Content-Type: multipart/mixed; boundary="-------------0303061518111" This is a multi-part message in MIME format. ---------------0303061518111 Content-Type: text/plain; name="03-96.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-96.keywords" Slowly decaying potential, dissipative Schrodinger operator, absolutely continuous spectrum ---------------0303061518111 Content-Type: application/postscript; name="abscontspectrum.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="abscontspectrum.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: abscontspectrum.dvi %%CreationDate: Tue Mar 04 18:44:29 2003 %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMCSC10 CMR12 CMMI12 CMR8 CMMI8 CMTI12 %%+ CMSY10 MSBM10 CMSY8 CMTI10 CMR9 CMEX10 MSBM7 CMMI6 MSAM10 CMR6 %%+ CMMI10 CMBX10 CMSY7 CMMI7 CMTT10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: C:\TEXMF\MIKTEX\BIN\DVIPS.EXE abscontspectrum %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.03.04:1843 %%BeginProcSet: texc.pro %! 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Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put dup 105 /i put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82 ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96 0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0 24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772 0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2 364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba 0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279 617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a387b3 80db88cca083b06f5af70d768d1699826fb12ce12efc2b4c70923e052dbb964f 5fa957c3ce225c0fda64d9b5321ee1ade207c1cc93105096cc73118f4082594c 8ecddeb0d7bfde6f70bc62f10407c26a476ed88be7999d64a15912493829a9de 62c71f5a34fbf5a843e311873cd98817dc9f8a4aeb7e0738b5de10043f5cfea7 147e63b9abf3eb818128e9889ca384f115247195c3b4aec77d67fa22d38e4dbd e9c631dc3c03b2add673b2ec7d4b74a06089ba7095e73506993f46996910479e 695c25bcd69fd1f32d1d8535bf31de5cd10a0ce88bbb6ce923f1ae9c6a0be8af 70b0958051beba9aee3fcecaceaae53e39b3389dc33ea306ae0eb037654a5f47 b85d69442e402bf071ce17053fb1baeba8627dd44511da294b60dc816bfb90cd 0339052516c416a6aad1e6d40392d62328ef1460393d37ac49f35adc1363b476 b6148d86c849fae4e0043077a4ff4dd0ce953f0e03224f62b30cca8f43741748 ef222033f9bfdcc8c0e5ced0c6505f59ef8d30ca2110dc24301c1a33088b5aea 382d4f3d87499dea77ff54c0cedd8c6ebd0c356c22878c612e489a54625815b8 3e855273e1d151f661d1b91a3ae22f0d0e7693a526b5fa09efa1ad0b3b17e5fb 30591082abe211c1627adda67a9b0d4300ec13f60c7b5037c4790230cd98645b eec7f9a23524b1543377957156cadb29d8697c2aa3a39c67745b5da06adcc80e 9398ba9ef9e5bfd3cea77363967bc30869140f0077d04e69b1c5c5821629658a 12b0c97bbd6efe1a1cf019f6b2fff89836a9897bb21b748856327c550b7ecfc0 5fed9bbf0db664a433818b1c976be2c84b355d4096c7c088f79574c297ee78f6 38fde511bee2f663 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /prime put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b872c2d3ac4391eedd46c6cae184e1af981f95ce213181b697819ba31f f3e3ed201f4914426e805de77334e00eed5adea5f5d61825725d49fa68a47dff c7dff4d05cf6f360d8527294e94f599911c9b1c6ee95a83babcb7b57d31308bf 2640919d126b479a8eea2b7131aaf0903d6b3f9519ece17464f3d605fee01d6e 3e58fc4c89f6b777941084ca85af30f25e654413f4375bc8cb6a1a646f67e625 fc908b99cc334b2fdce43d5fb1cfc6818380ec001b2cd1512737559d840e7314 38f466bcd2a38f39407a24126b5740c84b061f1e16f5e2a86e4861655d1ce449 244d642b6101c0b80b742dcae02855 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 80f59351e84bfc88c87b3a4a1d25e168b9d134554f6a581378c7d2d6eca8ac09 045cc3a5e0ed86f147133f094029e3483bebc81cfde69942cf645ea20d0a2b64 5140ccc2f9cb4a3d969f4b0a79cd3329b440dfcff5285494406f3dd08d804c86 df191e57232f6f1f83df6430f214e03fa5412b1e13d83c60c52a698bc9a38159 19a64162af7b83a9468fae9507c6cb55ea80df8c696dfbc3296c663902d77e89 a181502627281181ac8624f65be9de5fb32f056cc7dd7cbc7366a91717b5892a 34ef6b441871c6993da3a81afc9bf70ff3842a21a29c0e49da1ccba37dd6b920 2702db510b8b1109acf4c27ee8d676bdbd16abe189f34a9b61532eb777457698 cee0561838eaab2d3939c5093afbb215bac433d1918c739b62566906bb2187f3 378521fb52e70c18886e1aa15f53a1f8a169528cf2ddd54c203613ff88e619f2 6c9c50c2c3b8b8c868a88afab1dc8472e7b6f3f992a161723a3c0904865a7c42 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43fe51fde8b2e4ff2178ba19df9143f36e43aace1d6b519b223ffa625d4502a5 d8a1946fd8467180a6ea6b965cf238752f4d1e78c68b4f2a10059c9a31606194 da30c561e40f79390f8783297f11dbc07d17d9a15a4f7f06df06fe09d9846116 66cc422acf75303da4ce5d0b7e0684f6ef53240059a49466523d235c6b5ca26b d7018985216ebea4ee3db39857e201904dc67ec80b23c98b8ca4788fe0d832fe 5d83f2981bf5bb329ea1f7ce624e4c2fec890c3b1ea7d4b9943db3e4fe83009a 01668957e762c00fc0f3b0740bb11040b1750212330487e5354e1ed87f6665e6 b8b86a3dc65e83a9499a9c3e9dc7478a9fa9c1587c6c08e2506b87eeb4a69ceb 15ad6f95d1426641b3e1c021e47a3e96be92f89a204c49be0c422ae83dcb90ac 66a84ef8b89e06437d1bacfb1fe1e764c2856f80556368ff01e4fd8ad3d095eb 1da1c43572d786db676765e564808b1ec7d16919f5518568231d98acd0a389e1 acea91d393977c0fb3d28968106ffa727ff18d5038f45e1ea52d471f50c181de 3003aa5d0f54d5ee73f26d3681a373fdfd6ce9f90c637c27c90dd4fe23fe3aa4 12ce507174c593c69e3bde9602733593f5133d6bc76afcab2f446c4792a1a3df cbb83013fb56c8317c64fcbfe3591dd0808aed7e6ceba616910aa9cbb2a199f3 0fb436ef9bfd3cde80561ce764b05d8b7cde9a9336ac1ad9cf3e3ca85f958a78 45905b97f41440c63129acf9f5361b3baef0892b90f9c4b049bab6156e96afbb ae1f1a2162be7e52112d8b2ec3a9ed66a1ea45efbe9fb9ccba003ae2f1b4b8c0 147618e290f14233c6f4582c0350fb97f4995a59ebee4d1a60643f239a8aa8bf 2cdd6aec4eeeba601100c5691407560dec39400a1d0f6b3e94f4518ff749b8d1 e4a670b5edb54ceced4595e1ecb44755d44365e31b749229e28916f644205e11 b7373ddca2ee4e8357498c65df45328bda30864e20ca8a5af3d387cd24618c45 78b2e1608898aef5d92c65fe2cddbdd1fcf53f25a4c0d560a530bf8e007cfea1 f485595b3b7ab4e800e2db2a35be170de7d2195f1aca6e1c45fadefdd725a334 7afed8cae070e47c21590cc3a181ea17922a53a9c3ae81ba26dd7637096cc507 e8591d7a1fa7f1b1e7bd926dc6a5d28c3e98f937bfb0e7abd119cc62a2d8a91c a9e04ddb4405884425fc35d21f3bb33e19d15d5ea5b78575b6241602ad4d13bd 7dc72ad21d6277398d257c9f9095a16eead85b4518cbe038871ae1f728d977bd 4cc81dc03f1eaea75f4f4eef947ffeb212e124f7088469e607d46d24e50224dd 108ab520ac52b817cd7a7b620a56bcbf40417021c9e515a0d2ba2585db8a19c2 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b2d10311268528083ec55a8ad364cb2cb048cc240f690d379d5ed1ae5e688b26 9f3a0565fedb9c9d0a7d0b32acb642057b1c112ad3730c1e48d5279f23087a5b a74d10593e31ac032f4252e2cf0f17b5b6d6df5574aac3e48cf9010aa3d7b9e1 9d930a05c6d222ca94e6eb7b17677290a7bd7300f5f416c51cb95c4763a17635 3481af095c2c85d3809ff448fa02ee41ff30a0dc6e6f45deb30c7efd3de5121b d207d29e225b0e13a6a3e7ab87b91d532c18867c32aa12c0ae49fb6014087412 8cbb55d387059684a0f3ddd67f3c0c82a55981ca2505e64649c6924d71f2f486 5148882da0c544722b5b6653d6ef50c866b6c9893ed9b6eafb1f22c1fd879723 0562245794439896bc38f238ff68aa02aaabb251e2f8df782b1c9ec01ce185fe 8c5569bbbbd141b615aa5b5beae0f4131e416f3c8f5c3e3dd36da9ffea0eceb3 b93237e8d2e1c7c469c7f24444748fbe477f585c306832053288e2c27de91947 d230c5a7 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 6 /plusminus put dup 16 /equivasymptotic put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 27 /propersuperset put dup 33 /arrowright put dup 35 /arrowdown put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 65 /A put dup 68 /D put dup 72 /H put dup 76 /L put dup 91 /union 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 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c430024c2b2db82e06262dacff21cd21d846b73836a8e6b73fca483e599b6 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Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 77 /M put dup 107 /k put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2 b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc 55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7 8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316 ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325 e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd45416d f3459365434123a76ccf883a4973bab19807e1f0c4bab03a45f7ed69ff2660ff 3963e4def11001eec4238c368a39d874fd30b3c14f4186ec7700fbce22abe468 eb32baf7b0164f8f21a9b5e706b91411faaa44467cb2180ab03de375c1ab93e9 76e11ab92fdd4a7280a6d1a8dc65c4c89d04c8ed6988045a2a3de9a4c7b1efd3 75b6d05a48a30c24d13b30ca0bd0790ff38c7bf80a746d0ff40277695ccc4a7f 7c4d3e72d53b3a52924560a7f2f8632eaff4309cd87aa6c5e92c5bcad9cf6b78 cbb9c4eaee1eb91427d156f0339ad3c08647517f5f0c7ab89f6cd87535c49160 d4b4d535d5130f27ca72348597b9f78c6ba9372f870e9923ffbd91f3d1252cbf eb3b7e3065b86f89ae990c25db2b7ac6b92096e82a29ecc8f17cf9d90f28abef 68ec6a802e6e24513443776c4e79d496dd07d6408a2cb98092a6fcea1d251eff 0b2fe8b35c4a230f64c6e11d8bb6eef4f95aa3f83beb7d7f32bc2122ec631b22 36becc596732126aba0df2a3faba2f5de7932262bd3aa29d4b15987168cd9118 223fb1d3a85aeb28416ba8b787c908daef06e334e35ea205b3cb6ba90d3f180e 795e1e2f22f417295b17cfeaa83c8c7390ee895a858e3e9d1276b4ef718d442d 60ae4e5fcb4a6403d0c53597f2abaab1a4fad0593de65b3343e9b2269f795f81 f51c8b6b49460d9bcfeca73ab361e64ef2dc937b808350691da3971a171c668a 674928cfe7106ecc02d543d54d34faba9c09d0352fe2e37c7647e69707b3fa18 4750f3728e9d6c4f42438bb2fe57f2a622cfe596e190bc621772d30c51545951 0fb1a04595ed8e1f5a37b66e24f1851d1f5a5fb7042b63627ccce021df3c9dcb ce2f491f06b1232255a2a521801ae1f5289ca8a3678b60e236df5f0acf7406ea 9f1c09b9a544a8d807601ecab6efebac5be02227582b365ff168cdeede4a3a88 d2ae5ee6a92f1054e78859e3f801856c0b1ae30c64e26c678581439c05b36d8e 9b03204d8950711c8719230fda7341ac3a871a7e20e1ce34f3787afdf44dbbc6 1bb4aa9c8cc126ead58a7735cfda94f3ff671f481b2c1e11dd87363d691958ec fd1ff7f179842fe7c7f550dd76f7a61aef1437c7569c92bb87af510af62bbe46 96e2253e68fd743a04f7f0c19a2d3d101e4ae298d60f0e24 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523de97a57cbed59a39 c235a135d115ebd4abbd5c9600b26694d650c64477d24d3e668cf2f77c682069 8a49e801bc835101d0380ff234ffc28ff2f6fe6f1ad59d35142a82e252b03506 4eefbe506595eee4c52ed8c9e252fe3a9894b250b5a8765bd0a3ccec511fc398 f294b9ef281f87d76802eced7414297358d29f12e1d246c0f39f9ec4536c3f4f 0549474956b5667672941778cd589fde416abb9915c030ac96e1b70221c9b072 04f75663bcb1dc96dbafd3ddde72bd6af74b96324b707d58c89ca136d07c38f1 bd08201d21d46b9067a4c1ec2857c203487a9237cfbf1dbef5af4c59fc1e726d f49161e746feae8bab48ec220e62fc4437ae29ddff8582dfeb1afa3531a3f86a 22606ab4a62e2107e4569716d1b12297b276035d91ee77babb02b1a5a9428528 b13475a731a58f734f2640f57946f21fd852f775db7637444b84f2dcf1a530e5 964667948960b901dcee0d45e7fbe71331faf54efa7462dd3d6c0e88334556a5 b1418fab410355d9856668d76d6943ca25da0ea62be33599f490997674a9eb45 5f94c730ca6580cdc3a7bd5f362d0ecffecb99b24d7301bca4a0fe45 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa581ff3172367ca325e6d23102c5c6a2 02cc99580287dbd76a05bb4cca591b12a9dd3d602d7957376ec30b16051a63c7 e26ddf009e21fdca5a31cc973f0b1f6967a66b30b973ddd9d9a3095b673ea8f8 5db8dbf3acb7bb2d85c04a0ea8853e4592e4f8e581adaadb78bc3ae58a2d4c80 3b09839eafc7bc3e7cdf784e852d6590ab1c4b7558e28505887c6858072f09dc 2caba91b6871920e5256b602a0de02b87e5eb456878d3634e8eb0e069fa2bb5c c10d5cd98401de1cf07ec9f7de62aaa20b583e2f7aad2fb7e727ebc43f712c74 e8eed1fa76133428ac71589b933cc37ad200c516045fc1a06d0086c541103b5d 4ec54dc77b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 33 /omega put dup 78 /N put dup 101 /e put dup 110 /n put dup 114 /r put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425 5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f 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7e3d0d1ec9a89aea32f7817846b127dfcfb67d11114795b4bff461a5f0302142 ff9d1346a5913c6f78999b18f70cfc6369279443f7787a43ac912456aff22ee6 8216befa0d35f72b66c5bf7e148636da8807910a8beb28624fd39af6c11a92dd 9f3cc8c58221fdfe0bc3572b2981ef84b334935fd455c304f26e7a88579838c9 90d5a17a6855ee00089269cac9105a242fb20876700f199192179552b589e5b0 ad784e04380aa0b22e95f37a1aa0059b7b3cd71ad08f0541f725e20d10c02514 86950a4275ff2a45bf9acd5ac0fb1ba5909bb2be7baeb3432399f56cae976616 d700a36ef61ee24e21a9a04f79091e5b36b452b636aeb103096b2224fc208a00 13b77da65d39f369fa1894d2c38569bab6ed8d0d88c207bd3ba670ce8e1d8e3b a0165a550820893db8db8163ab7655c9da3c083fd3e6130097562a78f7112d28 e12091f8358ba9572138e12058a604b21e26bb7db47722cce5c06affabe93888 a915ab402fad7c62008661c6b374054ff3a0f31b76c19c6822ac87ea1974b6bf d5cc50fa6674de8b60e6c9ed25d17d4018e3621446465cecf92bea874da26868 e886a96cae9cd1082e9cf02fd8feba85d8355bba7f24a36ddf7067c65a60af93 238b264abd1bb15a65f9a4f1af23de51712ba0c540b93bbb5d77694afc8fda93 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b48d5d21d6c29aee4faca71bd775bb9defa37ff627f1e4926f10d59313e 77d81a511027ef9a8ed5b7fa9b5bd67758cd13bab6ac18411c974a65d0c90085 67bf5860d0930d7f43e557ee45e76ecb2806d21f4732bb282ac8b591f2b8775d 4b3ce2a37ebb371cb74a3cc513bdd70a0115de4760c21f034f5080d769f7ff83 554af524184702a02e534d1eb98dd3f7c5d51900409354dea37de4ac74a12c3a 69320913de6a728bd887c57f4ee5dcb8772249587ce3190bb662ac853abcff77 d4bd77985a4a805f44f8cc8597416c488866ff8429f65cd0edeec1fe2f0015a3 2bb098b0b3d8c913007f5846ca593c491e1efabc8f420a5fa338c47fd2427813 3279d27f12022195e15827797fe71d898f17b8af955e5bd5ce1da5fae7b3ece8 87aa52db81daa819242c6acb7fbed098d59a27bbcb12dca67e16915a4709fa5e 16311a55ddda46359ab51be5964874f1d3612ec10d2444576c508ae6a285a57f b978458b6f5f93c00882f2227d43d42c648437715a27cefd8d4ffb490e3e9980 1d1b4f1cacbc8b9e59c04c677a04047cc4b655fd8985d8e619a99e71cad67c94 2744577e185ac8b225e5352ae93ef0d804b73b943353266c74677b899d45b286 869cbe8ce9ad231007381de74bd3c6c84958f07ffce0620e42902a01fd15c98a 421ff110e5de48cd65568060afaa1e11e9893e720f22b754c47c334a1f5d0933 9b1b1b91b036b981a6be8a3276634fd4e39af829e2f2ac2b2dde35379abd1bf5 3a1071f07537db5fff44d145fce9713d8a9e2660900c41b83f948e16731d3048 2c8fa2aef8de49e3cf649e8ff62a2748cd9e299c7b 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 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 68 /angbracketleftBig put dup 69 /angbracketrightBig put dup 80 /summationtext put dup 82 /integraltext put dup 87 /logicalortext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 101 /tildewide put dup 102 /tildewider put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 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e69b200b4c0c1e4915e0628322b328d6354948fd570d73cbf4fa1210ee31b674 0de670961f8bea78e15880d7dba27d9b3553b1cefa5dbbfb7589 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 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 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 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 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 dup 122 /z put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 7dbcc4a8e4e85cd3259f40d3caf55c742cbb40ad0db1044c20a4f122a63f7b81 1d945bfa69662189ce4d089464d2ead9f6ed60b581b04114d5d45e97be27a576 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CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 35 /arrowdown put dup 48 /prime put dup 49 /infinity put dup 54 /negationslash put dup 72 /H put dup 76 /L put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a4254c8f517e6ea430fac1155de17dc54e402e9f22beb39a64dbf0f4 ac415a28a2342100ebae2bbdd0e51225bd1825c5e0a2b0a5b4be4818bf1211e0 c4d56495f952a0a94dcc6ef1db7da90c9dd357202bfcee62fb05105a08c954c7 100cb2b7a78db25b19482b52485c73718f0978bc8677f96e9bfdb43d37c62a7b b7333146c0addce183cdbef937bb40a242d332f0ae19c0fa20cc606cb17c0b96 7e05c35df373cab82b25de3e37bd957b8048e4d5efba59f32c289fb7fd6d3287 480e90d492c9c499ab0c112c3a62a032c101804dec6cfef5e10fc123d012b1d6 b9ea3915527110c20952124ac0a11ecc640958e247cb334d4ed812ec8d07471d 2aef40981fcc48dd1043b12b3a6393270c7d12a6ddf55bb6b71126164799cb7d 087a6e4ca827deeca0ffbbac3634b9e779d21edc6766acd5527c879737d2760f d1317d6d11562a46d6a880371c230c43fb23c49d42039bdc7e485072c78b3d5d 8af9be483f05caf747e9e349607cfb445235284c2738194878731cbfdaf7617c 0eb255b24882c15157521b69a2842a9fe5985936c61ee4732c2509188e85c10c a756043a6bdb4400fbfcf54d302178de4659d65f90a080e9e65595260f7cbf7b 2461ce360252e95405a2c3c675f1f88871b90292bdedb5cb55554361a143ebed eca3a106cf2c6ca7034e9802d2bb123121d62e26bd74755aba3abf6d5f4c2d76 ee3c729505f79ca83e3913c0b1efaeca00072191196ae0617a77bf5691d52d1d 87cdd47b2d9c2c3333efee370738a4897f64c8414b8ed7018d4a89baf8475bf7 d84597c598613a3e4ec26fbdb330cd73bc54ce5e821b900dd8244d9d212177b0 d7c0e5792182db782ac271370aca79670457e9f51e0301477b588f1a3af9c7ef bc95f5bef49843fbf64f0c5e297fc06abfd66f8b22662273ca58749179a41ef4 987f7223f43aa8a2ef8d7e023d18f9e1990299c0c6e95d98af4ee69be5693847 bb0caeb7f1535a7f45c7c854fcfa436b2ed93b4375bf421ef57165ba78274fb3 238bb1e1031bfee3352fbe4b5cb6eee04a1b651dc6f70e68709f77cec739e8a8 974f7468902fcf58d9d0e9c71f1d68d938012b6748846617eedb6a722c9dc4cd db7224d1dd2847959e08fe0115af1139f414c230f51da39b7297e511e4a0f9b7 1723b57797993ec7383a8abbeb47015c3ff8d99d69a0e748400f682e053766a7 af23dc08712a1dba0d3a0c7673084304bc9932b76c2add5eb1306ccf0afa352a 815ee23e4e9adee5f0037dccebaa5636a18ca2d9d1f62e8ba5eb501be81d9911 cb9653a220c78fea9e3651635b9291fcedb563d15daabe470726ad7a823f3f9b d69ed3858245a3507848d718d8f64165ed15954443e1603431131f42ab7a9491 eb2090c3a99d6218f270cd1a03abb9fba6e30a383e17cc4b4a12d048ccc91f35 e5ee3b8b279d0839a6cf3036b6b3d1316514f243cfbf61bbda282033cebc94c3 f819bedd1e6da471a4acce58cdeaf3ed976e489b1a2e49cd5af7695c9ff3f456 544ad883316354fc2f5a0f47f27e3aff61d871b5f89cea4d80787ab81456147c b67c41aeafe220ecb0aa64394a19be0710fee7b8e6d841bcd3fc8de557915438 5645e5e135caf5566d090f9abe7de59adcc8dd7964f2410e8337a92aa4048d0c 8d592559b4393ee190a38d53b2e851075f31a4808f021380356daf61cfc42b1b e44c8ed1a54faa9aba0466da0b9b4072802cd62e1f19df17e6f9fc811255c446 801e16d3164abef8abfc8a0c7520dd61084112f314b6446b98e4eb3ff70be3c9 b0e8df99b65b47654558713cb198d3748f3bd9d85ac229c4dc827bda1587b31b c87486817eacc5fc1fea993f9ace9eeb9f6afa737d238e7d09fa1c309e981ce2 5e190605eaf68d36520f553993f106437b36c062292ca870f25033d92e9a4968 b97fabca18a18d3334e3ae7b69dea91f2aa384f97329701c6758cfb91b728b68 65f03050f814db30df0298540adbd948c200d0ebdf4fc4f84567dc55474377e1 fac76c502b5f8a18163b312451f4c0075dd8e25747ed7d599bcc3af26d430e87 3939dcfc5c93d804194666a4880603a439d4365b2d719ab79ffdc6fec3c18dcb 7b6ea811b3096fe4e2f0f3b7ef2f3d11a8980562640f3d691fba4f64c20dc24e 51c64e4f82d65a2edca2974f892d6643d17ab3f85fdb0a66b9e57887842e2cf2 f9aaa8983d7bd9421b56e9403c187ea8c1e990d2a2e86fec7a5f596c80371464 e8b73c81375d7c9b3f90be8db83a2b98fc9b8f6ac9899444df3a270e747736d3 a3280b2b0b5033e73375a4c6663745398f484db3e83a0d23c6b7a6d39b646c1c c9f4faccf05d7167be0eb6a3d9666179058a732be294f61e304f9bd1cd7c084c d7447b60fbcae32b5d13af89fcbe085675d33adb13854ff1c057dd99ed54953f 37bd0c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812b1188a10f6327c9e8714449de2ae636420f56a44cebd774f0b131c629 818455cc8dd8d40939f3ba8aa5abc54590c7286b172193c23adb1b4f9931a9f7 73b960b1f5b760438028478e4442dc93a567b07e20017c18fca2a1daa2649dee 5a6ec51fd6c3f4b27367c31e95a56ba4bbeda0493bc02306037e2ba69add9b94 373364db316691e73d6811cd76fbc92b0c67ca18dcdf05807f17d1b309456ea9 d113ea0fccd6eb73bd8dfdbd5905a5e38bbf61cfe58fb01ec95a4bdd9565433d 4a7abb8dca6f76c459484ad29c3480b588fae3d782340da9ccf5a3d15ebc4b0e 37e0e981f80deda1e9edc94ebc4269488bc7d09c3feaf61f454abe05a5c41289 f919b23cbd7cc570de9de9854d6be3f91530fd17c83115c02f6b34beeff7942c fae26f720a6defb2716a35ceb107fb9fdb87b6bcc3481ae05e08ca8eadc508b0 4b7ff96b6d32f54dec7e8b464057722370f5903fbc264c89eb31ed7e18c1a047 a7c173d8e80fe2fe10bfd4ef52781a5ac7d618463633c73d8e414e9129e2f05e abf6f3f2e9ff1a5e48863c810ba563fc8c1a1f1945422414ba0eb4086eaf68bf f0eabc6258f2d9015cef22a54c9417a293521eaa35917ff95937ae1b1a0dd3f9 98835ce49a704000529dd9cb93afebbebb69155c0b158bc0aadb786f1cde5f35 26cb4dc0baefde30ea5e277dc17e6037df3fe03283cc889a55498040985817ef 6af3b4d335e85314aa81a6fab86184ecb0f9cd53ab6b52673c6e0ce1afed5e83 50f55d705184b3f2e1f1ef51bb8b217e9f5c34314b677b375e7099d51e0b79eb ad84d113b155df64e6aaa5e1a80427862cc1c4c7ae5b6bd3dffa0f5312c6fc5a 66c6015faf233d08e090f7bd1907844c8a55b0d078afe863ab50469b5101ee45 6132a08a5901e40e3834f9c0bdafd9c29884f077783a3c1a1e9a6742f73f0d1b 599f84733fda79fbcc7a2ab64f3e722b6ab3a5d085d19b53bd3663ed7f80b2ae 650101063e7033b1c5c29ffa251605d6f4f7bb4a086068823a7bf37b091002e9 6ffb935b164d92835ebe08648d7312a5b26b82b9fcef182eb69fbdc7bcfbc509 a441d6e9f815949503bad5deee7a641293d740e6c942a4f4477f16fb6cd73296 e755c5db4b7246db87cfef1cbcfc76da11e1ffc136eec32a4bbae4e17e88aa30 b5b14695fc99a342d3bac179ff423edeea8dd6ae38c20120922daa7fc9ef1a4a 372067795107cf12b8ae6297a37fa4ac7056a97fb38b6f8ffe8212fb8399dca1 f7b6c29e821a92905579eae68c8c9343a7f5c1c9233f26d15ea56b3be0e9c6ee 717053a5eb4508632e8f93eba56eb5548999b000e17c300f1e7b589bd69398bd 6e0a084ca920a9b4e22a97d976c93edc285eb39638af274b5334ac1ac52a27e7 888b666b2ca668d7a54016260725afc68b239a54a918500667a57e96feac5d05 a293f9fb751d306a36f2e409f028fd267a7229f4188213e80449643c264741e0 194732d842ad35cfd947de0a43ef9fb9d9577ffffdbae496c1078aec6f050067 4a0123525ce76ba027b9e1c62b0690c7e2eba30ba3454f6492 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 52 /four put dup 54 /six put dup 66 /B put dup 68 /D put dup 70 /F put dup 71 /G put dup 73 /I put dup 75 /K put dup 76 /L put dup 78 /N put dup 80 /P put dup 83 /S put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueXX 5000829 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36e555668d9578b338402f8c259f6813b0b71e6cbd95e19c20ced8495 2559e47577e612a4d94de3c1b4c6c41a6a3fa9e2313457242de74c7e4c0d722b 3e224d18baa726369542682e9459b951b2ac638494880c42be4e2175a3c067e5 945bfc1a05d3de8c3e8ab97f80ab6000e1f78fc258b85d3c84b038d7d0f5be85 0d43fe03e26cdfbb41c36d14cb552e8447ca678efea1d275e85503123a2263b1 4077587683de69a8f5a88d666172668411d0d0fed3e037ee468627207505dbb3 59cfdc5d7f526fca5416d741073284f5dd2471e09f5916f4bff1a90eea4d1283 7731f6a36e5ea695f4efc3bf5669b7f60ab606df5819149c0c8a4817f06dc172 0543467645daeffe4457293e0c0407c4ec7857558d0452de2ac773f141783edf 81b30215ae8d2d062aeb3cb69eb0d62bf04780997c9c027a22896f456b784378 7f2ccdd4804375321e7946d3d254521249a4d28a360f4d3163912a688c16e807 15d0440bd27bb78fcbc89bc28028aab2f594f8b641e45b9c599180b69663eef0 03465a2425aa4f8b29dade493002fb335b23eb145108ef3ab828755d3753ea8d f0683265497b1cb5cb484c13f7a4e003fa6ab3ed5e24fcc6125cee4e33936122 3cc907af3c64e5aaad882c356e673e6ca2509a71920e99549d8797e9aea189f7 fe18bbf718017cd2e32b4652acf12f16e785462980f5895afc917ea83e9c3eab 6297f1de23785f79172538b39984ab261f14ee296a42cca3159e63fb30583af1 911646257a99b4162635fb79e25404242cccc3bf224d4c279e731333107ab2cb 2598dc582dd185669c1fad35d2be0428389a4b175db159508c08a77e842fd400 ba88c31af8fa638e78fef3a6d4282d4af42763394d3bb73d46d06d2be36a1da0 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037492c530463f0f9fa3ed49bfe6c1e7bb774c85a905bbe8431f91b5b274dd9f 31347a5b988182eebb7dd065ffc69da9d3b5afbc01e0ebc94461886f7a19a151 1e2c06aef91ed5 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 12 /beta put dup 24 /xi put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 72 /H put dup 73 /I put dup 76 /L put dup 78 /N put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 120 /x put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 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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 1 /Delta put dup 9 /Psi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put dup 73 /I put dup 109 /m put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e50ce572fcc9fc546f deba1eeaeb3eeb7b26c3390a2a45b5700b1127adf6fb32522ae8b4e9f0da4554 a7690936a0b092a7de04dbf43ca3367a63de1fbb2f65b3c9ae398b8bc3f3218e b762b2954e23c8525da7b20b989ccd9f8e7467f8866b4b265fd4dde96bf1ace0 3f48e6de4dcfb6c0af9f7d222129e08053087399093a3b368555ff5df0b7ab7e 0997cd66b0540a704fa2b71ff0632cef58cfcaece81d07154dba483192bcbb41 be3b1bf2d1dd405127208c7650326aa3bb3067ab67e9019b143b758827dbee77 c02bdf1684e448f24f7f86a54902918beb59f69d861b6809706bbc80931c1350 ba30215d30a19bbabff96eeb94174673782e90187ce2359bd2f0c39fd420ff09 cd1e279553625736d2da09022875e7c16bb5971b20f5073e6bccf3ef1ee3c35e 9fc452df7cb19310f04d8e5920f6a6404f4907a464e76de3ae658772d9a22a3f 4fdcdbf542c915ca328fe627650c72d7ae4fbb27e7b4767fc4699c7bd11bcb4c 0b890e2fb497523909d822c2eeaa00036528a78111d39806f7a5032425a6cf9f aec79c0b426145c2df82fb5d8ae908f8b3cfb7ff62e9e1853d4ba164e958b1e8 fd4f65dcdf7452e5d35d931a894887c339f25900fc979ee17316e97699e0a6e9 1cbeec773e14bfdbb6a49653ceb9313d0e2b7c32b5b8e3fe3a21535561b360d8 b04ca8f3f4f71f4b024066cdf31dd93c2f98c7ef15a0447b77bcecf2bf478bbb 0406f86ca083dd46b88b094a99e5c948488a0b83b2d6a106d6578fc837dab3a3 63cb8bfe2fb6cd422c45ac01821b9727fcfb37bf28ffd1e7310e1e9cde778eb0 14bc5e8651b3f8829e7a87b90364b49509e1d0258ffd412e01c1e9855331c002 dc92a24361cfe772fd9fa06b29918a0d8188ec2b0d70c521dfae18ef71a7076f d66929ee4cf293521892771fa41972694272a65671f894393cec3f179098521b 665ada471bc0fd3555af06d85d5a52286887c65908581ed4b98ba9739790f7f8 ee42e7983b7b8735550f942a675be8367a654fa8c691ccc2bfc5f570fd455571 f4d508dcd51251a560834a6436c4359d0590a347566f1d221074972ca4472504 a5bbab800f616e4af847155e071d78e4ff9c80eb8122c945c743a5fd59c5e6a0 13e3742a3692e425028b71803f4f89b1db746fd2579f7d85ec185abfc886c515 9708dca6814ebb872f1a76ed082a4f97b08647b2bde3548707afe24a9f2bdab5 cf0653e98e005a8f2cbd50f7d8641fc1342c392715a3bea6127aad55fc6baa53 76ad8200fb86da779f7d0c4b89dfcbf7dd60ee123c6eee93c70ff637507f3dc9 859f2c856c4fd2154fd334ff3ed3fd253f06b32e2a71d471011f1e6273ffb083 c8f77555c093aa2af83cfcec6c4c1bda631dd27668d63abb5071c91f55ed7373 af98efd7ad5c0080b9f81735b421275423099ff41825a4f42e96c6b8d7710f11 c9731453483632e5090cc9e6db585041b388aae76caa04db3096b5187c2792a5 31a2b903a4fc2eaa59f212accfb6dcedf03e8278349f7f58bb58dd46135f93e6 20dfecd1efcd704b3d7a8bbe498a394979ac3bf5a66099137aaf47df17393edb 58199f75bb7f85fd45e0e69114ad52ee51d1b7f642fd0ce516683ac58deedb98 c4f18a4fc07c2f9b73c37f9bdf73955ad43af6d08dae3070b797d1050a738f9e 22476085d4f82692e95eca2999d526d2c8190ccfdb3f91c15c6f72696fd1f089 feb7e2a14c4fd142f2ad29317c6bb0b02eb55af8ed720a4f35ca142952801626 76bd26c9a20bdad3478adb67ff55a804732a235e9bd3fbbadf27579c27888ac4 fafe4142800e1113badb4a4bad55b8d4b77a52b89a5c4948f3fdcd406bffeccd 168eaa5c9217f5fb50ae74e0fe21364095ee75cf276c24bdb1214ea6ffe6e326 f3f215940f297ec095d55b8c6b7fe413ce2fbbdb85822aa5fbfa2bb03c283fb7 187814c22acb82773a2f0997ebdf602b8d366bfc9f7ffabdb0c2991975e64d2f 0889493ef71afc89b3e1094929f922e314f1591a21b7d01acf64ace9a0d27335 876f77dfde4ecfc14fe7c2fa25dfb9eb17b152c57b1c48ea2d7db98c141815aa 0702535f840d901fd2eb7213e3e6717c6d7474249cc9201f71631ccc656f708d a70f578a5019ff876ca74ff4daff21d39d011a9da7bf95ad9d00738abab7b51a 77827cdda76ac2d35c29f5c14ebc5b53e1b9db38c234fe668b19f361b03b74f0 2d1e6d014ec92b7f124b9aee378db01d4bd66c3d08cb876917fea4d4f5b2beb0 340ad446eb3da7ad585eefb2234a5f5072d684a3159d3c3b849cff5626c0d691 46a562e9caa477d236abe2c31e6c41c9a1f0372ce9c97a0474710aa8e85fc670 4fdfea04aa95b70656ce2f8d233b91448c21b8c8e1295f2930f3d4b57884d8b2 0d690dc9bce68b720330ba9a33aef0424db70da3c92a276090676add23d01afc 56730758765aa45591a4e47009f987d165ebfb9383593211eed141f84b0c7c75 69b61cd977006f124378c38376d634b1607abf37c07a0740212a97a07da1eb48 dd675c9590d8660872babf87e4c8fd566b293d04ec0b1268294144a8fd76e401 6068c2225e9bb047f216407f4387277f735d7cd018a82942724318d6e4c0b7fe c39a98d094281de6644a75132876155c40ef26552dce18bbe3e94bfa8c8acebb 5127 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 14 /delta put dup 16 /zeta put dup 22 /mu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 67 /C put dup 68 /D put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueXX 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 3c3346a1093e6b1036902c1bf42fc317c80abf04020a47b344c36de42f05c490 a0ff44ab6d5249e9f552a8707bb7661e242644814001c8430ebd5e5f0b944ceb 666ee64359d663e355b2f17093a964139d17287f6ca6a024767eba4fe4873855 babe2f07b91560f68300b06dfe27264c163195d446980c35bca0b48f7806626a e72636593a05ba403ce1c0f8b2cea3ecd586e90ac17d034ba4af708304f23131 3459fbbbfb97d4834d0395754ab3f22d6495d2144087d448616fa1ce27bc50d3 46543287e3860d99b433624119bb9920a2113604c0e260fd275ba55e0fd19c83 e19addc3baa1f32f6b7284038845ccee71a3311ddb17b84975f7a984bed7c6ec 2a06e5b335a763d081c6273f86a46632fd9141a27902074fc860df3a2eb59b89 774c767022dbb577e30da128bd7706a43af886d0c256b50fa968ef06776aac0b a5387e9011eb2334c1f42c090f06a1125c207ea6324e87f46414050d88004e87 79bd39f94399c3f1de84b8aae5edc6c3611e8ac49460509e672000d0afd94568 4ab67ff5c6bf2301522775398e192532677826b8cc7821a3a6a2765ee6edd840 b30d07f445681d61f0af1154c46147dfea6f3500f327b50eb05b5007e9e2a5e1 50be9f8fb62b781a609cfc01a10c69b3c05cb9368d5080db5967cb19b03aeb8a 38d5229ecec9a0453df594e38df4004c27fbd2230371a01fa865070b1de53b95 3c9422ec87ff72882f150c22a5d364ca8c1f2723231101b6ac7f8506f5d25825 91b9aa77d893bfea886d0dc93a91c7fccb621382bd048902b63c0591b53cbd3d 2b9bcded964afcc4ff41e2dd980b68fef4c07232e952c423bed8b2edeeb0ecd1 53407bc29192867a109c442a041423632d14ebf47eb30fbad54f2e8c53b9c93c 28dc841cdbee459b73a91e44b5ed1c6f4765eda6450e9e580a99f0c1b7d7d765 e35f97ad63b64e797d49a512311094e29d5fbc4a7ffd7e4f5d6fed0dfa386a39 fc6cb336c3a5b0d7137d44a87abe4424b83444b94a006dcff2b266c1739618d3 d2fa9f07cce3c986dffb7525d899eb3391f576e1156cc43259b5641c1193e9c5 eb7936478ffb34e4c34fce550ded14d406c1c8143537be246a96d8508a5004b2 28ba6e68f26e431f4bad36352eb653ee3fcb03b9a0e4bbbba0dc3a3accc15bdc a312c30d7957a7510223f4579d3ff72cc12fb1e33ac7d5902863c78ab171815a 8df0cc4fb801851c3c52249d37b839cb0bf55a0cf3cf40feb9c99d85f81d13cb 79b6746e856edcf486f6bc4141f92dc7e4d50e38843ba69ee52cf3807ca2a1dc 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266ca19c75ed638599fb6851c30be550c48437744947e286c8be511dc7583d34 c8cb35ff336ebb97ce603922566eb5452d55935090c615ee8598e155dcd7cf8e a8ffe7304817e3dcc1678b06de58793f9b47c549a1111bada22a7cb9760fd64b aaa054c32e81e42aca8584fd61a133c85c3fce5759cc52536fa8b6da1344854b 0f2cad72172551875c06e404f36a866bb6422f9ad8dd98c565bbc454c1abd379 03ab44c54c645de82fab5b44207070407b83ee2c272d0685c97847465fbef385 c4fcfb7be735624cd504e99843aca8eb72822ca99ff24b0d3a791e356d8e1caa 5301cb945f08dfcaf2730663646316f847847ee0d6a6545aa95a54770d746e93 53f8056a1fdf19890ad6be563fba7ff92bd0742f3599c3486b3084410065c8f3 5a80658a957a25865979ed650524debaff04025c8cbb733aadef7e758320d26b be3059b286fb22306eab88f56fb5cb4587d1a931d5fe4521a9882fbf56744fe3 2c9e3327c437799e5b93347b395a6b3acda66b47a51e6a7715e1f59a151f1228 05990c777b79fb0016893ea868594a112e77c01533816c639ecf55aaf1663256 6e321810d18d909aa933be3a708030eea649575f5a631c09aa4eaa6304186c39 bf311b1ccdec067ddee138186eb8ccc94e73423b058bfcea576a3ad5a381e69c 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /quoteright put dup 44 /comma put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 73 /I put dup 75 /K put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 88 /X put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueXX 5000772 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd800bcb325468c79ffacb9cd3037a112066957 7889d67fff57549064b985d67ede2fb03272083723541051ebe936eff01a4ab3 cd845d565dfdf25d9ddd2792db17f52f894bea484480f06c832140fdd6c3af0e fef0584c6b78b5e2bbb9a752f10581fd1c48cb498a822afb18cddebba34695b9 b418010368fdfb7bf758d50f3af03360b81c776325c33c9c81130b1e1be840cf 68c71ffd091dccc0df7b507fe8953dc3836af0da08ff9ff3e9cf7288d9eb8baf 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20d0ae2009c8eb1ee5cb3ddd117669e74bc2a87ca9bcb516e99a75e9027d171c 5fc0f3fbed887950a90bccb9c2eb8d7c4992c79fe955ab6b74a58b8e00270960 81678c835565125a5a2abb4e1abc01eb4fabefb9fc81b16fdd8fc21a4b5f66bc 1c3b0c4a0416a746ed5fbb0bacfe70d1072bb0dbb8c54ff1320acc 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 2 /Theta put dup 3 /Lambda put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 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 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 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%!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 16 /dotlessi put dup 20 /caron put dup 21 /breve put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon 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 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 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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 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 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e 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 119 /w put dup 127 /dieresis put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueXX 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c 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Fv(\()p Ft(z)t Fv(\))e(is)h(a)149 466 y(con)m(tractiv)m(e)j(analytic)f (op)s(erator-function)e(in)h Fo(C)1992 481 y Fs(+)2086 466 y Fv(suc)m(h)h(that)f Ft(I)d Fp(\000)24 b Ft(G)p Fv(\()p Ft(z)t Fv(\))32 b Fp(2)g Fy(S)3092 430 y Fs(1)3132 466 y Fv(.)50 b(Hence,)37 b(b)m(y)f(the)149 582 y(Sz.-Nagy)26 b(theorem)h([8)o(],)h(it)d(admits)h(scalar)g(m)m(ultiple,)j(that)c(is,) j(there)e(exists)h(a)f(scalar)g(con)m(tractiv)m(e)149 698 y(analytic)33 b(function,)g Ft(g)e Fp(6\021)d Fv(0,)33 b(suc)m(h)g(that)f Ft(G)p Fv(\()p Ft(z)t Fv(\)\012\()p Ft(z)t Fv(\))e(=)d Ft(g)t Fv(\()p Ft(z)t Fv(\))22 b Fp(\001)f Ft(I)40 b Fv(for)32 b(a)g(certain)h(b)s(ounded)g(analytic)149 814 y(function)42 b(\012.)68 b(By)41 b(the)g(op)s(erator)f(F)-8 b(atou)40 b(theorem)h([8])g(it)f(follo)m(ws)i(that)e(the)h(strong)g(b)s (oundary)149 931 y(v)-5 b(alues,)35 b Ft(G)545 895 y Fn(\000)p Fs(1)639 931 y Fv(\()p Ft(k)s Fv(\))29 b(=)g(s-lim)1110 946 y Fr(")p Fn(#)p Fs(0)1234 931 y Ft(G)1311 895 y Fn(\000)p Fs(1)1405 931 y Fv(\()p Ft(k)c Fv(+)e Ft(i")p Fv(\))33 b(of)g(the)h(function)g Ft(G)2509 895 y Fn(\000)p Fs(1)2636 931 y Fv(exist)h(for)e(a.)45 b(e.)i Ft(k)32 b Fp(2)d Fo(R)p Fv(.)46 b(F)-8 b(rom)149 1047 y(this)34 b(w)m(e)f(infer)g(that)g (for)f(a.)43 b(e.)h Ft(k)30 b Fp(2)e Fo(R)816 1157 y Fp(p)p 899 1157 46 4 v 76 x Ft(")16 b Fv(\()p Ft(L)1065 1192 y Fn(\003)1127 1233 y Fp(\000)23 b Ft(z)t Fv(\))1315 1185 y Fn(\000)p Fs(1)1426 1144 y Fp(p)p 1509 1144 61 4 v 89 x Fv(\000)k(=)1701 1157 y Fp(p)p 1784 1157 46 4 v 76 x Ft(")1846 1123 y Fk(\020)1914 1208 y(e)1906 1233 y Ft(L)1972 1192 y Fn(\003)2033 1233 y Fp(\000)c Ft(z)2182 1123 y Fk(\021)2242 1145 y Fn(\000)p Fs(1)2353 1144 y Fp(p)p 2436 1144 61 4 v 89 x Fv(\000)f Fp(\001)g Ft(G)2646 1192 y Fn(\000)p Fs(1)2740 1233 y Fv(\()p Ft(z)t Fv(\))2947 1177 y Fr(s)2883 1233 y Fp(\000)-16 b(!)2911 1296 y Fr(")p Fn(#)p Fs(0)3060 1233 y Fv(0)p Ft(:)249 1445 y Fv(One)33 b(can)g(no)m(w)g(v)m(erify)h(the)f(condition)g (\(2.1\))f(for)g(the)h(op)s(erator)f Ft(L)p Fv(.)44 b(W)-8 b(e)33 b(ha)m(v)m(e,)149 1652 y(\(2.4\))613 1575 y Fp(p)p 696 1575 46 4 v 77 x Ft(")16 b Fv(\()p Ft(L)862 1611 y Fn(\003)924 1652 y Fp(\000)23 b Ft(z)t Fv(\))1111 1604 y Fn(\000)p Fs(1)1222 1563 y Fp(p)p 1305 1563 79 4 v 89 x Ft(V)50 b Fv(=)1515 1575 y Fp(p)p 1598 1575 46 4 v 77 x Ft(")1660 1541 y Fk(\020)1728 1627 y(e)1720 1652 y Ft(L)1786 1611 y Fn(\003)1848 1652 y Fp(\000)22 b Ft(z)1996 1541 y Fk(\021)2057 1564 y Fn(\000)p Fs(1)2168 1563 y Fp(p)p 2251 1563 79 4 v 89 x Ft(V)43 b Fp(\000)23 b Ft(i)2484 1575 y Fp(p)p 2567 1575 46 4 v 77 x Ft(")16 b Fv(\()p Ft(L)2733 1611 y Fn(\003)2795 1652 y Fp(\000)23 b Ft(z)t Fv(\))2983 1604 y Fn(\000)p Fs(1)3094 1563 y Fp(p)p 3177 1563 61 4 v 89 x Fv(\000)f Fp(\001)g Ft(Q)p Fv(\()p Ft(z)t Fv(\))p Ft(;)149 1899 y Fv(where)36 b Ft(Q)p Fv(\()p Ft(z)t Fv(\))31 b(=)772 1815 y Fp(p)p 855 1815 V 84 x Fv(\000)932 1789 y Fk(\020)1000 1874 y(e)992 1899 y Ft(L)1058 1863 y Fn(\003)1120 1899 y Fp(\000)22 b Ft(z)1268 1789 y Fk(\021)1328 1811 y Fn(\000)p Fs(1)1439 1815 y Fp(p)p 1522 1815 79 4 v 84 x Ft(V)56 b Fv(is)34 b(a)g(b)s(ounded)h(analytic)g (function)f(in)g Fo(C)3160 1914 y Fs(+)3253 1899 y Fv(since)i Ft(Q)p Fv(\()p Ft(z)t Fv(\))31 b(=)149 2103 y Ft(T)206 2118 y Fs(1)272 2103 y Fp(\001)325 1994 y Fk(p)p 424 1994 V 436 2078 a(e)424 2103 y Ft(V)520 1993 y Fk(\020)587 2078 y(e)579 2103 y Ft(L)645 2067 y Fn(\003)707 2103 y Fp(\000)23 b Ft(z)856 1993 y Fk(\021)916 2015 y Fn(\000)p Fs(1)1027 1994 y Fk(p)p 1126 1994 V 1138 2078 a(e)1126 2103 y Ft(V)48 b Fp(\001)25 b Ft(T)1341 2118 y Fs(2)1418 2103 y Fv(with)38 b(b)s(ounded)g Ft(T)2105 2118 y Fs(1)2145 2103 y Fv(,)h Ft(T)2268 2118 y Fs(2)2307 2103 y Fv(,)g(and)f(a)f (calculation)h(similar)h(to)e(\(2.3\))149 2251 y(sho)m(ws)h(that)f(the) f(middle)i(factor)e(is)h(a)f(con)m(traction.)55 b(The)38 b(\014rst)f(term)f(in)h(the)g(r.)55 b(h.)g(s.)g(of)36 b(\(2.4\))149 2367 y(con)m(v)m(erges)30 b(strongly)e(to)f(zero)h(b)m(y) g(the)g(assumption,)i(and)e(an)f(application)h(of)f(the)h(F)-8 b(atou)27 b(theorem)149 2484 y(to)g(the)f(function)h Ft(Q)p Fv(\()p Ft(z)t Fv(\))h(sho)m(ws)g(that)e(the)h(second)h(term)f (con)m(v)m(erges)h(strongly)f(to)f(zero)h(as)g(w)m(ell.)99 b Fh(\003)1088 2688 y Fv(3.)49 b Fu(Discrete)35 b(Schr)1942 2680 y(\177)1938 2688 y(odinger)j(Opera)-7 b(tor)249 2862 y Fv(Let)42 b Fp(f)p Ft(q)526 2877 y Fr(n)573 2862 y Fp(g)f Fv(b)s(e)h(an)g(arbitrary)f(b)s(ounded)h(sequence)j(of)c (complex)i(n)m(um)m(b)s(ers)g(with)g(Im)17 b Ft(q)3516 2877 y Fr(n)3606 2862 y Fp(\025)44 b Fv(0.)149 2978 y(De\014ne)34 b(\002\()p Ft(z)t Fv(\))f(and)f(\010\()p Ft(z)t Fv(\),)i Ft(z)e Fp(2)c Fo(C)p Fv(,)33 b(to)f(b)s(e)h(the)g(solutions)h(of)e(the) h(di\013erence)h(equation)149 3138 y(\(3.1\))1075 b Ft(u)1481 3153 y Fr(n)p Fs(+1)1640 3138 y Fv(+)22 b Ft(u)1794 3153 y Fr(n)p Fn(\000)p Fs(1)1953 3138 y Fv(+)g Ft(q)2094 3153 y Fr(n)2141 3138 y Ft(u)2197 3153 y Fr(n)2271 3138 y Fv(=)28 b Ft(z)t(u)2480 3153 y Fr(n)149 3297 y Fv(for)k Ft(n)c(>)g Fv(1)k(with)h(the)g(initial)g(conditions)h(\002)1784 3312 y Fs(1)1851 3297 y Fv(=)27 b(0,)33 b(\002)2139 3312 y Fs(2)2206 3297 y Fv(=)27 b Fp(\000)p Fv(1,)33 b(\010)2565 3312 y Fs(1)2633 3297 y Fv(=)27 b(1,)33 b(\010)2915 3312 y Fs(2)2982 3297 y Fv(=)28 b Ft(z)f Fp(\000)22 b Ft(q)3300 3312 y Fs(1)3340 3297 y Fv(.)249 3413 y(The)38 b(discrete)g(Sc)m (hr\177)-49 b(odinger)39 b(op)s(erator,)e Ft(l)r Fv(,)h(acts)g(in)f (the)g(Hilb)s(ert)g(space)h Ft(H)43 b Fv(=)35 b Ft(l)3243 3377 y Fs(2)3282 3413 y Fv(\()p Fo(N)p Fv(\))i(and)g(has)149 3529 y(the)c(form)1637 3648 y Ft(l)d Fv(=)d Ft(S)h Fv(+)22 b Ft(S)2051 3607 y Fn(\003)2113 3648 y Fv(+)g Ft(Q;)149 3787 y Fv(where)38 b(\()p Ft(S)6 b(u)p Fv(\))633 3816 y Fr(n)714 3787 y Fv(=)35 b Ft(u)881 3802 y Fr(n)p Fs(+1)1018 3787 y Fv(,)j(\()p Ft(Qu)p Fv(\))1291 3816 y Fr(n)1373 3787 y Fv(=)d Ft(q)1527 3802 y Fr(n)1574 3787 y Ft(u)1630 3802 y Fr(n)1676 3787 y Fv(.)56 b(Then)38 b Ft(l)h Fv(is)f(a)e(b)s (ounded)i(dissipativ)m(e)h(op)s(erator)d(whic)m(h)149 3915 y(is)41 b(completely)i(nonself-adjoin)m(t)e(if)f(Im)17 b Ft(q)45 b Fp(6\021)c Fv(0.)67 b(F)-8 b(or)40 b Ft(z)46 b Fp(2)41 b Fo(C)2453 3930 y Fn(\000)2553 3915 y Fv(let)f Ft(u)p Fv(\()p Ft(z)t Fv(\))i(=)f(\()o Ft(l)25 b Fp(\000)d Ft(z)t Fv(\))3319 3867 y Fn(\000)p Fs(1)3430 3915 y Ft(\016)3473 3930 y Fs(1)3553 3915 y Fv(where)149 4031 y Ft(H)50 b Fp(3)43 b Ft(\016)432 4046 y Fs(1)513 4031 y Fv(=)f(\(1)p Ft(;)17 b Fv(0)p Ft(;)g(:)g(:)g(:)e Fv(\),)44 b(so)d Ft(u)p Fv(\()p Ft(z)t Fv(\))g(is)h(an)f Ft(l)1726 3995 y Fs(2)1806 4031 y Fv(-)g(solution)g(to)g(\(3.1\))g(for)f Ft(n)j(>)f Fv(1.)68 b(The)42 b(function)g Ft(u)149 4148 y Fv(satis\014es)1417 4266 y Ft(u)p Fv(\()p Ft(z)t Fv(\))27 b(=)h Fp(\000)p Fv(\002\()p Ft(z)t Fv(\))23 b(+)f Ft(m)p Fv(\()p Ft(z)t Fv(\)\010\()p Ft(z)t Fv(\))149 4438 y(where)35 b Ft(m)p Fv(\()p Ft(z)t Fv(\))671 4378 y Fr(def)688 4438 y Fv(=)810 4357 y Fk(\012)857 4438 y Fv(\()p Ft(l)24 b Fp(\000)f Ft(z)t Fv(\))1136 4390 y Fn(\000)p Fs(1)1247 4438 y Ft(\016)1290 4453 y Fs(1)1329 4438 y Ft(;)17 b(\016)1416 4453 y Fs(1)1456 4357 y Fk(\013)1536 4438 y Fv(is)33 b(a)g(min)m(us)h(Nev)-5 b(anlinna)34 b(function)g(in)f Fo(C)3080 4453 y Fn(\000)3172 4438 y Fv(\(Im)17 b Ft(m)p Fv(\()p Ft(z)t Fv(\))30 b Fp(\024)f Fv(0\).)149 4556 y(By)45 b(general)g(prop)s(erties)h(of)e(Nev)-5 b(anlinna)45 b(functions,)j(the)d(\014nite)g(b)s(oundary)g(v)-5 b(alues,)48 b Ft(m)p Fv(\()p Ft(k)s Fv(\))h(=)149 4672 y(lim)166 4735 y Fr(")p Fn(#)p Fs(0)302 4672 y Ft(m)p Fv(\()p Ft(k)32 b Fp(\000)e Ft(i")p Fv(\),)46 b(exist)f(for)e(almost)g(all)h Ft(k)49 b Fp(2)d Fo(R)p Fv(.)76 b(A)m(t)44 b(suc)m(h)h Ft(k)s Fv('s,)h(the)e(solution)g Ft(u)p Fv(\()p Ft(k)s Fv(\),)i Ft(u)3515 4687 y Fr(j)3551 4672 y Fv(\()p Ft(k)s Fv(\))g(=)149 4841 y(lim)166 4904 y Fr(")p Fn(#)p Fs(0)302 4841 y Ft(u)358 4856 y Fr(j)394 4841 y Fv(\()p Ft(k)25 b Fp(\000)d Ft(i")p Fv(\),)33 b(to)f(\(3.1\))g(with)h Ft(z)g Fv(=)27 b Ft(k)36 b Fv(is)d(de\014ned.)149 5085 y Fy(Lemma)40 b(3.1.)h Fq(F)-7 b(or)34 b(a.)45 b(e.)f Ft(k)31 b Fp(2)d Fo(R)35 b Fq(the)g(sum)1840 5011 y Fk(P)1945 5114 y Fr(j)1998 5085 y Fv(Im)17 b Ft(q)2174 5100 y Fr(j)2227 5085 y Fp(j)p Ft(u)2311 5100 y Fr(j)2347 5085 y Fv(\()p Ft(k)s Fv(\))p Fp(j)2505 5037 y Fs(2)2579 5085 y Fq(is)35 b(\014nite,)f(and)149 5270 y Fv(\(3.2\))1108 b(sup)1425 5349 y Fs(0)p Fr(<"<)p Fs(1)1654 5270 y Ft(")17 b Fp(k)o Ft(u)p Fv(\()p Ft(k)25 b Fp(\000)d Ft(i")p Fv(\))p Fp(k)2202 5221 y Fs(2)2202 5299 y Fr(H)2297 5270 y Ft(<)28 b Fp(1)p Ft(:)p eop %%Page: 6 6 6 5 bop 125 66 a Fl(6)1418 b(R)n(OMAN)24 b(R)n(OMANO)n(V)125 266 y Fq(Pr)-5 b(o)g(of.)41 b Fv(Both)47 b(assertions)i(result)f(from)f (consideration)i(of)e(the)h(limit)g Ft(")k Fp(#)h Fv(0)47 b(in)h(the)g(iden)m(tit)m(y)125 382 y(\()p Ft(z)32 b Fv(=)27 b Ft(k)f Fp(\000)c Ft(i")p Fv(\))1226 458 y Fn(1)1189 488 y Fk(X)1200 698 y Fr(j)t Fs(=1)1350 583 y Fv(\()o(Im)c Ft(q)1564 598 y Fr(j)1622 583 y Fv(+)23 b Ft(")p Fv(\))16 b Fp(j)o Ft(u)1904 598 y Fr(j)1940 583 y Fv(\()p Ft(z)t Fv(\))p Fp(j)2094 534 y Fs(2)2161 583 y Fv(=)27 b Fp(\000)p Fv(Im)18 b Ft(m)p Fv(\()p Ft(z)t Fv(\))p Ft(:)125 823 y Fv(T)-8 b(o)32 b(v)m(erify)i(this)f(iden)m(tit)m(y)i(w)m(e)e(notice)h (that)e(the)h(l.)43 b(h.)h(s.)g(equals)34 b(to)651 991 y(Im)17 b Fp(h)p Fv(\()p Ft(l)24 b Fp(\000)f Ft(z)t Fv(\))p Ft(u)p Fv(\()p Ft(z)t Fv(\))p Ft(;)17 b(u)p Fv(\()p Ft(z)t Fv(\))p Fp(i)28 b Fv(=)g(Im)17 b Fp(h)p Ft(\016)1893 1006 y Fs(1)1932 991 y Ft(;)g(u)p Fv(\()p Ft(z)t Fv(\))p Fp(i)27 b Fv(=)h(Im)p 2460 904 211 4 v 17 w Ft(m)p Fv(\()p Ft(z)t Fv(\))h(=)e Fp(\000)p Fv(Im)18 b Ft(m)p Fv(\()p Ft(z)t Fv(\))p Ft(:)3700 1152 y Fh(\003)224 1323 y Fv(Our)38 b(aim)h(no)m(w)g(is)f(to)g(apply)h(the)g(criterion)g(from)f(prop)s (osition)g(2.2.)60 b(F)-8 b(or)37 b(a)h(function)h(\011)f(an-)125 1449 y(alytic)46 b(in)h Fo(C)606 1464 y Fn(\000)711 1449 y Fv(in)m(tro)s(duce)g(the)f(notation)1760 1423 y Fk(e)1743 1449 y Ft( )t Fv(\()p Ft(z)t Fv(\))51 b(=)p 2113 1363 210 4 v 51 w Ft( )20 b Fv(\()p 2234 1395 50 4 v Ft(z)5 b Fv(\).)84 b(On)46 b(calculating)h(the)f(W)-8 b(ronskian,)125 1566 y Ft(W)14 b Fv([\010\()p Ft(z)t Fv(\))p Ft(;)j(u)p Fv(\()p Ft(z)t Fv(\)])28 b Fp(\021)g Fv(\010)908 1581 y Fr(j)t Fn(\000)p Fs(1)1035 1566 y Fv(\()p Ft(z)t Fv(\))p Ft(u)1216 1581 y Fr(j)1253 1566 y Fv(\()p Ft(z)t Fv(\))23 b Fp(\000)f Fv(\010)1570 1581 y Fr(j)1607 1566 y Fv(\()p Ft(z)t Fv(\))p Ft(u)1788 1581 y Fr(j)t Fn(\000)p Fs(1)1915 1566 y Fv(\()p Ft(z)t Fv(\))28 b(=)g(1,)k(w)m(e)i(obtain)588 1749 y Fk(\002)630 1829 y Fv(\()p Ft(l)699 1788 y Fn(\003)761 1829 y Fp(\000)22 b Ft(z)t Fv(\))948 1781 y Fn(\000)p Fs(1)1059 1829 y Ft(f)1118 1749 y Fk(\003)1159 1868 y Fr(j)1223 1829 y Fv(=)1334 1804 y Fk(e)1327 1829 y Fv(\010)1397 1844 y Fr(j)1434 1829 y Fv(\()p Ft(z)t Fv(\))1613 1705 y Fn(1)1576 1735 y Fk(X)1583 1945 y Fr(n)p Fs(=)p Fr(j)1739 1829 y Fk(e)-57 b Ft(u)1793 1844 y Fr(n)1839 1829 y Fv(\()p Ft(z)t Fv(\))p Ft(f)2012 1844 y Fr(n)2082 1829 y Fv(+)25 b Fk(e)-58 b Ft(u)2236 1844 y Fr(j)2272 1829 y Fv(\()p Ft(z)t Fv(\))2425 1701 y Fr(j)t Fn(\000)p Fs(1)2414 1735 y Fk(X)2420 1944 y Fr(n)p Fs(=1)2582 1804 y Fk(e)2575 1829 y Fv(\010)2645 1844 y Fr(n)2692 1829 y Fv(\()p Ft(z)t Fv(\))p Ft(f)2865 1844 y Fr(n)2913 1829 y Ft(;)44 b(z)33 b Fp(2)28 b Fo(C)3228 1844 y Fs(+)3287 1829 y Ft(:)224 2096 y Fv(Let)33 b Ft(D)s Fv(\()p Ft(z)t Fv(\),)g Ft(z)f Fv(=)c Ft(k)d Fv(+)d Ft(i")p Fv(,)33 b(b)s(e)f(the)h(op)s(erator)f (de\014ned)i(in)f(\(2.1\))f(with)h Ft(L)28 b Fv(=)g Ft(l)r Fv(.)125 2273 y Fy(Lemma)46 b(3.2.)f Fq(If)857 2198 y Fp(p)p 940 2198 180 4 v 75 x Fv(Im)17 b Ft(q)j Fv(\010\()p Ft(k)s Fv(\))51 b Ft(=)-61 b Fp(2)39 b Ft(l)1511 2236 y Fs(2)1592 2273 y Fq(for)h(a.)63 b(e.)f Ft(k)42 b Fp(2)d Ft(M)52 b Fq(for)40 b(a)h(set)g Ft(M)51 b Fq(of)41 b(p)-5 b(ositive)40 b(L)-5 b(eb)g(esgue)125 2401 y(me)g(asur)g(e,)34 b(then)g Ft(D)s Fv(\()p Ft(k)25 b Fv(+)d Ft(i")p Fv(\))1242 2344 y Fr(s)1178 2401 y Fp(\000)-16 b(!)1206 2464 y Fr(")p Fn(#)p Fs(0)1355 2401 y Fv(0)35 b Fq(for)f(a.)45 b(e.)f Ft(k)31 b Fp(2)d Ft(M)10 b Fq(.)125 2650 y(Pr)-5 b(o)g(of.)41 b Fv(W)-8 b(e)46 b(shall)h(actually)g(sho)m(w)g(that)f Ft(D)s Fv(\()p Ft(k)34 b Fv(+)d Ft(i")p Fv(\))2257 2594 y Fr(s)2193 2650 y Fp(\000)-16 b(!)50 b Fv(0)c(for)g(all)g Ft(k)53 b Fp(2)f Ft(M)57 b Fv(suc)m(h)47 b(that)f(the)125 2767 y(assumption)27 b(holds)f(and)g Ft(m)p Fv(\()p Ft(k)s Fv(\))g(exists)i(and)e(is)g(\014nite,)i(and)e(so)g(\(3.2\))f(is)h (satis\014ed.)43 b(Notice)26 b(that)g(the)125 2914 y(set)39 b Fp(D)h Fv(=)514 2804 y Fk(n)581 2914 y Ft(v)31 b Fp(2)d Ft(l)784 2878 y Fs(2)824 2914 y Fv(\()p Fo(N)p Fv(\))f(:)h Ft(v)36 b Fv(is)d(compactly)h(supp)s(orted,)g(and)2364 2840 y Fk(P)2469 2944 y Fr(j)2522 2914 y Ft(v)2569 2929 y Fr(j)2605 2834 y Fk(p)p 2705 2834 213 4 v 80 x Fv(Im)17 b Ft(q)2881 2929 y Fr(j)2925 2889 y Fk(e)2918 2914 y Fv(\010)2988 2929 y Fr(j)3025 2914 y Fv(\()p Ft(k)s Fv(\))28 b(=)f(0)3335 2804 y Fk(o)3440 2914 y Fv(is)39 b(dense)125 3070 y(in)h Ft(l)277 3034 y Fs(2)357 3070 y Fv(when)619 2995 y Fp(p)p 702 2995 180 4 v 75 x Fv(Im)17 b Ft(q)k Fv(\010\()p Ft(k)s Fv(\))53 b Ft(=)-61 b Fp(2)41 b Ft(l)1278 3034 y Fs(2)1318 3070 y Fv(.)66 b(Hence,)44 b(it)c(is)h(enough)g(to)e (c)m(hec)m(k)k(that)d Ft(D)s Fv(\()p Ft(k)30 b Fv(+)d Ft(i")p Fv(\))p Ft(f)52 b Fp(!)40 b Fv(0)g(for)125 3186 y Ft(f)e Fp(2)28 b(D)s Fv(.)224 3303 y(One)33 b(has)g(for)f Ft(z)h Fv(=)27 b Ft(k)e Fv(+)d Ft(i")p Fv(,)315 3447 y Fk(h)362 3558 y Fv(\()p Ft(l)431 3517 y Fn(\003)493 3558 y Fp(\000)g Ft(z)t Fv(\))680 3509 y Fn(\000)p Fs(1)791 3468 y Fp(p)p 874 3468 165 4 v 90 x Fv(Im)17 b Ft(l)r(f)1097 3447 y Fk(i)1144 3627 y Fr(j)1208 3558 y Fv(=)1319 3533 y Fk(e)1312 3558 y Fv(\010)1382 3573 y Fr(j)1419 3558 y Fv(\()p Ft(z)t Fv(\))1598 3433 y Fn(1)1561 3463 y Fk(X)1568 3673 y Fr(n)p Fs(=)p Fr(j)1721 3468 y Fk(p)p 1821 3468 224 4 v 90 x Fv(Im)g Ft(q)1997 3573 y Fr(n)2047 3558 y Fk(e)-58 b Ft(u)2100 3573 y Fr(n)2147 3558 y Fv(\()p Ft(z)t Fv(\))p Ft(f)2320 3573 y Fr(n)2390 3558 y Fv(+)24 b Fk(e)-57 b Ft(u)2544 3573 y Fr(j)2580 3558 y Fv(\()p Ft(z)t Fv(\))2733 3429 y Fr(j)t Fn(\000)p Fs(1)2722 3463 y Fk(X)2727 3672 y Fr(n)p Fs(=1)2882 3468 y Fk(p)p 2982 3468 V 90 x Fv(Im)17 b Ft(q)3158 3573 y Fr(n)3230 3533 y Fk(e)3222 3558 y Fv(\010)3292 3573 y Fr(n)3339 3558 y Fv(\()p Ft(z)t Fv(\))p Ft(f)3512 3573 y Fr(n)3560 3558 y Ft(:)125 3819 y Fv(The)48 b(\014rst)g(term)g(in)g(the)g(r.)88 b(h.)g(s.)h(v)-5 b(anishes)49 b(for)e Ft(j)6 b Fv('s)48 b(to)f(the)h(righ)m(t)g(of)f(the)h(supp)s(ort)g(of)f Ft(f)11 b Fv(.)125 3935 y(Considering)43 b(that)j Fk(e)-58 b Ft(u)949 3950 y Fr(n)995 3935 y Fv(\()p Ft(z)t Fv(\))43 b(is)g(b)s(ounded)g(in)g Ft(")f Fv(for)g(eac)m(h)h Ft(n)p Fv(,)j(one)c(concludes)j(that)d(this)h(term)g(is)125 4051 y(uniformly)33 b(b)s(ounded)g(in)g Ft(")f Fv(and)h Ft(j)38 b Fv(when)c Ft(j)39 b Fv(ranges)33 b(o)m(v)m(er)g(compacts.)45 b(F)-8 b(rom)32 b(this)h(w)m(e)h(infer)f(that)1221 4213 y Ft(D)s Fv(\()p Ft(z)t Fv(\))p Ft(f)39 b Fv(=)27 b Ft(g)1667 4228 y Fr(")1704 4136 y Fp(p)p 1787 4136 46 4 v 77 x Ft(")r Fk(e)-57 b Ft(u)o Fv(\()p Ft(z)t Fv(\))23 b(+)f Ft(o)p Fv(\(1\))p Ft(;)71 b(")28 b Fp(!)f Fv(0)p Ft(;)125 4374 y Fv(where)1158 4550 y Ft(g)1205 4565 y Fr(")1269 4550 y Fv(=)1409 4425 y Fn(1)1373 4455 y Fk(X)1378 4664 y Fr(n)p Fs(=1)1533 4460 y Fk(p)p 1633 4460 224 4 v 90 x Fv(Im)17 b Ft(q)1809 4565 y Fr(n)1880 4525 y Fk(e)1873 4550 y Fv(\010)1943 4565 y Fr(n)1990 4550 y Fv(\()p Ft(k)25 b Fv(+)d Ft(i")p Fv(\))p Ft(f)2367 4565 y Fr(n)2442 4550 y Fv(=)27 b Ft(O)s Fv(\()p Ft(")p Fv(\))125 4805 y(since)38 b Ft(g)415 4820 y Fs(0)488 4805 y Fv(=)d(0)h(b)m(y)i(the)f(c)m(hoice)h (of)e(the)h(set)g Fp(D)s Fv(,)h(and)f(all)2219 4779 y Fk(e)2211 4805 y Fv(\010)2281 4820 y Fr(n)2328 4805 y Fv(\()p Ft(z)t Fv(\))h(are)e(analytic)i(in)f Ft(z)t Fv(.)56 b(T)-8 b(aking)37 b(in)m(to)125 4929 y(accoun)m(t)j(that)f Ft(")17 b Fp(k)q Fk(e)-57 b Ft(u)o Fv(\()p Ft(k)25 b Fv(+)d Ft(i")p Fv(\))p Fp(k)1256 4881 y Fs(2)1335 4929 y Fv(is)39 b(b)s(ounded)h(as)g 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Fk(e)1066 495 y Fv(\010\()p Ft(k)s Fv(\))p Ft(;)19 b Fk(e)-57 b Ft(u)o Fv(\()p Ft(k)s Fv(\)])28 b Fp(\021)1662 469 y Fk(e)1655 495 y Fv(\010)1725 510 y Fr(j)t Fn(\000)p Fs(1)1852 495 y Fv(\()p Ft(k)s Fv(\))s Fk(e)-58 b Ft(u)2038 510 y Fr(j)2074 495 y Fv(\()p Ft(k)s Fv(\))22 b Fp(\000)2333 469 y Fk(e)2326 495 y Fv(\010)2396 510 y Fr(j)2433 495 y Fv(\()p Ft(k)s Fv(\))s Fk(e)-58 b Ft(u)2619 510 y Fr(j)t Fn(\000)p Fs(1)2745 495 y Fv(\()p Ft(k)s Fv(\))p Ft(;)44 b(j)34 b(>)27 b Fv(1)p Ft(:)149 751 y Fv(Multiplying)35 b(this)e(b)m(y)g Ft(\013)1068 766 y Fr(j)1105 751 y Ft(\013)1167 766 y Fr(j)t Fn(\000)p Fs(1)1294 751 y Fv(,)f Ft(\013)1415 766 y Fr(j)1479 691 y(def)1497 751 y Fv(=)1617 670 y Fk(p)p 1717 670 213 4 v 81 x Fv(Im)17 b Ft(q)1893 766 y Fr(j)1930 751 y Fv(,)32 b(and)h(summing)h(o)m(v)m(er)g Ft(j)6 b Fv(,)32 b(w)m(e)i(obtain)337 937 y Fr(n)286 967 y Fk(X)447 1062 y Ft(\013)509 1077 y Fr(j)546 1062 y Ft(\013)608 1077 y Fr(j)t Fn(\000)p Fs(1)762 1062 y Fp(\024)918 937 y Fr(n)867 967 y Fk(X)1028 1062 y Ft(\013)1090 1077 y Fr(j)t Fn(\000)p Fs(1)1233 1062 y Fp(j)p Fv(\010)1331 1077 y Fr(j)t Fn(\000)p Fs(1)1458 1062 y Fv(\()p Ft(k)s Fv(\))p Fp(j)22 b(\001)f Ft(\013)1749 1077 y Fr(j)1803 1062 y Fp(j)o Ft(u)1886 1077 y Fr(j)1922 1062 y Fv(\()p Ft(k)s Fv(\))p Fp(j)h Fv(+)2251 937 y Fr(n)2200 967 y Fk(X)2361 1062 y Ft(\013)2423 1077 y Fr(j)2476 1062 y Fp(j)o Fv(\010)2573 1077 y Fr(j)2610 1062 y Fv(\()p Ft(k)s Fv(\))p Fp(j)g(\001)g Ft(\013)2902 1077 y Fr(j)t Fn(\000)p Fs(1)3045 1062 y Fp(j)p Ft(u)3129 1077 y Fr(j)t Fn(\000)p Fs(1)3255 1062 y Fv(\()p Ft(k)s Fv(\))p Fp(j)27 b(\024)240 1352 y Fv(2)306 1181 y Fk( )435 1227 y Fr(n)384 1257 y Fk(X)545 1352 y Fv(Im)17 b Ft(q)721 1367 y Fr(j)774 1352 y Fp(j)p Fv(\010)872 1367 y Fr(j)909 1352 y Fv(\()p Ft(k)s Fv(\))p Fp(j)1067 1303 y Fs(2)1106 1181 y Fk(!)1185 1204 y Fs(1)p Fr(=)p Fs(2)1312 1181 y Fk( )1441 1227 y Fr(n)1390 1257 y Fk(X)1551 1352 y Fv(Im)g Ft(q)1727 1367 y Fr(j)1780 1352 y Fp(j)p Ft(u)1864 1367 y Fr(j)1900 1352 y Fv(\()p Ft(k)s Fv(\))p Fp(j)2058 1303 y Fs(2)2097 1181 y Fk(!)2176 1204 y Fs(1)p Fr(=)p Fs(2)2314 1352 y Fp(\024)28 b Ft(C)2512 1181 y Fk( )2642 1227 y Fr(n)2591 1257 y Fk(X)2752 1352 y Fv(Im)17 b Ft(q)2928 1367 y Fr(j)2981 1352 y Fp(j)p Fv(\010)3079 1367 y Fr(j)3116 1352 y Fv(\()p Ft(k)s Fv(\))p Fp(j)3274 1303 y Fs(2)3313 1181 y Fk(!)3392 1204 y Fs(1)p Fr(=)p Fs(2)3519 1352 y Ft(;)149 1658 y Fv(where)40 b(the)f(\014rst)g(assertion)h(of)e(lemma)h(3.1)f(has)h(b)s (een)h(tak)m(en)f(in)m(to)g(accoun)m(t.)62 b(W)-8 b(e)39 b(obtain)g(that)149 1774 y(if)244 1699 y Fk(P)349 1803 y Fr(j)402 1774 y Ft(\013)464 1789 y Fr(j)501 1774 y Ft(\013)563 1789 y Fr(j)t Fn(\000)p Fs(1)726 1774 y Fv(=)d Fp(1)h Fv(then)1202 1699 y Fk(P)1307 1803 y Fr(j)1360 1774 y Fv(Im)17 b Ft(q)1536 1789 y Fr(j)1590 1774 y Fp(j)p Fv(\010)1688 1789 y Fr(j)1725 1774 y Fv(\()p Ft(k)s Fv(\))p Fp(j)1882 1726 y Fs(2)1958 1774 y Fv(=)36 b Fp(1)h Fv(for)g(a.)58 b(e.)h Ft(k)39 b Fp(2)e Fo(R)p Fv(,)i(and)f(the)g(lemma)g(just)149 1899 y(pro)m(v)m(ed)c(implies)h(that)d Ft(N)1087 1914 y Fr(e)1152 1899 y Fv(=)27 b Fp(f)p Fv(0)p Fp(g)p Fv(.)249 2015 y(The)43 b(general)f(case)g(is)g(reduced)h(to)e(the)h(one)g (considered)i(ab)s(o)m(v)m(e,)g(since)f(if)f(Im)17 b Ft(q)58 b(=)-60 b Fp(2)43 b Ft(l)3502 1979 y Fs(1)3542 2015 y Fv(,)h(then)149 2058 y Fk(P)255 2162 y Fr(j)314 2133 y Fk(e)-61 b Ft(\013)370 2148 y Fr(j)413 2133 y Fk(e)f Ft(\013)468 2148 y Fr(j)t Fn(\000)p Fs(1)629 2133 y Fv(=)34 b Fp(1)p Fv(,)43 b Fk(e)-62 b Ft(\013)964 2148 y Fr(j)1035 2133 y Fp(\021)1146 2051 y Fk(p)p 1246 2051 V 82 x Fv(Im)21 b Fk(e)-59 b Ft(q)1422 2148 y Fr(j)1459 2133 y Fv(,)37 b(for)i Fk(e)-59 b Ft(q)38 b Fv(=)c Ft(q)28 b Fv(+)d Ft(id)36 b Fv(with)h(a)e(nonnegativ)m(e)j Ft(d)c Fp(2)g Ft(l)3230 2097 y Fs(1)3269 2133 y Fv(.)55 b(Indeed,)38 b(b)m(y)149 2266 y(the)d(uniform)f(b)s(oundedness)i(principle,)1690 2191 y Fp(p)p 1773 2191 180 4 v 75 x Fv(Im)17 b Ft(q)46 b(=)-61 b Fp(2)31 b Ft(l)2111 2230 y Fs(2)2184 2266 y Fv(implies)36 b(that)d(there)i(exists)h(a)e Ft(\032)c Fp(2)g Ft(l)3541 2230 y Fs(2)3615 2266 y Fv(suc)m(h)149 2382 y(that)364 2308 y Fk(P)469 2411 y Fr(j)522 2382 y Ft(\032)572 2397 y Fr(j)609 2382 y Ft(\013)671 2397 y Fr(j)741 2382 y Fv(=)k Fp(1)p Fv(,)i(and,)h(ob)m(viously)-8 b(,)39 b(the)d Ft(\032)h Fv(can)f(b)s(e)g(c)m(hosen)i(to)d(b)s(e)h (nonnegativ)m(e.)56 b(No)m(w)36 b(one)149 2512 y(can)f(set)f Ft(d)534 2527 y Fr(j)601 2512 y Fv(=)c Ft(\032)757 2475 y Fs(2)757 2536 y Fr(j)t Fn(\000)p Fs(1)884 2512 y Fv(,)k(for)40 b Fk(e)-61 b Ft(\013)1158 2527 y Fr(j)1201 2512 y Fk(e)f Ft(\013)1256 2527 y Fr(j)t Fn(\000)p Fs(1)1413 2512 y Fp(\025)31 b Ft(\032)1571 2527 y Fr(j)t Fn(\000)p Fs(1)1698 2512 y Ft(\013)1760 2527 y Fr(j)t Fn(\000)p Fs(1)1887 2512 y Fv(.)47 b(An)35 b(application)f(of)g(lemma)g(2.4)g(completes)i (the)149 2628 y(pro)s(of.)3326 b Fh(\003)249 2871 y Fv(It)36 b(should)h(b)s(e)g(men)m(tioned)h(that)e(in)g(the)h(case)g(Im)17 b Ft(q)37 b Fp(2)e Ft(l)2345 2835 y Fs(1)2420 2871 y Fv(the)i(imaginary)f(part)g(of)g Ft(l)j Fv(is)d(of)g(the)149 2988 y(trace)e(class,)g(and)f(therefore)g Ft(\033)1325 2907 y Fk(\000)1381 2988 y Ft(l)r Fp(j)1440 3017 y Fr(N)1496 3025 y Fi(e)1533 2907 y Fk(\001)1607 2988 y Fv(=)28 b Ft(\033)1766 3003 y Fr(ac)1839 2988 y Fv(\(Re)17 b Ft(l)r Fv(\).)44 b(Th)m(us)35 b(the)e(problem)h(of)e(description)i(of)f(the) 149 3104 y(a.)44 b(c.)f(sp)s(ectrum)34 b(of)f(dissipativ)m(e)i (discrete)f(Sc)m(hr\177)-49 b(odinger)34 b(op)s(erator)d(is)j(solv)m (ed)g(completely)-8 b(.)249 3220 y(The)29 b(ab)s(o)m(v)m(e)h(pro)s(of)d (extends)j(straigh)m(tforw)m(ardly)g(to)e(the)g(case)i(of)e(general)g (Jacobi)h(matrix)g(with)149 3336 y(asymptotically)35 b(constan)m(t)f Fq(r)-5 b(e)g(al)33 b Fv(w)m(eigh)m(t.)46 b(Namely)-8 b(,)34 b(giv)m(en)g(a)f(b)s(ounded)h(sequence,)i Fp(f)p Ft(\032)3377 3351 y Fr(n)3424 3336 y Fp(g)p Fv(,)d(of)f(real)149 3453 y(nonzero)i(n)m(um)m(b)s(ers,)g(de\014ne)g(the)f(Jacobi)g(matrix) 1553 3673 y Ft(J)k Fv(=)28 b(\003)p Ft(S)f Fv(+)22 b Ft(S)2067 3632 y Fn(\003)2106 3673 y Fv(\003)g(+)g Ft(Q;)149 3893 y Fv(where)39 b(\(\003)p Ft(u)p Fv(\))635 3922 y Fr(n)718 3893 y Fv(=)d Ft(\032)880 3908 y Fr(n)928 3893 y Ft(u)984 3908 y Fr(n)1030 3893 y Fv(,)j(and)f Ft(Q)g Fv(is)g(as)f(b)s(efore.)59 b(Then)39 b Ft(J)46 b Fv(is)38 b(a)g(b)s(ounded)g(dissipativ)m(e)i(op)s(erator,)149 4010 y(and)33 b(the)g(corresp)s(onding)h(v)m(ersion)g(of)e(theorem)h (3.3)f(reads)i(as,)149 4220 y Fy(Theorem)41 b(3.4.)j Fq(L)-5 b(et)37 b Ft(\032)1065 4235 y Fr(n)1144 4220 y Fp(!)32 b Ft(c)g Fp(6)p Fv(=)g(0)37 b Fq(and)f Fp(f)p Ft(q)1828 4235 y Fr(j)1865 4220 y Fp(g)h Fq(b)-5 b(e)37 b(a)g(b)-5 b(ounde)g(d)36 b(se)-5 b(quenc)g(e)36 b(of)h(c)-5 b(omplex)36 b(numb)-5 b(ers,)149 4336 y Fv(Im)18 b Ft(q)326 4351 y Fr(j)390 4336 y Fp(\025)28 b Fv(0)p Fq(,)35 b(such)f(that)i Ft(\033)1085 4351 y Fr(ess)1187 4336 y Fv(\()p Ft(J)9 b Fv(\))28 b Fp(\032)g Fo(R)p Fq(.)45 b(Then)34 b Ft(N)1938 4351 y Fr(e)1975 4336 y Fv(\()p Ft(J)9 b Fv(\))27 b Fp(6)p Fv(=)h Fp(f)p Fv(0)p Fp(g)f Fv(=)-17 b Fp(\))28 b Fv(Im)17 b Ft(q)31 b Fp(2)d Ft(l)2940 4300 y Fs(1)2980 4336 y Fq(.)249 4547 y Fv(Indeed,)i(assuming)f(without)f(loss)g(of)f (generalit)m(y)h(that)f Ft(\032)2352 4562 y Fs(1)2420 4547 y Fv(=)g(1,)i(one)e(can)h(de\014ne)h(the)e(functions)149 4663 y(\002,)37 b(\010)f(as)g(solutions)g(of)f(the)h(corresp)s(onding)h (equations)g(with)f(the)g(same)g(b)s(oundary)g(conditions)149 4782 y(as)j(ab)s(o)m(v)m(e)g(and)f(let)h Ft(u)p Fv(\()p Ft(z)t Fv(\))e(=)h(\()p Ft(J)31 b Fp(\000)22 b Ft(z)t Fv(\))1541 4734 y Fn(\000)p Fs(1)1652 4782 y Ft(\016)1695 4797 y Fs(1)1735 4782 y Fv(.)60 b(The)39 b(pro)s(of)f(then)h(pro)s (ceeds)g(v)m(erbatim)h(un)m(til)f(\(3.3\),)149 4898 y(where)d(w)m(e)f (will)g(ha)m(v)m(e)g Ft(\032)1040 4913 y Fr(j)t Fn(\000)p Fs(1)1201 4898 y Fv(in)g(the)f(l.)49 b(h.)f(s.)h(at)34 b(the)g(place)h(of)f(1.)48 b(Still,)35 b(it)f(sho)m(ws)h(that)f(the)h (r.)48 b(h.)149 5015 y(s.)c(is)33 b(b)s(ounded)h(a)m(w)m(a)m(y)g(from)e (zero,)h(since)h(so)f(is)g Ft(\032)1969 5030 y Fr(j)2006 5015 y Fv(,)f(and)h(the)g(pro)s(of)f(pro)s(ceeds)i(as)e(b)s(efore.)249 5131 y(It)45 b(is)g(not)f(clear)h(whether)h(the)g(metho)s(ds)f(ab)s(o)m (v)m(e)h(can)e(b)s(e)h(extended)i(to)d(co)m(v)m(er)i(the)f(case)h(of) 149 5247 y(complex)29 b(w)m(eigh)m(t)g Ft(\032)p Fv(.)42 b(This)29 b(lea)m(v)m(es)h(op)s(en)d(the)h(question)h(whether)g(there)f (exist)h(dissipativ)m(e)h(Jacobi)149 5363 y(matrices)k(with)f(non)m (trivial)h(a.)43 b(c.)h(subspace)34 b(in)f(the)g(case)h(when)f Fp(j)p Fv(Im)17 b Ft(\032)p Fp(j)22 b Fv(+)g(Im)17 b Ft(q)43 b(=)-60 b Fp(2)28 b Ft(l)3282 5327 y Fs(1)3322 5363 y Fv(.)p eop %%Page: 8 8 8 7 bop 125 66 a Fl(8)1418 b(R)n(OMAN)24 b(R)n(OMANO)n(V)1467 266 y Fv(4.)49 b Fu(Continuous)39 b(case)224 440 y Fv(Let)f Ft(q)h Fp(2)d Ft(L)654 404 y Fn(1)729 440 y Fv(\()p Fo(R)839 455 y Fs(+)898 440 y Fv(\))h(b)s(e)h(a)f(function)h(satisfying)g(Im)17 b Ft(q)t Fv(\()p Ft(x)p Fv(\))36 b Fp(\025)g Fv(0)h(a.)57 b(e.)h(and)37 b Ft(h)h Fv(b)s(e)f(an)g(arbitrary)125 556 y(real)32 b(n)m(um)m(b)s(er.)45 b(De\014ne)33 b(\002\()p Ft(x;)17 b(z)t Fv(\))33 b(and)g(\010\()p Ft(x;)17 b(z)t Fv(\))34 b(to)e(b)s(e)h(the)g(solutions)g(to)125 723 y(\(4.1\))1137 b Fp(\000)p Ft(u)1596 682 y Fn(00)1660 723 y Fv(+)22 b Ft(q)t(u)27 b Fv(=)h Ft(z)t(u;)45 b(z)32 b Fp(2)c Fo(C)p Ft(;)125 890 y Fv(with)49 b(the)g(Cauc)m(h)m(y)i(data)d (\010\(0)p Ft(;)17 b(z)t Fv(\))56 b(=)g(\002)1703 854 y Fn(0)1726 890 y Fv(\(0)p Ft(;)17 b(z)t Fv(\))55 b(=)g(0,)e(\010)2329 854 y Fn(0)2353 890 y Fv(\(0)p Ft(;)17 b(z)t Fv(\))55 b(=)g Fp(\000)p Fv(1,)f(\002)3040 854 y Fn(0)3063 890 y Fv(\(0)p Ft(;)17 b(z)t Fv(\))55 b(=)g(1.)92 b(Let)125 1006 y Ft(u)181 1021 y Fr(h)253 1006 y Fv(=)27 b(\002)22 b Fp(\000)h Ft(h)p Fv(\010.)224 1123 y(The)43 b(Sc)m(hr\177)-49 b(odinger)43 b(op)s(erator)e Ft(l)r Fv(,)k Ft(l)r(y)i Fv(=)d Fp(\000)p Ft(y)1857 1086 y Fn(00)1927 1123 y Fv(+)28 b Ft(q)t(y)t Fv(,)44 b(is)e(de\014ned)i(in)e(the)g(Hilb)s(ert)g(space)h Ft(H)52 b Fv(=)125 1239 y Ft(L)191 1203 y Fs(2)230 1239 y Fv(\()p Fo(R)340 1254 y Fs(+)399 1239 y Fv(\))22 b(on)h(the)g(domain) f(\014xed)i(b)m(y)f(the)g(self-adjoin)m(t)f(b)s(oundary)h(condition)g Ft(y)2978 1203 y Fn(0)3000 1239 y Fv(\(0\))28 b(=)f Ft(hy)t Fv(\(0\).)39 b(Then)125 1355 y Ft(l)d Fv(is)f(a)f(maximal)i(dissipativ) m(e)h(op)s(erator)d(of)g(the)g(class)i(considered)g(in)f(section)h(2,)f (pro)m(vided)h(that)125 1471 y(Im)17 b Ft(q)t Fv(\()p Ft(x)p Fv(\))23 b(deca)m(ys)j(at)d(in\014nit)m(y)i(in)f(an)f (appropriate)h(sense,)j(for)c(instance,)k(if)c(ess)34 b(sup)2912 1553 y Fr(x>A)3152 1471 y Fv(Im)17 b Ft(q)t Fv(\()p Ft(x)p Fv(\))28 b Fp(!)f Fv(0)c(as)125 1650 y Ft(A)29 b Fp(!)g(1)p Fv(,)34 b(whic)m(h)h(guaran)m(tees)g(that)e Ft(\033)1551 1665 y Fr(ess)1654 1650 y Fv(\()p Ft(L)p Fv(\))c Fp(\032)h Fo(R)p Fv(.)47 b(W)-8 b(e)34 b(shall)g(assume)h(this) g(condition)f(satis\014ed)125 1766 y(throughout.)224 1882 y(The)g(follo)m(wing)f(lemma)g(is)g(a)f(con)m(tin)m(uous)j(analog) c(of)i(lemma)g(3.1.)125 2062 y Fy(Lemma)42 b(4.1.)i Fq(F)-7 b(or)37 b(al)5 b(l)37 b Ft(z)h Fp(2)c Fo(C)1325 2077 y Fn(\000)1422 2062 y Fq(ther)-5 b(e)38 b(exists)f(exactly)h(one)f (line)-5 b(ar)38 b(indep)-5 b(endent)36 b Ft(L)3339 2026 y Fs(2)3379 2062 y Fq(-solution,)125 2179 y Ft(u)p Fv(\()p Ft(x;)17 b(z)t Fv(\))p Fq(,)35 b(to)g(\(4.1\),)f(which)g(c)-5 b(an)34 b(b)-5 b(e)34 b(chosen)g(in)h(the)g(form)1282 2345 y Ft(u)p Fv(\()p Ft(x;)17 b(z)t Fv(\))28 b(=)f(\002\()p Ft(x;)17 b(z)t Fv(\))23 b(+)f Ft(m)p Fv(\()p Ft(z)t Fv(\)\010\()p Ft(x;)17 b(z)t Fv(\))125 2512 y Fq(wher)-5 b(e)31 b Ft(m)i Fq(is)g(an)f(analytic)g(function)g(in)g Fo(C)1691 2527 y Fn(\000)1750 2512 y Fq(.)44 b(F)-7 b(or)32 b(almost)g(al)5 b(l)32 b Ft(k)f Fp(2)d Fo(R)k Fq(the)h(function)f Ft(m)h Fq(has)f(\014nite)125 2629 y(b)-5 b(oundary)33 b(values,)g Ft(m)p Fv(\()p Ft(k)s Fv(\))28 b(=)g(lim)1226 2691 y Fr(")p Fn(#)p Fs(0)1362 2629 y Ft(m)p Fv(\()p Ft(k)23 b Fp(\000)d Ft(i")p Fv(\))p Fq(,)33 b(the)h(solution)g Ft(u)p Fv(\()p Ft(x;)17 b(k)s 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Fs(0)1514 5029 y Fv(\(Im)17 b Ft(q)t Fv(\()p Ft(t)p Fv(\))22 b(+)g Ft(")p Fv(\))16 b Fp(j)p Ft(u)p Fv(\()p Ft(t;)h(z)t Fv(\))p Fp(j)2378 4980 y Fs(2)2434 5029 y Ft(dt;)45 b(z)32 b Fv(=)c Ft(k)d Fp(\000)e Ft(i":)125 5247 y Fv(Alternativ)m(ely)-8 b(,)41 b(this)e(form)m(ula)f(can)g(b)s(e)g(established)i(on)e(the)g(basis)h (of)f(nesting)h(circles)g(analysis)125 5363 y([9)o(].)54 b(It)36 b(sho)m(ws)i(that)d Ft(m)p Fv(\()p Ft(z)t Fv(\))i(is)g(a)f(Nev) -5 b(anlinna)36 b(function)h(in)f Fo(C)2436 5378 y Fn(\000)2531 5363 y Fv(\(Im)17 b Ft(m)p Fv(\()p Ft(z)t Fv(\))34 b Fp(\025)g Fv(0\),)j(and)f(therefore)p eop %%Page: 9 9 9 8 bop 1240 66 a Fl(ON)33 b(INST)-6 b(ABILITY)32 b(OF)h(THE)g(SPECTR)n (UM)1053 b(9)149 266 y Fv(it)35 b(has)g(\014nite)g(b)s(oundary)f(v)-5 b(alues)36 b(a.)48 b(e.)i(on)34 b(the)h(real)f(axis.)50 b(The)35 b(rest)g(of)f(assertions)i(no)m(w)f(follo)m(w)149 382 y(immediately)g(from)d(consideration)i(of)e(the)h(limit)g Ft(")27 b Fp(!)h 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