a(=) p Fl 937 3224 a(f) p Fg 985 3239 a(h) p Fn 1030 3224 a(\() t(^) p Fl 1068 3224 a(e) p Fi 1141 3224 a(!) p 1268 3224 a(\000) p Fn 1349 3224 a(^) p Fl 1345 3224 a(e) p Fn 1391 3224 a(;) p Fl 1435 3224 a(\013) p Fg 1497 3239 a(j) p Fl 1533 3224 a(;) p 1577 3224 a(e) p Fg 1622 3239 a(j) p Fn 1658 3224 a(\).) 146 3389 y(The) p 350 3389 a(results) p 663 3389 a(in) p 779 3389 a(Remarks) p 1188 3389 a(6.1) p 1348 3389 a(and) p 1541 3389 a(6.3) p 1701 3389 a(are) p 1866 3389 a(obtained) p 2270 3389 a(as) p 2393 3389 a(immediate) p 2873 3389 a(consequences) p 3465 3389 a(of) 0 3510 y(the) p 167 3510 a(previous) p 554 3510 a(w) m(orks) p 830 3510 a([8,) p 964 3510 a(Theorem) p 1375 3510 a(1.1]) p 1559 3510 a(and) p 1747 3510 a([9,) p 1882 3510 a(Theorem) p 2293 3510 a(1.2,) p 2476 3510 a(Remark) p 2842 3510 a(1.1]) p 3025 3510 a(resp) s(ectiv) m(ely) p 3513 3510 a(,) 0 3630 y(where) p 285 3630 a(w) m(e) p 432 3630 a(ha) m(v) m(e) p 660 3630 a(studied) p 1005 3630 a(the) p 1176 3630 a(magnetic) p 1596 3630 a(scattering) p 2050 3630 a(b) m(y) p 2189 3630 a(t) m(w) m(o) p 2376 3630 a(or) p 2498 3630 a(three) p 2751 3630 a(p) s(oin) m(t{lik) m(e) p 3204 3630 a(\014elds) p 3457 3630 a(at) 0 3751 y(large) p 238 3751 a(separation.) p Fm 1509 4079 a(References) p Fn 92 4426 a([1]) p 244 4426 a(R.) p 381 4426 a(Adami) p 704 4426 a(and) p 900 4426 a(A.) p 1038 4426 a(T) p 1100 4426 a(eta,) p 1298 4426 a(On) p 1466 4426 a(the) p 1640 4426 a(Aharono) m(v{Bohm) p 2395 4426 a(Hamiltonian,) p Fb 3037 4426 a(L) p 3093 4426 a(ett.) p 3294 4426 a(Math.) 244 4546 y(Phys.) p Fm 520 4546 a(43) p Fn 665 4546 a(\(1998\),) p 995 4546 a(43{53.) 92 4745 y([2]) p 244 4745 a(G.) p 392 4745 a(N.) p 536 4745 a(Afanasiev,) p Fb 1025 4745 a(T) p 1088 4745 a(op) p 1183 4745 a(olo) p 1303 4745 a(gic) p 1418 4745 a(al) p 1536 4745 a(E\013e) p 1702 4745 a(cts) p 1865 4745 a(in) p 1995 4745 a(Quantum) p 2436 4745 a(Me) p 2563 4745 a(chanics) p Fn(,) p 2998 4745 a(Klu) m(w) m(er) p 3346 4745 a(Aca-) 244 4865 y(demic) p 526 4865 a(Publishers) p 1000 4865 a(\(1999\).) 92 5064 y([3]) p 244 5064 a(Y.) p 384 5064 a(Aharono) m(v) p 839 5064 a(and) p 1037 5064 a(D.) p 1179 5064 a(Bohm,) p 1502 5064 a(Signi\014cance) p 2041 5064 a(of) p 2159 5064 a(electromagnetic) p 2866 5064 a(p) s(oten) m(tial) p 3286 5064 a(in) p 3408 5064 a(the) 244 5185 y(quan) m(tum) p 656 5185 a(theory) p 921 5185 a(,) p Fb 1027 5185 a(Phys.) p 1305 5185 a(R) p 1371 5185 a(ev.) p Fm 1534 5185 a(115) p Fn 1735 5185 a(\(1959\),) p 2065 5185 a(485{491.) 92 5384 y([4]) p 244 5384 a(I.) p 330 5384 a(Alexandro) m(v) p 811 5384 a(a,) p 914 5384 a(Structure) p 1339 5384 a(of) p 1441 5384 a(the) p 1600 5384 a(semi{classical) p 2206 5384 a(amplitude) p 2658 5384 a(for) p 2798 5384 a(general) p 3125 5384 a(scattering) 244 5504 y(relations,) p Fb 714 5504 a(Commun.) p 1164 5504 a(Partial) p 1493 5504 a(Di\013er.) p 1817 5504 a(Eqs.) p Fn(,) p Fm 2057 5504 a(30) p Fn 2202 5504 a(\(2005\),) p 2533 5504 a(1505{1535.) 1723 5753 y(25) p 90 rotate dyy eop %%Page: 26 26 26 25 bop Fn 92 407 a([5]) p 244 407 a(L.) p 358 407 a(Dabro) m(wski) p 834 407 a(and) p 1017 407 a(P) p 1075 407 a(.) p 1129 407 a(Sto) m(vicek,) p 1539 407 a(Aharono) m(v{Bohm) p 2282 407 a(e\013ect) p 2533 407 a(with) p Fl 2749 407 a(\016) p Fn 2796 407 a({t) m(yp) s(e) p 3058 407 a(in) m(teraction,) p Fb 244 527 a(J.) p 360 527 a(Math.) p 654 527 a(Phys.) p Fm 930 527 a(39) p Fn 1075 527 a(\(1998\),) p 1405 527 a(47{62.) 92 731 y([6]) p 244 731 a(H.) p 386 731 a(Isozaki) p 720 731 a(and) p 919 731 a(H.) p 1060 731 a(Kitada,) p 1424 731 a(A) p 1538 731 a(remark) p 1880 731 a(on) p 2025 731 a(the) p 2202 731 a(micro{lo) s(cal) p 2728 731 a(resolv) m(en) m(t) p 3147 731 a(estimates) 244 851 y(for) p 402 851 a(t) m(w) m(o) p 595 851 a(b) s(o) s(dy) p 850 851 a(Sc) m(hr\177) p 1036 851 a(odinger) p 1393 851 a(op) s(erators,) p Fb 1909 851 a(Publ.) p 2170 851 a(RIMS,) p 2493 851 a(Kyoto) p 2790 851 a(Univ.) p Fm 3092 851 a(21) p Fn 3245 851 a(\(1985\),) 244 971 y(889{910.) 92 1175 y([7]) p 244 1175 a(H.) p 381 1175 a(Isozaki) p 711 1175 a(and) p 905 1175 a(H.) p 1042 1175 a(Kitada,) p 1400 1175 a(Scattering) p 1870 1175 a(matrices) p 2265 1175 a(for) p 2418 1175 a(t) m(w) m(o{b) s(o) s(dy) p 2870 1175 a(Sc) m(hr\177) p 3056 1175 a(odinger) p 3408 1175 a(op-) 244 1295 y(erators,) p Fb 643 1295 a(Sci.) p 837 1295 a(Pap) p 998 1295 a(ers) p 1159 1295 a(Col) p 1309 1295 a(l.) p 1398 1295 a(of) p 1513 1295 a(A) n(rts) p 1731 1295 a(and) p 1920 1295 a(Sci.,) p 2144 1295 a(T) p 2207 1295 a(okyo) p 2433 1295 a(Univ.) p Fm 2708 1295 a(35) p Fn 2853 1295 a(\(1985\),) p 3183 1295 a(81{107.) 92 1499 y([8]) p 244 1499 a(H.) p 381 1499 a(T.) p 515 1499 a(Ito) p 673 1499 a(and) p 867 1499 a(H.) p 1004 1499 a(T) p 1066 1499 a(am) m(ura,) p 1399 1499 a(Aharono) m(v{Bohm) p 2153 1499 a(e\013ect) p 2414 1499 a(in) p 2532 1499 a(scattering) p 2986 1499 a(b) m(y) p 3126 1499 a(p) s(oin) m(t{lik) m(e) 244 1619 y(magnetic) p 661 1619 a(\014elds) p 911 1619 a(at) p 1030 1619 a(large) p 1269 1619 a(separation,) p Fb 1814 1619 a(A) n(nn.) p 2059 1619 a(H.) p 2196 1619 a(Poinc) p 2437 1619 a(ar) n(\023) p 2529 1619 a(e) p Fm 2604 1619 a(2) p Fn 2693 1619 a(\(2001\),) p 3024 1619 a(309{359.) 92 1822 y([9]) p 244 1822 a(H.) p 380 1822 a(T.) p 514 1822 a(Ito) p 672 1822 a(and) p 865 1822 a(H.) p 1001 1822 a(T) p 1063 1822 a(am) m(ura,) p 1395 1822 a(Aharono) m(v{Bohm) p 2148 1822 a(e\013ect) p 2409 1822 a(in) p 2526 1822 a(scattering) p 2980 1822 a(b) m(y) p 3119 1822 a(a) p 3204 1822 a(c) m(hain) p 3465 1822 a(of) 244 1943 y(p) s(oin) m(t{lik) m(e) p 694 1943 a(magnetic) p 1111 1943 a(\014elds,) p Fb 1434 1943 a(Asymptotic) p 1948 1943 a(A) n(nalysis) p Fm 2337 1943 a(34) p Fn 2481 1943 a(\(2003\),) p 2812 1943 a(199{240.) 43 2146 y([10]) p 244 2146 a(V.) p 378 2146 a(Kostrykin) p 835 2146 a(and) p 1026 2146 a(R.) p 1159 2146 a(Sc) m(hrader,) p 1592 2146 a(Cluster) p 1935 2146 a(prop) s(erties) p 2395 2146 a(of) p 2508 2146 a(one) p 2688 2146 a(particle) p 3042 2146 a(Sc) m(hr\177) p 3228 2146 a(odinger) 244 2267 y(op) s(erators,) p 702 2267 a(I) s(I,) p Fb 882 2267 a(R) p 948 2267 a(ev.) p 1112 2267 a(Math.) p 1406 2267 a(Phys.) p Fm 1682 2267 a(10) p Fn 1827 2267 a(\(1998\),) p 2158 2267 a(627{683.) 43 2470 y([11]) p 244 2470 a(E.) p 382 2470 a(Mourre,) p 769 2470 a(Absence) p 1164 2470 a(of) p 1287 2470 a(singular) p 1669 2470 a(con) m(tin) m(uous) p 2169 2470 a(sp) s(ectrum) p 2608 2470 a(for) p 2769 2470 a(certain) p 3107 2470 a(selfadjoin) m(t) 244 2590 y(op) s(erators,) p Fb 749 2590 a(Comm.) p 1093 2590 a(Math.) p 1377 2590 a(Phys.) p Fm 1653 2590 a(78) p Fn 1798 2590 a(\(1981\),) p 2128 2590 a(391{408.) 43 2794 y([12]) p 244 2794 a(Y.) p 403 2794 a(Nam) m(bu,) p 804 2794 a(The) p 1031 2794 a(Aharono) m(v{Bohm) p 1806 2794 a(problem) p 2212 2794 a(revisited,) p Fb 2666 2794 a(Nucle) p 2900 2794 a(ar) p 3050 2794 a(Phys.) p Fn(,) p Fm 3375 2794 a(579) p Fn 244 2914 a(\(2000\),) p 574 2914 a(590{616.) 43 3117 y([13]) p 244 3117 a(M.) p 403 3117 a(Reed) p 658 3117 a(and) p 858 3117 a(B.) p 996 3117 a(Simon,) p Fb 1334 3117 a(Metho) p 1593 3117 a(ds) p 1727 3117 a(of) p 1850 3117 a(Mo) p 1982 3117 a(dern) p 2217 3117 a(Mathematic) p 2713 3117 a(al) p 2831 3117 a(A) n(nalysis) p Fn(,) p 3260 3117 a(V) p 3325 3117 a(ol) p 3443 3117 a(I) s(I,) 244 3238 y(Academic) p 691 3238 a(Press,) p 975 3238 a(\(1976\).) 43 3441 y([14]) p 244 3441 a(S.) p 381 3441 a(N.) p 536 3441 a(M.) p 708 3441 a(Ruijsenaars,) p 1289 3441 a(The) p 1513 3441 a(Aharono) m(v{Bohm) p 2285 3441 a(e\013ect) p 2565 3441 a(and) p 2777 3441 a(scattering) p 3251 3441 a(theory) p 3516 3441 a(,) p Fb 244 3562 a(A) n(nn.) p 488 3562 a(of) p 603 3562 a(Phys.) p Fm 879 3562 a(146) p Fn 1080 3562 a(\(1983\),) p 1410 3562 a(1{34.) 43 3765 y([15]) p 244 3765 a(P) p 302 3765 a(.) p 373 3765 a(Sto) m(vicek,) p 801 3765 a(Scattering) p 1278 3765 a(matrix) p 1606 3765 a(for) p 1766 3765 a(the) p 1945 3765 a(t) m(w) m(o{solenoid) p 2531 3765 a(Aharono) m(v{Bohm) p 3291 3765 a(e\013ect,) p Fb 244 3885 a(Phys.) p 522 3885 a(L) p 578 3885 a(ett.) p 762 3885 a(A) p Fm 867 3885 a(161) p Fn 1068 3885 a(\(1991\),) p 1398 3885 a(13{20.) 43 4089 y([16]) p 244 4089 a(P) p 302 4089 a(.) p 355 4089 a(Sto) m(vicek,) p 764 4089 a(Scattering) p 1224 4089 a(on) p 1353 4089 a(t) m(w) m(o) p 1530 4089 a(solenoids,) p Fb 2012 4089 a(Phys.) p 2287 4089 a(R) p 2353 4089 a(ev.) p 2516 4089 a(A) p Fm 2614 4089 a(48) p Fn 2752 4089 a(\(1993\),) p 3077 4089 a(3987{3990.) 43 4292 y([17]) p 244 4292 a(D.) p 386 4292 a(Y) p 451 4292 a(afaev,) p Fb 742 4292 a(Sc) p 837 4292 a(attering) p 1209 4292 a(The) p 1369 4292 a(ory) p 1549 4292 a(:) p 1638 4292 a(Some) p 1909 4292 a(old) p 2076 4292 a(and) p 2273 4292 a(new) p 2479 4292 a(pr) p 2565 4292 a(oblems) p Fn(,) p 2965 4292 a(Lec.) p 3180 4292 a(Notes) p 3462 4292 a(in) 244 4413 y(Math.,) p 561 4413 a(1735,) p 816 4413 a(Springer) p 1206 4413 a(\(2000\).) 1723 5753 y(26) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0608200130467--