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lwt132.ps
%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92a Copyright 2002 Radical Eye Software %%Title: lwt132.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMSY8 CMR12 CMBX9 CMR9 CMMI9 CMMI6 CMSY6 %%+ TeX-cmex9 CMR6 CMMI5 CMSY9 CMR10 CMMI10 CMMI7 CMSY7 CMR7 CMSY10 CMR8 %%+ CMEX10 CMR5 CMBX10 CMTI10 CMSY5 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o lwt132.ps lwt132.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.05.18:1243 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 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All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 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 /.notdef put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. 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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 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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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 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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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 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 88 /summationdisplay put dup 112 /radicalbig put dup 113 /radicalBig put dup 115 /radicalBigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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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 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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%%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 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 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 /.notdef put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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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 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: TeX-cmex9 %!PS-AdobeFont-1.0: TeX-cmex9 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex9) def /FullName (TeX\040cmex9\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put readonly def /FontBBox {-26 -2961 1503 773} readonly def /UniqueID 4314405 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFB7605D7BA557CC35D6 49F6EB651B83771034BA0C39DB8D426A24543EF4529E2D939125B5157482688E 9045C2242F4AFA4C489D975C029177CD6497EACD181FF151A45F521A4C4043C2 1F3E76EF5B3291A941583E27DFC68B9211105827590393ABFB8AA4D1623D1761 6AC0DF1D3154B0277BE821712BE7B33385E7A4105E8F3370F981B8FE9E3CF3E0 007B8C9F2D934F24D591C330487DDF179CECEC5258C47E4B32538F948AB00673 F9D549C971B0822056B339600FC1E3A5E51844CC8A75B857F15E7276260ED115 C5FD550F53CE5583743B50B0F9B7C4F836DEF1B263DB260571DCE3DFEC496E93 CB244233D14265C75105A52752F6FD65BEB401C8874BC659BC1D3ACB2B494652 F074549FA28873558649A150EC72E3ADBC7803BC5D9544F32F69E37E51E68023 1EFE3D08447DCF002B47E5E74B40AE0A68591CE2FDAC076767F59A91616E6C8B 0902351041A9E39EB7D5B3C6BA9955A5F8EE7D61EC0C68E5D07BE984CE262DE5 298990ECFC5AE969DEEEF69A96E9AEC39DE53580FDC2B6369E7792A2E9F95063 171960EEAFBDF7813CA061F160F2002CD33994953ABB7F0E6413C125DB49D747 EA9315E79269CCA9C3065CD21FBDD6E4FA1A92A39447BB7988C5E6AC715E6E17 686483A23891AA43B18D621721106248257EE902751023BBEFCFA95F2AD87EEE ADCFCFE321F98E88C11557EE0582656B8FE9888F1E738132EF9B5B6BD3004F3E 39CC36BC3F9D9A3148799CC266A967ABDE78EA4FB6FEA0D136483C8598000FE3 A7F637778D9DBDC326FBED094F8C060E01AA6E260FFD567394C2C109300A2881 BE1B2ED06FF90C7448F19BF0A3CF7A01ABDD66446EAB9E647A93ACFDF1AD29AA 4FEFDD6F96C705878ECB5EC51D863BE49A47488C63F3125870406EFAC20B9CF7 11AF72C2A69F279973D8FD125AF0BB43D630E0686EBB4AB2092466A3FEBE36F5 52309609F4075B7FE6B49FBBFC2723E0C992A16134CB5A6ABA8C2909F7B4E217 65640349503A9F40E4E7F9902BE8C364FA428C72FF69324A8ACA23C8EC7B2D99 83EAE5CB476157BBC570FBE1757524A58E4C126A04F304CABF91D5B338721E3A B5F5A4DF2685004482F54A6C1298BF7EAD6D93A4A946864177ADE9205AE74A7E 878005047B915C93F81B829DF8BD76B6B410DBBA57D914220D20EA8515A2A9 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 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D6F5CA5FED4F9AC9ADE41E04F9FC52E758C9F45A92BED935 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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 0 /.notdef put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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Fl(\(\001)p Fk(z)1899 252 y Fj(n)1944 240 y Fl(\))k(and)f(this)g(con)n(tradicts)f (the)i(fact)g(that)f Fg(f)p Fk(a)3346 252 y Fj(n)3405 240 y Fl(\(\001)p Fk(z)3545 252 y Fj(n)3590 240 y Fl(\))p Fg(g)g Fl(is)150 340 y(nonincreasing)c(sequence,)h(then)h(\001)1297 310 y Fh(2)1335 340 y Fk(z)1374 352 y Fj(n)1441 340 y Fg(\024)23 b Fl(0)k(and)h(therefore)e(w)n(e)i(ha)n(v)n(e)1030 507 y Fk(z)1069 519 y Fj(n)1137 507 y Fk(>)23 b Fl(0)p Fk(;)179 b Fl(\001)p Fk(z)1577 519 y Fj(n)1645 507 y Fg(\025)23 b Fl(0)96 b(and)69 b(\001)2143 473 y Fh(2)2181 507 y Fk(z)2220 519 y Fj(n)2288 507 y Fg(\024)22 b Fl(0)55 b(for)27 b Fk(n)c Fg(\025)g Fk(n)2810 519 y Fh(0)2847 507 y Fk(;)774 b Fl(\(6\))150 675 y(and)27 b(then)i(from)e(\(5\))h(and) f(\(6\))h(w)n(e)f(ha)n(v)n(e)f Fk(x)1486 687 y Fj(n)1555 675 y Fg(\025)d Fl(\(1)18 b Fg(\000)g Fk(p)1860 687 y Fj(n)1905 675 y Fl(\))p Fk(z)1976 687 y Fj(n)2049 675 y Fl(and)27 b(this)h(implies)g(that)g(for)f Fk(n)c Fg(\025)f Fk(n)3171 687 y Fh(1)3231 675 y Fl(=)h Fk(n)3369 687 y Fh(0)3425 675 y Fl(+)18 b Fk(\033)1509 843 y(x)1556 855 y Fj(n)p Fi(\000)p Fj(\033)1717 843 y Fg(\025)23 b Fl(\(1)18 b Fg(\000)g Fk(p)2022 855 y Fj(n)p Fi(\000)p Fj(\033)2159 843 y Fl(\))p Fk(z)2230 855 y Fj(n)p Fi(\000)p Fj(\033)2368 843 y Fk(:)150 1010 y Fl(>F)-7 b(rom)27 b(Eq.\(1\))h(and)f(the)h(last)f(inequalit)n(y)-7 b(,)27 b(w)n(e)h(ha)n(v)n(e)1303 1178 y(\001\()p Fk(a)1448 1190 y Fj(n)1494 1178 y Fl(\001)p Fk(z)1602 1190 y Fj(n)1647 1178 y Fl(\))19 b(+)f Fk(Q)1847 1190 y Fj(n)1891 1178 y Fk(z)1934 1138 y Fj(\015)1930 1199 y(n)p Fi(\000)p Fj(\033)2091 1178 y Fg(\024)k Fl(0)p Fk(;)83 b(n)23 b Fg(\025)g Fk(n)2537 1190 y Fh(1)2574 1178 y Fk(:)1047 b Fl(\(7\))150 1346 y(De\014ne)28 b(the)g(function)1656 1467 y Fk(w)1715 1479 y Fj(n)1783 1467 y Fl(=)23 b Fk(\032)1914 1479 y Fj(n)1969 1411 y Fk(a)2013 1423 y Fj(n)2058 1411 y Fl(\001)p Fk(z)2166 1423 y Fj(n)p 1969 1448 243 4 v 2002 1524 a Fk(z)2045 1484 y Fj(\015)2041 1545 y(n)p Fi(\000)p Fj(\033)2221 1467 y Fk(:)1400 b Fl(\(8\))150 1658 y(Then)28 b Fk(w)426 1670 y Fj(n)494 1658 y Fk(>)23 b Fl(0)k(and)1115 1799 y(\001)p Fk(w)1243 1811 y Fj(n)1312 1799 y Fl(=)c Fk(a)1444 1811 y Fj(n)p Fh(+1)1573 1799 y Fl(\001)p Fk(z)1681 1811 y Fj(n)p Fh(+1)1810 1799 y Fl(\001)1893 1682 y Fe(\024)1991 1743 y Fk(\032)2034 1755 y Fj(n)p 1947 1780 177 4 v 1947 1856 a Fk(z)1990 1816 y Fj(\015)1986 1877 y(n)p Fi(\000)p Fj(\033)2133 1682 y Fe(\025)2195 1799 y Fl(+)2288 1743 y Fk(\032)2331 1755 y Fj(n)2376 1743 y Fl(\001\()p Fk(a)2521 1755 y Fj(n)2567 1743 y Fl(\001)p Fk(z)2675 1755 y Fj(n)2720 1743 y Fl(\))p 2288 1780 464 4 v 2432 1856 a Fk(z)2475 1816 y Fj(\015)2471 1877 y(n)p Fi(\000)p Fj(\033)2762 1799 y Fk(:)859 b Fl(\(9\))150 1991 y(>F)-7 b(rom)27 b(the)h(fact)g(that)1143 2090 y(\001)p Fk(z)1251 2102 y Fj(n)1319 2090 y Fg(\025)23 b Fl(0)96 b(and)h(\001\()p Fk(a)1921 2102 y Fj(n)1966 2090 y Fl(\001)p Fk(z)2074 2102 y Fj(n)2119 2090 y Fl(\))24 b Fg(\024)e Fl(0)55 b(for)27 b Fk(n)c Fg(\025)g Fk(n)2697 2102 y Fh(1)2734 2090 y Fk(;)150 2231 y Fl(w)n(e)k(ha)n(v)n(e)1055 2330 y Fk(a)1099 2342 y Fj(n)p Fi(\000)p Fj(\033)1236 2330 y Fl(\001)p Fk(z)1344 2342 y Fj(n)p Fi(\000)p Fj(\033)1505 2330 y Fg(\025)c Fk(a)1637 2342 y Fj(n)p Fh(+1)1766 2330 y Fl(\001)p Fk(z)1874 2342 y Fj(n)p Fh(+1)2030 2330 y Fl(and)111 b Fk(z)2314 2342 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2558 2330 y Fg(\025)23 b Fk(z)2685 2342 y Fj(n)p Fi(\000)p Fj(\033)2822 2330 y Fk(:)757 b Fl(\(10\))150 2471 y(Then,)28 b(from)f(Eq.\(1\),)g(\(8\))h(and)f(\(9\),)h(w)n(e)g (get)991 2693 y(\001)p Fk(w)1119 2705 y Fj(n)1188 2693 y Fl(=)22 b Fg(\000)p Fk(\032)1383 2705 y Fj(n)1428 2693 y Fk(Q)1494 2705 y Fj(n)1557 2693 y Fl(+)1658 2637 y(\001)p Fk(\032)1770 2649 y Fj(n)p 1650 2674 173 4 v 1650 2750 a Fk(\032)1693 2762 y Fj(n)p Fh(+1)1832 2693 y Fk(w)1891 2705 y Fj(n)p Fh(+1)2039 2693 y Fg(\000)2132 2633 y Fk(\032)2175 2645 y Fj(n)2221 2633 y Fk(a)2265 2645 y Fj(n)p Fh(+1)2394 2633 y Fl(\001)p Fk(z)2502 2645 y Fj(n)p Fh(+1)2631 2633 y Fl(\001)p Fk(z)2743 2593 y Fj(\015)2739 2653 y(n)p Fi(\000)p Fj(\033)p 2132 2674 744 4 v 2286 2750 a Fk(z)2329 2710 y Fj(\015)2325 2772 y(n)p Fh(+1)p Fi(\000)p Fj(\033)2546 2750 y Fk(z)2589 2710 y Fj(\015)2585 2770 y(n)p Fi(\000)p Fj(\033)2886 2693 y Fk(:)693 b Fl(\(11\))150 2917 y(>F)-7 b(rom)27 b(\(10\))h(and)f(\(11\),)g(w)n(e)h(ha)n(v)n(e)991 3139 y(\001)p Fk(w)1119 3151 y Fj(n)1188 3139 y Fg(\024)22 b(\000)p Fk(\032)1383 3151 y Fj(n)1428 3139 y Fk(Q)1494 3151 y Fj(n)1557 3139 y Fl(+)1658 3083 y(\001)p Fk(\032)1770 3095 y Fj(n)p 1650 3120 173 4 v 1650 3196 a Fk(\032)1693 3208 y Fj(n)p Fh(+1)1832 3139 y Fk(w)1891 3151 y Fj(n)p Fh(+1)2039 3139 y Fg(\000)2132 3079 y Fk(\032)2175 3091 y Fj(n)2221 3079 y Fk(a)2265 3091 y Fj(n)p Fh(+1)2394 3079 y Fl(\001)p Fk(z)2502 3091 y Fj(n)p Fh(+1)2631 3079 y Fl(\001)p Fk(z)2743 3039 y Fj(\015)2739 3100 y(n)p Fi(\000)p Fj(\033)p 2132 3120 744 4 v 2318 3150 a Fe(\000)2356 3218 y Fk(z)2399 3178 y Fj(\015)2395 3240 y(n)p Fh(+1)p Fi(\000)p Fj(\033)2616 3150 y Fe(\001)2654 3168 y Fh(2)2886 3139 y Fk(:)693 b Fl(\(12\))150 3385 y(No)n(w,)27 b(b)n(y)g(using)h (the)g(inequalit)n(y)f(\(cf.)37 b([5,)28 b(p.)37 b(39]\))922 3553 y Fk(x)969 3519 y Fj(\015)1030 3553 y Fg(\000)18 b Fk(y)1157 3519 y Fj(\015)1223 3553 y Fg(\025)k Fk(\015)5 b(x)1405 3519 y Fj(\015)t Fi(\000)p Fh(1)1533 3553 y Fl(\()p Fk(x)19 b Fg(\000)f Fk(y)s Fl(\))28 b(for)f(all)g Fk(x)d Fg(\025)e Fk(y)k(>)d Fl(0)k(and)g(0)c Fk(<)f(\015)28 b Fg(\024)23 b Fl(1)p Fk(;)150 3721 y Fl(w)n(e)k(\014nd)h(that)822 3888 y(\001)p Fk(z)934 3848 y Fj(\015)930 3909 y(n)p Fi(\000)p Fj(\033)1151 3888 y Fl(=)83 b Fk(z)1342 3848 y Fj(\015)1338 3910 y(n)p Fh(+1)p Fi(\000)p Fj(\033)1577 3888 y Fg(\000)18 b Fk(z)1703 3848 y Fj(\015)1699 3909 y(n)p Fi(\000)p Fj(\033)1860 3888 y Fg(\025)k Fk(\015)d Fl(\()p Fk(z)2080 3900 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2301 3888 y Fl(\))2334 3846 y Fj(\015)t Fi(\000)p Fh(1)2475 3888 y Fl(\()p Fk(z)2546 3900 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2786 3888 y Fg(\000)f Fk(z)2908 3900 y Fj(n)p Fi(\000)p Fj(\033)3045 3888 y Fl(\))525 b(\(13\))1151 4030 y(=)83 b Fk(\015)18 b Fl(\()p Fk(z)1431 4042 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)1653 4030 y Fl(\))1685 3988 y Fj(\015)t Fi(\000)p Fh(1)1826 4030 y Fl(\()q(\001)p Fk(z)1967 4042 y Fj(n)p Fi(\000)p Fj(\033)2104 4030 y Fl(\))c Fk(:)150 4197 y Fl(Substitute)29 b(from)e(\(13\))g(in)h (\(12\),)f(w)n(e)h(ha)n(v)n(e)688 4413 y(\001)p Fk(w)816 4425 y Fj(n)885 4413 y Fg(\024)22 b(\000)p Fk(\032)1080 4425 y Fj(n)1125 4413 y Fk(Q)1191 4425 y Fj(n)1254 4413 y Fl(+)1355 4357 y(\001)p Fk(\032)1467 4369 y Fj(n)p 1347 4394 173 4 v 1347 4470 a Fk(\032)1390 4482 y Fj(n)p Fh(+1)1529 4413 y Fk(w)1588 4425 y Fj(n)p Fh(+1)1736 4413 y Fg(\000)c Fk(\015)h Fl(\()p Fk(z)1952 4425 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2173 4413 y Fl(\))2206 4371 y Fj(\015)t Fi(\000)p Fh(1)2347 4413 y Fk(\032)2390 4425 y Fj(n)2435 4413 y Fk(a)2479 4425 y Fj(n)p Fh(+1)2618 4357 y Fl(\001)p Fk(z)2726 4369 y Fj(n)p Fh(+1)2869 4357 y Fl(\()q(\001)p Fk(z)3010 4369 y Fj(n)p Fi(\000)p Fj(\033)3147 4357 y Fl(\))p 2618 4394 561 4 v 2712 4424 a Fe(\000)2750 4491 y Fk(z)2793 4451 y Fj(\015)2789 4513 y(n)p Fh(+1)p Fi(\000)p Fj(\033)3010 4424 y Fe(\001)3048 4441 y Fh(2)3189 4413 y Fk(:)390 b Fl(\(14\))150 4659 y(Again,)27 b(from)g(\(10\))h(in)g (\(14\),)f(w)n(e)g(obtain)720 4891 y(\001)p Fk(w)848 4903 y Fj(n)917 4891 y Fg(\024)c(\000)p Fk(\032)1113 4903 y Fj(n)1158 4891 y Fk(Q)1224 4903 y Fj(n)1287 4891 y Fl(+)1387 4835 y(\001)p Fk(\032)1499 4847 y Fj(n)p 1380 4872 173 4 v 1380 4948 a Fk(\032)1423 4960 y Fj(n)p Fh(+1)1562 4891 y Fk(w)1621 4903 y Fj(n)p Fh(+1)1769 4891 y Fg(\000)18 b Fk(\015)h Fl(\()p Fk(z)1985 4903 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2206 4891 y Fl(\))2239 4850 y Fj(\015)t Fi(\000)p Fh(1)2380 4891 y Fk(\032)2423 4903 y Fj(n)2478 4835 y Fl(\()p Fk(a)2554 4847 y Fj(n)p Fh(+1)2683 4835 y Fl(\))2716 4793 y Fh(2)p 2478 4872 275 4 v 2492 4948 a Fl(\()q Fk(a)2569 4960 y Fj(n)p Fi(\000)p Fj(\033)2706 4948 y Fl(\))2790 4835 y(\()q(\001)p Fk(z)2931 4847 y Fj(n)p Fh(+1)3060 4835 y Fl(\))3092 4793 y Fh(2)p 2773 4872 374 4 v 2773 4902 a Fe(\000)2811 4970 y Fk(z)2854 4930 y Fj(\015)2850 4992 y(n)p Fh(+1)p Fi(\000)p Fj(\033)3071 4902 y Fe(\001)3109 4920 y Fh(2)3156 4891 y Fk(;)423 b Fl(\(15\))1929 5206 y(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 150 240 a Fl(and)27 b(hence,)742 400 y(\001)p Fk(w)870 412 y Fj(n)939 400 y Fg(\024)22 b(\000)p Fk(\032)1134 412 y Fj(n)1179 400 y Fk(Q)1245 412 y Fj(n)1308 400 y Fl(+)1409 344 y(\001)p Fk(\032)1521 356 y Fj(n)p 1401 381 173 4 v 1401 457 a Fk(\032)1444 469 y Fj(n)p Fh(+1)1583 400 y Fk(w)1642 412 y Fj(n)p Fh(+1)1791 400 y Fg(\000)c Fk(\015)5 b(\032)1965 412 y Fj(n)2238 344 y Fl(\()p Fk(a)2314 356 y Fj(n)p Fh(+1)2443 344 y Fl(\))2476 302 y Fh(2)p 2019 381 713 4 v 2019 470 a Fl(\()p Fk(a)2095 482 y Fj(n)p Fi(\000)p Fj(\033)2233 470 y Fl(\))14 b(\()p Fk(z)2350 482 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2572 470 y Fl(\))2604 428 y Fh(1)p Fi(\000)p Fj(\015)2769 344 y Fl(\(\001)p Fk(z)2909 356 y Fj(n)p Fh(+1)3038 344 y Fl(\))3071 302 y Fh(2)p 2752 381 374 4 v 2752 411 a Fe(\000)2790 478 y Fk(z)2833 438 y Fj(\015)2829 501 y(n)p Fh(+1)p Fi(\000)p Fj(\033)3050 411 y Fe(\001)3088 428 y Fh(2)3135 400 y Fk(:)444 b Fl(\(16\))150 623 y(>F)-7 b(rom)27 b(\(8\))h(and)g(\(16\),)f(w)n(e)g(\014nd)765 840 y(\001)p Fk(w)893 852 y Fj(n)962 840 y Fg(\024)c(\000)p Fk(\032)1158 852 y Fj(n)1202 840 y Fk(Q)1268 852 y Fj(n)1332 840 y Fl(+)1432 784 y(\001)p Fk(\032)1544 796 y Fj(n)p 1425 821 173 4 v 1425 897 a Fk(\032)1468 909 y Fj(n)p Fh(+1)1607 840 y Fk(w)1666 852 y Fj(n)p Fh(+1)1814 840 y Fg(\000)2106 784 y Fk(\015)5 b(\032)2197 796 y Fj(n)p 1907 821 534 4 v 1907 910 a Fl(\()p Fk(a)1983 922 y Fj(n)p Fi(\000)p Fj(\033)2121 910 y Fl(\))14 b(\()p Fk(\032)2242 922 y Fj(n)p Fh(+1)2371 910 y Fl(\))2404 868 y Fh(2)2451 840 y Fk(w)2512 806 y Fh(2)2510 861 y Fj(n)p Fh(+1)2855 784 y Fl(1)p 2649 821 453 4 v 2649 910 a(\()q Fk(z)2721 922 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)2942 910 y Fl(\))2974 868 y Fh(1)p Fi(\000)p Fj(\015)3112 840 y Fk(:)467 b Fl(\(17\))150 1076 y(>F)-7 b(rom)27 b(\(6\),)h(w)n(e)f(conclude)h(that) 1249 1251 y Fk(z)1288 1263 y Fj(n)1356 1251 y Fg(\024)23 b Fk(z)1483 1263 y Fj(n)1524 1271 y Fd(0)1578 1251 y Fl(+)18 b(\001)p Fk(z)1769 1263 y Fj(n)1810 1271 y Fd(0)1847 1251 y Fl(\()p Fk(n)g Fg(\000)g Fk(n)2080 1263 y Fh(0)2117 1251 y Fl(\))p Fk(;)208 b(n)23 b Fg(\025)g Fk(n)2591 1263 y Fh(0)2628 1251 y Fk(;)150 1426 y Fl(and)k(consequen)n(tly)g (there)h(exists)f(a)g Fk(n)1364 1438 y Fh(1)1424 1426 y Fg(\025)c Fk(n)1562 1438 y Fh(0)1626 1426 y Fl(and)28 b(appropriate)e(constan)n(t)h Fk(\013)c Fg(\025)g Fl(1)k(suc)n(h)g (that)1561 1600 y Fk(z)1600 1612 y Fj(n)1668 1600 y Fg(\024)22 b Fk(\013n)84 b Fl(for)27 b Fk(n)22 b Fg(\025)h Fk(n)2279 1612 y Fh(1)2316 1600 y Fk(;)150 1775 y Fl(and)k(this)h(implies)g(that) 1046 1950 y Fk(z)1085 1962 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)1330 1950 y Fg(\024)22 b Fk(\013)p Fl(\()p Fk(n)d Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\))84 b(for)27 b Fk(n)c Fg(\025)g Fk(n)2301 1962 y Fh(2)2361 1950 y Fl(=)g Fk(n)2499 1962 y Fh(1)2554 1950 y Fl(+)18 b Fk(\033)k Fg(\000)c Fl(1)p Fk(;)150 2124 y Fl(and,)27 b(hence)1525 2202 y(1)p 1320 2239 V 1320 2329 a(\()p Fk(z)1391 2341 y Fj(n)p Fh(+1)p Fi(\000)p Fj(\033)1612 2329 y Fl(\))1644 2287 y Fh(1)p Fi(\000)p Fj(\015)1805 2259 y Fg(\025)2209 2202 y Fl(1)p 1903 2239 655 4 v 1903 2329 a(\()p Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2430 2287 y Fh(1)p Fi(\000)p Fj(\015)2567 2259 y Fk(:)150 2465 y Fl(Substitute)29 b(from)e(the)h(last)f(inequalit)n(y)g(in)h (\(17\),)g(w)n(e)f(\014nd)365 2682 y(\001)p Fk(w)493 2694 y Fj(n)622 2682 y Fg(\024)82 b(\000)p Fk(\032)877 2694 y Fj(n)922 2682 y Fk(Q)988 2694 y Fj(n)1051 2682 y Fl(+)1152 2626 y(\001)p Fk(\032)1264 2638 y Fj(n)p 1144 2663 173 4 v 1144 2739 a Fk(\032)1187 2751 y Fj(n)p Fh(+1)1326 2682 y Fk(w)1385 2694 y Fj(n)p Fh(+1)1533 2682 y Fg(\000)2128 2626 y Fk(\015)5 b(\032)2219 2638 y Fj(n)p 1626 2663 1139 4 v 1626 2752 a Fl(\()q Fk(\032)1702 2764 y Fj(n)p Fh(+1)1831 2752 y Fl(\))1863 2710 y Fh(2)1914 2752 y Fk(a)1958 2764 y Fj(n)p Fi(\000)p Fj(\033)2110 2752 y Fl(\()p Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2637 2710 y Fh(1)p Fi(\000)p Fj(\015)2774 2682 y Fk(w)2835 2648 y Fh(2)2833 2702 y Fj(n)p Fh(+1)3602 2682 y Fl(\(18\))622 2941 y(=)82 b Fg(\000)p Fk(\032)877 2953 y Fj(n)922 2941 y Fk(Q)988 2953 y Fj(n)1051 2941 y Fl(+)1144 2885 y Fk(a)1188 2897 y Fj(n)p Fi(\000)p Fj(\033)1339 2885 y Fl(\()q Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))1867 2843 y Fh(1)p Fi(\000)p Fj(\015)2008 2885 y Fl(\(\001)p Fk(\032)2152 2897 y Fj(n)2198 2885 y Fl(\))2230 2855 y Fh(2)p 1144 2922 1124 4 v 1617 2998 a Fl(4)p Fk(\015)5 b(\032)1750 3010 y Fj(n)769 3250 y Fg(\000)848 3083 y Fe(2)848 3232 y(4)1363 3138 y Fg(p)p 1432 3138 136 4 v 51 x Fk(\015)g(\032)1523 3201 y Fj(n)p 913 3231 1106 4 v 913 3352 a Fk(\032)956 3364 y Fj(n)p Fh(+1)1085 3247 y Fe(q)p 1168 3247 851 4 v 105 x Fl(\()p Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))1695 3310 y Fh(1)p Fi(\000)p Fj(\015)1837 3352 y Fk(a)1881 3364 y Fj(n)p Fi(\000)p Fj(\033)2028 3250 y Fk(w)2087 3262 y Fj(n)p Fh(+1)2235 3250 y Fg(\000)2328 3071 y Fe(q)p 2411 3071 V 105 x Fl(\()q Fk(\013)p Fl(\()p Fk(n)h Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2939 3134 y Fh(1)p Fi(\000)p Fj(\015)3080 3176 y Fk(a)3124 3188 y Fj(n)p Fi(\000)p Fj(\033)3262 3176 y Fl(\001)p Fk(\032)3374 3188 y Fj(n)p 2328 3231 1091 4 v 2750 3307 a Fl(2)2792 3255 y Fg(p)p 2861 3255 136 4 v 52 x Fk(\015)5 b(\032)2952 3319 y Fj(n)3429 3083 y Fe(3)3429 3232 y(5)3484 3085 y Fh(2)622 3572 y Fk(<)82 b Fg(\000)848 3430 y Fe(")896 3572 y Fk(\032)939 3584 y Fj(n)984 3572 y Fk(Q)1050 3584 y Fj(n)1113 3572 y Fg(\000)1206 3516 y Fl(\()q Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))1734 3474 y Fh(1)p Fi(\000)p Fj(\015)1875 3516 y Fk(a)1919 3528 y Fj(n)p Fi(\000)p Fj(\033)2057 3516 y Fl(\(\001)p Fk(\032)2201 3528 y Fj(n)2246 3516 y Fl(\))2278 3485 y Fh(2)p 1206 3553 1110 4 v 1672 3629 a Fl(4)p Fk(\015)5 b(\032)1805 3641 y Fj(n)2326 3430 y Fe(#)2388 3572 y Fk(:)150 3817 y Fl(Then,)28 b(w)n(e)f(ha)n(v)n(e)948 3986 y(\001)p Fk(w)1076 3998 y Fj(n)1145 3986 y Fk(<)22 b Fg(\000)1311 3844 y Fe(")1359 3986 y Fk(\032)1402 3998 y Fj(n)1447 3986 y Fk(Q)1513 3998 y Fj(n)1576 3986 y Fg(\000)1669 3930 y Fl(\()q Fk(a)1746 3942 y Fj(n)p Fi(\000)p Fj(\033)1883 3930 y Fl(\))14 b(\()q Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2457 3888 y Fh(1)p Fi(\000)p Fj(\015)2598 3930 y Fl(\(\001)p Fk(\032)2742 3942 y Fj(n)2788 3930 y Fl(\))2820 3900 y Fh(2)p 1669 3967 1188 4 v 2175 4043 a Fl(4)p Fk(\015)5 b(\032)2308 4055 y Fj(n)2867 3844 y Fe(#)2929 3986 y Fk(:)650 b Fl(\(19\))150 4206 y(Summing)28 b(\(19\))f(from)h Fk(n)941 4218 y Fh(2)1005 4206 y Fl(to)g Fk(n)p Fl(,)f(w)n(e)h(obtain)636 4455 y Fg(\000)p Fk(w)760 4467 y Fj(n)801 4475 y Fd(2)861 4455 y Fk(<)22 b(w)1007 4467 y Fj(n)p Fh(+1)1156 4455 y Fg(\000)c Fk(w)1298 4467 y Fj(n)1339 4475 y Fd(2)1399 4455 y Fk(<)k Fg(\000)1617 4351 y Fj(n)1578 4376 y Fe(X)1565 4555 y Fj(l)p Fh(=)p Fj(n)1678 4563 y Fd(2)1724 4313 y Fe(")1773 4455 y Fk(\032)1816 4467 y Fj(l)1841 4455 y Fk(Q)1907 4467 y Fj(l)1951 4455 y Fg(\000)2044 4399 y Fl(\()p Fk(a)2120 4411 y Fj(l)p Fi(\000)p Fj(\033)2238 4399 y Fl(\))14 b(\()p Fk(\013)p Fl(\()p Fk(l)21 b Fl(+)d(1)g Fg(\000)g Fk(\033)s Fl(\)\))2788 4357 y Fh(1)p Fi(\000)p Fj(\015)2929 4399 y Fl(\(\001)p Fk(\032)3073 4411 y Fj(l)3099 4399 y Fl(\))3131 4369 y Fh(2)p 2044 4436 1125 4 v 2527 4512 a Fl(4)p Fk(\015)5 b(\032)2660 4524 y Fj(l)3179 4313 y Fe(#)3241 4455 y Fk(;)150 4712 y Fl(whic)n(h)28 b(yields)1100 4778 y Fj(n)1061 4803 y Fe(X)1048 4982 y Fj(l)p Fh(=)p Fj(n)1161 4990 y Fd(2)1207 4740 y Fe(")1256 4882 y Fk(\032)1299 4894 y Fj(l)1324 4882 y Fk(Q)1390 4894 y Fj(l)1434 4882 y Fg(\000)1527 4826 y Fk(a)1571 4838 y Fj(l)p Fi(\000)p Fj(\033)1702 4826 y Fl(\()q Fk(\013)p Fl(\()p Fk(l)20 b Fl(+)e(1)g Fg(\000)g Fk(\033)s Fl(\)\))2206 4784 y Fh(1)p Fi(\000)p Fj(\015)2348 4826 y Fl(\(\001)p Fk(\032)2492 4838 y Fj(l)2517 4826 y Fl(\))2549 4796 y Fh(2)p 1527 4863 1061 4 v 1978 4939 a Fl(4)p Fk(\015)5 b(\032)2111 4951 y Fj(l)2597 4740 y Fe(#)2668 4882 y Fk(<)23 b(c)2792 4894 y Fh(1)2829 4882 y Fk(;)1929 5206 y Fl(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 150 240 a Fl(for)27 b(all)g(large)g(n,)g(whic)n (h)h(is)f(con)n(trary)f(to)h(\(4\).)37 b(The)28 b(pro)r(of)f(is)h (complete.)275 340 y Fc(Remark)j(2.1.)36 b Fl(Note)27 b(that)h(from)f(Theorem)g(2.1,)g(w)n(e)g(can)g(obtain)g(di\013eren)n(t) h(conditions)f(for)g(oscillation)f(of)150 439 y(all)j(solutions)g(of)h (Eq.\(1\))f(when)g(\(2\))h(holds)f(b)n(y)g(di\013eren)n(t)h(c)n(hoices) f(of)g Fg(f)p Fk(\032)2455 451 y Fj(n)2500 439 y Fg(g)p Fk(:)g Fl(Let)h Fk(\032)2788 451 y Fj(n)2859 439 y Fl(=)c Fk(n)3000 409 y Fj(\025)3043 439 y Fk(;)k(n)c Fg(\025)g Fk(n)3313 451 y Fh(0)3380 439 y Fl(and)j Fk(\025)e(>)e Fl(1)150 539 y(is)i(a)h(constan)n(t.)36 b(By)27 b(Theorem)g(2.2)g(w)n (e)g(ha)n(v)n(e)f(the)i(follo)n(wing)f(result.)275 639 y Fc(Corollary)33 b(2.1.)39 b Fl(Assume)29 b(that)g(all)f(the)h (assumption)g(of)f(Theorem)g(2.1)g(hold,)h(except)g(the)g(condition)g (\(4\))150 738 y(is)e(replaced)g(b)n(y)707 995 y(lim)678 1045 y Fj(n)p Fi(!1)865 995 y Fl(sup)1061 891 y Fj(n)1022 916 y Fe(X)1004 1090 y Fj(s)p Fh(=)p Fj(n)1127 1098 y Fd(0)1173 853 y Fe(")1222 995 y Fk(s)1261 960 y Fj(\025)1304 995 y Fk(Q)1370 1007 y Fj(s)1424 995 y Fg(\000)1517 933 y Fk(a)1561 945 y Fj(s)p Fi(\000)p Fj(\033)1702 933 y Fl(\()q Fk(\013)p Fl(\()p Fk(s)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2219 892 y Fh(1)p Fi(\000)p Fj(\015)2360 866 y Fe(\000)2398 933 y Fl(\()p Fk(s)h Fl(+)f(1\))2645 903 y Fj(\025)2707 933 y Fg(\000)g Fk(s)2829 903 y Fj(\025)2872 866 y Fe(\001)2910 883 y Fh(2)p 1517 976 1431 4 v 2146 1052 a Fl(4)p Fk(\015)5 b(s)2275 1028 y Fj(\025)2957 853 y Fe(#)3029 995 y Fl(=)22 b Fg(1)p Fk(;)380 b Fl(\(20\))150 1260 y(where)27 b Fk(Q)456 1272 y Fj(n)524 1260 y Fl(=)c Fk(q)649 1272 y Fj(n)694 1260 y Fl(\(1)18 b Fg(\000)g Fk(p)911 1272 y Fj(n)p Fi(\000)p Fj(\033)1049 1260 y Fl(\))1081 1230 y Fj(\015)1123 1260 y Fk(:)28 b Fl(Then)g(ev)n(ery)e (solution)h(of)h(Eq.\(1\))f(oscillates.)275 1360 y Fc(Remark)k(2.2.)41 b Fl(When)29 b Fk(\015)e Fl(=)c(1,)k(Eq.\(1\))g(reduces)g(to)h(the)g (linear)e(dela)n(y)h(di\013erence)h(equation)978 1559 y(\001\()p Fk(a)1123 1571 y Fj(n)1169 1559 y Fl(\(\001)p Fk(x)1317 1571 y Fj(n)1381 1559 y Fl(+)18 b Fk(p)1506 1571 y Fj(n)1551 1559 y Fk(x)1598 1571 y Fj(n)p Fi(\000)p Fj(\034)1733 1559 y Fl(\)\))h(+)f Fk(q)1936 1571 y Fj(n)1981 1559 y Fk(x)2028 1571 y Fj(n)p Fi(\000)p Fj(\033)2189 1559 y Fl(=)23 b(0)p Fk(;)152 b(n)23 b Fl(=)f(0)p Fk(;)14 b Fl(1)p Fk(;)g Fl(2)p Fk(:::)679 b Fl(\(21\))150 1709 y(and)27 b(the)h(condition)g(\(4\))g(in)f(Theorem)g(2.1)g(reduces)g(to) 1047 1954 y(lim)1018 2004 y Fj(n)p Fi(!1)1206 1954 y Fl(sup)1384 1850 y Fj(n)1344 1875 y Fe(X)1352 2054 y Fj(l)p Fh(=0)1478 1837 y Fe(\024)1522 1954 y Fk(\032)1565 1966 y Fj(l)1590 1954 y Fk(q)1627 1966 y Fj(l)1653 1954 y Fl(\(1)18 b Fg(\000)g Fk(p)1870 1966 y Fj(l)p Fi(\000)p Fj(\033)1988 1954 y Fl(\))h Fg(\000)2132 1898 y Fl(\()p Fk(a)2208 1910 y Fj(l)p Fi(\000)p Fj(\033)2326 1898 y Fl(\))14 b(\(\001)p Fk(\032)2516 1910 y Fj(l)2542 1898 y Fl(\))2574 1867 y Fh(2)p 2132 1935 480 4 v 2316 2011 a Fl(4)p Fk(\032)2401 2023 y Fj(l)2621 1837 y Fe(\025)2688 1954 y Fl(=)23 b Fg(1)p Fk(:)720 b Fl(\(22\))150 2182 y(Then)28 b(Theorem)f(2.1)g(and)h(Theorem)f(1)g(in)h([15)o(])g(are)f (the)h(same)g(in)g(linear)f(case.)36 b(Also)28 b(when)g Fk(p)3162 2194 y Fj(n)3230 2182 y Fl(=)23 b(0)28 b(and)f Fk(\015)h Fl(=)23 b(1)150 2282 y(Theorem)k(2.1)g(and)g(Corollary)e(1)i (in)h([16)o(])g(are)f(the)h(same.)275 2382 y Fc(Theorem)f(2.2.)35 b Fl(Assume)24 b(that)h(\(2\))f(holds,)h(and)f(let)h Fg(f)p Fk(\032)2070 2394 y Fj(n)2115 2382 y Fg(g)2157 2351 y Fi(1)2157 2402 y Fj(n)p Fh(=0)2310 2382 y Fl(b)r(e)g(a)f(p)r (ositiv)n(e)f(sequence)p Fk(:)h Fl(F)-7 b(urthermore,)24 b(w)n(e)150 2481 y(assume)j(that)h(there)g(exists)f(a)g(double)h (sequence)f Fg(f)p Fk(H)1851 2493 y Fj(m;n)1998 2481 y Fl(:)c Fk(m)g Fg(\025)g Fk(n)g Fg(\025)g Fl(0)p Fg(g)k Fl(suc)n(h)g(that)i(\(i\))f Fk(H)3052 2493 y Fj(m;m)3217 2481 y Fl(=)23 b(0)k(for)g Fk(m)d Fg(\025)e Fl(0)p Fk(;)150 2581 y Fl(\(ii\))42 b Fk(H)371 2593 y Fj(m;n)518 2581 y Fk(>)23 b Fl(0)14 b(for)26 b Fk(m)d(>)g(n)g(>)f Fl(0,)28 b(\(iii\))g(\001)1455 2593 y Fh(2)1492 2581 y Fk(H)1561 2593 y Fj(m;n)1708 2581 y Fl(=)23 b Fk(H)1865 2593 y Fj(m;n)p Fh(+1)2091 2581 y Fg(\000)18 b Fk(H)2243 2593 y Fj(m;n)2367 2581 y Fk(:)28 b Fl(If)569 2845 y(lim)531 2895 y Fj(m)p Fi(!1)736 2845 y Fl(sup)956 2789 y(1)p 884 2826 185 4 v 884 2902 a Fk(H)953 2914 y Fj(m;)p Fh(0)1104 2742 y Fj(m)p Fi(\000)p Fh(1)1116 2767 y Fe(X)1093 2941 y Fj(n)p Fh(=)p Fj(n)1226 2949 y Fd(0)1272 2703 y Fe(")1321 2845 y Fk(H)1390 2857 y Fj(m;n)1514 2845 y Fk(\032)1557 2857 y Fj(n)1602 2845 y Fk(Q)1668 2857 y Fj(n)1731 2845 y Fg(\000)1824 2786 y Fk(\032)1867 2755 y Fh(2)1867 2806 y Fj(n)p Fh(+1)p 1824 2826 173 4 v 1829 2944 a Fl(4)1894 2881 y Fi(\000)1898 2933 y Fk(\032)1946 2956 y Fj(n)2020 2728 y Fe(\022)2081 2845 y Fk(h)2129 2857 y Fj(m;n)2253 2775 y Fe(p)p 2336 2775 193 4 v 70 x Fk(H)2405 2857 y Fj(m;n)2547 2845 y Fg(\000)2648 2789 y Fl(\001)p Fk(\032)2760 2801 y Fj(n)p 2640 2826 173 4 v 2640 2902 a Fk(\032)2683 2914 y Fj(n)p Fh(+1)2822 2845 y Fk(H)2891 2857 y Fj(m;n)3015 2728 y Fe(\023)3076 2746 y Fh(2)3113 2703 y Fe(#)3176 2845 y Fl(=)22 b Fg(1)p Fk(;)233 b Fl(\(23\))150 3106 y(where)871 3228 y Fk(h)919 3240 y Fj(m;n)1066 3228 y Fl(=)1164 3172 y Fg(\000)p Fl(\001)1298 3184 y Fh(2)1335 3172 y Fk(H)1404 3184 y Fj(m;n)p 1164 3209 364 4 v 1208 3225 a Fe(p)p 1291 3225 193 4 v 67 x Fk(H)1360 3304 y Fj(m;n)1537 3228 y Fk(;)1625 3164 y Fi(\000)1630 3217 y Fk(\032)1677 3240 y Fj(n)1722 3228 y Fl(=)23 b Fk(\015)5 b(\032)1901 3240 y Fj(n)1946 3228 y Fk(=)2002 3160 y Fe(\000)2039 3228 y Fl(\()p Fk(\013)p Fl(\()p Fk(n)19 b Fl(+)f(1)g Fg(\000)g Fk(\033)s Fl(\)\))2565 3193 y Fh(1)p Fi(\000)p Fj(\015)2708 3228 y Fl(\()p Fk(a)2784 3240 y Fj(n)p Fi(\000)p Fj(\033)2921 3228 y Fl(\))2954 3160 y Fe(\001)3006 3228 y Fk(:)150 3442 y Fl(Then)28 b(ev)n(ery)e(solution)h(of)h(Eq.\(1\))f(oscillates.)275 3541 y Fc(Pro)s(of.)36 b Fl(Pro)r(ceeding)25 b(as)i(in)h(Theorem)e (2.1,)h(w)n(e)g(assume)f(that)i(Eq.\(1\))f(has)f(a)h(nonoscillatory)e (solution,)i(sa)n(y)150 3641 y Fk(x)197 3653 y Fj(n)267 3641 y Fk(>)d Fl(0)k(and)g Fk(x)635 3653 y Fj(n)p Fi(\000)p Fj(\033)798 3641 y Fk(>)23 b Fl(0)28 b(for)g(all)g Fk(n)d Fg(\025)e Fk(n)1413 3653 y Fh(0)1451 3641 y Fl(.)39 b(F)-7 b(rom)28 b(the)h(pro)r(of)e(of)i(Theorem)e(2.1)h(w)n(e)g(obtain)g (\(18\))g(for)g(all)g Fk(n)c Fg(\025)g Fk(n)3690 3653 y Fh(2)3727 3641 y Fl(.)150 3741 y(F)-7 b(rom)27 b(\(18\),)g(since)h (\001)p Fk(\032)882 3753 y Fj(n)950 3741 y Fg(\024)23 b Fl(0)p Fk(;)k Fl(w)n(e)g(ha)n(v)n(e)g(for)g Fk(n)c Fg(\025)f Fk(n)1781 3753 y Fh(2)1131 4017 y Fl(\001)p Fk(w)1259 4029 y Fj(n)1328 4017 y Fg(\024)h(\000)p Fk(\032)1524 4029 y Fj(n)1568 4017 y Fk(Q)1634 4029 y Fj(n)1698 4017 y Fl(+)1798 3960 y(\001)p Fk(\032)1910 3972 y Fj(n)p 1791 3997 173 4 v 1791 4074 a Fk(\032)1834 4086 y Fj(n)p Fh(+1)1973 4017 y Fk(w)2032 4029 y Fj(n)p Fh(+1)2180 4017 y Fg(\000)2361 3897 y Fi(\000)2366 3949 y Fk(\032)2413 3972 y Fj(n)p 2273 3997 274 4 v 2273 4087 a Fl(\()p Fk(\032)2348 4099 y Fj(n)p Fh(+1)2477 4087 y Fl(\))2510 4045 y Fh(2)2557 4017 y Fk(w)2618 3982 y Fh(2)2616 4037 y Fj(n)p Fh(+1)2746 4017 y Fk(;)833 b Fl(\(24\))150 4234 y(or)1131 4407 y Fk(\032)1174 4419 y Fj(n)1219 4407 y Fk(Q)1285 4419 y Fj(n)1353 4407 y Fg(\024)23 b(\000)p Fl(\001)p Fk(w)1634 4419 y Fj(n)1698 4407 y Fl(+)1798 4350 y(\001)p Fk(\032)1910 4362 y Fj(n)p 1791 4387 173 4 v 1791 4463 a Fk(\032)1834 4475 y Fj(n)p Fh(+1)1973 4407 y Fk(w)2032 4419 y Fj(n)p Fh(+1)2180 4407 y Fg(\000)2361 4287 y Fi(\000)2366 4339 y Fk(\032)2413 4362 y Fj(n)p 2273 4387 274 4 v 2273 4477 a Fl(\()p Fk(\032)2348 4489 y Fj(n)p Fh(+1)2477 4477 y Fl(\))2510 4435 y Fh(2)2557 4407 y Fk(w)2618 4372 y Fh(2)2616 4427 y Fj(n)p Fh(+1)2746 4407 y Fk(:)833 b Fl(\(25\))150 4613 y(Therefore,)26 b(w)n(e)i(ha)n(v)n(e)317 4781 y Fj(m)p Fi(\000)p Fh(1)329 4805 y Fe(X)306 4980 y Fj(n)p Fh(=)p Fj(n)439 4988 y Fd(2)486 4884 y Fk(H)555 4896 y Fj(m;n)678 4884 y Fk(\032)721 4896 y Fj(n)767 4884 y Fk(Q)833 4896 y Fj(n)900 4884 y Fg(\024)23 b(\000)1077 4781 y Fj(m)p Fi(\000)p Fh(1)1089 4805 y Fe(X)1067 4980 y Fj(n)p Fh(=)p Fj(n)1200 4988 y Fd(2)1246 4884 y Fk(H)1315 4896 y Fj(m;n)1439 4884 y Fl(\001)p Fk(w)1567 4896 y Fj(n)1631 4884 y Fl(+)1725 4781 y Fj(m)p Fi(\000)p Fh(1)1737 4805 y Fe(X)1714 4980 y Fj(n)p Fh(=)p Fj(n)1847 4988 y Fd(2)1893 4884 y Fk(H)1962 4896 y Fj(m;n)2103 4828 y Fl(\001)p Fk(\032)2215 4840 y Fj(n)p 2096 4865 173 4 v 2096 4941 a Fk(\032)2139 4953 y Fj(n)p Fh(+1)2278 4884 y Fk(w)2337 4896 y Fj(n)p Fh(+1)2485 4884 y Fg(\000)2579 4781 y Fj(m)p Fi(\000)p Fh(1)2591 4805 y Fe(X)2568 4980 y Fj(n)p Fh(=)p Fj(n)2701 4988 y Fd(2)2748 4884 y Fk(H)2817 4896 y Fj(m;n)3039 4765 y Fi(\000)3043 4817 y Fk(\032)3091 4840 y Fj(n)p 2950 4865 274 4 v 2950 4954 a Fl(\()q Fk(\032)3026 4966 y Fj(n)p Fh(+1)3155 4954 y Fl(\))3187 4913 y Fh(2)3234 4884 y Fk(w)3295 4850 y Fh(2)3293 4905 y Fj(n)p Fh(+1)3423 4884 y Fk(:)156 b Fl(\(26\))1929 5206 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 150 240 a Fl(whic)n(h)28 b(yields,)f(after)g (summing)h(b)n(y)f(parts,)531 380 y Fj(m)p Fi(\000)p Fh(1)543 405 y Fe(X)520 579 y Fj(n)p Fh(=)p Fj(n)653 587 y Fd(2)700 484 y Fk(H)769 496 y Fj(m;n)893 484 y Fk(\032)936 496 y Fj(n)981 484 y Fk(q)1018 496 y Fj(n)p Fh(+1)373 793 y Fg(\024)82 b Fk(H)589 805 y Fj(m;n)709 813 y Fd(2)746 793 y Fk(w)805 805 y Fj(n)846 813 y Fd(2)901 793 y Fl(+)995 689 y Fj(m)p Fi(\000)p Fh(1)1007 714 y Fe(X)984 888 y Fj(n)p Fh(=)p Fj(n)1117 896 y Fd(2)1163 793 y Fk(w)1222 805 y Fj(n)p Fh(+1)1352 793 y Fl(\001)1421 805 y Fh(2)1459 793 y Fk(H)1528 805 y Fj(m;n)1670 793 y Fl(+)1764 689 y Fj(m)p Fi(\000)p Fh(1)1776 714 y Fe(X)1753 888 y Fj(n)p Fh(=)p Fj(n)1886 896 y Fd(2)1932 793 y Fk(H)2001 805 y Fj(m;n)2142 737 y Fl(\001)p Fk(\032)2254 749 y Fj(n)p 2135 774 173 4 v 2135 850 a Fk(\032)2178 862 y Fj(n)p Fh(+1)2317 793 y Fk(w)2376 805 y Fj(n)p Fh(+1)2524 793 y Fg(\000)2618 689 y Fj(m)p Fi(\000)p Fh(1)2630 714 y Fe(X)2607 888 y Fj(n)p Fh(=)p Fj(n)2740 896 y Fd(2)2787 793 y Fk(H)2856 805 y Fj(m;n)3078 674 y Fi(\000)3082 726 y Fk(\032)3130 749 y Fj(n)p 2989 774 274 4 v 2989 863 a Fl(\()q Fk(\032)3065 875 y Fj(n)p Fh(+1)3194 863 y Fl(\))3226 821 y Fh(2)3273 793 y Fk(w)3334 759 y Fh(2)3332 814 y Fj(n)p Fh(+1)373 1102 y Fl(=)g Fk(H)589 1114 y Fj(m;n)709 1122 y Fd(2)746 1102 y Fk(w)805 1114 y Fj(n)846 1122 y Fd(2)901 1102 y Fg(\000)995 998 y Fj(m)p Fi(\000)p Fh(1)1007 1023 y Fe(X)984 1198 y Fj(n)p Fh(=)p Fj(n)1117 1206 y Fd(2)1163 1102 y Fk(h)1211 1114 y Fj(m;n)1335 1031 y Fe(p)p 1418 1031 193 4 v 71 x Fk(H)1487 1114 y Fj(m;n)1611 1102 y Fk(w)1670 1114 y Fj(n)p Fh(+1)1818 1102 y Fl(+)1912 998 y Fj(m)p Fi(\000)p Fh(1)1924 1023 y Fe(X)1901 1198 y Fj(n)p Fh(=)p Fj(n)2034 1206 y Fd(2)2080 1102 y Fk(H)2149 1114 y Fj(m;n)2291 1046 y Fl(\001)p Fk(\032)2403 1058 y Fj(n)p 2283 1083 173 4 v 2283 1159 a Fk(\032)2326 1171 y Fj(n)p Fh(+1)2465 1102 y Fk(w)2524 1114 y Fj(n)p Fh(+1)2672 1102 y Fg(\000)2766 998 y Fj(m)p Fi(\000)p Fh(1)2778 1023 y Fe(X)2755 1198 y Fj(n)p Fh(=)p Fj(n)2888 1206 y Fd(2)2935 1102 y Fk(H)3004 1114 y Fj(m;n)3226 983 y Fi(\000)3231 1035 y Fk(\032)3278 1058 y Fj(n)p 3138 1083 274 4 v 3138 1172 a Fl(\()p Fk(\032)3213 1184 y Fj(n)p Fh(+1)3342 1172 y Fl(\))3374 1130 y Fh(2)3422 1102 y Fk(w)3483 1068 y Fh(2)3481 1123 y Fj(n)p Fh(+1)373 1304 y Fl(=)g Fk(H)589 1316 y Fj(m;n)709 1324 y Fd(2)746 1304 y Fk(w)805 1316 y Fj(n)846 1324 y Fd(2)520 1563 y Fg(\000)610 1459 y Fj(m)p Fi(\000)p Fh(1)622 1484 y Fe(X)599 1659 y Fj(n)p Fh(=)p Fj(n)732 1667 y Fd(2)778 1396 y Fe(2)778 1546 y(4)843 1385 y(q)p 926 1385 313 4 v 117 x Fk(H)995 1514 y Fj(m;n)1142 1438 y Fi(\000)1147 1491 y Fk(\032)1194 1514 y Fj(n)p 843 1544 396 4 v 955 1620 a Fk(\032)998 1632 y Fj(n)p Fh(+1)1249 1563 y Fk(w)1308 1575 y Fj(n)p Fh(+1)1457 1563 y Fl(+)1682 1507 y Fk(\032)1725 1519 y Fj(n)p Fh(+1)p 1549 1544 438 4 v 1549 1678 a Fl(2)1591 1561 y Fe(q)p 1674 1561 313 4 v 117 x Fk(H)1743 1690 y Fj(m;n)1890 1614 y Fi(\000)1894 1667 y Fk(\032)1942 1690 y Fj(n)2011 1446 y Fe(\022)2072 1563 y Fk(h)2120 1575 y Fj(m;n)2244 1492 y Fe(p)p 2327 1492 193 4 v 71 x Fk(H)2396 1575 y Fj(m;n)2538 1563 y Fg(\000)2638 1507 y Fl(\001)p Fk(\032)2750 1519 y Fj(n)p 2631 1544 173 4 v 2631 1620 a Fk(\032)2674 1632 y Fj(n)p Fh(+1)2813 1563 y Fk(H)2882 1575 y Fj(m;n)3006 1446 y Fe(\023)3067 1396 y(3)3067 1546 y(5)3122 1398 y Fh(2)520 1889 y Fl(+)595 1833 y(1)p 595 1870 42 4 v 595 1946 a(4)660 1786 y Fj(m)p Fi(\000)p Fh(1)672 1811 y Fe(X)668 1989 y Fj(n)p Fh(=)p Fj(k)828 1833 y Fl(\()p Fk(\032)903 1845 y Fj(n)p Fh(+1)1032 1833 y Fl(\))1065 1792 y Fh(2)p 828 1870 274 4 v 916 1925 a Fi(\000)921 1977 y Fk(\032)968 2000 y Fj(n)1126 1772 y Fe(\022)1187 1889 y Fk(h)1235 1901 y Fj(m;n)1377 1889 y Fg(\000)1477 1833 y Fl(\001)p Fk(\032)1589 1845 y Fj(n)p 1470 1870 173 4 v 1470 1946 a Fk(\032)1513 1958 y Fj(n)p Fh(+1)1652 1819 y Fe(p)p 1735 1819 193 4 v 70 x Fk(H)1804 1901 y Fj(m;n)1928 1772 y Fe(\023)1989 1790 y Fh(2)150 2136 y Fl(Then,)584 2206 y Fj(m)p Fi(\000)p Fh(1)596 2231 y Fe(X)574 2406 y Fj(n)p Fh(=)p Fj(n)707 2414 y Fd(2)753 2168 y Fe(")801 2310 y Fk(H)870 2322 y Fj(m;n)994 2310 y Fk(\032)1037 2322 y Fj(n)1082 2310 y Fk(q)1119 2322 y Fj(n)1183 2310 y Fg(\000)1276 2250 y Fk(\032)1319 2220 y Fh(2)1319 2271 y Fj(n)p Fh(+1)p 1276 2291 173 4 v 1297 2367 a Fl(4)8 b(\026)-50 b Fk(\032)1382 2379 y Fj(n)1472 2193 y Fe(\022)1533 2310 y Fk(h)1581 2322 y Fj(m;n)1723 2310 y Fg(\000)1824 2254 y Fl(\001)p Fk(\032)1936 2266 y Fj(n)p 1816 2291 V 1816 2367 a Fk(\032)1859 2379 y Fj(n)p Fh(+1)1998 2239 y Fe(p)p 2081 2239 193 4 v 71 x Fk(H)2150 2322 y Fj(m;n)2274 2193 y Fe(\023)2335 2210 y Fh(2)2372 2168 y Fe(#)2444 2310 y Fk(<)23 b(H)2601 2322 y Fj(m;n)2721 2330 y Fd(2)2757 2310 y Fk(w)2816 2322 y Fj(n)2857 2330 y Fd(2)2917 2310 y Fg(\024)g Fk(H)3074 2322 y Fj(m;)p Fh(0)3189 2310 y Fk(w)3248 2322 y Fj(n)3289 2330 y Fd(2)150 2530 y Fl(whic)n(h)28 b(implies)f(that)446 2671 y Fj(m)p Fi(\000)p Fh(1)458 2696 y Fe(X)455 2872 y Fj(n)p Fh(=0)604 2633 y Fe(")652 2775 y Fk(H)721 2787 y Fj(m;n)845 2775 y Fk(\032)888 2787 y Fj(n)933 2775 y Fk(q)970 2787 y Fj(n)1034 2775 y Fg(\000)1127 2715 y Fk(\032)1170 2685 y Fh(2)1170 2735 y Fj(n)p Fh(+1)p 1127 2756 173 4 v 1148 2832 a Fl(4)8 b(\026)-50 b Fk(\032)1233 2844 y Fj(n)1323 2658 y Fe(\022)1384 2775 y Fk(h)1432 2787 y Fj(m;n)1574 2775 y Fg(\000)1674 2719 y Fl(\001)p Fk(\032)1786 2731 y Fj(n)p 1667 2756 V 1667 2832 a Fk(\032)1710 2844 y Fj(n)p Fh(+1)1849 2704 y Fe(p)p 1932 2704 193 4 v 71 x Fk(H)2001 2787 y Fj(m;n)2125 2658 y Fe(\023)2186 2675 y Fh(2)2223 2633 y Fe(#)2295 2775 y Fk(<)22 b(H)2451 2787 y Fj(m;)p Fh(0)2581 2670 y Fj(n)2622 2678 y Fd(2)2654 2670 y Fi(\000)p Fh(1)2600 2696 y Fe(X)2598 2872 y Fj(n)p Fh(=0)2753 2775 y Fk(\032)2796 2787 y Fj(n)2841 2775 y Fk(q)2878 2787 y Fj(n)p Fh(+1)3026 2775 y Fl(+)c Fk(H)3178 2787 y Fj(m;)p Fh(0)3294 2775 y Fk(w)3353 2787 y Fj(n)3394 2795 y Fd(2)3431 2775 y Fk(:)150 3015 y Fl(Hence)685 3173 y(lim)c(sup)717 3239 y Fj(m)p Fi(!1)1035 3116 y Fl(1)p 963 3154 185 4 v 963 3230 a Fk(H)1032 3242 y Fj(m;)p Fh(0)1172 3069 y Fj(m)p Fi(\000)p Fh(1)1184 3094 y Fe(X)1181 3270 y Fj(n)p Fh(=0)1330 3031 y Fe(")1378 3173 y Fk(H)1447 3185 y Fj(m;n)1571 3173 y Fk(\032)1614 3185 y Fj(n)1659 3173 y Fk(q)1696 3185 y Fj(n)1760 3173 y Fg(\000)1853 3113 y Fk(\032)1896 3083 y Fh(2)1896 3133 y Fj(n)p Fh(+1)p 1853 3154 173 4 v 1874 3230 a Fl(4)8 b(\026)-50 b Fk(\032)1959 3242 y Fj(n)2049 3056 y Fe(\022)2110 3173 y Fk(h)2158 3185 y Fj(m;n)2300 3173 y Fg(\000)2400 3116 y Fl(\001)p Fk(\032)2512 3128 y Fj(n)p 2393 3154 V 2393 3230 a Fk(\032)2436 3242 y Fj(n)p Fh(+1)2575 3102 y Fe(p)p 2658 3102 193 4 v 71 x Fk(H)2727 3185 y Fj(m;n)2851 3056 y Fe(\023)2912 3073 y Fh(2)2949 3031 y Fe(#)3021 3173 y Fk(<)22 b Fg(1)p Fk(;)150 3390 y Fl(whic)n(h)28 b(is)f(con)n(trary)f(to)h(\(23\).)37 b(The)27 b(pro)r(of)g(is)h(complete.)275 3590 y(By)40 b(c)n(ho)r(osing)f(the)i(sequence)f Fg(f)p Fk(H)1392 3602 y Fj(m;n)1516 3590 y Fg(g)g Fl(in)h(appropriate)e(manners,)k(w)n (e)d(can)h(deriv)n(e)e(sev)n(eral)g(oscillation)150 3689 y(criteria)26 b(for)h(\(1.1\).)37 b(F)-7 b(or)27 b(instance,)g(let)h (us)g(consider)f(the)g(double)h(sequence)f Fg(f)p Fk(H)2705 3701 y Fj(m;n)2828 3689 y Fg(g)h Fl(de\014ned)g(b)n(y)1621 3859 y Fk(H)1690 3871 y Fj(m;n)1836 3859 y Fl(=)23 b(\()p Fk(m)c Fg(\000)f Fk(n)p Fl(\))2213 3824 y Fj(\025)2256 3859 y Fk(;)150 4028 y Fl(or)1457 4177 y Fk(H)1526 4189 y Fj(m;n)1673 4177 y Fl(=)1761 4059 y Fe(\022)1822 4177 y Fl(log)1943 4059 y Fe(\022)2014 4120 y Fk(m)g Fl(+)h(1)p 2014 4157 216 4 v 2026 4233 a Fk(n)f Fl(+)g(1)2240 4059 y Fe(\023\023)2362 4077 y Fj(\025)2420 4177 y Fk(;)150 4363 y Fl(where)45 b Fk(\025)23 b Fg(\025)g Fl(1)p Fk(;)f(m)h Fg(\025)g Fk(n)f Fg(\025)h Fl(0.)35 b(Then)23 b Fk(H)1379 4375 y Fj(m;m)1543 4363 y Fl(=)g(0)f(for)g Fk(m)h Fg(\025)g Fl(0)f(and)g Fk(H)2290 4375 y Fj(m;n)2437 4363 y Fk(>)h Fl(0)f(and)g(\001)2814 4375 y Fh(2)2852 4363 y Fk(H)2921 4375 y Fj(m;n)3068 4363 y Fg(\024)g Fl(0)g(for)g Fk(m)h(>)g(n)g(>)f Fl(0)p Fk(:)150 4463 y Fl(Hence)28 b(w)n(e)f(ha)n(v)n(e)f(the)i(follo)n (wing)f(results.)275 4562 y Fc(Corollary)g(2.2.)34 b Fl(Assume)23 b(that)h(all)f(the)h(assumptions)f(of)g(Theorem)g(2.2)f (hold,)j(except)e(the)h(condition)f(\(23\))150 4662 y(is)k(replaced)g (b)n(y)450 4893 y(lim)412 4943 y Fj(m)p Fi(!1)617 4893 y Fl(sup)803 4837 y(1)p 766 4874 117 4 v 766 4950 a Fk(m)839 4926 y Fj(\025)939 4790 y(m)908 4815 y Fe(X)906 4990 y Fj(n)p Fh(=0)1045 4776 y Fe(\024)1089 4893 y Fl(\()p Fk(m)18 b Fg(\000)g Fk(n)p Fl(\))1377 4859 y Fj(\025)1421 4893 y Fk(\032)1464 4905 y Fj(n)1509 4893 y Fk(Q)1575 4905 y Fj(n)1638 4893 y Fg(\000)1731 4834 y Fk(\032)1774 4803 y Fh(2)1774 4854 y Fj(n)p Fh(+1)p 1731 4874 173 4 v 1753 4950 a Fl(4)p 1795 4905 43 4 v Fk(\032)1837 4971 y Fj(n)1927 4776 y Fe(\022)1988 4893 y Fk(\025)p Fl(\()p Fk(m)h Fg(\000)f Fk(n)p Fl(\))2335 4833 y Fo(\025)p Fa(\000)p Fd(2)p 2336 4846 109 3 v 2375 4879 a(2)2476 4893 y Fg(\000)2577 4837 y Fl(\001)p Fk(\032)2689 4849 y Fj(n)p 2569 4874 173 4 v 2569 4950 a Fk(\032)2612 4962 y Fj(n)p Fh(+1)2751 4792 y Fe(q)p 2834 4792 333 4 v 101 x Fl(\()p Fk(m)h Fg(\000)f Fk(n)p Fl(\))3123 4869 y Fj(\025)3167 4776 y Fe(\023\025)3295 4893 y Fl(=)k Fg(1)p Fk(:)1929 5206 y Fl(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 150 240 a Fl(where)27 b Fk(Q)456 252 y Fj(n)524 240 y Fl(=)c Fk(q)649 252 y Fj(n)694 240 y Fl(\(1)18 b Fg(\000)g Fk(p)911 252 y Fj(n)p Fi(\000)p Fj(\033)1049 240 y Fl(\))1081 210 y Fj(\015)1123 240 y Fl(.)37 b(Then)28 b(ev)n(ery)e(solution)i(of)f(Eq.\(1\))g (oscillates.)275 340 y Fc(Corollary)g(2.3.)34 b Fl(Assume)23 b(that)h(all)f(the)h(assumptions)f(of)g(Theorem)g(2.2)f(hold,)j(except) e(the)h(condition)f(\(23\))150 439 y(is)k(replaced)g(b)n(y)656 692 y(lim)618 742 y Fj(m)p Fi(!1)823 692 y Fl(sup)1199 636 y(1)p 972 673 496 4 v 972 765 a(\(log\()p Fk(m)19 b Fl(+)f(1\)\))1424 723 y Fj(\025)1525 588 y(m)1494 613 y Fe(X)1491 789 y Fj(n)p Fh(=0)1630 550 y Fe(")1679 575 y(\022)1740 692 y Fl(log)1861 575 y Fe(\022)1932 636 y Fk(m)g Fl(+)g(1)p 1932 673 216 4 v 1944 749 a Fk(n)g Fl(+)g(1)2158 575 y Fe(\023\023)2280 592 y Fj(\025)2338 692 y Fk(\032)2381 704 y Fj(n)2426 692 y Fk(Q)2492 704 y Fj(n)2555 692 y Fg(\000)2648 632 y Fk(\032)2691 602 y Fh(2)2691 653 y Fj(n)p Fh(+1)p 2648 673 173 4 v 2669 749 a Fl(4)p 2711 703 43 4 v Fk(\032)2754 769 y Fj(n)2830 692 y Fk(B)2893 704 y Fj(m;n)3017 550 y Fe(#)3088 692 y Fl(=)23 b Fg(1)p Fk(:)150 946 y Fl(where)879 1142 y Fk(B)942 1154 y Fj(m;n)1089 1142 y Fl(=)1177 975 y Fe(0)1177 1124 y(@)1332 1086 y Fk(\025)p 1260 1123 193 4 v 1260 1199 a(n)18 b Fl(+)g(1)1476 1025 y Fe(\022)1537 1142 y Fl(ln)1630 1086 y Fk(m)h Fl(+)f(1)p 1630 1123 216 4 v 1642 1199 a Fk(n)g Fl(+)g(1)1856 1025 y Fe(\023)1927 1016 y Fo(\025)p Fa(\000)p Fd(2)p 1927 1029 109 3 v 1967 1062 a(2)2068 1142 y Fg(\000)2168 1086 y Fl(\001)p Fk(\032)2280 1098 y Fj(n)p 2161 1123 173 4 v 2161 1199 a Fk(\032)2204 1211 y Fj(n)p Fh(+1)2343 982 y Fe(s)p 2426 982 485 4 v 43 x(\022)2487 1142 y Fl(ln)2580 1086 y Fk(m)g Fl(+)g(1)p 2580 1123 216 4 v 2592 1199 a Fk(n)g Fl(+)g(1)2806 1025 y Fe(\023)2867 1042 y Fj(\025)2911 975 y Fe(1)2911 1124 y(A)2983 992 y Fh(2)150 1391 y Fl(Then)28 b(ev)n(ery)e(solution)h(of)h (Eq.\(1\))f(oscillates.)275 1590 y(Another)g Fk(H)669 1602 y Fj(m;n)820 1590 y Fl(ma)n(y)g(b)r(e)h(c)n(hosen)f(as)1395 1773 y Fk(H)1464 1785 y Fj(m;n)1611 1773 y Fl(=)22 b Fk(\036)p Fl(\()p Fk(m)d Fg(\000)f Fk(n)p Fl(\))p Fk(;)38 b(m)22 b Fg(\025)h Fk(n)g Fg(\025)g Fl(0)p Fk(;)1235 1966 y(H)1304 1978 y Fj(m;n)1450 1966 y Fl(=)g(\()p Fk(m)c Fg(\000)f Fk(n)p Fl(\))1827 1932 y Fh(\()p Fj(\025)p Fh(\))1992 1966 y Fk(\025)23 b(>)g Fl(2)p Fk(;)41 b(m)23 b Fg(\025)f Fk(n)h Fg(\025)g Fl(0)p Fk(:)150 2115 y Fl(where)36 b Fk(\036)j Fl(:)f([0)p Fk(;)14 b Fg(1)p Fl(\))37 b Fg(!)i Fl([0)p Fk(;)14 b Fg(1)p Fl(\))36 b(is)g(a)h(con)n(tin)n(uously)e (di\013eren)n(tiable)h(function)i(whic)n(h)e(satis\014es)g Fk(\036)p Fl(\(0\))i(=)g(0)e(and)150 2215 y Fk(\036)p Fl(\()p Fk(u)p Fl(\))24 b Fk(>)e Fl(0)p Fk(;)28 b(\036)564 2185 y Fi(0)587 2215 y Fl(\()p Fk(u)p Fl(\))23 b Fg(\025)g Fl(0)k(for)g Fk(u)c(>)g Fl(0)p Fk(;)k Fl(and)g(\()p Fk(m)19 b Fg(\000)f Fk(n)p Fl(\))1707 2185 y Fh(\()p Fj(\025)p Fh(\))1825 2215 y Fl(=)23 b(\()p Fk(m)c Fg(\000)f Fk(n)p Fl(\)\()p Fk(m)h Fg(\000)f Fk(n)g Fl(+)g(1\))p Fk(:::)p Fl(\()p Fk(m)g Fg(\000)g Fk(n)h Fl(+)f Fk(\025)h Fg(\000)f Fl(1\))27 b(and)796 2397 y(\001)865 2409 y Fh(2)903 2397 y Fl(\()p Fk(m)19 b Fg(\000)f Fk(n)p Fl(\))1192 2363 y Fh(\()p Fj(\025)p Fh(\))1310 2397 y Fl(=)23 b(\()p Fk(m)18 b Fg(\000)g Fk(n)h Fg(\000)f Fl(1\))1830 2363 y Fh(\()p Fj(\025)p Fh(\))1943 2397 y Fg(\000)g Fl(\()p Fk(m)h Fg(\000)f Fk(n)p Fl(\))2315 2363 y Fh(\()p Fj(\025)p Fh(\))2434 2397 y Fl(=)k Fg(\000)p Fk(\025)p Fl(\()p Fk(m)d Fg(\000)f Fk(n)p Fl(\))2923 2363 y Fh(\()p Fj(\025)p Fi(\000)p Fh(1\))150 2580 y Fl(Corresp)r(onding)26 b(corollaries)f(can) i(also)f(b)r(e)i(stated.)150 2855 y Fm(References)192 3037 y Fl([1])41 b(R.)27 b(P)-7 b(.)27 b(Agarw)n(al,)f(Di\013erence)h (Equations)g(and)g(Inequalities,)g(Theory)-7 b(,)26 b(Metho)r(ds)i(and) f(Applications,)g(Sec-)321 3136 y(ond)g(Edition,)g(Revised)h(and)f (Expanded,)g(Marcel)g(Dekk)n(er,)g(New)g(Y)-7 b(ork,)27 b(2000.)192 3302 y([2])41 b(R.)26 b(P)-7 b(.)26 b(Agarw)n(al)e(and)i(P) -7 b(.)26 b(J.)g(Y.)g(W)-7 b(ong,)27 b(Adv)-5 b(anced)26 b(T)-7 b(opics)25 b(in)i(Di\013erence)f(Equations,)f(Klu)n(w)n(er)g (Academic)321 3402 y(Publishers,)h(1997.)192 3568 y([3])41 b(R.)30 b(P)-7 b(.)30 b(Agarw)n(al,)f(M.)h(M.)g(S.)h(Man)n(uel)f(and)g (E.)f(Thandapani,)h(Oscillatory)f(and)h(nonoscillatory)d(b)r(eha)n (vior)321 3668 y(of)f(second-order)e(neutral)i(dela)n(y)f(di\013erence) i(equations,)e(Mathl.)i(Comput.)g(Mo)r(delling,)f(24)f(\(1996\),)h (5-11.)192 3834 y([4])41 b(R.)30 b(P)-7 b(.)30 b(Agarw)n(al,)f(M.)h(M.) g(S.)h(Man)n(uel)f(and)g(E.)f(Thandapani,)h(Oscillatory)f(and)h (nonoscillatory)d(b)r(eha)n(vior)321 3933 y(of)g(second-order)e (neutral)j(dela)n(y)e(di\013erence)i(equations)f(I)r(I,)h(Appl.)g (Math.)g(Lett.,)g(10)f(\(1997\),)f(103-109.)192 4099 y([5])41 b(G.)24 b(H.)g(Hardy)-7 b(,)24 b(J.)f(E.)g(Littlew)n(o)r(o)r (d)h(and)g(G.)g(P)n(oly)n(a,)e(Inequalities,)i(2nd)g(Ed.)f(Cam)n (bridge)g(Univ.)h(Press)e(1952.)192 4265 y([6])41 b(H.)31 b(F.)h(Huo)g(and)f(W.)h(T.)f(Li,)i(Oscillation)d(of)h(the)h(Emden-F)-7 b(o)n(wler)30 b(di\013erence)h(systems,)h(J.)f(Math.)h(Anal.)321 4365 y(Appl.,)c(256\(2001\),)d(478-485.)192 4531 y([7])41 b(J.)27 b(C.)g(Jiang,)g(Oscillatory)f(criteria)g(for)h(second-order)e (quasilinear)h(neutral)h(dela)n(y)f(di\013erence)i(equations,)321 4631 y(Appl.)g(Math.)g(Comp.,)f(125)g(\(2002\),)f(287-293.)192 4797 y([8])41 b(B.)34 b(S.)h(Lalli)f(and)g(B.)g(G.)h(Zhang,)g(On)f (existence)h(of)f(p)r(ositiv)n(e)g(solutions)g(and)g(b)r(ounded)h (oscillations)e(for)321 4896 y(neutral)27 b(di\013erence)g(equations,)g (J.)h(Math.)f(Anal.)h(Appl.,)g(166)f(\(1992\),)f(272-287.)1929 5206 y(7)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 192 240 a Fl([9])41 b(W.)26 b(T.)f(Li,)i (Oscillation)d(theorems)h(for)g(second)g(order)f(nonlinear)h (di\013erence)h(equations,)f(Math.)h(Comput.)321 340 y(Mo)r(delling,)h(31\(7\)\(2000\),)f(71-79.)150 506 y([10])41 b(W.)20 b(T.)g(Li)f(and)h(S.)g(S.)g(Cheng,)h(Classi\014cations)d (existence)i(of)g(p)r(ositiv)n(e)f(solutions)g(of)h(second)f(order)f (nonlinear)321 606 y(neutral)27 b(di\013erence)g(equations)g(F)-7 b(unk.)28 b(Ev)-5 b(ac.,)27 b(40)g(\(1997\),)f(371-393.)150 772 y([11])41 b(W.)23 b(T.)g(Li)g(and)f(S.)h(S.)h(Cheng,)f (Asymptotically)g(linear)f(solutions)g(of)h(a)f(discrete)g(Emden-F)-7 b(o)n(wler)22 b(equation,)321 871 y(F)-7 b(ar)27 b(East)f(J.)i(Math.)g (Sci.,)f(6\(4\)\(1998\),)f(521-542.)150 1037 y([12])41 b(W.)34 b(T.)g(Li)g(and)f(S.)h(S.)g(Cheng,)i(Characterzing)31 b(conditions)j(for)f(the)h(existence)g(of)f(nonoscillatory)f(solu-)321 1137 y(tions)e(of)h(a)g(discrete)f(Emden-F)-7 b(o)n(wler)30 b(equation)g(with)h(summable)g(co)r(e\016cien)n(ts,)g(Dynamic)g (Systems)g(and)321 1236 y(Applications,)c(9\(2000\),)f(457-461.)150 1403 y([13])41 b(W.)20 b(T.)g(Li,)h(X.)f(L.)g(F)-7 b(an)20 b(and)f(C.)h(K.)g(Zhong,)g(On)g(un)n(b)r(ounded)g(p)r(ositiv)n(e)f (solutions)g(of)h(second)f(order)f(di\013erence)321 1502 y(equations)26 b(with)j(singular)d(nonlinear)g(term,)i(J.)f(Math.)h (Anal.)g(Appl.,)g(246\(2000\),)d(80-88.)150 1668 y([14])41 b(W.)34 b(T.)g(Li,)h(X.)f(L.)g(F)-7 b(an)33 b(and)h(C.)g(K.)f(Zhong,)i (P)n(ositiv)n(e)d(solutions)h(of)g(discrete)g(Emden-F)-7 b(o)n(wler)33 b(equation)321 1768 y(with)28 b(singular)e(nonlinear)h (term,)g(Dynamic)h(Systems)f(and)h(Applications,)f(9\(2000\),)f (247-254.)150 1934 y([15])41 b(Z.)23 b(Szafranski)g(and)h(B.)f (Szmanda,)i(Oscillation)d(of)i(some)g(di\013erence)f(equations,)h(F)-7 b(asc.)24 b(Math.,)g(28)f(\(1998\),)321 2033 y(149-155.)150 2200 y([16])41 b(Z.)33 b(Szafranski)g(and)h(B.)g(Szmanda,)h (Oscillation)e(theorems)g(for)h(some)f(nonlinear)g(di\013erence)h (equations,)321 2299 y(Appl.)28 b(Math.)g(Comp.,)f(83)g(\(1997\),)f (43-52.)150 2465 y([17])41 b(B.)23 b(G.)h(Zhang)e(and)i(G.)g(D.)g (Chen,)g(Oscillation)f(of)g(certain)g(second)g(order)f(nonlinear)g (di\013erence)i(equations,)321 2565 y(J.)j(Math.)h(Anal.)g(Appl.,)g (199\(1996\),)d(827-841.)150 2731 y([18])41 b(Z.)28 b(Zhang,)g(J.)h (Chen)g(and)f(C.)h(Zhang,)f(Oscillation)g(of)g(solutions)g(for)g (second-order)e(nonlinear)i(di\013erence)321 2830 y(equations)e(with)j (nonlinear)d(neutral)h(term,)h(Comp.)f(Math.)h(Appl.,)h(41)d(\(2001\),) h(1487-1494.)1929 5206 y(8)p eop end %%Trailer userdict /end-hook 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