Content-Type: multipart/mixed; boundary="-------------0501171001136" This is a multi-part message in MIME format. ---------------0501171001136 Content-Type: text/plain; name="05-22.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-22.keywords" Absolutely continuous spectrum, multidimensional Schrodinger operator, Caley tree, Bethe lattice, step-by-step sum rules ---------------0501171001136 Content-Type: application/postscript; name="scattering.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="scattering.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: scattering.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX12 CMR10 CMCSC10 CMR12 CMTI12 CMMI12 CMSY10 MSBM10 %%+ CMMI8 CMEX10 CMMI6 CMR8 CMSY8 CMTI10 CMR9 MSAM10 CMR6 CMMI10 CMR7 %%+ CMTT10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o scattering.ps scattering.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.01.17:1044 %%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 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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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 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 76 /L put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 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 48 /zero put dup 49 /one put dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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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 /UniqueID 5031981 def currentdict end currentfile eexec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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 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 52 /four put dup 53 /five put dup 56 /eight put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 73 /I put dup 74 /J put dup 75 /K put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A30EB76029337 900ECFB1390CA5C0C3A04528044F266BA17BE487C79B94FAC6D6484684C5BFEA 87BCCC77D40AD11552035E95E3007126418ED49B68468B38A14E88E68A267B98 076F1C9769A5AFBC285E5B158EAC9F926F1D6C0B8F1D57D9C31D25AE27123518 9D2CD92E5689E0213089BD268DA5E47525CB8EABAA4B78A15AEA34705889AB3A FFB8953B5B3482E52BFA0940630ADF8C0AC2177D907324299EE980E850F203CD B627962F43D5A678C44243CDE97853BDC6AB45FD5C09AD274DAF89929F583CC9 CCC24BDFC68B92111055ABA5F26D2DC67C70906F71C2957701D65AE746A60C30 40E6CB24B97FCDAD0487AE38A201FBF0E41BABD2181981A71940F1E707F91E5D C8CA50CB16D8702D188E56D014D92F76CE0B52ABDB9110E32438D2BBF3E6A40B 7B005F10BB437812CAC6ED2996F7606DC962C4FDE207FF322782C343DF44CEC5 FF06A55C630C20E9AE1B0D1C5673753C43BA0767D65D1B451CC6380D8BB3C4DC 81E8FD8AA79BE993218686F29D3CD925566DD587F541A0DA1B1CC3BCEA2E6C7D 5E1016F6917A871F1BBAD96AF9E867735017119A381FCF33EB2D3E1E7093FD90 CDB0CED4818CFD9E201A03430CEC713620BE0D3254158931FB657C6AD4B2482A 0E7D070D7497892E9E942DF58E88CAF0C8221BF36BF7C435BF2C683A4A2EF4CB E85820A8AD3486155A40143011BA9D76297F46DEF69ECA4596D6E4CAABF84091 22A96A4BC78A8DD072FEB759A68A44BE1164638B6D952147EE3C628F9A022060 1D1941E73310943FA782532ABCCC88593FD63E7E2CECF6665C04DB48D641ABD3 AE1BB468638681E96394B9E7BED1D13E534B897DB90EA6EC706BAAE06BE2FEFF 1DFA5258113E9B4CD2D36655973864574E0E8D6291E48A8C62203F679B7ED838 6F7CBD523C2943ECA994CACE6677D0DEC2FFC19442354627BF9EB0A475766A48 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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. 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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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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 20 /lessequal put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 106 /bar put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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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 1 /Delta put dup 10 /Omega 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 52 /four put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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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 100 /d put dup 106 /j put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 40 /braceleftBigg put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 101 /tildewide put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 114 /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: 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 13 /gamma put dup 15 /epsilon1 put dup 18 /theta put dup 25 /pi put dup 59 /comma put dup 79 /O 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 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 112 /p put dup 115 /s put dup 116 /t put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 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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. 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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. 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 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 27 /sigma 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 66 /B put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 75 /K put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 96 /lscript 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 112 /p 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 /UniqueID 5087386 def currentdict end currentfile eexec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26EEEFBE97AFBFE470816445C94DE41A8EFD8C93 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 13 /fl put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 72 /H put dup 73 /I put dup 76 /L put dup 80 /P put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put readonly def 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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. 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 1 /Delta put dup 5 /Pi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl 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 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 78 /N put dup 79 /O 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 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 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 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 14 /ffi put dup 20 /caron put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright 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 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z 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 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 123 /endash put dup 125 /hungarumlaut put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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%%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 46 /period put dup 49 /one put dup 50 /two 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 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 101 /e put dup 104 /h 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 114 /r put dup 116 /t put dup 117 /u put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def 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2601 3359 147 4 v 2629 3450 a Fr(p)2678 3465 y Fo(k)2780 3382 y Fq(\001)2864 3314 y Fr(p)2913 3329 y Fo(k)2978 3314 y Fq(\000)22 b Fr(z)p 2840 3359 312 4 v 2840 3450 a Ft(1)g Fq(\000)g Fr(p)3059 3465 y Fo(k)3102 3450 y Fr(z)337 3621 y Ft(Let)33 b(us)h(divide)f(b)s(oth)g (sides)h(of)e(\(2.5\))g(b)m(y)i Fr(z)t Ft(,)f(tak)m(e)g(ln)q(,)f(and)h (expand)h(in)m(to)f(the)g(T)-8 b(a)m(ylor)33 b(series)337 3737 y(around)g(0.)43 b(W)-8 b(e)33 b(ha)m(v)m(e)555 4056 y Fr(f)11 b Ft(\()p Fr(z)t Ft(\))28 b(=)922 3989 y(1)p 880 4033 132 4 v 880 4053 a Fq(p)p 964 4053 49 4 v 964 4136 a Ft(2)1136 3989 y Fr(z)p 1032 4033 259 4 v 1032 4125 a(z)1081 4096 y Fk(2)1144 4125 y Ft(+)22 b(1)1322 4056 y(+)1430 3989 y Fr(V)g Ft(\()p Fr(O)s Ft(\))p 1430 4033 232 4 v 1522 4125 a(2)1694 4056 y Fq(\001)1896 3989 y Fr(z)1945 3953 y Fk(2)p 1754 4033 374 4 v 1754 4125 a Ft(\()p Fr(z)1841 4096 y Fk(2)1903 4125 y Ft(+)g(1\))2088 4096 y Fk(2)2159 4056 y Ft(+)2267 3989 y(2)g(+)g Fr(V)2515 3953 y Fk(2)2554 3989 y Ft(\()p 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4623 y Ft(1)p 1658 4668 49 4 v 1658 4759 a(2)1734 4691 y(ln)17 b(2)22 b(+)2011 4623 y Fr(V)g Ft(\()p Fr(O)s Ft(\))p 2011 4668 232 4 v 2061 4688 a Fq(p)p 2144 4688 49 4 v 82 x Ft(2)2253 4691 y Fr(z)27 b Ft(+)2433 4623 y Fr(V)2511 4587 y Fk(2)2551 4623 y Ft(\()p Fr(O)s Ft(\))p 2433 4668 272 4 v 2544 4759 a(4)2714 4691 y Fr(z)2763 4650 y Fk(2)2825 4691 y Ft(+)22 b Fr(:)17 b(:)g(:)f Ft(;)659 5019 y(1)p 629 5063 108 4 v 629 5155 a(2)p Fr(\031)814 4931 y Fo(\031)764 4951 y Fn(Z)742 5232 y Fj(\000)p Fo(\031)891 5019 y Fr(t)22 b Ft(+)g Fr(z)p 890 5063 207 4 v 890 5155 a(t)g Fq(\000)h Fr(z)1123 5086 y Ft(ln)17 b Fq(j)p Fr(f)11 b Ft(\()p Fr(t)p Ft(\))p Fq(j)p Fr(d\022)30 b Ft(=)1716 5019 y(1)p 1686 5063 108 4 v 1686 5155 a(2)p Fr(\031)1871 4931 y Fo(\031)1820 4951 y Fn(Z)1799 5232 y Fj(\000)p Fo(\031)1937 5086 y Ft(ln)17 b Fq(j)p Fr(f)11 b Ft(\()p Fr(t)p Ft(\))p Fq(j)p Ft(\(1)21 b(+)h(2)p Fr(z)t(t)2600 5045 y Fj(\000)p Fk(1)2717 5086 y Ft(+)g(2)p Fr(z)2913 5045 y Fk(2)2953 5086 y Fr(t)2988 5045 y Fj(\000)p Fk(2)3104 5086 y Ft(+)g Fr(:)17 b(:)g(:)p Ft(\))p Fr(d\022)s Ft(;)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 236 251 a Fh(8)1273 b(SER)n(GEY)25 b(A.)h(DENISO)n(V)805 627 y Ft(ln)903 516 y Fn(\020)997 559 y Fr(z)1046 518 y Fk(+)1042 587 y Fo(k)1128 559 y Fq(\000)c Fr(z)p 972 604 330 4 v 972 697 a Ft(1)g Fq(\000)h Fr(z)1192 656 y Fk(+)1188 725 y Fo(k)1252 697 y Fr(z)1311 516 y Fn(\021)1398 627 y Ft(=)28 b(ln[\()p Fr(z)1697 585 y Fk(+)1693 654 y Fo(k)1779 627 y Fq(\000)23 b Fr(z)t Ft(\)\(1)f(+)g Fr(z)2222 585 y Fk(+)2218 654 y Fo(k)2282 627 y Fr(z)27 b Ft(+)22 b Fr(z)2501 585 y Fk(+)2497 654 y Fo(k)2561 572 y Fk(2)2600 627 y Fr(z)2649 585 y Fk(2)2712 627 y Ft(+)g Fr(:)17 b(:)g(:)o Ft(\)])28 b(=)845 890 y(=)f(ln)17 b Fr(z)1095 849 y Fk(+)1091 918 y Fo(k)1177 890 y Ft(+)22 b Fr(z)t Ft(\()p Fr(z)1411 849 y Fk(+)1407 918 y Fo(k)1494 890 y Fq(\000)g Fr(z)1642 849 y Fk(+)1638 918 y Fo(k)1702 835 y Fj(\000)p Fk(1)1797 890 y Ft(\))g(+)g Fr(z)2004 849 y Fk(2)2044 890 y Ft(\()p Fr(z)2131 849 y Fk(+)2127 918 y Fo(k)2191 835 y Fk(2)2252 890 y Fq(\000)h Fr(z)2401 849 y Fk(+)2397 918 y Fo(k)2461 835 y Fj(\000)p Fk(2)2555 890 y Ft(\))p Fr(=)p Ft(2)f(+)g Fr(O)s Ft(\()p Fr(z)2976 849 y Fk(3)3015 890 y Ft(\))236 1046 y(Comparing)33 b(the)g(\014rst)g(and)g(the)g(third)g(co)s(e\016cien)m(ts,)i(w)m(e)e (obtain)236 1328 y(\(2.6\))426 b Fq(\000)950 1261 y Ft(1)p 950 1305 49 4 v 950 1396 a(2)1026 1328 y(ln)16 b(2)28 b(=)1343 1261 y(1)p 1313 1305 108 4 v 1313 1396 a(2)p Fr(\031)1498 1173 y Fo(\031)1448 1192 y Fn(Z)1426 1474 y Fj(\000)p Fo(\031)1564 1328 y Ft(ln)17 b Fq(j)p Fr(f)11 b Ft(\()p Fr(t)p Ft(\))p Fq(j)p Fr(d\022)24 b Ft(+)2106 1233 y Fn(X)2159 1446 y Fo(k)2266 1328 y Ft(ln)17 b Fq(j)p Fr(z)2437 1343 y Fo(k)2480 1328 y Fq(j)22 b(\000)2629 1233 y Fn(X)2682 1446 y Fo(k)2790 1328 y Ft(ln)17 b Fq(j)p Fr(p)2965 1343 y Fo(k)3007 1328 y Fq(j)236 1628 y Ft(and)236 1891 y(\(2.7\))619 1823 y Fr(V)698 1787 y Fk(2)737 1823 y Ft(\()p Fr(O)s Ft(\))p 619 1868 272 4 v 730 1959 a(4)928 1891 y(=)1046 1823 y(1)p 1041 1868 59 4 v 1041 1959 a Fr(\031)1177 1735 y Fo(\031)1127 1755 y Fn(Z)1106 2036 y Fj(\000)p Fo(\031)1243 1891 y Ft(ln)g Fq(j)p Fr(f)11 b Ft(\()p Fr(t)p Ft(\))p Fq(j)p Fr(t)1602 1849 y Fj(\000)p Fk(2)1696 1891 y Fr(d\022)25 b Ft(+)1915 1796 y Fn(X)1967 2008 y Fo(k)2085 1823 y Fq(j)p Fr(z)2158 1838 y Fo(k)2201 1823 y Fq(j)2229 1787 y Fk(2)2290 1823 y Fq(\000)e(j)p Fr(z)2463 1838 y Fo(k)2505 1823 y Fq(j)2533 1787 y Fj(\000)p Fk(2)p 2085 1868 543 4 v 2332 1959 a Ft(2)2659 1891 y Fq(\000)2759 1796 y Fn(X)2812 2008 y Fo(k)2930 1823 y Fq(j)p Fr(p)3007 1838 y Fo(k)3049 1823 y Fq(j)3077 1787 y Fk(2)3138 1823 y Fq(\000)g(j)p Fr(p)3315 1838 y Fo(k)3357 1823 y Fq(j)3385 1787 y Fj(\000)p Fk(2)p 2930 1868 550 4 v 3180 1959 a Ft(2)236 2196 y(T)-8 b(ak)m(e)34 b(\(2.6\)-1)p Fr(=)p Ft(2)17 b Fq(\001)30 b Ft(\(2.7\).)43 b(W)-8 b(e)33 b(then)g(ha)m(v)m(e)367 2575 y Fq(\000)454 2508 y Ft(1)p 454 2552 49 4 v 454 2643 a(2)530 2575 y(ln)17 b(2)k Fq(\000)808 2508 y Fr(V)887 2471 y Fk(2)926 2508 y Ft(\()p Fr(O)s Ft(\))p 808 2552 272 4 v 919 2643 a(8)1117 2575 y(=)1260 2508 y(1)p 1230 2552 108 4 v 1230 2643 a(2)p Fr(\031)1415 2419 y Fo(\031)1365 2439 y Fn(Z)1343 2720 y Fj(\000)p Fo(\031)1481 2575 y Ft(ln)c Fq(j)p Fr(f)11 b Ft(\()p Fr(t)p Ft(\))p Fq(j)p Ft(\(1)21 b Fq(\000)h Fr(t)2047 2534 y Fj(\000)p Fk(2)2142 2575 y Ft(\))p Fr(d\022)j Fq(\000)2400 2464 y Fn(n)2483 2480 y(X)2536 2692 y Fo(k)2644 2575 y Fr(Y)c Ft(\()2780 2550 y Fn(e)2760 2575 y Fr(E)2832 2590 y Fo(k)2875 2575 y Ft(\))h Fq(\000)3035 2480 y Fn(X)3087 2692 y Fo(k)3195 2575 y Fr(Y)g Ft(\()p Fr(E)3384 2590 y Fo(k)3426 2575 y Ft(\))3464 2464 y Fn(o)236 2875 y Ft(where)318 3206 y Fr(Y)f Ft(\()p Fq(\000)p Fr(E)6 b Ft(\))28 b(=)g Fr(Y)21 b Ft(\()p Fr(E)6 b Ft(\))27 b(=)1132 3139 y Fq(j)p Fr(z)t Fq(j)1237 3102 y Fk(2)1299 3139 y Fq(\000)22 b(j)p Fr(z)t Fq(j)1503 3102 y Fj(\000)p Fk(2)p 1132 3183 466 4 v 1340 3274 a Ft(4)1630 3206 y Fq(\000)g Ft(ln)17 b Fq(j)p Fr(z)t Fq(j)p Fr(;)g(E)34 b Ft(=)2185 3119 y Fq(p)p 2268 3119 49 4 v 87 x Ft(2\()p Fq(j)p Fr(z)t Fq(j)22 b Ft(+)g Fq(j)p Fr(z)t Fq(j)2685 3165 y Fj(\000)p Fk(1)2780 3206 y Ft(\))p Fr(;)17 b Fq(j)p Fr(z)t Fq(j)27 b Fr(<)h Ft(1)p Fr(;)17 b(E)33 b(>)27 b Ft(2)3448 3119 y Fq(p)p 3531 3119 V 87 x Ft(2)236 3412 y(and)832 3548 y Fr(E)910 3506 y Fj(\006)904 3575 y Fo(k)996 3548 y Ft(=)h Fq(\006)1177 3460 y(p)p 1260 3460 V 88 x Ft(2\()p Fq(j)p Fr(p)1424 3506 y Fj(\006)1424 3575 y Fo(k)1483 3548 y Fq(j)22 b Ft(+)g Fq(j)p Fr(p)1708 3506 y Fj(\006)1708 3575 y Fo(k)1766 3548 y Fq(j)1794 3506 y Fj(\000)p Fk(1)1888 3548 y Ft(\))p Fr(;)1989 3522 y Fn(e)1970 3548 y Fr(E)2048 3506 y Fj(\006)2042 3575 y Fo(k)2135 3548 y Ft(=)27 b Fq(\006)2315 3460 y(p)p 2399 3460 V 2399 3548 a Ft(2)o(\()p Fq(j)p Fr(z)2562 3506 y Fj(\006)2558 3575 y Fo(k)2622 3548 y Fq(j)22 b Ft(+)g Fq(j)p Fr(z)2847 3506 y Fj(\006)2843 3575 y Fo(k)2906 3548 y Fq(j)2934 3506 y Fj(\000)p Fk(1)3028 3548 y Ft(\))336 3704 y(Recall)33 b(\(2.4\))1371 3883 y(1)p 1342 3927 108 4 v 1342 4019 a(2)p Fr(\031)1526 3795 y Fo(\031)1476 3815 y Fn(Z)1486 4096 y Fk(0)1602 3883 y Ft(ln)49 b Fq(=)p Fr(f)p 1602 3927 262 4 v 1609 4019 a Ft(ln)17 b Fq(=)p Fr(F)1873 3950 y Ft(\(1)22 b Fq(\000)h Ft(cos)17 b(2)p Fr(\022)s Ft(\))p Fr(d\022)30 b Ft(=)391 4320 y(=)d Fq(\000)581 4252 y Ft(1)p 581 4297 49 4 v 581 4388 a(2)657 4320 y(ln)17 b(2)22 b Fq(\000)935 4252 y Fr(V)1014 4216 y Fk(2)1053 4252 y Ft(\()p Fr(O)s Ft(\))p 935 4297 272 4 v 1046 4388 a(8)1238 4320 y(+)1336 4225 y Fn(X)1389 4437 y Fo(k)1497 4320 y Fr(Y)f Ft(\()1633 4295 y Fn(e)1613 4320 y Fr(E)1691 4279 y Fk(+)1685 4347 y Fo(k)1750 4320 y Ft(\))h Fq(\000)1910 4225 y Fn(X)1963 4437 y Fo(k)2070 4320 y Fr(Y)g Ft(\()p Fr(E)2265 4279 y Fk(+)2259 4347 y Fo(k)2324 4320 y Ft(\))g(+)2482 4225 y Fn(X)2535 4437 y Fo(k)2642 4320 y Fr(Y)g Ft(\()2778 4295 y Fn(e)2759 4320 y Fr(E)2837 4279 y Fj(\000)2831 4347 y Fo(k)2896 4320 y Ft(\))g Fq(\000)3055 4225 y Fn(X)3108 4437 y Fo(k)3216 4320 y Fr(Y)f Ft(\()p Fr(E)3410 4279 y Fj(\000)3404 4347 y Fo(k)3469 4320 y Ft(\))336 4565 y(F)-8 b(or)32 b(the)h(sp)s(ectral)g(measures,)1157 4748 y Fq(=)p Fr(m)p Ft(\()p Fr(\025)p Ft(\))27 b(=)h Fr(\031)t(\033)1696 4706 y Fj(0)1692 4772 y Fo(O)1752 4748 y Ft(\()p Fr(\025)p Ft(\))p Fr(;)114 b(\025)27 b Fq(2)i Ft([)p Fq(\000)p Ft(2)2358 4660 y Fq(p)p 2441 4660 49 4 v 88 x Ft(2)p Fr(;)17 b Ft(2)2583 4660 y Fq(p)p 2665 4660 V 2665 4748 a Ft(2])865 5060 y Fq(=)p Fr(M)10 b Ft(\()p Fr(\025)p Ft(\))28 b(=)g Fq(=)p Fr(m)1463 5075 y Fk(1)1503 5060 y Ft(\()p Fr(\025)p Ft(\))22 b(+)g Fq(=)p Fr(m)1913 5075 y Fk(2)1952 5060 y Ft(\()p Fr(\025)p Ft(\))28 b(=)f Fr(\031)t Ft(\()p Fr(\033)2372 5018 y Fj(0)2368 5084 y Fo(O)2422 5093 y Fe(1)2461 5060 y Ft(\()p Fr(\025)p Ft(\))22 b(+)g Fr(\033)2773 5018 y Fj(0)2769 5084 y Fo(O)2823 5093 y Fe(2)2862 5060 y Ft(\()p Fr(\025)p Ft(\)\))236 5216 y(Then,)34 b(the)f(m)m(ultidimensional)i(step-b)m(y-step)f(sum)g(rule)f(is)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 633 251 a Fh(ON)33 b(THE)g(PRESER)-9 b(V)g(A)j(TION)32 b(OF)h(ABSOLUTEL)-6 b(Y)32 b(CONTINUOUS)g(SPECTR)n (UM)h(...)300 b(9)697 642 y Ft(1)p 668 686 108 4 v 668 778 a(8)p Fr(\031)852 554 y Fk(2)887 499 y Fj(p)p 946 499 36 3 v 55 x Fk(2)844 574 y Fn(Z)780 873 y Fj(\000)p Fk(2)870 818 y Fj(p)p 929 818 V 55 x Fk(2)1003 623 y Fq(p)p 1086 623 267 4 v 86 x Ft(8)22 b Fq(\000)g Fr(\025)1313 681 y Fk(2)1369 709 y Ft(ln)q([)p Fr(\031)t(\033)1596 668 y Fj(0)1619 709 y Ft(\()p Fr(\025)p Ft(\)])p Fr(d\025)27 b Ft(=)2057 642 y(1)p 2028 686 108 4 v 2028 778 a(8)p Fr(\031)2211 554 y Fk(2)2246 499 y Fj(p)p 2306 499 36 3 v 2306 554 a Fk(2)2204 574 y Fn(Z)2140 873 y Fj(\000)p Fk(2)2230 818 y Fj(p)p 2289 818 V 55 x Fk(2)2363 623 y Fq(p)p 2446 623 267 4 v 86 x Ft(8)22 b Fq(\000)g Fr(\025)2673 681 y Fk(2)2729 709 y Ft(ln)2827 599 y Fn(\020)2887 709 y Fr(\031)2956 642 y(\033)3015 606 y Fj(0)3011 667 y Fk(1)3073 642 y Ft(+)g Fr(\033)3230 606 y Fj(0)3226 667 y Fk(2)p 2955 686 310 4 v 3086 778 a Ft(2)3275 599 y Fn(\021)3335 709 y Fr(d\025)1315 1123 y Fq(\000)1402 1056 y Fr(V)1481 1020 y Fk(2)1521 1056 y Ft(\()p Fr(O)s Ft(\))p 1402 1100 272 4 v 1514 1192 a(8)1706 1123 y(+)1804 1029 y Fn(X)1857 1241 y Fo(k)1965 1123 y Fr(Y)f Ft(\()2100 1098 y Fn(e)2081 1123 y Fr(E)2153 1138 y Fo(k)2196 1123 y Ft(\))h Fq(\000)2355 1029 y Fn(X)2408 1241 y Fo(k)2516 1123 y Fr(Y)f Ft(\()p Fr(E)2704 1138 y Fo(k)2747 1123 y Ft(\))437 1373 y(Let)33 b(us)g(sho)m(w)h(that)337 1554 y(\(2.8\))1554 1460 y Fn(X)1607 1672 y Fo(k)1715 1554 y Fr(Y)21 b Ft(\()1850 1529 y Fn(e)1831 1554 y Fr(E)1903 1569 y Fo(k)1946 1554 y Ft(\))27 b Fq(\025)2117 1460 y Fn(X)2169 1672 y Fo(k)2277 1554 y Fr(Y)21 b Ft(\()p Fr(E)2465 1569 y Fo(k)2508 1554 y Ft(\))437 1846 y(Indeed,)48 b Fr(Y)22 b Ft(\(2)961 1763 y Fq(p)p 1043 1763 49 4 v 1043 1846 a Ft(2\))47 b(=)g(0,)g Fr(Y)21 b Ft(\()p Fr(E)6 b Ft(\))44 b(is)g(ev)m(en,)49 b(negativ)m(e,)f(and)c(decreasing)h(in)f Fr(E)53 b(>)47 b Ft(2)3604 1763 y Fq(p)p 3687 1763 V 83 x Ft(2.)337 1976 y(Notice)38 b(that)g Fr(E)937 1991 y Fo(k)1017 1976 y Ft(are)f(p)s(oles)h(of)f Fr(m)p Ft(\()p Fr(\025)p Ft(\),)1855 1951 y Fn(e)1836 1976 y Fr(E)1908 1991 y Fo(k)1988 1976 y Ft(are)g(zero)s(es)i(of)e Fr(m)p Ft(\(\()p Fr(\025)p Ft(\))g(\(and)g(p)s(oles)h(of)f Fr(M)10 b Ft(\()p Fr(\025)p Ft(\)\).)337 2092 y(F)-8 b(rom)33 b(\(2.3\))f(and)g(in)m(tegral)h(represen)m(tation)i(of)d Fr(m)p Ft(\()p Fr(\025)p Ft(\))g(w)m(e)i(ha)m(v)m(e)g(the)f(in)m (terlacing)g(prop)s(ert)m(y)1396 2349 y Fr(E)1474 2308 y Fj(\000)1468 2374 y Fk(1)1561 2349 y Fr(<)1684 2324 y Fn(e)1664 2349 y Fr(E)1742 2308 y Fj(\000)1736 2374 y Fk(1)1829 2349 y Fr(<)27 b(E)2010 2308 y Fj(\000)2004 2374 y Fk(2)2097 2349 y Fr(<)h(:)17 b(:)g(:)27 b(<)g Fq(\000)p Ft(2)2572 2262 y Fq(p)p 2656 2262 V 2656 2349 a Ft(2)1434 2549 y(2)1483 2461 y Fq(p)p 1566 2461 V 88 x Ft(2)h Fr(<)f(:)17 b(:)g(:)27 b(<)h(E)2070 2508 y Fk(+)2064 2573 y(2)2157 2549 y Fr(<)2280 2523 y Fn(e)2260 2549 y Fr(E)2338 2508 y Fk(+)2332 2573 y(1)2425 2549 y Fr(<)g(E)2607 2508 y Fk(+)2601 2573 y(1)337 2710 y Ft(So,)33 b(\(2.8\))f(holds)h(and) 337 2942 y(\(2.9\))353 3134 y(1)p 347 3179 59 4 v 347 3270 a Fr(\031)483 3046 y Fk(2)518 2991 y Fj(p)p 577 2991 36 3 v 55 x Fk(2)475 3066 y Fn(Z)411 3365 y Fj(\000)p Fk(2)501 3310 y Fj(p)p 560 3310 V 55 x Fk(2)634 3115 y Fq(p)p 717 3115 267 4 v 87 x Ft(8)22 b Fq(\000)g Fr(\025)944 3173 y Fk(2)1000 3202 y Ft(ln)q([)p Fr(\031)t(\033)1227 3161 y Fj(0)1223 3226 y Fo(O)1283 3202 y Ft(\()p Fr(\025)p Ft(\)])p Fr(d\025)27 b Fq(\025)1698 3134 y Ft(1)p 1693 3179 59 4 v 1693 3270 a Fr(\031)1828 3046 y Fk(2)1863 2991 y Fj(p)p 1922 2991 36 3 v 55 x Fk(2)1821 3066 y Fn(Z)1756 3365 y Fj(\000)p Fk(2)1846 3310 y Fj(p)p 1905 3310 V 55 x Fk(2)1979 3115 y Fq(p)p 2062 3115 267 4 v 87 x Ft(8)22 b Fq(\000)h Fr(\025)2290 3173 y Fk(2)2346 3202 y Ft(ln)2444 3091 y Fn(\020)2503 3202 y Fr(\031)2572 3129 y(\033)2631 3092 y Fj(0)2627 3154 y Fo(O)2681 3163 y Fe(1)2720 3129 y Ft(\()p Fr(\025)p Ft(\))f(+)g Fr(\033)3032 3092 y Fj(0)3028 3154 y Fo(O)3082 3163 y Fe(2)3120 3129 y Ft(\()p Fr(\025)p 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f(con)n(tin)n(uous)g(sp)r(ectrum)h(of)g(one-dimensional)f(Sc)n(hr\177) -42 b(odinger)508 1529 y(op)r(erators)23 b(with)j(square)d(summable)i (p)r(oten)n(tials,)g(Comm.)g(Math.)h(Ph)n(ys.,)e(V)-7 b(ol.)25 b(203,)f(1999,)g(341{347.)379 1629 y([3])41 b(S.)f(Deniso)n(v,)i(On)e(the)g(existence)f(of)h(the)g(absolutely)f (con)n(tin)n(uous)g(comp)r(onen)n(t)g(for)h(the)g(measure)508 1729 y(asso)r(ciated)26 b(with)j(some)e(orthogonal)e(systems,)i(Comm.)h (Math.)f(Ph)n(ys.,)g(V)-7 b(ol.)28 b(226,)e(2002,)g(205{220.)379 1828 y([4])41 b(S.)27 b(Deniso)n(v,)f(On)g(the)h(absolutely)f(con)n (tin)n(uous)f(sp)r(ectrum)i(of)f(Dirac)g(op)r(erator,)f(\(to)i(app)r (ear)f(in)g(Com-)508 1928 y(m)n(unications)h(in)h(PDE\).)379 2028 y([5])41 b(S.)24 b(Deniso)n(v,)g(Absolutely)g(con)n(tin)n(uous)e (sp)r(ectrum)i(of)g(m)n(ultidimensional)f(Sc)n(hr\177)-42 b(odinger)22 b(op)r(erator,)h(\(to)508 2127 y(app)r(ear)k(in)h(IMRN\).) 379 2227 y([6])41 b(R.)32 b(F)-7 b(ro)r(ese,)32 b(D.)f(Hasler,)h(W.)g (Spitzer,)g(T)-7 b(ransfer)31 b(matrices,)g(h)n(yp)r(erb)r(olic)g (geometry)f(and)i(absolutely)508 2326 y(con)n(tin)n(uous)27 b(sp)r(ectrum)g(for)h(some)f(discrete)g(Sc)n(hr\177)-42 b(odinger)25 b(op)r(erators)h(on)h(graphs,)g(\(preprin)n(t\).)379 2426 y([7])41 b(T.)28 b(Kato,)e(P)n(erturbation)g(theory)g(for)h (linear)g(op)r(erators.)e(Reprin)n(t)i(of)h(the)f(1980)f(edition.)h (Classics)g(in)508 2526 y(Mathematics.)h(Springer-V)-7 b(erlag,)25 b(Berlin,)i(1995.)379 2625 y([8])41 b(S.)25 b(Khrushc)n(hev,)f(Sc)n(h)n(ur's)g(algorithm,)g(orthogonal)e(p)r (olynomials,)j(and)f(con)n(v)n(ergence)e(of)j(W)-7 b(all's)24 b(con-)508 2725 y(tin)n(ued)k(fractions)f(in)h Fd(L)1258 2695 y Fc(2)1294 2725 y Fv(\()p Fb(T)p Fv(\),)h(J.)e(Appro)n(x.)g (Theory)-7 b(,)27 b(V)-7 b(ol.)28 b(108,)e(2001,)g(no.)h(2,)g(161{248.) 379 2825 y([9])41 b(R.)21 b(Killip,)i(B.)e(Simon,)h(Sum)g(rules)e(for)h (Jacobi)f(matrices)g(and)h(their)g(applications)f(to)h(sp)r(ectral)f (theory)-7 b(,)508 2924 y(Annals)28 b(of)f(Math.,)h(V)-7 b(ol.)28 b(158,)e(2003,)g(253{321.)337 3024 y([10])41 b(A.)35 b(Kiselev,)h(Y.)f(Last,)g(B.)g(Simon,)h(Mo)r(di\014ed)f(Pr)r (\177)-44 b(ufer)34 b(and)g(EF)n(GP)g(transforms)f(and)h(the)h(sp)r (ectral)508 3123 y(analysis)e(of)h(one-dimensional)f(Sc)n(hr\177)-42 b(odinger)32 b(op)r(erators,)i(Comm.)g(Math.)g(Ph)n(ys.,)h(V)-7 b(ol.)34 b(194,)h(1998,)508 3223 y(no.)28 b(1,)f(1{45.)337 3323 y([11])41 b(A.)31 b(Klein,)g(Extended)f(states)g(in)g(the)h (Anderson)f(mo)r(del)g(on)g(the)h(Bethe)g(lattice,)g(Adv.)f(Math.,)i(V) -7 b(ol.)508 3422 y(133,)26 b(1998,)g(no.)i(1,)f(163{184.)337 3522 y([12])41 b(M.)36 b(Krein,)i(Con)n(tin)n(uous)d(analogues)f(of)i (prop)r(ositions)f(on)g(p)r(olynomials)g(orthogonal)f(on)i(the)g(unit) 508 3622 y(circle,)27 b(Dokl.)h(Ak)-5 b(ad.)28 b(Nauk)f(SSSR,)h(V)-7 b(ol.)28 b(105,)e(1955,)g(637{640.)337 3721 y([13])41 b(A.)23 b(Laptev,)g(S.)g(Nab)r(ok)n(o,)f(O.)g(Safrono)n(v,)g(On)g(new)h (relations)e(b)r(et)n(w)n(een)h(sp)r(ectral)g(prop)r(erties)g(of)g (Jacobi)508 3821 y(matrices)27 b(and)g(their)h(co)r(e\016cien)n(ts,)f (Comm.)h(Math.)g(Ph)n(ys.,)e(V)-7 b(ol.)28 b(241,)e(2003,)g(no.)h(1,)h (91{110.)337 3920 y([14])41 b(A.)26 b(Laptev,)f(S.)h(Nab)r(ok)n(o,)f (O.)g(Safrono)n(v,)f(A)i(Szeg\177)-42 b(o)24 b(condition)h(for)g(a)g(m) n(ultidimensional)h(Sc)n(hr\177)-42 b(odinger)508 4020 y(op)r(erator,)26 b(\(to)i(app)r(ear)e(in)i(J.)g(F)-7 b(unc.)28 b(Anal.\).)337 4120 y([15])41 b(A.)28 b(Laptev,)g(S.)g(Nab)r (ok)n(o,)e(O.)i(Safrono)n(v,)e(Absolutely)i(con)n(tin)n(uous)e(sp)r (ectrum)i(of)g(Sc)n(hr\177)-42 b(odinger)26 b(op)r(er-)508 4219 y(ators)g(with)j(slo)n(wly)d(deca)n(ying)g(and)i(oscillating)e(p)r (oten)n(tials,)i(\(to)f(app)r(ear)g(in)h(Comm.)f(Math.)h(Ph)n(ys.\).) 337 4319 y([16])41 b(A.)31 b(Mikhailo)n(v)-5 b(a,)30 b(B.)h(P)n(a)n(vlo)n(v,)e(I.)i(P)n(op)r(o)n(v,)e(T.)i(Rudak)n(o)n(v)-5 b(a,)30 b(A.)h(Y)-7 b(afy)n(aso)n(v,)30 b(Scattering)g(on)g(a)g (compact)508 4419 y(domain)38 b(with)h(few)f(semi-in\014nite)g(wires)g (attac)n(hed:)57 b(resonance)37 b(case,)j(Math.)e(Nac)n(hr.,)i(V)-7 b(ol.)38 b(235,)508 4518 y(2002,)26 b(101{128.)337 4618 y([17])41 b(S.)32 b(Molc)n(hano)n(v,)f(M.)h(No)n(vitskii,)g(B.)g(V)-7 b(ain)n(b)r(erg,)32 b(First)f(KdV)h(in)n(tegrals)e(and)i(absolutely)f (con)n(tin)n(uous)508 4717 y(sp)r(ectrum)d(for)f(1-D)g(Sc)n(hr\177)-42 b(odinger)26 b(op)r(erator,)g(Comm.)i(Math.)f(Ph)n(ys.,)g(V)-7 b(ol.)28 b(216,)e(2001,)g(195{213.)337 4817 y([18])41 b(S.)25 b(Molc)n(hano)n(v,)f(B.)h(V)-7 b(ain)n(b)r(erg,)25 b(Sc)n(hr\177)-42 b(odinger)23 b(op)r(erators)g(with)j(matrix)e(p)r (oten)n(tials.)h(T)-7 b(ransition)24 b(from)508 4917 y(the)j(absolutely)g(con)n(tin)n(uous)f(to)g(the)i(singular)d(sp)r (ectrum,)j(J.)e(F)-7 b(unct.)28 b(Anal.,)f(V)-7 b(ol.)27 b(215,)f(2004,)f(no.)i(1,)508 5016 y(111{129.)337 5116 y([19])41 b(B.)26 b(Simon,)g(Sc)n(hr\177)-42 b(odinger)24 b(op)r(erator)f(in)j(the)g(21-st)f(cen)n(tury)-7 b(,)25 b(Imp.)h(Coll.)g(Press,)e(London,)h(2000,)g(283{)508 5216 y(288.)p eop end %%Page: 12 12 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