Content-Type: multipart/mixed; boundary="-------------0210090005337" This is a multi-part message in MIME format. ---------------0210090005337 Content-Type: text/plain; name="02-419.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-419.keywords" stochastic Ising model, spectral gap, lower bound ---------------0210090005337 Content-Type: application/postscript; name="sgmn.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="sgmn.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.78 p1.4c Copyright 1996-99 ASCII Corp.(www-ptex@ascii.co.jp) %%dvipsk 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: paper.dvi %%Pages: 38 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips paper.dvi %DVIPSParameters: dpi=300 %DVIPSSource: TeX output 2002.09.30:1634 %%BeginProcSet: tex.pro %! /TeXDict 300 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}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{dup dup 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 /IE 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 IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /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 dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup 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 /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]{ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]} if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 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 dup 1 get dup mul exch 0 get dup 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 /IE 256 array N 2 string 0 1 255{IE S dup 360 add 36 4 index cvrs cvn put}for pop 65781.76 div /vsize X 65781.76 div /hsize X}N /dir 0 def /dyy{/dir 0 def}B /dyt{/dir 1 def}B /dty{/dir 2 def}B /dtt{/dir 3 def}B /p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}B /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V{}B /RV statusdict begin /product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{dup length product length le{dup 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 rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}} ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /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 TeXDict begin 39158280 55380996 1000 300 300 (paper.dvi) @start %DVIPSBitmapFont: Fa cmex8 8 1 /Fa 1 101 df<000001E000000000003FFF0000000003FE1FF00000007FC000FF800007 F0000003F800FC000000000FC03206809833> 100 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmbx8 8 1 /Fb 1 68 df<007F8103FFF707E03F0F000F1E00073C00077C0003780003F80000F80000 F80000F80000F80000F80000F800007800037C00033C00031E00060F000C07E03803FFF0 007FC018177E961D> 67 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmsy6 6 4 /Fc 4 108 df 0 D<1E003F006180C0C0C0C0C0C0C0C0C0 C0C0C061803F001E000A0C7D8B10> 14 D<081C1C3838383070706060C0C0060D7E8D09> 48 D<81C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C3C381081A7C9210> 107 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmti12 12 38 /Fd 38 122 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmmi6 6 12 /Fe 12 122 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Ff msbm8 8 5 /Ff 5 91 df 70 D<07FF01040088008800880088008800880088008800880088 0088008800880088008800880088708888888888889090A071C00F00101A809619> 74 D 78 D 87 D<7FFFE04304404C08405008806010804021004022000042000084000084 000108000110000210000420000420100840100880301080302100602200A04201204406 20FFFFE014177F9629> 90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmbx12 12 46 /Fg 46 123 df<000FF000007FFC0001F80E0003E01F0007C03F000F803F000F803F000F 801E000F800C000F8000000F8000000F8000000F800000FFFFFF00FFFFFF000F801F000F 801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F000F 801F000F801F000F801F000F801F000F801F000F801F000F801F000F801F007FF0FFE07F F0FFE01B237FA21F> 12 D<387CFEFEFE7C3807077C8610> 46 D<00FE0007FFC00F83E0 1F01F03E00F83E00F87C007C7C007C7C007CFC007CFC007EFC007EFC007EFC007EFC007E FC007EFC007EFC007EFC007EFC007EFC007EFC007EFC007E7C007C7C007C7C007C3E00F8 3E00F81F01F00F83E007FFC000FE0017207E9F1C> 48 D<00180000780001F800FFF800 FFF80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F80001F800 01F80001F8007FFFE07FFFE013207C9F1C> I<03FC000FFF003C1FC07007E07C07F0FE03 F0FE03F8FE03F8FE01F87C01F83803F80003F80003F00003F00007E00007C0000F80001F 00003E0000380000700000E01801C0180380180700180E00380FFFF01FFFF03FFFF07FFF F0FFFFF0FFFFF015207D9F1C> I<00FE0007FFC00F07E01E03F03F03F03F81F83F81F83F 81F81F03F81F03F00003F00003E00007C0001F8001FE0001FF000007C00001F00001F800 00FC0000FC3C00FE7E00FEFF00FEFF00FEFF00FEFF00FC7E01FC7801F81E07F00FFFC001 FE0017207E9F1C> I<0000E00001E00003E00003E00007E0000FE0001FE0001FE00037E0 0077E000E7E001C7E00187E00307E00707E00E07E00C07E01807E03807E07007E0E007E0 FFFFFFFFFFFF0007E00007E00007E00007E00007E00007E00007E000FFFF00FFFF18207E 9F1C> I<3000203E01E03FFFC03FFF803FFF003FFE003FF80033C0003000003000003000 0030000031FC0037FF003E0FC03807E03003E00003F00003F00003F80003F83803F87C03 F8FE03F8FE03F8FC03F0FC03F07007E03007C03C1F800FFF0003F80015207D9F1C> I<00 1F8000FFE003E07007C0F00F01F81F01F83E01F83E01F87E00F07C00007C0000FC0800FC 7FC0FCFFE0FD80F0FF00F8FE007CFE007CFC007EFC007EFC007EFC007E7C007E7C007E7C 007E3C007C3E007C1E00F80F00F00783E003FFC000FF0017207E9F1C> I<600000780000 7FFFFE7FFFFE7FFFFC7FFFF87FFFF87FFFF0E00060E000C0C00180C00300C00300000600 000C00001C0000180000380000780000780000F00000F00000F00001F00001F00001F000 03F00003F00003F00003F00003F00003F00003F00001E00017227DA11C> I<00FE0003FF C00703E00E00F01C00F01C00783C00783E00783F00783F80783FE0F01FF9E01FFFC00FFF 8007FFC003FFE007FFF01E7FF83C1FFC7807FC7801FEF000FEF0003EF0001EF0001EF000 1EF8001C7800383C00381F00F00FFFC001FF0017207E9F1C> I<00007000000000700000 0000F800000000F800000000F800000001FC00000001FC00000003FE00000003FE000000 03FE000000067F000000067F0000000C7F8000000C3F8000000C3F800000181FC0000018 1FC00000301FE00000300FE00000700FF000006007F000006007F00000C007F80000FFFF F80001FFFFFC00018001FC00018001FC00030001FE00030000FE00070000FF000600007F 000600007F00FFE007FFF8FFE007FFF825227EA12A> 65 D I<0003FE0080001FFF818000FF01E3 8001F8003F8003E0001F8007C0000F800F800007801F800007803F000003803F00000380 7F000001807E000001807E00000180FE00000000FE00000000FE00000000FE00000000FE 00000000FE00000000FE00000000FE000000007E000000007E000001807F000001803F00 0001803F000003801F800003000F8000030007C000060003F0000C0001F800380000FF00 F000001FFFC0000003FE000021227DA128> I I I 76 D I<0007FC0000003FFF800000FC07E00003F001F80007E000FC00 0FC0007E001F80003F001F80003F003F00001F803F00001F807F00001FC07E00000FC07E 00000FC0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00000FE0FE00 000FE0FE00000FE0FE00000FE07E00000FC07F00001FC07F00001FC03F00001F803F8000 3F801F80003F000FC0007E0007E000FC0003F001F80000FC07E000003FFF80000007FC00 0023227DA12A> 79 D I 82 D<01FE0207FF861F01FE3C007E7C001E78000E78000EF80006F80006FC 0006FC0000FF0000FFE0007FFF007FFFC03FFFF01FFFF80FFFFC03FFFE003FFE0003FE00 007F00003F00003FC0001FC0001FC0001FE0001EE0001EF0003CFC003CFF00F8C7FFE080 FF8018227DA11F> I<7FFFFFFF807FFFFFFF807E03F80F807803F807807003F803806003 F80180E003F801C0E003F801C0C003F800C0C003F800C0C003F800C0C003F800C00003F8 00000003F800000003F800000003F800000003F800000003F800000003F800000003F800 000003F800000003F800000003F800000003F800000003F800000003F800000003F80000 0003F800000003F800000003F800000003F800000003F8000001FFFFF00001FFFFF00022 227EA127> I 87 D<0FFC003FFF807E07C07E03E07E01E07E01F03C01F00001F00001F0003FF003FDF01FC1 F03F01F07E01F0FC01F0FC01F0FC01F0FC01F07E02F07E0CF81FF87F07E03F18167E951B > 97 D<00FF8007FFE00F83F01F03F03E03F07E03F07C01E07C0000FC0000FC0000FC00 00FC0000FC0000FC00007C00007E00007E00003E00181F00300FC06007FFC000FF001516 7E9519> 99 D<0001FE000001FE0000003E0000003E0000003E0000003E0000003E0000 003E0000003E0000003E0000003E0000003E0000003E0001FC3E0007FFBE000F81FE001F 007E003E003E007E003E007C003E00FC003E00FC003E00FC003E00FC003E00FC003E00FC 003E00FC003E00FC003E007C003E007C003E003E007E001F00FE000F83BE0007FF3FC001 FC3FC01A237EA21F> I<00FE0007FF800F87C01E01E03E01F07C00F07C00F8FC00F8FC00 F8FFFFF8FFFFF8FC0000FC0000FC00007C00007C00007E00003E00181F00300FC07003FF C000FF0015167E951A> I<001FC0007FE000F1F001E3F003E3F007C3F007C1E007C00007 C00007C00007C00007C00007C000FFFE00FFFE0007C00007C00007C00007C00007C00007 C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007 C0003FFC003FFC00142380A211> I<01FE0F0007FFBF800F87C7801F03E7801E01E0003E 01F0003E01F0003E01F0003E01F0003E01F0001E01E0001F03E0000F87C0000FFF800009 FE000018000000180000001C0000001FFFE0000FFFF80007FFFE001FFFFF003C003F0078 000F80F0000780F0000780F0000780F000078078000F003C001E001F007C000FFFF80001 FFC00019217F951C> I I<1C003E007F007F007F003E001C00000000000000000000 0000000000FF00FF001F001F001F001F001F001F001F001F001F001F001F001F001F001F 001F001F001F001F00FFE0FFE00B247EA310> I 107 D I I I<00FE0007FFC00F83E01E00F03E00F87C007C7C007C7C007C FC007EFC007EFC007EFC007EFC007EFC007EFC007E7C007C7C007C3E00F81F01F00F83E0 07FFC000FE0017167E951C> I I 114 D<0FF3003FFF00781F00600700E00300E00300F00300FC00007FE0007FF8 003FFE000FFF0001FF00000F80C00780C00380E00380E00380F00700FC0E00EFFC00C7F0 0011167E9516> I<0180000180000180000180000380000380000780000780000F80003F 8000FFFF00FFFF000F80000F80000F80000F80000F80000F80000F80000F80000F80000F 80000F80000F81800F81800F81800F81800F81800F830007C30003FE0000F80011207F9F 16> I I 119 D I I<7FFFF07FFFF07C03E07007C0600FC0E01F80C01F00 C03E00C07E0000FC0000F80001F00003F03007E03007C0300F80701F80703F00603E00E0 7C03E0FFFFE0FFFFE014167E9519> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmr10 10 44 /Fh 44 122 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmsy7 7 2 /Fi 2 122 df<040004000400C460F5E03F800E003F80F5E0C4600400040004000B0D7E 8D11> 3 D<0C000C000C000C000C000C00FFC0FFC00C000C000C000C000C000C000C000C 000C000C000C000C000C000C000C000C000C000C000A1A7E9310> 121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr6 6 10 /Fj 10 62 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmex10 12 28 /Fk 28 112 df<000800100020004000C0018003000300060006000C000C001C00180038 003800300070007000700070006000E000E000E000E000E000E000E000E000E000E000E0 00E000E000E000E0006000700070007000700030003800380018001C000C000C00060006 0003000300018000C000400020001000080D3B798117> 0 D<800040002000100018000C 0006000600030003000180018001C000C000E000E0006000700070007000700030003800 380038003800380038003800380038003800380038003800380038003000700070007000 70006000E000E000C001C00180018003000300060006000C00180010002000400080000D 3B7E8117> I I I 12 D<00000C00000C00001C000018000018000038000030000030000070 0000600000E00000C00000C00001C0000180000180000380000300000300000700000600 000600000E00000C00000C00001C00001800001800003800003000007000006000006000 00E00000C00000C00001C000018000018000038000030000030000070000060000060000 0E00000C00000C00001C0000180000380000300000300000700000600000600000E00000 C00000C00000163B7D811D> 14 D<0000600000C0000180000300000600000E00001C00 00180000380000700000600000E00001C00001C000038000038000078000070000070000 0F00000E00001E00001E00001C00001C00003C00003C0000380000380000780000780000 780000780000780000700000F00000F00000F00000F00000F00000F00000F00000F00000 F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000700000 7800007800007800007800007800003800003800003C00003C00001C00001C00001E0000 1E00000E00000F000007000007000007800003800003800001C00001C00000E000006000 007000003800001800001C00000E000006000003000001800000C0000060135977811E> 16 D I<0000018000000300000006 0000000C000000180000003000000060000000E0000001C0000001800000038000000700 00000E0000000E0000001C0000001C000000380000007800000070000000F0000000E000 0001E0000001C0000001C0000003C00000038000000780000007800000070000000F0000 000F0000000E0000001E0000001E0000001E0000001C0000003C0000003C0000003C0000 003C00000038000000780000007800000078000000780000007800000078000000780000 0070000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00000 00F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00000 00F0000000F0000000F0000000F000000070000000780000007800000078000000780000 00780000007800000078000000380000003C0000003C0000003C0000003C0000001C0000 001E0000001E0000001E0000000E0000000F0000000F0000000700000007800000078000 000380000003C0000001C0000001C0000001E0000000E0000000F0000000700000007800 0000380000001C0000001C0000000E0000000E00000007000000038000000180000001C0 000000E00000006000000030000000180000000C00000006000000030000000180197776 8125> I I<00000700001F00003C0000F80001E00003 C0000780000780000F00001E00001E00001E00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C0000780000780000700000F00000E00001C0 0003C0000780000E00003C0000780000E000007800003C00000E000007800003C00001C0 0000E00000F000007000007800007800003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C00003C 00003C00003C00003C00003C00003C00001E00001E00001E00000F000007800007800003 C00001E00000F800003C00001F00000718777A8125> 26 D I<00000001800000 000180000000038000000003000000000300000000070000000006000000000600000000 0E000000000C000000001C00000000180000000018000000003800000000300000000030 00000000700000000060000000006000000000E000000000C000000000C000000001C000 000001800000000380000000030000000003000000000700000000060000000006000000 000E000000000C000000000C000000001C00000000180000000018000000003800000000 3000000000700000000060000000006000000000E000000000C000000000C000000001C0 000000018000000001800000000380000000030000000003000000000700000000060000 00000E000000000C000000000C000000001C000000001800000000180000000038000000 0030000000003000000000700000000060000000006000000000E000000000C000000001 C00000000180000000018000000003800000000300000000030000000007000000000600 00000006000000000E000000000C000000000C000000001C000000001800000000380000 000030000000003000000000700000000060000000006000000000E000000000C0000000 00C00000000021597D8128> 46 D<0006001E003C007800F001E003C007C00F800F801F 001F003E003E007E007E007C00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC 00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC00FC000F2D6D 7E2C> 56 D I I<003F003F003F003F003F003F003F003F 003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F 003F003E007E007E007E007C00FC00F801F801F003E003E007C00F801F003E007800F000 C000102D77802C> I<003F003F003F003F003F003F003F003F003F003F003F003F003F00 3F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003E007E007E00 7E007C00FC00F800F801F001E003E003C007800F001E003C007800E000E00078003C001E 000F00078003C003E001E001F000F800F800FC007C007E007E007E003E003F003F003F00 3F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F003F00 3F003F003F003F003F003F003F105C77802C> I I 80 D I 88 D I<000000007C0000000000000007FFC00000000000007FFFFC000000000007FF01FF C0000000007FE0000FFC00000007FC0000007FC000007F0000000001FC0007E000000000 000FC07C000000000000007C800000000000000002470A80A548> 100 D 104 D I<0000700001F00003C0000F80001E00003C00003C000078 0000F80000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F00000F00000F00000F00001E00001E00003C00003C0000780000F00003C00007800 00E000007800003C00000F000007800003C00003C00001E00001E00000F00000F00000F0 0000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F00000F0 0000F800007800003C00003C00001E00000F800003C00001F000007014597A8121> 110 D I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmr8 8 30 /Fl 30 127 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy8 8 27 /Fm 27 111 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fn msbm10 12 7 /Fn 7 91 df 70 D<01FFFE01FFFE0018600018600018600018600018600018600018600018 600018600018600018600018600018600018600018600018600018600018600018600018 600018600018600018600018600018600018603818607C1860C61860C618C0C618C0C619 806C1B003E7E001FFC0003C000172680A11F> 74 D 77 D I 82 D 87 D<1FFFFFF03FFFFFF033C0306036 0060C03C0060C07800C1807000C18070018300600306006003060000060C0000060C0000 0C1800001830000018300000306000003060000060C00000C1800000C180000183000003 03000803060018060C0018060C00180C1800381830003818300070306000F0306001F060 C003B0C1800E30FFFFFFF0FFFFFFF01D227EA12F> 90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmsy10 12 43 /Fo 43 111 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi8 8 45 /Fp 45 123 df<000F0000308000C0C00100400100600200C00400C0040080040180083F 00083E00080100080180100180100180100180100180300300300300300600280C004418 0043E000400000400000800000800000800000800000131D7F9614> 12 D<0780401FC04038E080603080C01080801100000900000A00000A00000A00000C00000C 00000C000008000008000008000010000010000010000010001214808D12> I<01C007F0 043808000C000C00040006000300030007800DC010C020C06060C060C060C060804080C0 C080C18063003C000D187E9710> I<004000800080007801F8030004000C001800300030 0060006000C000C000C000C000C000C000C000600078003F000FC000E0006000600C4003 800D1D7E9610> 16 D<383C44C6470246028E060C060C060C06180C180C180C180C3018 30180018001800300030003000200F147F8D12> I<08181818303030606061C1C2447808 0E7E8D0C> 19 D<080E183E184C198032003C003FC030706030603160316031C032C01C 100E7E8D14> I<0FFFC03FFFC02108004108008310000210000210000610000410000410 000C18000C1800181800180800120E7F8D14> 25 D<03FF8007FF801C30001818003018 00601800601800601800C03000C030004060006040002180001E0000110E7F8D14> 27 D<0FFF3FFF208040808080018001800100010003000300030006000600100E7F8D10> I< 10002020003040003040003080202080602080602080606080404080C0C081C180E76700 7E7E003C3C00140E7F8D16> 33 D<60F0F06004047D830A> 58 D<60F0F0701010202040 40040A7D830A> I<0008001800300030003000600060006000C000C000C0018001800180 030003000600060006000C000C000C00180018001800300030003000600060006000C000 C0000D217E9812> 61 D<03F00408080410021C03380300030003000303E30C13100B20 076006C006C006C00C800C8018C010402020C01F0010177E9613> 64 D<07FFF800E00E00E00700E00300E00301C00301C00701C00701C00E03803C03FFF003FF F003803C07001C07000E07000E07000E0E001C0E001C0E00380E00701C01E0FFFF001817 7F961B> 66 D<001F8200E04403802C07001C0C001C1C00083800083000087000086000 00E00000E00000E00000C00000C00020C00020C00040E000406000806001003002001C1C 0007E00017177E9619> I<07FFF80000E00E0000E0030000E0038000E0018001C001C001 C001C001C000C001C000C0038001C0038001C0038001C0038001C0070003800700038007 000300070007000E000E000E000C000E0018000E0070001C01C000FFFF00001A177F961D > I<07FFFF8000E0038000E0010000E0010000E0010001C0010001C0010001C0400001C0 4000038080000381800003FF800003818000070100000701000007010000070000000E00 00000E0000000E0000000E0000001C000000FFC0000019177F9616> 70 D<07FE03F800E001C000E0010000E0020000E0080001C0100001C0200001C0800001C100 0003830000038F00000393800003A380000781C0000701C0000700E0000700E0000E0070 000E0070000E0038000E0038001C003C00FF80FF001D177F961E> 75 D<07FF0000E00000E00000E00000E00001C00001C00001C00001C0000380000380000380 000380000700000700080700080700100E00100E00300E00200E00601C01E0FFFFC01517 7F9618> I<07F0000FE000F0001E0000B8001E0000B8002E0000B8004E000138005C0001 38009C000138011C00011C011C00021C023800021C043800021C043800021C083800041C 107000040E107000040E207000040E407000080E40E000080E80E000080F00E000080700 E000180601C000FE040FF80023177F9622> I<07F007F800F000C000B8008000B8008000 9C0080011C0100011E0100010E0100010E01000207020002070200020382000203820004 01C4000401C4000400E4000400E4000800780008007800080038000800380018001000FE 0010001D177F961C> I<001FC000707001C03803001C06000C0E000E1C000E18000E3800 0E30000E70000E70000E70000E60001CE0001C60003860003870007070F0E03109C0190B 800F0E0003F810000810000C30000C60000FC0000FC0000700171D7F961C> 81 D<07FFF00000E01C0000E0060000E0070000E0070001C0070001C0070001C0070001C00E 0003801C000380700003FF80000380E000070070000700380007003800070038000E0070 000E0070000E0070800E0070801C003100FF801E0019177F961B> I 86 D I<03FE0FE0007807000078060000380C000038080000 3C1000001C2000001E4000000E8000000F00000007000000070000000F80000013800000 23C0000061C00000C1C0000181E0000100E0000200F000040070001C007000FF03FE001B 177F961D> I<7C0018001800180018003000300030003000678068C070406060C060C060 C060C06080C080C08180C10046003C000B177E960F> 98 D<07C00C20107020706000C0 00C000C00080008000C010C02060C03F000C0E7E8D0F> I<003E000C000C000C000C0018 001800180018073018F0307060706060C060C060C06080C080C480C4C1C446C838700F17 7E9612> I<07C01C20301060106020FFC0C000C000C000C000C010402060C01F000C0E7E 8D10> I<00E2031E060E0C0E0C0C180C180C180C101810181018183808F0073000300030 6060E060C1C07F000F14808D11> 103 D<1F0006000600060006000C000C000C000C0018 F01B181C08180838183018301830186030603160616062C026C03810177E9614> I<0300 038003000000000000000000000000001C002400460046008C000C001800180018003100 3100320032001C0009177F960C> I<00180038001000000000000000000000000001C002 2004300430086000600060006000C000C000C000C001800180018001806300E300C60078 000D1D80960E> I<1F0006000600060006000C000C000C000C00181C1866188E190C3200 3C003F00318060C060C460C460C4C0C8C0700F177E9612> I<3E0C0C0C0C181818183030 303060606060C0C8C8C8D07007177E960B> I<383C1E0044C6630047028100460301008E 0703000C0603000C0603000C060300180C0600180C0620180C0C20180C0C40301804C030 1807001B0E7F8D1F> I<383C0044C6004702004602008E06000C06000C06000C0600180C 00180C40181840181880300980300E00120E7F8D15> I<1C3C2246238223034603060306 0306030C060C060C0C0C081A3019E018001800300030003000FC001014808D12> 112 D<30F049184E384C309C001800180018003000300030003000600060000D0E7F8D10> 114 D<0F1F0011A18020C38020C300418000018000018000018000030000030200C30200 E70400C5080078F000110E7F8D14> 120 D<1C02260646064606860C0C0C0C0C0C0C1818 1818181818380C7007B000300060706070C021801E000F147F8D11> I<07040FCC187810 1000200040018002000400080810083C3043E081C00E0E7F8D10> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmmi12 12 68 /Fq 68 123 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr12 12 85 /Fr 85 127 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmbx12 17.28 28 /Fs 28 122 df<1E003F007F80FFC0FFC0FFC0FFC07F803F001E000A0A7A8916> 46 D<0001C0000003C000000FC000007FC0001FFFC000FFFFC000FFBFC000E03FC000003FC0 00003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC0 00003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC0 00003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC0 00003FC000003FC000003FC000003FC000003FC000003FC000003FC0007FFFFFF07FFFFF F07FFFFFF01C2E7AAD28> 49 D<003FE00001FFFE0007FFFF800F80FFC01E003FE03800 1FF07C000FF87E0007FCFF0007FCFF8007FEFF8007FEFF8003FEFF8003FE7F0003FE3E00 07FE000007FE000007FC000007FC00000FF800000FF800000FF000001FE000001FC00000 3F8000007F0000007E000000F8000001F0000003E0000007C000000F0000001E000E003C 000E0038000E0070001E00E0001C01C0001C0300003C07FFFFFC0FFFFFFC1FFFFFFC3FFF FFFC7FFFFFF8FFFFFFF8FFFFFFF8FFFFFFF81F2E7CAD28> I<001FF8000000FFFF000003 FFFFC00007E01FF0000F0007F8001F8007FC003FC007FC003FC003FE003FC003FE003FC0 03FE003FC003FE001F8003FE000F0007FE00000007FC00000007FC00000007F80000000F F00000001FE00000003F80000000FF0000003FF80000003FFF800000001FE00000000FF0 00000007F800000003FC00000003FE00000001FF00000001FF00000001FF80000001FF80 000001FF801C0001FF803E0001FF807F0001FF80FF8001FF80FF8001FF00FF8001FF00FF 8003FE007F0003FE007E0007FC003C0007F8001FC01FF0000FFFFFC00003FFFF0000003F F80000212E7DAD28> I<0000007000000000F000000001F000000003F000000007F00000 000FF00000000FF00000001FF00000003FF000000077F0000000F7F0000000E7F0000001 C7F000000387F000000707F000000F07F000000E07F000001C07F000003807F000007007 F00000F007F00000E007F00001C007F000038007F000070007F0000F0007F0000E0007F0 001C0007F000380007F000700007F000E00007F000FFFFFFFFE0FFFFFFFFE0FFFFFFFFE0 00000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000 000FF00000000FF000000FFFFFE0000FFFFFE0000FFFFFE0232E7EAD28> I<0000007800 000000000078000000000000FC000000000000FC000000000000FC000000000001FE0000 00000001FE000000000003FF000000000003FF000000000007FF800000000007FF800000 000007FF80000000000FFFC0000000000E7FC0000000001E7FE0000000001C3FE0000000 001C3FE000000000383FF000000000381FF000000000781FF800000000700FF800000000 700FF800000000E00FFC00000000E007FC00000001E007FE00000001C003FE00000001C0 03FE000000038001FF000000038001FF000000078001FF800000070000FF8000000F0000 FFC000000FFFFFFFC000000FFFFFFFC000001FFFFFFFE000001C00003FE000003C00003F F000003800001FF000003800001FF000007000001FF800007000000FF80000F000000FFC 0000E0000007FC0000E0000007FC0001C0000007FE0003E0000003FE00FFFF0001FFFFFC FFFF0001FFFFFCFFFF0001FFFFFC36317DB03D> 65 D 73 D 75 D 80 D 82 D<7FFFFFFFFFFF007FFFFFFFFFFF007FFFFFFFFFFF007FC00FF801FF007E00 0FF8003F007C000FF8001F0078000FF8000F0078000FF8000F0070000FF8000700F0000F F8000780F0000FF8000780F0000FF8000780E0000FF8000380E0000FF8000380E0000FF8 000380E0000FF8000380E0000FF800038000000FF800000000000FF800000000000FF800 000000000FF800000000000FF800000000000FF800000000000FF800000000000FF80000 0000000FF800000000000FF800000000000FF800000000000FF800000000000FF8000000 00000FF800000000000FF800000000000FF800000000000FF800000000000FF800000000 000FF800000000000FF800000000000FF800000000000FF800000000000FF80000000000 0FF800000000000FF800000000000FF800000000000FF800000000000FF8000000007FFF FFFF0000007FFFFFFF0000007FFFFFFF000031307DAF38> 84 D<00FFF0000003FFFF00 000F803F80000FC00FE0001FE007F0001FE007F0001FE003F8000FC003FC00078003FC00 000003FC00000003FC00000003FC00000003FC000000FFFC00001FFFFC0000FFE3FC0003 FC03FC000FF003FC001FC003FC003FC003FC007F8003FC007F8003FC00FF0003FC00FF00 03FC00FF0003FC00FF0007FC00FF0007FC007F800DFC003FC01DFE001FE078FFF007FFE0 7FF000FF803FF024207E9F27> 97 D<000FFF00007FFFC001FC01F003F003F007E007F8 0FE007F81FC007F83FC003F03FC001E07F8000007F8000007F800000FF800000FF800000 FF800000FF800000FF800000FF800000FF800000FF8000007F8000007F8000007F800000 3FC0001C3FC0001C1FC000380FE0003807E0007003F001E001FC07C0007FFF00000FF800 1E207D9F24> 99 D<0000000FC0000007FFC0000007FFC0000007FFC00000007FC00000 003FC00000003FC00000003FC00000003FC00000003FC00000003FC00000003FC0000000 3FC00000003FC00000003FC00000003FC00000003FC00000003FC00007F83FC0003FFF3F C000FE07BFC003F801FFC007E0007FC00FE0007FC01FC0003FC03FC0003FC03FC0003FC0 7F80003FC07F80003FC07F80003FC0FF80003FC0FF80003FC0FF80003FC0FF80003FC0FF 80003FC0FF80003FC0FF80003FC0FF80003FC07F80003FC07F80003FC07F80003FC03FC0 003FC03FC0003FC01FC0003FC00FE0007FC007E000FFC003F003FFE001FC0F3FFE007FFE 3FFE000FF03FFE27327DB12D> I<000FFC00007FFF8001FC0FC003F003E007E001F00FE0 01F81FC000FC3FC000FE3FC000FE7F80007E7F80007F7F80007FFF80007FFF80007FFFFF FFFFFFFFFFFFFF800000FF800000FF800000FF8000007F8000007F8000007F8000003FC0 00071FC000071FC0000E0FE0000E07F0001C03F8007800FE03E0003FFFC00007FE002020 7E9F25> I<0001FE00000FFF80001FC3C0007F07E000FE0FF001FE0FF001FC0FF003FC0F F003FC07E003FC018003FC000003FC000003FC000003FC000003FC000003FC000003FC00 0003FC0000FFFFFC00FFFFFC00FFFFFC0003FC000003FC000003FC000003FC000003FC00 0003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC00 0003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC00 0003FC000003FC000003FC00007FFFF0007FFFF0007FFFF0001C327EB119> I<01F80000 00FFF8000000FFF8000000FFF80000000FF800000007F800000007F800000007F8000000 07F800000007F800000007F800000007F800000007F800000007F800000007F800000007 F800000007F800000007F800000007F807F80007F83FFE0007F8783F0007F8C03F8007F9 801FC007FB001FC007FE001FE007FC001FE007FC001FE007FC001FE007F8001FE007F800 1FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001F E007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE0 07F8001FE007F8001FE007F8001FE0FFFFC3FFFFFFFFC3FFFFFFFFC3FFFF28327DB12D> 104 D<03C00007E0000FF0001FF8001FF8001FF8001FF8000FF00007E00003C000000000 00000000000000000000000000000000000000000000000001F8007FF8007FF8007FF800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F80007F800 07F800FFFF80FFFF80FFFF8011337DB217> I<03F007F8001FE000FFF03FFE00FFF800FF F0783F01E0FC00FFF0C03F8300FE000FF1801FC6007F0007F3001FCC007F0007F6001FF8 007F8007FC001FF0007F8007FC001FF0007F8007FC001FF0007F8007F8001FE0007F8007 F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0 007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007 F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0 007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F8007F8001FE0007F80FF FFC3FFFF0FFFFCFFFFC3FFFF0FFFFCFFFFC3FFFF0FFFFC3E207D9F43> 109 D<03F007F800FFF03FFE00FFF0783F00FFF0C03F800FF1801FC007F3001FC007F6001FE0 07FC001FE007FC001FE007FC001FE007F8001FE007F8001FE007F8001FE007F8001FE007 F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8 001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F800 1FE0FFFFC3FFFFFFFFC3FFFFFFFFC3FFFF28207D9F2D> I<0007FC0000007FFFC00001FC 07F00003F001F80007E000FC000FC0007E001FC0007F003FC0007F803F80003F807F8000 3FC07F80003FC07F80003FC0FF80003FE0FF80003FE0FF80003FE0FF80003FE0FF80003F E0FF80003FE0FF80003FE0FF80003FE07F80003FC07F80003FC07F80003FC03FC0007F80 3FC0007F801FC0007F000FE000FE0007E000FC0003F803F80001FE0FF000007FFFC00000 07FC000023207E9F28> I<01F83FE000FFF8FFFC00FFFBE07F00FFFF003F8007FE001FC0 07FC000FE007F8000FF007F80007F807F80007F807F80007FC07F80003FC07F80003FC07 F80003FE07F80003FE07F80003FE07F80003FE07F80003FE07F80003FE07F80003FE07F8 0003FE07F80003FC07F80007FC07F80007FC07F80007F807F80007F807F8000FF007FC00 0FE007FE001FC007FF003F8007FBC0FE0007F8FFF80007F83FC00007F800000007F80000 0007F800000007F800000007F800000007F800000007F800000007F800000007F8000000 07F800000007F8000000FFFFC00000FFFFC00000FFFFC00000272E7E9F2D> I<03F03F00 FFF07FC0FFF1C3E0FFF187E00FF30FF007F60FF007F60FF007FC07E007FC03C007FC0000 07FC000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F80000 07F8000007F8000007F8000007F8000007F8000007F8000007F8000007F8000007F80000 07F80000FFFFE000FFFFE000FFFFE0001C207E9F21> 114 D<01FF860007FFFE001F00FE 003C003E0078001E0078000E00F8000E00F8000E00F8000E00FC000000FF800000FFFC00 007FFFC0003FFFF0003FFFF8001FFFFC0007FFFE0001FFFF00003FFF000000FF8000003F 8060001F80E0000F80E0000F80F0000F80F0000F00F8000F00FC001E00FE001C00FF8078 00F3FFF000C07F800019207D9F20> I<001C0000001C0000001C0000001C0000001C0000 003C0000003C0000003C0000007C0000007C000000FC000001FC000003FC000007FC0000 1FFFFE00FFFFFE00FFFFFE0003FC000003FC000003FC000003FC000003FC000003FC0000 03FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC000003FC0000 03FC000003FC038003FC038003FC038003FC038003FC038003FC038003FC038001FC0380 01FC070000FE0700007F0E00003FFC000007F000192E7FAD1F> I<01F80007E0FFF803FF E0FFF803FFE0FFF803FFE00FF8003FE007F8001FE007F8001FE007F8001FE007F8001FE0 07F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007 F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8001FE007F8 001FE007F8003FE007F8003FE003F8007FE003F8007FE001FC00DFF000FE039FFF007FFF 1FFF000FFC1FFF28207D9F2D> I<7FFF807FFC7FFF807FFC7FFF807FFC03FC000F0001FE 001E0000FF003C0000FF803800007FC07800003FC0F000001FE1E000000FF3C000000FFF 80000007FF00000003FE00000001FE00000000FF00000000FF80000000FFC0000001FFC0 000003DFE00000078FF00000078FF800000F07FC00001E03FE00003C01FE00007800FF00 00F000FF8001E0007FC003E0003FE0FFFC01FFFFFFFC01FFFFFFFC01FFFF28207F9F2B> 120 D I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmsy10 10 2 /Ft 2 122 df<0300030003000300C30CE31C73381FE0078007801FE07338E31CC30C03 000300030003000E127D9215> 3 D<020007000700070007000700070002000200020072 70FFF8727002000200070007000700070007000700070007000700070007000700070007 000700070007000200020002000200020002000D267E9C12> 121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmr12 14.4 12 /Fu 12 118 df 78 D<00FE010003FF83000F81E3001E0037003C001F0038000F0078000700700007 00F0000300F0000300F0000300F0000100F8000100F8000100FC0000007E0000007F0000 003FE000001FFE00000FFFE00007FFF80003FFFC00007FFE000007FF0000007F0000001F 8000000F80000007C0000007C0800003C0800003C0800003C0800003C0C00003C0C00003 80C0000380E0000780F0000700F8000E00EE001C00C3C07800C1FFF000803FC0001A2B7D A921> 83 D<03FC00000C070000100380003C01C0003E01E0003E00F0001C00F0000800 F0000000F0000000F0000000F000007FF00003E0F0000F80F0001E00F0003C00F0007C00 F0007800F040F800F040F800F040F800F040F801F0407C01F0403C0278801E0C7F8007F0 1E001A1A7E991D> 97 D<0F000000FF000000FF0000001F0000000F0000000F0000000F 0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F 0000000F07E0000F1838000F600E000F8007000F8007800F0003C00F0003C00F0001E00F 0001E00F0001F00F0001F00F0001F00F0001F00F0001F00F0001F00F0001F00F0001E00F 0001E00F0003E00F0003C00F0003800F8007800E800F000E401C000C303800080FC0001C 2A7EA921> I<00FC000387800701C00E01E01C00E03C00F03C00F0780078780078F80078 F80078FFFFF8F80000F80000F80000F80000F800007800007800003C00083C00081E0010 0E002007004001C180007E00151A7E991A> 101 D<00000F0001FC3080070743800E03C3 801E03C1003C01E0003C01E0007C01F0007C01F0007C01F0007C01F0007C01F0003C01E0 003C01E0001E03C0000E0380001707000011FC0000300000003000000030000000300000 00180000001FFF80000FFFF00007FFF80018007C0030001E0070000E0060000700E00007 00E0000700E0000700E000070070000E0070000E0038001C001C0038000781E00000FF00 0019287E9A1D> 103 D<1E003F003F003F003F001E000000000000000000000000000000 000000000F00FF00FF001F000F000F000F000F000F000F000F000F000F000F000F000F00 0F000F000F000F000F000F000F000F00FFF0FFF00C297EA811> 105 D<0F000000FF000000FF0000001F0000000F0000000F0000000F0000000F0000000F0000 000F0000000F0000000F0000000F0000000F0000000F0000000F0000000F00FFC00F00FF C00F007E000F0030000F0060000F0040000F0080000F0300000F0400000F0C00000F1E00 000F3E00000F5F00000F8F00000F0780000F07C0000F03C0000F03E0000F01F0000F00F0 000F00F8000F0078000F007C000F007E00FFF1FFE0FFF1FFE01B2A7EA91F> 107 D<0F07F007F000FF1838183800FF201C201C001F400E400E000F400F400F000F800F800F 000F800F800F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F 000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F 000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F 00FFF0FFF0FFF0FFF0FFF0FFF02C1A7E9931> 109 D<0F07F000FF183800FF201C001F40 0E000F400F000F800F000F800F000F000F000F000F000F000F000F000F000F000F000F00 0F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F00 0F000F000F000F000F00FFF0FFF0FFF0FFF01C1A7E9921> I<007E0003C3C00700E00E00 701C00383C003C3C003C78001E78001EF8001FF8001FF8001FF8001FF8001FF8001FF800 1FF8001F78001E78001E3C003C3C003C1C00380E00700700E003C3C0007E00181A7E991D > I<0F000F00FF00FF00FF00FF001F001F000F000F000F000F000F000F000F000F000F00 0F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F000F00 0F000F000F000F000F000F001F000F001F0007002F0003804F8001C08FF0007F0FF01C1A 7E9921> 117 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmr17 20.74 23 /Fv 23 120 df 45 D<000FF80000007FFF000001F01F800003C007E000070003F0000C0001F8001C0000F800 180000FC003C0000FC003F0000FE003F00007E003F80007E003F00007E001F0000FE000C 0000FE00000000FC00000000FC00000000FC00000001F800000001F000000001E0000000 03E000000007800000000F000000001C00000000F00000003FF8000000001F0000000007 8000000003E000000001F000000000F800000000FC000000007E000000007E000000007F 000000003F000000003F800000003F801000003F807C00003F80FE00003F80FE00003F80 FE00003F80FE00003F80FC00003F007000007F006000007F006000007E00300000FC0018 0000FC001C0001F800060003F000038007E00001F01F8000007FFE0000000FF800002139 7DB727> 51 D<000000180000000000003C0000000000003C0000000000003C00000000 00007E0000000000007E0000000000007E000000000000FF000000000000FF0000000000 00FF0000000000019F8000000000019F8000000000019F8000000000030FC00000000003 0FC000000000070FE0000000000607E0000000000607E0000000000E07F0000000000C03 F0000000000C03F0000000001803F8000000001801F8000000001801F8000000003000FC 000000003000FC000000003000FC0000000060007E0000000060007E0000000060007E00 000000C0003F00000000C0003F00000001C0003F8000000180001F8000000180001F8000 000380001FC000000300000FC000000300000FC0000007FFFFFFE0000007FFFFFFE00000 06000007E000000C000003F000000C000003F000000C000003F0000018000001F8000018 000001F8000038000001FC000030000000FC000030000000FC000070000000FE00006000 00007E0000600000007E0000C00000007F0000C00000003F0001C00000003F0001E00000 003F8003E00000003F800FF00000007FC0FFFE000007FFFFFFFE000007FFFF383C7EBB3C > 65 D 73 D<003F80000001C0F0000003003C000004001E00000C000F000018 000780001C0007C0003E0003C0003F0003E0003F0003E0003F0003E0001E0003E0000000 03E000000003E000000003E00000003FE000000FF3E000007E03E00001F803E00003E003 E0000FC003E0001F8003E0003F0003E0003E0003E0007E0003E0007E0003E060FC0003E0 60FC0003E060FC0003E060FC0007E060FC0007E0607C000BE0607E000BE0603E0011F0C0 1F0060F0C007C1807F8000FE003E0023257CA427> 97 D<03E0000000FFE0000000FFE0 00000007E000000003E000000003E000000003E000000003E000000003E000000003E000 000003E000000003E000000003E000000003E000000003E000000003E000000003E00000 0003E000000003E000000003E000000003E000000003E000000003E000000003E03FC000 03E0E0780003E3001C0003E6000F0003E800078003F80003C003F00001E003E00001F003 E00000F003E00000F803E00000F803E00000FC03E000007C03E000007C03E000007E03E0 00007E03E000007E03E000007E03E000007E03E000007E03E000007E03E000007E03E000 007E03E000007C03E000007C03E00000FC03E00000F803E00000F803E00001F003E00001 E003F00003E003D80003C003C80007800384000E000383001C000381C0F00003003F8000 273C7EBB2C> I<0007F800003C0E0000F0018001E000C003C00060078000300F0000701F 0000F81F0001F83E0001F83E0001F87E0000F07C0000007C000000FC000000FC000000FC 000000FC000000FC000000FC000000FC000000FC000000FC0000007C0000007C0000007E 0000003E0000003E00000C1F00000C1F0000180F8000180780003003C0006001E000C000 F00180003C0E000007F8001E257DA423> I<0000000F80000003FF80000003FF80000000 1F800000000F800000000F800000000F800000000F800000000F800000000F800000000F 800000000F800000000F800000000F800000000F800000000F800000000F800000000F80 0000000F800000000F800000000F800000000F800000000F800003F80F80001E070F8000 70018F8000E0004F8003C0002F800780001F800F80001F800F00000F801F00000F803E00 000F803E00000F807E00000F807C00000F807C00000F80FC00000F80FC00000F80FC0000 0F80FC00000F80FC00000F80FC00000F80FC00000F80FC00000F80FC00000F807C00000F 807C00000F807E00000F803E00000F803E00000F801E00000F801F00000F800F00001F80 0780003F8003C0006F8001E000CF800070018FC0003C0E0FFE0007F00FFE273C7DBB2C> I<0007F800003C1E0000F0078001C003C003C001E0078000F00F0000F81F0000781E0000 7C3E00007C3E00007C7E00003E7C00003E7C00003EFC00003EFC00003EFFFFFFFEFC0000 00FC000000FC000000FC000000FC000000FC0000007C0000007C0000007E0000003E0000 003E0000061F0000060F00000C0F80000C0780001803C0003000E00060007000C0001E07 000003FC001F257EA423> I<0000FC0000078300000E0380001C07C0003C0FC000780FC0 00F80FC000F8078000F0000001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0000001F0000001F0000001F00000FFFFFC00 FFFFFC0001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0000001F0000003F800007FFFE0007FFFE000 1A3C7FBB18> I<00000007C0000FE01860003838207000F01E40F001E00F80F003C00780 6007C007C0000F8003E0000F8003E0000F8003E0001F8003F0001F8003F0001F8003F000 1F8003F0001F8003F0001F8003F0000F8003E0000F8003E0000F8003E00007C007C00003 C007800001E00F000002F01E00000238380000060FE00000040000000004000000000C00 0000000C000000000E000000000E000000000700000000078000000003FFFF000003FFFF F00001FFFFFC0000FFFFFE00078000FF000E00001F801C000007C038000003C078000003 C070000001E0F0000001E0F0000001E0F0000001E0F0000001E0F0000001E078000003C0 38000003803C000007801E00000F000700001C0003C0007800007803C000000FFE000024 387EA527> I<03E0000000FFE0000000FFE000000007E000000003E000000003E0000000 03E000000003E000000003E000000003E000000003E000000003E000000003E000000003 E000000003E000000003E000000003E000000003E000000003E000000003E000000003E0 00000003E000000003E000000003E01FE00003E0607C0003E0801E0003E3000F0003E400 0F8003E4000F8003E800078003E80007C003F00007C003F00007C003E00007C003E00007 C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C0 03E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003 E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E0 0007C007F0000FE0FFFF81FFFFFFFF81FFFF283C7EBB2C> I<07000F801FC01FC01FC00F 800700000000000000000000000000000000000000000000000000000007C0FFC0FFC00F C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007 C007C007C007C007C007C007C007C007C007C007C007C007C00FE0FFFEFFFE0F397DB815 > I<07C0FFC0FFC00FC007C007C007C007C007C007C007C007C007C007C007C007C007C0 07C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C0 07C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C007C0 07C007C007C007C00FE0FFFEFFFE0F3C7DBB15> 108 D<03E01FE0003FC000FFE0607C00 C0F800FFE0801E01003C0007E3000F06001E0003E4000F88001F0003E4000F88001F0003 E8000790000F0003E80007D0000F8003F00007E0000F8003F00007E0000F8003E00007C0 000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003 E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0 000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003 E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0 000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003E00007C0000F8003 E00007C0000F8007F0000FE0001FC0FFFF81FFFF03FFFEFFFF81FFFF03FFFE3F257EA443 > I<03E01FE000FFE0607C00FFE0801E0007E3000F0003E4000F8003E4000F8003E80007 8003E80007C003F00007C003F00007C003E00007C003E00007C003E00007C003E00007C0 03E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003 E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E0 0007C003E00007C003E00007C003E00007C003E00007C003E00007C007F0000FE0FFFF81 FFFFFFFF81FFFF28257EA42C> I<0007FC0000001C070000007001C00001E000F00003C0 0078000780003C000F00001E001F00001F001E00000F003E00000F803E00000F807C0000 07C07C000007C07C000007C0FC000007E0FC000007E0FC000007E0FC000007E0FC000007 E0FC000007E0FC000007E0FC000007E0FC000007E07C000007C07C000007C07E00000FC0 3E00000F803E00000F801E00000F001F00001F000F00001E000780003C0003C000780001 E000F000007001C000001C0700000007FC000023257EA427> I<03E03FC000FFE0E07800 FFE3001C0007E6000F0003E800078003F80003C003F00003E003E00001F003E00001F003 E00000F803E00000F803E00000FC03E00000FC03E000007C03E000007E03E000007E03E0 00007E03E000007E03E000007E03E000007E03E000007E03E000007E03E000007E03E000 007C03E00000FC03E00000FC03E00000F803E00001F803E00001F003E00003E003F00003 E003F80007C003E8000F8003E4000E0003E3003C0003E1C0F00003E03F800003E0000000 03E000000003E000000003E000000003E000000003E000000003E000000003E000000003 E000000003E000000003E000000003E000000003E000000003E000000007F0000000FFFF 800000FFFF80000027367EA42C> I<03E03E00FFE0C300FFE1078007E20FC003E40FC003 E80FC003E8078003E8030003F0000003F0000003F0000003E0000003E0000003E0000003 E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003 E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E0000003 E0000003E0000007F00000FFFFC000FFFFC0001A257EA41E> 114 D<00FF02000700C6000C002E0010001E0030001E0060000E0060000E00E0000600E00006 00E0000600F0000600F8000600FC0000007F0000003FF000003FFF80000FFFE00007FFF0 0001FFFC00003FFE000001FE0000003F00C0001F00C0000F80C0000780E0000380E00003 80E0000380E0000380F0000300F0000300F8000700F8000600E4000C00E2001800C18070 00807F800019257DA41F> I<003000000030000000300000003000000030000000300000 0070000000700000007000000070000000F0000000F0000001F0000001F0000003F00000 07F000001FFFFE00FFFFFE0001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0000001F0000001F0000001F0000001F00000 01F0000001F0000001F0000001F0000001F0018001F0018001F0018001F0018001F00180 01F0018001F0018001F0018001F0018000F0010000F8030000F8030000780200003C0400 000E08000003F00019357FB41E> I<03E00007C0FFE001FFC0FFE001FFC007E0000FC003 E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E0 0007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E000 07C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007C003E00007 C003E00007C003E0000FC003E0000FC003E0000FC001E00017C001E00017C000F00027C0 00F00047C000780087E0001E0307FF0003FC07FF28257EA42C> I 119 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 300dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop Fv 352 475 a(A) p 438 475 a(lo) n(w) n(er) p 643 475 a(b) r(ound) p 887 475 a(on) p 996 475 a(the) p 1132 475 a(sp) r(ectral) p 1427 475 a(gap) 193 579 y(of) p 282 579 a(the) p 417 579 a(3-dimensional) p 917 579 a(sto) r(c) n (hastic) p 1280 579 a(Ising) p 1470 579 a(mo) r(dels) p Fu 697 727 a(Nobuaki) p 932 727 a(Sugimine) p Ft 1185 705 a(\003) o(y) p Fs 0 1009 a(1) p 121 1009 a(In) n(tro) r(duction) p Fr 73 1119 a(Let) p 159 1119 a(us) p 221 1119 a(consider) p 411 1119 a(the) p 494 1119 a(Glaub) q(er) p 682 1119 a(dynamics) p 898 1119 a(at) p 957 1119 a(lo) o(w) p 1044 1119 a(temp) q(erature) p 1321 1119 a(\(large) p Fq 1459 1119 a(\014) p 1503 1119 a(>) p Fr 1555 1119 a(0\)) p 1614 1119 a(whic) o(h) p 1753 1119 a(ev) o(olv) o(es) 0 1179 y(on) p 69 1179 a(a) p 111 1179 a(cub) q(e) p 227 1179 a(\003) p Fp 261 1186 a(d) p Fr 281 1179 a(\() p Fq(L) p Fr(\)) p 368 1179 a(=) p 422 1179 a(\() p Fo(\000) p Fq(L;) p 535 1179 a(L) p Fr(]) p Fp 582 1161 a(d) p Fo 614 1179 a(\\) p Fn 659 1179 a(Z) p Fp 695 1161 a(d) p Fr 730 1179 a(\() p Fq(L) p Fo 798 1179 a(2) p Fn 847 1179 a(N) p Fr(\)) p 919 1179 a(whose) p 1065 1179 a(side-length) p 1313 1179 a(is) p 1363 1179 a(2) p Fq(L) p Fr 1438 1179 a(with) p 1550 1179 a(a) p 1592 1179 a(b) q(oundary) p 1813 1179 a(con-) 0 1239 y(dition) p Fq 141 1239 a(!) p Fr 173 1239 a(.) p 208 1239 a(By) p 284 1239 a(gap) q(\(\003) p Fp 413 1246 a(d) p Fr 433 1239 a(\() p Fq(L) p Fr(\)) p Fq(;) p 526 1239 a(!) p Fr 558 1239 a(\),) p 607 1239 a(w) o(e) p 679 1239 a(will) p 771 1239 a(denote) p 927 1239 a(the) p 1011 1239 a(sp) q(ectral) p 1194 1239 a(gap) p 1286 1239 a(corresp) q(onding) p 1599 1239 a(to) p 1659 1239 a(a) p 1699 1239 a(b) q(oundary) 0 1299 y(condition) p Fq 214 1299 a(!) p Fr 246 1299 a(.) p 282 1299 a(Esp) q(ecially) l(,) p 523 1299 a(By) p 600 1299 a(gap\(\003) p Fp 728 1306 a(d) p Fr 748 1299 a(\() p Fq(L) p Fr(\)) p Fq(;) p 841 1299 a(\036) p Fr(\)) p 906 1299 a(and) p 1001 1299 a(gap) q(\(\003) p Fp 1130 1306 a(d) p Fr 1150 1299 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 1243 1299 a(+\),) p 1329 1299 a(w) o(e) p 1401 1299 a(will) p 1494 1299 a(mean) p 1624 1299 a(sp) q(ectral) p 1807 1299 a(gaps) 0 1359 y(corresp) q(onding) p 315 1359 a(to) p 377 1359 a(free) p 473 1359 a(and) p 570 1359 a(+) p 626 1359 a(b) q(oundary) p 848 1359 a(conditions,) p 1097 1359 a(resp) q(ectiv) o(ely) l(.) p 1384 1359 a(L.) p 1446 1359 a(E.) p 1512 1359 a(Thomas) p 1701 1359 a(pro) o(v) o(ed) p 1862 1359 a(in) 0 1420 y([Tho,89) q(]) p 192 1420 a(that) 376 1521 y(gap\(\003) p Fp 504 1528 a(d) p Fr 525 1521 a(\() p Fq(L) p Fr(\)) p Fq(;) p 618 1521 a(\036) p Fr(\)) p Fo 679 1521 a(\024) p Fq 732 1521 a(B) p Fr 780 1521 a(exp) o(\() p Fo(\000) p Fq(\014) s(C) t(L) p Fp 1015 1500 a(d) p Fm(\000) p Fl(1) p Fr 1079 1521 a(\)) p 1147 1521 a(for) p 1221 1521 a(an) o(y) p Fq 1314 1521 a(L) p Fo 1361 1521 a(2) p Fn 1408 1521 a(N) p Fr 1802 1521 a(\(1.1\)) 0 1622 y(for) p 76 1622 a(an) o(y) p Fq 169 1622 a(d) p Fo 210 1622 a(\025) p Fr 264 1622 a(2) p 306 1622 a(and) p 401 1622 a(su\016cien) o(tly) p 647 1622 a(large) p Fq 767 1622 a(\014) p 813 1622 a(>) p Fr 866 1622 a(0,) p 922 1622 a(where) p Fq 1064 1622 a(B) p Fr 1119 1622 a(=) p Fq 1172 1622 a(B) p Fr 1212 1622 a(\() p Fq(\014) s(;) p 1284 1622 a(d) p Fr(\)) p Fq 1343 1622 a(>) p Fr 1396 1622 a(0) p 1438 1622 a(and) p Fq 1534 1622 a(C) p Fr 1588 1622 a(=) p Fq 1641 1622 a(C) p Fr 1680 1622 a(\() p Fq(\014) s(;) p 1752 1622 a(d) p Fr(\)) p Fq 1811 1622 a(>) p Fr 1864 1622 a(0.) 0 1682 y(F) l(or) p Fq 85 1682 a(d) p Fr 124 1682 a(=) p 176 1682 a(2) p 214 1682 a(and) p 306 1682 a(an) o(y) p Fq 396 1682 a(\014) p 440 1682 a(>) p 492 1682 a(\014) p Fp 520 1689 a(c) p Fr 537 1682 a(\(2\),) p 627 1682 a(it) p 673 1682 a(is) p 720 1682 a(kno) o(wn) p 872 1682 a(that) p 975 1682 a(the) p 1056 1682 a(sp) q(eed) p 1188 1682 a(at) p 1245 1682 a(whic) o(h) p 1382 1682 a(gap) q(\(\003) p Fl 1511 1689 a(2) p Fr 1531 1682 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 1624 1682 a(+\)) p 1694 1682 a(shrinks) p 1859 1682 a(to) 0 1742 y(zero) p 101 1742 a(as) p Fq 159 1742 a(L) p Fo 206 1742 a(\045) p 270 1742 a(1) p Fr 334 1742 a(is) p 381 1742 a(di\013eren) o(t) p 571 1742 a(from) p 685 1742 a(the) p 767 1742 a(one) p 854 1742 a(at) p 912 1742 a(whic) o(h) p 1049 1742 a(gap) q(\(\003) p Fl 1178 1749 a(2) p Fr 1198 1742 a(\() p Fq(L) p Fr(\)) p Fq(;) p 1291 1742 a(\036) p Fr(\)) p 1353 1742 a(do) q(es) p 1461 1742 a(\(see) p 1557 1742 a([Ma,94],) p 1744 1742 a([Ma,99]) 0 1802 y(and) p 96 1802 a([CGMS,96]\).) p 390 1802 a(In) p 452 1802 a(this) p 549 1802 a(pap) q(er,) p 701 1802 a(w) o(e) p 774 1802 a(con\014rm) p 952 1802 a(that) p 1059 1802 a(it) p 1109 1802 a(is) p 1160 1802 a(also) p 1259 1802 a(true) p 1363 1802 a(for) p Fq 1439 1802 a(d) p Fo 1481 1802 a(\025) p Fr 1536 1802 a(3) p 1578 1802 a(and) p 1674 1802 a(su\016cien) o(tly) 0 1863 y(large) p Fq 123 1863 a(\014) p 173 1863 a(>) p Fr 230 1863 a(0.) p 300 1863 a(In) p 364 1863 a(fact,) p 478 1863 a(w) o(e) p 554 1863 a(pro) o(v) o(e) p 688 1863 a(that) p 797 1863 a(for) p 875 1863 a(su\016cien) o(tly) p 1123 1863 a(large) p Fq 1246 1863 a(\014) p 1296 1863 a(>) p Fr 1353 1863 a(0,) p 1412 1863 a(some) p Fq 1537 1863 a(B) p 1596 1863 a(>) p Fr 1654 1863 a(0) p 1698 1863 a(and) p 1796 1863 a(some) p Fq 0 1923 a(C) p 52 1923 a(>) p Fr 104 1923 a(0,) 283 2024 y(gap) q(\(\003) p Fp 412 2031 a(d) p Fr 432 2024 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 525 2024 a(+\)) p Fo 596 2024 a(\025) p Fq 648 2024 a(B) p Fr 696 2024 a(exp\() p Fo(\000) p Fq(\014) s(C) t(L) p Fp 932 2003 a(d) p Fm(\000) p Fl(2) p Fr 996 2024 a(\(log) p Fq 1086 2024 a(L) p Fr(\)) p Fl 1138 2003 a(2) p Fr 1158 2024 a(\)) p 1226 2024 a(for) p 1300 2024 a(an) o(y) p Fq 1392 2024 a(L) p Fo 1439 2024 a(2) p Fn 1486 2024 a(N) p Fq(:) p Fr 1802 2024 a(\(1.2\)) 0 2125 y(F) l(or) p 87 2125 a(eac) o(h) p Fq 197 2125 a(\016) p Fo 234 2125 a(2) p Fr 281 2125 a([0) p Fq(;) p Fr 341 2125 a(1],) p 409 2125 a(w) o(e) p 481 2125 a(will) p 573 2125 a(consider) p 763 2125 a(the) p 847 2125 a(b) q(oundary) p 1066 2125 a(condition) p Fq 1280 2125 a(\021) p Fp 1304 2132 a(\016) p Fr 1340 2125 a(whic) o(h) p 1479 2125 a(is) p 1528 2125 a(de\014ned) p 1696 2125 a(b) o(y) p Fq 296 2255 a(\021) p Fp 320 2262 a(\016) p Fr 339 2255 a(\() p Fq(x) p Fr(\)) p 419 2255 a(=) p Fk 471 2185 a(\032) p Fr 529 2225 a(+1) p 633 2225 a(if) p Fq 677 2225 a(x) p Fp 705 2207 a(d) p Fr 739 2225 a(=) p Fo 791 2225 a(\000) p Fq(L) p Fr 879 2225 a(and) p Fo 985 2225 a(\000) p Fq 1035 2225 a(\016) r(L) p 1105 2225 a(<) p 1157 2225 a(x) p Fp 1185 2207 a(i) p Fo 1213 2225 a(\024) p Fq 1265 2225 a(\016) r(L) p Fr 1338 2225 a(\() p Fq(i) p Fo 1388 2225 a(6) p Fr(=) p Fq 1439 2225 a(d) p Fr(\)) p Fq(;) p Fr 548 2285 a(0) p 633 2285 a(otherwise) p Fq 833 2285 a(:) p Fr 1802 2255 a(\(1.3\)) 0 2383 y(F) l(or) p Fq 87 2383 a(d) p Fr 127 2383 a(=) p 178 2383 a(3,) p 233 2383 a(w) o(e) p 304 2383 a(also) p 402 2383 a(pro) o(v) o(e) p 534 2383 a(that) p 639 2383 a(for) p 714 2383 a(su\016cien) o(tly) p 958 2383 a(large) p Fq 1077 2383 a(\014) p 1121 2383 a(>) p Fr 1173 2383 a(0,) p 1227 2383 a(some) p Fq 1349 2383 a(B) p 1403 2383 a(>) p Fr 1455 2383 a(0) p 1495 2383 a(and) p 1590 2383 a(some) p Fq 1712 2383 a(C) p 1765 2383 a(>) p Fr 1816 2383 a(0,) 300 2484 y(gap\(\003) p Fl 428 2491 a(3) p Fr 448 2484 a(\() p Fq(L) p Fr(\)) p Fq(;) p 541 2484 a(\021) p Fl 565 2491 a(1) p Fr 585 2484 a(\)) p Fo 618 2484 a(\025) p Fq 670 2484 a(B) p Fr 718 2484 a(exp\() p Fo(\000) p Fq(\014) s(C) t(L) p Fj 959 2450 a(5) p 957 2456 16 2 v 957 2477 a(3) p Fr 979 2484 a(\(log) p Fq 1070 2484 a(L) p Fr(\)) p Fl 1122 2463 a(2) p Fr 1142 2484 a(\)) p 1209 2484 a(for) p 1284 2484 a(an) o(y) p Fq 1376 2484 a(L) p Fo 1423 2484 a(2) p Fn 1470 2484 a(N) p Fq(;) p Fr 1802 2484 a(\(1.4\)) 0 2585 y(whic) o(h) p 141 2585 a(implies) p 309 2585 a(at) p 370 2585 a(least) p 486 2585 a(that) p 593 2585 a(the) p 679 2585 a(sp) q(eed) p 815 2585 a(at) p 876 2585 a(whic) o(h) p 1017 2585 a(gap) q(\(\003) p Fl 1146 2592 a(3) p Fr 1166 2585 a(\() p Fq(L) p Fr(\)) p Fq(;) p 1259 2585 a(\021) p Fl 1283 2592 a(1) p Fr 1303 2585 a(\)) p 1339 2585 a(shrinks) p 1508 2585 a(to) p 1570 2585 a(zero) p 1674 2585 a(as) p Fq 1736 2585 a(L) p Fo 1786 2585 a(\045) p 1852 2585 a(1) p Fr 0 2645 a(is) p 49 2645 a(di\013eren) o(t) p 241 2645 a(from) p 355 2645 a(the) p 439 2645 a(one) p 528 2645 a(at) p 587 2645 a(whic) o(h) p 726 2645 a(gap) q(\(\003) p Fl 855 2652 a(3) p Fr 875 2645 a(\() p Fq(L) p Fr(\)) p Fq(;) p 968 2645 a(\036) p Fr(\)) p 1031 2645 a(do) q(es,) p 1155 2645 a(as) p 1214 2645 a(w) o(as) p 1307 2645 a(exp) q(ected) p 1510 2645 a(from) p 1625 2645 a(the) p 1709 2645 a(result) p 1844 2645 a(for) p 0 2677 761 2 v Fi 56 2708 a(\003) p Fh 75 2723 a(Division) p 239 2723 a(of) p 287 2723 a(Information) p 517 2723 a(and) p 600 2723 a(Media) p 727 2723 a(Science,) p 886 2723 a(Graduate) p 1072 2723 a(Sc) o(ho) q(ol) p 1205 2723 a(of) p 1254 2723 a(Science) p 1401 2723 a(and) p 1484 2723 a(T) m(ec) o(hnology) m(,) p 1712 2723 a(Kob) q(e) p 1823 2723 a(Uni-) 0 2772 y(v) o(ersit) o(y) m(,) p 142 2772 a(Rokk) o(o) p 271 2772 a(Kob) q(e) p 380 2772 a(657-8501,) p 565 2772 a(Japan) p Fi 57 2808 a(y) p Fh 75 2823 a(E-mail:) p 225 2823 a(sugimine@math.k) o(o) o(b) q(e-u.ac.jp) p Fr 939 2947 a(1) p 90 rotate dyy eop %%Page: 2 2 2 1 bop Fq 0 274 a(d) p Fr 42 274 a(=) p 96 274 a(2) p 139 274 a(\(see) p 238 274 a([Ma,94]\).) p 456 274 a(The) p 557 274 a(pro) q(of) p 686 274 a(of) p 743 274 a(\(1.2\)) p 862 274 a(and) p 958 274 a(\(1.4\)) p 1076 274 a(go) q(es) p 1185 274 a(along) p 1317 274 a(the) p 1402 274 a(line) p 1496 274 a(of) p 1553 274 a([Ma,94],) p 1743 274 a(but) p 1834 274 a(the) 0 334 y(dimensionalit) o(y) p 325 334 a(comes) p 469 334 a(in,) p 539 334 a(and) p 634 334 a(w) o(e) p 705 334 a(ha) o(v) o(e) p 817 334 a(to) p 877 334 a(in) o(tro) q(duce) p 1093 334 a(some) p 1215 334 a(new) p 1315 334 a(geometrical) p 1575 334 a(lemmas) p 1751 334 a(b) q(esides) 0 394 y(estimates) p 215 394 a(giv) o(en) p 342 394 a(in) p 399 394 a([D,72].) p Fg 0 484 a(Organization) p 340 484 a(of) p 409 484 a(the) p 512 484 a(pap) r(er.) p Fr 704 484 a(In) p 770 484 a(Section) p 945 484 a(1,) p 1006 484 a(w) o(e) p 1082 484 a(will) p 1179 484 a(in) o(tro) q(duce) p 1401 484 a(our) p 1493 484 a(results) p 1653 484 a(and) p 1752 484 a(k) o(ey) p 1845 484 a(in-) 0 544 y(gredien) o(ts) p 213 544 a(of) p 274 544 a(cluster) p 438 544 a(expansion) p 670 544 a(and) p 770 544 a(the) p 860 544 a(notion) p 1017 544 a(of) p 1079 544 a(standard) p 1288 544 a(w) o(alls.) p 1445 544 a(In) p 1511 544 a(Section) p 1688 544 a(2,) p 1749 544 a(w) o(e) p 1826 544 a(will) 0 604 y(in) o(tro) q(duce) p 220 604 a(Prop) q(ositions) p 506 604 a(2.1) p 588 604 a(and) p 687 604 a(2.2) p 769 604 a(and) p 867 604 a(sk) o(etc) o(h) p 1019 604 a(the) p 1107 604 a(pro) q(of) p 1238 604 a(of) p 1297 604 a(our) p 1387 604 a(results) p 1546 604 a(along) p 1679 604 a(the) p 1767 604 a(line) p 1863 604 a(of) 0 664 y([Ma,94].) p 204 664 a(In) p 269 664 a(Section) p 443 664 a(3,) p 502 664 a(w) o(e) p 577 664 a(will) p 673 664 a(in) o(tro) q(duce) p 893 664 a(a) p 937 664 a(lemma) p 1098 664 a(ab) q(out) p 1241 664 a(cluster) p 1402 664 a(expansion) p 1632 664 a(and) p 1731 664 a(giv) o(e) p 1834 664 a(the) 0 724 y(pro) q(of) p 128 724 a(of) p 184 724 a(Prop) q(osition) p 447 724 a(2.1.) p 547 724 a(In) p 608 724 a(Section) p 780 724 a(4,) p 835 724 a(w) o(e) p 907 724 a(will) p 1000 724 a(giv) o(e) p 1101 724 a(the) p 1185 724 a(pro) q(of) p 1313 724 a(of) p 1369 724 a(Prop) q(osition) p 1632 724 a(2.2.) p 1732 724 a(Because) 0 785 y(of) p 53 785 a(the) p 134 785 a(b) q(oundary) p 351 785 a(condition) p Fq 563 785 a(\021) p Fl 587 792 a(1) p Fr 606 785 a(,) p 634 785 a(the) p 715 785 a(standard) p 916 785 a(w) o(all) p 1015 785 a(whic) o(h) p 1152 785 a(includes) p 1337 785 a(m) o(uc) o(h) p 1464 785 a(more) p 1583 785 a(b) q(oundary) p 1800 785 a(faces) 0 845 y(than) p 114 845 a(in) o(terior) p 287 845 a(faces) p 405 845 a(has) p 492 845 a(less) p 583 845 a(energy) p 739 845 a(than) p 853 845 a(w) o(e) p 925 845 a(exp) q(ect) p 1080 845 a(from) p 1196 845 a(the) p 1280 845 a(size) p 1373 845 a(of) p 1429 845 a(it.) p 1497 845 a(F) l(or) p 1585 845 a(this) p 1681 845 a(reason,) p 1847 845 a(w) o(e) 0 905 y(decomp) q(ose) p 242 905 a(suc) o(h) p 348 905 a(a) p 386 905 a(standard) p 586 905 a(w) o(all) p 684 905 a(in) o(to) p 779 905 a(pieces) p 917 905 a(whic) o(h) p 1053 905 a(do) p 1117 905 a(not) p 1200 905 a(b) q(elong) p 1352 905 a(the) p 1433 905 a(b) q(oundary) p 1649 905 a(of) p Fq 1701 905 a(Q) p Fr(\(\003) p Fl 1793 912 a(3) p Fr 1812 905 a(\() p Fq(L) p Fr(\)\)) 0 965 y(\(see) p 97 965 a(\(4.38\)-\(4.46\)\).) p 416 965 a(W) l(e) p 500 965 a(analyze) p 674 965 a(the) p 757 965 a(energy-en) o(trop) o(y) p 1089 965 a(comp) q(etition) p 1358 965 a(coming) p 1525 965 a(from) p 1640 965 a(these) p 1764 965 a(pieces.) 0 1025 y(In) p 61 1025 a(App) q(endix,) p 298 1025 a(w) o(e) p 370 1025 a(will) p 462 1025 a(pro) o(v) o(e) p 593 1025 a(geometrical) p 854 1025 a(lemm) o(as) p 1030 1025 a(used) p 1141 1025 a(in) p 1198 1025 a(Section) p 1369 1025 a(4.) p Fg 0 1115 a(Basic) p 150 1115 a(De\014nitions.) p Fr 456 1115 a(F) l(or) p Fq 545 1115 a(x) p Fr 589 1115 a(=) p 643 1115 a(\() p Fq(x) p Fp 690 1096 a(i) p Fr 704 1115 a(\)) p Fp 723 1096 a(d) 723 1127 y(i) p Fl(=1) p Fo 798 1115 a(2) p Fn 847 1115 a(Z) p Fp 883 1096 a(d) p Fr 901 1115 a(,) p 932 1115 a(w) o(e) p 1005 1115 a(will) p 1099 1115 a(use) p 1184 1115 a(the) p Fq 1270 1115 a(l) p Fl 1285 1122 a(1) p Fr 1304 1115 a(-norm) p Fo 1449 1115 a(k) p Fq(x) p Fo(k) p Fl 1527 1122 a(1) p Fr 1562 1115 a(=) p Fk 1616 1077 a(P) p Fp 1669 1090 a(d) 1669 1129 y(i) p Fl(=1) p Fo 1737 1115 a(j) p Fq(x) p Fp 1779 1096 a(i) p Fo 1792 1115 a(j) p Fr 1824 1115 a(and) p Fq 0 1175 a(l) p Fm 15 1182 a(1) p Fr 52 1175 a(-norm) p Fo 200 1175 a(k) p Fq(x) p Fo(k) p Fm 278 1182 a(1) p Fr 337 1175 a(=) p 397 1175 a(max) p Fo 488 1175 a(fj) p Fq(x) p Fl 555 1157 a(1) p Fo 574 1175 a(j) p Fq(;) p Fo 610 1175 a(\001) p 632 1175 a(\001) p 654 1175 a(\001) p Fq 684 1175 a(;) p Fo 706 1175 a(j) p Fq(x) p Fp 748 1157 a(d) p Fo 768 1175 a(jg) p Fr(.) p 856 1175 a(Let) p Fq 948 1175 a(p) p Fr 995 1175 a(=) p 1055 1175 a(1) p 1100 1175 a(or) p Fq 1165 1175 a(p) p Fr 1211 1175 a(=) p Fo 1271 1175 a(1) p Fr(.) p 1370 1175 a(A) p 1428 1175 a(set) p 1509 1175 a(\003) p Fo 1565 1175 a(\032) p Fn 1625 1175 a(Z) p Fp 1661 1157 a(d) p Fr 1700 1175 a(is) p 1754 1175 a(said) p 1859 1175 a(to) 0 1235 y(b) q(e) p Fq 71 1235 a(l) p Fp 86 1242 a(p) p Fr 106 1235 a(-connected) p 354 1235 a(if) p 404 1235 a(for) p 484 1235 a(eac) o(h) p 598 1235 a(distinct) p Fq 779 1235 a(x;) p 829 1235 a(y) p Fo 877 1235 a(2) p Fr 932 1235 a(\003,) p 1002 1235 a(w) o(e) p 1079 1235 a(can) p 1173 1235 a(\014nd) p 1276 1235 a(some) p Fo 1403 1235 a(f) p Fq(z) p Fl 1451 1242 a(0) p Fq 1470 1235 a(;) p Fo 1492 1235 a(\001) p 1514 1235 a(\001) p 1536 1235 a(\001) p Fq 1567 1235 a(;) p 1589 1235 a(z) p Fp 1612 1242 a(m) p Fo 1644 1235 a(g) p 1691 1235 a(\032) p Fr 1752 1235 a(\003) p 1807 1235 a(with) p Fq 0 1295 a(z) p Fl 23 1302 a(0) p Fr 58 1295 a(=) p Fq 112 1295 a(x;) p 179 1295 a(z) p Fp 202 1302 a(m) p Fr 251 1295 a(=) p Fq 304 1295 a(y) p Fr 347 1295 a(and) p Fo 443 1295 a(k) p Fq(z) p Fp 491 1302 a(i) p Fo 517 1295 a(\000) p Fq 567 1295 a(z) p Fp 590 1302 a(i) p Fm(\000) p Fl(1) p Fo 649 1295 a(k) p Fp 674 1302 a(p) p Fr 710 1295 a(=) p 764 1295 a(1) p 805 1295 a(for) p 881 1295 a(all) p Fq 950 1295 a(i) p Fo 982 1295 a(\024) p Fq 1037 1295 a(m) p Fr(.) p 1118 1295 a(The) p 1220 1295 a(in) o(terior) p 1393 1295 a(and) p 1489 1295 a(exterior) p 1670 1295 a(b) q(oundaries) 0 1355 y(of) p 56 1355 a(a) p 96 1355 a(set) p 172 1355 a(\003) p Fo 220 1355 a(\032) p Fn 273 1355 a(Z) p Fp 309 1337 a(d) p Fr 342 1355 a(will) p 434 1355 a(b) q(e) p 501 1355 a(denoted) p 685 1355 a(resp) q(ectiv) o (ely) p 951 1355 a(b) o(y) p Fq 470 1460 a(@) p Fp 496 1467 a(in) p Fr 531 1460 a(\003) p 579 1460 a(=) p Fo 631 1460 a(f) p Fq(x) p Fo 697 1460 a(2) p Fr 744 1460 a(\003;) p Fo 800 1460 a(k) p Fq(x) p Fo 864 1460 a(\000) p Fq 914 1460 a(y) p Fo 940 1460 a(k) p Fl 965 1467 a(1) p Fr 998 1460 a(=) p 1049 1460 a(1) p 1090 1460 a(for) p 1165 1460 a(some) p Fq 1287 1460 a(y) p 1332 1460 a(=) p Fo 1326 1460 a(2) p Fr 1373 1460 a(\003) p Fo(g) p Fr 0 1565 a(and) p Fq 462 1626 a(@) p Fp 488 1633 a(ex) p Fr 526 1626 a(\003) p 574 1626 a(=) p Fo 626 1626 a(f) p Fq(y) p 696 1626 a(=) p Fo 690 1626 a(2) p Fr 737 1626 a(\003;) p Fo 793 1626 a(k) p Fq(x) p Fo 856 1626 a(\000) p Fq 906 1626 a(y) p Fo 932 1626 a(k) p Fl 957 1633 a(1) p Fr 990 1626 a(=) p 1042 1626 a(1) p 1083 1626 a(for) p 1157 1626 a(some) p Fq 1279 1626 a(x) p Fo 1321 1626 a(2) p Fr 1368 1626 a(\003) p Fo(g) p Fq(:) p Fr 0 1711 a(W) l(e) p 85 1711 a(will) p 179 1711 a(use) p 264 1711 a(the) p 349 1711 a(notation) p 546 1711 a(\003) p Fo 595 1711 a(\032\032) p Fn 689 1711 a(Z) p Fp 725 1692 a(d) p Fr 760 1711 a(to) p 821 1711 a(indicate) p 1006 1711 a(that) p 1113 1711 a(\003) p 1164 1711 a(is) p 1215 1711 a(a) p 1257 1711 a(non-empt) o(y) p 1502 1711 a(\014nite) p 1628 1711 a(subset) p 1778 1711 a(of) p Fn 1835 1711 a(Z) p Fp 1871 1692 a(d) p Fr 1889 1711 a(.) 0 1771 y(The) p 100 1771 a(n) o(um) o(b) q(er) p 278 1771 a(of) p 333 1771 a(p) q(oin) o(ts) p 480 1771 a(con) o(tained) p 701 1771 a(in) p 758 1771 a(a) p 798 1771 a(set) p 874 1771 a(\003) p Fo 922 1771 a(\032\032) p Fn 1013 1771 a(Z) p Fp 1050 1753 a(d) p Fr 1083 1771 a(will) p 1175 1771 a(b) q(e) p 1242 1771 a(denoted) p 1426 1771 a(b) o(y) p Fo 1494 1771 a(j) p Fr(\003) p Fo(j) p Fr(.) p Fq 73 1860 a(T) p 109 1860 a(he) p 175 1860 a(boundar) q(y) p 391 1860 a(conditions) p 632 1860 a(and) p 728 1860 a(the) p 811 1860 a(Gibbs) p 946 1860 a(states) p Fr(.) p 1111 1860 a(In) p 1171 1860 a(addition) p 1363 1860 a(to) p 1422 1860 a(the) p 1505 1860 a(usual) p 1632 1860 a(spin) p 1734 1860 a(con\014gu-) 0 1920 y(ration) p 144 1920 a(spaces) 319 2025 y(\012) p Fl 354 2032 a(\003) p Fr 395 2025 a(=) p Fo 446 2025 a(f) p Fq(\033) p Fr 515 2025 a(=) p 566 2025 a(\() p Fq(\033) p Fr 615 2025 a(\() p Fq(x) p Fr(\)\)) p Fp 700 2032 a(x) p Fm(2) p Fl(\003) p Fr 769 2025 a(;) p Fq 791 2025 a(\033) p Fr 821 2025 a(\() p Fq(x) p Fr(\)) p 900 2025 a(=) p 952 2025 a(+1) p 1031 2025 a(or) p Fo 1101 2025 a(\000) p Fr 1151 2025 a(1) p Fo(g) p Fr 1249 2025 a(for) p 1324 2025 a(an) o(y) p 1416 2025 a(\003) p Fo 1464 2025 a(\032) p Fn 1516 2025 a(Z) p Fp 1552 2005 a(d) p Fq 1570 2025 a(;) p Fr 0 2130 a(w) o(e) p 72 2130 a(will) p 164 2130 a(in) o(tro) q(duce) p 381 2130 a(a) p 421 2130 a(con\014guration) p 717 2130 a(space) p 847 2130 a(\012) p Fl 882 2137 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 956 2130 a(for) p 1030 2130 a(b) q(oundary) p 1250 2130 a(conditions) 445 2235 y(\012) p Fl 480 2242 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 551 2235 a(=) p Fo 603 2235 a(f) p Fq(!) p Fr 674 2235 a(=) p 726 2235 a(\() p Fq(!) p Fr 777 2235 a(\() p Fq(x) p Fr(\)\)) p Fp 862 2245 a(x) p Fm(2) p Ff(Z) p Fe 930 2235 a(d) p Fr 947 2235 a(;) p Fq 969 2235 a(!) p Fr 1001 2235 a(\() p Fq(x) p Fr(\)) p 1081 2235 a(=) p 1132 2235 a(+1) p Fq(;) p Fr 1233 2235 a(0) p 1274 2235 a(or) p Fo 1344 2235 a(\000) p Fr 1394 2235 a(1) p Fo(g) p Fq(:) p Fr 0 2340 a(W) l(e) p 84 2340 a(de\014ne) p Fq 225 2340 a(\036) p Fo 268 2340 a(2) p Fr 315 2340 a(\012) p Fl 350 2347 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 423 2340 a(and) p 518 2340 a(+) p Fo 570 2340 a(2) p Fr 617 2340 a(\012) p Fl 652 2347 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 725 2340 a(b) o(y) p Fq 144 2445 a(\036) p Fr(\() p Fq(x) p Fr(\)) p 252 2445 a(=) p 304 2445 a(0) p 377 2445 a(for) p 452 2445 a(all) p Fq 520 2445 a(x) p Fo 561 2445 a(2) p Fn 608 2445 a(Z) p Fp 644 2425 a(d) p Fr 710 2445 a(and) p 849 2445 a(+) p 898 2445 a(\() p Fq(x) p Fr(\)) p 977 2445 a(=) p 1029 2445 a(+1) p 1140 2445 a(for) p 1215 2445 a(all) p Fq 1282 2445 a(x) p Fo 1324 2445 a(2) p Fn 1371 2445 a(Z) p Fp 1407 2425 a(d) p Fq 1424 2445 a(;) p Fr 1495 2445 a(resp) q(ectiv) o(ely) p Fq 1745 2445 a(:) p Fr 0 2550 a(The) p 103 2550 a(set) p 182 2550 a(of) p 240 2550 a(all) p 310 2550 a(real) p 408 2550 a(functions) p 621 2550 a(on) p 691 2550 a(\012) p Fl 726 2557 a(\003) p Fr 772 2550 a(will) p 866 2550 a(b) q(e) p 935 2550 a(denoted) p 1122 2550 a(b) o(y) p Fo 1193 2550 a(C) p Fl 1219 2557 a(\003) p Fr 1245 2550 a(.) p 1289 2550 a(F) l(or) p 1379 2550 a(eac) o(h) p 1491 2550 a(\003) p Fo 1543 2550 a(\032\032) p Fn 1639 2550 a(Z) p Fp 1675 2532 a(d) p Fr 1711 2550 a(and) p 1809 2550 a(eac) o(h) p Fq 0 2610 a(!) p Fo 46 2610 a(2) p Fr 93 2610 a(\012) p Fl 128 2617 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 185 2610 a(,) p 215 2610 a(the) p Fq 299 2610 a(H) t(amil) q(tonian) p 602 2610 a(H) p Fp 646 2592 a(!) p Fl 642 2623 a(\003) p Fo 685 2610 a(2) p 732 2610 a(C) p Fl 758 2617 a(\003) p Fr 801 2610 a(is) p 850 2610 a(de\014ned) p 1018 2610 a(b) o(y) p Fq 401 2738 a(H) p Fp 445 2717 a(!) p Fl 441 2750 a(\003) p Fr 470 2738 a(\() p Fq(\033) p Fr 519 2738 a(\)) p 551 2738 a(=) p Fo 603 2738 a(\000) p Fr 647 2704 a(1) p 647 2726 25 2 v 647 2772 a(2) p Fk 735 2690 a(X) p Fp 723 2796 a(x;y) p Fm 771 2796 a(2) p Fl(\003) p Fm 689 2832 a(k) p Fp(x) p Fm(\000) p Fp(y) p Fm 772 2832 a(k) p Fj 790 2837 a(1) p Fl 808 2832 a(=1) p Fq 866 2738 a(\033) p Fr 896 2738 a(\() p Fq(x) p Fr(\)) p Fq(\033) p Fr 992 2738 a(\() p Fq(y) p Fr 1037 2738 a(\)) p Fo 1066 2738 a(\000) p Fk 1166 2690 a(X) p Fp 1127 2798 a(x) p Fm(2) p Fl(\003) p Fp(;) p 1211 2798 a(y) p 1233 2798 a(=) p Fm 1229 2798 a(2) p Fl(\003) p Fm 1120 2834 a(k) p Fp(x) p Fm(\000) p Fp(y) p Fm 1203 2834 a(k) p Fj 1221 2839 a(1) p Fl 1239 2834 a(=1) p Fq 1297 2738 a(\033) p Fr 1327 2738 a(\() p Fq(x) p Fr(\)) p Fq(!) p Fr 1425 2738 a(\() p Fq(y) p Fr 1470 2738 a(\)) p Fq(:) p Fr 939 2947 a(2) p 90 rotate dyy eop %%Page: 3 3 3 2 bop Fr 73 274 a(A) p Fq 122 274 a(Gibbs) p 253 274 a(state) p Fr 371 274 a(in) p 424 274 a(\003) p Fo 472 274 a(\032\032) p Fn 563 274 a(Z) p Fp 599 256 a(d) p Fr 628 274 a(with) p 735 274 a(a) p 771 274 a(b) q(oundary) p 986 274 a(condition) p Fq 1196 274 a(!) p Fo 1242 274 a(2) p Fr 1289 274 a(\012) p Fl 1324 281 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1393 274 a(and) p 1484 274 a(in) o(v) o(erse) p 1641 274 a(temp) q(erature) p Fq 0 334 a(\014) p 50 334 a(>) p Fr 107 334 a(0) p 151 334 a(is) p 204 334 a(the) p 291 334 a(probabilit) o(y) p 544 334 a(distribution) p Fq 813 334 a(\026) p Fp 842 316 a(!) p Fl 842 347 a(\003) p Fr 889 334 a(suc) o(h) p 1002 334 a(that) p 1111 334 a(the) p 1198 334 a(probabilit) o(y) p 1451 334 a(of) p 1510 334 a(eac) o(h) p 1623 334 a(con\014guration) p Fq 0 394 a(\033) p Fo 43 394 a(2) p Fr 90 394 a(\012) p Fl 125 401 a(\003) p Fr 168 394 a(is) p 217 394 a(giv) o(en) p 345 394 a(b) o(y) p Fq 634 474 a(\026) p Fp 663 453 a(!) p Fl 663 486 a(\003) p Fr 690 474 a(\() p Fo(f) p Fq(\033) p Fo 764 474 a(g) p Fr(\)) p 821 474 a(=) 894 440 y(1) p 878 463 57 2 v 878 508 a(Z) p Fp 908 491 a(!) p Fl 908 522 a(\003) p Fr 947 474 a(exp[) p Fo(\000) p Fq(\014) s(H) p Fp 1150 453 a(!) p Fl 1146 486 a(\003) p Fr 1174 474 a(\() p Fq(\033) p Fr 1223 474 a(\)]) p Fq(;) p Fr 0 582 a(where) p 141 582 a(Z) p Fp 171 564 a(!) p Fl 171 595 a(\003) p Fr 214 582 a(is) p 263 582 a(the) p 347 582 a(normalization) p 655 582 a(constan) o(t.) p Fq 73 671 a(S) s(tochastic) p 312 671 a(I) t(sing) p 444 671 a(model) q(s) p Fr(.) p 631 671 a(Let) p 714 671 a(\003) p Fo 762 671 a(\032\032) p Fn 853 671 a(Z) p Fp 889 653 a(d) p Fr 919 671 a(and) p 1010 671 a(let) p Fq 1076 671 a(!) p Fo 1122 671 a(2) p Fr 1169 671 a(\012) p Fl 1204 678 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1262 671 a(.) p 1295 671 a(The) p 1392 671 a(generator) p 1605 671 a(of) p 1656 671 a(a) p 1693 671 a(sto) q(c) o(hastic) 0 731 y(Ising) p 118 731 a(mo) q(del) p 263 731 a(is) p 312 731 a(the) p 396 731 a(linear) p 532 731 a(op) q(erator) p Fq 728 731 a(A) p Fp 765 713 a(!) p Fl 765 744 a(\003) p Fr 805 731 a(:) p Fo 832 731 a(C) p Fl 858 738 a(\003) p Fo 899 731 a(!) p 963 731 a(C) p Fl 989 738 a(\003) p Fr 1032 731 a(giv) o(en) p 1159 731 a(b) o(y) p Fq 583 838 a(A) p Fp 620 817 a(!) p Fl 620 850 a(\003) p Fq 646 838 a(f) p Fr 675 838 a(\() p Fq(\033) p Fr 724 838 a(\)) p 757 838 a(=) p Fk 808 791 a(X) p Fp 810 896 a(x) p Fm(2) p Fl(\003) p Fq 889 838 a(c) p Fp 910 817 a(!) 910 850 y(x) p Fr 935 838 a(\() p Fq(\033) p Fr 984 838 a(\)[) p Fq(f) p Fr 1046 838 a(\() p Fq(\033) p Fp 1095 817 a(x) p Fr 1116 838 a(\)) p Fo 1146 838 a(\000) p Fq 1195 838 a(f) p Fr 1224 838 a(\() p Fq(\033) p Fr 1273 838 a(\)]) p Fq(;) p Fr 0 979 a(where) p Fq 147 979 a(c) p Fp 168 961 a(!) 168 992 y(x) p Fo 217 979 a(2) p 274 979 a(C) p Fl 300 986 a(\003) p Fr 349 979 a(is) p 405 979 a(the) p Fq 495 979 a(tr) q(ansition) p 739 979 a(r) q(ate) p Fr 850 979 a(and) p Fq 951 979 a(\033) p Fp 981 961 a(x) p Fr 1025 979 a(is) p 1080 979 a(the) p 1170 979 a(con\014guration) p 1471 979 a(obtained) p 1678 979 a(from) p Fq 1799 979 a(\033) p Fr 1851 979 a(b) o(y) 0 1040 y(replacing) p Fq 207 1040 a(\033) p Fr 237 1040 a(\() p Fq(x) p Fr(\)) p 316 1040 a(with) p Fo 425 1040 a(\000) p Fq(\033) p Fr 494 1040 a(\() p Fq(x) p Fr(\).) p 594 1040 a(W) l(e) p 676 1040 a(will) p 766 1040 a(assume) p 933 1040 a(the) p 1015 1040 a(follo) o(wing) p 1219 1040 a(conditions) p 1450 1040 a(on) p 1516 1040 a(the) p 1598 1040 a(transition) p 1818 1040 a(rate) p Fq 0 1100 a(c) p Fp 21 1082 a(!) 21 1112 y(x) p Fr 46 1100 a(:) -1 1191 y(\(H1\)) p Fq 122 1191 a(D) q(etail) q(ed) p 326 1191 a(bal) q(ance) p 503 1191 a(condition) p Fr(.) p 740 1191 a(It) p 793 1191 a(holds) p 921 1191 a(that) p Fq 363 1288 a(c) p Fp 384 1268 a(!) 384 1301 y(x) p Fr 409 1288 a(\() p Fq(\033) p Fr 458 1288 a(\)) p 485 1288 a(exp) o([) p Fo(\000) p Fq(\014) s(H) p Fp 687 1266 a(\033) p Fj 707 1272 a(\003) p Fp 729 1266 a(!) p Fm 683 1304 a(f) p Fp(x) p Fm(g) p Fr 754 1288 a(\() p Fq(\033) p Fr 803 1288 a(\() p Fq(x) p Fr(\)\)]) p 914 1288 a(=) p Fq 966 1288 a(c) p Fp 987 1268 a(!) 987 1301 y(x) p Fr 1012 1288 a(\() p Fq(\033) p Fp 1061 1268 a(x) p Fr 1083 1288 a(\)) p 1110 1288 a(exp[) p Fo(\000) p Fq(\014) s(H) p Fp 1313 1266 a(\033) p Fj 1333 1272 a(\003) p Fp 1354 1266 a(!) p Fm 1309 1304 a(f) p Fp(x) p Fm(g) p Fr 1380 1288 a(\() p Fo(\000) p Fq(\033) p Fr 1468 1288 a(\() p Fq(x) p Fr(\)\)]) p Fq(;) p Fr 1802 1288 a(\(1.5\)) 122 1386 y(where) p Fq 263 1386 a(\033) p Fl 291 1393 a(\003) p Fq 317 1386 a(!) p Fr 366 1386 a(is) p 415 1386 a(the) p 499 1386 a(con\014guration) p 794 1386 a(suc) o(h) p 904 1386 a(that) p Fq 1010 1386 a(\033) p Fl 1038 1393 a(\003) p Fq 1064 1386 a(!) p Fr 1110 1386 a(=) p Fq 1162 1386 a(\033) p Fr 1207 1386 a(on) p 1275 1386 a(\003) p 1325 1386 a(and) p Fq 1420 1386 a(\033) p Fl 1448 1393 a(\003) p Fq 1474 1386 a(!) p Fr 1520 1386 a(=) p Fq 1572 1386 a(!) p Fr 1621 1386 a(on) p 1688 1386 a(\003) p Fp 1722 1368 a(c) p Fr 1740 1386 a(.) -1 1484 y(\(H2\)) p Fq 122 1484 a(P) p 160 1484 a(ositiv) r(ity) p 369 1484 a(and) p 475 1484 a(boundedness) p Fr(.) p 813 1484 a(There) p 964 1484 a(exist) p Fq 1089 1484 a(c) p Fp 1110 1491 a(m) p Fr 1174 1484 a(=) p Fq 1243 1484 a(c) p Fp 1264 1491 a(m) p Fr 1297 1484 a(\() p Fq(\014) s(;) p 1369 1484 a(d) p Fr(\)) p Fo 1444 1484 a(2) p Fr 1508 1484 a(\(0) p Fq(;) p Fo 1573 1484 a(1) p Fr(\)) p 1668 1484 a(and) p Fq 1773 1484 a(c) p Fp 1794 1491 a(M) p Fr 1864 1484 a(=) p Fq 122 1544 a(c) p Fp 143 1551 a(M) p Fr 182 1544 a(\() p Fq(\014) s(;) p 254 1544 a(d) p Fr(\)) p Fo 312 1544 a(2) p Fr 359 1544 a(\(0) p Fq(;) p Fo 424 1544 a(1) p Fr(\)) p 509 1544 a(suc) o(h) p 619 1544 a(that) p 725 1544 a(for) p 799 1544 a(an) o(y) p 891 1544 a(\003) p Fo 939 1544 a(\032\032) p Fn 1030 1544 a(Z) p Fp 1067 1526 a(d) p Fq 420 1642 a(c) p Fp 441 1649 a(m) p Fo 516 1642 a(\024) p Fr 596 1642 a(inf) p Fo 655 1642 a(f) p Fq(c) p Fp 701 1621 a(!) 701 1654 y(x) p Fr 726 1642 a(\() p Fq(\033) p Fr 775 1642 a(\);) p Fq 816 1642 a(x) p Fo 857 1642 a(2) p Fr 904 1642 a(\003) p Fq(;) p 976 1642 a(!) p Fo 1022 1642 a(2) p Fr 1069 1642 a(\012) p Fl 1104 1649 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1177 1642 a(and) p Fq 1272 1642 a(\033) p Fo 1316 1642 a(2) p Fr 1363 1642 a(\012) p Fl 1398 1649 a(\003) p Fo 1424 1642 a(g) 516 1714 y(\024) p Fr 596 1714 a(sup) p Fo(f) p Fq(c) p Fp 715 1694 a(!) 715 1727 y(x) p Fr 741 1714 a(\() p Fq(\033) p Fr 790 1714 a(\);) p Fq 831 1714 a(x) p Fo 871 1714 a(2) p Fr 918 1714 a(\003) p Fq(;) p 990 1714 a(!) p Fo 1036 1714 a(2) p Fr 1083 1714 a(\012) p Fl 1118 1721 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1192 1714 a(and) p Fq 1287 1714 a(\033) p Fo 1330 1714 a(2) p Fr 1377 1714 a(\012) p Fl 1412 1721 a(\003) p Fo 1439 1714 a(g) p 1478 1714 a(\024) p Fq 1530 1714 a(c) p Fp 1551 1721 a(M) p Fq 1591 1714 a(:) p Fr 1802 1714 a(\(1.6\)) -1 1831 y(\(H3\)) p Fq 122 1831 a(N) p 166 1831 a(ear) q(est) p 319 1831 a(neig) r(hbor) p 525 1831 a(inter) q(action) p Fr(.) p 808 1831 a(If) p Fq 858 1831 a(\033) p Fr 888 1831 a(\() p Fq(y) p Fr 933 1831 a(\)) p 967 1831 a(=) p Fq 1022 1831 a(\033) p Fm 1052 1813 a(0) p Fr 1063 1831 a(\() p Fq(y) p Fr 1108 1831 a(\)) p 1144 1831 a(for) p 1220 1831 a(all) p Fq 1289 1831 a(y) p Fr 1332 1831 a(with) p Fo 1445 1831 a(k) p Fq(y) p Fo 1507 1831 a(\000) p Fq 1558 1831 a(x) p Fo(k) p Fl 1611 1838 a(1) p Fr 1647 1831 a(=) p 1701 1831 a(1,) p 1757 1831 a(then) p 1870 1831 a(it) 122 1891 y(holds) p 250 1891 a(that) p Fq 355 1891 a(c) p Fp 376 1873 a(!) 376 1903 y(x) p Fr 401 1891 a(\() p Fq(\033) p Fr 450 1891 a(\)) p 483 1891 a(=) p Fq 534 1891 a(c) p Fp 555 1873 a(!) 555 1903 y(x) p Fr 581 1891 a(\() p Fq(\033) p Fm 630 1873 a(0) p Fr 641 1891 a(\).) -1 1989 y(\(H4\)) p Fq 122 1989 a(Attr) q(activ) r(ity) p Fr 386 1989 a(.) p 418 1989 a(If) p Fq 467 1989 a(\033) p Fo 510 1989 a(\024) p Fq 563 1989 a(\033) p Fm 593 1971 a(0) p Fr 620 1989 a(and) p Fq 715 1989 a(\033) p Fr 745 1989 a(\() p Fq(x) p Fr(\)) p 824 1989 a(=) p Fq 876 1989 a(\033) p Fm 906 1971 a(0) p Fr 917 1989 a(\() p Fq(x) p Fr(\),) p 1013 1989 a(then) p 1124 1989 a(it) p 1173 1989 a(holds) p 1300 1989 a(that) p Fq 710 2087 a(\033) p Fr 740 2087 a(\() p Fq(x) p Fr(\)) p Fq(c) p Fp 827 2066 a(!) 827 2099 y(x) p Fr 851 2087 a(\() p Fq(\033) p Fr 900 2087 a(\)) p Fo 933 2087 a(\025) p Fq 985 2087 a(\033) p Fm 1015 2066 a(0) p Fr 1027 2087 a(\() p Fq(x) p Fr(\)) p Fq(c) p Fp 1114 2066 a(!) 1114 2099 y(x) p Fr 1138 2087 a(\() p Fq(\033) p Fm 1187 2066 a(0) p Fr 1198 2087 a(\)) p Fq(:) p Fr 1802 2087 a(\(1.7\)) 0 2203 y(An) p 80 2203 a(example) p 271 2203 a(of) p 327 2203 a(functions) p Fq 537 2203 a(c) p Fp 558 2185 a(!) 558 2216 y(x) p Fr 599 2203 a(is) p 648 2203 a(giv) o(en) p 776 2203 a(b) o(y) p Fq 282 2325 a(c) p Fp 303 2305 a(!) 303 2338 y(x) p Fr 328 2325 a(\() p Fq(\033) p Fr 377 2325 a(\)) p 437 2325 a(=) p 516 2325 a(exp) p Fk 591 2270 a(h) p Fo 614 2325 a(\000) p Fq 658 2292 a(\014) p 658 2314 31 2 v Fr 661 2360 a(2) p Fk 693 2270 a(\020) p Fq 723 2325 a(H) p Fp 767 2303 a(\033) p Fj 787 2309 a(\003) p Fp 810 2303 a(!) p Fm 763 2341 a(f) p Fp(x) p Fm(g) p Fr 836 2325 a(\() p Fq(\033) p Fp 885 2305 a(x) p Fr 906 2325 a(\)) p Fo 936 2325 a(\000) p Fq 986 2325 a(H) p Fp 1030 2303 a(\033) p Fj 1050 2309 a(\003) p Fp 1073 2303 a(!) p Fm 1026 2341 a(f) p Fp(x) p Fm(g) p Fr 1098 2325 a(\() p Fq(\033) p Fr 1147 2325 a(\)) p Fk 1166 2270 a(\021) o(i) p Fr 437 2433 a(=) p 516 2433 a(exp) p Fk 591 2378 a(h) p Fo 614 2433 a(\000) p Fq(\014) s(\033) p Fr 714 2433 a(\() p Fq(x) p Fr(\)) p Fk 780 2378 a(\020) 892 2386 y(X) p Fp 808 2494 a(y) p Fm 826 2494 a(2) p Fl(\003;) p Fm(k) p Fp(x) p Fm(\000) p Fp(y) p Fm 967 2494 a(k) p Fj 985 2499 a(1) p Fl 1003 2494 a(=1) p Fq 1057 2433 a(\033) p Fr 1087 2433 a(\() p Fq(y) p Fr 1132 2433 a(\)) p 1161 2433 a(+) p Fk 1294 2386 a(X) p Fp 1210 2494 a(y) p 1232 2494 a(=) p Fm 1228 2494 a(2) p Fl(\003;) p Fm(k) p Fp(x) p Fm(\000) p Fp(y) p Fm 1369 2494 a(k) p Fj 1387 2499 a(1) p Fl 1405 2494 a(=1) p Fq 1458 2433 a(!) p Fr 1490 2433 a(\() p Fq(y) p Fr 1535 2433 a(\)) p Fk 1554 2378 a(\021) o(i) p Fq 1607 2433 a(:) p Fr 0 2586 a(It) p 53 2586 a(can) p 142 2586 a(b) q(e) p 209 2586 a(seen) p 315 2586 a(b) o(y) p 382 2586 a(\(1.5\)) p 499 2586 a(that) p 605 2586 a(for) p 679 2586 a(an) o(y) p Fq 771 2586 a(f) s(;) p 820 2586 a(g) p Fo 859 2586 a(2) p 906 2586 a(C) p Fl 932 2593 a(\003) p Fo 234 2684 a(\000) p Fq(\026) p Fp 302 2663 a(!) p Fl 302 2696 a(\003) p Fr 329 2684 a([) p Fq(f) p 372 2684 a(A) p Fp 409 2663 a(!) p Fl 409 2696 a(\003) p Fq 435 2684 a(g) p Fr 460 2684 a(]) p 515 2684 a(=) p Fo 595 2684 a(\000) p Fq(\026) p Fp 663 2663 a(!) p Fl 663 2696 a(\003) p Fr 689 2684 a([) p Fq(g) r(A) p Fp 765 2663 a(!) p Fl 765 2696 a(\003) p Fq 791 2684 a(f) p Fr 820 2684 a(]) 515 2779 y(=) 599 2745 y(1) p 599 2767 25 2 v 599 2813 a(2) p Fk 637 2731 a(X) p Fp 639 2837 a(x) p Fm(2) p Fl(\003) p Fk 728 2731 a(X) p Fp 717 2837 a(\033) p Fm 738 2837 a(2) p Fl(\012) p Fj 787 2843 a(\003) p Fq 819 2779 a(\026) p Fp 848 2758 a(!) p Fl 848 2791 a(\003) p Fr 875 2779 a(\() p Fq(\033) p Fr 924 2779 a(\)) p Fq(c) p Fp 964 2758 a(!) 964 2791 y(x) p Fr 988 2779 a(\() p Fq(\033) p Fr 1037 2779 a(\)[) p Fq(f) p Fr 1099 2779 a(\() p Fq(\033) p Fp 1148 2758 a(x) p Fr 1169 2779 a(\)) p Fo 1199 2779 a(\000) p Fq 1249 2779 a(f) p Fr 1278 2779 a(\() p Fq(\033) p Fr 1327 2779 a(\)][) p Fq(g) p Fr 1399 2779 a(\() p Fq(\033) p Fp 1448 2758 a(x) p Fr 1468 2779 a(\)) p Fo 1499 2779 a(\000) p Fq 1548 2779 a(g) p Fr 1573 2779 a(\() p Fq(\033) p Fr 1622 2779 a(\)]) p Fq(:) p Fr 939 2947 a(3) p 90 rotate dyy eop %%Page: 4 4 4 3 bop Fr 0 274 a(Finally) l(,) p 175 274 a(w) o(e) p 247 274 a(de\014ne) 444 409 y(gap) q(\(\003) p Fq(;) p 595 409 a(!) p Fr 627 409 a(\)) p 660 409 a(=) p 712 409 a(inf) p Fk 771 353 a(n) p Fo 862 375 a(\000) p Fq(\026) p Fp 930 357 a(!) p Fl 930 388 a(\003) p Fr 956 375 a([) p Fq(f) p 999 375 a(A) p Fp 1036 357 a(!) p Fl 1036 388 a(\003) p Fq 1062 375 a(f) p Fr 1091 375 a(]) p 809 397 350 2 v Fq 809 443 a(\026) p Fp 838 426 a(!) p Fl 838 456 a(\003) p Fr 865 443 a([) p Fo 887 443 a(j) p Fq(f) p Fo 941 443 a(\000) p Fq 991 443 a(\026) p Fp 1020 426 a(!) p Fl 1020 456 a(\003) p Fr 1046 443 a([) p Fq(f) p Fr 1089 443 a(]) p Fo(j) p Fl 1117 428 a(2) p Fr 1145 443 a(]) 1163 409 y(;) p Fq 1185 409 a(f) p Fo 1228 409 a(2) p 1275 409 a(C) p Fl 1301 416 a(\003) p Fk 1328 353 a(o) p Fq 1361 409 a(;) p Fr 1802 409 a(\(1.8\)) 0 545 y(whic) o(h) p 140 545 a(is) p 189 545 a(the) p 273 545 a(smallest) p 460 545 a(p) q(ositiv) o(e) p 641 545 a(eigen) o(v) m(alue) p 874 545 a(of) p Fo 929 545 a(\000) p Fq(A) p Fp 1005 527 a(!) p Fl 1005 557 a(\003) p Fr 1031 545 a(,) p 1061 545 a(and) p 1156 545 a(hence) p 1291 545 a(it) p 1340 545 a(is) p 1389 545 a(called) p 1527 545 a(the) p Fq 1611 545 a(spectr) q(al) p 1801 545 a(g) r(ap) p Fr(.) p Fg 0 634 a(Main) p 146 634 a(Results.) p Fr 363 634 a(Let) p 450 634 a(\003) p Fp 484 641 a(d) p Fr 504 634 a(\() p Fq(L) p Fr(\)) p 589 634 a(=) p 641 634 a(\() p Fo(\000) p Fq(L;) p 754 634 a(L) p Fr(]) p Fp 801 616 a(d) p Fo 831 634 a(\\) p Fn 875 634 a(Z) p Fp 912 616 a(d) p Fr 945 634 a(for) p 1019 634 a(eac) o(h) p Fq 1129 634 a(L) p Fo 1176 634 a(2) p Fn 1223 634 a(N) p Fr(.) p 1294 634 a(F) l(or) p 1381 634 a(eac) o(h) p Fq 1491 634 a(!) p Fo 1537 634 a(2) p Fr 1584 634 a(\012) p Fl 1619 641 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1676 634 a(,) p 1706 634 a(w) o(e) p 1778 634 a(de\014ne) p Fq 557 744 a(F) p Fl 596 724 a(+) p Fp 589 758 a(L) p Fr 625 744 a(\() p Fq(!) p Fr 676 744 a(\)) p 709 744 a(=) p Fo 761 744 a(f) p Fq(y) p Fo 825 744 a(2) p Fq 872 744 a(@) p Fp 898 751 a(ex) p Fr 936 744 a(\003) p Fp 970 751 a(d) p Fr 990 744 a(\() p Fq(L) p Fr(\);) p Fq 1083 744 a(!) p Fr 1115 744 a(\() p Fq(y) p Fr 1160 744 a(\)) p 1193 744 a(=) p 1244 744 a(+1) p Fo(g) p Fq(:) p Fg 73 854 a(Theorem) p 316 854 a(1.1.) p Fd 426 854 a(L) n(et) p Fq 514 854 a(d) p Fo 561 854 a(\025) p Fr 621 854 a(3) p Fd(.) p 695 854 a(Consider) p 907 854 a(a) p 953 854 a(sto) n(chastic) p 1179 854 a(Ising) p 1304 854 a(mo) n(del) p 1448 854 a(on) p 1522 854 a(the) p 1607 854 a(squar) n(e) p Fr 1762 854 a(\003) p Fp 1796 861 a(d) p Fr 1816 854 a(\() p Fq(L) p Fr(\)) p Fd(.) 0 914 y(Then,) p 142 914 a(ther) n(e) p 263 914 a(exists) p Fq 397 914 a(\014) p Fl 425 921 a(0) p Fr 458 914 a(=) p Fq 510 914 a(\014) p Fl 538 921 a(0) p Fr 557 914 a(\() p Fq(d) p Fr(\)) p Fq 634 914 a(>) p Fr 686 914 a(0) p Fd 727 914 a(such) p 838 914 a(that) p 938 914 a(for) p 1016 914 a(any) p Fq 1109 914 a(\014) p Fo 1153 914 a(\025) p Fq 1206 914 a(\014) p Fl 1234 921 a(0) p Fd 1271 914 a(and) p 1365 914 a(any) p Fq 1459 914 a(L) p Fo 1506 914 a(2) p Fn 1553 914 a(N) p Fr 463 1024 a(gap) q(\(\003) p Fp 592 1031 a(d) p Fr 612 1024 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 705 1024 a(+\)) p Fo 775 1024 a(\025) p Fq 828 1024 a(B) p Fr 876 1024 a(exp) o(\() p Fo(\000) p Fq(\014) s(C) t(L) p Fp 1111 1004 a(d) p Fm(\000) p Fl(2) p Fr 1175 1024 a(\(log) p Fq 1266 1024 a(L) p Fr(\)) p Fl 1318 1004 a(2) p Fr 1337 1024 a(\)) p 1802 1024 a(\(1.9\)) p Fd 0 1134 a(holds,) p 139 1134 a(wher) n(e) p Fq 277 1134 a(B) p Fr 330 1134 a(=) p Fq 382 1134 a(B) p Fr 422 1134 a(\() p Fq(c) p Fp 462 1141 a(m) p Fq 495 1134 a(;) p 517 1134 a(c) p Fp 538 1141 a(M) p Fq 577 1134 a(;) p 599 1134 a(d) p Fr(\)) p Fq 657 1134 a(>) p Fr 709 1134 a(0) p Fd 751 1134 a(and) p Fq 846 1134 a(C) p Fr 898 1134 a(=) p Fq 950 1134 a(C) p Fr 989 1134 a(\() p Fq(\014) s(;) p 1061 1134 a(d) p Fr(\)) p Fq 1117 1134 a(>) p Fr 1169 1134 a(0) p Fd(.) p Fg 73 1236 a(Theorem) p 316 1236 a(1.2.) p Fd 426 1236 a(L) n(et) p Fq 514 1236 a(d) p Fr 561 1236 a(=) p 621 1236 a(3) p Fd(.) p 695 1236 a(Consider) p 907 1236 a(a) p 953 1236 a(sto) n(chastic) p 1179 1236 a(Ising) p 1304 1236 a(mo) n(del) p 1448 1236 a(on) p 1522 1236 a(the) p 1607 1236 a(squar) n(e) p Fr 1763 1236 a(\003) p Fl 1797 1243 a(3) p Fr 1816 1236 a(\() p Fq(L) p Fr(\)) p Fd(.) 0 1296 y(Supp) n(ose) p 186 1296 a(that) p 285 1296 a(a) p 328 1296 a(b) n(oundary) p 537 1296 a(c) n(ondition) p Fq 750 1296 a(!) p Fo 796 1296 a(2) p Fr 843 1296 a(\012) p Fl 878 1303 a(b) p Fp(:) p Fl(c) p Fp(:) p Fd 953 1296 a(satis\014es) p 1136 1296 a(that) p Fq 1236 1296 a(!) p Fr 1268 1296 a(\() p Fq(x) p Fr(\)) p Fo 1347 1296 a(\025) p Fr 1400 1296 a(0) p Fd 1442 1296 a(for) p 1520 1296 a(al) r(l) p Fq 1589 1296 a(x) p Fo 1631 1296 a(2) p Fn 1678 1296 a(Z) p Fp 1714 1278 a(d) p Fd 1749 1296 a(and) p Fq 536 1406 a(F) p Fl 575 1386 a(+) p Fp 568 1420 a(L) p Fr 604 1406 a(\() p Fq(!) p Fr 655 1406 a(\)) p Fo 688 1406 a(\033) p 740 1406 a(f) p Fq(y) p Fo 804 1406 a(2) p Fq 852 1406 a(@) p Fp 878 1413 a(ex) p Fr 916 1406 a(\003) p Fl 950 1413 a(3) p Fr 969 1406 a(\() p Fq(L) p Fr(\);) p Fq 1062 1406 a(y) p Fl 1088 1386 a(3) p Fr 1121 1406 a(=) p Fo 1173 1406 a(\000) p Fq(L) p Fo(g) p Fq(:) p Fr 1778 1406 a(\(1.10\)) p Fd 0 1516 a(Then,) p 142 1516 a(ther) n(e) p 263 1516 a(exists) p Fq 397 1516 a(\014) p Fm 428 1498 a(0) p Fl 425 1529 a(0) p Fq 458 1516 a(>) p Fr 510 1516 a(0) p Fd 551 1516 a(such) p 662 1516 a(that) p 762 1516 a(for) p 840 1516 a(any) p Fq 933 1516 a(\014) p Fo 977 1516 a(\025) p Fq 1030 1516 a(\014) p Fm 1061 1498 a(0) p Fl 1058 1529 a(0) p Fd 1094 1516 a(and) p 1189 1516 a(any) p Fq 1282 1516 a(L) p Fo 1329 1516 a(2) p Fn 1377 1516 a(N) p Fr 473 1633 a(gap) q(\(\003) p Fl 602 1640 a(3) p Fr 622 1633 a(\() p Fq(L) p Fr(\)) p Fq(;) p 715 1633 a(!) p Fr 747 1633 a(\)) p Fo 780 1633 a(\025) p Fq 832 1633 a(B) p Fm 872 1612 a(0) p Fr 892 1633 a(exp) o(\() p Fo(\000) p Fq(\014) s(C) p Fm 1094 1612 a(0) p Fq 1104 1633 a(L) p Fj 1142 1599 a(5) p 1143 1605 16 2 v 1143 1625 a(3) p Fr 1165 1633 a(\(log) p Fq 1255 1633 a(L) p Fr(\)) p Fl 1307 1612 a(2) p Fr 1327 1633 a(\)) p 1778 1633 a(\(1.11\)) p Fd 0 1743 a(holds,) p 139 1743 a(wher) n(e) p Fq 277 1743 a(B) p Fm 317 1725 a(0) p Fr 342 1743 a(=) p Fq 394 1743 a(B) p Fm 434 1725 a(0) p Fr 445 1743 a(\() p Fq(c) p Fp 485 1750 a(m) p Fq 518 1743 a(;) p 540 1743 a(c) p Fp 561 1750 a(M) p Fr 601 1743 a(\)) p Fq 634 1743 a(>) p Fr 685 1743 a(0) p Fd 727 1743 a(and) p Fq 822 1743 a(C) p Fm 861 1725 a(0) p Fr 886 1743 a(=) p Fq 937 1743 a(C) p Fm 976 1725 a(0) p Fr 988 1743 a(\() p Fq(\014) p Fr 1038 1743 a(\)) p Fq 1070 1743 a(>) p Fr 1121 1743 a(0) p Fd(.) p Fr 73 1874 a(Hereafter,) p 299 1874 a(w) o(e) p 370 1874 a(will) p 460 1874 a(in) o(tro) q(duce) p 675 1874 a(k) o(ey) p 762 1874 a(ingredien) o(ts) p 1009 1874 a(for) p 1081 1874 a(the) p 1164 1874 a(pro) q(of) p 1290 1874 a(of) p 1344 1874 a(Theorems) p 1567 1874 a(1.1) p 1644 1874 a(and) p 1737 1874 a(1.2.) p 1834 1874 a(W) l(e) 0 1934 y(will) p 92 1934 a(also) p 190 1934 a(in) o(tro) q(duce) p 407 1934 a(some) p 529 1934 a(basic) p 651 1934 a(lemmas) p 828 1934 a(whic) o(h) p 967 1934 a(w) o(e) p 1039 1934 a(will) p 1131 1934 a(use) p 1215 1934 a(here.) p Fg 0 2023 a(Blo) r(c) n(k) p 162 2023 a(Dynamics) p Fr 422 2023 a(\(See) p 532 2023 a([Ma,94]) p 711 2023 a(and) p 811 2023 a([Ma,99) o(]\)) p Fg(.) p Fr 1038 2023 a(F) l(rom) p 1170 2023 a(no) o(w) p 1276 2023 a(on,) p 1363 2023 a(w) o(e) p 1439 2023 a(will) p 1536 2023 a(use) p 1624 2023 a(the) p 1713 2023 a(follo) o(wing) 0 2083 y(mo) q(di\014ed) p 207 2083 a(Hamiltonian) p 495 2083 a(for) p 578 2083 a(con) o(v) o(enience:) p 880 2083 a(F) l(or) p 975 2083 a(eac) o(h) p 1093 2083 a(\003) p Fo 1154 2083 a(\032\032) p Fn 1259 2083 a(Z) p Fp 1295 2065 a(d) p Fr 1312 2083 a(,) p 1352 2083 a(eac) o(h) p Fq 1470 2083 a(!) p Fo 1529 2083 a(2) p Fr 1590 2083 a(\012) p Fl 1625 2090 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 1706 2083 a(and) p 1809 2083 a(eac) o(h) p Fn 0 2143 a(J) p Fr 39 2143 a(=) p 91 2143 a(\(J) p Fp 135 2150 a(x;y) p Fr 185 2143 a(\)) p Fo 218 2143 a(2) p Fr 265 2143 a([0) p Fq(;) p Fr 325 2143 a(1]) p Ff 363 2125 a(Z) p Fe 388 2114 a(d) p Fm 403 2125 a(\002) p Ff(Z) p Fe 455 2114 a(d) p Fr 472 2143 a(,) p 502 2143 a(w) o(e) p 574 2143 a(de\014ne) p Fq 205 2277 a(H) p Fp 249 2253 a(!) q(;) p Ff(J) p Fl 245 2291 a(\003) p Fr 301 2277 a(\() p Fq(\033) p Fr 350 2277 a(\)) p 382 2277 a(=) p Fo 434 2277 a(\000) p Fr 478 2243 a(1) p 478 2266 25 2 v 478 2311 a(2) p Fk 557 2230 a(X) p Fp 545 2335 a(x;y) p Fm 593 2335 a(2) p Fl(\003) p Fc 520 2365 a(k) p Fe(x) p Fc(\000) p Fe(y) p Fc 594 2365 a(k) p Fj 610 2372 a(1) 627 2365 y(=1) p Fr 671 2277 a(\() p Fq(\033) p Fr 720 2277 a(\() p Fq(x) p Fr(\)) p Fq(\033) p Fr 816 2277 a(\() p Fq(y) p Fr 861 2277 a(\)) p Fo 889 2277 a(\000) p Fr 939 2277 a(1\)) p Fo 993 2277 a(\000) p Fk 1087 2230 a(X) p Fp 1048 2338 a(x) p Fm(2) p Fl(\003) p Fp(;) p 1132 2338 a(y) p 1154 2338 a(=) p Fm 1150 2338 a(2) p Fl(\003) p Fc 1050 2367 a(k) p Fe(x) p Fc(\000) p Fe(y) p Fc 1124 2367 a(k) p Fj 1140 2374 a(1) 1157 2367 y(=1) p Fr 1211 2277 a(J) p Fp 1236 2284 a(x;y) p Fr 1287 2277 a(\() p Fq(\033) p Fr 1336 2277 a(\() p Fq(x) p Fr(\)) p Fq(!) p Fr 1434 2277 a(\() p Fq(y) p Fr 1479 2277 a(\)) p Fo 1508 2277 a(\000) p Fr 1558 2277 a(1\)) p Fq(:) p Fr 1778 2434 a(\(1.12\)) 0 2544 y(By) p Fq 75 2544 a(\026) p Fp 104 2520 a(!) q(;) p Ff(J) p Fl 104 2557 a(\003) p Fr 171 2544 a(and) p 264 2544 a(Z\(\003) p Fq(;) p 369 2544 a(!) r(;) p Fn 423 2544 a(J) p Fr 451 2544 a(\),) p 495 2544 a(w) o(e) p 565 2544 a(will) p 656 2544 a(denote) p 812 2544 a(the) p 894 2544 a(Gibbs) p 1034 2544 a(state) p 1152 2544 a(in) p 1208 2544 a(\003) p 1256 2544 a(with) p 1366 2544 a(ha) o(ving) p Fq 1522 2544 a(H) p Fp 1566 2520 a(!) q(;) p Ff(J) p Fl 1562 2557 a(\003) p Fr 1632 2544 a(as) p 1691 2544 a(its) p 1757 2544 a(Hamil-) 0 2604 y(tonian) p 153 2604 a(and) p 249 2604 a(the) p 334 2604 a(normalization) p 644 2604 a(constan) o(t,) p 855 2604 a(resp) q(ectiv) o(ely) l(.) p 1139 2604 a(By) p 1217 2604 a(gap) q(\(\003) p Fq(;) p 1368 2604 a(!) r(;) p Fn 1422 2604 a(J) p Fr 1449 2604 a(\),) p 1496 2604 a(w) o(e) p 1569 2604 a(will) p 1662 2604 a(also) p 1761 2604 a(denote) 0 2664 y(the) p 84 2664 a(sp) q(ectral) p 267 2664 a(gap) p 359 2664 a(of) p 415 2664 a(the) p 499 2664 a(generator) 538 2780 y(\() p Fq(A) p Fp 594 2756 a(!) q(;) p Ff(J) p Fl 594 2794 a(\003) p Fq 645 2780 a(f) p Fr 674 2780 a(\)\() p Fq(\033) p Fr 742 2780 a(\)) p 775 2780 a(=) p Fk 827 2733 a(X) p Fp 829 2838 a(x) p Fm(2) p Fl(\003) p Fq 907 2780 a(c) p Fp 928 2759 a(!) q(;) p Ff(J) p Fp 928 2792 a(x) p Fr 980 2780 a(\() p Fq(\033) p Fr 1029 2780 a(\)[) p Fq(f) p Fr 1091 2780 a(\() p Fq(\033) p Fp 1140 2759 a(x) p Fr 1160 2780 a(\)) p Fo 1190 2780 a(\000) p Fq 1240 2780 a(f) p Fr 1269 2780 a(\() p Fq(\033) p Fr 1318 2780 a(\)]) p Fq(;) p Fr 939 2947 a(4) p 90 rotate dyy eop %%Page: 5 5 5 4 bop Fr 0 274 a(where) p Fq 141 274 a(c) p Fp 162 256 a(!) q(;) p Ff(J) p Fp 162 286 a(x) p Fr 230 274 a(satisfy) p 382 274 a(\(H1\)) p 497 274 a(for) p Fq 572 274 a(H) p Fp 616 250 a(!) q(;) p Ff(J) p Fl 612 287 a(\003) p Fr 668 274 a(,) p 697 274 a(\(H3\),) p 826 274 a(\(H4\)) p 941 274 a(and) p 1036 274 a(that) p 1142 274 a(for) p 1216 274 a(an) o(y) p 1308 274 a(\003) p Fo 1356 274 a(\032\032) p Fn 1447 274 a(Z) p Fp 1484 256 a(d) p Fq 180 391 a(c) p Fp 201 398 a(m) p Fo 276 391 a(\024) p Fr 356 391 a(inf) p Fo 415 391 a(f) p Fq(c) p Fp 461 370 a(!) q(;) p Ff(J) p Fp 461 403 a(x) p Fr 513 391 a(\() p Fq(\033) p Fr 562 391 a(\);) p Fq 603 391 a(x) p Fo 643 391 a(2) p Fr 690 391 a(\003) p Fq(;) p 762 391 a(!) p Fo 808 391 a(2) p Fr 855 391 a(\012) p Fl 890 398 a(b) p Fp(:) p Fl(c) p Fp(:) p Fq 948 391 a(;) p 986 391 a(\033) p Fo 1029 391 a(2) p Fr 1076 391 a(\012) p Fl 1111 398 a(\003) p Fr 1154 391 a(and) p Fn 1249 391 a(J) p Fo 1288 391 a(2) p Fr 1335 391 a([0) p Fq(;) p Fr 1395 391 a(1]) p Ff 1433 370 a(Z) p Fe 1458 359 a(d) p Fm 1473 370 a(\002) p Ff(Z) p Fe 1525 359 a(d) p Fo 1542 391 a(g) 276 470 y(\024) p Fr 356 470 a(sup) p Fo(f) p Fq(c) p Fp 475 449 a(!) q(;) p Ff(J) p Fp 475 482 a(x) p Fr 527 470 a(\() p Fq(\033) p Fr 576 470 a(\);) p Fq 617 470 a(x) p Fo 658 470 a(2) p Fr 705 470 a(\003) p Fq(;) p 777 470 a(!) p Fo 823 470 a(2) p Fr 870 470 a(\012) p Fl 905 477 a(b) p Fp(:) p Fl(c) p Fp(:) p Fq 962 470 a(;) p 1000 470 a(\033) p Fo 1044 470 a(2) p Fr 1091 470 a(\012) p Fl 1126 477 a(\003) p Fr 1169 470 a(and) p Fn 1263 470 a(J) p Fo 1302 470 a(2) p Fr 1349 470 a([0) p Fq(;) p Fr 1409 470 a(1]) p Ff 1447 449 a(Z) p Fe 1472 437 a(d) p Fm 1487 449 a(\002) p Ff(Z) p Fe 1540 437 a(d) p Fo 1557 470 a(g) p 1596 470 a(\024) p Fq 1648 470 a(c) p Fp 1669 477 a(M) p Fq 1709 470 a(:) p Fr 0 580 a(F) l(or) p 87 580 a(a) p 128 580 a(\014nite) p 253 580 a(family) p Fo 402 580 a(f) p Fq(Q) p Fp 466 587 a(i) p Fo 479 580 a(g) p Fr 520 580 a(with) p Fq 632 580 a(Q) p Fp 671 587 a(i) p Fo 698 580 a(\032) p Fr 751 580 a(\003) p 801 580 a(and) p Fo 896 580 a([) p Fp 929 587 a(i) p Fq 943 580 a(Q) p Fp 982 587 a(i) p Fr 1010 580 a(=) p 1061 580 a(\003,) p 1125 580 a(w) o(e) p 1197 580 a(de\014ne) 378 698 y(\() p Fq(A) p Fm 434 673 a(f) p Fp(Q) p Fe 480 678 a(i) p Fm 492 673 a(g) p Fp(;\034) r(;) p Ff(J) p Fl 434 712 a(\003) p Fq 566 698 a(f) p Fr 595 698 a(\)\() p Fq(\033) p Fr 663 698 a(\)) p 695 698 a(=) p Fk 747 651 a(X) p Fp 777 756 a(i) p Fk 845 651 a(X) p Fp 827 757 a(\021) p Fm 846 757 a(2) p Fl(\012) p Fe 895 763 a(Q) 919 770 y(i) p Fq 943 698 a(\026) p Fp 972 675 a(\033) p Fj 992 681 a(\003) p Fp 1015 675 a(\034) r(;) p Ff(J) p Fp 972 712 a(Q) p Fe 1000 717 a(i) p Fr 1061 698 a(\() p Fq(\021) p Fr 1106 698 a(\)[) p Fq(f) p Fr 1168 698 a(\() p Fq(\033) p Fp 1217 678 a(\021) p Fr 1237 698 a(\)) p Fo 1267 698 a(\000) p Fq 1317 698 a(f) p Fr 1346 698 a(\() p Fq(\033) p Fr 1395 698 a(\)]) p Fq(;) p Fr 1778 698 a(\(1.13\)) 0 864 y(where) p Fq 143 864 a(\033) p Fp 173 846 a(\021) p Fr 211 864 a(is) p 262 864 a(the) p 347 864 a(con\014guration) p 644 864 a(suc) o(h) p 756 864 a(that) p Fq 864 864 a(\033) p Fp 894 846 a(\021) p Fr 931 864 a(=) p Fq 985 864 a(\021) p Fr 1029 864 a(on) p Fq 1099 864 a(Q) p Fp 1138 871 a(i) p Fr 1169 864 a(and) p Fq 1266 864 a(\033) p Fp 1296 846 a(\021) p Fr 1333 864 a(=) p Fq 1388 864 a(\033) p Fr 1435 864 a(on) p Fq 1505 864 a(Q) p Fp 1544 846 a(c) 1544 876 y(i) p Fr 1561 864 a(.) p 1601 864 a(The) p 1703 864 a(dynamics) 0 931 y(ha) o(ving) p Fq 160 931 a(A) p Fm 197 905 a(f) p Fp(Q) p Fe 243 910 a(i) p Fm 255 905 a(g) p Fp(;\034) r(;) p Ff(J) p Fl 197 944 a(\003) p Fr 348 931 a(as) p 411 931 a(its) p 482 931 a(generator) p 701 931 a(is) p 753 931 a(called) p 894 931 a(the) p Fq 981 931 a(bl) q(ock) p 1108 931 a(dy) r(namics) p Fr(.) p 1361 931 a(By) p 1440 931 a(gap) q(\(\003) p Fq(;) p Fo 1591 931 a(f) p Fq(Q) p Fp 1655 938 a(i) p Fo 1669 931 a(g) p Fq(;) p 1716 931 a(!) r(;) p Fn 1770 931 a(J) p Fr 1797 931 a(\),) p 1847 931 a(w) o(e) 0 999 y(will) p 92 999 a(denote) p 249 999 a(the) p 333 999 a(sp) q(ectral) p 516 999 a(gap) p 609 999 a(of) p 664 999 a(the) p 748 999 a(generator) p Fq 965 999 a(A) p Fm 1002 973 a(f) p Fp(Q) p Fe 1048 978 a(i) p Fm 1060 973 a(g) p Fp(;\034) r(;) p Ff(J) p Fl 1002 1012 a(\003) p Fr 1134 999 a(,) p 1163 999 a(and) p 1258 999 a(w) o(e) p 1330 999 a(ha) o(v) o(e) p 1442 999 a(that) 375 1150 y(gap) q(\(\003) p Fq(;) p Fo 526 1150 a(f) p Fq(Q) p Fp 590 1157 a(i) p Fo 603 1150 a(g) p Fq(;) p 650 1150 a(!) r(;) p Fn 704 1150 a(J) p Fr 732 1150 a(\)) p 762 1150 a(=) p 814 1150 a(inf) p Fk 873 1095 a(n) p Fo 924 1117 a(\000) p Fq(\026) p Fp 992 1093 a(!) q(;) p Ff(J) p Fl 992 1130 a(\003) p Fr 1043 1117 a([) p Fq(f) p 1086 1117 a(A) p Fm 1123 1091 a(f) p Fp(Q) p Fe 1169 1096 a(i) p Fm 1181 1091 a(g) p Fp(;\034) r(;) p Ff(J) p Fl 1123 1130 a(\003) p Fq 1255 1117 a(f) p Fr 1284 1117 a(]) p 911 1139 400 2 v Fq 911 1191 a(\026) p Fp 940 1168 a(!) q(;) p Ff(J) p Fl 940 1205 a(\003) p Fr 992 1191 a([) p Fo 1014 1191 a(j) p Fq(f) p Fo 1068 1191 a(\000) p Fq 1118 1191 a(\026) p Fp 1147 1168 a(!) q(;) p Ff(J) p Fl 1147 1205 a(\003) p Fr 1199 1191 a([) p Fq(f) p Fr 1242 1191 a(]) p Fo(j) p Fl 1270 1177 a(2) p Fr 1297 1191 a(]) 1315 1150 y(;) p Fq 1337 1150 a(f) p Fo 1381 1150 a(2) p 1428 1150 a(C) p Fl 1454 1157 a(\003) p Fk 1480 1095 a(o) p Fq 1514 1150 a(:) p Fr 73 1293 a(F) l(or) p 161 1293 a(eac) o(h) p Fq 270 1293 a(l) p Fo 300 1293 a(\024) p Fr 352 1293 a(2) p Fq(L) p Fr(,) p 440 1293 a(set) p Fq 365 1403 a(Q) p Fp 404 1410 a(i) p Fr 432 1403 a(=) p Fo 484 1403 a(f) p Fq(x) p Fo 550 1403 a(2) p Fr 597 1403 a(\003) p Fp 631 1410 a(d) p Fr 651 1403 a(\() p Fq(L) p Fr(\);) p Fo 744 1403 a(\000) p Fq(L) p Fr 827 1403 a(+) p 876 1403 a(\() p Fq(i) p Fo 923 1403 a(\000) p Fr 973 1403 a(1\)) p Fq(l) p 1046 1403 a(<) p 1097 1403 a(x) p Fp 1125 1383 a(d) p Fo 1159 1403 a(\024) p 1212 1403 a(\000) p Fq(L) p Fr 1295 1403 a(+) p 1344 1403 a(\() p Fq(i) p Fr 1390 1403 a(+) p 1439 1403 a(3\)) p Fq(l) p Fo 1498 1403 a(g) p Fq(:) p Fr 0 1513 a(Then,) p 141 1513 a(w) o(e) p 213 1513 a(ha) o(v) o(e) p 325 1513 a(\(see) p 423 1513 a(Section) p 594 1513 a(2) p 634 1513 a(in) p 691 1513 a([Ma,94]) p 866 1513 a(or) p 926 1513 a(the) p 1010 1513 a(pro) q(of) p 1137 1513 a(of) p 1193 1513 a(Theorem) p 1398 1513 a(5) p 1439 1513 a(in) p 1496 1513 a([Sc) o(h,94) o(]\)) p 1695 1513 a(that) 357 1623 y(gap) q(\(\003) p Fp 486 1630 a(d) p Fr 506 1623 a(\() p Fq(L) p Fr(\)) p Fq(;) p 599 1623 a(!) r(;) p Fn 653 1623 a(J) p Fr 680 1623 a(\)) p Fo 276 1743 a(\025) p Fq 417 1709 a(c) p Fp 438 1716 a(m) p 362 1731 166 2 v Fr 362 1777 a(4) p Fq(c) p Fp 407 1784 a(M) p Fo 447 1777 a(j) p Fq(Q) p Fp 500 1784 a(i) p Fo 513 1777 a(j) p Fr 540 1743 a(exp) p Fk 615 1687 a(h) p Fo 638 1743 a(\000) p Fr(4) p Fq(\014) p Fk 732 1687 a(\020) p Fr 761 1743 a(4) p Fq(l) p Fp 837 1680 a(d) p Fk 810 1695 a(X) p Fp 814 1801 a(k) p Fl 833 1801 a(=2) p Fr 882 1743 a(\(2) p Fq(L) p Fr(\)) p Fp 977 1722 a(k) p Fm 996 1722 a(\000) p Fl(2) p Fr 1055 1743 a(+) p 1104 1743 a(1) p Fk 1128 1687 a(\021i) p Fr 1190 1743 a(gap) q(\(\003) p Fp 1319 1750 a(d) p Fr 1339 1743 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fo 1432 1743 a(f) p Fq(Q) p Fp 1496 1750 a(i) p Fo 1509 1743 a(g) p Fq(;) p 1556 1743 a(!) r(;) p Fn 1610 1743 a(J) p Fr 1638 1743 a(\)) p Fq(:) p Fr 1778 1743 a(\(1.14\)) p Fg 0 1937 a(Con) n(tours) p 238 1937 a(and) p 342 1937 a(The) p 452 1937 a(Cluster) p 646 1937 a(Expansion) p Fr 912 1937 a(\(See) p 1014 1937 a([KP) l(,86]\)) p Fg(.) p Fr 1225 1937 a(Let) p Fq 1309 1937 a(Q) p Fr(\() p Fq(x) p Fr(\)) p 1427 1937 a(=) p Fk 1479 1899 a(Q) p Fp 1526 1912 a(d) 1526 1951 y(i) p Fl(=1) p Fr 1585 1937 a([) p Fq(x) p Fp 1627 1919 a(i) p Fo 1644 1937 a(\000) p Fr 1687 1937 a(\(1) p Fq(=) p Fr(2\)) p Fq(;) p 1819 1937 a(x) p Fp 1847 1919 a(i) p Fr 1864 1937 a(+) 0 1997 y(\(1) p Fq(=) p Fr(2\)]) p Fo 139 1997 a(\032) p Fn 192 1997 a(R) p Fp 231 1979 a(d) p Fr 264 1997 a(and) p 359 1997 a(let) p Fq 430 1997 a(Q) p Fr(\() p Fq(V) p Fr 527 1997 a(\)) p 560 1997 a(=) p Fo 612 1997 a([) p Fp 645 2004 a(x) p Fm(2) p Fp(V) p Fq 719 1997 a(Q) p Fr(\() p Fq(x) p Fr(\)) p Fo 838 1997 a(\032) p Fn 890 1997 a(R) p Fp 929 1979 a(d) p Fr 963 1997 a(for) p 1038 1997 a(eac) o(h) p Fq 1148 1997 a(V) p Fo 1201 1997 a(\032) p Fn 1254 1997 a(R) p Fp 1293 1979 a(d) p Fr 1310 1997 a(.) p 1346 1997 a(By) p Fq 1423 1997 a(@) s(Q) p Fr(\() p Fq(V) p Fr 1548 1997 a(\),) p 1597 1997 a(w) o(e) p 1669 1997 a(will) p 1761 1997 a(denote) 0 2057 y(the) p 86 2057 a(b) q(oundary) p 308 2057 a(of) p Fq 366 2057 a(Q) p Fr(\() p Fq(V) p Fr 463 2057 a(\)) p 501 2057 a(in) p Fn 560 2057 a(R) p Fp 599 2039 a(d) p Fr 617 2057 a(.) p 659 2057 a(Let) p 749 2057 a(us) p 814 2057 a(\014x) p Fq 886 2057 a(L) p Fo 937 2057 a(2) p Fn 988 2057 a(N) p Fr(.) p 1067 2057 a(F) l(or) p 1156 2057 a(eac) o(h) p Fq 1269 2057 a(L) p Fl 1302 2064 a(1) p Fo 1340 2057 a(2) p Fn 1391 2057 a(Z) p Fo 1437 2057 a([) p 1483 2057 a(f\0001) p Fq(;) p Fo 1619 2057 a(1g) p Fr 1711 2057 a(and) p 1809 2057 a(eac) o(h) p Fq 0 2117 a(L) p Fl 33 2124 a(2) p Fo 67 2117 a(2) p Fn 114 2117 a(Z) p Fo 158 2117 a([) p 202 2117 a(f\0001) p Fq(;) p Fo 338 2117 a(1g) p Fr(,) p 442 2117 a(w) o(e) p 514 2117 a(set) 225 2227 y(\003\() p Fq(L) p Fl 311 2234 a(1) p Fq 331 2227 a(;) p 353 2227 a(L) p Fl 386 2234 a(2) p Fr 406 2227 a(\)) p 466 2227 a(=) p 546 2227 a(\003) p Fp 580 2234 a(d) p Fr 600 2227 a(\() p Fq(L) p Fl 652 2234 a(1) p Fq 672 2227 a(;) p 694 2227 a(L) p Fl 727 2234 a(2) p Fr 747 2227 a(\)) 466 2300 y(=) p Fo 546 2300 a(f) p Fq(x) p Fo 612 2300 a(2) p Fn 659 2300 a(Z) p Fp 696 2279 a(d) p Fr 713 2300 a(;) p Fq 735 2300 a(L) p Fl 768 2307 a(1) p Fq 801 2300 a(<) p 853 2300 a(x) p Fp 881 2279 a(d) p Fq 915 2300 a(<) p 967 2300 a(L) p Fl 1000 2307 a(2) p Fr 1031 2300 a(+) p 1080 2300 a(1) p Fq(;) p Fo 1142 2300 a(\000) p Fq(L) p 1228 2300 a(<) p 1280 2300 a(x) p Fl 1308 2279 a(1) p Fq 1327 2300 a(;) p Fo 1349 2300 a(\001) p 1371 2300 a(\001) p 1393 2300 a(\001) p Fq 1424 2300 a(;) p 1446 2300 a(x) p Fp 1474 2279 a(d) p Fm(\000) p Fl(1) p Fo 1553 2300 a(\024) p Fq 1605 2300 a(L) p Fo(g) p Fq(:) p Fr 0 2410 a(W) l(e) p 90 2410 a(will) p 188 2410 a(call) p Fq 284 2410 a(\015) p Fo 336 2410 a(\032) p Fn 399 2410 a(R) p Fp 438 2392 a(d) p Fr 477 2410 a(a) p Fq 524 2410 a(contour) p Fr 712 2410 a(\(in) p 794 2410 a(\003\() p Fq(L) p Fl 880 2417 a(1) p Fq 900 2410 a(;) p 922 2410 a(L) p Fl 955 2417 a(2) p Fr 974 2410 a(\)\)) p 1035 2410 a(if) p Fq 1085 2410 a(\015) p Fr 1137 2410 a(=) p Fq 1200 2410 a(@) s(Q) p Fr(\(\002\)) p 1365 2410 a(for) p 1445 2410 a(a) p 1492 2410 a(\014nite) p Fq 1623 2410 a(l) p Fm 1638 2417 a(1) p Fr 1675 2410 a(-connected) 0 2470 y(set) p 78 2470 a(\002) p Fo 134 2470 a(\032) p Fr 190 2470 a(\003\() p Fq(L) p Fl 276 2477 a(1) p Fq 296 2470 a(;) p 318 2470 a(L) p Fl 351 2477 a(2) p Fr 371 2470 a(\)) p 408 2470 a(whic) o(h) p 550 2470 a(satis\014es) p 732 2470 a(that) p 840 2470 a(\002) p Fp 878 2452 a(c) p Fr 914 2470 a(is) p Fq 965 2470 a(l) p Fm 980 2477 a(1) p Fr 1017 2470 a(-connected.) p 1287 2470 a(By) p Fo 1366 2470 a(C) p Fr 1395 2470 a(\() p Fq(L) p Fl 1447 2477 a(1) p Fq 1467 2470 a(;) p 1489 2470 a(L) p Fl 1522 2477 a(2) p Fr 1541 2470 a(\),) p 1593 2470 a(w) o(e) p 1667 2470 a(will) p 1761 2470 a(denote) 0 2530 y(the) p 86 2530 a(collection) p 305 2530 a(of) p 362 2530 a(con) o(tours) p 561 2530 a(in) p 620 2530 a(\003\() p Fq(L) p Fl 706 2537 a(1) p Fq 726 2530 a(;) p 748 2530 a(L) p Fl 781 2537 a(2) p Fr 800 2530 a(\).) p 860 2530 a(F) l(or) p 950 2530 a(eac) o(h) p Fq 1061 2530 a(n) p Fo 1108 2530 a(2) p Fn 1158 2530 a(Z) p Fr 1194 2530 a(,) p 1224 2530 a(w) o(e) p 1297 2530 a(de\014ne) p 1440 2530 a(a) p 1483 2530 a(b) q(oundary) p 1704 2530 a(condition) p Fq 0 2591 a(!) p Fp 30 2598 a(n) p Fo 68 2591 a(2) p Fr 115 2591 a(\012) p Fl 150 2598 a(b) p Fp(:) p Fl(c) p Fp(:) p Fr 223 2591 a(b) o(y) p Fq 616 2727 a(!) p Fp 646 2734 a(n) p Fr 669 2727 a(\() p Fq(x) p Fr(\)) p 749 2727 a(=) p Fk 801 2657 a(\032) p Fo 859 2696 a(\000) p Fr(1) p 964 2696 a(if) p Fq 1008 2696 a(x) p Fp 1036 2678 a(d) p Fo 1070 2696 a(\025) p Fq 1123 2696 a(n;) p Fr 859 2756 a(+1) p 964 2756 a(otherwise) p Fq 1164 2756 a(:) p Fr 1778 2727 a(\(1.15\)) 939 2947 y(5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop Fr 0 274 a(W) l(e) p 82 274 a(will) p 172 274 a(write) p Fq 295 274 a(!) p Fr 341 274 a(=) p Fq 393 274 a(!) p Fl 423 281 a(0) p Fr 443 274 a(.) p 477 274 a(Let) p 563 274 a(us) p 623 274 a(\014x) p 691 274 a(a) p 729 274 a(negativ) o(e) p 920 274 a(in) o(teger) p Fq 1079 274 a(L) p Fl 1112 281 a(1) p Fr 1146 274 a(and) p Fq 1239 274 a(L) p Fl 1272 281 a(2) p Fo 1306 274 a(2) p Fn 1353 274 a(N) p Fr(.) p 1423 274 a(F) l(or) p 1509 274 a(eac) o(h) p Fq 1617 274 a(\033) p Fo 1660 274 a(2) p Fr 1707 274 a(\012) p Fl 1742 282 a(\003\() p Fp(L) p Fj 1804 287 a(1) p Fp 1822 282 a(;L) p Fj 1856 287 a(2) p Fl 1873 282 a(\)) p Fr 1889 274 a(,) 0 334 y(let) 297 441 y(\003\() p Fq(L) p Fl 383 448 a(1) p Fq 402 441 a(;) p 424 441 a(L) p Fl 457 448 a(2) p Fq 477 441 a(;) p 499 441 a(\033) o(;) p 548 441 a(!) p Fr 580 441 a(\)) p 613 441 a(=) p Fk 664 339 a(8) 664 384 y(<) 664 473 y(:) p Fr 709 441 a(\() p Fq(x;) p 778 441 a(y) p Fr 804 441 a(\);) p Fq 864 380 a(x;) p 914 380 a(y) p Fo 953 380 a(2) p Fr 1000 380 a(\003\() p Fq(L) p Fl 1086 387 a(1) p Fq 1106 380 a(;) p 1128 380 a(L) p Fl 1161 387 a(2) p Fr 1181 380 a(\)) p Fo 1211 380 a([) p Fq 1255 380 a(@) p Fp 1281 387 a(ex) p Fr 1319 380 a(\003\() p Fq(L) p Fl 1405 387 a(1) p Fq 1425 380 a(;) p 1447 380 a(L) p Fl 1480 387 a(2) p Fr 1500 380 a(\)) 864 441 y(suc) o(h) p 974 441 a(that) p Fo 1080 441 a(k) p Fq(x) p Fo 1144 441 a(\000) p Fq 1194 441 a(y) p Fo 1220 441 a(k) p Fl 1245 448 a(1) p Fr 1278 441 a(=) p 1329 441 a(1) p 1370 441 a(and) p Fq 864 501 a(\033) p Fl 892 509 a(\003\() p Fp(L) p Fj 954 514 a(1) p Fp 972 509 a(;L) p Fj 1006 514 a(2) p Fl 1023 509 a(\)) p Fq 1038 501 a(!) p Fr 1070 501 a(\() p Fq(x) p Fr(\)) p Fo 1150 501 a(6) p Fr(=) p Fq 1202 501 a(\033) p Fl 1230 509 a(\003\() p Fp(L) p Fj 1292 514 a(1) p Fp 1309 509 a(;L) p Fj 1343 514 a(2) p Fl 1360 509 a(\)) p Fq 1376 501 a(!) p Fr 1408 501 a(\() p Fq(y) p Fr 1453 501 a(\)) p Fk 1539 339 a(9) 1539 384 y(=) 1539 473 y(;) p Fq 1592 441 a(:) p Fr 0 585 a(F) l(or) p 87 585 a(a) p 128 585 a(giv) o(en) p 255 585 a(con\014guration) p Fq 551 585 a(\033) p Fo 594 585 a(2) p Fr 641 585 a(\012) p Fl 676 592 a(\003\() p Fp(L) p Fj 738 597 a(1) p Fp 756 592 a(;L) p Fj 790 597 a(2) p Fl 807 592 a(\)) p Fr 823 585 a(,) p 853 585 a(w) o(e) p 924 585 a(decomp) q(ose) p Fo 589 695 a([) p Fl 622 702 a(\() p Fp(x;y) p Fl 684 702 a(\)) p Fm(2) p Fl(\003\() p Fp(L) p Fj 784 707 a(1) p Fp 801 702 a(;L) p Fj 835 707 a(2) p Fp 852 702 a(;\033) o(;!) p Fl 914 702 a(\)) p Fr 930 695 a(\() p Fq(Q) p Fr(\() p Fq(x) p Fr(\)) p Fo 1065 695 a(\\) p Fq 1109 695 a(Q) p Fr(\() p Fq(y) p Fr 1193 695 a(\)\)) p 1778 695 a(\(1.16\)) 0 805 y(in) o(to) p 108 805 a(the) p 201 805 a(connected) p 438 805 a(comp) q(onen) o(ts.) p 753 805 a(Then,) p 906 805 a(there) p 1040 805 a(exists) p 1184 805 a(a) p 1233 805 a(unique) p 1401 805 a(comp) q(onen) o(t) p 1660 805 a(whic) o(h) p 1808 805 a(do) q(es) 0 865 y(not) p 95 865 a(b) q(elong) p 259 865 a(to) p Fo 327 865 a(C) p Fr 356 865 a(\() p Fq(L) p Fl 408 872 a(1) p Fq 428 865 a(;) p 450 865 a(L) p Fl 483 872 a(2) p Fr 503 865 a(\).) p 582 865 a(W) l(e) p 674 865 a(will) p 774 865 a(call) p 872 865 a(suc) o(h) p 990 865 a(a) p 1039 865 a(comp) q(onen) o(t) p 1297 865 a(an) p Fq 1373 865 a(open) p 1497 865 a(contour) p Fr 1687 865 a(in) p Fq 1752 865 a(\033) p Fr 1782 865 a(.) p 1842 865 a(By) 0 925 y(\000) p Fp 30 907 a(!) p Fl 30 940 a(\003\() p Fp(L) p Fj 92 945 a(1) p Fp 110 940 a(;L) p Fj 144 945 a(2) p Fl 161 940 a(\)) p Fr 177 925 a(\() p Fq(\033) p Fr 226 925 a(\),) p 275 925 a(w) o(e) p 347 925 a(will) p 440 925 a(denote) p 598 925 a(the) p 683 925 a(op) q(en) p 801 925 a(con) o(tour) p 980 925 a(in) p Fq 1037 925 a(\033) p Fr 1067 925 a(.) p 1104 925 a(By) p Fo 1181 925 a(O) p Fr 1222 925 a(\() p Fq(L) p Fl 1274 932 a(1) p Fq 1294 925 a(;) p 1316 925 a(L) p Fl 1349 932 a(2) p Fr 1369 925 a(\),) p 1418 925 a(w) o(e) p 1491 925 a(will) p 1584 925 a(denote) p 1742 925 a(the) p 1826 925 a(col-) 0 990 y(lection) p 159 990 a(of) p 216 990 a(op) q(en) p 335 990 a(con) o(tours) p 533 990 a(for) p 609 990 a(some) p Fq 733 990 a(\033) p Fo 778 990 a(2) p Fr 828 990 a(\012) p Fl 863 997 a(\003\() p Fp(L) p Fj 925 1002 a(1) p Fp 943 997 a(;L) p Fj 977 1002 a(2) p Fl 994 997 a(\)) p Fr 1009 990 a(.) p 1049 990 a(W) l(e) p 1134 990 a(de\014ne) p Fo 1277 990 a(C) p Fr 1306 990 a(\() p Fo(\0001) p Fq(;) p Fo 1436 990 a(1) p Fr(\)) p 1520 990 a(=) p Fo 1574 990 a([) p Fp 1607 997 a(N) p Fm 1639 997 a(2) p Ff(N) p Fo 1689 990 a(C) p Fr 1718 990 a(\() p Fo(\000) p Fq(N) r(;) p 1839 990 a(N) p Fr 1883 990 a(\)) 0 1050 y(and) p Fo 103 1050 a(O) p Fr 144 1050 a(\() p Fo(\0001) p Fq(;) p Fo 274 1050 a(1) p Fr(\)) p 369 1050 a(=) p Fo 434 1050 a([) p Fp 467 1057 a(N) p Fm 499 1057 a(2) p Ff(N) p Fo 548 1050 a(O) p Fr 589 1050 a(\() p Fo(\000) p Fq(N) r(;) p 710 1050 a(N) p Fr 754 1050 a(\).) p 832 1050 a(W) l(e) p 924 1050 a(de\014ne) p 1072 1050 a(the) p 1164 1050 a(maps) p 1299 1050 a(h) p Fl 1326 1032 a(+) p Fr 1383 1050 a(:) p Fo 1423 1050 a(O) p Fr 1464 1050 a(\() p Fo(\0001) p Fq(;) p Fo 1594 1050 a(1) p Fr(\)) p Fo 1690 1050 a(!) p Fn 1766 1050 a(Z) p Fr 1824 1050 a(and) 0 1110 y(h) p Fm 27 1092 a(\000) p Fr 70 1110 a(:) p Fo 98 1110 a(O) p Fr 139 1110 a(\() p Fo(\0001) p Fq(;) p Fo 269 1110 a(1) p Fr(\)) p Fo 351 1110 a(!) p Fn 415 1110 a(Z) p Fr 451 1110 a(,) p 478 1110 a(resp) q(ectiv) o(ely) l(,) p 753 1110 a(b) o(y) 211 1220 y(h) p Fl 238 1199 a(+) p Fr 268 1220 a(\(\000\)) p 350 1220 a(=) p 402 1220 a(max) p Fo 493 1220 a(f) p Fq(x) p Fp 546 1199 a(d) p Fr 577 1220 a(+) p 626 1220 a(\(1) p Fq(=) p Fr(2\);) p Fq 758 1220 a(x) p Fo 800 1220 a(2) p Fr 847 1220 a(\000) p Fo(g) p Fr 951 1220 a(and) p 1079 1220 a(h) p Fm 1106 1199 a(\000) p Fr 1135 1220 a(\(\000\)) p 1218 1220 a(=) p 1269 1220 a(min) p Fo 1351 1220 a(f) p Fq(x) p Fp 1404 1199 a(d) p Fr 1435 1220 a(+) p 1484 1220 a(\(1) p Fq(=) p Fr(2\);) p Fq 1616 1220 a(x) p Fo 1658 1220 a(2) p Fr 1705 1220 a(\000) p Fo(g) p Fq(:) p Fr 1778 1293 a(\(1.17\)) 73 1403 y(Let) p 159 1403 a(us) p 220 1403 a(\014x) p 288 1403 a(\000) p Fo 332 1403 a(2) p 379 1403 a(O) p Fr 420 1403 a(\() p Fq(L) p Fl 472 1410 a(1) p Fq 492 1403 a(;) p 514 1403 a(L) p Fl 547 1410 a(2) p Fr 567 1403 a(\)) p 601 1403 a(and) p Fq 694 1403 a(\015) p Fo 736 1403 a(2) p 783 1403 a(C) p Fr 812 1403 a(\() p Fq(L) p Fl 864 1410 a(1) p Fq 884 1403 a(;) p 906 1403 a(L) p Fl 939 1410 a(2) p Fr 959 1403 a(\)) p 992 1403 a(suc) o(h) p 1101 1403 a(that) p 1205 1403 a(\000) p Fo 1243 1403 a(\\) p Fq 1284 1403 a(\015) p Fr 1327 1403 a(=) p Fo 1379 1403 a(;) p Fr(.) p 1438 1403 a(Then,) p 1578 1403 a(there) p 1701 1403 a(exists) p 1834 1403 a(the) 0 1463 y(unique) p 160 1463 a(con\014guration) p Fq 456 1463 a(\033) p Fl 484 1470 a(\000) p Fo 524 1463 a(2) p Fr 573 1463 a(\012) p Fl 608 1471 a(\003\() p Fp(L) p Fj 670 1476 a(1) p Fp 688 1471 a(;L) p Fj 722 1476 a(2) p Fl 739 1471 a(\)) p Fr 772 1463 a(whic) o(h) p 913 1463 a(satis\014es) p 1094 1463 a(that) p 1201 1463 a(\000) p 1249 1463 a(is) p 1299 1463 a(the) p 1384 1463 a(op) q(en) p 1504 1463 a(con) o(tour) p 1682 1463 a(in) p Fq 1740 1463 a(\033) p Fl 1768 1470 a(\000) p Fr 1792 1463 a(,) p 1824 1463 a(and) 0 1523 y(that) p 102 1523 a(there) p 223 1523 a(are) p 301 1523 a(no) p 365 1523 a(con) o(tours) p 558 1523 a(in) p Fq 612 1523 a(\033) p Fl 640 1530 a(\000) p Fr 663 1523 a(.) p 698 1523 a(W) l(e) p 778 1523 a(can) p 864 1523 a(also) p 958 1523 a(see) p 1033 1523 a(that) p 1136 1523 a(there) p 1257 1523 a(exists) p 1388 1523 a(the) p 1468 1523 a(unique) p 1623 1523 a(con\014guration) p Fq 0 1583 a(\033) p Fl 28 1590 a(\000) p Fp(;\015) p Fo 96 1583 a(2) p Fr 143 1583 a(\012) p Fl 178 1591 a(\003\() p Fp(L) p Fj 240 1596 a(1) p Fp 257 1591 a(;L) p Fj 291 1596 a(2) p Fl 308 1591 a(\)) p Fr 338 1583 a(in) p 392 1583 a(whic) o(h) p 528 1583 a(\000) p 572 1583 a(is) p 619 1583 a(the) p 700 1583 a(op) q(en) p 815 1583 a(con) o(tour) p 989 1583 a(and) p Fq 1081 1583 a(\015) p Fr 1123 1583 a(is) p 1169 1583 a(also) p 1264 1583 a(the) p 1345 1583 a(unique) p 1501 1583 a(con) o(tour.) p 1696 1583 a(W) l(e) p 1778 1583 a(de\014ne) 634 1700 y(\010) p Ff 669 1707 a(J) p Fr 687 1700 a(\(\000\)) p 770 1700 a(=) p 821 1700 a(exp[) p Fo(\000) p Fq(\014) s(H) p Fp 1024 1676 a(!) q(;) p Ff(J) p Fl 1020 1715 a(\003\() p Fp(L) p Fj 1082 1720 a(1) p Fp 1098 1715 a(;L) p Fj 1132 1720 a(2) p Fl 1150 1715 a(\)) p Fr 1165 1700 a(\() p Fq(\033) p Fl 1212 1707 a(\000) p Fr 1236 1700 a(\)]) 0 1810 y(and) 425 1870 y(\010) p Ff 460 1877 a(J) p Fr 479 1870 a(\() p Fq(\015) p Fr 526 1870 a(\)) p 559 1870 a(=) p 611 1870 a(exp) o([) p Fo(\000) p Fq(\014) p Fr 769 1870 a(\() p Fq(H) p Fp 832 1846 a(!) q(;) p Ff(J) p Fl 828 1886 a(\003\() p Fp(L) p Fj 890 1891 a(1) p Fp 907 1886 a(;L) p Fj 941 1891 a(2) p Fl 958 1886 a(\)) p Fr 974 1870 a(\() p Fq(\033) p Fl 1021 1877 a(\000) p Fp(;\015) p Fr 1074 1870 a(\)) p Fo 1104 1870 a(\000) p Fq 1154 1870 a(H) p Fp 1198 1846 a(!) q(;) p Ff(J) p Fl 1194 1886 a(\003\() p Fp(L) p Fj 1256 1891 a(1) p Fp 1274 1886 a(;L) p Fj 1308 1891 a(2) p Fl 1325 1886 a(\)) p Fr 1341 1870 a(\() p Fq(\033) p Fl 1388 1877 a(\000) p Fr 1412 1870 a(\)\)]) p Fq(:) p Fr 0 1962 a(F) l(or) p 90 1962 a(eac) o(h) p 202 1962 a(pair) p Fo 305 1962 a(f) p Fq(\015) p Fl 355 1969 a(1) p Fq 375 1962 a(;) p 397 1962 a(\015) p Fl 422 1969 a(2) p Fo 442 1962 a(g) p 485 1962 a(\032) p 542 1962 a(C) p Fr 571 1962 a(\() p Fq(L) p Fl 623 1969 a(1) p Fq 643 1962 a(;) p 665 1962 a(L) p Fl 698 1969 a(2) p Fr 717 1962 a(\)) p Fo 749 1962 a([) p 795 1962 a(O) p Fr 836 1962 a(\() p Fq(L) p Fl 888 1969 a(1) p Fq 908 1962 a(;) p 930 1962 a(L) p Fl 963 1969 a(2) p Fr 983 1962 a(\),) p 1035 1962 a(w) o(e) p 1109 1962 a(will) p 1204 1962 a(mean) p 1336 1962 a(b) o(y) p Fq 1407 1962 a(\015) p Fl 1432 1969 a(1) p Fq 1452 1962 a(\023\015) p Fl 1494 1969 a(2) p Fr 1533 1962 a(that) p Fq 1641 1962 a(\015) p Fl 1666 1969 a(1) p Fo 1699 1962 a(\\) p Fq 1745 1962 a(\015) p Fl 1770 1969 a(2) p Fo 1808 1962 a(6) p Fr(=) p Fo 1864 1962 a(;) p Fr(.) 0 2023 y(W) l(e) p 87 2023 a(will) p 182 2023 a(call) p 274 2023 a(a) p 318 2023 a(nonempt) o(y) p 548 2023 a(set) p Fq 628 2023 a(C) p Fo 685 2023 a(\032) p 742 2023 a(C) p Fr 771 2023 a(\() p Fq(L) p Fl 823 2030 a(1) p Fq 843 2023 a(;) p 865 2023 a(L) p Fl 898 2030 a(2) p Fr 918 2023 a(\)) p 956 2023 a(a) p Fq 1000 2023 a(cl) q(uster) p Fr 1170 2023 a(if) p 1218 2023 a(it) p 1269 2023 a(is) p 1321 2023 a(not) p 1411 2023 a(decomp) q(osable) p 1725 2023 a(in) o(to) p 1826 2023 a(t) o(w) o(o) 0 2083 y(nonempt) o(y) p 231 2083 a(sets,) p Fq 343 2083 a(C) p Fr 401 2083 a(=) p Fq 458 2083 a(C) p Fl 493 2090 a(1) p Fo 525 2083 a([) p Fq 572 2083 a(C) p Fl 607 2090 a(2) p Fr 626 2083 a(,) p 660 2083 a(suc) o(h) p 773 2083 a(that) p 882 2083 a(there) p 1009 2083 a(are) p 1094 2083 a(no) p 1164 2083 a(pairs) p 1287 2083 a(\() p Fq(\015) p Fl 1331 2090 a(1) p Fq 1351 2083 a(;) p 1373 2083 a(\015) p Fl 1398 2090 a(2) p Fr 1418 2083 a(\)) p Fo 1456 2083 a(2) p Fq 1508 2083 a(C) p Fl 1543 2090 a(1) p Fo 1575 2083 a(\002) p Fq 1627 2083 a(C) p Fl 1662 2090 a(2) p Fr 1701 2083 a(satisfying) 0 2143 y(that) p Fq 104 2143 a(\015) p Fl 129 2150 a(1) p Fq 149 2143 a(\023\015) p Fl 191 2150 a(2) p Fr 211 2143 a(.) p 246 2143 a(F) l(or) p 332 2143 a(eac) o(h) p 440 2143 a(\000) p Fo 485 2143 a(2) p 532 2143 a(O) p Fr 573 2143 a(\() p Fq(L) p Fl 625 2150 a(1) p Fq 644 2143 a(;) p 666 2143 a(L) p Fl 699 2150 a(2) p Fr 719 2143 a(\)) p 753 2143 a(and) p 846 2143 a(eac) o(h) p 954 2143 a(cluster) p Fq 1110 2143 a(C) p Fo 1163 2143 a(\032) p 1215 2143 a(C) p Fr 1244 2143 a(\() p Fq(L) p Fl 1296 2150 a(1) p Fq 1316 2143 a(;) p 1338 2143 a(L) p Fl 1371 2150 a(2) p Fr 1391 2143 a(\),) p 1439 2143 a(\000) p Fq(\023C) p Fr 1539 2143 a(will) p 1630 2143 a(indicate) p 1813 2143 a(that) 0 2203 y(\000) p Fo 42 2203 a(\\) p Fq 86 2203 a(C) p Fo 138 2203 a(6) p Fr(=) p Fo 190 2203 a(;) p Fr(.) 73 2263 y(Let) p Fq 162 2263 a(X) p Fo 224 2263 a(\032) p 279 2263 a(C) p Fr 308 2263 a(\() p Fq(L) p Fl 360 2270 a(1) p Fq 380 2263 a(;) p 402 2263 a(L) p Fl 435 2270 a(2) p Fr 455 2263 a(\).) p 515 2263 a(By) p Fo 593 2263 a(D) p Fr 632 2263 a(\() p Fq(X) p Fr 695 2263 a(\),) p 747 2263 a(w) o(e) p 821 2263 a(will) p 915 2263 a(denote) p 1074 2263 a(the) p 1159 2263 a(family) p 1310 2263 a(of) p 1367 2263 a(subsets) p Fq 1538 2263 a(\015) p 1538 2281 29 2 v Fo 1583 2263 a(\032) p Fq 1639 2263 a(X) p Fr 1701 2263 a(suc) o(h) p 1813 2263 a(that) 0 2324 y(there) p 125 2324 a(are) p 206 2324 a(no) p 274 2324 a(pairs) p Fo 393 2324 a(f) p Fq(\015) p Fl 443 2331 a(1) p Fq 463 2324 a(;) p 485 2324 a(\015) p Fl 510 2331 a(2) p Fo 530 2324 a(g) p 569 2324 a(\032) p Fq 621 2324 a(\015) p 621 2341 V Fr 666 2324 a(with) p Fq 777 2324 a(\015) p Fl 802 2331 a(1) p Fq 822 2324 a(\023\015) p Fl 864 2331 a(2) p Fr 884 2324 a(.) p 919 2324 a(W) l(e) p 1003 2324 a(de\014ne) 659 2450 y(Z\() p Fq(X) p Fr 752 2450 a(;) p 774 2450 a(\010) p Ff 809 2457 a(J) p Fr 828 2450 a(\)) p 860 2450 a(=) p Fk 942 2402 a(X) p Fp 912 2510 a(\015) p 912 2523 21 2 v Fm 932 2510 a(2D) p Fl 984 2510 a(\() p Fp(X) p Fl 1030 2510 a(\)) p Fk 1052 2402 a(Y) p Fp 1052 2507 a(\015) p Fm 1072 2507 a(2) p Fp(\015) p 1096 2519 V Fr 1124 2450 a(\010) p Ff 1159 2457 a(J) p Fr 1178 2450 a(\() p Fq(\015) p Fr 1225 2450 a(\)) 0 2620 y(if) p Fq 50 2620 a(X) p Fr 115 2620 a(is) p 169 2620 a(non-empt) o(y) l(,) p 429 2620 a(and) p 528 2620 a(de\014ne) p 674 2620 a(Z\() p Fo(;) p Fr(;) p 770 2620 a(\010) p Ff 805 2627 a(J) p Fr 824 2620 a(\)) p 865 2620 a(=) p 925 2620 a(1.) p 999 2620 a(Let) p Fo 1092 2620 a(P) p Fp 1127 2627 a(L) p Fj 1151 2632 a(1) p Fp 1168 2627 a(;L) p Fj 1202 2632 a(2) p Fr 1242 2620 a(b) q(e) p 1313 2620 a(the) p 1402 2620 a(family) p 1556 2620 a(of) p 1617 2620 a(all) p 1689 2620 a(subsets) p 1863 2620 a(of) p Fo 0 2681 a(C) p Fr 29 2681 a(\() p Fq(L) p Fl 81 2688 a(1) p Fq 101 2681 a(;) p 123 2681 a(L) p Fl 156 2688 a(2) p Fr 176 2681 a(\).) 939 2947 y(6) p 90 rotate dyy eop %%Page: 7 7 7 6 bop Fg 73 274 a(Lemma) p 272 274 a(1.3.) p Fd 380 274 a(L) n(et) p 465 274 a(functions) p Fq 677 274 a(a) p Fr 717 274 a(:) p Fo 745 274 a(C) p Fr 774 274 a(\() p Fq(L) p Fl 826 281 a(1) p Fq 846 274 a(;) p 868 274 a(L) p Fl 901 281 a(2) p Fr 921 274 a(\)) p Fo 955 274 a(!) p Fr 1019 274 a([0) p Fq(;) p Fo 1079 274 a(1) p Fr(\)) p Fd 1165 274 a(and) p Fq 1260 274 a(d) p Fr 1300 274 a(:) p Fo 1329 274 a(C) p Fr 1358 274 a(\() p Fq(L) p Fl 1410 281 a(1) p Fq 1430 274 a(;) p 1452 274 a(L) p Fl 1485 281 a(2) p Fr 1504 274 a(\)) p Fo 1538 274 a(!) p Fr 1602 274 a([0) p Fq(;) p Fo 1662 274 a(1) p Fr(\)) p Fd 1749 274 a(b) n(e) p 1809 274 a(such) 0 334 y(that) p Fk 527 394 a(X) p Fp 429 502 a(\015) p Fc 449 492 a(0) p Fm 460 502 a(2C) p Fl 505 502 a(\() p Fp(L) p Fj 543 507 a(1) p Fp 559 502 a(;L) p Fj 593 507 a(2) p Fl 610 502 a(\);) p Fp(\015) p Fc 654 492 a(0) p Fp 665 502 a(\023\015) p Fr 706 441 a(exp) o([) p Fq(a) p Fr(\() p Fq(\015) p Fm 867 420 a(0) p Fr 878 441 a(\)) p 908 441 a(+) p Fq 957 441 a(d) p Fr(\() p Fq(\015) p Fm 1029 420 a(0) p Fr 1041 441 a(\)]) p Fo(j) p Fr(\010) p Ff 1123 448 a(J) p Fr 1141 441 a(\() p Fq(\015) p Fm 1188 420 a(0) p Fr 1200 441 a(\)) p Fo(j) p 1247 441 a(\024) p Fq 1299 441 a(a) p Fr(\() p Fq(\015) p Fr 1372 441 a(\)) p 1778 441 a(\(1.18\)) p Fd 0 606 a(for) p 83 606 a(e) n(ach) p Fq 199 606 a(\015) p Fo 251 606 a(2) p 308 606 a(C) p Fr 337 606 a(\() p Fq(L) p Fl 389 613 a(1) p Fq 409 606 a(;) p 431 606 a(L) p Fl 464 613 a(2) p Fr 484 606 a(\)) p Fd(.) p 557 606 a(Then,) p Fr 706 606 a(Z\() p Fq(X) p Fr 799 606 a(;) p 821 606 a(\010) p Ff 856 613 a(J) p Fr 875 606 a(\)) p Fo 918 606 a(6) p Fr(=) p 980 606 a(0) p Fd 1028 606 a(and) p 1128 606 a(ther) n(e) p 1255 606 a(exists) p 1394 606 a(a) p 1442 606 a(unique) p 1604 606 a(function) p Fr 1802 606 a(\010) p Fl 1837 588 a(T) p Ff 1837 619 a(J) p Fr 1889 606 a(:) p Fo 0 666 a(P) p Fp 35 673 a(L) p Fj 59 678 a(1) p Fp 76 673 a(;L) p Fj 110 678 a(2) p Fo 143 666 a(!) p Fn 207 666 a(R) p Fd 260 666 a(such) p 371 666 a(that) p Fr 612 783 a(log) p 683 783 a(Z\() p Fq(X) p Fr 776 783 a(;) p 798 783 a(\010) p Ff 833 790 a(J) p Fr 852 783 a(\)) p 885 783 a(=) p Fk 962 736 a(X) p Fp 936 842 a(C) p Fl 963 842 a(;) p Fp(C) p Fm 1000 842 a(\032) p Fp(X) p Fr 1068 783 a(\010) p Fl 1103 763 a(T) p Ff 1103 796 a(J) p Fr 1131 783 a(\() p Fq(C) p Fr 1189 783 a(\)) p 1778 783 a(\(1.19\)) p Fd 0 945 a(for) p 78 945 a(every) p Fq 207 945 a(X) p Fo 265 945 a(\032) p 318 945 a(C) p Fr 347 945 a(\() p Fq(L) p Fl 399 952 a(1) p Fq 419 945 a(;) p 441 945 a(L) p Fl 474 952 a(2) p Fr 493 945 a(\)) p Fd(.) p 550 945 a(Mor) n(e) n(over,) p 779 945 a(the) p 860 945 a(function) p Fr 1052 945 a(\010) p Fl 1087 927 a(T) p Ff 1087 958 a(J) p Fd 1132 945 a(is) p 1184 945 a(given) p 1311 945 a(by) p 1375 945 a(the) p 1456 945 a(formula) p Fr 496 1066 a(\010) p Fl 531 1046 a(T) p Ff 531 1078 a(J) p Fr 558 1066 a(\() p Fq(C) p Fr 616 1066 a(\)) p 649 1066 a(=) p Fk 725 1019 a(X) p Fp 701 1124 a(B) p Fl 730 1124 a(;) p Fp(B) p Fm 769 1124 a(\032) p Fp(C) p Fr 822 1066 a(\() p Fo(\000) p Fr(1\)) p Fm 923 1046 a(j) p Fp(C) p Fm 960 1046 a(j\000j) p Fp(B) p Fm 1036 1046 a(j) p Fr 1056 1066 a(log) p 1127 1066 a(Z\() p Fq(B) p Fr 1216 1066 a(;) p 1238 1066 a(\010) p Ff 1273 1073 a(J) p Fr 1291 1066 a(\)) p Fq(;) p Fr 1778 1066 a(\(1.20\)) p Fd 0 1221 a(the) p 81 1221 a(estimate) p Fk 555 1281 a(X) p Fp 513 1386 a(C) p Fm 540 1386 a(\032) p Fp(X) p Fl 599 1386 a(;) p Fp(C) r(\023\015) p Fo 678 1328 a(j) p Fr(\010) p Fl 727 1307 a(T) p Ff 727 1340 a(J) p Fr 754 1328 a(\() p Fq(C) p Fr 812 1328 a(\)) p Fo(j) p Fr 853 1328 a(exp[) p Fk 947 1281 a(X) p Fp 942 1387 a(\015) p Fc 962 1378 a(0) p Fm 972 1387 a(2) p Fp(C) p Fq 1032 1328 a(d) p Fr(\() p Fq(\015) p Fm 1104 1307 a(0) p Fr 1116 1328 a(\)]) p Fo 1162 1328 a(\024) p Fq 1215 1328 a(a) p Fr(\() p Fq(\015) p Fr 1288 1328 a(\)) p 1778 1328 a(\(1.21\)) p Fd 0 1486 a(holds) p 125 1486 a(true) p 227 1486 a(for) p 305 1486 a(every) p Fq 434 1486 a(\015) p Fo 476 1486 a(2) p 523 1486 a(C) p Fr 552 1486 a(\() p Fq(L) p Fl 604 1493 a(1) p Fq 624 1486 a(;) p 646 1486 a(L) p Fl 679 1493 a(2) p Fr 699 1486 a(\)) p Fd(,) p 750 1486 a(and) p Fr 484 1593 a(\010) p Fl 519 1573 a(T) p Ff 519 1606 a(J) p Fr 547 1593 a(\() p Fq(C) p Fr 605 1593 a(\)) p 637 1593 a(=) p 689 1593 a(0) p Fd 731 1593 a(whenever) p Fq 943 1593 a(C) p Fd 999 1593 a(is) p 1052 1593 a(not) p 1137 1593 a(a) p 1180 1593 a(cluster.) p Fr 1778 1593 a(\(1.22\)) p Fg 0 1729 a(Standard) p 241 1729 a(W) p 294 1729 a(alls) p Fr 391 1729 a(\(See) p 495 1729 a([D,72) q(]\)) p Fg(.) p Fr 678 1729 a(Let) p Fq 765 1729 a(d) p Fo 804 1729 a(\025) p Fr 856 1729 a(3.) p 916 1729 a(W) l(e) p 999 1729 a(will) p 1090 1729 a(in) o(tro) q(duce) p 1306 1729 a(the) p 1389 1729 a(notion) p 1540 1729 a(of) p 1595 1729 a(standard) p 1798 1729 a(w) o(alls) 0 1789 y(to) p 59 1789 a(express) p 229 1789 a(con) o(tour) p 406 1789 a(mo) q(dels) p 569 1789 a(and) p 664 1789 a(to) p 723 1789 a(use) p 807 1789 a(it) p 855 1789 a(in) p 911 1789 a(the) p 995 1789 a(pro) q(of) p 1122 1789 a(of) p 1177 1789 a(k) o(ey) p 1265 1789 a(prop) q(ositions) p 1540 1789 a(\(Prop) q(ositions) p 1840 1789 a(2.1) 0 1849 y(and) p 97 1849 a(2.2\).) p 222 1849 a(W) l(e) p 308 1849 a(de\014ne) p 452 1849 a(H\() p Fq(z) p Fr 533 1849 a(\)) p 570 1849 a(=) p Fo 626 1849 a(f) p Fq(x) p Fo 697 1849 a(2) p Fn 748 1849 a(R) p Fp 787 1831 a(d) p Fr 804 1849 a(;) p Fq 826 1849 a(x) p Fp 854 1831 a(d) p Fr 893 1849 a(=) p Fq 949 1849 a(z) p Fo 974 1849 a(g) p Fr 1017 1849 a(for) p 1095 1849 a(eac) o(h) p Fq 1207 1849 a(z) p Fo 1250 1849 a(2) p Fn 1302 1849 a(R) p Fr(.) p 1381 1849 a(Let) p Fq 1471 1849 a(\031) p Fr 1519 1849 a(b) q(e) p 1588 1849 a(the) p 1675 1849 a(orthogonal) 0 1910 y(pro) s(jection:) p Fn 250 1910 a(R) p Fp 289 1892 a(d) p Fo 320 1910 a(!) p Fr 384 1910 a(H\() p Fo(\000) p Fl 484 1890 a(1) p 484 1898 18 2 v 484 1927 a(2) p Fr 506 1910 a(\)) p 540 1910 a(and) p 633 1910 a(let) p Fn 703 1910 a(M) p Fp 747 1892 a(n) p Fr 788 1910 a(b) q(e) p 854 1910 a(the) p Fq 936 1910 a(n) p Fr(-dimensional) p 1249 1910 a(standard) p 1451 1910 a(Hausdor\013) p 1673 1910 a(measure) p 1862 1910 a(in) p Fn 0 1970 a(R) p Fp 39 1952 a(d) p Fr 72 1970 a(for) p 147 1970 a(eac) o(h) p Fq 257 1970 a(n) p Fo 300 1970 a(\024) p Fq 352 1970 a(d) p Fo 389 1970 a(\000) p Fr 438 1970 a(1.) p 498 1970 a(W) l(e) p 582 1970 a(will) p 674 1970 a(call) p Fq 764 1970 a(w) p Fr 816 1970 a(a) p Fq 857 1970 a(f) p 886 1970 a(ace) p Fr 972 1970 a(if) p Fq 382 2077 a(w) p Fo 432 2077 a(2) p 479 2077 a(f) p Fq(Q) p Fr(\() p Fq(x) p Fr(\)) p Fo 619 2077 a(\\) p Fq 663 2077 a(Q) p Fr(\() p Fq(y) p Fr 747 2077 a(\);) p Fq 788 2077 a(x;) p 838 2077 a(y) p Fo 876 2077 a(2) p Fn 923 2077 a(Z) p Fp 959 2056 a(d) p Fr 993 2077 a(suc) o(h) p 1103 2077 a(that) p Fo 1209 2077 a(k) p Fq(x) p Fo 1272 2077 a(\000) p Fq 1322 2077 a(y) p Fo 1348 2077 a(k) p Fl 1373 2084 a(1) p Fr 1406 2077 a(=) p 1458 2077 a(1) p Fo(g) p Fq(:) p Fr 0 2183 a(Let) p 85 2183 a(us) p 146 2183 a(\014x) p 213 2183 a(\003\() p Fq(L) p Fl 299 2190 a(1) p Fq 319 2183 a(;) p 341 2183 a(L) p Fl 374 2190 a(2) p Fr 393 2183 a(\)) p 427 2183 a(and) p 519 2183 a(\000) p Fo 564 2183 a(2) p 611 2183 a(O) p Fr 652 2183 a(\() p Fq(L) p Fl 704 2190 a(1) p Fq 724 2183 a(;) p 746 2183 a(L) p Fl 779 2190 a(2) p Fr 798 2183 a(\).) p 852 2183 a(F) l(or) p 937 2183 a(a) p 976 2183 a(face) p Fq 1073 2183 a(w) p Fo 1123 2183 a(\032) p Fr 1175 2183 a(\000,) p 1234 2183 a(w) o(e) p 1304 2183 a(will) p 1394 2183 a(call) p Fq 1481 2183 a(w) p Fr 1532 2183 a(a) p Fq 1570 2183 a(ceil) q(ing) p 1731 2183 a(f) p 1760 2183 a(ace) p Fr 1844 2183 a(\(of) 0 2244 y(\000\)) p 63 2244 a(if) p Fn 105 2244 a(M) p Fp 149 2225 a(d) p Fm(\000) p Fl(1) p Fr 217 2244 a(\() p Fq(\031) p Fr 266 2244 a(\() p Fq(w) p Fr 321 2244 a(\)\)) p 372 2244 a(=) p 424 2244 a(1) p 462 2244 a(and) p 554 2244 a(there) p 676 2244 a(is) p 722 2244 a(no) p 787 2244 a(other) p 911 2244 a(face) p Fq 1007 2244 a(w) p Fm 1043 2225 a(0) p Fo 1069 2244 a(\032) p Fr 1121 2244 a(\000) p 1165 2244 a(suc) o(h) p 1272 2244 a(that) p Fq 1375 2244 a(\031) p Fr 1405 2244 a(\() p Fq(w) p Fr 1460 2244 a(\)) p 1492 2244 a(=) p Fq 1544 2244 a(\031) p Fr 1574 2244 a(\() p Fq(w) p Fm 1629 2225 a(0) p Fr 1641 2244 a(\).) p 1694 2244 a(The) p 1791 2244 a(other) 0 2304 y(faces) p 122 2304 a(\(in) p 201 2304 a(\000\)) p 271 2304 a(will) p 367 2304 a(b) q(e) p 437 2304 a(called) p Fq 579 2304 a(w) q(al) q(l) p 692 2304 a(f) p 721 2304 a(aces) p Fr 833 2304 a(\(of) p 912 2304 a(\000\).) p 1007 2304 a(By) p Fq 1088 2304 a(w) q(al) q(l) q(s) p Fr 1224 2304 a(\(of) p 1302 2304 a(\000\),) p 1386 2304 a(w) o(e) p 1461 2304 a(will) p 1557 2304 a(mean) p 1691 2304 a(connected) 0 2364 y(comp) q(onen) o(ts) p 269 2364 a(of) p 324 2364 a(the) p 408 2364 a(set) p Fo 497 2471 a(f) p Fq(v) p Fo 561 2471 a(2) p Fn 608 2471 a(R) p Fp 647 2450 a(d) p Fr 665 2471 a(;) p 687 2471 a(for) p 761 2471 a(some) p 883 2471 a(w) o(all) p 985 2471 a(face) p Fq 1084 2471 a(w) p Fr 1136 2471 a(of) p 1192 2471 a(\000) p Fq(;) p 1244 2471 a(v) p Fo 1283 2471 a(2) p Fq 1330 2471 a(w) p Fo 1366 2471 a(g) p Fq(:) p Fr 0 2577 a(Let) p Fq 87 2577 a(W) p Fm 140 2559 a(0) p Fr 167 2577 a(b) q(e) p 233 2577 a(a) p 273 2577 a(w) o(all.) p 394 2577 a(Then,) p 534 2577 a(there) p 659 2577 a(exists) p 793 2577 a(a) p 833 2577 a(con\014guration) p Fq 1128 2577 a(\033) p Fo 1171 2577 a(2) p Fr 1218 2577 a(\012) p Fl 1253 2585 a(\003\() p Fp(L) p Fj 1315 2590 a(1) p Fp 1333 2585 a(;L) p Fj 1367 2590 a(2) p Fl 1384 2585 a(\)) p Fr 1416 2577 a(suc) o(h) p 1525 2577 a(that) p 1631 2577 a(the) p 1714 2577 a(family) p 1863 2577 a(of) 0 2638 y(w) o(alls) p 123 2638 a(corresp) q(onding) p 438 2638 a(to) p 499 2638 a(\000) p Fp 529 2620 a(!) p Fl 529 2652 a(\003\() p Fp(L) p Fj 591 2657 a(1) p Fp 609 2652 a(;L) p Fj 643 2657 a(2) p Fl 660 2652 a(\)) p Fr 676 2638 a(\() p Fq(\033) p Fr 725 2638 a(\)) p 762 2638 a(consists) p 943 2638 a(of) p 1001 2638 a(the) p 1087 2638 a(only) p 1196 2638 a(w) o(all) p Fq 1299 2638 a(W) p Fr 1370 2638 a(whic) o(h) p 1512 2638 a(is) p 1562 2638 a(obtained) p 1765 2638 a(b) o(y) p 1834 2638 a(the) 0 2702 y(v) o(ertical) p 172 2702 a(shift) p 282 2702 a(of) p Fq 336 2702 a(W) p Fm 389 2684 a(0) p Fr 401 2702 a(.) p 435 2702 a(W) l(e) p 518 2702 a(will) p 610 2702 a(call) p Fq 698 2702 a(W) p Fr 766 2702 a(a) p Fq 806 2702 a(standar) q(d) p 1016 2702 a(w) q(al) q(l) p Fr 1110 2702 a(.) p 1144 2702 a(F) l(or) p 1231 2702 a(the) p 1314 2702 a(family) p 1462 2702 a(of) p 1516 2702 a(w) o(alls) p Fo 1636 2702 a(f) p Fq(W) p Fm 1714 2684 a(0) p Fp 1707 2715 a(i) p Fo 1725 2702 a(g) p Fr 1766 2702 a(\(of) p 1839 2702 a(\000\),) 0 2762 y(w) o(e) p 70 2762 a(ha) o(v) o(e) p 180 2762 a(a) p 219 2762 a(unique) p 375 2762 a(family) p 522 2762 a(of) p 575 2762 a(standard) p 777 2762 a(w) o(alls) p Fo 896 2762 a(f) p Fq(W) p Fp 967 2769 a(i) p Fo 981 2762 a(g) p Fr 1020 2762 a(\(corresp) q(onding) p 1350 2762 a(to) p 1407 2762 a(\000\).) p 1491 2762 a(By) p Fo 1566 2762 a(S) t(W) p Fr 1653 2762 a(\() p Fq(L) p Fl 1705 2769 a(1) p Fq 1725 2762 a(;) p 1747 2762 a(L) p Fl 1780 2769 a(2) p Fr 1800 2762 a(\),) p 1847 2762 a(w) o(e) 0 2823 y(will) p 90 2823 a(denote) p 245 2823 a(the) p 327 2823 a(collection) p 542 2823 a(of) p 595 2823 a(families) p 771 2823 a(of) p 824 2823 a(standard) p 1026 2823 a(w) o(alls) p 1144 2823 a(whic) o(h) p 1282 2823 a(corresp) q(ond) p 1528 2823 a(to) p 1586 2823 a(\000) p Fp 1616 2805 a(!) p Fl 1616 2837 a(\003\() p Fp(L) p Fj 1678 2842 a(1) p Fp 1695 2837 a(;L) p Fj 1729 2842 a(2) p Fl 1747 2837 a(\)) p Fr 1762 2823 a(\() p Fq(\033) p Fr 1811 2823 a(\)) p 1844 2823 a(for) 939 2947 y(7) p 90 rotate dyy eop %%Page: 8 8 8 7 bop Fr 0 274 a(some) p Fq 121 274 a(\033) p Fo 164 274 a(2) p Fr 211 274 a(\012) p Fl 246 282 a(\003\() p Fp(L) p Fj 308 287 a(1) p Fp 326 282 a(;L) p Fj 360 287 a(2) p Fl 377 282 a(\)) p Fr 393 274 a(.) p 428 274 a(W) l(e) p 510 274 a(de\014ne) p Fo 650 274 a(S) t(W) p Fr 737 274 a(\() p Fo(\0001) p Fq(;) p Fo 867 274 a(1) p Fr(\)) p 949 274 a(=) p Fo 1001 274 a([) p Fp 1034 281 a(N) p Fm 1066 281 a(2) p Ff(N) p Fo 1115 274 a(S) t(W) p Fr 1202 274 a(\() p Fo(\000) p Fq(N) r(;) p 1323 274 a(N) p Fr 1367 274 a(\).) p 1421 274 a(Note) p 1538 274 a(that) p 1642 274 a(there) p 1765 274 a(is) p 1813 274 a(one-) 0 334 y(to-one) p 153 334 a(corresp) q(ondence) p 497 334 a(b) q(et) o(w) o(een) p Fo 689 334 a(O) p Fr 730 334 a(\() p Fo(\0001) p Fq(;) p Fo 860 334 a(1) p Fr(\)) p 948 334 a(and) p Fo 1046 334 a(S) t(W) p Fr 1133 334 a(\() p Fo(\0001) p Fq(;) p Fo 1263 334 a(1) p Fr(\).) p 1377 334 a(By) p Fn 1458 334 a(W) p Fr 1504 334 a(\(\000) q(\)) p 1596 334 a(and) p 1694 334 a(\000\() p Fn(W) p Fr 1790 334 a(\),) p 1847 334 a(w) o(e) 0 394 y(will) p 91 394 a(mean) p 220 394 a(the) p 302 394 a(family) p 450 394 a(of) p 504 394 a(standard) p 706 394 a(w) o(alls) p 826 394 a(corresp) q(onding) p 1138 394 a(to) p 1196 394 a(the) p 1279 394 a(op) q(en) p 1395 394 a(con) o(tour) p 1572 394 a(\000) p Fo 1616 394 a(2) p 1663 394 a(O) p Fr 1704 394 a(\() p Fo(\0001) p Fq(;) p Fo 1834 394 a(1) p Fr(\)) 0 455 y(and) p 97 455 a(the) p 183 455 a(op) q(en) p 304 455 a(con) o(tour) p 483 455 a(corresp) q(onding) p 799 455 a(to) p 861 455 a(the) p 947 455 a(family) p 1098 455 a(of) p 1156 455 a(standard) p 1362 455 a(w) o(alls) p Fn 1485 455 a(W) p Fo 1552 455 a(2) p 1603 455 a(S) t(W) p Fr 1691 455 a(\() p Fo(\0001) p Fq(;) p Fo 1821 455 a(1) p Fr(\),) 0 515 y(resp) q(ectiv) o(ely) l(.) p 281 515 a(F) l(or) p 368 515 a(eac) o(h) p Fn 478 515 a(W) p Fo 542 515 a(2) p 589 515 a(S) t(W) p Fr 676 515 a(\() p Fo(\0001) p Fq(;) p Fo 806 515 a(1) p Fr(\),) p 904 515 a(w) o(e) p 976 515 a(de\014ne) 343 623 y(h) p Fl 370 602 a(+) p Fr 400 623 a(\() p Fn(W) p Fr 466 623 a(\)) p 501 623 a(=) p 553 623 a(h) p Fl 580 602 a(+) p Fr 610 623 a(\(\000\() p Fn(W) p Fr 725 623 a(\)\)) p 864 623 a(and) p 1040 623 a(h) p Fm 1067 602 a(\000) p Fr 1096 623 a(\() p Fn(W) p Fr 1162 623 a(\)) p 1198 623 a(=) p 1250 623 a(h) p Fm 1277 602 a(\000) p Fr 1306 623 a(\(\000\() p Fn(W) p Fr 1421 623 a(\)\)) p Fq(:) p Fr 1778 623 a(\(1.23\)) 73 731 y(W) l(e) p 157 731 a(will) p 248 731 a(in) o(tro) q(duce) p 464 731 a(a) p 504 731 a(partial) p 661 731 a(order) p Fo 788 731 a(\036) p Fr 842 731 a(for) p 916 731 a(standard) p 1119 731 a(w) o(alls) p 1239 731 a(of) p 1294 731 a(eac) o(h) p Fn 1403 731 a(W) p Fo 1467 731 a(2) p 1514 731 a(S) t(W) p Fr 1601 731 a(\() p Fo(\0001) p Fq(;) p Fo 1731 731 a(1) p Fr(\).) p 1834 731 a(W) l(e) 0 791 y(de\014ne) p 141 791 a(the) p 225 791 a(map) p 336 791 a(^) p Fq 333 791 a(\031) p Fr 377 791 a(:) p Fn 404 791 a(R) p Fp 443 773 a(d) p Fo 474 791 a(\033) p Fq 527 791 a(V) p Fo 580 791 a(7!) p Fr 646 791 a(^) p Fq 643 791 a(\031) p Fr 673 791 a(\() p Fq(V) p Fr 731 791 a(\)) p Fo 764 791 a(\032) p Fr 816 791 a(H\() p Fo(\000) p Fl 916 771 a(1) p 916 779 18 2 v 916 808 a(2) p Fr 938 791 a(\)) p 974 791 a(b) o(y) 177 899 y(^) p Fq 175 899 a(\031) p Fr 204 899 a(\() p Fq(V) p Fr 262 899 a(\)) p 295 899 a(=) p Fo 347 899 a(f) p Fq(x) p Fo 413 899 a(2) p Fr 460 899 a(H\() p Fo(\000) p Fl 560 879 a(1) p 560 887 V 560 916 a(2) p Fr 582 899 a(\);) p 623 899 a(an) o(y) p 715 899 a(path) p Fq 829 899 a(\015) p Fr 871 899 a(:) p Fq 898 899 a(x) p Fo 940 899 a(!) p 1003 899 a(1) p Fr 1070 899 a(in) p 1126 899 a(H\() p Fo(\000) p Fl 1226 879 a(1) p 1226 887 V 1226 916 a(2) p Fr 1248 899 a(\)) p 1284 899 a(in) o(tersects) p Fq 1499 899 a(\031) p Fr 1529 899 a(\() p Fq(V) p Fr 1587 899 a(\)) p Fo(g) p Fq(:) p Fr 1778 971 a(\(1.24\)) 0 1079 y(W) l(e) p 87 1079 a(de\014ne) p 230 1079 a(the) p 316 1079 a(partial) p 476 1079 a(order) p Fo 606 1079 a(\036) p Fr 664 1079 a(naturally) p 876 1079 a(induced) p 1060 1079 a(b) o(y) p 1130 1079 a(\() p Fo(f) p Fr 1177 1079 a(^) p Fq 1174 1079 a(\031) p Fr 1204 1079 a(\() p Fq(W) p Fr 1276 1079 a(\);) p Fq 1317 1079 a(W) p Fo 1387 1079 a(2) p Fn 1439 1079 a(W) p Fo 1485 1079 a(g) p Fq(;) p Fo 1532 1079 a(\032) p Fr(\)) p 1612 1079 a(for) p 1689 1079 a(eac) o(h) p Fn 1801 1079 a(W) p Fo 1869 1079 a(2) 0 1139 y(S) t(W) p Fr 87 1139 a(\() p Fo(\0001) p Fq(;) p Fo 217 1139 a(1) p Fr(\).) p 321 1139 a(Let) p Fn 408 1139 a(W) p Fo 472 1139 a(2) p 519 1139 a(S) t(W) p Fr 606 1139 a(\() p Fo(\0001) p Fq(;) p Fo 736 1139 a(1) p Fr(\)) p 820 1139 a(and) p 915 1139 a(let) p Fq 986 1139 a(W) p Fo 1052 1139 a(2) p Fn 1099 1139 a(W) p Fr 1146 1139 a(.) p 1184 1139 a(W) l(e) p 1268 1139 a(de\014ne) p Fn 521 1247 a(W) p Fr 568 1247 a(\() p Fq(W) p Fr 640 1247 a(\)) p 675 1247 a(=) p Fo 727 1247 a(f) p Fq(W) p Fm 805 1227 a(0) p Fo 830 1247 a(2) p Fn 877 1247 a(W) p Fo 924 1247 a(nf) p Fq(W) p Fo 1027 1247 a(g) p Fr(;) p Fq 1074 1247 a(W) p Fm 1127 1227 a(0) p Fo 1155 1247 a(\037) p Fq 1207 1247 a(W) p Fo 1260 1247 a(g) p Fq(:) p Fr 1778 1247 a(\(1.25\)) 0 1355 y(Note) p 118 1355 a(that) p Fn 224 1355 a(W) p Fr 270 1355 a(\() p Fq(W) p Fr 342 1355 a(\)) p Fo 378 1355 a(2) p 425 1355 a(S) t(W) p Fr 513 1355 a(\() p Fo(\0001) p Fq(;) p Fo 643 1355 a(1) p Fr(\).) p 746 1355 a(W) l(e) p 830 1355 a(can) p 920 1355 a(see) p 999 1355 a(that) p Fq 1104 1355 a(x) p Fp 1132 1337 a(d) p Fr 1166 1355 a(=) p Fq 1218 1355 a(y) p Fp 1244 1337 a(d) p Fr 1280 1355 a(for) p 1355 1355 a(an) o(y) p Fq 1447 1355 a(x;) p 1497 1355 a(y) p Fo 1536 1355 a(2) p Fr 1583 1355 a(\000\() p Fn(W) p Fr 1679 1355 a(\() p Fq(W) p Fr 1751 1355 a(\)\)) p 1808 1355 a(suc) o(h) 0 1415 y(that) p Fq 106 1415 a(\031) p Fr 136 1415 a(\() p Fq(x) p Fr(\)) p Fo 215 1415 a(2) p Fr 264 1415 a(^) p Fq 262 1415 a(\031) p Fr 291 1415 a(\() p Fq(W) p Fr 363 1415 a(\)) p 398 1415 a(and) p Fq 493 1415 a(\031) p Fr 523 1415 a(\() p Fq(y) p Fr 568 1415 a(\)) p Fo 600 1415 a(2) p Fr 649 1415 a(^) p Fq 647 1415 a(\031) p Fr 676 1415 a(\() p Fq(W) p Fr 748 1415 a(\).) p 802 1415 a(Then,) 151 1523 y(b\() p Fq(W) o(;) p Fn 264 1523 a(W) p Fr 310 1523 a(\)) p 346 1523 a(=) p Fq 398 1523 a(x) p Fp 426 1503 a(d) p Fr 457 1523 a(+) p 506 1523 a(\(1) p Fq(=) p Fr(2\)) p 666 1523 a(for) p 740 1523 a(some) p Fq 863 1523 a(x) p Fo 904 1523 a(2) p Fr 951 1523 a(\000\() p Fn(W) p Fr 1047 1523 a(\() p Fq(W) p Fr 1119 1523 a(\)\)) p 1176 1523 a(suc) o(h) p 1286 1523 a(that) p Fq 1392 1523 a(\031) p Fr 1422 1523 a(\() p Fq(x) p Fr(\)) p Fo 1501 1523 a(2) p Fr 1551 1523 a(^) p Fq 1548 1523 a(\031) p Fr 1578 1523 a(\() p Fq(W) p Fr 1650 1523 a(\)) 1778 1596 y(\(1.26\)) 0 1704 y(is) p 49 1704 a(w) o(ell-de\014ned.) p 335 1704 a(F) l(or) p 422 1704 a(eac) o(h) p 532 1704 a(\000) p Fo 576 1704 a(2) p 623 1704 a(O) p Fr 664 1704 a(\() p Fo(\0001) p Fq(;) p Fo 794 1704 a(1) p Fr(\)) p 879 1704 a(and) p 974 1704 a(eac) o(h) p Fq 1083 1704 a(W) p Fo 1150 1704 a(2) p Fn 1197 1704 a(W) p Fr 1244 1704 a(\(\000\),) p 1345 1704 a(w) o(e) p 1417 1704 a(also) p 1515 1704 a(de\014ne) 664 1812 y(b\() p Fq(W) o(;) p Fr 777 1812 a(\000\)) p 840 1812 a(=) p 892 1812 a(b\() p Fq(W) o(;) p Fn 1005 1812 a(W) p Fr 1051 1812 a(\(\000) q(\)\)) p Fq(:) p Fr 1778 1812 a(\(1.27\)) p Fg 73 1920 a(Lemma) p 269 1920 a(1.4.) p Fd 374 1920 a(L) n(et) p Fn 456 1920 a(W) p Fo 520 1920 a(2) p 567 1920 a(S) t(W) p Fr 654 1920 a(\() p Fo(\0001) p Fq(;) p Fo 784 1920 a(1) p Fr(\)) p Fd(.) p 889 1920 a(Supp) n(ose) p 1072 1920 a(that) p Fo 1169 1920 a(f) p Fq(W) p Fp 1240 1927 a(i) p Fo 1254 1920 a(g) p Fp 1279 1902 a(n) 1279 1932 y(i) p Fl(=1) p Fo 1352 1920 a(\032) p Fn 1404 1920 a(W) p Fd 1469 1920 a(and) p Fq 1561 1920 a(W) p Fl 1607 1927 a(1) p Fo 1641 1920 a(\036) p 1693 1920 a(\001) p 1715 1920 a(\001) p 1737 1920 a(\001) p 1765 1920 a(\036) p Fq 1818 1920 a(W) p Fp 1864 1927 a(n) p Fd 1887 1920 a(.) 0 1980 y(Then,) p 142 1980 a(it) p 191 1980 a(holds) p 315 1980 a(that) p Fn 415 1980 a(M) p Fp 459 1962 a(d) p Fm(\000) p Fl(1) p Fr 527 1980 a(\() p Fq(W) p Fp 592 1987 a(n) p Fr 616 1980 a(\)) p Fo 648 1980 a(\025) p Fq 701 1980 a(n) p Fd(.) p Fg 73 2080 a(Lemma) p 276 2080 a(1.5.) p Fd 386 2080 a(L) n(et) p Fn 474 2080 a(W) p Fo 544 2080 a(2) p 598 2080 a(S) t(W) p Fr 685 2080 a(\() p Fo(\0001) p Fq(;) p Fo 815 2080 a(1) p Fr(\)) p Fd(.) p 931 2080 a(Supp) n(ose) p 1121 2080 a(that) p Fo 1224 2080 a(f) p Fq(W) p Fl 1295 2087 a(1) p Fq 1315 2080 a(;) p 1337 2080 a(W) p Fl 1383 2087 a(2) p Fo 1402 2080 a(g) p 1448 2080 a(\032) p Fn 1507 2080 a(W) p Fd 1578 2080 a(and) p Fq 1676 2080 a(W) p Fl 1722 2087 a(1) p Fo 1762 2080 a(\036) p Fq 1822 2080 a(W) p Fl 1868 2087 a(2) p Fd 1887 2080 a(.) 0 2140 y(Then,) p 142 2140 a(it) p 191 2140 a(holds) p 315 2140 a(that) p Fr 670 2200 a(h) p Fl 697 2180 a(+) p Fr 726 2200 a(\() p Fn(W) p Fr 792 2200 a(\() p Fq(W) p Fl 857 2207 a(2) p Fr 880 2200 a(\)\)) p Fo 932 2200 a(\024) p Fr 984 2200 a(h) p Fl 1011 2180 a(+) p Fr 1041 2200 a(\() p Fn(W) p Fr 1107 2200 a(\() p Fq(W) p Fl 1172 2207 a(1) p Fr 1194 2200 a(\)\)) p Fd 0 2287 a(and) p Fr 663 2347 a(h) p Fm 690 2326 a(\000) p Fr 720 2347 a(\() p Fn(W) p Fr 785 2347 a(\() p Fq(W) p Fl 850 2354 a(2) p Fr 873 2347 a(\)\)) p Fo 925 2347 a(\025) p Fr 978 2347 a(h) p Fm 1005 2326 a(\000) p Fr 1034 2347 a(\() p Fn(W) p Fr 1100 2347 a(\() p Fq(W) p Fl 1165 2354 a(1) p Fr 1188 2347 a(\)\)) p Fq(:) p Fg 73 2447 a(Lemma) p 272 2447 a(1.6.) p Fd 380 2447 a(L) n(et) p Fn 464 2447 a(W) p Fo 527 2447 a(2) p 574 2447 a(S) t(W) p Fr 662 2447 a(\() p Fo(\0001) p Fq(;) p Fo 792 2447 a(1) p Fr(\)) p Fd(.) p 897 2447 a(Then,) p 1039 2447 a(it) p 1088 2447 a(holds) p 1212 2447 a(that) p Fr 185 2555 a(h) p Fl 212 2534 a(+) p Fr 241 2555 a(\() p Fn(W) p Fr 307 2555 a(\)) p 343 2555 a(=) p 395 2555 a(max) p Fo 486 2555 a(f) p Fr(h) p Fl 538 2534 a(+) p Fr 567 2555 a(\() p Fn(W) p Fr 633 2555 a(\() p Fq(W) p Fr 705 2555 a(\)) p Fo 738 2555 a([) p 782 2555 a(f) p Fq(W) p Fo 860 2555 a(g) p Fr(\);) p Fq 926 2555 a(W) p Fd 996 2555 a(is) p 1048 2555 a(a) p 1090 2555 a(minimal) p 1282 2555 a(standar) n(d) p 1481 2555 a(wal) r(l) p 1583 2555 a(in) p Fn 1643 2555 a(W) p Fo 1689 2555 a(g) p Fd 0 2662 a(and) p Fr 183 2723 a(h) p Fm 210 2702 a(\000) p Fr 239 2723 a(\() p Fn(W) p Fr 305 2723 a(\)) p 341 2723 a(=) p 393 2723 a(min) p Fo 474 2723 a(f) p Fr(h) p Fm 526 2702 a(\000) p Fr 556 2723 a(\() p Fn(W) p Fr 621 2723 a(\() p Fq(W) p Fr 693 2723 a(\)) p Fo 726 2723 a([) p 770 2723 a(f) p Fq(W) p Fo 848 2723 a(g) p Fr(\);) p Fq 914 2723 a(W) p Fd 984 2723 a(is) p 1036 2723 a(a) p 1079 2723 a(minimal) p 1271 2723 a(standar) n(d) p 1469 2723 a(wal) r(l) p 1571 2723 a(in) p Fn 1631 2723 a(W) p Fo 1678 2723 a(g) p Fq(:) p Fr 73 2823 a(W) l(e) p 157 2823 a(omit) p 271 2823 a(the) p 355 2823 a(pro) q(of) p 482 2823 a(of) p 538 2823 a(these) p 663 2823 a(lemm) o(as.) 939 2947 y(8) p 90 rotate dyy eop %%Page: 9 9 9 8 bop Fg 73 274 a(Lemma) p 281 274 a(1.7.) p Fd 393 274 a(Supp) n(ose) p 586 274 a(that) p Fo 693 274 a(f) p Fn(W) p Fq 765 274 a(;) p Fn 787 274 a(W) p Fm 836 256 a(0) p Fo 851 274 a(g) p 903 274 a(\032) p 970 274 a(S) t(W) p Fr 1057 274 a(\() p Fo(\0001) p Fq(;) p Fo 1187 274 a(1) p Fr(\)) p Fd 1280 274 a(such) p 1398 274 a(that) p Fn 1505 274 a(W) p Fo 1571 274 a(\\) p Fn 1621 274 a(W) p Fm 1668 256 a(0) p Fr 1710 274 a(=) p Fo 1775 274 a(;) p Fd 1825 274 a(and) p Fn 0 334 a(W) p Fo 61 334 a([) p Fn 105 334 a(W) p Fm 152 316 a(0) p Fo 180 334 a(2) p 228 334 a(S) t(W) p Fr 315 334 a(\() p Fo(\0001) p Fq(;) p Fo 445 334 a(1) p Fr(\)) p Fd(.) p 550 334 a(Then,) p 692 334 a(we) p 764 334 a(have) p 877 334 a(that) p Fr 607 434 a(h) p Fl 634 413 a(+) p Fr 664 434 a(\() p Fn(W) p Fo 744 434 a([) p Fn 788 434 a(W) p Fm 835 413 a(0) p Fr 849 434 a(\)) p Fo 882 434 a(\024) p Fr 935 434 a(h) p Fl 962 413 a(+) p Fr 991 434 a(\() p Fn(W) p Fr 1057 434 a(\)) p 1090 434 a(+) p 1139 434 a(h) p Fl 1166 413 a(+) p Fr 1196 434 a(\() p Fn(W) p Fm 1262 413 a(0) p Fr 1276 434 a(\)) p Fd 0 534 a(and) p Fr 600 594 a(h) p Fm 627 573 a(\000) p Fr 657 594 a(\() p Fn(W) p Fo 737 594 a([) p Fn 781 594 a(W) p Fm 828 573 a(0) p Fr 843 594 a(\)) p Fo 875 594 a(\025) p Fr 928 594 a(h) p Fm 955 573 a(\000) p Fr 985 594 a(\() p Fn(W) p Fr 1050 594 a(\)) p 1083 594 a(+) p 1132 594 a(h) p Fm 1159 573 a(\000) p Fr 1189 594 a(\() p Fn(W) p Fm 1255 573 a(0) p Fr 1269 594 a(\)) p Fq(:) 73 687 y(P) p 111 687 a(r) q(oof) p Fr 209 687 a(.) p 253 687 a(Without) p 452 687 a(loss) p 547 687 a(of) p 605 687 a(generalit) o(y) l(,) p 842 687 a(w) o(e) p 916 687 a(can) p 1008 687 a(assume) p 1179 687 a(b) o(y) p 1249 687 a(Lemma) p 1425 687 a(1.6) p 1506 687 a(that) p 1614 687 a(there) p 1741 687 a(exists) p 1878 687 a(a) 0 747 y(unique) p 163 747 a(minimal) p 357 747 a(standard) p 565 747 a(w) o(all) p Fq 672 747 a(W) p Fo 746 747 a(2) p Fn 801 747 a(W) p Fo 865 747 a([) p Fn 912 747 a(W) p Fm 959 729 a(0) p Fr 974 747 a(.) p 1023 747 a(Moreo) o(v) o(er,) p 1256 747 a(w) o(e) p 1332 747 a(can) p 1426 747 a(assume) p 1599 747 a(that) p Fq 1710 747 a(W) p Fo 1784 747 a(2) p Fn 1839 747 a(W) p Fr 1886 747 a(.) 0 807 y(Note) p 118 807 a(that) p 223 807 a(there) p 348 807 a(exist) p 463 807 a(unique) p 621 807 a(minimal) p 811 807 a(standard) p 1014 807 a(w) o(alls) p 1135 807 a(in) p Fn 1191 807 a(W) p Fr 1257 807 a(and) p Fn 1352 807 a(W) p Fm 1399 789 a(0) p Fr 1413 807 a(,) p 1443 807 a(resp) q(ectiv) o(ely) l(,) p 1718 807 a(and) p 1813 807 a(that) 0 868 y(there) p 123 868 a(exist) p 236 868 a(unique) p 392 868 a(maximal) p 589 868 a(standard) p 791 868 a(w) o(alls) p 910 868 a(in) p Fn 964 868 a(W) p Fo 1018 868 a([) p Fn 1058 868 a(W) p Fm 1108 849 a(0) p Fq 1122 868 a(;) p Fn 1158 868 a(W) p Fr 1222 868 a(and) p Fn 1315 868 a(W) p Fm 1362 849 a(0) p Fr 1377 868 a(,) p 1405 868 a(resp) q(ectiv) o(ely) l(.) p 1685 868 a(Rearrange) p Fn 0 928 a(W) p Fo 64 928 a([) p Fn 111 928 a(W) p Fm 158 910 a(0) p Fr 193 928 a(in) p 254 928 a(order) p 386 928 a(of) p Fo 446 928 a(\037) p Fr(.) p 533 928 a(The) p 638 928 a(family) p 791 928 a(of) p 851 928 a(standard) p 1059 928 a(w) o(alls) p Fn 1184 928 a(W) p Fo 1248 928 a([) p Fn 1295 928 a(W) p Fm 1342 910 a(0) p Fr 1377 928 a(is) p 1431 928 a(divided) p 1607 928 a(in) o(to) p 1711 928 a(blo) q(c) o(ks) p 1863 928 a(of) 0 988 y(standard) p 202 988 a(w) o(alls) p 322 988 a(eac) o(h) p 430 988 a(of) p 484 988 a(whic) o(h) p 623 988 a(is) p 670 988 a(a) p 710 988 a(subset) p 858 988 a(of) p 912 988 a(either) p Fn 1049 988 a(W) p Fr 1114 988 a(or) p Fn 1172 988 a(W) p Fm 1219 970 a(0) p Fr 1234 988 a(.) p 1268 988 a(W) l(e) p 1351 988 a(will) p 1442 988 a(sho) o(w) p 1561 988 a(Lemma) p 1734 988 a(1.7) p 1811 988 a(only) 0 1048 y(for) p 76 1048 a(h) p Fl 103 1030 a(+) p Fr 150 1048 a(b) o(y) p 219 1048 a(induction) p 437 1048 a(on) p 506 1048 a(the) p 591 1048 a(n) o(um) o(b) q(er) p 770 1048 a(of) p 826 1048 a(these) p 953 1048 a(blo) q(c) o(ks.) p 1123 1048 a(T) l(o) p 1196 1048 a(b) q(e) p 1264 1048 a(more) p 1387 1048 a(precise,) p 1562 1048 a(w) o(e) p 1635 1048 a(will) p 1729 1048 a(sho) o(w) p 1851 1048 a(b) o(y) 0 1108 y(induction) p 217 1108 a(that) p 322 1108 a(for) p 397 1108 a(an) o(y) p Fq 489 1108 a(k) p Fo 530 1108 a(2) p Fn 577 1108 a(N) p Fr(,) 607 1208 y(h) p Fl 634 1188 a(+) p Fr 664 1208 a(\() p Fn(W) p Fo 744 1208 a([) p Fn 788 1208 a(W) p Fm 835 1188 a(0) p Fr 849 1208 a(\)) p Fo 882 1208 a(\024) p Fr 935 1208 a(h) p Fl 962 1188 a(+) p Fr 991 1208 a(\() p Fn(W) p Fr 1057 1208 a(\)) p 1090 1208 a(+) p 1139 1208 a(h) p Fl 1166 1188 a(+) p Fr 1196 1208 a(\() p Fn(W) p Fm 1262 1188 a(0) p Fr 1276 1208 a(\)) 0 1308 y(if) p Fn 271 1368 a(W) p Fo 332 1368 a([) p Fn 376 1368 a(W) p Fm 423 1348 a(0) p Fr 452 1368 a(=) p Fo 504 1368 a(f) p Fq(W) p Fp 582 1348 a(k) p Fl 601 1348 a(+1) p Fp 575 1380 a(n) p Fe 596 1386 a(k) p Fj 613 1386 a(+1) p Fq 656 1368 a(;) p Fo 678 1368 a(\001) p 700 1368 a(\001) p 722 1368 a(\001) p Fq 752 1368 a(;) p 774 1368 a(W) p Fp 827 1348 a(k) p Fl 846 1348 a(+1) 820 1380 y(1) p Fq 893 1368 a(;) p 915 1368 a(W) p Fp 968 1348 a(k) 961 1380 y(n) p Fe 982 1386 a(k) p Fq 1004 1368 a(;) p Fo 1026 1368 a(\001) p 1048 1368 a(\001) p 1070 1368 a(\001) p Fq 1100 1368 a(;) p 1122 1368 a(W) p Fp 1175 1348 a(k) p Fl 1168 1380 a(1) p Fq 1196 1368 a(;) p Fo 1218 1368 a(\001) p 1240 1368 a(\001) p 1262 1368 a(\001) p Fq 1293 1368 a(;) p 1315 1368 a(W) p Fl 1368 1348 a(1) p Fp 1361 1380 a(n) p Fj 1382 1385 a(1) p Fq 1401 1368 a(;) p Fo 1423 1368 a(\001) p 1445 1368 a(\001) p 1467 1368 a(\001) p Fq 1498 1368 a(;) p 1520 1368 a(W) p Fl 1573 1348 a(1) 1566 1380 y(1) p Fo 1592 1368 a(g) p Fq(;) p Fo 341 1462 a(f) p Fq(W) p Fp 419 1438 a(j) 412 1475 y(i) p Fo 437 1462 a(g) p Fp 462 1435 a(n) p Fe 483 1440 a(j) p Fp 462 1475 a(i) p Fl(=1) p Fo 535 1462 a(\032) p Fn 587 1462 a(W) p Fr 686 1462 a(for) p 760 1462 a(o) q(dd) p Fq 857 1462 a(j;) p Fo 996 1462 a(f) p Fq(W) p Fp 1074 1438 a(j) 1067 1475 y(i) p Fo 1092 1462 a(g) p Fp 1117 1435 a(n) p Fe 1138 1440 a(j) p Fp 1117 1475 a(i) p Fl(=1) p Fo 1190 1462 a(\032) p Fn 1243 1462 a(W) p Fm 1289 1441 a(0) p Fr 1353 1462 a(for) p 1427 1462 a(ev) o(en) p Fq 1539 1462 a(j) p Fr 0 1545 a(and) p Fo 179 1645 a(f) p Fq(W) p Fp 257 1624 a(k) p Fl 276 1624 a(+1) p Fp 250 1657 a(n) p Fe 271 1663 a(k) p Fj 288 1663 a(+1) p Fo 344 1645 a(\037) p 397 1645 a(\001) p 419 1645 a(\001) p 441 1645 a(\001) p 469 1645 a(\037) p Fq 522 1645 a(W) p Fp 575 1624 a(k) p Fl 594 1624 a(+1) 568 1657 y(1) p Fo 655 1645 a(\037) p Fq 707 1645 a(W) p Fp 760 1624 a(k) 753 1657 y(n) p Fe 774 1663 a(k) p Fo 810 1645 a(\037) p 862 1645 a(\001) p 884 1645 a(\001) p 906 1645 a(\001) p 934 1645 a(\037) p Fq 987 1645 a(W) p Fp 1040 1624 a(k) p Fl 1033 1657 a(1) p Fo 1075 1645 a(\037) p 1127 1645 a(\001) p 1149 1645 a(\001) p 1171 1645 a(\001) p 1199 1645 a(\037) p Fq 1252 1645 a(W) p Fl 1305 1624 a(1) p Fp 1298 1657 a(n) p Fj 1319 1662 a(1) p Fo 1353 1645 a(\037) p 1405 1645 a(\001) p 1427 1645 a(\001) p 1449 1645 a(\001) p 1477 1645 a(\037) p Fq 1530 1645 a(W) p Fl 1583 1624 a(1) 1576 1657 y(1) p Fo 1602 1645 a(g) p Fq(:) p Fr 1778 1717 a(\(1.28\)) 0 1817 y(The) p 100 1817 a(inequalit) o(y) p 327 1817 a(for) p 401 1817 a(h) p Fm 428 1799 a(\000) p Fr 474 1817 a(can) p 563 1817 a(b) q(e) p 630 1817 a(obtained) p 830 1817 a(in) p 887 1817 a(a) p 928 1817 a(similar) p 1088 1817 a(w) o(a) o(y) l(.) 73 1877 y(W) l(e) p 159 1877 a(will) p 252 1877 a(\014rst) p 355 1877 a(consider) p 546 1877 a(the) p 632 1877 a(case) p 736 1877 a(where) p Fq 879 1877 a(k) p Fr 922 1877 a(=) p 977 1877 a(1.) p 1041 1877 a(In) p 1104 1877 a(this) p 1200 1877 a(case,) p 1319 1877 a(w) o(e) p 1392 1877 a(can) p 1483 1877 a(see) p 1564 1877 a(that) p Fq 1671 1877 a(W) p Fl 1724 1859 a(2) 1717 1890 y(1) p Fo 1760 1877 a(\037) p Fq 1815 1877 a(W) p Fl 1868 1859 a(1) p Fp 1861 1890 a(n) p Fj 1882 1895 a(1) p Fr 0 1937 a(for) p 74 1937 a(the) p 158 1937 a(maximal) p 357 1937 a(standard) p 560 1937 a(w) o(all) p Fq 662 1937 a(W) p Fl 715 1919 a(1) p Fp 708 1950 a(n) p Fj 729 1955 a(1) p Fo 762 1937 a(2) p Fn 809 1937 a(W) p Fr 875 1937 a(and) p 970 1937 a(the) p 1053 1937 a(minimal) p 1243 1937 a(standard) p 1446 1937 a(w) o(all) p Fq 1548 1937 a(W) p Fl 1601 1919 a(2) 1594 1950 y(1) p Fo 1634 1937 a(2) p Fn 1681 1937 a(W) p Fm 1728 1919 a(0) p Fr 1742 1937 a(.) p 1778 1937 a(Then,) 0 1998 y(w) o(e) p 72 1998 a(can) p 161 1998 a(see) p 240 1998 a(that) 298 2097 y(\() p Fn(W) p Fo 378 2097 a([) p Fn 422 2097 a(W) p Fm 469 2077 a(0) p Fr 484 2097 a(\)\() p Fq(W) p Fl 575 2077 a(1) p Fp 568 2110 a(n) p Fj 589 2115 a(1) p Fr 608 2097 a(\)) p 641 2097 a(=) p Fn 693 2097 a(W) p Fm 740 2077 a(0) p Fr 852 2097 a(and) p 1028 2097 a(b\() p Fq(W) p Fl 1127 2077 a(1) p Fp 1120 2110 a(n) p Fj 1141 2115 a(1) p Fq 1161 2097 a(;) p Fn 1183 2097 a(W) p Fo 1244 2097 a([) p Fn 1288 2097 a(W) p Fm 1335 2077 a(0) p Fr 1349 2097 a(\)) p Fo 1382 2097 a(\024) p Fr 1435 2097 a(h) p Fl 1462 2077 a(+) p Fr 1491 2097 a(\() p Fn(W) p Fm 1557 2077 a(0) p Fr 1572 2097 a(\)) p Fq(:) p Fr 0 2197 a(Therefore,) p 234 2197 a(w) o(e) p 306 2197 a(ha) o(v) o(e) p 419 2197 a(that) 438 2297 y(h) p Fl 465 2277 a(+) p Fr 495 2297 a(\() p Fn(W) p Fo 575 2297 a([) p Fn 619 2297 a(W) p Fm 666 2277 a(0) p Fr 681 2297 a(\)) 358 2370 y(=) p 438 2370 a(max) p Fo 529 2370 a(f) p Fr(h) p Fl 581 2349 a(+) p Fr 611 2370 a(\(\() p Fn(W) p Fo 709 2370 a([) p Fn 754 2370 a(W) p Fm 801 2349 a(0) p Fr 815 2370 a(\)\() p Fq(W) p Fl 906 2349 a(1) p Fp 899 2382 a(n) p Fj 920 2387 a(1) p Fr 940 2370 a(\)\)) p Fq(;) p Fr 1016 2370 a(b\() p Fq(W) p Fl 1115 2349 a(1) p Fp 1108 2382 a(n) p Fj 1129 2387 a(1) p Fq 1149 2370 a(;) p Fn 1171 2370 a(W) p Fo 1232 2370 a([) p Fn 1276 2370 a(W) p Fm 1323 2349 a(0) p Fr 1337 2370 a(\)) p 1367 2370 a(+) p 1416 2370 a(h) p Fl 1443 2349 a(+) p Fr 1473 2370 a(\() p Fn(W) p Fr 1539 2370 a(\)) p Fo(g) 358 2442 y(\024) p Fr 438 2442 a(h) p Fl 465 2422 a(+) p Fr 495 2442 a(\() p Fn(W) p Fm 561 2422 a(0) p Fr 575 2442 a(\)) p 605 2442 a(+) p 654 2442 a(h) p Fl 681 2422 a(+) p Fr 711 2442 a(\() p Fn(W) p Fr 777 2442 a(\)) p Fq(;) p Fr 1778 2442 a(\(1.29\)) 0 2542 y(whic) o(h) p 140 2542 a(implies) p 305 2542 a(\(1.28\)) p 446 2542 a(for) p Fq 521 2542 a(k) p Fr 561 2542 a(=) p 613 2542 a(1.) 73 2602 y(W) l(e) p 160 2602 a(will) p 255 2602 a(next) p 368 2602 a(consider) p 561 2602 a(the) p 648 2602 a(case) p 754 2602 a(where) p Fq 898 2602 a(k) p Fr 944 2602 a(=) p Fq 1001 2602 a(m) p Fr 1063 2602 a(assuming) p 1278 2602 a(that) p 1386 2602 a(\(1.28\)) p 1530 2602 a(is) p 1582 2602 a(true) p 1688 2602 a(when) p Fq 1818 2602 a(k) p Fr 1864 2602 a(=) p Fq 0 2663 a(m) p Fo 53 2663 a(\000) p Fr 102 2663 a(1.) p 162 2663 a(Supp) q(ose) p 353 2663 a(that) p 458 2663 a(the) p 542 2663 a(maximal) p 740 2663 a(standard) p 944 2663 a(w) o(all) p 1045 2663 a(in) p Fn 1101 2663 a(W) p Fo 1162 2663 a([) p Fn 1205 2663 a(W) p Fm 1252 2645 a(0) p Fr 1283 2663 a(is) p 1331 2663 a(the) p 1415 2663 a(maximal) p 1614 2663 a(standard) p 1817 2663 a(w) o(all) 0 2723 y(in) p Fn 57 2723 a(W) p Fr 123 2723 a(\() p Fq(m) p Fr 201 2723 a(is) p 250 2723 a(ev) o(en\).) p 399 2723 a(Note) p 517 2723 a(that) 556 2823 y(b\() p Fq(W) p Fp 655 2802 a(m) 648 2835 y(n) p Fe 669 2839 a(m) p Fq 701 2823 a(;) p Fn 723 2823 a(W) p Fo 784 2823 a([) p Fn 828 2823 a(W) p Fm 875 2802 a(0) p Fr 890 2823 a(\)) p 923 2823 a(=) p 974 2823 a(b\() p Fq(W) p Fp 1073 2802 a(m) p Fm(\000) p Fl(1) p Fp 1066 2835 a(n) p Fe 1087 2840 a(m) p Fc(\000) p Fj(1) p Fq 1159 2823 a(;) p Fn 1181 2823 a(W) p Fr 1227 2823 a(\)) p Fq(:) p Fr 1778 2823 a(\(1.30\)) 939 2947 y(9) p 90 rotate dyy eop %%Page: 10 10 10 9 bop Fr 0 274 a(Then,) p 141 274 a(w) o(e) p 213 274 a(ha) o(v) o(e) p 325 274 a(b) o(y) p 393 274 a(induction) p 610 274 a(h) o(yp) q(othesis,) p 864 274 a(\(1.30\)) p 1004 274 a(and) p 1099 274 a(Lemmas) p 1293 274 a(1.5) p 1371 274 a(and) p 1466 274 a(1.6) p 1545 274 a(that) 354 384 y(h) p Fl 381 363 a(+) p Fr 411 384 a(\() p Fn(W) p Fo 491 384 a([) p Fn 535 384 a(W) p Fm 582 363 a(0) p Fr 596 384 a(\)) 274 457 y(=) p 354 457 a(max) p Fo 445 457 a(f) p Fr(h) p Fl 497 436 a(+) p Fr 527 457 a(\(\() p Fn(W) p Fo 625 457 a([) p Fn 670 457 a(W) p Fm 716 436 a(0) p Fr 731 457 a(\)\() p Fq(W) p Fp 822 436 a(m) 815 469 y(n) p Fe 836 473 a(m) p Fr 868 457 a(\)\)) p Fq(;) p Fr 647 529 a(b\() p Fq(W) p Fp 746 509 a(m) 739 542 y(n) p Fe 760 546 a(m) p Fq 792 529 a(;) p Fn 814 529 a(W) p Fo 875 529 a([) p Fn 919 529 a(W) p Fm 966 509 a(0) p Fr 980 529 a(\)) p 1010 529 a(+) p 1059 529 a(h) p Fl 1086 509 a(+) p Fr 1116 529 a(\() p Fo(f) p Fq(W) p Fp 1213 509 a(m) 1206 542 y(n) p Fe 1227 546 a(m) p Fq 1259 529 a(;) p Fo 1281 529 a(\001) p 1303 529 a(\001) p 1325 529 a(\001) p Fq 1355 529 a(;) p 1377 529 a(W) p Fl 1430 509 a(1) 1423 542 y(1) p Fo 1450 529 a(g) p Fr(\)) p Fo(g) 274 602 y(\024) p Fr 354 602 a(max) p Fo 445 602 a(f) p Fr(h) p Fl 497 581 a(+) p Fr 527 602 a(\() p Fn(W) p Fr 592 602 a(\)) p Fq(;) p Fr 652 602 a(b\() p Fq(W) p Fp 751 581 a(m) p Fm(\000) p Fl(1) p Fp 744 614 a(n) p Fe 765 619 a(m) p Fc(\000) p Fj(1) p Fq 836 602 a(;) p Fn 858 602 a(W) p Fr 905 602 a(\)) p 938 602 a(+) p 987 602 a(h) p Fl 1014 581 a(+) p Fr 1044 602 a(\() p Fn(W) p Fo 1110 602 a(nf) p Fq(W) p Fp 1213 581 a(m) p Fl(+1) p Fp 1206 615 a(i) p Fo 1294 602 a(g) p Fp 1319 577 a(n) p Fe 1340 582 a(m) p Fj(+1) p Fp 1319 615 a(i) p Fl(=1) p Fr 1410 602 a(\)) p 1440 602 a(+) p 1489 602 a(h) p Fl 1516 581 a(+) p Fr 1545 602 a(\() p Fn(W) p Fm 1611 581 a(0) p Fr 1626 602 a(\)) p Fo(g) 274 680 y(\024) p Fr 354 680 a(h) p Fl 381 659 a(+) p Fr 411 680 a(\() p Fn(W) p Fr 477 680 a(\)) p 510 680 a(+) p 559 680 a(h) p Fl 586 659 a(+) p Fr 615 680 a(\() p Fn(W) p Fm 681 659 a(0) p Fr 696 680 a(\)) p Fq(;) p Fr 1778 680 a(\(1.31\)) 0 790 y(whic) o(h) p 144 790 a(implies) p 314 790 a(\(1.28\)) p 459 790 a(for) p Fq 538 790 a(k) p Fr 587 790 a(=) p Fq 646 790 a(m) p Fr(.) p 737 790 a(Similarly) l(,) p 960 790 a(w) o(e) p 1036 790 a(can) p 1130 790 a(obtain) p 1286 790 a(\(1.31\)) p 1432 790 a(in) p 1493 790 a(the) p 1581 790 a(case) p 1689 790 a(where) p 1834 790 a(the) 0 850 y(maximal) p 199 850 a(standard) p 403 850 a(w) o(all) p 504 850 a(in) p Fn 561 850 a(W) p Fo 622 850 a([) p Fn 666 850 a(W) p Fm 713 832 a(0) p Fr 744 850 a(is) p 793 850 a(the) p 877 850 a(maximal) p 1076 850 a(standard) p 1280 850 a(w) o(all) p 1381 850 a(in) p Fn 1438 850 a(W) p Fm 1485 832 a(0) p Fr 1516 850 a(\() p Fq(m) p Fr 1594 850 a(is) p 1643 850 a(o) q(dd\).) p Fs 0 1016 a(2) p 121 1016 a(Key) p 300 1016 a(Prop) r(ositions) p 776 1016 a(for) p 910 1016 a(The) p 1084 1016 a(Pro) r(of) p 1315 1016 a(of) p 1416 1016 a(Theorems) p 1799 1016 a(1.1) 121 1107 y(and) p 277 1107 a(1.2) p Fr 0 1217 a(W) l(e) p 86 1217 a(ha) o(v) o(e) p 201 1217 a(only) p 311 1217 a(to) p 373 1217 a(mo) q(dify) p 539 1217 a(Prop) q(ositions) p 823 1217 a(3.1) p 904 1217 a(and) p 1002 1217 a(4.1) p 1083 1217 a(in) p 1142 1217 a([Ma,94]) p 1319 1217 a(to) p 1381 1217 a(pro) o(v) o(e) p 1515 1217 a(Theorems) p 1743 1217 a(1.1) p 1824 1217 a(and) 0 1277 y(1.2,) p 92 1277 a(resp) q(ectiv) o(ely) l(.) p 373 1277 a(Throughout) p 644 1277 a(this) p 740 1277 a(section,) p 916 1277 a(w) o(e) p 988 1277 a(assume) p 1157 1277 a(that) p Fq 1262 1277 a(\014) p 1307 1277 a(>) p Fr 1359 1277 a(0) p 1399 1277 a(is) p 1448 1277 a(su\016cien) o(tly) p 1693 1277 a(large.) p 1831 1277 a(F) l(or) p Fq 0 1337 a(r) p 37 1337 a(>) p Fr 89 1337 a(0,) p Fo 141 1337 a(d) p Fq(r) p Fo 186 1337 a(e) p Fr 222 1337 a(stands) p 371 1337 a(for) p 442 1337 a(the) p 523 1337 a(smallest) p 708 1337 a(in) o(teger) p 866 1337 a(larger) p 1001 1337 a(or) p 1058 1337 a(equal) p 1184 1337 a(to) p Fq 1240 1337 a(r) p Fr 1263 1337 a(.) p 1298 1337 a(W) l(e) p 1379 1337 a(will) p 1468 1337 a(in) o(tro) q (duce) p 1682 1337 a(a) p 1719 1337 a(mo) q(di\014ed) 0 1398 y(prop) q(osition) p 258 1398 a(for) p 334 1398 a(the) p 420 1398 a(pro) q(of) p 549 1398 a(of) p 606 1398 a(Theorem) p 814 1398 a(1.1.) p 916 1398 a(W) l(e) p 1002 1398 a(consider) p 1193 1398 a(the) p 1279 1398 a(blo) q(c) o(k) p 1410 1398 a(dynamics) p 1627 1398 a(generated) p 1851 1398 a(b) o(y) p Fq 0 1458 a(A) p Fm 37 1432 a(f) p Fp(Q) p Fe 83 1437 a(i) p Fm 95 1432 a(g) p Fp(;) p Fl(+) p Fp(;) p Ff(J) p Fm 179 1432 a(\021) p Fl(1) 37 1473 y(\003) p Fe 61 1479 a(d) p Fl 79 1473 a(\() p Fp(L) p Fl(\)) p Fr 224 1458 a(.) p Fg 73 1567 a(Prop) r(osition) p 378 1567 a(2.1.) p Fd 487 1567 a(Supp) n(ose) p 674 1567 a(that) p Fq 775 1567 a(\014) p 823 1567 a(>) p Fr 877 1567 a(0) p Fd 921 1567 a(is) p 975 1567 a(su\016ciently) p 1223 1567 a(lar) n(ge.) p 1365 1567 a(L) n(et) p Fq 1451 1567 a(l) p Fr 1483 1567 a(=) p Fo 1538 1567 a(d) p Fq(K) p Fl 1601 1574 a(1) p Fr 1622 1567 a(\(log) p Fq 1712 1567 a(L) p Fr(\)) p Fl 1764 1549 a(2) p Fo 1784 1567 a(e) p Fd 1825 1567 a(and) p Fq 0 1627 a(M) p Fo 68 1627 a(2) p Fn 117 1627 a(N) p Fd 171 1627 a(with) p Fr 278 1627 a(4) p Fq(l) p Fo 333 1627 a(\024) p Fq 388 1627 a(M) p Fo 456 1627 a(\024) p Fr 510 1627 a(2) p Fq(L) p Fo 579 1627 a(\000) p Fq 630 1627 a(l) p Fd 646 1627 a(.) p 685 1627 a(Then,) p 829 1627 a(for) p 907 1627 a(any) p Fq 1002 1627 a(") p 1040 1627 a(>) p Fr 1093 1627 a(0) p Fd 1136 1627 a(ther) n(e) p 1259 1627 a(exists) p Fq 1393 1627 a(K) p Fl 1434 1634 a(1) p Fr 1469 1627 a(=) p Fq 1523 1627 a(K) p Fl 1564 1634 a(1) p Fr 1584 1627 a(\() p Fq(\014) s(;) p 1656 1627 a(") p Fr(\)) p Fq 1713 1627 a(>) p Fr 1766 1627 a(0) p Fd 1809 1627 a(such) 0 1687 y(that) p 100 1687 a(for) p 177 1687 a(su\016ciently) p 423 1687 a(lar) n(ge) p Fq 541 1687 a(L) p Fo 588 1687 a(2) p Fn 635 1687 a(N) p Fd 689 1687 a(and) p 783 1687 a(any) p Fq 877 1687 a(x) p Fo 918 1687 a(2) p Fr 965 1687 a(\003\() p Fo(\000) p Fq(L;) p Fo 1112 1687 a(\000) p Fq(L) p Fr 1195 1687 a(+) p Fq 1244 1687 a(M) p Fo 1307 1687 a(\000) p Fr 1357 1687 a(3) p Fq(l) p Fr 1397 1687 a(\)) p Fq 265 1797 a(\026) p Fl 294 1774 a(+) p Fp(;) p Ff(J) p Fm 352 1774 a(\021) p Fl(1) 294 1813 y(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 509 1813 a(\)) p Fr 526 1797 a(\() p Fq(\033) p Fr 575 1797 a(\() p Fq(x) p Fr(\)) p 654 1797 a(=) p 706 1797 a(+1\)) p Fo 798 1797 a(\000) p Fq 848 1797 a(\026) p Fp 877 1774 a(\021) q(;) p Ff(J) p Fm 926 1774 a(\021) p Fl(1) 877 1813 y(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1092 1813 a(\)) p Fr 1109 1797 a(\() p Fq(\033) p Fr 1158 1797 a(\() p Fq(x) p Fr(\)) p 1237 1797 a(=) p 1289 1797 a(+1\)) p Fo 1384 1797 a(\024) p Fq 1437 1797 a("L) p Fm 1493 1777 a(\000) p Fp(d) p Fq 1540 1797 a(;) p Fr 1778 1797 a(\(2.32\)) p Fd 0 1913 a(wher) n(e) p 138 1913 a(we) p 210 1913 a(write) p Fq 334 1913 a(\021) p Fr 373 1913 a(=) p Fq 425 1913 a(!) p Fm 455 1920 a(\000) p Fp(L) p Fl(+) p Fp(M) p Fr 591 1913 a(\() p Fq(see) p Fr 696 1913 a(\(1) p Fq(:) p Fr(15\)\)) p Fd(.) p Fr 73 2014 a(W) l(e) p 157 2014 a(can) p 247 2014 a(obtain) p 398 2014 a(from) p 513 2014 a(\(2.32\)) p 654 2014 a(\(see) p 752 2014 a(Section) p 923 2014 a(3) p 964 2014 a(in) p 1020 2014 a([Ma,94]\)) p 1214 2014 a(that) p 1320 2014 a(for) p 1394 2014 a(su\016cien) o(tly) p 1639 2014 a(large) p Fq 1758 2014 a(L) p Fo 1805 2014 a(2) p Fn 1852 2014 a(N) p Fr(,) 502 2124 y(gap) q(\(\003) p Fp 631 2131 a(d) p Fr 651 2124 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fo 744 2124 a(f) p Fq(Q) p Fp 808 2131 a(i) p Fo 822 2124 a(g) p Fq(;) p Fr 869 2124 a(+) p Fq(;) p Fn 929 2124 a(J) p Fo 967 2124 a(\021) p Fr 1020 2124 a(1\)) p Fo 1077 2124 a(\025) p Fr 1130 2124 a(exp) o([) p Fo(\000) p Fq(L) p Fr(]) p Fq(:) p Fr 1778 2124 a(\(2.33\)) 0 2234 y(F) l(rom) p 138 2234 a(\(1.14\)) p 289 2234 a(and) p 394 2234 a(\(2.33\),) p 560 2234 a(w) o(e) p 642 2234 a(ha) o(v) o(e) p 765 2234 a(that) p 880 2234 a(for) p 965 2234 a(some) p Fq 1097 2234 a(B) p Fr 1167 2234 a(=) p Fq 1236 2234 a(B) p Fr 1276 2234 a(\() p Fq(c) p Fp 1316 2241 a(m) p Fq 1348 2234 a(;) p 1370 2234 a(c) p Fp 1391 2241 a(M) p Fq 1431 2234 a(;) p 1453 2234 a(d) p Fr(\)) p Fq 1528 2234 a(>) p Fr 1596 2234 a(0,) p 1663 2234 a(some) p Fq 1795 2234 a(C) p Fr 1864 2234 a(=) p Fq 0 2295 a(C) p Fr 39 2295 a(\() p Fq(K) p Fl 99 2302 a(1) p Fq 119 2295 a(;) p 141 2295 a(\014) s(;) p 194 2295 a(d) p Fr(\)) p Fq 251 2295 a(>) p Fr 303 2295 a(0) p 343 2295 a(and) p 438 2295 a(for) p 513 2295 a(an) o(y) p Fq 605 2295 a(L) p Fo 652 2295 a(2) p Fn 699 2295 a(N) p Fr 434 2405 a(gap) q(\(\003) p Fp 563 2412 a(d) p Fr 583 2405 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 676 2405 a(+) p Fq(;) p Fn 736 2405 a(J) p Fo 775 2405 a(\021) p Fr 827 2405 a(1\)) p Fo 884 2405 a(\025) p Fq 937 2405 a(B) p Fr 985 2405 a(exp) o([) p Fo(\000) p Fq(\014) s(C) t(L) p Fp 1215 2384 a(d) p Fm(\000) p Fl(2) p Fr 1279 2405 a(\(log) p Fq 1369 2405 a(L) p Fr(\)) p Fl 1421 2384 a(2) p Fr 1441 2405 a(]) p Fq(;) p Fr 0 2515 a(whic) o(h) p 140 2515 a(implies) p 305 2515 a(\(1.9\).) 73 2620 y(W) l(e) p 155 2620 a(will) p 245 2620 a(in) o(tro) q(duce) p 460 2620 a(a) p 498 2620 a(mo) q(di\014ed) p 695 2620 a(prop) q(osition) p 950 2620 a(for) p 1022 2620 a(the) p 1104 2620 a(pro) q(of) p 1229 2620 a(of) p 1283 2620 a(Theorem) p 1487 2620 a(1.2.) p 1584 2620 a(Let) 1669 2608 y(^) p Fn 1669 2620 a(J) p Fp 1697 2627 a(\016) p Fr 1727 2620 a(b) q(e) p 1791 2620 a(giv) o(en) 0 2681 y(b) o(y) 213 2754 y(\026) 213 2767 y(J) p Fp 238 2774 a(x;y) p Fr 302 2767 a(=) p Fk 354 2697 a(\032) p Fr 412 2737 a(1) p 478 2737 a(if) p Fq 522 2737 a(x) p Fo 564 2737 a(2) p Fr 611 2737 a(\003) p Fl 645 2744 a(3) p Fr 664 2737 a(\() p Fq(L) p Fr(\)) p Fq(;) p 774 2737 a(x) p Fl 802 2718 a(3) p Fr 835 2737 a(=) p Fo 887 2737 a(\000) p Fq(L) p Fr 970 2737 a(+) p 1019 2737 a(1) p Fq(;) p 1081 2737 a(y) p Fo 1121 2737 a(2) p Fq 1168 2737 a(@) p Fp 1194 2744 a(ex) p Fr 1232 2737 a(\003) p Fl 1266 2744 a(3) p Fr 1285 2737 a(\() p Fq(L) p Fr(\)) p 1373 2737 a(and) p Fq 1468 2737 a(y) p Fl 1494 2718 a(3) p Fr 1527 2737 a(=) p Fo 1578 2737 a(\000) p Fq(L;) 412 2797 y(\016) p Fr 478 2797 a(otherwise) p Fq 678 2797 a(:) p Fr 927 2947 a(10) p 90 rotate dyy eop %%Page: 11 11 11 10 bop Fr 0 274 a(F) l(rom) p 128 274 a(the) p 212 274 a(direct) p 350 274 a(calculation,) p 610 274 a(w) o(e) p 682 274 a(ha) o(v) o(e) p 795 274 a(that) 302 393 y(gap\(\003) p Fl 430 400 a(3) p Fr 450 393 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 543 393 a(+) p Fq(;) p Fr 603 380 a(^) p Fn 603 393 a(J) p Fl 631 400 a(0) p Fr 647 393 a(\)) p Fo 680 393 a(\025) p Fq 741 359 a(c) p Fp 762 366 a(m) p 738 381 61 2 v Fq 738 427 a(c) p Fp 759 434 a(M) p Fr 812 393 a(exp) o([) p Fo(\000) p Fr(160) p Fq(\014) s(\016) r(L) p Fl 1099 372 a(2) p Fr 1118 393 a(]) p 1140 393 a(gap) q(\(\003) p Fl 1269 400 a(3) p Fr 1288 393 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 1381 393 a(+) p Fq(;) p Fr 1441 380 a(^) p Fn 1441 393 a(J) p Fp 1469 400 a(\016) p Fr 1485 393 a(\)) p Fq(:) p Fr 1778 393 a(\(2.34\)) 0 545 y(W) l(e) p 84 545 a(consider) p 274 545 a(the) p 358 545 a(blo) q(c) o(k) p 487 545 a(dynamics) p 702 545 a(generated) p 925 545 a(b) o(y) p Fq 992 545 a(A) p Fm 1029 520 a(f) p Fp(Q) p Fe 1075 525 a(i) p Fm 1087 520 a(g) p Fp(;) p Fl(+) p Fp(;) p Fl 1151 511 a(^) p Ff 1152 520 a(J) p Fe 1172 526 a(\016) p Fl 1029 561 a(\003) p Fj 1053 566 a(3) p Fl 1071 561 a(\() p Fp(L) p Fl(\)) p Fr 1188 545 a(.) p Fg 73 647 a(Prop) r(osition) p 386 647 a(2.2.) p Fd 499 647 a(Supp) n(ose) p 692 647 a(that) p Fq 800 647 a(d) p Fr 855 647 a(=) p 921 647 a(3) p Fd 971 647 a(and) p Fq 1074 647 a(\014) p 1134 647 a(>) p Fr 1201 647 a(0) p Fd 1251 647 a(is) p 1311 647 a(su\016ciently) p 1565 647 a(lar) n(ge.) p 1727 647 a(L) n(et) p Fq 1820 647 a(l) p Fr 1864 647 a(=) p Fo 0 707 a(d) p Fq(K) p Fl 63 714 a(2) p Fq 83 707 a(L) p Fj 121 675 a(2) p 122 681 16 2 v 122 702 a(3) p Fr 144 707 a(\(log) p Fq 234 707 a(L) p Fr(\)) p Fl 286 689 a(2) p Fo 306 707 a(e) p Fd 352 707 a(and) p Fq 453 707 a(M) p Fo 531 707 a(2) p Fn 589 707 a(N) p Fd 649 707 a(with) p Fr 761 707 a(4) p Fq(l) p Fo 827 707 a(\024) p Fq 891 707 a(M) p Fo 969 707 a(\024) p Fr 1033 707 a(2) p Fq(L) p Fo 1106 707 a(\000) p Fq 1161 707 a(l) p Fd 1177 707 a(.) p 1232 707 a(L) n(et) p Fq 1323 707 a(\016) p Fr 1372 707 a(=) p Fq 1435 707 a(L) p Fm 1468 689 a(\000) p Fj 1500 675 a(2) p 1501 681 V 1501 702 a(3) p Fr 1531 707 a(log) p Fq 1603 707 a(L) p Fd(.) p 1692 707 a(Then,) p 1842 707 a(for) 0 768 y(any) p Fq 95 768 a(") p 135 768 a(>) p Fr 190 768 a(0) p Fd 233 768 a(ther) n(e) p 356 768 a(exists) p Fq 491 768 a(K) p Fl 532 775 a(2) p Fr 570 768 a(=) p Fq 625 768 a(K) p Fl 666 775 a(2) p Fr 686 768 a(\() p Fq(\014) s(;) p 758 768 a(") p Fr(\)) p Fq 816 768 a(>) p Fr 871 768 a(0) p Fd 914 768 a(such) p 1027 768 a(that) p 1128 768 a(for) p 1207 768 a(su\016ciently) p 1455 768 a(lar) n(ge) p Fq 1574 768 a(L) p Fo 1625 768 a(2) p Fn 1675 768 a(N) p Fd 1730 768 a(and) p 1826 768 a(any) p Fq 0 828 a(x) p Fo 42 828 a(2) p Fr 89 828 a(\003\() p Fo(\000) p Fq(L;) p Fo 236 828 a(\000) p Fq(L) p Fr 318 828 a(+) p Fq 367 828 a(M) p Fo 431 828 a(\000) p Fr 480 828 a(3) p Fq(l) p Fr 520 828 a(\)) p Fq 266 949 a(\026) p Fl 295 926 a(+) p Fp(;) p Fl 331 917 a(^) p Ff 332 926 a(J) p Fe 352 932 a(\016) p Fl 295 965 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 510 965 a(\)) p Fr 527 949 a(\() p Fq(\033) p Fr 576 949 a(\() p Fq(x) p Fr(\)) p 655 949 a(=) p 706 949 a(+1\)) p Fo 799 949 a(\000) p Fq 848 949 a(\026) p Fp 877 926 a(\021) q(;) p Fl 905 917 a(^) p Ff 906 926 a(J) p Fe 926 932 a(\016) p Fl 877 965 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1092 965 a(\)) p Fr 1109 949 a(\() p Fq(\033) p Fr 1158 949 a(\() p Fq(x) p Fr(\)) p 1237 949 a(=) p 1289 949 a(+1\)) p Fo 1384 949 a(\024) p Fq 1437 949 a("L) p Fm 1493 929 a(\000) p Fl(3) p Fq 1540 949 a(;) p Fr 1778 949 a(\(2.35\)) p Fd 0 1065 a(wher) n(e) p 138 1065 a(we) p 210 1065 a(write) p Fq 334 1065 a(\021) p Fr 373 1065 a(=) p Fq 425 1065 a(!) p Fm 455 1072 a(\000) p Fp(L) p Fl(+) p Fp(M) p Fr 591 1065 a(\() p Fq(see) p Fr 696 1065 a(\(1) p Fq(:) p Fr(15\)\)) p Fd(.) p Fr 73 1166 a(W) l(e) p 157 1166 a(can) p 247 1166 a(obtain) p 398 1166 a(from) p 513 1166 a(\(2.35\)) p 654 1166 a(that) p 760 1166 a(for) p 835 1166 a(su\016cien) o(tly) p 1079 1166 a(large) p Fq 1198 1166 a(L) p Fo 1245 1166 a(2) p Fn 1292 1166 a(N) p Fr(,) 539 1276 y(gap) q(\(\003) p Fl 668 1283 a(3) p Fr 687 1276 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fo 780 1276 a(f) p Fq(Q) p Fp 844 1283 a(i) p Fo 858 1276 a(g) p Fq(;) p Fr 905 1276 a(+) p Fq(;) p Fr 964 1264 a(^) p Fn 965 1276 a(J) p Fp 992 1283 a(\016) p Fr 1008 1276 a(\)) p Fo 1041 1276 a(\025) p Fr 1093 1276 a(exp[) p Fo(\000) p Fq(L) p Fr(]) p Fq(:) p Fr 1778 1276 a(\(2.36\)) 0 1386 y(F) l(rom) p 131 1386 a(\(1.14\),) p 288 1386 a(\(2.34\)) p 432 1386 a(and) p 529 1386 a(\(2.36\),) p 687 1386 a(w) o(e) p 762 1386 a(ha) o(v) o(e) p 877 1386 a(that) p 985 1386 a(for) p 1062 1386 a(some) p Fq 1187 1386 a(B) p Fm 1227 1368 a(0) p Fr 1257 1386 a(=) p Fq 1313 1386 a(B) p Fm 1353 1368 a(0) p Fr 1364 1386 a(\() p Fq(c) p Fp 1404 1393 a(m) p Fq 1437 1386 a(;) p 1459 1386 a(c) p Fp 1480 1393 a(M) p Fr 1520 1386 a(\)) p Fq 1557 1386 a(>) p Fr 1613 1386 a(0,) p 1671 1386 a(some) p Fq 1796 1386 a(C) p Fm 1835 1368 a(0) p Fr 1864 1386 a(=) p Fq 0 1447 a(C) p Fm 39 1429 a(0) p Fr 50 1447 a(\() p Fq(K) p Fl 110 1454 a(2) p Fq 130 1447 a(;) p 152 1447 a(\014) p Fr 183 1447 a(\)) p Fq 215 1447 a(>) p Fr 267 1447 a(0) p 308 1447 a(and) p 403 1447 a(for) p 477 1447 a(an) o(y) p Fq 569 1447 a(L) p Fo 616 1447 a(2) p Fn 663 1447 a(N) p Fr(,) 477 1563 y(gap) q(\(\003) p Fl 606 1570 a(3) p Fr 626 1563 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 719 1563 a(+) p Fq(;) p Fr 779 1550 a(^) p Fn 779 1563 a(J) p Fl 806 1570 a(0) p Fr 823 1563 a(\)) p Fo 856 1563 a(\025) p Fq 908 1563 a(B) p Fm 948 1543 a(0) p Fr 968 1563 a(exp[) p Fo(\000) p Fq(\014) s(C) p Fm 1166 1543 a(0) p Fq 1175 1563 a(L) p Fj 1213 1529 a(5) p 1213 1535 V 1213 1556 a(3) p Fr 1236 1563 a(\(log) p Fq 1326 1563 a(L) p Fr(\)) p Fl 1378 1543 a(2) p Fr 1398 1563 a(]) p Fq(;) p Fr 0 1673 a(whic) o(h) p 140 1673 a(implies) p 305 1673 a(\(1.11\).) p Fs 0 1840 a(3) p 121 1840 a(Pro) r(of) p 344 1840 a(of) p 436 1840 a(Prop) r(osition) p 872 1840 a(2.1) p Fr 81 1949 a(F) l(or) p 176 1949 a(simplicit) o(y) p 406 1949 a(w) o(e) p 486 1949 a(will) p 586 1949 a(pro) o(v) o(e) p 725 1949 a(Prop) q(osition) p 996 1949 a(2.1) p 1082 1949 a(for) p Fq 1164 1949 a(d) p Fr 1217 1949 a(=) p 1282 1949 a(3.) p 1365 1949 a(Let) p 1460 1949 a(us) p 1531 1949 a(\014x) p Fq 1607 1949 a(M) p Fo 1687 1949 a(2) p Fn 1747 1949 a(N) p Fr 1807 1949 a(with) 0 2009 y(4) p Fq(l) p Fo 62 2009 a(\024) p Fq 124 2009 a(M) p Fo 199 2009 a(\024) p Fr 260 2009 a(2) p Fq(L) p Fo 332 2009 a(\000) p Fq 385 2009 a(l) p Fr 401 2009 a(.) p 451 2009 a(W) l(e) p 540 2009 a(will) p 637 2009 a(omit) p 756 2009 a(the) p 845 2009 a(notation) p Fn 1045 2009 a(J) p Fo 1093 2009 a(\021) p Fr 1154 2009 a(1.) p 1229 2009 a(W) l(e) p 1318 2009 a(will) p 1415 2009 a(write) p Fq 1545 2009 a(\021) p Fr 1593 2009 a(=) p Fq 1654 2009 a(!) p Fm 1684 2016 a(\000) p Fp(L) p Fl(+) p Fp(M) p Fr 1824 2009 a(and) p Fq 0 2070 a(\020) p Fr 48 2070 a(=) p Fq 108 2070 a(!) p Fm 138 2077 a(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 254 2077 a(+2) p Fp(l) p Fr 335 2070 a(\(see) p 438 2070 a(\(1.15\)\)) p 603 2070 a(in) p 665 2070 a(this) p 765 2070 a(section.) p 962 2070 a(W) l(e) p 1052 2070 a(assume) p 1225 2070 a(that) p Fq 1336 2070 a(\014) p 1389 2070 a(>) p Fr 1450 2070 a(0) p 1496 2070 a(is) p 1550 2070 a(su\016cien) o(tly) p 1799 2070 a(large) 0 2130 y(throughout) p 259 2130 a(this) p 358 2130 a(section.) p 552 2130 a(W) l(e) p 640 2130 a(de\014ne) p 785 2130 a(op) q(en) p 907 2130 a(con) o(tours) p 1108 2130 a(for) p 1187 2130 a(eac) o(h) p Fq 1301 2130 a(\033) p Fo 1351 2130 a(2) p Fr 1405 2130 a(\012) p Fl 1440 2138 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1655 2138 a(\)) p Fr 1692 2130 a(under) p 1834 2130 a(the) 0 2197 y(b) q(oundary) p 217 2197 a(conditions) p Fq 447 2197 a(\021) p Fr 487 2197 a(and) p Fq 579 2197 a(\020) p Fr 618 2197 a(\(see) p 713 2197 a(\(1.16\)\).) p 891 2197 a(By) p 965 2197 a(\000) p Fp 995 2173 a(\021) p Fl 995 2212 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1210 2212 a(\)) p Fr 1227 2197 a(\() p Fq(\033) p Fr 1276 2197 a(\)) p 1308 2197 a(and) p 1400 2197 a(\000) p Fp 1430 2173 a(\020) p Fl 1430 2212 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1645 2212 a(\)) p Fr 1662 2197 a(\() p Fq(\033) p Fr 1711 2197 a(\),) p 1757 2197 a(w) o(e) p 1826 2197 a(will) 0 2257 y(denote) p 157 2257 a(the) p 240 2257 a(op) q(en) p 357 2257 a(con) o(tours) p 553 2257 a(for) p 627 2257 a(eac) o(h) p Fq 737 2257 a(\033) p Fo 780 2257 a(2) p Fr 827 2257 a(\012) p Fl 862 2265 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1077 2265 a(\)) p Fr 1109 2257 a(under) p 1247 2257 a(the) p 1330 2257 a(b) q(oundary) p 1549 2257 a(conditions) p Fq 1782 2257 a(\021) p Fr 1824 2257 a(and) p Fq 0 2317 a(\020) p Fr 25 2317 a(,) p 55 2317 a(resp) q(ectiv) o(ely) l (.) p 336 2317 a(W) l(e) p 420 2317 a(consider) p 610 2317 a(the) p 694 2317 a(ev) o(en) o(ts) p Fo 181 2427 a(A) p Fp 221 2403 a(\021) p Fl 221 2443 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 436 2443 a(\)) p Fr 466 2427 a(=) p Fo 518 2427 a(f) p Fq(\033) p Fo 586 2427 a(2) p Fr 633 2427 a(\012) p Fl 668 2435 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 883 2435 a(\)) p Fr 900 2427 a(;) p 922 2427 a(h) p Fm 949 2406 a(\000) p Fr 978 2427 a(\(\000) p Fp 1027 2403 a(\021) p Fl 1027 2443 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1242 2443 a(\)) p Fr 1259 2427 a(\() p Fq(\033) p Fr 1308 2427 a(\)\)) p Fq 1359 2427 a(>) p Fo 1411 2427 a(\000) p Fq(L) p Fr 1494 2427 a(+) p Fq 1543 2427 a(M) p Fo 1607 2427 a(\000) p Fr 1657 2427 a(3) p Fq(l) p Fo 1697 2427 a(g) p Fr 0 2537 a(and) p Fo 174 2647 a(A) p Fp 214 2623 a(\020) p Fl 214 2663 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 429 2663 a(\)) p Fr 459 2647 a(=) p Fo 511 2647 a(f) p Fq(\033) p Fo 579 2647 a(2) p Fr 626 2647 a(\012) p Fl 661 2655 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 876 2655 a(\)) p Fr 893 2647 a(;) p 915 2647 a(h) p Fm 942 2626 a(\000) p Fr 971 2647 a(\(\000) p Fp 1020 2623 a(\020) p Fl 1020 2663 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1235 2663 a(\)) p Fr 1252 2647 a(\() p Fq(\033) p Fr 1301 2647 a(\)\)) p Fq 1353 2647 a(>) p Fo 1404 2647 a(\000) p Fq(L) p Fr 1487 2647 a(+) p Fq 1536 2647 a(M) p Fo 1600 2647 a(\000) p Fr 1650 2647 a(3) p Fq(l) p Fo 1690 2647 a(g) p Fq(:) p Fr 927 2947 a(11) p 90 rotate dyy eop %%Page: 12 12 12 11 bop Fr 0 274 a(Then,) p 141 274 a(w) o(e) p 213 274 a(ha) o(v) o(e) p 325 274 a(b) o(y) p 393 274 a(FK) o(G) p 516 274 a(inequalit) o(y) p 742 274 a(that) p 848 274 a(for) p 922 274 a(an) o(y) p Fq 1014 274 a(x) p Fo 1056 274 a(2) p Fr 1103 274 a(\003\() p Fo(\000) p Fq(L;) p Fo 1250 274 a(\000) p Fq(L) p Fr 1333 274 a(+) p Fq 1382 274 a(M) p Fo 1445 274 a(\000) p Fr 1495 274 a(3) p Fq(l) p Fr 1535 274 a(\),) p Fq 266 369 a(\026) p Fl 295 348 a(+) 295 385 y(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 510 385 a(\)) p Fr 527 369 a(\() p Fq(\033) p Fr 576 369 a(\() p Fq(x) p Fr(\)) p 655 369 a(=) p 706 369 a(+1\)) p Fo 799 369 a(\000) p Fq 849 369 a(\026) p Fp 878 345 a(\021) p Fl 878 385 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1093 385 a(\)) p Fr 1109 369 a(\() p Fq(\033) p Fr 1158 369 a(\() p Fq(x) p Fr(\)) p 1237 369 a(=) p 1289 369 a(+1\)) p Fo 186 450 a(\024) p Fq 266 450 a(\026) p Fl 295 430 a(+) 295 466 y(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 510 466 a(\)) p Fr 527 450 a(\() p Fq(\033) p Fr 576 450 a(\() p Fq(x) p Fr(\)) p 655 450 a(=) p 706 450 a(+1\)) p Fo 315 529 a(\000) p Fq(\026) p Fp 383 505 a(\021) p Fl 383 544 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 598 544 a(\)) p Fr 614 529 a(\() p Fq(\033) p Fr 663 529 a(\() p Fq(x) p Fr(\)) p 742 529 a(=) p 794 529 a(+1) p Fo 870 529 a(j) p 898 529 a(A) p Fp 938 505 a(\021) p Fl 938 544 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1153 544 a(\)) p Fr 1169 529 a(\)) p Fq(\026) p Fp 1217 505 a(\021) p Fl 1217 544 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1432 544 a(\)) p Fr 1449 529 a(\() p Fo(A) p Fp 1508 505 a(\021) p Fl 1508 544 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1723 544 a(\)) p Fr 1739 529 a(\)) p Fo 186 607 a(\024) p Fq 266 607 a(\026) p Fp 295 584 a(\021) p Fl 295 623 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 510 623 a(\)) p Fr 527 607 a(\(\() p Fo(A) p Fp 605 584 a(\021) p Fl 605 623 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 820 623 a(\)) p Fr 836 607 a(\)) p Fp 855 587 a(c) p Fr 872 607 a(\)) p Fo 186 695 a(\024) p Fq 266 695 a(\026) p Fp 295 671 a(\020) p Fl 295 710 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 510 710 a(\)) p Fr 527 695 a(\(\() p Fo(A) p Fp 605 671 a(\020) p Fl 605 710 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 820 710 a(\)) p Fr 836 695 a(\)) p Fp 855 674 a(c) p Fr 872 695 a(\)) p Fq(:) p Fr 1802 695 a(\(3.1\)) 0 789 y(W) l(e) p 84 789 a(de\014ne) p 225 789 a(the) p 309 789 a(ev) o(en) o(t) p Fo 311 884 a(A) p Fp 351 864 a(!) p Fl 351 897 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 582 884 a(=) p Fo 633 884 a(f) p Fq(\033) p Fo 702 884 a(2) p Fr 749 884 a(\012) p Fl 784 892 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1001 884 a(;) p 1023 884 a(h) p Fm 1050 864 a(\000) p Fr 1080 884 a(\(\000) p Fp 1129 864 a(!) p Fl 1129 897 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1347 884 a(\() p Fq(\033) p Fr 1396 884 a(\)\)) p Fq 1447 884 a(>) p Fo 1499 884 a(\000) p Fq(l) p Fo 1554 884 a(g) p Fq(;) p Fr 0 979 a(where) p 141 979 a(w) o(e) p 213 979 a(write) p Fq 337 979 a(!) p Fr 383 979 a(=) p Fq 435 979 a(!) p Fl 465 986 a(0) p Fr 501 979 a(\(see) p 599 979 a(\(1.15\)\).) p 778 979 a(W) l(e) p 862 979 a(also) p 960 979 a(ha) o(v) o(e) p 1072 979 a(b) o(y) p 1140 979 a(FK) o(G) p 1263 979 a(inequalit) o(y) p 1489 979 a(that) p Fq 258 1074 a(\026) p Fp 287 1051 a(\020) p Fl 287 1090 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 502 1090 a(\)) p Fr 519 1074 a(\(\() p Fo(A) p Fp 597 1051 a(\020) p Fl 597 1090 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 812 1090 a(\)) p Fr 828 1074 a(\)) p Fp 847 1054 a(c) p Fr 865 1074 a(\)) p Fo 898 1074 a(\024) p Fq 950 1074 a(\026) p Fp 979 1054 a(!) p Fl 979 1086 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1197 1074 a(\(\() p Fo(A) p Fp 1275 1054 a(!) p Fl 1275 1086 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1492 1074 a(\)) p Fp 1511 1054 a(c) p Fr 1528 1074 a(\)) p Fq(:) p Fr 1802 1074 a(\(3.2\)) 0 1174 y(Therefore,) p 234 1174 a(w) o(e) p 306 1174 a(can) p 396 1174 a(obtain) p 547 1174 a(Prop) q(osition) p 810 1174 a(2.1) p 888 1174 a(from) p 1004 1174 a(\(3.1\),) p 1134 1174 a(\(3.2\)) p 1250 1174 a(and) p 1345 1174 a(the) p 1429 1174 a(follo) o(wing) p 1635 1174 a(lemm) o(a.) p Fg 73 1263 a(Lemma) p 271 1263 a(3.1.) p Fd 378 1263 a(Supp) n(ose) p 562 1263 a(that) p Fq 661 1263 a(\014) p 705 1263 a(>) p Fr 757 1263 a(0) p Fd 798 1263 a(is) p 849 1263 a(su\016ciently) p 1094 1263 a(lar) n(ge.) p 1232 1263 a(L) n(et) p Fq 1315 1263 a(l) p Fr 1344 1263 a(=) p Fo 1396 1263 a(d) p Fq(K) p Fl 1459 1270 a(1) p Fr 1479 1263 a(\(log) p Fq 1570 1263 a(L) p Fr(\)) p Fl 1622 1245 a(2) p Fo 1641 1263 a(e) p Fd(.) p 1701 1263 a(Then,) p 1842 1263 a(for) 0 1323 y(any) p Fq 93 1323 a(") p 130 1323 a(>) p Fr 182 1323 a(0) p Fd 224 1323 a(ther) n(e) p 345 1323 a(exists) p Fq 478 1323 a(K) p Fl 519 1330 a(1) p Fr 553 1323 a(=) p Fq 605 1323 a(K) p Fl 646 1330 a(1) p Fr 666 1323 a(\() p Fq(\014) s(;) p 738 1323 a(") p Fr(\)) p Fq 793 1323 a(>) p Fr 845 1323 a(0) p Fd 887 1323 a(such) p 998 1323 a(that) p 1097 1323 a(for) p 1175 1323 a(su\016ciently) p 1421 1323 a(lar) n(ge) p Fq 1539 1323 a(L) p Fo 1586 1323 a(2) p Fn 1633 1323 a(N) p Fq 519 1418 a(\026) p Fp 548 1398 a(!) p Fl 548 1431 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 766 1418 a(\(\() p Fo(A) p Fp 844 1398 a(!) p Fl 844 1431 a(\003\() p Fm(\000) p Fl(2) p Fp(L) p Fl(+2) p Fp(l;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1061 1418 a(\)) p Fp 1080 1398 a(c) p Fr 1098 1418 a(\)) p Fo 1130 1418 a(\024) p Fq 1183 1418 a("L) p Fm 1239 1398 a(\000) p Fl(3) p Fq 1286 1418 a(:) p Fr 1802 1418 a(\(3.3\)) 73 1542 y(W) l(e) p 160 1542 a(will) p 254 1542 a(use) p 341 1542 a(cluster) p 501 1542 a(expansion) p 730 1542 a(to) p 792 1542 a(pro) o(v) o(e) p 926 1542 a(Lemma) p 1103 1542 a(3.1.) p 1208 1542 a(Recall) p 1358 1542 a(that) p 1466 1542 a(b) o(y) p Fn 1536 1542 a(W) p Fr 1583 1542 a(\(\000\)) p 1673 1542 a(and) p 1770 1542 a(\000\() p Fn(W) p Fr 1867 1542 a(\),) 0 1602 y(w) o(e) p 74 1602 a(will) p 168 1602 a(mean) p 301 1602 a(the) p 387 1602 a(family) p 538 1602 a(of) p 596 1602 a(standard) p 802 1602 a(w) o(alls) p 925 1602 a(corresp) q (onding) p 1240 1602 a(to) p 1302 1602 a(the) p 1389 1602 a(op) q(en) p 1509 1602 a(con) o(tour) p 1688 1602 a(\000) p 1737 1602 a(and) p 1834 1602 a(the) 0 1663 y(op) q(en) p 124 1663 a(con) o(tour) p 308 1663 a(corresp) q(onding) p 628 1663 a(to) p 694 1663 a(the) p 785 1663 a(family) p 941 1663 a(of) p 1003 1663 a(standard) p 1213 1663 a(w) o(alls) p Fn 1340 1663 a(W) p Fr 1387 1663 a(,) p 1428 1663 a(resp) q(ectiv) o (ely) l(,) p 1711 1663 a(and) p 1813 1663 a(that) p Fo 0 1723 a(S) t(W) p Fr 87 1723 a(\() p Fo(\0001) p Fq(;) p Fo 217 1723 a(1) p Fr(\)) p 307 1723 a(=) p Fo 367 1723 a([) p Fp 400 1730 a(N) p Fm 432 1730 a(2) p Ff(N) p Fo 481 1723 a(S) t(W) p Fr 568 1723 a(\() p Fo(\000) p Fq(N) r(;) p 689 1723 a(N) p Fr 733 1723 a(\).) p 802 1723 a(W) l(e) p 890 1723 a(de\014ne) p Fo 1036 1723 a(S) t(W) p Fr 1123 1723 a(\() p Fo(\000) p Fq(L) p Fl 1214 1730 a(1) p Fq 1234 1723 a(;) p Fo 1256 1723 a(1) p Fr(\)) p 1346 1723 a(=) p Fo 1406 1723 a([) p Fp 1439 1730 a(N) p Fm 1471 1730 a(2) p Ff(N) p Fo 1520 1723 a(S) t(W) p Fr 1607 1723 a(\() p Fo(\000) p Fq(L) p Fl 1698 1730 a(1) p Fq 1718 1723 a(;) p 1740 1723 a(N) p Fr 1784 1723 a(\)) p 1824 1723 a(and) p Fo 0 1783 a(S) t(W) p Fr 87 1783 a(\() p Fo(\0001) p Fq(;) p 217 1783 a(L) p Fl 250 1790 a(1) p Fr 269 1783 a(\)) p 310 1783 a(=) p Fo 370 1783 a([) p Fp 403 1790 a(N) p Fm 435 1790 a(2) p Ff(N) p Fo 484 1783 a(S) t(W) p Fr 571 1783 a(\() p Fo(\000) p Fq(N) r(;) p 692 1783 a(L) p Fl 725 1790 a(1) p Fr 745 1783 a(\)) p 785 1783 a(for) p 864 1783 a(eac) o(h) p Fq 979 1783 a(L) p Fl 1012 1790 a(1) p Fo 1053 1783 a(2) p Fn 1108 1783 a(N) p Fr(.) p 1193 1783 a(F) l(or) p 1285 1783 a(eac) o(h) p Fn 1399 1783 a(W) p Fo 1471 1783 a(2) p 1526 1783 a(S) t(W) p Fr 1613 1783 a(\() p Fo(\0001) p Fq(;) p Fo 1743 1783 a(1) p Fr(\),) p 1847 1783 a(w) o(e) 0 1843 y(de\014ne) 494 1938 y(\010\() p Fn(W) p Fr 595 1938 a(\)) p 658 1938 a(=) p 738 1938 a(\010\(\000\() p Fn(W) p Fr 888 1938 a(\)\)) p Fq(=e) p Fm 973 1917 a(\000) p Fl 1001 1917 a(8) p Fp(\014) r(L) p Fj 1065 1906 a(2) p Fr 658 2015 a(=) p 738 2015 a(exp) o([) p Fo(\000) p Fq(\014) s(H) p Fp 940 1995 a(!) p Fl 936 2028 a(\003\() p Fm(\000) p Fp(N) r(;N) p Fl 1073 2028 a(\)) p Fr 1088 2015 a(\() p Fq(\033) p Fl 1135 2023 a(\000\() p Ff(W) p Fl 1206 2023 a(\)) p Fr 1219 2015 a(\)]) p Fq(=e) p Fm 1299 1995 a(\000) p Fl(8) p Fp(\014) r(L) p Fj 1390 1983 a(2) p Fr 1802 2015 a(\(3.4\)) 0 2110 y(for) p 78 2110 a(some) p Fq 204 2110 a(N) p Fo 268 2110 a(2) p Fn 321 2110 a(N) p Fr 377 2110 a(suc) o(h) p 490 2110 a(that) p 599 2110 a(\000\() p Fn(W) p Fr 695 2110 a(\)) p Fo 737 2110 a(2) p 790 2110 a(O) p Fr 831 2110 a(\() p Fo(\000) p Fq(N) r(;) p 952 2110 a(N) p Fr 996 2110 a(\).) p 1061 2110 a(W) l(e) p 1149 2110 a(can) p 1242 2110 a(see) p 1324 2110 a(that) p 1433 2110 a(it) p 1486 2110 a(is) p 1538 2110 a(w) o(ell-de\014ned.) p 1834 2110 a(W) l(e) 0 2170 y(de\014ne) p Fg 496 2231 a(C) p Fr 551 2231 a(=) p Fo 602 2231 a([) p Fp 635 2238 a(N) p Fm 667 2238 a(2) p Ff(N) p Fo 717 2231 a(f) p Fq(C) p Fo 794 2231 a(\032) p 847 2231 a(C) p Fr 876 2231 a(\() p Fo(\000) p Fq(N) r(;) p 997 2231 a(N) p Fr 1041 2231 a(\);) p Fq 1082 2231 a(C) p Fr 1137 2231 a(is) p 1186 2231 a(a) p 1226 2231 a(cluster) p Fo 1367 2231 a(g) p Fq(:) p Fr 0 2311 a(W) l(e) p 84 2311 a(also) p 182 2311 a(de\014ne) p 323 2311 a(for) p 397 2311 a(eac) o(h) p Fq 507 2311 a(n) p Fo 550 2311 a(2) p Fn 597 2311 a(N) p Fg 572 2406 a(C) p Fr(\() p Fq(n) p Fr(\)) p 693 2406 a(=) p Fo 745 2406 a(f) p Fq(C) p Fo 822 2406 a(2) p Fg 869 2406 a(C) p Fr(;) p 931 2406 a(diam) o(\() p Fq(C) p Fr 1095 2406 a(\)) p Fo 1127 2406 a(\025) p Fq 1180 2406 a(n) p Fo(g) p Fq(;) p Fr 1802 2406 a(\(3.5\)) 0 2501 y(where) p 144 2501 a(diam) o(\() p Fq(C) p Fr 308 2501 a(\)) p 345 2501 a(=) p 402 2501 a(sup) p Fo(f) p Fr(dist) p Fl 579 2508 a(1) p Fr 599 2501 a(\() p Fq(x;) p 668 2501 a(y) p Fr 694 2501 a(\);) p Fq 735 2501 a(x;) p 785 2501 a(y) p Fo 828 2501 a(2) p Fq 880 2501 a(C) p Fo 919 2501 a(g) p Fr 962 2501 a(and) p 1060 2501 a(dist) p Fl 1139 2508 a(1) p Fr 1178 2501 a(is) p 1230 2501 a(the) p 1317 2501 a(metric) p 1472 2501 a(induced) p 1656 2501 a(b) o(y) p Fq 1727 2501 a(l) p Fl 1742 2508 a(1) p Fr 1761 2501 a(-norm.) 0 2570 y(F) l(or) p 88 2570 a(eac) o(h) p 199 2570 a(\000) p Fo 245 2570 a(2) p 294 2570 a(O) p Fr 335 2570 a(\() p Fo(\0001) p Fq(;) p Fo 465 2570 a(1) p Fr(\),) p 564 2570 a(let) p Fk 636 2523 a(X) p Fp 641 2628 a(C) r(\023) p Fl(\000) p Fr 725 2570 a(stand) p 859 2570 a(for) p 935 2570 a(the) p 1020 2570 a(summation) p 1273 2570 a(o) o(v) o(er) p 1379 2570 a(all) p 1447 2570 a(elemen) o(ts) p Fq 1648 2570 a(C) p Fo 1702 2570 a(2) p Fg 1751 2570 a(C) p Fr 1808 2570 a(suc) o(h) 0 2672 y(that) p Fq 106 2672 a(C) t(\023) p Fr(\000.) p 227 2672 a(F) l(or) p 314 2672 a(eac) o(h) p Fq 424 2672 a(\033) p Fo 468 2672 a(2) p Fr 515 2672 a(\012) p Fl 550 2680 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 712 2672 a(,) p 741 2672 a(let) 194 2800 y(\003\() p Fq(\033) o(;) p 296 2800 a(!) p Fr 328 2800 a(\)) p 360 2800 a(=) p Fk 412 2730 a(\032) p Fr 450 2800 a(\() p Fq(x;) p 519 2800 a(y) p Fr 545 2800 a(\);) p Fq 605 2769 a(x;) p 655 2769 a(y) p Fo 694 2769 a(2) p Fr 741 2769 a(\003\() p Fo(\0001) p Fq(;) p Fo 905 2769 a(1) p Fr(\)) p Fo 984 2769 a([) p Fq 1029 2769 a(@) p Fp 1055 2776 a(ex) p Fr 1093 2769 a(\003\() p Fo(\0001) p Fq(;) p Fo 1257 2769 a(1) p Fr(\)) p 1341 2769 a(suc) o(h) p 1451 2769 a(that) p Fo 605 2829 a(k) p Fq(x) p Fo 669 2829 a(\000) p Fq 719 2829 a(y) p Fo 745 2829 a(k) p Fl 770 2836 a(1) p Fr 803 2829 a(=) p 855 2829 a(1) p 895 2829 a(and) p Fq 990 2829 a(\033) p Fl 1018 2837 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fq 1180 2829 a(!) p Fr 1212 2829 a(\() p Fq(x) p Fr(\)) p Fo 1291 2829 a(6) p Fr(=) p Fq 1343 2829 a(\033) p Fl 1371 2837 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fq 1533 2829 a(!) p Fr 1565 2829 a(\() p Fq(y) p Fr 1610 2829 a(\)) p Fk 1649 2730 a(\033) p Fq 1695 2800 a(:) p Fr 927 2947 a(12) p 90 rotate dyy eop %%Page: 13 13 13 12 bop Fr 0 274 a(F) l(or) p 87 274 a(a) p 128 274 a(giv) o(en) p 255 274 a(con\014guration) p Fq 551 274 a(\033) p Fo 594 274 a(2) p Fr 641 274 a(\012) p Fl 676 282 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 838 274 a(,) p 868 274 a(w) o(e) p 940 274 a(decomp) q(ose) p Fo 682 384 a([) p Fl 715 392 a(\() p Fp(x;y) p Fl 777 392 a(\)) p Fm(2) p Fl(\003\() p Fp(\033) o(;!) p Fl 905 392 a(\)) p Fr 921 384 a(\() p Fq(Q) p Fr(\() p Fq(x) p Fr(\)) p Fo 1055 384 a(\\) p Fq 1099 384 a(Q) p Fr(\() p Fq(y) p Fr 1183 384 a(\)\)) 0 494 y(in) o(to) p 99 494 a(the) p 184 494 a(connected) p 412 494 a(comp) q(onen) o(ts.) p 700 494 a(Then,) p 841 494 a(there) p 966 494 a(exists) p 1101 494 a(a) p 1142 494 a(unique) p 1301 494 a(connected) p 1529 494 a(comp) q(onen) o(t) p 1779 494 a(whic) o(h) 0 554 y(includes) p 186 554 a(a) p 225 554 a(p) q(oin) o(t) p 351 554 a(\() p Fq(L) p Fr 411 554 a(+) p 457 554 a(1) p Fq(;) p Fr 503 554 a(0) p Fq(;) p Fo 549 554 a(\000) p Fr(1) p Fq(=) p Fr(2\).) p 715 554 a(W) l(e) p 798 554 a(will) p 889 554 a(denote) p 1044 554 a(suc) o(h) p 1153 554 a(a) p 1192 554 a(comp) q(onen) o(t) p 1440 554 a(b) o(y) p 1506 554 a(\000) p Fp 1536 536 a(!) p Fl 1536 569 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1698 554 a(\() p Fq(\033) p Fr 1747 554 a(\).) p 1801 554 a(Note) 0 619 y(that) p 106 619 a(\000) p Fp 136 601 a(!) p Fl 136 634 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 298 619 a(\() p Fq(\033) p Fr 347 619 a(\)) p 382 619 a(includes) p Fo 673 683 a([) p Fl 706 691 a(\() p Fp(x;y) p Fl 768 691 a(\)) p Fm(2) p Fl(\003) p Fe 830 695 a(ex) p Fl 864 691 a(\() p Fp(!) p Fl 901 691 a(\)) p Fr 916 683 a(\() p Fq(Q) p Fr(\() p Fq(x) p Fr(\)) p Fo 1051 683 a(\\) p Fq 1095 683 a(Q) p Fr(\() p Fq(y) p Fr 1179 683 a(\)\)) p Fq(;) p Fr 0 771 a(where) 428 897 y(\003) p Fp 462 904 a(ex) p Fr 500 897 a(\() p Fq(!) p Fr 551 897 a(\)) p 584 897 a(=) p Fk 636 827 a(\032) p Fr 674 897 a(\() p Fq(x;) p 743 897 a(y) p Fr 769 897 a(\);) p Fq 829 867 a(x;) p 879 867 a(y) p Fo 918 867 a(2) p Fq 965 867 a(@) p Fp 991 874 a(ex) p Fr 1029 867 a(\003\() p Fo(\0001) p Fq(;) p Fo 1193 867 a(1) p Fr(\)) p 1278 867 a(suc) o(h) p 1388 867 a(that) p Fo 829 927 a(k) p Fq(x) p Fo 893 927 a(\000) p Fq 943 927 a(y) p Fo 969 927 a(k) p Fl 994 934 a(1) p Fr 1027 927 a(=) p 1079 927 a(1) p 1119 927 a(and) p Fq 1214 927 a(!) p Fr 1246 927 a(\() p Fq(x) p Fr(\)) p Fo 1326 927 a(6) p Fr(=) p Fq 1377 927 a(!) p Fr 1409 927 a(\() p Fq(y) p Fr 1454 927 a(\)) p Fk 1498 827 a(\033) p Fq 1543 897 a(:) p Fr 0 1036 a(Let) p Fq 91 1036 a(L) p Fl 124 1043 a(1) p Fo 164 1036 a(2) p Fn 217 1036 a(N) p Fr(.) p 300 1036 a(W) l(e) p 387 1036 a(similarly) p 590 1036 a(de\014ne) p 735 1036 a(\000) p Fp 765 1018 a(!) p Fl 765 1051 a(\003\() p Fm(\000) p Fp(L) p Fj 854 1056 a(1) p Fp 872 1051 a(;) p Fm(1) p Fl(\)) p Fr 933 1036 a(\() p Fq(\033) p Fr 982 1036 a(\)) p 1021 1036 a(and) p 1119 1036 a(\000) p Fp 1149 1018 a(!) p Fl 1149 1051 a(\003\() p Fm(\0001) p Fp(;L) p Fj 1283 1056 a(1) p Fl 1302 1051 a(\)) p Fr 1317 1036 a(\() p Fq(\033) p Fr 1366 1036 a(\)) p 1405 1036 a(for) p 1483 1036 a(eac) o(h) p Fq 1596 1036 a(\033) p Fo 1646 1036 a(2) p Fr 1699 1036 a(\012) p Fl 1734 1044 a(\003\() p Fm(\000) p Fp(L) p Fj 1823 1049 a(1) p Fp 1841 1044 a(;) p Fm(1) p Fl(\)) p Fr 0 1096 a(and) p 95 1096 a(eac) o(h) p Fq 205 1096 a(\033) p Fo 248 1096 a(2) p Fr 295 1096 a(\012) p Fl 330 1104 a(\003\() p Fm(\0001) p Fp(;L) p Fj 464 1109 a(1) p Fl 482 1104 a(\)) p Fr 498 1096 a(,) p 528 1096 a(resp) q(ectiv) o(ely) l(.) p Fg 73 1198 a(Lemma) p 280 1198 a(3.2.) p Fd 391 1198 a(Supp) n(ose) p 583 1198 a(that) p Fq 689 1198 a(\014) p 745 1198 a(>) p Fr 808 1198 a(0) p Fd 856 1198 a(is) p 915 1198 a(su\016ciently) p 1167 1198 a(lar) n(ge,) p Fq 1308 1198 a(L) p Fl 1341 1205 a(1) p Fo 1386 1198 a(2) p Fn 1445 1198 a(N) p Fd 1505 1198 a(and) p Fq 1606 1198 a(L) p Fl 1639 1205 a(2) p Fo 1684 1198 a(2) p Fn 1743 1198 a(N) p Fd(.) p 1836 1198 a(L) n(et) p Fg 0 1258 a(1) p Fp 28 1265 a(L) p Fj 52 1270 a(1) p Fp 69 1265 a(;L) p Fj 103 1270 a(2) p Fr 143 1258 a(:) p Fg 176 1258 a(C) p Fo 237 1258 a(!) p 307 1258 a(f) p Fr(0) p Fq(;) p Fr 378 1258 a(1) p Fo(g) p Fd 448 1258 a(b) n(e) p 511 1258 a(the) p 595 1258 a(indic) n(ator) p 805 1258 a(function) p 1000 1258 a(of) p 1061 1258 a(the) p 1145 1258 a(event) p 1276 1258 a(that) p Fq 1379 1258 a(C) p Fo 1438 1258 a(\032) p 1497 1258 a(C) p Fr 1526 1258 a(\() p Fo(\000) p Fq(L) p Fl 1617 1265 a(1) p Fq 1637 1258 a(;) p 1659 1258 a(L) p Fl 1692 1265 a(2) p Fr 1711 1258 a(\)) p Fd(.) p 1778 1258 a(Then,) 0 1319 y(ther) n(e) p 121 1319 a(exists) p 255 1319 a(a) p 297 1319 a(function) p Fr 489 1319 a(\010) p Fl 524 1300 a(T) p Fd 569 1319 a(such) p 680 1319 a(that) p 779 1319 a(for) p 857 1319 a(e) n(ach) p Fr 967 1319 a(\000) p Fo 1011 1319 a(2) p 1058 1319 a(O) p Fr 1099 1319 a(\() p Fo(\000) p Fq(L) p Fl 1190 1326 a(1) p Fq 1210 1319 a(;) p 1232 1319 a(L) p Fl 1265 1326 a(2) p Fr 1285 1319 a(\)) p Fq 324 1429 a(\026) p Fp 353 1408 a(!) p Fl 353 1441 a(\003\() p Fm(\000) p Fp(L) p Fj 442 1446 a(1) p Fp 460 1441 a(;L) p Fj 494 1446 a(2) p Fl 511 1441 a(\)) p Fr 527 1429 a(\(\000) p Fp 576 1408 a(!) p Fl 576 1441 a(\003\() p Fm(\000) p Fp(L) p Fj 665 1446 a(1) p Fp 683 1441 a(;L) p Fj 717 1446 a(2) p Fl 734 1441 a(\)) p Fr 750 1429 a(\() p Fq(\033) p Fr 799 1429 a(\)) p 831 1429 a(=) p 883 1429 a(\000\)) 423 1518 y(=) p 475 1518 a(Z\() p Fo(S) t(W) p Fr 611 1518 a(\() p Fo(\000) p Fq(L) p Fl 702 1525 a(1) p Fq 722 1518 a(;) p 744 1518 a(L) p Fl 777 1525 a(2) p Fr 796 1518 a(\)\)) p Fm 834 1497 a(\000) p Fl(1) p Fr 881 1518 a(\010\() p Fn(W) p Fr 982 1518 a(\(\000) q(\)\)) p 1078 1518 a(exp) s([) p Fo(\000) p Fk 1217 1471 a(X) p Fp 1221 1576 a(C) r(\023) p Fl(\000) p Fg 1296 1518 a(1) p Fp 1324 1525 a(L) p Fj 1348 1530 a(1) p Fp 1366 1525 a(;L) p Fj 1400 1530 a(2) p Fr 1419 1518 a(\() p Fq(C) p Fr 1477 1518 a(\)\010) p Fl 1531 1497 a(T) p Fr 1558 1518 a(\() p Fq(C) p Fr 1616 1518 a(\)]) p Fq(;) p Fr 1802 1518 a(\(3.6\)) p Fd 0 1670 a(wher) n(e) p Fr 220 1730 a(Z\() p Fo(S) t(W) p Fr 356 1730 a(\() p Fo(\000) p Fq(L) p Fl 447 1737 a(1) p Fq 467 1730 a(;) p 489 1730 a(L) p Fl 522 1737 a(2) p Fr 542 1730 a(\)\)) p 594 1730 a(=) p Fk 742 1683 a(X) p Ff 645 1791 a(W) p Fm 682 1791 a(2) o(S) r(W) p Fl 764 1791 a(\() p Fm(\000) p Fp(L) p Fj 829 1796 a(1) p Fp 846 1791 a(;L) p Fj 880 1796 a(2) p Fl 897 1791 a(\)) p Fr 919 1730 a(\010\() p Fn(W) p Fr 1020 1730 a(\)) p 1048 1730 a(exp) r([) p Fo(\000) p Fk 1211 1683 a(X) p Fp 1186 1791 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1298 1791 a(\)) p Fg 1317 1730 a(1) p Fp 1345 1737 a(L) p Fj 1369 1742 a(1) p Fp 1386 1737 a(;L) p Fj 1420 1742 a(2) p Fr 1439 1730 a(\() p Fq(C) p Fr 1497 1730 a(\)\010) p Fl 1551 1710 a(T) p Fr 1578 1730 a(\() p Fq(C) p Fr 1636 1730 a(\)]) p Fq(:) p Fd 0 1870 a(Mor) n(e) n(over,) p 229 1870 a(we) p 301 1870 a(have) p 414 1870 a(that) p Fr 230 1986 a(Z\() p Fo(S) t(W) p Fr 366 1986 a(\() p Fo(\0001) p Fq(;) p Fo 496 1986 a(1) p Fr(\)\)) p 597 1986 a(=) p Fk 739 1938 a(X) p Ff 648 2046 a(W) p Fm 685 2046 a(2) o(S) r(W) p Fl 767 2046 a(\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 910 1986 a(\010\() p Fn(W) p Fr 1011 1986 a(\)) p 1039 1986 a(exp) r([) p Fo(\000) p Fk 1202 1938 a(X) p Fp 1177 2046 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1289 2046 a(\)) p Fr 1308 1986 a(\010) p Fl 1343 1965 a(T) p Fr 1371 1986 a(\() p Fq(C) p Fr 1429 1986 a(\)]) p Fq 1474 1986 a(<) p Fo 1526 1986 a(1) p Fq(;) p Fr 1802 1986 a(\(3.7\)) p Fd 0 2151 a(and) p 95 2151 a(that) p 194 2151 a(for) p 272 2151 a(e) n(ach) p Fr 382 2151 a(\000) p Fo 426 2151 a(2) p 473 2151 a(O) p Fr 514 2151 a(\() p Fo(\0001) p Fq(;) p Fo 644 2151 a(1) p Fr(\)) p Fq 426 2261 a(\026) p Fp 455 2240 a(!) p Fl 455 2273 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 617 2261 a(\(\000) p Fp 666 2240 a(!) p Fl 666 2273 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 829 2261 a(\() p Fq(\033) p Fr 878 2261 a(\)) p 910 2261 a(=) p 962 2261 a(\000\)) 526 2350 y(=) p 578 2350 a(Z\() p Fo(S) t(W) p Fr 713 2350 a(\() p Fo(\0001) p Fq(;) p Fo 843 2350 a(1) p Fr(\)\)) p Fm 931 2330 a(\000) p Fl(1) p Fr 978 2350 a(\010\() p Fn(W) p Fr 1079 2350 a(\(\000\)\)) p 1174 2350 a(exp) s([) p Fo(\000) p Fk 1313 2303 a(X) p Fp 1318 2409 a(C) r(\023) p Fl(\000) p Fr 1393 2350 a(\010) p Fl 1428 2330 a(T) p Fr 1456 2350 a(\() p Fq(C) p Fr 1514 2350 a(\)]) p Fq(:) p Fr 1802 2350 a(\(3.8\)) p Fd 0 2505 a(We) p 89 2505 a(also) p 188 2505 a(have) p 300 2505 a(that) p 400 2505 a(for) p 478 2505 a(e) n(ach) p Fr 587 2505 a(\000) p Fo 632 2505 a(2) p 679 2505 a(O) p Fr 720 2505 a(\() p Fo(\000) p Fq(L) p Fl 811 2512 a(1) p Fq 830 2505 a(;) p Fo 852 2505 a(1) p Fr(\)) p Fq 328 2615 a(\026) p Fp 357 2595 a(!) p Fl 357 2627 a(\003\() p Fm(\000) p Fp(L) p Fj 446 2632 a(1) p Fp 464 2627 a(;) p Fm(1) p Fl(\)) p Fr 525 2615 a(\(\000) p Fp 574 2595 a(!) p Fl 574 2627 a(\003\() p Fm(\000) p Fp(L) p Fj 663 2632 a(1) p Fp 682 2627 a(;) p Fm(1) p Fl(\)) p Fr 743 2615 a(\() p Fq(\033) p Fr 792 2615 a(\)) p 824 2615 a(=) p 876 2615 a(\000\)) 428 2705 y(=) p 480 2705 a(Z\() p Fo(S) t(W) p Fr 616 2705 a(\() p Fo(\000) p Fq(L) p Fl 707 2712 a(1) p Fq 726 2705 a(;) p Fo 748 2705 a(1) p Fr(\)\)) p Fm 836 2684 a(\000) p Fl(1) p Fr 883 2705 a(\010\() p Fn(W) p Fr 984 2705 a(\(\000\)\)) p 1080 2705 a(exp) r([) p Fo(\000) p Fk 1218 2657 a(X) p Fp 1223 2763 a(C) r(\023) p Fl(\000) p Fg 1298 2705 a(1) p Fp 1326 2712 a(L) p Fj 1350 2717 a(1) p Fp 1367 2712 a(;) p Fm(1) p Fr 1414 2705 a(\() p Fq(C) p Fr 1472 2705 a(\)\010) p Fl 1526 2684 a(T) p Fr 1554 2705 a(\() p Fq(C) p Fr 1612 2705 a(\)]) p Fq(;) p Fr 1802 2705 a(\(3.9\)) 927 2947 y(13) p 90 rotate dyy eop %%Page: 14 14 14 13 bop Fd 0 274 a(wher) n(e) p Fr 182 367 a(Z\() p Fo(S) t(W) p Fr 318 367 a(\() p Fo(\000) p Fq(L) p Fl 409 374 a(1) p Fq 429 367 a(;) p Fo 451 367 a(1) p Fr(\)\)) p 552 367 a(=) p Fk 698 320 a(X) p Ff 604 428 a(W) p Fm 640 428 a(2S) r(W) p Fl(\() p Fm(\000) p Fp(L) p Fj 787 433 a(1) p Fp 805 428 a(;) p Fm(1) p Fl(\)) p Fr 872 367 a(\010\() p Fn(W) p Fr 973 367 a(\)) p 1000 367 a(exp) s([) p Fo(\000) p Fk 1164 320 a(X) p Fp 1139 428 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1250 428 a(\)) p Fg 1269 367 a(1) p Fp 1297 374 a(L) p Fj 1321 379 a(1) p Fp 1339 374 a(;) p Fm(1) p Fr 1386 367 a(\() p Fq(C) p Fr 1444 367 a(\)\010) p Fl 1498 346 a(T) p Fr 1525 367 a(\() p Fq(C) p Fr 1583 367 a(\)]) p Fq(;) p Fr 1778 495 a(\(3.10\)) p Fd 0 588 a(and) p 95 588 a(that) p 194 588 a(for) p 272 588 a(e) n(ach) p Fr 382 588 a(\000) p Fo 426 588 a(2) p 473 588 a(O) p Fr 514 588 a(\() p Fo(\0001) p Fq(;) p 644 588 a(L) p Fl 677 595 a(1) p Fr 696 588 a(\)) p Fq 328 681 a(\026) p Fp 357 660 a(!) p Fl 357 693 a(\003\() p Fm(\0001) p Fp(;L) p Fj 491 698 a(1) p Fl 509 693 a(\)) p Fr 525 681 a(\(\000) p Fp 574 660 a(!) p Fl 574 693 a(\003\() p Fm(\0001) p Fp(;L) p Fj 708 698 a(1) p Fl 727 693 a(\)) p Fr 743 681 a(\() p Fq(\033) p Fr 792 681 a(\)) p 824 681 a(=) p 876 681 a(\000\)) 428 770 y(=) p 480 770 a(Z\() p Fo(S) t(W) p Fr 616 770 a(\() p Fo(\0001) p Fq(;) p 746 770 a(L) p Fl 779 777 a(1) p Fr 798 770 a(\)\)) p Fm 836 750 a(\000) p Fl(1) p Fr 883 770 a(\010\() p Fn(W) p Fr 984 770 a(\(\000\)\)) p 1080 770 a(exp) r([) p Fo(\000) p Fk 1218 723 a(X) p Fp 1223 829 a(C) r(\023) p Fl(\000) p Fg 1298 770 a(1) p Fm 1326 777 a(1) p Fp(;L) p Fj 1395 782 a(1) p Fr 1414 770 a(\() p Fq(C) p Fr 1472 770 a(\)\010) p Fl 1526 750 a(T) p Fr 1554 770 a(\() p Fq(C) p Fr 1612 770 a(\)]) p Fq(;) p Fr 1778 770 a(\(3.11\)) p Fd 0 905 a(wher) n(e) p Fr 186 998 a(Z\() p Fo(S) t(W) p Fr 322 998 a(\() p Fo(\0001) p Fq(;) p 452 998 a(L) p Fl 485 1005 a(1) p Fr 505 998 a(\)\)) p 557 998 a(=) p Fk 702 951 a(X) p Ff 608 1059 a(W) p Fm 644 1059 a(2S) r(W) p Fl 727 1059 a(\() p Fm(\0001) p Fp(;L) p Fj 837 1064 a(1) p Fl 854 1059 a(\)) p Fr 876 998 a(\010\() p Fn(W) p Fr 977 998 a(\)) p 1004 998 a(exp) s([) p Fo(\000) p Fk 1168 951 a(X) p Fp 1143 1059 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1255 1059 a(\)) p Fg 1274 998 a(1) p Fm 1302 1005 a(1) p Fp(;L) p Fj 1371 1010 a(1) p Fr 1390 998 a(\() p Fq(C) p Fr 1448 998 a(\)\010) p Fl 1502 978 a(T) p Fr 1529 998 a(\() p Fq(C) p Fr 1587 998 a(\)]) p Fq(:) p Fr 1778 1126 a(\(3.12\)) p Fq 73 1219 a(P) p 111 1219 a(r) q(oof) p Fr 209 1219 a(.) p 251 1219 a(Let) p 339 1219 a(us) p 404 1219 a(\014x) p Fq 474 1219 a(L) p Fl 507 1226 a(1) p Fo 543 1219 a(2) p Fn 593 1219 a(N) p Fr 647 1219 a(and) p Fq 743 1219 a(L) p Fl 776 1226 a(2) p Fo 812 1219 a(2) p Fn 862 1219 a(N) p Fr(.) p 937 1219 a(Set) p 1023 1219 a(\003) p 1073 1219 a(=) p 1127 1219 a(\003\() p Fo(\000) p Fq(L) p Fl 1252 1226 a(1) p Fq 1272 1219 a(;) p 1294 1219 a(L) p Fl 1327 1226 a(2) p Fr 1347 1219 a(\)) p 1383 1219 a(and) p 1480 1219 a(\000\() p Fo(\001) p Fr(\)) p 1578 1219 a(=) p 1633 1219 a(\000) p Fp 1663 1201 a(!) p Fl 1663 1234 a(\003\() p Fm(\000) p Fp(L) p Fj 1752 1239 a(1) p Fp 1770 1234 a(;L) p Fj 1804 1239 a(2) p Fl 1821 1234 a(\)) p Fr 1837 1219 a(\() p Fo(\001) p Fr(\).) 0 1286 y(Let) p 92 1286 a(\001\(\000\)) p 222 1286 a(=) p Fo 282 1286 a(f) p Fq(x) p Fo 356 1286 a(2) p Fn 410 1286 a(Z) p Fl 446 1268 a(3) p Fr 463 1286 a(;) p 485 1286 a(dist) p Fm 564 1293 a(1) p Fr 601 1286 a(\() p Fq(x;) p Fr 670 1286 a(\000\)) p 740 1286 a(=) p 800 1286 a(1) p Fq(=) p Fr(2) p Fo(g) p Fr 919 1286 a(for) p 997 1286 a(eac) o(h) p 1112 1286 a(\000) p Fo 1163 1286 a(2) p 1218 1286 a(O) p Fr 1259 1286 a(\() p Fo(\000) p Fq(L) p Fl 1350 1293 a(1) p Fq 1370 1286 a(;) p 1392 1286 a(L) p Fl 1425 1293 a(2) p Fr 1444 1286 a(\),) p 1499 1286 a(where) p 1644 1286 a(dist) p Fm 1723 1293 a(1) p Fr 1781 1286 a(is) p 1834 1286 a(the) 0 1346 y(metric) p 152 1346 a(induced) p 334 1346 a(b) o(y) p Fq 402 1346 a(l) p Fm 417 1353 a(1) p Fr 454 1346 a(-norm.) p 618 1346 a(Let) p 706 1346 a(us) p 769 1346 a(\014x) p 838 1346 a(\000) p Fo 883 1346 a(2) p 931 1346 a(O) p Fr 972 1346 a(\() p Fo(\000) p Fq(L) p Fl 1063 1353 a(1) p Fq 1082 1346 a(;) p 1104 1346 a(L) p Fl 1137 1353 a(2) p Fr 1157 1346 a(\).) p 1212 1346 a(W) l(e) p 1297 1346 a(decomp) q(ose) p 1543 1346 a(\003) p Fo(n) p Fr(\001\(\000\)) p 1727 1346 a(in) o(to) p 1826 1346 a(t) o(w) o(o) 0 1406 y(sets) p Fq 95 1406 a(R) p Fl 132 1386 a(+) 132 1420 y(\000) p Fr 177 1406 a(and) p Fq 272 1406 a(R) p Fm 309 1386 a(\000) p Fl 309 1420 a(\000) p Fr 354 1406 a(whic) o(h) p 493 1406 a(lie,) p 571 1406 a(in) p 628 1406 a(a) p 668 1406 a(natural) p 838 1406 a(w) o(a) o(y) l(,) p 946 1406 a(b) q(elo) o(w) p 1083 1406 a(and) p 1178 1406 a(ab) q(o) o(v) o(e) p 1315 1406 a(\000,) p 1375 1406 a(resp) q(ectiv) o(ely) l(.) p 1656 1406 a(W) l(e) p 1739 1406 a(ha) o(v) o(e) p 1851 1406 a(b) o(y) 0 1467 y(Lemma) p 174 1467 a(1.3) p 253 1467 a(that) p Fk 270 1512 a(X) p Fp 194 1620 a(\033) p Fm 215 1620 a(2) p Fl(\012) p Fj 264 1626 a(\003) p Fl 287 1620 a(;\000\() p Fp(\033) p Fl 354 1620 a(\)=\000) p Fr 426 1560 a(exp) o([) p Fo(\000) p Fq(\014) s(H) p Fp 628 1539 a(!) p Fl 624 1572 a(\003) p Fr 652 1560 a(\() p Fq(\033) p Fr 701 1560 a(\)]) p 775 1560 a(=) p 854 1560 a(\010\(\000\)Z\() p Fq(R) p Fl 1043 1539 a(+) 1043 1573 y(\000) p Fq 1074 1560 a(;) p Fr 1096 1560 a(+\)Z\() p Fq(R) p Fm 1239 1539 a(\000) p Fl 1239 1573 a(\000) p Fq 1268 1560 a(;) p Fo 1290 1560 a(\000) p Fr(\)) 775 1702 y(=) p 854 1702 a(Z\(\003) p Fq(;) p Fr 959 1702 a(+\)\010\(\000\)) p 1127 1702 a(exp[) p Fo(\000) p Fk 1263 1655 a(X) p Fp 1268 1761 a(C) r(\023) p Fl(\000) p Fg 1343 1702 a(1) p Fp 1371 1709 a(L) p Fj 1395 1714 a(1) p Fp 1412 1709 a(;L) p Fj 1446 1714 a(2) p Fr 1465 1702 a(\() p Fq(C) p Fr 1523 1702 a(\)\010) p Fl 1577 1682 a(T) p Fr 1605 1702 a(\() p Fq(C) p Fr 1663 1702 a(\)]) p Fq(:) p Fr 1778 1820 a(\(3.13\)) 0 1913 y(Set) p 84 1913 a(in) p 141 1913 a(Lemma) p 315 1913 a(1.3,) p Fq 407 1913 a(a) p Fr(\() p Fo(\001) p Fr(\)) p 498 1913 a(=) p 550 1913 a(6) p Fn(M) p Fl 619 1895 a(2) p Fr 641 1913 a(\() p Fo(\001) p Fr(\)) p 709 1913 a(and) p Fq 804 1913 a(d) p Fr(\() p Fo(\001) p Fr(\)) p 895 1913 a(=) p 947 1913 a(\() p Fq(\014) p Fo 1007 1913 a(\000) p Fr 1064 1900 a(^) p Fq 1057 1913 a(\014) p Fr 1087 1913 a(\)) p Fn(M) p Fl 1150 1895 a(2) p Fr 1173 1913 a(\() p Fo(\001) p Fr(\)) p 1241 1913 a(for) p 1316 1913 a(su\016cien) o(tly) p 1560 1913 a(large) 1686 1900 y(^) p Fq 1679 1913 a(\014) p 1723 1913 a(>) p Fr 1775 1913 a(0.) p 1834 1913 a(W) l(e) 0 1973 y(ha) o(v) o(e) p 112 1973 a(that) p 218 1973 a(for) p 293 1973 a(an) o(y) p Fq 385 1973 a(\015) p Fo 427 1973 a(2) p 474 1973 a(C) p Fr 503 1973 a(\() p Fo(\000) p Fq(L) p Fl 594 1980 a(1) p Fq 613 1973 a(;) p 635 1973 a(L) p Fl 668 1980 a(2) p Fr 688 1973 a(\)) 656 2066 y(\010\() p Fq(\015) p Fr 738 2066 a(\)) p 771 2066 a(=) p 822 2066 a(exp[) p Fo(\000) p Fr(2) p Fq(\014) p Fn 1005 2066 a(M) p Fl 1048 2045 a(2) p Fr 1071 2066 a(\() p Fq(\015) p Fr 1118 2066 a(\)]) p Fq(:) p Fr 1778 2066 a(\(3.14\)) 0 2159 y(Therefore,) p 234 2159 a(w) o(e) p 305 2159 a(can) p 394 2159 a(see) p 472 2159 a(b) o(y) p 539 2159 a(Lemma) p 712 2159 a(1.3) p 790 2159 a(that) p 895 2159 a(there) p 1019 2159 a(exist) p Fq 1134 2159 a(c) p Fl 1155 2166 a(1) p Fq 1188 2159 a(>) p Fr 1240 2159 a(0) p 1280 2159 a(and) p Fq 1374 2159 a(c) p Fl 1395 2166 a(2) p Fq 1429 2159 a(>) p Fr 1481 2159 a(0) p 1521 2159 a(suc) o(h) p 1630 2159 a(that) p 1735 2159 a(for) p 1809 2159 a(eac) o(h) p Fq 0 2219 a(x) p Fo 42 2219 a(2) p Fr 89 2219 a(\003\() p Fo(\0001) p Fq(;) p Fo 253 2219 a(1) p Fr(\)) p 337 2219 a(and) p 432 2219 a(an) o(y) p Fq 524 2219 a(n) p Fo 567 2219 a(2) p Fn 614 2219 a(N) p Fr 666 2219 a(\(see) p 764 2219 a(\(3.5\)\),) p Fk 544 2273 a(X) p Fp 442 2381 a(C) p Fm 469 2381 a(2) p Fb(C) p Fl(\() p Fp(n) p Fl(\);) p Fp(C) r(\023@) r(Q) p Fl(\() p Fp(x) p Fl(\)) p Fo 725 2321 a(j) p Fr(\010) p Fl 774 2300 a(T) p Fr 802 2321 a(\() p Fq(C) p Fr 860 2321 a(\)) p Fo(j) p 906 2321 a(\024) p Fq 958 2321 a(c) p Fl 979 2328 a(1) p Fr 1007 2321 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1195 2321 a(\000) p Fr 1251 2308 a(^) p Fq 1244 2321 a(\014) p Fr 1275 2321 a(\)) p Fq(c) p Fl 1315 2328 a(2) p Fq 1334 2321 a(n) p Fr(]) p 1778 2321 a(\(3.15\)) 0 2479 y(Note) p 118 2479 a(that) 231 2466 y(^) p Fq 224 2479 a(\014) r(;) p 292 2479 a(c) p Fl 313 2486 a(1) p Fr 349 2479 a(and) p Fq 444 2479 a(c) p Fl 465 2486 a(2) p Fr 501 2479 a(do) p 568 2479 a(not) p 655 2479 a(dep) q(end) p 825 2479 a(on) p Fq 892 2479 a(\014) p 936 2479 a(>) p Fr 988 2479 a(0) p Fq(;) p 1051 2479 a(L) p Fl 1084 2486 a(1) p Fo 1117 2479 a(2) p Fn 1164 2479 a(N) p Fq(;) p 1239 2479 a(L) p Fl 1272 2486 a(2) p Fo 1305 2479 a(2) p Fn 1352 2479 a(N) p Fr 1405 2479 a(and) p Fq 1499 2479 a(L) p Fo 1546 2479 a(2) p Fn 1593 2479 a(N) p Fr(.) 73 2540 y(F) l(or) p 161 2540 a(eac) o(h) p 270 2540 a(\000) p Fo 315 2540 a(2) p 362 2540 a(O) p Fr 403 2540 a(\() p Fo(\000) p Fq(L) p Fl 494 2547 a(1) p Fq 513 2540 a(;) p 535 2540 a(L) p Fl 568 2547 a(2) p Fr 588 2540 a(\),) p 637 2540 a(w) o(e) p 709 2540 a(can) p 798 2540 a(see) p 877 2540 a(from) p 992 2540 a(\(3.4\)) p 1109 2540 a(and) p 1203 2540 a(\(3.13\)) p 1344 2540 a(that) p Fk 408 2594 a(X) p Fp 332 2702 a(\033) p Fm 353 2702 a(2) p Fl(\012) p Fj 402 2708 a(\003) p Fl 425 2702 a(;\000\() p Fp(\033) p Fl 492 2702 a(\)=\000) p Fr 564 2641 a(exp) o([) p Fo(\000) p Fq(\014) s(H) p Fp 766 2621 a(!) p Fl 762 2654 a(\003) p Fr 790 2641 a(\() p Fq(\033) p Fr 839 2641 a(\)]) 527 2784 y(=) p Fq 579 2784 a(e) p Fm 602 2764 a(\000) p Fl(8) p Fp(\014) r(L) p Fj 693 2752 a(2) p Fr 712 2784 a(Z\(\003) p Fq(;) p Fr 817 2784 a(+\)\010\() p Fn(W) p Fr 974 2784 a(\(\000\)\)) p 1070 2784 a(exp) r([) p Fo(\000) p Fk 1208 2737 a(X) p Fp 1213 2843 a(C) r(\023) p Fl(\000) p Fg 1288 2784 a(1) p Fp 1316 2791 a(L) p Fj 1340 2796 a(1) p Fp 1357 2791 a(;L) p Fj 1391 2796 a(2) p Fr 1410 2784 a(\() p Fq(C) p Fr 1468 2784 a(\)\010) p Fl 1522 2764 a(T) p Fr 1550 2784 a(\() p Fq(C) p Fr 1608 2784 a(\)]) p Fq(:) p Fr 1778 2784 a(\(3.16\)) 927 2947 y(14) p 90 rotate dyy eop %%Page: 15 15 15 14 bop Fr 0 274 a(Then,) p 141 274 a(w) o(e) p 213 274 a(ha) o(v) o(e) p 325 274 a(that) p Fq 135 386 a(\026) p Fp 164 366 a(!) p Fl 164 399 a(\003) p Fr 191 386 a(\(\000\() p Fq(\033) p Fr 289 386 a(\)) p 322 386 a(=) p 374 386 a(\000\)) p 437 386 a(=) p 489 386 a(Z\() p Fo(S) t(W) p Fr 625 386 a(\() p Fo(\000) p Fq(L) p Fl 716 393 a(1) p Fq 735 386 a(;) p 757 386 a(L) p Fl 790 393 a(2) p Fr 810 386 a(\)\)) p Fm 848 366 a(\000) p Fl(1) p Fr 895 386 a(\010\() p Fn(W) p Fr 996 386 a(\(\000) q(\)\)) p 1092 386 a(exp) r([) p Fo(\000) p Fk 1230 339 a(X) p Fp 1235 445 a(C) r(\023) p Fl(\000) p Fg 1310 386 a(1) p Fp 1338 393 a(L) p Fj 1362 398 a(1) p Fp 1380 393 a(;L) p Fj 1414 398 a(2) p Fr 1433 386 a(\() p Fq(C) p Fr 1491 386 a(\)\010) p Fl 1545 366 a(T) p Fr 1572 386 a(\() p Fq(C) p Fr 1630 386 a(\)]) p Fq(;) p Fr 1778 504 a(\(3.17\)) 0 610 y(where) 220 716 y(Z\() p Fo(S) t(W) p Fr 356 716 a(\() p Fo(\000) p Fq(L) p Fl 447 723 a(1) p Fq 467 716 a(;) p 489 716 a(L) p Fl 522 723 a(2) p Fr 542 716 a(\)\)) p 594 716 a(=) p Fk 742 669 a(X) p Ff 645 777 a(W) p Fm 682 777 a(2) o(S) r(W) p Fl 764 777 a(\() p Fm(\000) p Fp(L) p Fj 829 782 a(1) p Fp 846 777 a(;L) p Fj 880 782 a(2) p Fl 897 777 a(\)) p Fr 919 716 a(\010\() p Fn(W) p Fr 1020 716 a(\)) p 1048 716 a(exp) r([) p Fo(\000) p Fk 1211 669 a(X) p Fp 1186 777 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1298 777 a(\)) p Fg 1317 716 a(1) p Fp 1345 723 a(L) p Fj 1369 728 a(1) p Fp 1386 723 a(;L) p Fj 1420 728 a(2) p Fr 1439 716 a(\() p Fq(C) p Fr 1497 716 a(\)\010) p Fl 1551 696 a(T) p Fr 1578 716 a(\() p Fq(C) p Fr 1636 716 a(\)]) p Fq(:) p Fr 0 878 a(W) l(e) p 84 878 a(obtained) p 285 878 a(\(3.6\).) p 420 878 a(W) l(e) p 504 878 a(can) p 593 878 a(also) p 691 878 a(obtain) p 843 878 a(from) p 958 878 a(\(3.4\)) p 1075 878 a(and) p 1169 878 a(\(3.15\)) p 1310 878 a(that) p Fk 581 946 a(X) p Ff 490 1053 a(W) p Fm 527 1053 a(2) o(S) r(W) p Fl 609 1053 a(\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 752 993 a(\010\() p Fn(W) p Fr 853 993 a(\)) p 880 993 a(exp) s([) p Fk 997 946 a(X) p Fp 972 1053 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1083 1053 a(\)) p Fo 1103 993 a(j) p Fr(\010) p Fl 1152 972 a(T) p Fr 1179 993 a(\() p Fq(C) p Fr 1237 993 a(\)) p Fo(j) p Fr(]) p Fq 1297 993 a(<) p Fo 1349 993 a(1) p Fq(;) p Fr 0 1154 a(whic) o(h) p 140 1154 a(implies) p 305 1154 a(\(3.7\).) p 441 1154 a(W) l(e) p 525 1154 a(ha) o(v) o(e) p 637 1154 a(b) o(y) p 705 1154 a(the) p 789 1154 a(de\014nition) p 1006 1154 a(of) p 1061 1154 a(Z\() p Fo(S) t(W) p Fr 1197 1154 a(\() p Fo(\0001) p Fq(;) p Fo 1327 1154 a(1) p Fr(\)\)) p 1430 1154 a(that) 527 1261 y(lim) p Fp 510 1292 a(N) p Fm 542 1292 a(!1) p Fr 621 1261 a(Z\() p Fo(S) t(W) p Fr 757 1261 a(\() p Fo(\000) p Fq(N) r(;) p 878 1261 a(N) p Fr 922 1261 a(\)\)) p 974 1261 a(=) p 1025 1261 a(Z\() p Fo(S) t(W) p Fr 1161 1261 a(\() p Fo(\0001) p Fq(;) p Fo 1291 1261 a(1) p Fr(\)\)) p Fq(;) p Fr 0 1384 a(whic) o(h) p 140 1384 a(implies) p 305 1384 a(\(3.8\).) p 441 1384 a(Similarly) l(,) p 657 1384 a(w) o(e) p 729 1384 a(can) p 819 1384 a(obtain) p 970 1384 a(\(3.9\)) p 1087 1384 a(and) p 1182 1384 a(\(3.11\).) 73 1490 y(Let) p Fq 161 1490 a(L) p Fl 194 1497 a(1) p Fo 227 1490 a(2) p Fn 274 1490 a(N) p Fo 321 1490 a([) p 366 1490 a(f1g) p Fr 482 1490 a(and) p Fq 576 1490 a(L) p Fl 609 1497 a(2) p Fo 643 1490 a(2) p Fn 690 1490 a(N) p Fo 737 1490 a([) p 781 1490 a(f1g) p Fr(.) p 916 1490 a(F) l(or) p 1004 1490 a(eac) o(h) p Fn 1113 1490 a(W) p Fo 1177 1490 a(2) p 1224 1490 a(S) t(W) p Fr 1311 1490 a(\() p Fo(\000) p Fq(L) p Fl 1402 1497 a(1) p Fq 1422 1490 a(;) p 1444 1490 a(L) p Fl 1477 1497 a(2) p Fr 1497 1490 a(\),) p 1546 1490 a(w) o(e) p 1617 1490 a(de\014ne) p Fq 146 1605 a(P) p Fl 177 1613 a(\003\() p Fm(\000) p Fp(L) p Fj 266 1618 a(1) p Fp 284 1613 a(;L) p Fj 318 1618 a(2) p Fl 335 1613 a(\)) p Fr 351 1605 a(\() p Fn(W) p Fr 417 1605 a(\)) p 453 1605 a(=) p 504 1605 a(Z\() p Fo(S) t(W) p Fr 640 1605 a(\() p Fo(\000) p Fq(L) p Fl 731 1612 a(1) p Fq 751 1605 a(;) p 773 1605 a(L) p Fl 806 1612 a(2) p Fr 826 1605 a(\)\)) p Fm 864 1585 a(\000) p Fl(1) p Fr 911 1605 a(\010\() p Fn(W) p Fr 1012 1605 a(\)) p 1039 1605 a(exp) s([) p Fo(\000) p Fk 1203 1558 a(X) p Fp 1178 1666 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1289 1666 a(\)) p Fg 1308 1605 a(1) p Fp 1336 1612 a(L) p Fj 1360 1617 a(1) p Fp 1378 1612 a(;L) p Fj 1412 1617 a(2) p Fr 1431 1605 a(\() p Fq(C) p Fr 1489 1605 a(\)\010) p Fl 1543 1585 a(T) p Fr 1570 1605 a(\() p Fq(C) p Fr 1628 1605 a(\)]) p Fq(:) p Fr 1778 1733 a(\(3.18\)) p Fq 73 1839 a(P) p 111 1839 a(r) q(oof) p 228 1839 a(of) p 298 1839 a(Lemma) p Fr 482 1839 a(3) p Fq(:) p Fr(1.) p 582 1839 a(Let) p 671 1839 a(\003) p 720 1839 a(=) p 773 1839 a(\003\() p Fo(\000) p Fr(2) p Fq(L) p Fr 934 1839 a(+) p 984 1839 a(2) p Fq(l) q(;) p Fr 1046 1839 a(2) p Fq(l) p Fr 1086 1839 a(\)) p 1122 1839 a(and) p Fq 1217 1839 a(L) p Fm 1250 1821 a(0) p Fr 1278 1839 a(=) p 1331 1839 a(2) p Fq(L) p Fo 1400 1839 a(\000) p Fr 1451 1839 a(2) p Fq(l) p Fr 1491 1839 a(.) p 1529 1839 a(W) l(e) p 1614 1839 a(ha) o(v) o(e) p 1727 1839 a(b) o(y) p 1796 1839 a(FK) o(G) 0 1900 y(inequalit) o(y) p 226 1900 a(that) p Fq 621 2006 a(\026) p Fp 650 1985 a(!) p Fl 650 2018 a(\003) p Fr 677 2006 a(\(\() p Fo(A) p Fp 755 1985 a(!) p Fl 755 2018 a(\003) p Fr 781 2006 a(\)) p Fp 800 1985 a(c) p Fr 817 2006 a(\)) p Fo 850 2006 a(\024) p Fq 903 2006 a(\026) p Fp 932 1985 a(!) p Fl 932 2018 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1087 2006 a(\() p Fo(A) p Fm 1146 1985 a(0) p Fl 1146 2018 a(1) p Fr 1166 2006 a(\)) p Fq(;) p Fr 1778 2006 a(\(3.19\)) 0 2112 y(where) p Fo 471 2173 a(A) p Fm 511 2152 a(0) p Fl 511 2185 a(1) p Fr 545 2173 a(=) p Fo 597 2173 a(f) p Fq(\033) p Fo 665 2173 a(2) p Fr 712 2173 a(\012) p Fl 747 2180 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 902 2173 a(;) p 924 2173 a(h) p Fm 951 2152 a(\000) p Fr 981 2173 a(\(\000) p Fp 1030 2152 a(!) p Fl 1030 2185 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1185 2173 a(\() p Fq(\033) p Fr 1234 2173 a(\)\)) p Fo 1285 2173 a(\024) p 1338 2173 a(\000) p Fq(l) p Fo 1393 2173 a(g) p Fq(:) p Fr 0 2258 a(W) l(e) p 84 2258 a(also) p 182 2258 a(ha) o(v) o(e) p 294 2258 a(b) o(y) p 362 2258 a(FK) o(G) p 485 2258 a(inequalit) o(y) p 711 2258 a(that) p Fq 584 2364 a(\026) p Fp 613 2344 a(!) p Fl 613 2377 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 768 2364 a(\() p Fo(A) p Fm 827 2344 a(0) p Fl 827 2377 a(2) p Fr 847 2364 a(\)) p Fo 879 2364 a(\024) p Fq 932 2364 a(\026) p Fp 961 2344 a(!) p Fl 961 2377 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1123 2364 a(\() p Fo(A) p Fm 1182 2344 a(00) p Fl 1182 2377 a(2) p Fr 1203 2364 a(\)) p Fq(;) p Fr 1778 2364 a(\(3.20\)) 0 2471 y(where) p Fo 498 2531 a(A) p Fm 538 2510 a(0) p Fl 538 2543 a(2) p Fr 571 2531 a(=) p Fo 623 2531 a(f) p Fq(\033) p Fo 691 2531 a(2) p Fr 738 2531 a(\012) p Fl 773 2539 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 928 2531 a(;) p 950 2531 a(h) p Fl 977 2510 a(+) p Fr 1007 2531 a(\(\000) p Fp 1056 2510 a(!) p Fl 1056 2543 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1211 2531 a(\() p Fq(\033) p Fr 1260 2531 a(\)\)) p Fo 1312 2531 a(\025) p Fq 1364 2531 a(l) p Fo 1380 2531 a(g) p Fr 0 2617 a(and) p Fo 483 2677 a(A) p Fm 523 2656 a(00) p Fl 523 2689 a(2) p Fr 558 2677 a(=) p Fo 610 2677 a(f) p Fq(\033) p Fo 678 2677 a(2) p Fr 725 2677 a(\012) p Fl 760 2685 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 922 2677 a(;) p 944 2677 a(h) p Fl 971 2656 a(+) p Fr 1001 2677 a(\(\000) p Fp 1050 2656 a(!) p Fl 1050 2689 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1212 2677 a(\() p Fq(\033) p Fr 1261 2677 a(\)\)) p Fo 1312 2677 a(\025) p Fq 1365 2677 a(l) p Fo 1381 2677 a(g) p Fq(:) p Fr 0 2762 a(Let) p Fk 374 2810 a(d) p Fo 367 2823 a(S) t(W) p Fm 454 2786 a(\000) p Fr 497 2823 a(=) p Fo 549 2823 a(f) p Fn(W) p Fo 637 2823 a(2) p 684 2823 a(S) t(W) p Fr 772 2823 a(\() p Fo(\0001) p Fq(;) p Fr 902 2823 a(2) p Fq(l) p Fr 942 2823 a(\);) p 983 2823 a(h) p Fm 1010 2802 a(\000) p Fr 1039 2823 a(\() p Fn(W) p Fr 1104 2823 a(\)) p Fo 1140 2823 a(\024) p 1193 2823 a(\000) p Fq(l) q(;) p Fr 1285 2823 a(h) p Fl 1312 2802 a(+) p Fr 1342 2823 a(\() p Fn(W) p Fr 1408 2823 a(\)) p Fq 1443 2823 a(<) p 1495 2823 a(l) p Fo 1511 2823 a(g) p Fr 927 2947 a(15) p 90 rotate dyy eop %%Page: 16 16 16 15 bop Fr 0 274 a(and) p 95 274 a(let) p Fk 514 322 a(d) p Fo 506 334 a(S) t(W) p Fl 593 297 a(+) p Fr 637 334 a(=) p Fo 688 334 a(f) p Fn(W) p Fo 777 334 a(2) p 824 334 a(S) t(W) p Fr 911 334 a(\() p Fo(\0001) p Fq(;) p Fo 1041 334 a(1) p Fr(\);) p 1132 334 a(h) p Fl 1159 314 a(+) p Fr 1188 334 a(\() p Fn(W) p Fr 1254 334 a(\)) p Fo 1289 334 a(\025) p Fq 1342 334 a(l) p Fo 1358 334 a(g) p Fq(:) p Fr 0 419 a(Then,) p 141 419 a(w) o(e) p 213 419 a(ha) o(v) o(e) p 325 419 a(from) p 440 419 a(\(3.8\),) p 570 419 a(\(3.11\),) p 725 419 a(\(3.18\),) p 879 419 a(\(3.19\)) p 1020 419 a(and) p 1115 419 a(\(3.20\)) p 1256 419 a(that) p Fq 316 523 a(\026) p Fp 345 503 a(!) p Fl 345 536 a(\003) p Fr 372 523 a(\(\() p Fo(A) p Fp 450 503 a(!) p Fl 450 536 a(\003) p Fr 476 523 a(\)) p Fp 495 503 a(c) p Fr 512 523 a(\)) p Fo 573 523 a(\024) p Fq 653 523 a(\026) p Fp 682 503 a(!) p Fl 682 536 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 837 523 a(\() p Fo(A) p Fm 896 503 a(0) p Fl 896 536 a(1) p Fo 916 523 a(nA) p Fm 981 503 a(0) p Fl 981 536 a(2) p Fr 1000 523 a(\)) p 1030 523 a(+) p Fq 1079 523 a(\026) p Fp 1108 503 a(!) p Fl 1108 536 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1270 523 a(\() p Fo(A) p Fm 1329 503 a(00) p Fl 1329 536 a(2) p Fr 1350 523 a(\)) 573 613 y(=) p Fk 689 565 a(X) p Ff 653 687 a(W) p Fm 689 687 a(2) p Fa 718 679 a(d) p Fm 713 687 a(S) r(W) p Fc 771 664 a(\000) p Fq 806 613 a(P) p Fl 837 621 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 992 613 a(\() p Fn(W) p Fr 1058 613 a(\)) p 1091 613 a(+) p Fk 1176 565 a(X) p Ff 1140 687 a(W) p Fm 1176 687 a(2) p Fa 1205 679 a(d) p Fm 1200 687 a(S) r(W) p Fj 1258 664 a(+) p Fq 1292 613 a(P) p Fl 1323 621 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1485 613 a(\() p Fn(W) p Fr 1551 613 a(\)) p Fq(:) p Fr 1778 613 a(\(3.21\)) 73 784 y(W) l(e) p 163 784 a(will) p 261 784 a(estimate) p 462 784 a(the) p 552 784 a(\014rst) p 659 784 a(term) p 781 784 a(in) p 844 784 a(RHS) p 966 784 a(of) p 1027 784 a(\(3.21\)) p 1174 784 a(from) p 1295 784 a(ab) q(o) o(v) o(e.) p 1470 784 a(Note) p 1594 784 a(that) p 1705 784 a(\010) p Fl 1740 766 a(T) p Fr 1790 784 a(is) p 1845 784 a(in-) 0 844 y(v) m(arian) o(t) p 171 844 a(under) p 315 844 a(the) p 405 844 a(v) o(ertical) p 585 844 a(shift.) p 732 844 a(Therefore,) p 974 844 a(w) o(e) p 1051 844 a(can) p 1147 844 a(sho) o(w) p 1274 844 a(from) p 1395 844 a(\(3.15\)) p 1542 844 a(that) p 1653 844 a(there) p 1784 844 a(exists) p Fq 0 904 a(c) p Fl 21 911 a(3) p Fr 55 904 a(=) p Fq 106 904 a(c) p Fl 127 911 a(3) p Fr 147 904 a(\() p Fq(\014) s(;) p 219 904 a(c) p Fl 240 911 a(1) p Fq 259 904 a(;) p 281 904 a(c) p Fl 302 911 a(2) p Fr 321 904 a(\)) p Fq 354 904 a(>) p Fr 406 904 a(0) p 447 904 a(suc) o(h) p 557 904 a(that) p 662 904 a(for) p 737 904 a(an) o(y) p Fn 829 904 a(W) p Fo 893 904 a(2) p 940 904 a(S) t(W) p Fr 1027 904 a(\() p Fo(\0001) p Fq(;) p Fo 1157 904 a(1) p Fr(\),) p Fk 230 965 a(\014) 230 995 y(\014) 230 1025 y(\014) 318 975 y(X) p Fp 247 1083 a(C) r(\023) p Fl(\000\() p Ff(W) p Fm 359 1083 a(nf) p Fp 394 1083 a(W) p Fm 432 1083 a(g) p Fl(\)) p Fr 469 1022 a(\010) p Fl 504 1001 a(T) p Fr 532 1022 a(\() p Fq(C) p Fr 590 1022 a(\)) p Fo 619 1022 a(\000) p Fk 695 975 a(X) p Fp 669 1083 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 781 1083 a(\)) p Fr 800 1022 a(\010) p Fl 835 1001 a(T) p Fr 863 1022 a(\() p Fq(C) p Fr 921 1022 a(\)) p Fk 940 965 a(\014) 940 995 y(\014) 940 1025 y(\014) p Fo 970 1022 a(\024) p Fq 1022 1022 a(c) p Fl 1043 1029 a(3) p Fn 1063 1022 a(M) p Fl 1107 1001 a(2) p Fr 1130 1022 a(\() p Fq(W) p Fr 1202 1022 a(\)) p 1269 1022 a(for) p 1344 1022 a(all) p Fq 1412 1022 a(W) p Fo 1478 1022 a(2) p Fn 1525 1022 a(W) p Fq 1572 1022 a(:) p Fr 1778 1150 a(\(3.22\)) 0 1254 y(Note) p 118 1254 a(that) p Fq 224 1254 a(c) p Fl 245 1261 a(3) p Fr 281 1254 a(is) p 330 1254 a(indep) q(enden) o(t) p 606 1254 a(of) p Fq 661 1254 a(L) p Fo 709 1254 a(2) p Fn 756 1254 a(N) p Fr(.) p 827 1254 a(W) l(e) p 911 1254 a(can) p 1000 1254 a(also) p 1098 1254 a(see) p 1177 1254 a(from) p 1292 1254 a(\(3.15\)) p 1433 1254 a(that) 246 1372 y(2) p Fk 328 1325 a(X) p Fp 278 1434 a(x) p Fm(2) p Fl(\003;) p Fp(x) p Fj 376 1424 a(3) p Fl 393 1434 a(=2) p Fp(l) p Fk 465 1315 a(\014) 465 1345 y(\014) 465 1375 y(\014) 583 1325 y(X) p Fp 482 1433 a(C) p Fm 509 1433 a(2) p Fb(C) p Fl(\() p Fp(n) p Fl(\);) p Fp(C) r(\023@) r(Q) p Fl(\() p Fp(x) p Fl(\)) p Fr 765 1372 a(\010) p Fl 800 1352 a(T) p Fr 828 1372 a(\() p Fq(C) p Fr 886 1372 a(\)) p Fk 905 1315 a(\014) 905 1345 y(\014) 905 1375 y(\014) p Fo 935 1372 a(\024) p Fr 987 1372 a(8) p Fq(L) p Fl 1044 1352 a(2) p Fq 1064 1372 a(c) p Fl 1085 1379 a(1) p Fr 1113 1372 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1301 1372 a(\000) p Fr 1357 1359 a(^) p Fq 1350 1372 a(\014) p Fr 1381 1372 a(\)) p Fq(c) p Fl 1421 1379 a(2) p Fq 1440 1372 a(K) p Fl 1481 1379 a(1) p Fr 1502 1372 a(\(log) p Fq 1592 1372 a(L) p Fr(\)) p Fl 1644 1352 a(2) p Fq 1664 1372 a(=) p Fr(2]) p Fq(:) p Fr 1778 1500 a(\(3.23\)) 0 1605 y(Let) p Fo 87 1605 a(f) p Fq(c) p Fp 133 1612 a(i) p Fo 147 1605 a(g) p Fp 172 1612 a(i) p Fm(\025) p Fl(4) p Fr 247 1605 a(b) q(e) p 313 1605 a(some) p 434 1605 a(p) q(ositiv) o(e) p 614 1605 a(constan) o(ts) p 830 1605 a(whic) o(h) p 969 1605 a(ma) o(y) p 1074 1605 a(dep) q(end) p 1243 1605 a(on) 1317 1591 y(^) p Fq 1310 1605 a(\014) p 1354 1605 a(>) p Fr 1406 1605 a(0) p 1446 1605 a(and) p Fq 1540 1605 a(\014) p 1584 1605 a(>) p Fr 1636 1605 a(0.) p 1695 1605 a(Note) p 1813 1605 a(that) 0 1665 y(b) o(y) p 68 1665 a(the) p 152 1665 a(de\014nition) p 369 1665 a(of) p 424 1665 a(standard) p 628 1665 a(w) o(alls) p Fn 668 1789 a(M) p Fl 712 1768 a(2) p Fr 735 1789 a(\() p Fq(\031) p Fr 784 1789 a(\() p Fq(W) p Fr 856 1789 a(\)\)) p Fo 907 1789 a(\024) p Fr 964 1755 a(1) p 964 1777 25 2 v 964 1823 a(3) p Fn 994 1789 a(M) p Fl 1038 1768 a(2) p Fr 1060 1789 a(\() p Fq(W) p Fr 1132 1789 a(\)) p 1778 1789 a(\(3.24\)) 0 1908 y(for) p 80 1908 a(an) o(y) p Fo 177 1908 a(f) p Fq(W) p Fo 255 1908 a(g) p 302 1908 a(2) p 358 1908 a(S) t(W) p Fr 446 1908 a(\() p Fo(\0001) p Fq(;) p Fo 576 1908 a(1) p Fr(\).) p 695 1908 a(F) l(or) p 787 1908 a(an) o(y) p 884 1908 a(pair) p Fo 990 1908 a(f) p Fn(W) p Fq 1062 1908 a(;) p Fn 1084 1908 a(W) p Fm 1133 1890 a(0) p Fo 1148 1908 a(g) p 1196 1908 a(\032) p 1257 1908 a(S) t(W) p Fr 1344 1908 a(\() p Fo(\0001) p Fq(;) p Fr 1474 1908 a(2) p Fq(l) p Fr 1514 1908 a(\)) p 1554 1908 a(suc) o(h) p 1669 1908 a(that) p Fn 1780 1908 a(W) p Fm 1827 1890 a(0) p Fr 1864 1908 a(=) p Fn 0 1969 a(W) p Fo 47 1969 a(nf) p Fq(W) p Fo 150 1969 a(g) p Fr 196 1969 a(for) p 274 1969 a(some) p Fq 399 1969 a(W) p Fo 470 1969 a(2) p Fn 522 1969 a(W) p Fr 569 1969 a(,) p 605 1969 a(h) p Fl 632 1950 a(+) p Fr 662 1969 a(\() p Fn(W) p Fr 728 1969 a(\)) p Fq 768 1969 a(<) p 825 1969 a(l) p Fr 860 1969 a(and) p 957 1969 a(h) p Fl 984 1950 a(+) p Fr 1014 1969 a(\() p Fn(W) p Fm 1080 1950 a(0) p Fr 1094 1969 a(\)) p Fo 1132 1969 a(\024) p Fr 1189 1969 a(3) p Fq(l) q(=) p Fr(2,) p 1312 1969 a(w) o(e) p 1386 1969 a(ha) o(v) o(e) p 1502 1969 a(from) p 1620 1969 a(\(3.22\),) p 1778 1969 a(\(3.23\)) 0 2029 y(and) p 95 2029 a(\(3.24\)) p 236 2029 a(that) p 341 2029 a(for) p 416 2029 a(su\016cien) o(tly) p 660 2029 a(large) p Fq 779 2029 a(L) p Fo 826 2029 a(2) p Fn 873 2029 a(N) p Fr(,) p Fq 305 2147 a(P) p Fl 336 2155 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 491 2147 a(\() p Fn(W) p Fr 557 2147 a(\)) p Fk 576 2092 a(.) p Fq 619 2147 a(P) p Fl 650 2155 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 806 2147 a(\() p Fn(W) p Fm 872 2126 a(0) p Fr 886 2147 a(\)) 225 2253 y(=) p Fk 305 2198 a(\020) p Fr 334 2253 a(\010\() p Fn(W) p Fr 435 2253 a(\)) p Fk 454 2198 a(.) p Fr 498 2253 a(\010\() p Fn(W) p Fm 599 2233 a(0) p Fr 613 2253 a(\)) p Fk 632 2198 a(\021) p Fo 673 2253 a(\002) p Fk 402 2304 a(\020) p Fr 432 2359 a(exp) o([) p Fo(\000) p Fk 592 2312 a(X) p Fp 567 2420 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 679 2420 a(\)) p Fg 698 2359 a(1) p Fm 726 2366 a(1) p Fp(;) p Fl(2) p Fp(l) p Fr 802 2359 a(\() p Fq(C) p Fr 860 2359 a(\)\010) p Fl 914 2339 a(T) p Fr 941 2359 a(\() p Fq(C) p Fr 999 2359 a(\)]) p Fk 1032 2304 a(.) p Fr 1080 2359 a(exp) o([) p Fo(\000) p Fk 1246 2312 a(X) p Fp 1215 2420 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 1327 2410 a(0) p Fl 1335 2420 a(\)) p Fg 1357 2359 a(1) p Fm 1385 2366 a(1) p Fp(;) p Fl(2) p Fp(l) p Fr 1461 2359 a(\() p Fq(C) p Fr 1519 2359 a(\)\010) p Fl 1573 2339 a(T) p Fr 1600 2359 a(\() p Fq(C) p Fr 1658 2359 a(\)]) p Fk 1691 2304 a(\021) p Fo 224 2502 a(\024) p Fr 305 2502 a(\010\() p Fo(f) p Fq(W) p Fo 437 2502 a(g) p Fr(\)) p 489 2502 a(exp) o([) p Fq(c) p Fl 598 2509 a(3) p Fn 617 2502 a(M) p Fl 661 2482 a(2) p Fr 684 2502 a(\() p Fq(W) p Fr 756 2502 a(\)) p 786 2502 a(+) p Fq 835 2502 a(c) p Fl 856 2509 a(4) p Fq 876 2502 a(e) p Fm 899 2482 a(\000) p Fp(c) p Fj 941 2487 a(5) p Fl 958 2482 a(\() p Fp(\014) p Fm 994 2482 a(\000) p Fl 1026 2473 a(^) p Fp 1021 2482 a(\014) p Fl 1043 2482 a(\)) p Fp(K) p Fj 1087 2487 a(1) p Fl 1103 2482 a(\(log) p Fp 1168 2482 a(L) p Fl(\)) p Fj 1206 2470 a(2) p Fr 1226 2502 a(]) p Fo 224 2575 a(\024) p Fq 305 2575 a(c) p Fl 326 2582 a(6) p Fr 354 2575 a(exp) o([) p Fo(\000) p Fr(2) p Fq(\014) p Fk 536 2535 a(\000) p Fn 558 2575 a(M) p Fl 602 2554 a(2) p Fr 625 2575 a(\() p Fq(W) p Fr 697 2575 a(\)) p Fo 726 2575 a(\000) p Fn 776 2575 a(M) p Fl 820 2554 a(2) p Fr 843 2575 a(\() p Fq(\031) p Fr 892 2575 a(\() p Fq(W) p Fr 964 2575 a(\)\)) p Fk 1002 2535 a(\001) p Fr 1035 2575 a(+) p Fq 1084 2575 a(c) p Fl 1105 2582 a(3) p Fn 1125 2575 a(M) p Fl 1169 2554 a(2) p Fr 1192 2575 a(\() p Fq(W) p Fr 1264 2575 a(\)]) p Fo 224 2648 a(\024) p Fq 305 2648 a(c) p Fl 326 2655 a(6) p Fr 354 2648 a(exp) o([) p Fo(\000) p Fr(\() p Fq(\014) p Fo 541 2648 a(\000) p Fq 591 2648 a(c) p Fl 612 2655 a(3) p Fr 631 2648 a(\)) p Fn(M) p Fl 694 2627 a(2) p Fr 717 2648 a(\() p Fq(W) p Fr 789 2648 a(\)]) p Fq(:) p Fr 1778 2648 a(\(3.25\)) 0 2752 y(Let) p Fq 90 2752 a(K) p Fl 131 2759 a(3) p Fq 168 2752 a(>) p Fr 224 2752 a(0) p 266 2752 a(b) q(e) p 335 2752 a(a) p 378 2752 a(large) p 499 2752 a(constan) o(t) p 698 2752 a(to) p 760 2752 a(b) q(e) p 828 2752 a(sp) q(eci\014ed) p 1027 2752 a(later.) p 1166 2752 a(Supp) q(ose) p 1360 2752 a(that) p Fq 1467 2752 a(L) p Fo 1518 2752 a(2) p Fn 1569 2752 a(N) p Fr 1623 2752 a(is) p 1674 2752 a(su\016cien) o(tly) 0 2823 y(large) p 116 2823 a(and) p Fq 208 2823 a(K) p Fl 249 2830 a(1) p Fq 283 2823 a(>) p Fr 335 2823 a(2\() p Fq(K) p Fl 419 2830 a(3) p Fr 439 2823 a(\)) p Fl 458 2805 a(2) p Fr 478 2823 a(.) p 512 2823 a(Then,) p 651 2823 a(for) p 722 2823 a(an) o(y) p Fn 812 2823 a(W) p Fo 875 2823 a(2) p Fk 930 2810 a(d) p Fo 922 2823 a(S) t(W) p Fm 1009 2786 a(\000) p Fr 1052 2823 a(there) p 1174 2823 a(exists) p Fq 1306 2823 a(W) p Fo 1372 2823 a(2) p Fn 1419 2823 a(W) p Fr 1482 2823 a(suc) o(h) p 1589 2823 a(that) p Fn 1692 2823 a(M) p Fl 1736 2805 a(2) p Fr 1759 2823 a(\() p Fq(W) p Fr 1831 2823 a(\)) p Fo 1863 2823 a(\025) p Fr 927 2947 a(16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fq 0 274 a(K) p Fl 41 281 a(3) p Fr 70 274 a(log) p Fq 141 274 a(L) p Fr(,) p Fn 202 274 a(W) p Fo 249 274 a(nf) p Fq(W) p Fo 352 274 a(g) p 393 274 a(2) p 441 274 a(S) t(W) p Fr 528 274 a(\() p Fo(\0001) p Fq(;) p Fr 658 274 a(2) p Fq(l) p Fr 698 274 a(\)) p 730 274 a(and) p 823 274 a(h) p Fl 850 256 a(+) p Fr 880 274 a(\() p Fn(W) p Fo 946 274 a(nf) p Fq(W) p Fo 1049 274 a(g) p Fr(\)) p Fo 1109 274 a(\024) p Fr 1162 274 a(3) p Fq(l) q(=) p Fr(2.) p 1285 274 a(T) l(o) p 1355 274 a(see) p 1432 274 a(this,) p 1539 274 a(w) o(e) p 1609 274 a(will) p 1699 274 a(\014rst) p 1798 274 a(sho) o(w) 0 334 y(that) p 106 334 a(the) p 190 334 a(set) p Fn 500 438 a(W) p Fp 547 445 a(big) p Fr 611 438 a(=) p Fo 663 438 a(f) p Fq(W) p Fm 741 418 a(0) p Fo 766 438 a(2) p Fn 813 438 a(W) p Fr 860 438 a(;) p Fn 882 438 a(M) p Fl 929 418 a(2) p Fr 951 438 a(\() p Fq(W) p Fm 1023 418 a(0) p Fr 1035 438 a(\)) p Fo 1068 438 a(\025) p Fq 1120 438 a(K) p Fl 1161 445 a(3) p Fr 1190 438 a(log) p Fq 1261 438 a(L) p Fo(g) p Fr 1778 438 a(\(3.26\)) 0 542 y(is) p 49 542 a(not) p 136 542 a(empt) o(y) l(.) p 300 542 a(Assuming) p 524 542 a(that) p Fn 629 542 a(W) p Fp 676 549 a(big) p Fr 743 542 a(is) p 792 542 a(empt) o(y) l(,) p 950 542 a(w) o(e) p 1022 542 a(can) p 1111 542 a(see) p 1190 542 a(b) o(y) p 1258 542 a(Lemma) p 1432 542 a(1.4) p 1511 542 a(that) 453 646 y(the) p 537 646 a(n) o(um) o(b) q(er) p 714 646 a(of) p 770 646 a(elemen) o(ts) p 969 646 a(of) p Fn 1025 646 a(W) p Fr 1072 646 a(\() p Fq(W) p Fr 1144 646 a(\)) p Fq 1179 646 a(<) p Fo 1231 646 a(b) p Fq(K) p Fl 1294 653 a(3) p Fr 1323 646 a(log) p Fq 1394 646 a(L) p Fo(c) p Fr 0 750 a(for) p 80 750 a(all) p Fq 152 750 a(W) p Fo 227 750 a(2) p Fn 283 750 a(W) p Fr 330 750 a(,) p 369 750 a(where) p Fo 515 750 a(b) p Fq(r) p Fo 560 750 a(c) p Fr 604 750 a(denotes) p 785 750 a(the) p 874 750 a(in) o(teger) p 1040 750 a(part) p 1151 750 a(of) p Fq 1212 750 a(r) p Fr 1256 750 a(for) p 1336 750 a(eac) o(h) p Fq 1451 750 a(r) p Fo 1496 750 a(2) p Fn 1552 750 a(R) p Fr(.) p 1638 750 a(By) p 1720 750 a(this,) p 1834 750 a(the) 0 810 y(h) o(yp) q(othesis) p 240 810 a(that) p Fn 346 810 a(M) p Fl 390 792 a(2) p Fr 413 810 a(\() p Fq(W) p Fr 485 810 a(\)) p Fq 517 810 a(<) p 569 810 a(K) p Fl 610 817 a(3) p Fr 639 810 a(log) p Fq 710 810 a(L) p Fr 759 810 a(for) p 834 810 a(all) p Fq 902 810 a(W) p Fo 968 810 a(2) p Fn 1015 810 a(W) p Fr 1062 810 a(,) p 1095 810 a(Lemmas) p 1288 810 a(1.5) p 1367 810 a(and) p 1462 810 a(1.7,) p 1554 810 a(w) o(e) p 1626 810 a(ha) o(v) o(e) p 1738 810 a(that) 603 914 y(h) p Fm 630 894 a(\000) p Fr 659 914 a(\() p Fn(W) p Fr 725 914 a(\)) p Fq 761 914 a(>) p Fo 813 914 a(\000) p Fr(\() p Fq(K) p Fl 912 921 a(3) p Fr 940 914 a(log) p Fq 1011 914 a(L) p Fr(\)) p Fl 1063 894 a(2) p Fq 1097 914 a(>) p Fo 1149 914 a(\000) p Fq(l) q(;) p Fr 1778 914 a(\(3.27\)) 0 1031 y(whic) o(h) p 136 1031 a(con) o(tradicts) p 382 1031 a(that) p Fn 484 1031 a(W) p Fo 548 1031 a(2) p Fk 602 1019 a(d) p Fo 595 1031 a(S) t(W) p Fm 682 995 a(\000) p Fr 712 1031 a(.) p 745 1031 a(Since) p Fn 869 1031 a(W) p Fp 916 1038 a(big) p Fr 978 1031 a(is) p 1023 1031 a(not) p 1106 1031 a(empt) o(y) l(,) p 1261 1031 a(w) o(e) p 1329 1031 a(can) p 1414 1031 a(tak) o(e) p 1516 1031 a(a) p 1553 1031 a(minim) o(al) p 1738 1031 a(elemen) o(t) p Fq 0 1092 a(W) p Fr 70 1092 a(from) p Fn 186 1092 a(W) p Fp 233 1099 a(big) p Fr 283 1092 a(.) p 322 1092 a(W) l(e) p 407 1092 a(will) p 500 1092 a(next) p 610 1092 a(sho) o(w) p 732 1092 a(that) p 839 1092 a(h) p Fl 866 1073 a(+) p Fr 896 1092 a(\() p Fn(W) p Fo 961 1092 a(nf) p Fq(W) p Fo 1064 1092 a(g) p Fr(\)) p Fo 1127 1092 a(\024) p Fr 1181 1092 a(3) p Fq(l) q(=) p Fr(2.) p 1308 1092 a(W) l(e) p 1393 1092 a(can) p 1483 1092 a(see) p 1563 1092 a(b) o(y) p 1632 1092 a(Lemmas) p 1826 1092 a(1.5,) 0 1152 y(1.6) p 79 1152 a(and) p 173 1152 a(1.7) p 252 1152 a(that) 119 1256 y(h) p Fl 146 1235 a(+) p Fr 175 1256 a(\() p Fn(W) p Fo 241 1256 a(nf) p Fq(W) p Fo 344 1256 a(g) p Fr(\)) p 433 1256 a(=) p 513 1256 a(max) p Fo 603 1256 a(f) p Fr(h) p Fl 655 1235 a(+) p Fr 685 1256 a(\() p Fn(W) p Fr 751 1256 a(\)) p Fq(;) p Fr 811 1256 a(h) p Fl 838 1235 a(+) p Fr 867 1256 a(\() p Fn(W) p Fr 933 1256 a(\() p Fq(W) p Fr 1005 1256 a(\)) p Fo 1038 1256 a([) p 1082 1256 a(f) p Fq(W) p Fm 1160 1235 a(0) p Fo 1185 1256 a(2) p Fn 1232 1256 a(W) p Fo 1279 1256 a(nf) p Fq(W) p Fo 1382 1256 a(g) p Fr(;) p Fq 1429 1256 a(W) p Fm 1482 1235 a(0) p Fo 1510 1256 a(\036) p Fq 1563 1256 a(W) p Fo 1616 1256 a(g) p Fr(\)) p Fo(g) 432 1328 y(\024) p Fr 513 1328 a(max) p Fo 603 1328 a(f) p Fr(h) p Fl 655 1308 a(+) p Fr 685 1328 a(\() p Fn(W) p Fr 751 1328 a(\)) p Fq(;) p Fr 811 1328 a(h) p Fl 838 1308 a(+) p Fr 867 1328 a(\() p Fn(W) p Fr 933 1328 a(\() p Fq(W) p Fr 1005 1328 a(\)\)) p 1057 1328 a(+) p 1106 1328 a(h) p Fl 1133 1308 a(+) p Fr 1162 1328 a(\() p Fo(f) p Fq(W) p Fm 1259 1308 a(0) p Fo 1285 1328 a(2) p Fn 1332 1328 a(W) p Fo 1379 1328 a(nf) p Fq(W) p Fo 1482 1328 a(g) p Fr(;) p Fq 1529 1328 a(W) p Fm 1582 1308 a(0) p Fo 1609 1328 a(\036) p Fq 1662 1328 a(W) p Fo 1715 1328 a(g) p Fr(\)) p Fo(g) 432 1401 y(\024) p Fr 513 1401 a(h) p Fl 540 1380 a(+) p Fr 569 1401 a(\() p Fn(W) p Fr 635 1401 a(\)) p 668 1401 a(+) p 717 1401 a(h) p Fl 744 1380 a(+) p Fr 774 1401 a(\() p Fo(f) p Fq(W) p Fm 871 1380 a(0) p Fo 896 1401 a(2) p Fn 943 1401 a(W) p Fo 990 1401 a(nf) p Fq(W) p Fo 1093 1401 a(g) p Fr(;) p Fq 1140 1401 a(W) p Fm 1193 1380 a(0) p Fo 1220 1401 a(\036) p Fq 1273 1401 a(W) p Fo 1326 1401 a(g) p Fr(\)) p Fq(:) p Fr 1778 1401 a(\(3.28\)) 0 1505 y(W) l(e) p 84 1505 a(can) p 173 1505 a(also) p 271 1505 a(see) p 350 1505 a(b) o(y) p 418 1505 a(Lemmas) p 611 1505 a(1.4,) p 703 1505 a(1.7) p 782 1505 a(and) p 877 1505 a(the) p 961 1505 a(de\014nition) p 1177 1505 a(of) p Fq 1233 1505 a(W) p Fr 1302 1505 a(that) 363 1609 y(h) p Fl 390 1588 a(+) p Fr 419 1609 a(\() p Fo(f) p Fq(W) p Fm 516 1588 a(0) p Fo 542 1609 a(2) p Fn 589 1609 a(W) p Fo 636 1609 a(nf) p Fq(W) p Fo 739 1609 a(g) p Fr(;) p Fq 786 1609 a(W) p Fm 839 1588 a(0) p Fo 866 1609 a(\036) p Fq 919 1609 a(W) p Fo 972 1609 a(g) p Fr(\)) p Fq 1029 1609 a(<) p Fr 1081 1609 a(\() p Fq(K) p Fl 1141 1616 a(3) p Fr 1170 1609 a(log) p Fq 1241 1609 a(L) p Fr(\)) p Fl 1293 1588 a(2) p Fq 1327 1609 a(<) p 1378 1609 a(l) q(=) p Fr(2) p Fq(;) p Fr 1778 1609 a(\(3.29\)) 0 1726 y(whic) o(h) p 142 1726 a(together) p 336 1726 a(with) p Fn 449 1726 a(W) p Fo 516 1726 a(2) p Fk 575 1714 a(d) p Fo 567 1726 a(S) t(W) p Fm 654 1689 a(\000) p Fr 702 1726 a(and) p 799 1726 a(\(3.28\)) p 942 1726 a(implies) p 1110 1726 a(that) p 1217 1726 a(h) p Fl 1244 1708 a(+) p Fr 1274 1726 a(\() p Fn(W) p Fo 1340 1726 a(nf) p Fq(W) p Fo 1443 1726 a(g) p Fr(\)) p Fo 1507 1726 a(\024) p Fr 1563 1726 a(3) p Fq(l) q(=) p Fr(2.) p 1693 1726 a(Note) p 1813 1726 a(that) p Fq 0 1786 a(W) p Fr 69 1786 a(is) p 118 1786 a(the) p 202 1786 a(union) p 338 1786 a(of) p 393 1786 a(all) p 461 1786 a(faces) p 579 1786 a(b) q(elonging) p 800 1786 a(to) p Fq 860 1786 a(W) p Fr 913 1786 a(.) p 948 1786 a(Therefore,) p 1182 1786 a(w) o(e) p 1254 1786 a(ha) o(v) o(e) p 1366 1786 a(from) p 1481 1786 a(\(3.25\)) p 1622 1786 a(that) p Fk 409 1852 a(X) p Ff 373 1974 a(W) p Fm 409 1974 a(2) p Fa 438 1965 a(d) p Fm 433 1974 a(S) r(W) p Fc 491 1951 a(\000) p Fq 526 1899 a(P) p Fl 557 1907 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 712 1899 a(\() p Fn(W) p Fr 778 1899 a(\)) p Fo 293 2055 a(\024) p Fk 373 1999 a(\020) 496 2007 y(X) p Ff 403 2115 a(W) p Fc 439 2106 a(0) p Fm 447 2115 a(2S) r(W) p Fl 532 2115 a(\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fq 669 2055 a(P) p Fl 700 2062 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 856 2055 a(\() p Fn(W) p Fm 921 2034 a(0) p Fr 936 2055 a(\)) p Fk 955 1999 a(\021) p Fo 996 2055 a(\002) p Fk 1046 1999 a(\020) p Fr 1075 2055 a(4) p Fq(L) p Fl 1132 2034 a(2) p Fk 1214 2007 a(X) p Fp 1161 2113 a(n) p Fm(\025) p Fp(K) p Fj 1239 2118 a(3) p Fl 1263 2113 a(log) p Fp 1314 2113 a(L) p Fq 1346 2055 a(\024) p Fp 1374 2034 a(n) p Fq 1398 2055 a(c) p Fl 1419 2062 a(6) p Fq 1439 2055 a(e) p Fm 1462 2034 a(\000) p Fl(\() p Fp(\014) p Fm 1525 2034 a(\000) p Fp(c) p Fj 1567 2039 a(3) p Fl 1584 2034 a(\)) p Fp(n) p Fk 1621 1999 a(\021) p Fo 293 2182 a(\024) p Fq 373 2182 a(c) p Fl 394 2189 a(7) p Fr 422 2182 a(exp) o([) p Fo(\000) p Fr(\() p Fq(\014) p Fo 609 2182 a(\000) p Fq 659 2182 a(c) p Fl 680 2189 a(8) p Fr 700 2182 a(\)) p Fq(K) p Fl 760 2189 a(3) p Fr 788 2182 a(log) p Fq 859 2182 a(L) p Fr(]) p Fq(;) p Fr 1778 2182 a(\(3.30\)) 0 2286 y(where) p Fq 141 2286 a(\024) p 183 2286 a(>) p Fr 235 2286 a(0) p 275 2286 a(is) p 324 2286 a(the) p 408 2286 a(connectivit) o(y) p 683 2286 a(constan) o(t.) 73 2347 y(Similarly) l(,) p 290 2347 a(w) o(e) p 362 2347 a(can) p 451 2347 a(estimate) p 647 2347 a(the) p 731 2347 a(second) p 888 2347 a(term) p 1004 2347 a(in) p 1061 2347 a(RHS) p 1177 2347 a(of) p 1233 2347 a(\(3.21\)) p 1374 2347 a(from) p 1489 2347 a(ab) q(o) o(v) o(e) p 1627 2347 a(b) o(y) p Fq 627 2451 a(c) p Fl 648 2458 a(9) p Fr 676 2451 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 864 2451 a(\000) p Fq 913 2451 a(c) p Fl 934 2458 a(10) p Fr 972 2451 a(\)) p Fq(K) p Fl 1032 2458 a(3) p Fr 1060 2451 a(log) p Fq 1132 2451 a(L) p Fr(]) p Fq(:) p Fr 1778 2451 a(\(3.31\)) 0 2554 y(F) l(rom) p 128 2554 a(\(3.21\),) p 282 2554 a(\(3.30\)) p 423 2554 a(and) p 518 2554 a(\(3.31\),) p 673 2554 a(w) o(e) p 744 2554 a(ha) o(v) o(e) p 857 2554 a(that) p Fq 465 2658 a(\026) p Fp 494 2638 a(!) p Fl 494 2671 a(\003) p Fr 521 2658 a(\(\() p Fo(A) p Fp 599 2638 a(!) p Fl 599 2671 a(\003) p Fr 626 2658 a(\)) p Fp 645 2638 a(c) p Fr 662 2658 a(\)) p Fo 695 2658 a(\024) p Fr 747 2658 a(2) p Fq(c) p Fl 792 2665 a(11) p Fr 838 2658 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1026 2658 a(\000) p Fq 1075 2658 a(c) p Fl 1096 2665 a(12) p Fr 1134 2658 a(\)) p Fq(K) p Fl 1194 2665 a(3) p Fr 1222 2658 a(log) p Fq 1293 2658 a(L) p Fr(]) p Fq(:) p Fr 1778 2658 a(\(3.32\)) 73 2762 y(Let) p 161 2762 a(us) p 225 2762 a(\014x) p Fq 295 2762 a(") p 333 2762 a(>) p Fr 386 2762 a(0.) p 448 2762 a(F) l(rom) p 577 2762 a(\(3.32\),) p 732 2762 a(w) o(e) p 805 2762 a(can) p 895 2762 a(obtain) p 1047 2762 a(\(3.3\)) p 1165 2762 a(for) p 1240 2762 a(some) p Fq 1363 2762 a(K) p Fl 1404 2769 a(3) p Fq 1439 2762 a(>) p Fr 1492 2762 a(0) p 1534 2762 a(and) p Fq 1629 2762 a(K) p Fl 1670 2769 a(1) p Fq 1706 2762 a(>) p Fr 1759 2762 a(2\() p Fq(K) p Fl 1843 2769 a(3) p Fr 1864 2762 a(\)) p Fl 1883 2744 a(2) p Fr 0 2823 a(large) p 117 2823 a(enough) p 283 2823 a(and) p 376 2823 a(for) p 448 2823 a(su\016cien) o(tly) p 690 2823 a(large) p Fq 808 2823 a(L) p Fo 855 2823 a(2) p Fn 902 2823 a(N) p Fr(,) p 966 2823 a(and) p 1059 2823 a(w) o(e) p 1128 2823 a(\014nished) p 1305 2823 a(the) p 1387 2823 a(pro) q(of) p 1513 2823 a(of) p 1566 2823 a(Prop) q(osition) p 1826 2823 a(2.1.) 927 2947 y(17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fs 0 274 a(4) p 121 274 a(Pro) r(of) p 344 274 a(of) p 436 274 a(Prop) r(osition) p 872 274 a(2.2) p Fr 73 383 a(Let) p Fq 161 383 a(L) p Fm 194 365 a(0) p Fr 219 383 a(=) p 271 383 a(2) p Fq(L) p Fo 340 383 a(\000) p Fr 389 383 a(2) p Fq(l) p Fr 446 383 a(and) p Fq 541 383 a(L) p Fm 574 365 a(00) p Fr 609 383 a(=) p Fq 661 383 a(L) p Fm 694 365 a(0) p Fo 716 383 a(\000) p Fq 766 383 a(l) p Fr 782 383 a(.) p 817 383 a(W) l(e) p 901 383 a(de\014ne) p Fn 1042 383 a(J) p Fp 1070 390 a(\016) p Fr 1102 383 a(b) o(y) 164 510 y(J) p Fp 189 517 a(x;y) p Fr 253 510 a(=) p Fk 305 440 a(\032) p Fq 364 480 a(\016) p Fr 429 480 a(if) p Fq 474 480 a(x) p Fo 515 480 a(2) p Fr 562 480 a(\003\() p Fo(\000) p Fq(L) p Fm 687 462 a(0) p Fq 699 480 a(;) p Fr 721 480 a(2) p Fq(l) p Fr 761 480 a(\)) p Fq(;) p 818 480 a(y) p Fo 857 480 a(2) p Fq 904 480 a(@) p Fp 930 487 a(ex) p Fr 968 480 a(\003\() p Fo(\000) p Fq(L) p Fm 1093 462 a(0) p Fq 1105 480 a(;) p Fr 1127 480 a(2) p Fq(l) p Fr 1167 480 a(\)) p 1202 480 a(and) p Fo 1308 480 a(\000) p Fq 1357 480 a(L) p Fm 1390 462 a(00) p Fo 1426 480 a(\024) p Fq 1478 480 a(x) p Fl 1506 462 a(3) p Fq 1526 480 a(;) p 1564 480 a(y) p Fl 1590 462 a(3) p Fq 1623 480 a(<) p Fr 1675 480 a(0) p Fq(;) p Fr 363 540 a(1) p 429 540 a(otherwise) p Fq(:) p Fr 0 637 a(In) p 59 637 a(the) p 140 637 a(same) p 260 637 a(w) o(a) o(y) p 357 637 a(as) p 414 637 a(in) p 469 637 a(the) p 551 637 a(pro) q(of) p 676 637 a(of) p 729 637 a(Prop) q(osition) p 989 637 a(2.1,) p 1079 637 a(w) o(e) p 1149 637 a(can) p 1236 637 a(obtain) p 1385 637 a(Prop) q(osition) p 1645 637 a(2.2) p 1722 637 a(from) p 1834 637 a(the) 0 697 y(follo) o(wing) p 205 697 a(lemma.) p 381 697 a(Throughout) p 651 697 a(this) p 746 697 a(section,) p 922 697 a(w) o(e) p 993 697 a(assume) p 1161 697 a(that) p Fq 1266 697 a(\014) p 1310 697 a(>) p Fr 1361 697 a(0) p 1401 697 a(is) p 1450 697 a(su\016cien) o(tly) p 1693 697 a(large.) p 1831 697 a(Let) p Fo 0 757 a(f) p Fq(c) p Fp 46 764 a(i) p Fo 60 757 a(g) p Fp 85 764 a(i) p Fm(\025) p Fl(13) p Fr 178 757 a(b) q(e) p 244 757 a(some) p 367 757 a(p) q(ositiv) o(e) p 547 757 a(constan) o(ts) p 763 757 a(whic) o(h) p 903 757 a(ma) o(y) p 1008 757 a(dep) q(end) p 1178 757 a(on) 1252 744 y(\026) p Fq 1245 757 a(\014) p 1289 757 a(>) p Fr 1341 757 a(0) p 1382 757 a(\(see) p 1480 757 a(\(4.4\)\)) p 1615 757 a(and) p Fq 1710 757 a(\014) p 1754 757 a(>) p Fr 1806 757 a(0.) p Fg 73 856 a(Lemma) p 277 856 a(4.1.) p Fd 387 856 a(Supp) n(ose) p 576 856 a(that) p Fq 680 856 a(\014) p 731 856 a(>) p Fr 790 856 a(0) p Fd 836 856 a(is) p 892 856 a(su\016ciently) p 1142 856 a(lar) n(ge.) p 1292 856 a(L) n(et) p Fq 1380 856 a(l) p Fr 1416 856 a(=) p Fo 1476 856 a(d) p Fq(K) p Fl 1539 863 a(2) p Fq 1559 856 a(L) p Fj 1597 824 a(2) p 1597 830 16 2 v 1597 851 a(3) p Fr 1619 856 a(\(log) p Fq 1710 856 a(L) p Fr(\)) p Fl 1762 838 a(2) p Fo 1781 856 a(e) p Fd 1825 856 a(and) p Fq 0 921 a(\016) p Fr 51 921 a(=) p Fq 116 921 a(L) p Fm 149 902 a(\000) p Fj 181 889 a(2) p 182 895 V 182 915 a(3) p Fr 212 921 a(log) p Fq 284 921 a(L) p Fd(.) p 376 921 a(Then,) p 527 921 a(for) p 612 921 a(any) p Fq 713 921 a(") p 763 921 a(>) p Fr 829 921 a(0) p Fd 878 921 a(ther) n(e) p 1006 921 a(exists) p Fq 1147 921 a(K) p Fl 1188 928 a(2) p Fr 1236 921 a(=) p Fq 1301 921 a(K) p Fl 1342 928 a(2) p Fr 1362 921 a(\() p Fq(\014) s(;) p 1434 921 a(") p Fr(\)) p Fq 1502 921 a(>) p Fr 1568 921 a(0) p Fd 1617 921 a(such) p 1735 921 a(that) p 1842 921 a(for) 0 981 y(su\016ciently) p 246 981 a(lar) n(ge) p Fq 364 981 a(L) p Fo 411 981 a(2) p Fn 458 981 a(N) p Fq 582 1081 a(\026) p Fp 611 1058 a(!) q(;) p Ff(J) p Fe 664 1064 a(\016) p Fl 611 1097 a(\003\() p Fm(\000) p Fp(L) p Fc 700 1088 a(0) p Fp 712 1097 a(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 766 1081 a(\(\() p Fo(A) p Fp 844 1061 a(!) p Fl 844 1094 a(\003\() p Fm(\000) p Fp(L) p Fc 933 1084 a(0) p Fp 945 1094 a(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 999 1081 a(\)) p Fp 1018 1061 a(c) p Fr 1035 1081 a(\)) p Fo 1068 1081 a(\024) p Fq 1121 1081 a("L) p Fm 1177 1061 a(\000) p Fl(3) p Fq 1224 1081 a(:) p Fr 1802 1081 a(\(4.1\)) 73 1216 y(Let) p 161 1216 a(\003) p 208 1216 a(=) p 260 1216 a(\003\() p Fo(\000) p Fq(L) p Fm 385 1198 a(0) p Fq 396 1216 a(;) p Fr 418 1216 a(2) p Fq(l) p Fr 458 1216 a(\).) p 512 1216 a(F) l(or) p 600 1216 a(eac) o(h) p Fq 710 1216 a(\016) p Fo 747 1216 a(2) p Fr 794 1216 a([0) p Fq(;) p Fr 854 1216 a(1]) p 908 1216 a(and) p 1003 1216 a(eac) o(h) p Fn 1113 1216 a(W) p Fo 1176 1216 a(2) p 1223 1216 a(S) t(W) p Fr 1310 1216 a(\() p Fo(\000) p Fq(L) p Fm 1401 1198 a(0) p Fq 1413 1216 a(;) p Fr 1435 1216 a(2) p Fq(l) p Fr 1475 1216 a(\),) p 1524 1216 a(w) o(e) p 1595 1216 a(set) 517 1322 y(\010) p Fp 552 1329 a(\016) p Fr 572 1322 a(\() p Fn(W) p Fr 637 1322 a(\)) p 701 1322 a(=) p 780 1322 a(\010) p Fp 815 1329 a(\016) p Fr 834 1322 a(\(\000\() p Fn(W) p Fr 950 1322 a(\)\)) p Fq(=e) p Fm 1035 1301 a(\000) p Fl(8) p Fp(\014) r(L) p Fj 1126 1289 a(2) p Fr 701 1399 a(=) p 780 1399 a(exp[) p Fo(\000) p Fq(\014) s(H) p Fp 983 1375 a(!) q(;) p Ff(J) p Fe 1034 1381 a(\016) p Fl 979 1412 a(\003) p Fr 1050 1399 a(\() p Fq(\033) p Fl 1097 1407 a(\000\() p Ff(W) p Fl 1169 1407 a(\)) p Fr 1182 1399 a(\)]) p Fq(=e) p Fm 1262 1378 a(\000) p Fl(8) p Fp(\014) r(L) p Fj 1353 1367 a(2) p Fq 1371 1399 a(:) p Fr 1802 1399 a(\(4.2\)) p Fg 73 1499 a(Lemma) p 271 1499 a(4.2.) p Fd 378 1499 a(Supp) n(ose) p 563 1499 a(that) p Fq 661 1499 a(\014) p 705 1499 a(>) p Fr 757 1499 a(0) p Fd 798 1499 a(is) p 850 1499 a(su\016ciently) p 1095 1499 a(lar) n(ge) p 1212 1499 a(and) p Fq 1305 1499 a(\016) p Fo 1343 1499 a(2) p Fr 1390 1499 a([0) p Fq(;) p Fr 1450 1499 a(1]) p Fd(.) p 1525 1499 a(Then,) p 1666 1499 a(ther) n(e) p 1786 1499 a(exists) 0 1560 y(a) p 42 1560 a(function) p Fr 234 1560 a(\010) p Fl 269 1542 a(T) p Fp 269 1573 a(\016) p Fd 314 1560 a(such) p 425 1560 a(that) p 525 1560 a(for) p 603 1560 a(e) n(ach) p Fr 712 1560 a(\000) p Fo 757 1560 a(2) p 804 1560 a(O) p Fr 845 1560 a(\() p Fo(\000) p Fq(L) p Fm 936 1542 a(0) p Fq 947 1560 a(;) p Fr 969 1560 a(2) p Fq(l) p Fr 1009 1560 a(\)) p Fq 396 1660 a(\026) p Fp 425 1637 a(!) q(;) p Ff(J) p Fe 478 1643 a(\016) p Fl 425 1674 a(\003) p Fr 494 1660 a(\(\000) p Fp 543 1640 a(!) p Fl 543 1672 a(\003) p Fr 570 1660 a(\() p Fq(\033) p Fr 619 1660 a(\)) p 651 1660 a(=) p 703 1660 a(\000\)) 316 1743 y(=) p 396 1743 a(Z\() p Fo(S) t(W) p Fr 532 1743 a(\() p Fo(\000) p Fq(L) p Fm 623 1722 a(0) p Fq 634 1743 a(;) p Fr 656 1743 a(2) p Fq(l) p Fr 696 1743 a(\)) p Fq(;) p Fn 737 1743 a(J) p Fp 765 1750 a(\016) p Fr 781 1743 a(\)) p Fm 800 1722 a(\000) p Fl(1) p Fr 847 1743 a(\010) p Fp 882 1750 a(\016) p Fr 901 1743 a(\() p Fn(W) p Fr 967 1743 a(\(\000\)\)) p 1063 1743 a(exp) r([) p Fo(\000) p Fk 1201 1695 a(X) p Fp 1206 1801 a(C) r(\023) p Fl(\000) p Fg 1281 1743 a(1) p Fp 1309 1750 a(L) p Fc 1333 1741 a(0) p Fp 1344 1750 a(;) p Fl(2) p Fp(l) p Fr 1385 1743 a(\() p Fq(C) p Fr 1443 1743 a(\)\010) p Fl 1497 1722 a(T) p Fp 1497 1755 a(\016) p Fr 1524 1743 a(\() p Fq(C) p Fr 1582 1743 a(\)]) p Fq(;) p Fr 1802 1743 a(\(4.3\)) p Fd 0 1885 a(wher) n(e) p Fr 207 1985 a(Z\() p Fo(S) t(W) p Fr 343 1985 a(\() p Fo(\000) p Fq(L) p Fm 434 1965 a(0) p Fq 446 1985 a(;) p Fr 468 1985 a(2) p Fq(l) p Fr 508 1985 a(\)) p Fq(;) p Fn 549 1985 a(J) p Fp 577 1992 a(\016) p Fr 592 1985 a(\)) p 625 1985 a(=) p Fk 764 1938 a(X) p Ff 677 2046 a(W) p Fm 713 2046 a(2S) r(W) p Fl(\() p Fm(\000) p Fp(L) p Fc 860 2037 a(0) p Fp 872 2046 a(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 932 1985 a(\010) p Fp 967 1992 a(\016) p Fr 986 1985 a(\() p Fn(W) p Fr 1052 1985 a(\)) p 1079 1985 a(exp) s([) p Fo(\000) p Fk 1243 1938 a(X) p Fp 1218 2046 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1329 2046 a(\)) p Fg 1348 1985 a(1) p Fp 1376 1992 a(L) p Fc 1400 1984 a(0) p Fp 1412 1992 a(;) p Fl(2) p Fp(l) p Fr 1452 1985 a(\() p Fq(C) p Fr 1510 1985 a(\)\010) p Fl 1564 1965 a(T) p Fp 1564 1998 a(\016) p Fr 1591 1985 a(\() p Fq(C) p Fr 1649 1985 a(\)]) p Fq(:) p Fd 0 2145 a(Mor) n(e) n(over,) p 231 2145 a(ther) n(e) p 353 2145 a(exist) p Fr 475 2132 a(\026) p Fq 468 2145 a(\014) p 514 2145 a(>) p Fr 568 2145 a(0) p Fq(;) p 632 2145 a(c) p Fm 653 2127 a(0) p Fl 653 2157 a(1) p Fq 689 2145 a(>) p Fr 743 2145 a(0) p Fd 786 2145 a(and) p Fq 881 2145 a(c) p Fm 902 2127 a(0) p Fl 902 2157 a(2) p Fq 938 2145 a(>) p Fr 992 2145 a(0) p Fd 1035 2145 a(such) p 1147 2145 a(that) p 1247 2145 a(for) p 1326 2145 a(e) n(ach) p Fq 1437 2145 a(x) p Fo 1480 2145 a(2) p Fr 1530 2145 a(\003) p Fd 1582 2145 a(and) p 1678 2145 a(any) p Fq 1772 2145 a(n) p Fo 1817 2145 a(2) p Fn 1866 2145 a(N) p Fr 0 2205 a(\() p Fq(see) p Fr 105 2205 a(\(3) p Fq(:) p Fr(5\)\)) p Fd(,) p Fk 537 2267 a(X) p Fp 435 2375 a(C) p Fm 462 2375 a(2) p Fb(C) p Fl(\() p Fp(n) p Fl(\);) p Fp(C) r(\023@) r(Q) p Fl(\() p Fp(x) p Fl(\)) p Fo 718 2315 a(j) p Fr(\010) p Fl 767 2294 a(T) p Fp 767 2327 a(\016) p Fr 795 2315 a(\() p Fq(C) p Fr 853 2315 a(\)) p Fo(j) p 899 2315 a(\024) p Fq 952 2315 a(c) p Fm 973 2294 a(0) p Fl 973 2327 a(1) p Fr 1001 2315 a(exp) o([) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1188 2315 a(\000) p Fr 1245 2301 a(\026) p Fq 1238 2315 a(\014) p Fr 1268 2315 a(\)) p Fq(c) p Fm 1308 2294 a(0) p Fl 1308 2327 a(2) p Fq 1328 2315 a(n) p Fr(]) p Fq(:) p Fr 1802 2315 a(\(4.4\)) p Fd 0 2474 a(The) p 100 2474 a(c) n(onstants) p Fr 321 2461 a(\026) p Fq 314 2474 a(\014) r(;) p 383 2474 a(c) p Fm 404 2456 a(0) p Fl 404 2486 a(1) p Fd 442 2474 a(and) p Fq 536 2474 a(c) p Fm 557 2456 a(0) p Fl 557 2486 a(2) p Fd 594 2474 a(do) p 662 2474 a(not) p 748 2474 a(dep) n(end) p 909 2474 a(on) p Fq 979 2474 a(\014) p 1023 2474 a(>) p Fr 1075 2474 a(0) p Fq(;) p 1139 2474 a(\016) p Fo 1176 2474 a(2) p Fr 1223 2474 a([0) p Fq(;) p Fr 1283 2474 a(1]) p Fd 1338 2474 a(and) p Fq 1433 2474 a(L) p Fo 1480 2474 a(2) p Fn 1527 2474 a(N) p Fd(.) p Fq 73 2568 a(P) p 111 2568 a(r) q(oof) p Fr 209 2568 a(.) p 245 2568 a(In) p 301 2568 a(the) p 381 2568 a(same) p 499 2568 a(w) o(a) o(y) p 593 2568 a(as) p 648 2568 a(w) o(e) p 716 2568 a(obtained) p 912 2568 a(\(3.6\),) p 1038 2568 a(w) o(e) p 1106 2568 a(can) p 1191 2568 a(see) p 1265 2568 a(that) p 1366 2568 a(there) p 1486 2568 a(exists) p 1617 2568 a(a) p 1653 2568 a(function) p 1839 2568 a(\010) p Fl 1874 2550 a(T) p Fp 1874 2581 a(\016) p Fr 0 2628 a(satisfying) p 218 2628 a(\(4.3\).) p 354 2628 a(Set) p 438 2628 a(in) p 495 2628 a(Lemma) p 670 2628 a(1.3,) p Fq 762 2628 a(a) p Fr(\() p Fo(\001) p Fr(\)) p 854 2628 a(=) p 906 2628 a(6) p Fn(M) p Fl 975 2610 a(2) p Fr 997 2628 a(\() p Fo(\001) p Fr(\)) p 1066 2628 a(and) p Fq 1161 2628 a(d) p Fr(\() p Fo(\001) p Fr(\)) p 1252 2628 a(=) p 1305 2628 a(\() p Fq(\014) p Fo 1365 2628 a(\000) p Fr 1422 2615 a(\026) p Fq 1415 2628 a(\014) p Fr 1445 2628 a(\)) p Fn(M) p Fl 1508 2610 a(2) p Fr 1531 2628 a(\() p Fo(\001) p Fr(\)) p 1600 2628 a(for) p 1674 2628 a(su\016cien) o(tly) 0 2688 y(large) 126 2675 y(\026) p Fq 119 2688 a(\014) p 163 2688 a(>) p Fr 215 2688 a(0.) p 275 2688 a(W) l(e) p 359 2688 a(ha) o(v) o(e) p 471 2688 a(from) p 586 2688 a(\(A.6\)) p 715 2688 a(\(see) p 813 2688 a(App) q(endix\)) p 1055 2688 a(that) p 1161 2688 a(for) p 1236 2688 a(an) o(y) p Fq 1328 2688 a(\015) p Fo 1370 2688 a(2) p 1417 2688 a(C) p Fr 1446 2688 a(\() p Fo(\000) p Fq(L) p Fm 1537 2670 a(0) p Fq 1548 2688 a(;) p Fr 1570 2688 a(2) p Fq(l) p Fr 1610 2688 a(\),) 653 2813 y(\010) p Fl 688 2820 a(0) p Fr 707 2813 a(\() p Fq(\015) p Fr 754 2813 a(\)) p Fo 787 2813 a(\024) p Fr 840 2813 a(exp) o([) p Fo(\000) p Fq 972 2780 a(\014) p 972 2802 31 2 v Fr 975 2847 a(2) p Fn 1007 2813 a(M) p Fl 1051 2793 a(2) p Fr 1074 2813 a(\() p Fq(\015) p Fr 1121 2813 a(\)]) p Fq(:) p Fr 1802 2813 a(\(4.5\)) 927 2947 y(18) p 90 rotate dyy eop %%Page: 19 19 19 18 bop Fr 0 274 a(Therefore,) p 234 274 a(w) o(e) p 305 274 a(can) p 394 274 a(see) p 472 274 a(b) o(y) p 539 274 a(Lemma) p 712 274 a(1.3) p 790 274 a(that) p 895 274 a(there) p 1019 274 a(exist) p Fq 1134 274 a(c) p Fm 1155 256 a(0) p Fl 1155 286 a(1) p Fq 1188 274 a(>) p Fr 1240 274 a(0) p 1280 274 a(and) p Fq 1374 274 a(c) p Fm 1395 256 a(0) p Fl 1395 286 a(2) p Fq 1429 274 a(>) p Fr 1481 274 a(0) p 1521 274 a(suc) o(h) p 1630 274 a(that) p 1735 274 a(for) p 1809 274 a(eac) o(h) p Fq 0 334 a(x) p Fo 42 334 a(2) p Fr 89 334 a(\003) p 139 334 a(and) p 234 334 a(an) o(y) p Fq 326 334 a(n) p Fo 369 334 a(2) p Fn 416 334 a(N) p Fr(,) p Fk 578 403 a(X) p Fp 477 511 a(C) p Fm 504 511 a(2) p Fb(C) p Fl(\() p Fp(n) p Fl(\);) p Fp(C) r(\023@) r(Q) p Fl(\() p Fp(x) p Fl(\)) p Fo 760 450 a(j) p Fr(\010) p Fl 809 430 a(T) p Fp 809 462 a(\016) p Fr 836 450 a(\() p Fq(C) p Fr 894 450 a(\)) p Fo(j) p 941 450 a(\024) p Fq 993 450 a(c) p Fm 1014 430 a(0) p Fl 1014 462 a(1) p Fr 1042 450 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1229 450 a(\000) p Fr 1286 437 a(\026) p Fq 1279 450 a(\014) p Fr 1309 450 a(\)) p Fq(c) p Fm 1349 430 a(0) p Fl 1349 462 a(2) p Fq 1369 450 a(n) p Fr(]) p Fq(:) p Fr 0 619 a(Note) p 118 619 a(that) 231 606 y(\026) p Fq 224 619 a(\014) r(;) p 292 619 a(c) p Fm 313 601 a(0) p Fl 313 632 a(1) p Fr 349 619 a(and) p Fq 444 619 a(c) p Fm 465 601 a(0) p Fl 465 632 a(2) p Fr 501 619 a(do) p 568 619 a(not) p 655 619 a(dep) q(end) p 825 619 a(on) p Fq 892 619 a(\014) p 936 619 a(>) p Fr 988 619 a(0) p Fq(;) p 1051 619 a(\016) p Fo 1088 619 a(2) p Fr 1135 619 a([0) p Fq(;) p Fr 1195 619 a(1]) p 1249 619 a(and) p Fq 1344 619 a(L) p Fo 1391 619 a(2) p Fn 1438 619 a(N) p Fr(.) 73 725 y(F) l(or) p 161 725 a(eac) o(h) p Fn 270 725 a(W) p Fo 334 725 a(2) p 381 725 a(S) t(W) p Fr 468 725 a(\() p Fo(\000) p Fq(L) p Fm 559 707 a(0) p Fq 571 725 a(;) p Fr 593 725 a(2) p Fq(l) p Fr 633 725 a(\),) p 681 725 a(w) o(e) p 753 725 a(de\014ne) p Fq 280 844 a(P) p Fp 318 823 a(\016) p Fl 311 856 a(\003) p Fr 338 844 a(\() p Fn(W) p Fr 404 844 a(\)) p 440 844 a(=) p 491 844 a(Z\() p Fo(S) t(W) p Fr 627 844 a(\() p Fo(\000) p Fq(L) p Fm 718 823 a(0) p Fq 730 844 a(;) p Fr 752 844 a(2) p Fq(l) p Fr 792 844 a(\)) p Fq(;) p Fn 833 844 a(J) p Fp 860 851 a(\016) p Fr 876 844 a(\)) p Fm 895 823 a(\000) p Fl(1) p Fr 943 844 a(\010) p Fp 978 851 a(\016) p Fr 997 844 a(\() p Fn(W) p Fr 1062 844 a(\)) p 1090 844 a(exp) r([) p Fo(\000) p Fk 1253 797 a(X) p Fp 1228 904 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 1340 904 a(\)) p Fg 1359 844 a(1) p Fp 1387 851 a(L) p Fc 1411 842 a(0) p Fp 1422 851 a(;) p Fl(2) p Fp(l) p Fr 1463 844 a(\() p Fq(C) p Fr 1521 844 a(\)\010) p Fl 1575 823 a(T) p Fp 1575 856 a(\016) p Fr 1602 844 a(\() p Fq(C) p Fr 1660 844 a(\)]) p Fq(:) p Fr 1802 972 a(\(4.6\)) p Fq 73 1082 a(P) p 111 1082 a(r) q(oof) p 227 1082 a(of) p 296 1082 a(Lemma) p Fr 479 1082 a(4.1.) p 577 1082 a(W) l(e) p 661 1082 a(de\014ne) p 802 1082 a(the) p 886 1082 a(ev) o(en) o(ts) p Fo 628 1192 a(F) p Fl 664 1199 a(1) p Fr 697 1192 a(=) p Fo 749 1192 a(f) p Fq(\033) p Fo 817 1192 a(2) p Fr 865 1192 a(\012) p Fl 900 1199 a(\003) p Fr 926 1192 a(;) p 948 1192 a(h) p Fl 975 1171 a(+) p Fr 1005 1192 a(\(\000) p Fp 1054 1171 a(!) p Fl 1054 1204 a(\003) p Fr 1081 1192 a(\() p Fq(\033) p Fr 1130 1192 a(\)\)) p Fo 1181 1192 a(\025) p Fq 1234 1192 a(l) p Fo 1250 1192 a(g) p Fr 0 1302 a(and) p Fo 486 1362 a(F) p Fm 527 1341 a(0) p Fl 522 1374 a(1) p Fr 556 1362 a(=) p Fo 607 1362 a(f) p Fq(\033) p Fo 676 1362 a(2) p Fr 723 1362 a(\012) p Fl 758 1370 a(\003\() p Fm(\000) p Fp(L) p Fc 847 1360 a(0) p Fp 859 1370 a(;) p Fm(1) p Fl(\)) p Fr 920 1362 a(;) p 942 1362 a(h) p Fl 969 1341 a(+) p Fr 998 1362 a(\(\000) p Fp 1047 1341 a(!) p Fl 1047 1374 a(\003\() p Fm(\000) p Fp(L) p Fc 1136 1365 a(0) p Fp 1148 1374 a(;) p Fm(1) p Fl(\)) p Fr 1209 1362 a(\() p Fq(\033) p Fr 1258 1362 a(\)\)) p Fo 1309 1362 a(\025) p Fq 1362 1362 a(l) p Fo 1378 1362 a(g) p Fq(:) p Fr 0 1449 a(W) l(e) p 84 1449 a(ha) o(v) o(e) p 196 1449 a(b) o(y) p 264 1449 a(FK) o(G) p 387 1449 a(inequalit) o(y) p 613 1449 a(that) p Fq 632 1559 a(\026) p Fp 661 1535 a(!) q(;) p Ff(J) p Fe 714 1541 a(\016) p Fl 661 1573 a(\003) p Fr 730 1559 a(\() p Fo(F) p Fl 785 1566 a(1) p Fr 804 1559 a(\)) p Fo 837 1559 a(\024) p Fq 890 1559 a(\026) p Fp 919 1535 a(!) q(;) p Ff(J) p Fj 971 1540 a(1) p Fl 919 1575 a(\003\() p Fm(\000) p Fp(L) p Fc 1008 1565 a(0) p Fp 1020 1575 a(;) p Fm(1) p Fl(\)) p Fr 1081 1559 a(\() p Fo(F) p Fm 1141 1538 a(0) p Fl 1136 1571 a(1) p Fr 1155 1559 a(\)) p Fq(:) p Fr 1802 1559 a(\(4.7\)) 0 1669 y(W) l(e) p 84 1669 a(also) p 182 1669 a(ha) o(v) o(e) p 294 1669 a(b) o(y) p 362 1669 a(FK) o(G) p 485 1669 a(inequalit) o(y) p 711 1669 a(that) p Fq 582 1779 a(\026) p Fp 611 1755 a(!) q(;) p Ff(J) p Fj 664 1760 a(1) p Fl 611 1795 a(\003\() p Fm(\000) p Fp(L) p Fc 700 1785 a(0) p Fp 712 1795 a(;) p Fm(1) p Fl(\)) p Fr 773 1779 a(\() p Fo(F) p Fm 833 1759 a(0) p Fl 828 1791 a(2) p Fr 847 1779 a(\)) p Fo 880 1779 a(\024) p Fq 933 1779 a(\026) p Fp 962 1755 a(!) q(;) p Ff(J) p Fj 1015 1760 a(1) p Fl 962 1795 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1124 1779 a(\() p Fo(F) p Fm 1184 1759 a(00) p Fl 1179 1791 a(2) p Fr 1205 1779 a(\)) p Fq(;) p Fr 1802 1779 a(\(4.8\)) 0 1889 y(where) p Fo 474 1949 a(F) p Fm 515 1929 a(0) p Fl 510 1962 a(2) p Fr 543 1949 a(=) p Fo 595 1949 a(f) p Fq(\033) p Fo 663 1949 a(2) p Fr 710 1949 a(\012) p Fl 745 1957 a(\003\() p Fm(\000) p Fp(L) p Fc 834 1948 a(0) p Fp 846 1957 a(;) p Fm(1) p Fl(\)) p Fr 907 1949 a(;) p 929 1949 a(h) p Fm 956 1929 a(\000) p Fr 985 1949 a(\(\000) p Fp 1034 1929 a(!) p Fl 1034 1962 a(\003\() p Fm(\000) p Fp(L) p Fc 1123 1952 a(0) p Fp 1136 1962 a(;) p Fm(1) p Fl(\)) p Fr 1197 1949 a(\() p Fq(\033) p Fr 1246 1949 a(\)\)) p Fo 1297 1949 a(\024) p 1349 1949 a(\000) p Fq(l) p Fo 1404 1949 a(g) p Fr 0 2036 a(and) p Fo 463 2097 a(F) p Fm 504 2076 a(00) p Fl 499 2109 a(2) p Fr 539 2097 a(=) p Fo 591 2097 a(f) p Fq(\033) p Fo 659 2097 a(2) p Fr 706 2097 a(\012) p Fl 741 2104 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 903 2097 a(;) p 925 2097 a(h) p Fm 952 2076 a(\000) p Fr 982 2097 a(\(\000) p Fp 1031 2076 a(!) p Fl 1031 2109 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1193 2097 a(\() p Fq(\033) p Fr 1242 2097 a(\)\)) p Fo 1293 2097 a(\024) p 1346 2097 a(\000) p Fq(l) p Fo 1401 2097 a(g) p Fq(:) p Fr 0 2184 a(Let) p Fo 364 2244 a(S) t(W) p Fl 451 2223 a(+) p Fr 495 2244 a(=) p Fo 546 2244 a(f) p Fn(W) p Fo 635 2244 a(2) p 682 2244 a(S) t(W) p Fr 769 2244 a(\() p Fo(\000) p Fq(L) p Fm 860 2223 a(0) p Fq 872 2244 a(;) p Fo 894 2244 a(1) p Fr(\);) p 985 2244 a(h) p Fl 1012 2223 a(+) p Fr 1041 2244 a(\() p Fn(W) p Fr 1107 2244 a(\)) p Fo 1143 2244 a(\025) p Fq 1195 2244 a(l) q(;) p Fr 1249 2244 a(h) p Fm 1276 2223 a(\000) p Fr 1305 2244 a(\() p Fn(W) p Fr 1371 2244 a(\)) p Fq 1407 2244 a(>) p Fo 1459 2244 a(\000) p Fq(l) p Fo 1514 2244 a(g) p Fr 0 2331 a(and) p 95 2331 a(let) p Fo 487 2391 a(S) t(W) p Fm 574 2370 a(\000) p Fr 617 2391 a(=) p Fo 669 2391 a(f) p Fn(W) p Fo 758 2391 a(2) p 805 2391 a(S) t(W) p Fr 892 2391 a(\() p Fo(\0001) p Fq(;) p Fo 1022 2391 a(1) p Fr(\);) p 1113 2391 a(h) p Fm 1140 2371 a(\000) p Fr 1168 2391 a(\() p Fn(W) p Fr 1234 2391 a(\)) p Fo 1270 2391 a(\024) p 1323 2391 a(\000) p Fq(l) p Fo 1378 2391 a(g) p Fq(:) p Fr 0 2479 a(Then,) p 141 2479 a(w) o(e) p 213 2479 a(ha) o(v) o(e) p 325 2479 a(from) p 440 2479 a(\(3.8\),) p 570 2479 a(\(3.9\),) p 700 2479 a(\(4.7\)) p 817 2479 a(and) p 912 2479 a(\(4.8\)) p 1028 2479 a(that) p Fq 324 2589 a(\026) p Fp 353 2565 a(!) q(;) p Ff(J) p Fe 406 2571 a(\016) p Fl 353 2602 a(\003) p Fr 422 2589 a(\() p Fo(F) p Fl 477 2596 a(1) p Fr 497 2589 a(\)) p Fo 557 2589 a(\024) p Fq 638 2589 a(\026) p Fp 667 2565 a(!) q(;) p Ff(J) p Fj 720 2570 a(1) p Fl 667 2604 a(\003\() p Fm(\000) p Fp(L) p Fc 756 2595 a(0) p Fp 768 2604 a(;) p Fm(1) p Fl(\)) p Fr 829 2589 a(\() p Fo(F) p Fm 889 2568 a(0) p Fl 884 2601 a(1) p Fo 903 2589 a(nF) p Fm 969 2568 a(0) p Fl 964 2601 a(2) p Fr 984 2589 a(\)) p 1014 2589 a(+) p Fq 1063 2589 a(\026) p Fp 1092 2565 a(!) q(;) p Ff(J) p Fj 1145 2570 a(1) p Fl 1092 2604 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1254 2589 a(\() p Fo(F) p Fm 1314 2568 a(00) p Fl 1309 2601 a(2) p Fr 1335 2589 a(\)) 558 2681 y(=) p Fk 674 2634 a(X) p Ff 638 2746 a(W) p Fm 674 2746 a(2) o(S) r(W) p Fj 756 2733 a(+) p Fq 790 2681 a(P) p Fl 828 2661 a(1) 821 2694 y(\003\() p Fm(\000) p Fp(L) p Fc 910 2684 a(0) p Fp 922 2694 a(;) p Fm(1) p Fl(\)) p Fr 983 2681 a(\() p Fn(W) p Fr 1049 2681 a(\)) p 1082 2681 a(+) p Fk 1167 2634 a(X) p Ff 1131 2746 a(W) p Fm 1167 2746 a(2) o(S) r(W) p Fc 1249 2733 a(\000) p Fq 1283 2681 a(P) p Fl 1321 2661 a(1) 1314 2694 y(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1477 2681 a(\() p Fn(W) p Fr 1542 2681 a(\)) p Fq(:) p Fr 1802 2681 a(\(4.9\)) 927 2947 y(19) p 90 rotate dyy eop %%Page: 20 20 20 19 bop Fr 0 274 a(By) p 78 274 a(a) p 120 274 a(similar) p 282 274 a(argumen) o(t) p 502 274 a(as) p 563 274 a(in) p 622 274 a(\(3.21\)-\(3.32\),) p 919 274 a(w) o(e) p 993 274 a(can) p 1084 274 a(estimate) p 1281 274 a(the) p 1367 274 a(\014rst) p 1469 274 a(and) p 1565 274 a(second) p 1724 274 a(terms) p 1862 274 a(in) 0 334 y(RHS) p 116 334 a(of) p 171 334 a(\(4.9\)) p 288 334 a(from) p 403 334 a(ab) q(o) o(v) o(e,) p 555 334 a(resp) q(ectiv) o(ely) l(,) p 830 334 a(b) o(y) p Fq 619 439 a(c) p Fl 640 446 a(13) p Fr 685 439 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 872 439 a(\000) p Fq 922 439 a(c) p Fl 943 446 a(14) p Fr 981 439 a(\)) p Fq(K) p Fl 1041 446 a(3) p Fr 1069 439 a(log) p Fq 1140 439 a(L) p Fr(]) p Fq(:) p Fr 1778 439 a(\(4.10\)) 73 543 y(Set) p Fo 535 603 a(G) p Fl 565 610 a(1) p Fr 598 603 a(=) p Fo 650 603 a(f) p Fq(\033) p Fo 718 603 a(2) p Fr 765 603 a(\012) p Fl 800 610 a(\003) p Fr 827 603 a(;) p 849 603 a(h) p Fm 876 582 a(\000) p Fr 905 603 a(\(\000) p Fp 954 582 a(!) p Fl 954 615 a(\003) p Fr 981 603 a(\() p Fq(\033) p Fr 1030 603 a(\)\)) p Fo 1082 603 a(\024) p 1134 603 a(\000) p Fq(L) p Fm 1206 582 a(0) p Fr 1229 603 a(+) p Fq 1278 603 a(l) q(=) p Fr(2) p Fo(g) p Fr 0 688 a(and) p Fo 400 748 a(G) p Fm 433 727 a(0) p Fl 430 760 a(1) p Fr 463 748 a(=) p Fo 515 748 a(f) p Fq(\033) p Fo 583 748 a(2) p Fr 630 748 a(\012) p Fl 665 756 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 820 748 a(;) p 842 748 a(h) p Fm 869 727 a(\000) p Fr 899 748 a(\(\000) p Fp 948 724 a(\020) p Fl 948 764 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1103 748 a(\() p Fq(\033) p Fr 1152 748 a(\)\)) p Fo 1203 748 a(\024) p 1256 748 a(\000) p Fq(L) p Fm 1328 727 a(0) p Fr 1351 748 a(+) p Fq 1400 748 a(l) q(=) p Fr(2) p Fo(g) p Fq(;) p Fr 0 847 a(where) p 136 847 a(w) o(e) p 203 847 a(write) p Fq 323 847 a(\020) p Fr 362 847 a(=) p Fq 414 847 a(!) p Fm 444 854 a(\000) p Fp(L) p Fc 495 845 a(00) p Fr 530 847 a(\(see) p 623 847 a(\(1.15\)\).) p 800 847 a(W) l(e) p 880 847 a(de\014ne) p 1016 847 a(\000) p Fp 1046 824 a(\020) p Fl 1046 863 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1202 847 a(\() p Fo(\001) p Fr(\)) p 1265 847 a(in) p 1317 847 a(a) p 1353 847 a(similar) p 1509 847 a(w) o(a) o(y) p 1603 847 a(as) p 1658 847 a(\000) p Fp 1688 829 a(!) p Fl 1688 862 a(\003\() p Fm(\0001) p Fp(;) p Fm(1) p Fl(\)) p Fr 1850 847 a(\() p Fo(\001) p Fr(\)) 0 913 y(\(see) p 98 913 a(Section) p 269 913 a(3\).) p 347 913 a(Then,) p 488 913 a(w) o(e) p 560 913 a(ha) o(v) o(e) p 672 913 a(b) o(y) p 740 913 a(FK) o(G) p 863 913 a(inequalit) o(y) p 1089 913 a(that) p Fq 641 1017 a(\026) p Fp 670 994 a(!) q(;) p Ff(J) p Fe 723 1000 a(\016) p Fl 670 1031 a(\003) p Fr 739 1017 a(\() p Fo(G) p Fl 788 1024 a(1) p Fr 807 1017 a(\)) p Fo 840 1017 a(\024) p Fq 893 1017 a(\026) p Fp 922 994 a(\020) r(;) p Ff(J) p Fj 969 999 a(1) p Fl 922 1033 a(\003\() p Fm(\0001) p Fp(;) p Fl(2) p Fp(l) p Fl(\)) p Fr 1077 1017 a(\() p Fo(G) p Fm 1129 997 a(0) p Fl 1126 1030 a(1) p Fr 1146 1017 a(\)) p Fq(:) p Fr 1778 1017 a(\(4.11\)) 0 1127 y(Therefore,) p 234 1127 a(w) o(e) p 306 1127 a(can) p 396 1127 a(see) p 474 1127 a(b) o(y) p 542 1127 a(a) p 583 1127 a(similar) p 743 1127 a(argumen) o(t) p 961 1127 a(as) p 1021 1127 a(in) p 1078 1127 a(\(4.7\)-\(4.9\)) p 1311 1127 a(that) p Fq 493 1231 a(\026) p Fp 522 1208 a(!) q(;) p Ff(J) p Fe 575 1214 a(\016) p Fl 522 1245 a(\003) p Fr 591 1231 a(\() p Fo(G) p Fl 640 1238 a(1) p Fr 659 1231 a(\)) p Fo 692 1231 a(\024) p Fq 744 1231 a(c) p Fl 765 1238 a(15) p Fr 811 1231 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 998 1231 a(\000) p Fq 1048 1231 a(c) p Fl 1069 1238 a(16) p Fr 1106 1231 a(\)) p Fq(K) p Fl 1166 1238 a(3) p Fr 1195 1231 a(log) p Fq 1266 1231 a(L) p Fr(]) p Fq(:) p Fr 1778 1231 a(\(4.12\)) 73 1441 y(No) o(w,) p 198 1441 a(w) o(e) p 270 1441 a(are) p 351 1441 a(going) p 481 1441 a(to) p 541 1441 a(estimate) p Fq 736 1441 a(\026) p Fp 765 1418 a(!) q(;) p Ff(J) p Fe 818 1424 a(\016) p Fl 765 1455 a(\003) p Fr 834 1441 a(\(\() p Fo(A) p Fp 912 1423 a(!) p Fl 912 1454 a(\003) p Fr 938 1441 a(\)) p Fp 957 1423 a(c) p Fo 975 1441 a(n) p Fr(\() p Fo(F) p Fl 1055 1448 a(1) p Fo 1085 1441 a([) p 1129 1441 a(G) p Fl 1159 1448 a(1) p Fr 1179 1441 a(\)\).) p 1252 1441 a(Let) p Fo 163 1546 a(S) t(W) p Fr 264 1546 a(=) p Fo 316 1546 a(f) p Fn(W) p Fo 405 1546 a(2) p 452 1546 a(S) t(W) p Fr 539 1546 a(\() p Fo(\000) p Fq(L) p Fm 630 1525 a(0) p Fq 641 1546 a(;) p Fr 663 1546 a(2) p Fq(l) p Fr 703 1546 a(\);) p 744 1546 a(\000\() p Fn(W) p Fr 840 1546 a(\)) p 876 1546 a(=) p 928 1546 a(\000) p Fp 958 1525 a(!) p Fl 958 1558 a(\003) p Fr 985 1546 a(\() p Fq(\033) p Fr 1034 1546 a(\)) p 1069 1546 a(for) p 1143 1546 a(some) p Fq 1265 1546 a(\033) p Fo 1309 1546 a(2) p Fr 1356 1546 a(\() p Fo(A) p Fp 1415 1525 a(!) p Fl 1415 1558 a(\003) p Fr 1441 1546 a(\)) p Fp 1460 1525 a(c) p Fo 1477 1546 a(n) p Fr(\() p Fo(F) p Fl 1557 1553 a(1) p Fo 1588 1546 a([) p 1632 1546 a(G) p Fl 1662 1553 a(1) p Fr 1682 1546 a(\)) p Fo(g) p Fq(:) p Fr 73 1650 a(W) l(e) p 158 1650 a(will) p 252 1650 a(in) o(tro) q(duce) p 470 1650 a(some) p 593 1650 a(de\014nitions) p 831 1650 a(and) p 927 1650 a(notations.) p 1164 1650 a(F) l(or) p 1253 1650 a(eac) o(h) p 1364 1650 a(\002) p Fo 1418 1650 a(\032) p Fn 1473 1650 a(Z) p Fl 1509 1632 a(3) p Fr 1525 1650 a(,) p Fq 1557 1650 a(@) p Fr 1586 1650 a(\002) p 1641 1650 a(will) p 1734 1650 a(indicate) p Fq 0 1710 a(@) s(Q) p Fr(\(\002\).) p 178 1710 a(F) l(or) p 266 1710 a(eac) o(h) p 375 1710 a(\002) p Fo 427 1710 a(\032) p Fr 480 1710 a(\003,) p 543 1710 a(w) o(e) p 615 1710 a(de\014ne) p Fq 756 1710 a(T) p Fl 785 1717 a(\002) p Fr 828 1710 a(:) p 855 1710 a(\012) p Fl 890 1717 a(\003) p Fo 931 1710 a(!) p Fr 995 1710 a(\012) p Fl 1030 1717 a(\003) p Fr 1073 1710 a(b) o(y) p Fq 586 1844 a(T) p Fl 615 1851 a(\002) p Fr 644 1844 a(\() p Fq(\033) p Fr 693 1844 a(\)\() p Fq(x) p Fr(\)) p 791 1844 a(=) p Fk 843 1774 a(\032) p Fo 901 1813 a(\000) p Fq(\033) p Fr 970 1813 a(\() p Fq(x) p Fr(\)) p 1076 1813 a(if) p Fq 1121 1813 a(x) p Fo 1163 1813 a(2) p Fr 1210 1813 a(\002) p Fq(;) 920 1873 y(\033) p Fr 950 1873 a(\() p Fq(x) p Fr(\)) p 1076 1873 a(otherwise) p Fq(:) p Fr 0 1979 a(F) l(or) p 94 1979 a(eac) o(h) p 211 1979 a(\000) p Fo 266 1979 a(2) p 325 1979 a(O) p Fr 366 1979 a(\() p Fo(\000) p Fq(L) p Fm 457 1961 a(0) p Fq 469 1979 a(;) p Fr 491 1979 a(2) p Fq(l) p Fr 531 1979 a(\),) p 588 1979 a(there) p 719 1979 a(exists) p 861 1979 a(a) p 908 1979 a(unique) p 1073 1979 a(\014nite) p Fq 1205 1979 a(l) p Fm 1220 1986 a(1) p Fr 1257 1979 a(-connected) p 1507 1979 a(\002\(\000\)) p Fo 1639 1979 a(\032) p Fn 1703 1979 a(Z) p Fl 1739 1961 a(3) p Fr 1779 1979 a(whic) o(h) 0 2039 y(satis\014es) p 180 2039 a(the) p 264 2039 a(follo) o(wing) p 470 2039 a(conditions:) 46 2136 y(\(i\)) p Fo 122 2136 a(f) p Fq(x) p Fo 188 2136 a(2) p Fq 235 2136 a(@) p Fp 261 2143 a(ex) p Fr 299 2136 a(\003;) p Fq 355 2136 a(x) p Fl 383 2118 a(3) p Fo 416 2136 a(\025) p Fr 469 2136 a(0) p Fo(g) p 532 2136 a(\032) p Fr 585 2136 a(\002\(\000\)) p Fo 705 2136 a(\032) p Fr 758 2136 a(\(\003) p Fo 821 2136 a([) p 866 2136 a(f) p Fq(x) p Fo 932 2136 a(2) p Fq 979 2136 a(@) p Fp 1005 2143 a(ex) p Fr 1043 2136 a(\003;) p Fq 1099 2136 a(x) p Fl 1127 2118 a(3) p Fo 1160 2136 a(\025) p Fr 1213 2136 a(0) p Fo(g) p Fr(\),) 33 2236 y(\(ii\)) p 122 2236 a(\(\002\(\000\)\)) p Fp 266 2218 a(c) p Fr 300 2236 a(is) p Fq 349 2236 a(l) p Fm 364 2243 a(1) p Fr 401 2236 a(-connected,) p 658 2236 a(and) 19 2336 y(\(iii\)) p 122 2336 a(\000) p 166 2336 a(=) p Fq 218 2336 a(@) p Fr 247 2336 a(\002\(\000\)) p Fo(n) p Fq(@) p Fr 407 2336 a(\(\003) p Fo 470 2336 a([) p Fq 514 2336 a(@) p Fp 540 2343 a(ex) p Fr 578 2336 a(\003\).) 0 2433 y(Let) p Fq 86 2433 a(V) p Fo 139 2433 a(\032) p Fn 191 2433 a(R) p Fl 230 2415 a(3) p Fr 247 2433 a(.) p 282 2433 a(F) l(or) p 368 2433 a(eac) o(h) p Fq 476 2433 a(i) p Fo 506 2433 a(2) p Fn 553 2433 a(N) p Fr(,) p 618 2433 a(w) o(e) p 688 2433 a(de\014ne) p 827 2433 a(shift\() p Fq(V) s(;) p 993 2433 a(i) p Fr(\)) p 1042 2433 a(=) p Fq 1094 2433 a(V) p Fr 1141 2433 a(+) p 1187 2433 a(\(0) p Fq(;) p Fr 1252 2433 a(0) p Fq(;) p 1298 2433 a(i) p Fr(\).) p 1368 2433 a(F) l(or) p 1454 2433 a(eac) o(h) p Fq 1562 2433 a(r) p Fl 1584 2440 a(1) p Fo 1618 2433 a(2) p Fn 1665 2433 a(R) p Fr 1716 2433 a(and) p 1809 2433 a(eac) o(h) p Fq 0 2494 a(r) p Fl 22 2501 a(2) p Fo 56 2494 a(2) p Fn 103 2494 a(R) p Fr(,) p 168 2494 a(w) o(e) p 240 2494 a(de\014ne) 197 2598 y(cyl) o(\() p Fq(V) s(;) p 330 2598 a(r) p Fl 352 2605 a(1) p Fq 371 2598 a(;) p 393 2598 a(r) p Fl 415 2605 a(2) p Fr 435 2598 a(\)) p 468 2598 a(=) p Fo 519 2598 a(f) p Fq(x) p Fo 586 2598 a(2) p Fn 633 2598 a(R) p Fl 672 2577 a(3) p Fr 689 2598 a(;) p Fq 711 2598 a(\031) p Fr 741 2598 a(\() p Fq(x) p Fr(\)) p Fo 819 2598 a(2) p Fq 866 2598 a(@) p Fl 895 2577 a(2) p Fr 917 2598 a(^) p Fq 915 2598 a(\031) p Fr 944 2598 a(\() p Fq(V) p Fr 1002 2598 a(\)) p Fq(;) p 1059 2598 a(r) p Fl 1081 2605 a(1) p Fo 1112 2598 a(\000) p Fr 1162 2598 a(\(1) p Fq(=) p Fr(2\)) p Fo 1287 2598 a(\024) p Fq 1340 2598 a(x) p Fl 1368 2577 a(3) p Fo 1401 2598 a(\024) p Fq 1453 2598 a(r) p Fl 1475 2605 a(2) p Fo 1506 2598 a(\000) p Fr 1556 2598 a(\(1) p Fq(=) p Fr(2\)) p Fo(g) p Fq(;) p Fr 0 2702 a(where) p 140 2702 a(for) 222 2690 y(^) p Fq 214 2702 a(V) p Fo 267 2702 a(\032) p Fr 320 2702 a(H\() p Fo(\000) p Fl 420 2683 a(1) p 420 2691 18 2 v 420 2719 a(2) p Fr 442 2702 a(\),) p Fq 490 2702 a(@) p Fl 519 2684 a(2) p Fr 545 2690 a(^) p Fq 538 2702 a(V) p Fr 593 2702 a(indicates) p 796 2702 a(the) p 879 2702 a(b) q(oundary) p 1098 2702 a(of) 1160 2690 y(^) p Fq 1153 2702 a(V) p Fr 1208 2702 a(under) p 1345 2702 a(the) p 1428 2702 a(induced) p 1609 2702 a(2-dimensional) 0 2762 y(top) q(ology) p 202 2762 a(of) p 259 2762 a(H\() p Fo(\000) p Fl 359 2743 a(1) p 359 2751 V 359 2780 a(2) p Fr 381 2762 a(\).) p 440 2762 a(Esp) q(ecially) l(,) p 683 2762 a(cyl) o(\() p Fq(Q) p Fr(\() p Fq(V) p Fr 860 2762 a(\)) p Fq(;) p 901 2762 a(r) p Fl 923 2769 a(1) p Fq 942 2762 a(;) p 964 2762 a(r) p Fl 986 2769 a(2) p Fr 1006 2762 a(\)) p 1042 2762 a(will) p 1136 2762 a(b) q(e) p 1204 2762 a(indicated) p 1417 2762 a(b) o(y) p 1486 2762 a(cyl) o(\() p Fq(V) s(;) p 1619 2762 a(r) p Fl 1641 2769 a(1) p Fq 1661 2762 a(;) p 1683 2762 a(r) p Fl 1705 2769 a(2) p Fr 1725 2762 a(\)) p 1761 2762 a(if) p Fq 1808 2762 a(V) p Fo 1863 2762 a(\032) p Fn 0 2823 a(Z) p Fl 36 2805 a(3) p Fr 53 2823 a(.) 927 2947 y(20) p 90 rotate dyy eop %%Page: 21 21 21 20 bop Fr 73 274 a(Let) p 158 274 a(us) p 218 274 a(\014x) p Fn 285 274 a(W) p Fo 349 274 a(2) p 396 274 a(S) t(W) p Fr 497 274 a(and) p 589 274 a(let) p 658 274 a(\000) p 702 274 a(=) p 754 274 a(\000\() p Fn(W) p Fr 850 274 a(\).) p 906 274 a(W) l(e) p 988 274 a(decomp) q(ose) p 1231 274 a(\000) p Fo(n) p Fr(cyl) o(\(\003) p Fq(;) p Fo 1422 274 a(\000) p Fq(L) p Fm 1494 256 a(00) p Fq 1515 274 a(;) p Fr 1537 274 a(0\)) p 1594 274 a(in) o(to) p 1691 274 a(connected) 0 334 y(comp) q(onen) o(ts.) p 288 334 a(W) l(e) p 371 334 a(de\014ne) p Fn 512 334 a(F) p Fr 557 334 a(=) p Fn 608 334 a(F) p Fr 636 334 a(\(\000\)) p 721 334 a(=) p Fn 773 334 a(F) p Fr(\() p Fn(W) p Fr 869 334 a(\)) p 907 334 a(b) o(y) p Fk 141 401 a(8) 141 446 y(<) 141 536 y(:) p Fq 185 503 a(F) p Fr 224 503 a(;) p Fq 364 443 a(F) p Fr 419 443 a(is) p 468 443 a(a) p 508 443 a(connected) p 736 443 a(comp) q(onen) o(t) p 985 443 a(of) p 1041 443 a(\000) p Fo(n) p Fr(cyl) o(\(\003) p Fq(;) p Fo 1232 443 a(\000) p Fq(L) p Fm 1304 425 a(00) p Fq 1325 443 a(;) p Fr 1347 443 a(0\)) p 1407 443 a(and) 266 503 y(there) p 391 503 a(exists) p 525 503 a(a) p 566 503 a(unique) p Fq 724 503 a(l) p Fm 739 510 a(1) p Fr 776 503 a(-connected) p 1020 503 a(\002) p Fo 1072 503 a(\032) p Fr 1125 503 a(\003) p 1175 503 a(whic) o(h) p 1314 503 a(satis\014es) p 1494 503 a(that) 398 563 y(\002) p Fp 436 545 a(c) p Fr 469 563 a(is) p Fq 518 563 a(l) p Fm 533 570 a(1) p Fr 570 563 a(-connected) p 814 563 a(and) p Fq 925 563 a(F) p Fo 975 563 a(\011) p Fq 1025 563 a(@) p Fr 1054 563 a(\002) p Fo 1105 563 a(\032) p Fr 1157 563 a(cyl) o(\(\003) p Fq(;) p Fo 1293 563 a(\000) p Fq(L) p Fm 1365 545 a(00) p Fq 1386 563 a(;) p Fr 1408 563 a(0\)) p Fk 1604 401 a(9) 1604 446 y(=) 1604 536 y(;) p Fq 1657 503 a(;) p Fr 1778 635 a(\(4.13\)) 0 745 y(where) p Fo 146 745 a(\011) p Fr 206 745 a(denotes) p 388 745 a(the) p 477 745 a(symmetric) p 720 745 a(di\013erence.) p 972 745 a(The) p 1078 745 a(set) p 1159 745 a(\002) p 1219 745 a(is) p 1273 745 a(uniquely) p 1476 745 a(determined) p 1736 745 a(b) o(y) p 1809 745 a(eac) o(h) p Fq 0 805 a(F) p Fo 58 805 a(2) p Fn 111 805 a(F) p Fr(,) p 175 805 a(and) p 273 805 a(hence) p 412 805 a(is) p 465 805 a(denoted) p 652 805 a(b) o(y) p 723 805 a(\002\() p Fq(F) p Fr 819 805 a(\).) p 883 805 a(Let) p Fq 974 805 a(L) p Fo 1027 805 a(2) p Fn 1079 805 a(N) p Fr 1135 805 a(b) q(e) p 1205 805 a(su\016cien) o(tly) p 1452 805 a(large) p 1575 805 a(\() p Fq(\016) p 1637 805 a(>) p Fr 1694 805 a(0) p 1738 805 a(is) p 1791 805 a(small) 0 866 y(enough\).) p 206 866 a(By) p 282 866 a(the) p 366 866 a(de\014nition) p 583 866 a(of) p Fn 639 866 a(J) p Fp 667 873 a(\016) p Fr 699 866 a(and) p 794 866 a(\(A.6\),) p 936 866 a(w) o(e) p 1008 866 a(can) p 1097 866 a(see) p 1176 866 a(that) p 1282 866 a(for) p 1356 866 a(eac) o(h) p Fq 1466 866 a(F) p Fo 1518 866 a(2) p Fn 1565 866 a(F) p Fr 1593 866 a(,) p Fq 482 976 a(H) p Fp 526 952 a(!) q(;) p Ff(J) p Fe 578 958 a(\016) p Fl 522 989 a(\003) p Fr 594 976 a(\() p Fq(\033) p Fr 643 976 a(\)) p Fo 673 976 a(\000) p Fq 723 976 a(H) p Fp 767 952 a(!) q(;) p Ff(J) p Fe 820 958 a(\016) p Fl 763 989 a(\003) p Fr 836 976 a(\() p Fq(T) p Fl 884 983 a(\002\() p Fp(F) p Fl 952 983 a(\)) p Fq 967 976 a(\033) p Fr 997 976 a(\)) 579 1048 y(=) p 631 1048 a(2) p Fn(M) p Fl 699 1028 a(2) p Fr 722 1048 a(\() p Fq(F) p Fr 780 1048 a(\)) p Fo 809 1048 a(\000) p Fr 859 1048 a(2) p Fq(\016) p Fn 907 1048 a(M) p Fl 951 1028 a(2) p Fr 974 1048 a(\() p Fq(@) p Fr 1022 1048 a(\002\() p Fq(F) p Fr 1118 1048 a(\)) p Fo 1146 1048 a(\\) p Fr 1191 1048 a(cyl) o(\(\003) p Fq(;) p Fo 1327 1048 a(\000) p Fq(L) p Fm 1399 1028 a(00) p Fq 1420 1048 a(;) p Fr 1442 1048 a(0\)\)) p Fo 579 1143 a(\025) p Fr 637 1109 a(1) p 637 1132 25 2 v 637 1177 a(2) p Fn 666 1143 a(M) p Fl 710 1122 a(2) p Fr 733 1143 a(\() p Fq(@) p Fr 781 1143 a(\002\() p Fq(F) p Fr 877 1143 a(\)\)) p Fo 924 1143 a(\000) p Fr 974 1143 a(2) p Fq(\016) p Fn 1022 1143 a(M) p Fl 1066 1122 a(2) p Fr 1089 1143 a(\() p Fq(@) p Fr 1137 1143 a(\002\() p Fq(F) p Fr 1233 1143 a(\)\)) p Fo 579 1260 a(\025) p Fr 637 1226 a(1) p 637 1248 V 637 1294 a(3) p Fn 666 1260 a(M) p Fl 710 1239 a(2) p Fr 733 1260 a(\() p Fq(@) p Fr 781 1260 a(\002\() p Fq(F) p Fr 877 1260 a(\)\)) p Fq(;) p Fr 1778 1260 a(\(4.14\)) 0 1385 y(where) p Fq 141 1385 a(\033) p Fo 185 1385 a(2) p Fr 232 1385 a(\012) p Fl 267 1392 a(\003) p Fr 311 1385 a(satis\014es) p 491 1385 a(that) p 597 1385 a(\000) p Fp 627 1367 a(!) p Fl 627 1398 a(\003) p Fr 654 1385 a(\() p Fq(\033) p Fr 703 1385 a(\)) p 735 1385 a(=) p 788 1385 a(\000.) p 854 1385 a(Therefore,) p 1089 1385 a(w) o(e) p 1161 1385 a(ha) o(v) o(e) p 1274 1385 a(b) o(y) p 1342 1385 a(a) p 1383 1385 a(part) p 1489 1385 a(of) p 1544 1385 a(standard) p 1748 1385 a(P) o(eierls') 0 1445 y(argumen) o(t) p 218 1445 a(that) p 324 1445 a(for) p 398 1445 a(eac) o(h) p Fq 508 1445 a(F) p Fo 560 1445 a(2) p Fn 607 1445 a(F) p Fr 635 1445 a(,) p Fq 402 1577 a(\026) p Fp 431 1554 a(!) q(;) p Ff(J) p Fe 484 1560 a(\016) p Fl 431 1591 a(\003) p Fr 500 1577 a(\(\000) p Fp 549 1557 a(!) p Fl 549 1590 a(\003) p Fr 576 1577 a(\() p Fq(\033) p Fr 625 1577 a(\)) p 660 1577 a(con) o(tains) p Fq 851 1577 a(F) p Fr 890 1577 a(\)) p Fo 923 1577 a(\024) p Fr 975 1577 a(exp[) p Fo(\000) p Fq 1108 1544 a(\014) p 1108 1566 31 2 v Fr 1111 1611 a(3) p Fn 1142 1577 a(M) p Fl 1186 1557 a(2) p Fr 1209 1577 a(\() p Fq(@) p Fr 1257 1577 a(\002\() p Fq(F) p Fr 1353 1577 a(\)\)]) p Fq(:) p Fr 1778 1577 a(\(4.15\)) 0 1700 y(Let) p Fq 87 1700 a(K) p Fl 128 1707 a(4) p Fq 162 1700 a(>) p Fr 214 1700 a(0) p 255 1700 a(b) q(e) p 321 1700 a(a) p 362 1700 a(large) p 481 1700 a(constan) o(t) p 678 1700 a(to) p 737 1700 a(b) q(e) p 804 1700 a(sp) q(eci\014ed) p 1001 1700 a(later.) p 1133 1700 a(W) l(e) p 1217 1700 a(de\014ne) p Fo 286 1836 a(S) t(W) p Fm 373 1815 a(0) p Fr 399 1836 a(=) p Fk 451 1766 a(\032) p Fn 488 1836 a(W) p Fo 552 1836 a(2) p 599 1836 a(S) t(W) p Fr 686 1836 a(;) 728 1806 y(there) p 853 1806 a(exist) p 969 1806 a(no) p 1036 1806 a(elemen) o(ts) p Fq 1236 1806 a(F) p Fo 1288 1806 a(2) p Fn 1335 1806 a(F) p Fr(\() p Fn(W) p Fr 1431 1806 a(\)) 728 1866 y(suc) o(h) p 838 1866 a(that) p Fn 944 1866 a(M) p Fl 988 1848 a(2) p Fr 1011 1866 a(\() p Fq(F) p Fr 1069 1866 a(\)) p Fo 1101 1866 a(\025) p Fq 1154 1866 a(K) p Fl 1195 1873 a(4) p Fr 1223 1866 a(log) p Fq 1294 1866 a(L) p Fk 1474 1766 a(\033) p Fq 1520 1836 a(:) p Fr 1778 1836 a(\(4.16\)) 0 1977 y(Note) p 123 1977 a(that) p Fn 234 1977 a(M) p Fl 278 1959 a(2) p Fr 301 1977 a(\() p Fq(F) p Fr 359 1977 a(\)) p Fo 400 1977 a(\024) p Fn 462 1977 a(M) p Fl 506 1959 a(2) p Fr 528 1977 a(\() p Fq(@) p Fr 576 1977 a(\002\() p Fq(F) p Fr 672 1977 a(\)\)) p 730 1977 a(for) p 810 1977 a(eac) o(h) p Fq 925 1977 a(F) p Fo 986 1977 a(2) p Fn 1043 1977 a(F) p Fr(.) p 1124 1977 a(Then,) p 1272 1977 a(w) o(e) p 1349 1977 a(ha) o(v) o(e) p 1466 1977 a(b) o(y) p 1539 1977 a(standard) p 1748 1977 a(P) o(eierls') 0 2038 y(coun) o(ting) p 199 2038 a(argumen) o(t,) p 431 2038 a(\(4.15\)) p 572 2038 a(and) p 667 2038 a(\(4.16\)) p 807 2038 a(that) p Fk 467 2125 a(X) p Ff 399 2234 a(W) p Fm 435 2234 a(2S) r(WnS) r(W) p Fc 597 2222 a(0) p Fq 616 2172 a(P) p Fp 654 2152 a(\016) p Fl 647 2185 a(\003) p Fr 674 2172 a(\() p Fn(W) p Fr 740 2172 a(\)) p Fo 776 2172 a(\024) p Fq 828 2172 a(c) p Fl 849 2179 a(17) p Fr 895 2172 a(exp) o([) p Fo(\000) p Fr(\() p Fq 1046 2139 a(\014) p 1046 2161 V Fr 1049 2206 a(3) p Fo 1092 2172 a(\000) p Fq 1142 2172 a(c) p Fl 1163 2179 a(18) p Fr 1200 2172 a(\)) p Fq(K) p Fl 1260 2179 a(4) p Fr 1289 2172 a(log) p Fq 1360 2172 a(L) p Fr(]) p Fq(:) p Fr 1778 2172 a(\(4.17\)) 73 2336 y(Due) p 175 2336 a(to) p Fn 234 2336 a(J) p Fp 262 2343 a(\016) p Fr 278 2336 a(,) p 307 2336 a(there) p 432 2336 a(can) p 520 2336 a(exist) p 635 2336 a(a) p 676 2336 a(standard) p 879 2336 a(w) o(all) p 980 2336 a(ha) o(ving) p 1136 2336 a(less) p 1226 2336 a(energy) p 1381 2336 a(than) p 1495 2336 a(w) o(e) p 1566 2336 a(exp) q(ect) p 1720 2336 a(from) p 1834 2336 a(the) 0 2396 y(size) p 96 2396 a(of) p 155 2396 a(it.) p 233 2396 a(F) l(or) p 324 2396 a(this) p 423 2396 a(reason,) p 593 2396 a(w) o(e) p 668 2396 a(will) p 764 2396 a(estimate) p Fk 963 2359 a(P) p Ff 1015 2411 a(W) p Fm 1052 2411 a(2) o(S) r(W) p Fc 1134 2398 a(0) p Fq 1155 2396 a(P) p Fp 1193 2378 a(\016) p Fl 1186 2409 a(\003) p Fr 1213 2396 a(\() p Fn(W) p Fr 1279 2396 a(\)) p 1321 2396 a(in) p 1381 2396 a(separate) p 1577 2396 a(four) p 1682 2396 a(cases.) p 1834 2396 a(W) l(e) 0 2457 y(de\014ne) p Fo 233 2567 a(S) t(W) p Fl 320 2574 a(1) p Fr 354 2567 a(=) p Fo 406 2567 a(f) p Fn(W) p Fo 494 2567 a(2) p 541 2567 a(S) t(W) p Fm 628 2546 a(0) p Fr 640 2567 a(;) p 662 2567 a(\(\010) p Fl 716 2574 a(0) p Fr 736 2567 a(\() p Fo(f) p Fq(W) p Fo 833 2567 a(g) p Fr(\)\)) p Fl 896 2546 a(5) p Fq 915 2567 a(=) p Fr(\010) p Fl 974 2574 a(1) p Fr 994 2567 a(\() p Fo(f) p Fq(W) p Fo 1091 2567 a(g) p Fr(\)) p Fo 1149 2567 a(\024) p Fr 1201 2567 a(1) p 1242 2567 a(for) p 1316 2567 a(all) p Fq 1384 2567 a(W) p Fo 1451 2567 a(2) p Fn 1498 2567 a(W) p Fo 1545 2567 a(g) p Fq(;) p Fr 1778 2567 a(\(4.18\)) 0 2677 y(whic) o(h) p 138 2677 a(corresp) q(onds) p 405 2677 a(to) p 463 2677 a(the) p 546 2677 a(\014rst) p 645 2677 a(case) p 747 2677 a(where) p 887 2677 a(the) p 970 2677 a(energy) p 1124 2677 a(of) p 1179 2677 a(eac) o(h) p 1287 2677 a(standard) p 1490 2677 a(w) o(all) p 1590 2677 a(is) p 1638 2677 a(prop) q(ortional) 0 2737 y(to) p 60 2737 a(the) p 144 2737 a(size) p 236 2737 a(of) p 292 2737 a(it.) 927 2947 y(21) p 90 rotate dyy eop %%Page: 22 22 22 21 bop Fr 73 274 a(Let) p Fn 164 274 a(W) p Fo 233 274 a(2) p 286 274 a(S) t(W) p Fr 373 274 a(\() p Fo(\000) p Fq(L) p Fm 464 256 a(0) p Fq 476 274 a(;) p Fr 498 274 a(2) p Fq(l) p Fr 538 274 a(\)) p 576 274 a(and) p 674 274 a(let) p Fq 748 274 a(z) p Fo 793 274 a(2) p Fn 845 274 a(Z) p Fr 881 274 a(.) p 924 274 a(F) l(or) p 1014 274 a(eac) o(h) p Fq 1128 274 a(W) p Fo 1200 274 a(2) p Fn 1253 274 a(W) p Fr 1299 274 a(,) p 1336 274 a(w) o(e) p 1412 274 a(will) p 1507 274 a(denote) p 1668 274 a(b) o(y) p Fo 1739 274 a(B) p Fr 1774 274 a(\() p Fq(W) o(;) p 1860 274 a(z) p Fr 1885 274 a(\)) 0 334 y(the) p 83 334 a(collection) p 299 334 a(of) p 354 334 a(connected) p 581 334 a(comp) q(onen) o(ts) p 848 334 a(of) p Fq 903 334 a(W) p Fo 965 334 a(\\) p Fr 1008 334 a(H\() p Fq(z) p Fr 1089 334 a(\)) p 1122 334 a(if) p 1166 334 a(it) p 1214 334 a(is) p 1262 334 a(not) p 1348 334 a(empt) o(y) l(.) p 1512 334 a(W) l(e) p 1595 334 a(de\014ne) p 1735 334 a(for) p 1809 334 a(eac) o(h) p Fq 0 394 a(W) p Fo 67 394 a(2) p Fn 114 394 a(W) p Fr 161 394 a(,) p Fq 229 560 a(\032) p Fr(\() p Fq(W) o(;) p 340 560 a(z) p Fr 365 560 a(\)) p 397 560 a(=) p Fk 449 458 a(8) 449 503 y(<) 449 593 y(:) p Fr 514 531 a(inf) p Fk 573 476 a(n) p Fn 611 497 a(M) p Fl 655 479 a(1) p Fr 678 497 a(\() p Fq(B) p Fo 737 497 a(n) p Fq(@) p Fr 791 497 a(\003\)) p 611 520 232 2 v Fn 655 565 a(M) p Fl 699 551 a(1) p Fr 722 565 a(\() p Fq(B) p Fr 781 565 a(\)) 848 531 y(;) p Fq 870 531 a(B) p Fo 923 531 a(2) p 970 531 a(B) p Fr 1005 531 a(\() p Fq(W) o(;) p 1091 531 a(z) p Fr 1116 531 a(\)) p Fk 1135 476 a(o) p Fr 1208 531 a(if) p Fq 1253 531 a(W) p Fo 1317 531 a(\\) p Fr 1361 531 a(H\() p Fq(z) p Fr 1442 531 a(\)) p Fo 1474 531 a(6) p Fr(=) p Fo 1526 531 a(;) p Fq(;) p Fo 514 620 a(1) p Fr 1208 620 a(otherwise) p Fq(;) p Fr 1778 560 a(\(4.19\)) 0 727 y(and) p 95 727 a(de\014ne) p Fq 661 837 a(\032) p Fr(\() p Fn(W) p Fq 752 837 a(;) p 774 837 a(z) p Fr 799 837 a(\)) p 835 837 a(=) p 905 837 a(inf) p Fp 887 868 a(W) p Fm 925 868 a(2) p Ff(W) p Fq 990 837 a(\032) p Fr(\() p Fq(W) o(;) p 1101 837 a(z) p Fr 1126 837 a(\)) p Fq(:) p Fr 1778 837 a(\(4.20\)) 0 966 y(By) p 80 966 a(the) p 167 966 a(de\014nition) p 387 966 a(of) p Fn 446 966 a(J) p Fp 474 973 a(\016) p Fr 490 966 a(,) p 524 966 a(w) o(e) p 599 966 a(can) p 692 966 a(see) p 774 966 a(that) p Fn 883 966 a(W) p Fo 952 966 a(2) p 1005 966 a(S) t(W) p Fl 1092 973 a(1) p Fr 1131 966 a(if) p Fq 1179 966 a(\032) p Fr(\() p Fn(W) p Fq 1270 966 a(;) p 1292 966 a(z) p Fr 1317 966 a(\)) p Fo 1358 966 a(\025) p Fr 1416 966 a(1) p Fq(=) p Fr(5) p 1509 966 a(for) p 1587 966 a(all) p Fq 1658 966 a(z) p Fo 1702 966 a(2) p Fn 1755 966 a(Z) p Fr 1807 966 a(with) p Fo 0 1026 a(\000) p Fq(L) p Fm 72 1008 a(00) p Fo 107 1026 a(\024) p Fq 160 1026 a(z) p 198 1026 a(<) p Fr 250 1026 a(0.) p 310 1026 a(Hence,) p 468 1026 a(w) o(e) p 540 1026 a(will) p 632 1026 a(consider) p Fo 201 1136 a(S) t(W) p Fm 288 1115 a(00) p Fr 323 1136 a(=) p Fo 375 1136 a(f) p Fn(W) p Fo 463 1136 a(2) p 510 1136 a(S) t(W) p Fm 597 1115 a(0) p Fr 609 1136 a(;) p Fq 631 1136 a(\032) p Fr(\() p Fn(W) p Fq 722 1136 a(;) p 744 1136 a(z) p Fr 769 1136 a(\)) p Fq 804 1136 a(<) p Fr 856 1136 a(1) p Fq(=) p Fr(5) p 946 1136 a(for) p 1020 1136 a(some) p Fq 1142 1136 a(z) p Fo 1181 1136 a(2) p Fn 1228 1136 a(Z) p Fr 1278 1136 a(with) p Fo 1389 1136 a(\000) p Fq(L) p Fm 1461 1118 a(00) p Fo 1496 1136 a(\024) p Fq 1548 1136 a(z) p 1587 1136 a(<) p Fr 1639 1136 a(0) p Fo(g) p Fq(:) p Fg 73 1246 a(Lemma) p 272 1246 a(4.3.) p Fd 380 1246 a(F) l(or) p 471 1246 a(e) n(ach) p Fn 580 1246 a(W) p Fo 644 1246 a(2) p 691 1246 a(S) t(W) p Fr 778 1246 a(\() p Fo(\000) p Fq(L) p Fm 869 1228 a(0) p Fq 881 1246 a(;) p Fr 903 1246 a(2) p Fq(l) p Fr 943 1246 a(\)) p Fd(,) p 994 1246 a(we) p 1066 1246 a(have) p 1178 1246 a(the) p 1259 1246 a(fol) r(lowing) p 1466 1246 a(pr) n(op) n(erties:) 43 1348 y(\(i\)) p 122 1348 a(If) p Fq 172 1348 a(\032) p Fr(\() p Fn(W) p Fq 263 1348 a(;) p 285 1348 a(z) p Fl 308 1355 a(0) p Fr 330 1348 a(\)) p Fq 363 1348 a(<) p Fr 415 1348 a(1) p Fq(=) p Fr(5) p Fd 504 1348 a(for) p 580 1348 a(some) p Fq 704 1348 a(z) p Fl 727 1355 a(0) p Fo 760 1348 a(2) p Fn 807 1348 a(Z) p Fd 843 1348 a(,) p 872 1348 a(then) p 979 1348 a(ther) n(e) p 1099 1348 a(exists) p 1231 1348 a(a) p 1272 1348 a(unique) p 1428 1348 a(standar) n(d) p 1625 1348 a(wal) r(l) p Fq 1726 1348 a(W) p Fl 1772 1355 a(0) p Fo 1805 1348 a(2) p Fn 1852 1348 a(W) p Fd 122 1408 a(such) p 233 1408 a(that) p Fq 332 1408 a(\032) p Fr(\() p Fq(W) p Fl 422 1415 a(0) p Fq 442 1408 a(;) p 464 1408 a(z) p Fr 489 1408 a(\)) p Fq 522 1408 a(<) p Fr 574 1408 a(1) p Fq(=) p Fr(5) p Fd 664 1408 a(whenever) p Fq 877 1408 a(\032) p Fr(\() p Fn(W) p Fq 967 1408 a(;) p 989 1408 a(z) p Fr 1014 1408 a(\)) p Fq 1050 1408 a(<) p Fr 1102 1408 a(1) p Fq(=) p Fr(5) p Fd(.) 28 1510 y(\(ii\)) p 122 1510 a(F) l(or) p 213 1510 a(any) p Fq 306 1510 a(W) p Fo 373 1510 a(2) p Fn 420 1510 a(W) p Fo 467 1510 a(nf) p Fq(W) p Fl 563 1517 a(0) p Fo 585 1510 a(g) p Fd(,) p Fr 643 1510 a(\(\010) p Fl 697 1517 a(0) p Fr 717 1510 a(\() p Fo(f) p Fq(W) p Fo 814 1510 a(g) p Fr(\)\)) p Fl 877 1492 a(5) p Fk 896 1470 a(\016) p Fr 925 1510 a(\010) p Fl 960 1517 a(1) p Fr 980 1510 a(\() p Fo(f) p Fq(W) p Fo 1077 1510 a(g) p Fr(\)) p Fo 1134 1510 a(\024) p Fr 1187 1510 a(1) p Fd 1228 1510 a(holds.) p Fq 73 1612 a(P) p 111 1612 a(r) q(oof) p Fr 209 1612 a(.) p 249 1612 a(W) l(e) p 334 1612 a(will) p 428 1612 a(\014rst) p 529 1612 a(pro) o(v) o(e) p 662 1612 a(\(i\).) p 751 1612 a(Let) p Fq 840 1612 a(W) p Fo 908 1612 a(2) p Fn 957 1612 a(W) p Fr 1024 1612 a(and) p 1120 1612 a(let) p Fq 1192 1612 a(z) p Fl 1215 1619 a(0) p Fo 1249 1612 a(2) p Fn 1298 1612 a(Z) p Fr 1349 1612 a(b) q(e) p 1416 1612 a(some) p 1539 1612 a(in) o(teger) p 1702 1612 a(suc) o(h) p 1813 1612 a(that) p Fq 0 1672 a(\032) p Fr(\() p Fq(W) o(;) p 111 1672 a(z) p Fl 134 1679 a(0) p Fr 153 1672 a(\)) p Fq 186 1672 a(<) p Fr 238 1672 a(1) p Fq(=) p Fr(5.) p 346 1672 a(Then,) p 487 1672 a(w) o(e) p 559 1672 a(can) p 648 1672 a(see) p 727 1672 a(b) o(y) p 795 1672 a(the) p 879 1672 a(de\014nition) p 1096 1672 a(of) p Fq 1151 1672 a(\032) p Fr 1192 1672 a(and) p 1287 1672 a(\(A.11\)) p 1440 1672 a(that) p Fn 253 1782 a(M) p Fl 297 1761 a(1) p Fr 320 1782 a(\() p Fq(W) p Fo 403 1782 a(\\) p Fr 447 1782 a(H\() p Fq(z) p Fl 526 1789 a(0) p Fr 545 1782 a(\)\)) p Fo 597 1782 a(\025) p Fr 650 1782 a(8) p Fq(L) p Fr 805 1782 a(and) p Fn 981 1782 a(M) p Fl 1025 1761 a(1) p Fr 1048 1782 a(\() p Fq(W) p Fo 1130 1782 a(\\) p Fr 1175 1782 a(H\() p Fq(z) p Fl 1254 1789 a(0) p Fr 1273 1782 a(\)) p Fo 1303 1782 a(\\) p Fq 1347 1782 a(@) p Fr 1376 1782 a(\003\)) p Fo 1442 1782 a(\025) p Fr 1495 1782 a(6) p Fq(L:) p Fr 1778 1782 a(\(4.21\)) 0 1892 y(Hence,) p 162 1892 a(if) p 210 1892 a(there) p 337 1892 a(exist) p Fq 456 1892 a(W) p Fl 502 1899 a(1) p Fo 540 1892 a(2) p Fn 592 1892 a(W) p Fq 639 1892 a(;) p 683 1892 a(W) p Fl 729 1899 a(2) p Fo 767 1892 a(2) p Fn 819 1892 a(W) p Fq 866 1892 a(;) p 910 1892 a(z) p Fl 933 1899 a(1) p Fo 971 1892 a(2) p Fn 1023 1892 a(Z) p Fr 1076 1892 a(and) p Fq 1174 1892 a(z) p Fl 1197 1899 a(2) p Fo 1235 1892 a(2) p Fn 1287 1892 a(Z) p Fr 1339 1892 a(suc) o(h) p 1452 1892 a(that) p Fq 1560 1892 a(\032) p Fr(\() p Fq(W) p Fl 1650 1899 a(1) p Fq 1670 1892 a(;) p 1692 1892 a(z) p Fl 1715 1899 a(1) p Fr 1735 1892 a(\)) p Fq 1772 1892 a(<) p Fr 1829 1892 a(1) p Fq(=) p Fr(5) 0 1952 y(and) p Fq 98 1952 a(\032) p Fr(\() p Fq(W) p Fl 188 1959 a(2) p Fq 208 1952 a(;) p 230 1952 a(z) p Fl 253 1959 a(2) p Fr 272 1952 a(\)) p Fq 309 1952 a(<) p Fr 366 1952 a(1) p Fq(=) p Fr(5,) p 472 1952 a(w) o(e) p 547 1952 a(can) p 639 1952 a(see) p 721 1952 a(from) p 839 1952 a(\(4.21\)) p 982 1952 a(that) p Fq 1091 1952 a(\031) p Fr 1121 1952 a(\() p Fq(W) p Fl 1186 1959 a(1) p Fr 1205 1952 a(\)) p Fo 1237 1952 a(\\) p Fq 1283 1952 a(\031) p Fr 1313 1952 a(\() p Fq(W) p Fl 1378 1959 a(2) p Fr 1397 1952 a(\)) p Fo 1435 1952 a(6) p Fr(=) p Fo 1491 1952 a(;) p Fr(.) p 1560 1952 a(By) p 1639 1952 a(this) p 1737 1952 a(and) p 1834 1952 a(the) 0 2012 y(de\014nition) p 217 2012 a(of) p 272 2012 a(\(standard\)) p 514 2012 a(w) o(alls,) p 648 2012 a(it) p 697 2012 a(holds) p 825 2012 a(that) p Fq 930 2012 a(W) p Fl 976 2019 a(1) p Fr 1010 2012 a(=) p Fq 1062 2012 a(W) p Fl 1108 2019 a(2) p Fr 1127 2012 a(.) 73 2072 y(W) l(e) p 157 2072 a(will) p 249 2072 a(next) p 359 2072 a(pro) o(v) o(e) p 490 2072 a(\(ii\).) p 591 2072 a(Note) p 709 2072 a(that) p 814 2072 a(for) p 889 2072 a(eac) o(h) p Fq 998 2072 a(\016) p 1036 2072 a(>) p Fr 1088 2072 a(0,) 254 2196 y(\010) p Fp 289 2203 a(\016) p Fr 308 2196 a(\() p Fo(f) p Fq(W) p Fo 405 2196 a(g) p Fr(\)) p 490 2196 a(=) p Fq 569 2196 a(e) p Fl 592 2176 a(8) p Fp(\014) r(L) p Fj 656 2164 a(2) p Fr 683 2196 a(exp) p Fk 757 2141 a(h) p Fo 781 2196 a(\000) p Fr(2) p Fq(\014) p Fn 875 2196 a(M) p Fl 918 2176 a(2) p Fk 941 2156 a(\000) p Fr 964 2196 a(\000\() p Fo(f) p Fq(W) p Fo 1091 2196 a(g) p Fr(\)) p Fo(n) p Fr(cyl) o(\(\003) p Fq(;) p Fo 1296 2196 a(\000) p Fq(L) p Fm 1368 2176 a(00) p Fq 1388 2196 a(;) p Fr 1410 2196 a(0\)) p Fk 1453 2156 a(\001) p Fo 862 2302 a(\000) p Fr(2) p Fq(\014) s(\016) p Fn 980 2302 a(M) p Fl 1023 2282 a(2) p Fk 1046 2262 a(\000) p Fr 1068 2302 a(\000\() p Fo(f) p Fq(W) p Fo 1195 2302 a(g) p Fr(\)) p Fo 1250 2302 a(\\) p Fr 1295 2302 a(cyl) o(\(\003) p Fq(;) p Fo 1431 2302 a(\000) p Fq(L) p Fm 1503 2282 a(00) p Fq 1524 2302 a(;) p Fr 1546 2302 a(0\)) p Fk 1589 2262 a(\001) 1612 2247 y(i) p Fq 1635 2302 a(:) p Fr 1778 2389 a(\(4.22\)) 0 2499 y(By) p 77 2499 a(the) p 161 2499 a(de\014nition) p 377 2499 a(of) p Fq 433 2499 a(\032) p Fr(,) p 488 2499 a(\(i\)) p 556 2499 a(and) p 650 2499 a(\(4.22\),) p 805 2499 a(w) o(e) p 877 2499 a(ha) o(v) o(e) p 989 2499 a(that) p 1095 2499 a(for) p 1169 2499 a(an) o(y) p Fq 1261 2499 a(W) p Fo 1328 2499 a(2) p Fn 1375 2499 a(W) p Fo 1422 2499 a(nf) p Fq(W) p Fl 1518 2506 a(0) p Fo 1541 2499 a(g) p Fr 313 2609 a(\(\010) p Fl 367 2616 a(0) p Fr 387 2609 a(\() p Fo(f) p Fq(W) p Fo 484 2609 a(g) p Fr(\)\)) p Fl 547 2588 a(5) p Fo 608 2609 a(\024) p Fr 688 2609 a(exp) p Fk 763 2568 a(\002) p Fo 783 2609 a(\000) p Fr(10) p Fq(\014) p Fn 901 2609 a(M) p Fl 945 2588 a(2) p Fk 968 2568 a(\000) p Fr 991 2609 a(\() p Fq(W) p Fo 1063 2609 a(n) p Fq(\031) p Fr 1118 2609 a(\() p Fq(W) p Fr 1190 2609 a(\)\)) p Fo(n) p Fr(cyl) m(\(\003) p Fq(;) p Fo 1387 2609 a(\000) p Fq(L) p Fm 1459 2588 a(00) p Fq 1480 2609 a(;) p Fr 1502 2609 a(0\)) p Fk 1545 2568 a(\001\003) p Fo 608 2691 a(\024) p Fq 688 2691 a(e) p Fl 711 2671 a(8) p Fp(\014) r(L) p Fj 775 2659 a(2) p Fr 801 2691 a(exp[) p Fo(\000) p Fr(2) p Fq(\014) p Fn 984 2691 a(M) p Fl 1027 2671 a(2) p Fr 1050 2691 a(\(\000\() p Fo(f) p Fq(W) p Fo 1196 2691 a(g) p Fr(\)\)]) 608 2764 y(=) p 688 2764 a(\010) p Fl 723 2771 a(1) p Fr 743 2764 a(\() p Fo(f) p Fq(W) p Fo 840 2764 a(g) p Fr(\)) p Fq(:) p Fr 1778 2764 a(\(4.23\)) 927 2947 y(22) p 90 rotate dyy eop %%Page: 23 23 23 22 bop Fr 73 274 a(W) l(e) p 157 274 a(de\014ne) p Fo 276 395 a(S) t(W) p Fl 363 402 a(2) p Fr 397 395 a(=) p Fk 449 324 a(\032) p Fn 486 395 a(W) p Fo 550 395 a(2) p 597 395 a(S) t(W) p Fm 684 374 a(00) p Fo 705 395 a(nS) t(W) p Fl 817 402 a(1) p Fr 837 395 a(;) 880 364 y(there) p 1004 364 a(exist) p 1120 364 a(some) p Fq 1242 364 a(W) p Fo 1309 364 a(2) p Fn 1356 364 a(W) p Fo 1403 364 a(nf) p Fq(W) p Fl 1499 371 a(0) p Fo 1521 364 a(g) p Fr 880 424 a(with) p Fn 991 424 a(M) p Fl 1035 406 a(2) p Fr 1058 424 a(\() p Fq(W) p Fr 1130 424 a(\)) p Fo 1162 424 a(\025) p Fq 1215 424 a(K) p Fl 1256 431 a(5) p Fr 1284 424 a(log) p Fq 1356 424 a(L) p Fk 1567 324 a(\033) p Fq 1612 395 a(;) p Fr 0 528 a(where) p Fq 141 528 a(W) p Fl 187 535 a(0) p Fr 223 528 a(is) p 272 528 a(the) p 356 528 a(unique) p 514 528 a(standard) p 717 528 a(w) o(all) p 819 528 a(in) p 876 528 a(\(i\)) p 943 528 a(of) p 999 528 a(Lemma) p 1173 528 a(4.3) p 1251 528 a(and) p Fq 1346 528 a(K) p Fl 1387 535 a(5) p Fq 1421 528 a(>) p Fr 1473 528 a(0) p 1513 528 a(is) p 1562 528 a(a) p 1603 528 a(large) p 1722 528 a(constan) o(t) 0 588 y(to) p 60 588 a(b) q(e) p 127 588 a(sp) q(eci\014ed) p 324 588 a(later.) p Fo 458 588 a(S) t(W) p Fl 545 595 a(2) p Fr 582 588 a(corresp) q(onds) p 850 588 a(to) p 910 588 a(the) p 994 588 a(second) p 1152 588 a(case.) p 1276 588 a(In) p 1337 588 a(the) p 1422 588 a(same) p 1544 588 a(w) o(a) o(y) p 1644 588 a(as) p 1704 588 a(in) p 1761 588 a(\(3.27\)-) 0 648 y(\(3.29\),) p 154 648 a(w) o(e) p 226 648 a(can) p 316 648 a(see) p 395 648 a(that) p Fo 609 752 a(j) p Fr(h) p Fm 650 732 a(\003) p Fr 670 752 a(\() p Fn(W) p Fo 736 752 a(nf) p Fq(W) p Fl 832 759 a(0) p Fo 854 752 a(g) p Fr(\)) p Fo(j) p 926 752 a(\024) p Fr 978 752 a(\() p Fq(K) p Fl 1038 759 a(5) p Fr 1067 752 a(log) p Fq 1138 752 a(L) p Fr(\)) p Fl 1190 732 a(2) p Fr 1778 752 a(\(4.24\)) 0 857 y(for) p Fo 75 857 a(\003) p Fr 113 857 a(=) p 165 857 a(+) p 219 857 a(and) p Fo 314 857 a(\000) p Fr 369 857 a(if) p Fn 414 857 a(W) p Fo 477 857 a(2) p 524 857 a(S) t(W) p Fm 612 836 a(00) p Fo 633 857 a(n) p Fr(\() p Fo(S) t(W) p Fl 764 864 a(1) p Fo 795 857 a([) p 839 857 a(S) t(W) p Fl 926 864 a(2) p Fr 946 857 a(\).) p 1000 857 a(W) l(e) p 1084 857 a(de\014ne) p Fq 305 961 a(z) p Fl 328 968 a(min) p Fr 403 961 a(=) p Fq 455 961 a(z) p Fl 478 968 a(min) p Fr 538 961 a(\() p Fn(W) p Fr 604 961 a(\)) p 640 961 a(=) p 691 961 a(min) p Fo 773 961 a(f) p Fq(z) p Fo 836 961 a(2) p Fn 883 961 a(Z) p Fr 920 961 a(;) p Fq 941 961 a(\032) p Fr(\() p Fq(W) p Fl 1031 968 a(0) p Fq 1048 961 a(;) p 1070 961 a(z) p Fr 1095 961 a(\)) p Fq 1128 961 a(<) p Fr 1180 961 a(1) p Fq(=) p Fr(5) p Fq(;) p 1291 961 a(z) p Fo 1330 961 a(\025) p 1382 961 a(\000) p Fq(L) p Fm 1454 940 a(00) p Fo 1475 961 a(g) p Fq(;) p Fr 1778 961 a(\(4.25\)) 0 1065 y(for) p 75 1065 a(eac) o(h) p Fn 184 1065 a(W) p Fo 248 1065 a(2) p 295 1065 a(S) t(W) p Fm 382 1044 a(00) p Fr 403 1065 a(.) p 439 1065 a(W) l(e) p 523 1065 a(de\014ne) p Fo 383 1169 a(S) t(W) p Fl 470 1176 a(3) p Fr 504 1169 a(=) p Fo 556 1169 a(f) p Fn(W) p Fo 644 1169 a(2) p 691 1169 a(S) t(W) p Fm 778 1148 a(00) p Fo 800 1169 a(n) p Fr(\() p Fo(S) t(W) p Fl 931 1176 a(1) p Fo 961 1169 a([) p 1006 1169 a(S) t(W) p Fl 1093 1176 a(2) p Fr 1113 1169 a(\);) p Fq 1154 1169 a(z) p Fl 1177 1176 a(min) p Fr 1237 1169 a(\() p Fn(W) p Fr 1303 1169 a(\)) p Fo 1339 1169 a(\024) p 1391 1169 a(\000) p Fq(l) q(=) p Fr(2) p Fo(g) p Fr 0 1273 a(and) p Fo 377 1333 a(S) t(W) p Fl 464 1340 a(4) p Fr 497 1333 a(=) p Fo 549 1333 a(f) p Fn(W) p Fo 638 1333 a(2) p 685 1333 a(S) t(W) p Fm 772 1312 a(00) p Fo 793 1333 a(n) p Fr(\() p Fo(S) t(W) p Fl 924 1340 a(1) p Fo 955 1333 a([) p 999 1333 a(S) t(W) p Fl 1087 1340 a(2) p Fr 1106 1333 a(\);) p Fq 1147 1333 a(z) p Fl 1170 1340 a(min) p Fr 1231 1333 a(\() p Fn(W) p Fr 1296 1333 a(\)) p Fq 1332 1333 a(>) p Fo 1384 1333 a(\000) p Fq(l) q(=) p Fr(2) p Fo(g) p Fq(;) p Fr 0 1418 a(whic) o(h) p 140 1418 a(corresp) q(onds) p 407 1418 a(to) p 467 1418 a(the) p 551 1418 a(third) p 673 1418 a(and) p 767 1418 a(fourth) p 915 1418 a(cases,) p 1051 1418 a(resp) q(ectiv) o(ely) l(.) 73 1478 y(First,) p 206 1478 a(w) o(e) p 277 1478 a(claim) p 407 1478 a(that) p 513 1478 a(for) p 588 1478 a(an) o(y) p Fn 680 1478 a(W) p Fo 743 1478 a(2) p 790 1478 a(S) t(W) p Fm 878 1457 a(00) p Fo 899 1478 a(nS) t(W) p Fl 1011 1485 a(1) p Fr 1031 1478 a(,) p Fn 685 1582 a(M) p Fl 729 1562 a(1) p Fr 752 1582 a(\() p Fq(W) p Fl 817 1589 a(0) p Fo 848 1582 a(\\) p Fr 892 1582 a(H\() p Fq(z) p Fr 973 1582 a(\)\)) p Fq 1024 1582 a(>) p Fr 1076 1582 a(2) p Fq(L) p Fr 1778 1582 a(\(4.26\)) 0 1686 y(holds) p 129 1686 a(for) p 205 1686 a(all) p 274 1686 a(negativ) o(e) p 468 1686 a(in) o(teger) p Fq 631 1686 a(z) p Fr 673 1686 a(with) p Fq 786 1686 a(z) p Fo 827 1686 a(\025) p Fq 882 1686 a(z) p Fl 905 1693 a(min) p Fr 966 1686 a(.) p 1005 1686 a(T) l(o) p 1078 1686 a(see) p 1159 1686 a(this,) p 1269 1686 a(assume) p 1439 1686 a(that) p Fn 1546 1686 a(W) p Fo 1612 1686 a(2) p 1662 1686 a(S) t(W) p Fm 1749 1665 a(00) p Fo 1770 1686 a(nS) t(W) p Fl 1883 1693 a(1) p Fr 0 1747 a(and) p Fn 93 1747 a(M) p Fl 137 1728 a(1) p Fr 160 1747 a(\() p Fq(W) p Fl 225 1754 a(0) p Fo 251 1747 a(\\) p Fr 291 1747 a(H\() p Fq(z) p Fl 370 1754 a(0) p Fr 389 1747 a(\)\)) p Fo 441 1747 a(\024) p Fr 493 1747 a(2) p Fq(L) p Fr 565 1747 a(for) p 637 1747 a(some) p 758 1747 a(negativ) o(e) p 948 1747 a(in) o(teger) p Fq 1107 1747 a(z) p Fl 1130 1754 a(0) p Fr 1164 1747 a(with) p Fq 1273 1747 a(z) p Fl 1296 1754 a(0) p Fq 1329 1747 a(>) p 1381 1747 a(z) p Fl 1404 1754 a(min) p Fr 1464 1747 a(.) p 1499 1747 a(Then,) p 1638 1747 a(w) o(e) p 1708 1747 a(will) p 1798 1747 a(sho) o(w) 0 1807 y(that) p Fn 349 1927 a(M) p Fl 393 1907 a(2) p Fk 424 1857 a(\022\032) p Fq 498 1927 a(x) p Fo 540 1927 a(2) p Fn 587 1927 a(R) p Fl 626 1907 a(3) p Fr 643 1927 a(;) p Fq 685 1897 a(x) p Fo 727 1897 a(2) p Fq 774 1897 a(w) p Fr 826 1897 a(for) p 901 1897 a(some) p 1023 1897 a(face) p Fq 1122 1897 a(w) p Fo 1172 1897 a(2) p Fr 1219 1897 a(\000\() p Fo(f) p Fq(W) p Fl 1339 1904 a(0) p Fo 1359 1897 a(g) p Fr(\)) 685 1957 y(suc) o(h) p 795 1957 a(that) p Fn 901 1957 a(M) p Fl 945 1939 a(2) p Fr 968 1957 a(\() p Fq(\031) p Fr 1017 1957 a(\() p Fq(w) p Fr 1072 1957 a(\)\)) p 1123 1957 a(=) p 1175 1957 a(1) p Fk 1424 1857 a(\033\023) p Fo 1509 1927 a(\000) p Fr 1559 1927 a(4) p Fq(L) p Fl 1616 1907 a(2) p Fo 398 2034 a(\025) p Fr 451 2034 a(4) p Fq(L) p Fl 508 2013 a(2) p Fq 528 2034 a(;) p Fr 1778 2034 a(\(4.27\)) 0 2138 y(whic) o(h) p 134 2138 a(together) p 321 2138 a(with) p 427 2138 a(the) p 506 2138 a(de\014nitions) p 736 2138 a(of) p Fq 787 2138 a(W) p Fl 833 2145 a(0) p Fr 863 2138 a(and) p Fq 953 2138 a(z) p Fl 976 2145 a(min) p Fr 1047 2138 a(implies) p 1208 2138 a(that) p 1308 2138 a(\(\010) p Fl 1362 2145 a(0) p Fr 1382 2138 a(\() p Fo(f) p Fq(W) p Fl 1472 2145 a(0) p Fo 1492 2138 a(g) p Fr(\)\)) p Fl 1555 2120 a(5) p Fk 1574 2098 a(\016) p Fr 1603 2138 a(\010) p Fl 1638 2145 a(1) p Fr 1658 2138 a(\() p Fo(f) p Fq(W) p Fl 1748 2145 a(0) p Fo 1768 2138 a(g) p Fr(\)) p Fo 1825 2138 a(\024) p Fr 1878 2138 a(1) 0 2198 y(\(see) p 95 2198 a(\(4.22\)) p 234 2198 a(and) p 326 2198 a(\(4.23\)\).) p 505 2198 a(This) p 614 2198 a(together) p 804 2198 a(with) p 912 2198 a(\(ii) o(\)) p 991 2198 a(of) p 1044 2198 a(Lemma) p 1216 2198 a(4.3) p 1292 2198 a(sho) o(ws) p 1430 2198 a(that) p Fn 1533 2198 a(W) p Fo 1597 2198 a(2) p 1644 2198 a(S) t(W) p Fl 1731 2205 a(1) p Fr 1751 2198 a(,) p 1779 2198 a(whic) o(h) 0 2258 y(con) o(tradicts) p Fn 246 2258 a(W) p Fo 310 2258 a(2) p 357 2258 a(S) t(W) p Fm 444 2237 a(00) p Fo 465 2258 a(nS) t(W) p Fl 578 2265 a(1) p Fr 597 2258 a(.) p 631 2258 a(Th) o(us,) p 764 2258 a(w) o(e) p 832 2258 a(obtained) p 1028 2258 a(\(4.26\).) p 1186 2258 a(W) l(e) p 1265 2258 a(will) p 1353 2258 a(sho) o(w) p 1469 2258 a(\(4.27\)) p 1605 2258 a(assuming) p 1813 2258 a(that) p Fn 0 2319 a(W) p Fo 66 2319 a(2) p 116 2319 a(S) t(W) p Fm 203 2298 a(00) p Fo 224 2319 a(nS) t(W) p Fl 337 2326 a(1) p Fr 374 2319 a(and) p Fn 470 2319 a(M) p Fl 515 2300 a(1) p Fr 537 2319 a(\() p Fq(W) p Fl 602 2326 a(0) p Fo 634 2319 a(\\) p Fr 679 2319 a(H\() p Fq(z) p Fl 758 2326 a(0) p Fr 777 2319 a(\)\)) p Fo 832 2319 a(\024) p Fr 887 2319 a(2) p Fq(L) p Fr 962 2319 a(for) p 1038 2319 a(some) p 1162 2319 a(negativ) o(e) p 1356 2319 a(in) o(teger) p Fq 1519 2319 a(z) p Fl 1542 2326 a(0) p Fr 1579 2319 a(with) p Fq 1692 2319 a(z) p Fl 1715 2326 a(0) p Fq 1751 2319 a(>) p 1805 2319 a(z) p Fl 1828 2326 a(min) p Fr 1889 2319 a(.) 0 2379 y(Note) p 120 2379 a(that) p 228 2379 a(there) p 355 2379 a(exists) p 492 2379 a(a) p 535 2379 a(unique) p Fq 695 2379 a(B) p Fl 732 2386 a(0) p Fo 770 2379 a(2) p 821 2379 a(B) p Fr 856 2379 a(\() p Fq(W) p Fl 921 2386 a(0) p Fq 940 2379 a(;) p 962 2379 a(z) p Fl 985 2386 a(min) p Fr 1045 2379 a(\)) p 1082 2379 a(suc) o(h) p 1195 2379 a(that) p Fn 1303 2379 a(M) p Fl 1347 2361 a(1) p Fr 1369 2379 a(\() p Fq(B) p Fl 1425 2386 a(0) p Fo 1445 2379 a(n) p Fq(@) p Fr 1499 2379 a(\003\)) p Fk 1552 2338 a(\016) p Fn 1580 2379 a(M) p Fl 1624 2361 a(1) p Fr 1647 2379 a(\() p Fq(B) p Fl 1703 2386 a(0) p Fr 1723 2379 a(\)) p Fq 1760 2379 a(<) p Fr 1816 2379 a(1) p Fq(=) p Fr(5.) 0 2439 y(F) l(rom) p 128 2439 a(this) p 223 2439 a(and) p 318 2439 a(\(A.12\),) p 485 2439 a(w) o(e) p 556 2439 a(ha) o(v) o(e) p 669 2439 a(that) p Fn 775 2439 a(M) p Fl 819 2421 a(2) p Fr 841 2439 a(\() s(^) p Fq 860 2439 a(\031) p Fr 890 2439 a(\() p Fq(B) p Fl 946 2446 a(0) p Fr 965 2439 a(\)\)) p Fo 1017 2439 a(\025) p Fr 1070 2439 a(3\(4) p Fq(L) p Fl 1170 2421 a(2) p Fr 1190 2439 a(\)) p Fq(=) p Fr(4.) p 1293 2439 a(Therefore,) p 1528 2439 a(w) o(e) p 1600 2439 a(ha) o(v) o(e) p 1712 2439 a(that) p Fn 676 2565 a(M) p Fl 720 2545 a(2) p Fr 743 2565 a(\() s(^) p Fq 762 2565 a(\031) p Fr 791 2565 a(\() p Fq(W) p Fl 856 2572 a(0) p Fr 876 2565 a(\)\)) p Fo 928 2565 a(\025) p Fr 985 2532 a(3) p 985 2554 25 2 v 985 2599 a(4) 1015 2565 y(\(4) p Fq(L) p Fl 1091 2545 a(2) p Fr 1111 2565 a(\)) p Fq(:) p Fr 1778 2565 a(\(4.28\)) 0 2687 y(By) p 77 2687 a(the) p 161 2687 a(h) o(yp) q(othesis) p 401 2687 a(that) p Fn 507 2687 a(M) p Fl 551 2669 a(1) p Fr 573 2687 a(\() p Fq(W) p Fl 638 2694 a(0) p Fo 669 2687 a(\\) p Fr 713 2687 a(H\() p Fq(z) p Fl 792 2694 a(0) p Fr 811 2687 a(\)\)) p Fo 863 2687 a(\024) p Fr 916 2687 a(2) p Fq(L) p Fr 990 2687 a(and) p 1084 2687 a(Lemma) p 1258 2687 a(A.1,) p 1363 2687 a(w) o(e) p 1435 2687 a(ha) o(v) o(e) p 1547 2687 a(that) p Fn 617 2813 a(M) p Fl 661 2793 a(2) p Fk 684 2773 a(\000) p Fr 709 2813 a(^) p Fq 707 2813 a(\031) p Fr 736 2813 a(\() p Fq(W) p Fl 801 2820 a(0) p Fo 832 2813 a(\\) p Fr 876 2813 a(H\() p Fq(z) p Fl 955 2820 a(0) p Fr 974 2813 a(\)\)) p Fk 1012 2773 a(\001) p Fo 1049 2813 a(\024) p Fr 1106 2780 a(1) p 1106 2802 V 1106 2847 a(4) p Fq 1136 2813 a(L) p Fl 1169 2793 a(2) p Fq 1189 2813 a(:) p Fr 1778 2813 a(\(4.29\)) 927 2947 y(23) p 90 rotate dyy eop %%Page: 24 24 24 23 bop Fr 0 274 a(Therefore,) p 234 274 a(w) o(e) p 306 274 a(can) p 396 274 a(see) p 474 274 a(from) p 590 274 a(\(4.28\)) p 731 274 a(and) p 825 274 a(\(4.29\)) p 966 274 a(that) p Fn 322 413 a(M) p Fl 366 392 a(2) p Fk 397 343 a(\022\032) p Fq 471 413 a(x) p Fo 513 413 a(2) p Fn 560 413 a(R) p Fl 599 392 a(3) p Fr 615 413 a(;) p Fq 658 383 a(x) p Fo 700 383 a(2) p Fq 747 383 a(w) p Fr 799 383 a(for) p 874 383 a(some) p 996 383 a(face) p Fq 1095 383 a(w) p Fo 1145 383 a(2) p Fr 1192 383 a(\000\() p Fo(f) p Fq(W) p Fl 1312 390 a(0) p Fo 1332 383 a(g) p Fr(\)) 658 443 y(suc) o(h) p 768 443 a(that) p Fn 874 443 a(M) p Fl 918 425 a(2) p Fr 940 443 a(\() p Fq(\031) p Fr 989 443 a(\() p Fq(w) p Fr 1044 443 a(\)\)) p 1096 443 a(=) p 1148 443 a(1) p Fk 1396 343 a(\033) q(\023) p Fo 1482 413 a(\000) p Fr 1531 413 a(4) p Fq(L) p Fl 1588 392 a(2) p Fo 420 550 a(\025) p Fr 477 516 a(2) p 477 539 25 2 v 477 584 a(3) p Fn 506 550 a(M) p Fl 550 529 a(2) p Fk 582 480 a(\022) o(\032) p Fq 656 550 a(x) p Fo 697 550 a(2) p Fn 744 550 a(R) p Fl 783 529 a(3) p Fr 800 550 a(;) p Fq 842 520 a(x) p Fo 884 520 a(2) p Fq 931 520 a(w) p Fr 983 520 a(for) p 1058 520 a(some) p 1180 520 a(face) p Fq 1279 520 a(w) p Fo 1329 520 a(2) p Fr 1376 520 a(\000\() p Fo(f) p Fq(W) p Fl 1496 527 a(0) p Fo 1516 520 a(g) p Fr(\)) 842 580 y(suc) o(h) p 952 580 a(that) p Fn 1058 580 a(M) p Fl 1102 562 a(2) p Fr 1125 580 a(\() p Fq(\031) p Fr 1174 580 a(\() p Fq(w) p Fr 1229 580 a(\)\)) p 1280 580 a(=) p 1332 580 a(1) p Fk 1581 480 a(\033\023) p Fo 420 680 a(\025) p Fr 472 680 a(2) p Fk 496 625 a(\020) p Fr 531 646 a(3) p 531 669 V 531 714 a(4) 561 680 y(\(4) p Fq(L) p Fl 637 660 a(2) p Fr 657 680 a(\)) p Fo 687 680 a(\000) p Fr 742 646 a(1) p 742 669 V 742 714 a(4) p Fq 771 680 a(L) p Fl 804 660 a(2) p Fk 824 625 a(\021) p Fo 420 773 a(\025) p Fr 472 773 a(4) p Fq(L) p Fl 529 752 a(2) p Fq 549 773 a(:) p Fr 1778 773 a(\(4.30\)) 73 883 y(In) p 135 883 a(considering) p 391 883 a(the) p 475 883 a(four) p 578 883 a(cases,) p 715 883 a(w) o(e) p 787 883 a(ha) o(v) o(e) p 900 883 a(to) p 961 883 a(b) q(e) p 1028 883 a(a) o(w) o(are) p 1167 883 a(that) p 1273 883 a(\010) p Fl 1308 865 a(T) p Fp 1308 896 a(\016) p Fr 1353 883 a(is) p 1403 883 a(not) p 1490 883 a(in) o(v) m(arian) o(t) p 1696 883 a(under) p 1834 883 a(the) 0 943 y(v) o(ertical) p 175 943 a(shift) p 286 943 a(due) p 379 943 a(to) p Fn 440 943 a(J) p Fp 468 950 a(\016) p Fr 484 943 a(.) p 523 943 a(Hence,) p 683 943 a(w) o(e) p 756 943 a(will) p 849 943 a(in) o(tro) q(duce) p 1067 943 a(the) p 1152 943 a(follo) o(wing) p 1359 943 a(lemma) p 1518 943 a(b) q(efore) p 1665 943 a(w) o(e) p 1738 943 a(pro) q(ceed) 0 1003 y(to) p 60 1003 a(the) p 144 1003 a(four) p 245 1003 a(cases.) p Fg 73 1105 a(Lemma) p 272 1105 a(4.4.) p Fd 381 1105 a(Supp) n(ose) p 567 1105 a(that) p Fq 667 1105 a(\014) p 712 1105 a(>) p Fr 765 1105 a(0) p Fd 808 1105 a(and) p Fq 903 1105 a(L) p Fo 951 1105 a(2) p Fn 999 1105 a(N) p Fd 1053 1105 a(ar) n(e) p 1136 1105 a(su\016ciently) p 1383 1105 a(lar) n(ge.) p 1522 1105 a(L) n(et) p Fn 1607 1105 a(W) p Fo 1672 1105 a(2) p 1720 1105 a(S) t(W) p Fd 1825 1105 a(and) 0 1165 y(let) p Fq 72 1165 a(W) p Fo 144 1165 a(2) p Fn 197 1165 a(W) p Fd 244 1165 a(.) p 293 1165 a(L) n(et) p Fn 381 1165 a(W) p Fm 427 1147 a(0) p Fr 462 1165 a(=) p Fn 519 1165 a(W) p Fo 566 1165 a(nf) p Fq(W) p Fo 669 1165 a(g) p Fd(.) p 743 1165 a(Supp) n(ose) p 932 1165 a(that) p Fn 1035 1165 a(W) p Fm 1082 1147 a(0) p Fo 1116 1165 a(2) p 1169 1165 a(S) t(W) p Fr 1256 1165 a(\() p Fo(\000) p Fq(L) p Fm 1347 1147 a(0) p Fq 1358 1165 a(;) p Fr 1380 1165 a(2) p Fq(l) p Fr 1420 1165 a(\)) p Fq(;) p Fr 1482 1165 a(h) p Fl 1509 1147 a(+) p Fr 1538 1165 a(\() p Fn(W) p Fm 1604 1147 a(0) p Fr 1619 1165 a(\)) p Fo 1657 1165 a(\024) p Fr 1716 1165 a(3) p Fq(l) q(=) p Fr(2) p Fd 1825 1165 a(and) p Fr 0 1225 a(h) p Fm 27 1207 a(\000) p Fr 57 1225 a(\() p Fn(W) p Fm 122 1207 a(0) p Fr 137 1225 a(\)) p Fo 170 1225 a(\025) p 222 1225 a(\000) p Fq(L) p Fm 294 1207 a(0) p Fr 317 1225 a(+) p Fq 366 1225 a(l) q(=) p Fr(4) p Fd(.) p 468 1225 a(Then,) p 610 1225 a(we) p 682 1225 a(have) p 794 1225 a(that) p Fk 259 1292 a(\014) 259 1322 y(\014) 259 1352 y(\014) 301 1302 y(X) p Fp 275 1410 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 387 1410 a(\)) p Fg 406 1349 a(1) p Fp 434 1356 a(L) p Fc 458 1347 a(0) p Fp 470 1356 a(;) p Fl(2) p Fp(l) p Fr 510 1349 a(\() p Fq(C) p Fr 568 1349 a(\)\010) p Fl 622 1329 a(T) p Fp 622 1361 a(\016) p Fr 649 1349 a(\() p Fq(C) p Fr 707 1349 a(\)) p Fo 737 1349 a(\000) p Fk 817 1302 a(X) p Fp 787 1410 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 898 1400 a(0) p Fl 907 1410 a(\)) p Fg 929 1349 a(1) p Fp 957 1356 a(L) p Fc 981 1347 a(0) p Fp 992 1356 a(;) p Fl(2) p Fp(l) p Fr 1032 1349 a(\() p Fq(C) p Fr 1090 1349 a(\)\010) p Fl 1144 1329 a(T) p Fp 1144 1361 a(\016) p Fr 1172 1349 a(\() p Fq(C) p Fr 1230 1349 a(\)) p Fk 1249 1292 a(\014) 1249 1322 y(\014) 1249 1352 y(\014) p Fo 1278 1349 a(\024) p Fq 1331 1349 a(c) p Fl 1352 1356 a(19) p Fn 1389 1349 a(M) p Fl 1433 1329 a(2) p Fr 1456 1349 a(\() p Fq(W) p Fr 1528 1349 a(\)) p Fq(:) p Fr 1778 1349 a(\(4.31\)) p Fq 73 1514 a(P) p 111 1514 a(r) q(oof) p Fr 209 1514 a(.) p 252 1514 a(Let) p Fq 342 1514 a(\014) p 389 1514 a(>) p Fr 445 1514 a(0) p 487 1514 a(and) p Fq 584 1514 a(L) p Fo 635 1514 a(2) p Fn 685 1514 a(N) p Fr 740 1514 a(b) q(e) p 808 1514 a(su\016cien) o (tly) p 1054 1514 a(large.) p 1199 1514 a(W) l(e) p 1285 1514 a(will) p 1379 1514 a(\014rst) p 1481 1514 a(pro) o(v) o(e) p 1615 1514 a(\(4.31\)) p 1758 1514 a(for) p 1834 1514 a(the) 0 1574 y(sp) q(ecial) p 162 1574 a(case) p 268 1574 a(where) p Fq 412 1574 a(W) p Fr 484 1574 a(=) p 540 1574 a(cyl) o(\() p Fq(W) o(;) p Fo 687 1574 a(\000) p Fq(h;) p Fr 776 1574 a(0\)) p 838 1574 a(for) p 916 1574 a(some) p Fq 1041 1574 a(h) p Fo 1088 1574 a(2) p Fn 1140 1574 a(N) p Fr(.) p 1220 1574 a(W) l(e) p 1307 1574 a(ha) o(v) o(e) p 1422 1574 a(b) o(y) p 1493 1574 a(the) p 1580 1574 a(de\014nition) p 1800 1574 a(of) p Fn 1858 1574 a(J) p Fp 1886 1581 a(\016) p Fr 0 1635 a(and) p 95 1635 a(\(4.4\)) p 211 1635 a(\(see) p 309 1635 a(\(3.15\)) p 450 1635 a(and) p 545 1635 a(\(3.23\)\)) p 705 1635 a(that) p Fk 305 1701 a(\014) 305 1731 y(\014) 305 1761 y(\014) 346 1711 y(X) p Fp 321 1819 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 433 1819 a(\)) p Fg 452 1758 a(1) p Fp 480 1765 a(L) p Fc 504 1756 a(0) p Fp 515 1765 a(;) p Fl(2) p Fp(l) p Fr 556 1758 a(\() p Fq(C) p Fr 614 1758 a(\)\010) p Fl 668 1738 a(T) p Fp 668 1771 a(\016) p Fr 695 1758 a(\() p Fq(C) p Fr 753 1758 a(\)) p Fo 782 1758 a(\000) p Fk 863 1711 a(X) p Fp 832 1819 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 944 1810 a(0) p Fl 952 1819 a(\)) p Fg 974 1758 a(1) p Fp 1002 1765 a(L) p Fc 1026 1756 a(0) p Fp 1038 1765 a(;) p Fl(2) p Fp(l) p Fr 1078 1758 a(\() p Fq(C) p Fr 1136 1758 a(\)\010) p Fl 1190 1738 a(T) p Fp 1190 1771 a(\016) p Fr 1217 1758 a(\() p Fq(C) p Fr 1275 1758 a(\)) p Fk 1294 1701 a(\014) 1294 1731 y(\014) 1294 1761 y(\014) p Fo 224 1899 a(\024) p Fr 305 1899 a(16) p Fq(L) p Fl 386 1879 a(2) p Fq 406 1899 a(c) p Fm 427 1879 a(0) p Fl 427 1911 a(1) p Fr 455 1899 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 642 1899 a(\000) p Fr 699 1886 a(\026) p Fq 692 1899 a(\014) p Fr 722 1899 a(\)) p Fq(c) p Fl 762 1906 a(20) p Fq 800 1899 a(L) p Fj 838 1865 a(2) p 838 1871 16 2 v 838 1892 a(3) p Fr 860 1899 a(\(log) p Fq 950 1899 a(L) p Fr(\)) p Fl 1002 1879 a(2) p Fr 1022 1899 a(]) 353 2018 y(+) p Fq(c) p Fl 412 2025 a(21) p Fp 484 1956 a(h) p Fk 458 1971 a(X) p Fp 465 2076 a(i) p Fl(=1) p Fk 596 1971 a(X) p Fp 538 2079 a(x) p Fm(2) p Fp(D) p Fl 612 2079 a(\() p Fm(\000) p Fp(i) p Fl(;) p Fp(W) p Fl 713 2079 a(\)) p Fq 735 2018 a(c) p Fm 756 1998 a(0) p Fl 756 2031 a(1) p Fr 784 2018 a(exp) p Fk 858 1963 a(h) p Fo 882 2018 a(\000) p Fr(\() p Fq(\014) p Fo 981 2018 a(\000) p Fr 1038 2005 a(\026) p Fq 1031 2018 a(\014) p Fr 1061 2018 a(\)) p Fq(c) p Fl 1101 2025 a(20) p Fr 1138 2018 a(dist) p Fl 1217 2025 a(1) p Fr 1237 2018 a(\() p Fq(x;) p Fr 1306 2018 a(cyl) n(\(\003) p Fq(;) p Fo 1441 2018 a(\000) p Fq(i;) p Fo 1519 2018 a(\000) p Fq(i) p Fr 1585 2018 a(+) p 1634 2018 a(1\)\)) p Fk 1696 1963 a(i) p Fr 353 2199 a(+) p Fq(c) p Fl 412 2206 a(21) p Fp 484 2137 a(h) p Fk 458 2152 a(X) p Fp 465 2257 a(i) p Fl(=1) p Fk 596 2152 a(X) p Fp 538 2260 a(x) p Fm(2) p Fp(D) p Fl 612 2260 a(\() p Fm(\000) p Fp(i) p Fl(;) p Fp(W) p Fl 713 2260 a(\)) p Fq 735 2199 a(c) p Fm 756 2179 a(0) p Fl 756 2212 a(1) p Fr 784 2199 a(exp) p Fk 858 2144 a(h) p Fo 882 2199 a(\000) p Fr(\() p Fq(\014) p Fo 981 2199 a(\000) p Fr 1038 2186 a(\026) p Fq 1031 2199 a(\014) p Fr 1061 2199 a(\)) p Fo 1091 2199 a(\002) p Fq 548 2347 a(c) p Fl 569 2354 a(20) p Fr 607 2347 a(dist) p Fl 686 2354 a(1) p Fr 705 2347 a(\() p Fq(x;) p Fr 774 2347 a(cyl) o(\(\003) p Fq(;) p Fo 910 2347 a(\000) p Fq(L) p Fm 982 2326 a(00) p Fo 1014 2347 a(\000) p Fq 1064 2347 a(i;) p Fo 1103 2347 a(\000) p Fq(L) p Fm 1175 2326 a(00) p Fo 1206 2347 a(\000) p Fq 1256 2347 a(i) p Fr 1284 2347 a(+) p 1333 2347 a(1\)\)) p Fk 1395 2292 a(i) p Fo 224 2438 a(\024) p Fr 305 2438 a(\() p Fq(c) p Fl 345 2445 a(22) p Fr 393 2438 a(+) p Fq 442 2438 a(c) p Fl 463 2445 a(23) p Fr 500 2438 a(\)) p Fn(M) p Fl 563 2417 a(2) p Fr 586 2438 a(\() p Fq(W) p Fr 658 2438 a(\)) p Fq(;) p Fr 1778 2438 a(\(4.32\)) 0 2548 y(where) p Fq 141 2548 a(D) p Fr 182 2548 a(\() p Fo(\000) p Fq(i) p Fr(;) p Fq 279 2548 a(W) p Fr 332 2548 a(\)) p 365 2548 a(=) p Fo 416 2548 a(f) p Fq(x) p Fo 483 2548 a(2) p Fr 530 2548 a(cyl) o(\() p Fq(W) p Fo 674 2548 a(\\) p Fr 718 2548 a(H\() p Fo(\000) p Fq(i) p Fr(\)) p Fq(;) p Fo 871 2548 a(\000) p Fq(L) p Fm 943 2530 a(0) p Fq 953 2548 a(;) p Fr 975 2548 a(2) p Fq(l) p Fr 1026 2548 a(+) p 1075 2548 a(1\);) p Fq 1140 2548 a(x) p Fr 1179 2548 a(+) p 1228 2548 a(\(1) p Fq(=) p Fr(2) p Fq(;) p Fr 1341 2548 a(1) p Fq(=) p Fr(2) p Fq(;) p Fr 1435 2548 a(0\)) p Fo 1494 2548 a(2) p Fn 1541 2548 a(Z) p Fl 1578 2530 a(3) p Fo 1594 2548 a(g) p Fr(.) 73 2608 y(W) l(e) p 159 2608 a(will) p 253 2608 a(next) p 365 2608 a(pro) o(v) o(e) p 499 2608 a(\(4.31\)) p 642 2608 a(for) p 718 2608 a(a) p 761 2608 a(general) p 931 2608 a(case.) p 1060 2608 a(By) p 1138 2608 a(the) p 1224 2608 a(same) p 1348 2608 a(argumen) o(t) p 1569 2608 a(as) p 1631 2608 a(in) p 1690 2608 a(\(4.32\),) p 1847 2608 a(w) o(e) 927 2947 y(24) p 90 rotate dyy eop %%Page: 25 25 25 24 bop Fr 0 274 a(ha) o(v) o(e) p 112 274 a(that) p Fk 341 315 a(\014) 341 345 y(\014) 341 375 y(\014) 383 325 y(X) p Fp 358 433 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 470 433 a(\)) p Fg 489 372 a(1) p Fp 517 379 a(L) p Fc 541 370 a(0) p Fp 552 379 a(;) p Fl(2) p Fp(l) p Fr 592 372 a(\() p Fq(C) p Fr 650 372 a(\)\010) p Fl 704 352 a(T) p Fp 704 385 a(\016) p Fr 732 372 a(\() p Fq(C) p Fr 790 372 a(\)) p Fo 819 372 a(\000) p Fk 900 325 a(X) p Fp 869 433 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 981 423 a(0) p Fl 989 433 a(\)) p Fg 1011 372 a(1) p Fp 1039 379 a(L) p Fc 1063 370 a(0) p Fp 1074 379 a(;) p Fl(2) p Fp(l) p Fr 1115 372 a(\() p Fq(C) p Fr 1173 372 a(\)\010) p Fl 1227 352 a(T) p Fp 1227 385 a(\016) p Fr 1254 372 a(\() p Fq(C) p Fr 1312 372 a(\)) p Fk 1331 315 a(\014) 1331 345 y(\014) 1331 375 y(\014) p Fo 261 520 a(\024) p Fq 341 520 a(c) p Fl 362 527 a(22) p Fr 411 520 a(+) p Fq 460 520 a(c) p Fl 481 527 a(21) p Fk 526 473 a(X) p Fp 533 579 a(i) p Fm(2) p Ff(Z) p Fk 651 473 a(X) p Fp 606 581 a(x) p Fm(2) p Fp(D) p Fl 680 581 a(\() p Fp(i) p Fl(;) p Fp(W) p Fl 754 581 a(\)) p Fq 776 520 a(c) p Fm 797 499 a(0) p Fl 797 532 a(1) p Fr 825 520 a(exp) p Fk 899 465 a(h) p Fo 923 520 a(\000) p Fr(\() p Fq(\014) p Fo 1022 520 a(\000) p Fr 1078 507 a(\026) p Fq 1071 520 a(\014) p Fr 1102 520 a(\)) p Fq(c) p Fl 1142 527 a(20) p Fr 1179 520 a(dist) p Fl 1258 527 a(1) p Fr 1278 520 a(\() p Fq(x;) p Fr 1347 520 a(cyl) n(\(\003) p Fq(;) p 1482 520 a(i;) p 1521 520 a(i) p Fr 1548 520 a(+) p 1597 520 a(1\)\)) p Fk 1659 465 a(i) p Fr 390 668 a(+) p Fq(c) p Fl 449 675 a(21) p Fk 494 620 a(X) p Fp 502 726 a(i) p Fm(2) p Ff(Z) p Fk 619 620 a(X) p Fp 575 728 a(x) p Fm(2) p Fp(D) p Fl 649 728 a(\() p Fp(i) p Fl(;) p Fp(W) p Fl 723 728 a(\)) p Fq 744 668 a(c) p Fm 765 647 a(0) p Fl 765 680 a(1) p Fr 793 668 a(exp) p Fk 867 612 a(h) p Fo 891 668 a(\000) p Fr(\() p Fq(\014) p Fo 990 668 a(\000) p Fr 1047 655 a(\026) p Fq 1040 668 a(\014) p Fr 1070 668 a(\)) p Fo 1100 668 a(\002) p Fq 585 816 a(c) p Fl 606 823 a(20) p Fr 643 816 a(dist) p Fl 722 823 a(1) p Fr 742 816 a(\() p Fq(x;) p Fr 811 816 a(cyl) n(\(\003) p Fq(;) p Fo 946 816 a(\000) p Fq(L) p Fm 1018 795 a(00) p Fr 1050 816 a(+) p Fq 1099 816 a(i;) p Fo 1138 816 a(\000) p Fq(L) p Fm 1210 795 a(00) p Fr 1242 816 a(+) p Fq 1291 816 a(i) p Fr 1319 816 a(+) p 1368 816 a(1\)\)) p Fk 1430 760 a(i) p Fo 261 907 a(\024) p Fr 341 907 a(\() p Fq(c) p Fl 381 914 a(22) p Fr 430 907 a(+) p Fq 479 907 a(c) p Fl 500 914 a(23) p Fr 537 907 a(\)) p Fn(M) p Fl 600 886 a(2) p Fr 623 907 a(\() p Fq(W) p Fr 695 907 a(\)) p Fq(;) p Fr 1778 907 a(\(4.33\)) 0 1005 y(where) p Fq 141 1005 a(D) p Fr 182 1005 a(\() p Fq(i) p Fr(;) p Fq 240 1005 a(W) p Fr 293 1005 a(\)) p 327 1005 a(=) p Fo 380 1005 a(f) p Fq(x) p Fo 447 1005 a(2) p Fr 495 1005 a(cyl) n(\() p Fq(W) p Fo 639 1005 a(\\) p Fr 683 1005 a(H\() p Fq(i) p Fr(\)) p Fq(;) p Fo 797 1005 a(\000) p Fq(L) p Fm 869 987 a(0) p Fq 880 1005 a(;) p Fr 902 1005 a(2) p Fq(l) p Fr 953 1005 a(+) p 1002 1005 a(1\);) p Fq 1067 1005 a(x) p Fr 1107 1005 a(+) p 1156 1005 a(\(1) p Fq(=) p Fr(2) p Fq(;) p Fr 1269 1005 a(1) p Fq(=) p Fr(2) p Fq(;) p Fr 1363 1005 a(0\)) p Fo 1423 1005 a(2) p Fn 1471 1005 a(Z) p Fl 1507 987 a(3) p Fo 1524 1005 a(g) p Fr 1565 1005 a(if) p Fq 1610 1005 a(W) p Fo 1675 1005 a(\\) p Fr 1719 1005 a(H\() p Fq(i) p Fr(\)) p Fo 1825 1005 a(6) p Fr(=) p Fo 1877 1005 a(;) p Fr 0 1065 a(and) p Fq 95 1065 a(D) p Fr 136 1065 a(\() p Fq(i) p Fr(;) p Fq 194 1065 a(W) p Fr 247 1065 a(\)) p 280 1065 a(=) p Fo 332 1065 a(;) p Fr 373 1065 a(otherwise.) 73 1171 y(F) l(rom) p 201 1171 a(no) o(w) p 303 1171 a(on,) p 384 1171 a(w) o(e) p 456 1171 a(will) p 548 1171 a(estimate) p Fk 234 1228 a(X) p Ff 202 1334 a(W) p Fm 238 1334 a(2S) r(W) p Fj 321 1339 a(1) p Fq 346 1275 a(P) p Fp 384 1254 a(\016) p Fl 377 1287 a(\003) p Fr 404 1275 a(\() p Fn(W) p Fr 470 1275 a(\)) p Fq(;) p Fk 594 1228 a(X) p Ff 562 1334 a(W) p Fm 599 1334 a(2) o(S) r(W) p Fj 681 1339 a(2) p Fq 706 1275 a(P) p Fp 744 1254 a(\016) p Fl 737 1287 a(\003) p Fr 764 1275 a(\() p Fn(W) p Fr 830 1275 a(\)) p Fq(;) p Fk 955 1228 a(X) p Ff 923 1334 a(W) p Fm 959 1334 a(2) o(S) r(W) p Fj 1041 1339 a(3) p Fq 1067 1275 a(P) p Fp 1105 1254 a(\016) p Fl 1098 1287 a(\003) p Fr 1125 1275 a(\() p Fn(W) p Fr 1190 1275 a(\)) p 1261 1275 a(and) p Fk 1429 1228 a(X) p Ff 1397 1334 a(W) p Fm 1433 1334 a(2S) r(W) p Fj 1515 1339 a(4) p Fq 1541 1275 a(P) p Fp 1579 1254 a(\016) p Fl 1572 1287 a(\003) p Fr 1599 1275 a(\() p Fn(W) p Fr 1665 1275 a(\)) p Fq(:) p Fr 0 1423 a(W) l(e) p 87 1423 a(assume) p 259 1423 a(that) p Fq 368 1423 a(L) p Fo 421 1423 a(2) p Fn 474 1423 a(N) p Fr 529 1423 a(is) p 582 1423 a(su\016cien) o(tly) p 829 1423 a(large) p 952 1423 a(\() p Fq(\016) p 1014 1423 a(>) p Fr 1071 1423 a(0) p 1115 1423 a(is) p 1168 1423 a(su\016cien) o(tly) p 1415 1423 a(small\)) p 1565 1423 a(throughout) p 1823 1423 a(this) 0 1483 y(section.) p Fq 73 1572 a(C) t(ase) p Fr 199 1572 a(1.) p 259 1572 a(W) l(e) p 343 1572 a(will) p 435 1572 a(consider) p 625 1572 a(the) p 709 1572 a(case) p 812 1572 a(where) p Fn 953 1572 a(W) p Fo 1017 1572 a(2) p 1064 1572 a(S) t(W) p Fl 1151 1579 a(1) p Fr 1171 1572 a(.) p 1206 1572 a(Recall) p 1353 1572 a(that) p Fo 275 1670 a(S) t(W) p Fl 362 1677 a(1) p Fr 395 1670 a(=) p Fo 447 1670 a(f) p Fn(W) p Fo 536 1670 a(2) p 583 1670 a(S) t(W) p Fm 670 1650 a(0) p Fr 681 1670 a(;) p 703 1670 a(\(\010) p Fl 757 1677 a(0) p Fr 777 1670 a(\() p Fo(f) p Fq(W) p Fo 874 1670 a(g) p Fr(\)\)) p Fl 937 1650 a(5) p Fq 957 1670 a(=) p Fr(\010) p Fl 1016 1677 a(1) p Fr 1036 1670 a(\() p Fo(f) p Fq(W) p Fo 1133 1670 a(g) p Fr(\)) p Fo 1190 1670 a(\024) p Fr 1243 1670 a(1) p 1283 1670 a(for) p 1358 1670 a(all) p Fq 1426 1670 a(W) p Fo 1492 1670 a(2) p Fn 1539 1670 a(W) p Fo 1586 1670 a(g) p Fq(:) p Fr 0 1769 a(Note) p 119 1769 a(that) p 226 1769 a(\010) p Fp 261 1776 a(\016) p Fr 280 1769 a(\() p Fo(f) p Fq(W) p Fo 377 1769 a(g) p Fr(\)) p Fo 436 1769 a(\024) p Fr 491 1769 a(exp[) p Fo(\000) p Fq(\014) p Fn 650 1769 a(M) p Fl 692 1751 a(2) p Fr 715 1769 a(\() p Fq(W) p Fr 787 1769 a(\)) p Fq(=) p Fr(5]) p 885 1769 a(for) p 961 1769 a(all) p Fq 1030 1769 a(W) p Fo 1099 1769 a(2) p Fn 1148 1769 a(W) p Fr 1215 1769 a(if) p Fn 1261 1769 a(W) p Fo 1327 1769 a(2) p 1376 1769 a(S) t(W) p Fl 1463 1776 a(1) p Fr 1500 1769 a(\(see) p 1599 1769 a(\(3.24\)\).) p 1781 1769 a(Th) o(us,) 0 1829 y(b) o(y) p 68 1829 a(a) p 108 1829 a(similar) p 269 1829 a(argumen) o(t) p 487 1829 a(as) p 547 1829 a(in) p 603 1829 a(\(3.22\)-\(3.30\)) p 885 1829 a(together) p 1078 1829 a(with) p 1189 1829 a(\(4.31\),) p 1343 1829 a(w) o(e) p 1415 1829 a(ha) o(v) o(e) p 1527 1829 a(that) p Fk 467 1905 a(X) p Ff 436 2010 a(W) p Fm 472 2010 a(2) o(S) r(W) p Fj 554 2015 a(1) p Fq 579 1952 a(P) p Fp 617 1931 a(\016) p Fl 610 1964 a(\003) p Fr 637 1952 a(\() p Fn(W) p Fr 703 1952 a(\)) p Fo 739 1952 a(\024) p Fq 792 1952 a(c) p Fl 813 1959 a(24) p Fr 858 1952 a(exp[) p Fo(\000) p Fr(\() p Fq 1010 1918 a(\014) p 1010 1940 31 2 v Fr 1013 1986 a(5) p Fo 1055 1952 a(\000) p Fq 1105 1952 a(c) p Fl 1126 1959 a(25) p Fr 1164 1952 a(\)) p Fq(K) p Fl 1224 1959 a(5) p Fr 1252 1952 a(log) p Fq 1323 1952 a(L) p Fr(]) p Fq(:) p Fr 1778 1952 a(\(4.34\)) p Fq 73 2097 a(C) t(ase) p Fr 199 2097 a(2.) p 259 2097 a(W) l(e) p 343 2097 a(will) p 435 2097 a(consider) p 625 2097 a(the) p 709 2097 a(case) p 812 2097 a(where) p Fn 953 2097 a(W) p Fo 1017 2097 a(2) p 1064 2097 a(S) t(W) p Fl 1151 2104 a(2) p Fr 1171 2097 a(.) p 1206 2097 a(Recall) p 1353 2097 a(that) p Fo 276 2219 a(S) t(W) p Fl 363 2226 a(2) p Fr 397 2219 a(=) p Fk 449 2149 a(\032) p Fn 486 2219 a(W) p Fo 550 2219 a(2) p 597 2219 a(S) t(W) p Fm 684 2198 a(00) p Fo 705 2219 a(nS) t(W) p Fl 817 2226 a(1) p Fr 837 2219 a(;) 880 2189 y(there) p 1004 2189 a(exist) p 1120 2189 a(some) p Fq 1242 2189 a(W) p Fo 1309 2189 a(2) p Fn 1356 2189 a(W) p Fo 1403 2189 a(nf) p Fq(W) p Fl 1499 2196 a(0) p Fo 1521 2189 a(g) p Fr 880 2249 a(with) p Fn 991 2249 a(M) p Fl 1035 2231 a(2) p Fr 1058 2249 a(\() p Fq(W) p Fr 1130 2249 a(\)) p Fo 1162 2249 a(\025) p Fq 1215 2249 a(K) p Fl 1256 2256 a(5) p Fr 1284 2249 a(log) p Fq 1356 2249 a(L) p Fk 1567 2149 a(\033) p Fq 1612 2219 a(;) p Fr 0 2348 a(where) p Fo 138 2348 a(S) t(W) p Fm 226 2328 a(00) p Fr 261 2348 a(=) p Fo 312 2348 a(f) p Fn(W) p Fo 401 2348 a(2) p 448 2348 a(S) t(W) p Fm 535 2328 a(0) p Fr 547 2348 a(;) p Fq 569 2348 a(\032) p Fr(\() p Fn(W) p Fq 660 2348 a(;) p 682 2348 a(z) p Fr 707 2348 a(\)) p Fq 742 2348 a(<) p Fr 794 2348 a(1) p Fq(=) p Fr(5) p 881 2348 a(for) p 955 2348 a(some) p Fq 1078 2348 a(z) p Fo 1116 2348 a(2) p Fn 1163 2348 a(Z) p Fr 1213 2348 a(with) p Fo 1324 2348 a(\000) p Fq(L) p Fm 1396 2330 a(00) p Fo 1431 2348 a(\024) p Fq 1484 2348 a(z) p 1522 2348 a(<) p Fr 1574 2348 a(0) p Fo(g) p Fq(:) p Fr 1651 2348 a(In) p 1709 2348 a(this) p 1802 2348 a(case,) 0 2409 y(b) o(y) p 69 2409 a(a) p 111 2409 a(similar) p 272 2409 a(argumen) o(t) p 492 2409 a(as) p 553 2409 a(in) p 611 2409 a(\(3.22\)-\(3.30\)) p 894 2409 a(together) p 1088 2409 a(with) p 1200 2409 a(\(ii) o(\)) p 1283 2409 a(of) p 1339 2409 a(Lemma) p 1515 2409 a(4.3) p 1595 2409 a(and) p 1691 2409 a(\(4.31\),) p 1847 2409 a(w) o(e) 0 2469 y(also) p 98 2469 a(ha) o(v) o(e) p 210 2469 a(that) p Fk 467 2532 a(X) p Ff 436 2638 a(W) p Fm 472 2638 a(2) o(S) r(W) p Fj 554 2643 a(2) p Fq 579 2579 a(P) p Fp 617 2559 a(\016) p Fl 610 2592 a(\003) p Fr 637 2579 a(\() p Fn(W) p Fr 703 2579 a(\)) p Fo 739 2579 a(\024) p Fq 792 2579 a(c) p Fl 813 2586 a(26) p Fr 858 2579 a(exp[) p Fo(\000) p Fr(\() p Fq 1010 2546 a(\014) p 1010 2568 V Fr 1013 2614 a(5) p Fo 1055 2579 a(\000) p Fq 1105 2579 a(c) p Fl 1126 2586 a(27) p Fr 1164 2579 a(\)) p Fq(K) p Fl 1224 2586 a(5) p Fr 1252 2579 a(log) p Fq 1323 2579 a(L) p Fr(]) p Fq(:) p Fr 1778 2579 a(\(4.35\)) p Fq 73 2724 a(C) t(ase) p Fr 199 2724 a(3.) p 259 2724 a(W) l(e) p 343 2724 a(will) p 435 2724 a(consider) p 625 2724 a(the) p 709 2724 a(case) p 812 2724 a(where) p Fn 953 2724 a(W) p Fo 1017 2724 a(2) p 1064 2724 a(S) t(W) p Fl 1151 2731 a(3) p Fr 1171 2724 a(.) p 1206 2724 a(Recall) p 1353 2724 a(that) p Fo 376 2823 a(S) t(W) p Fl 463 2830 a(3) p Fr 497 2823 a(=) p Fo 549 2823 a(f) p Fn(W) p Fo 637 2823 a(2) p 684 2823 a(S) t(W) p Fm 772 2802 a(00) p Fo 793 2823 a(n) p Fr(\() p Fo(S) t(W) p Fl 924 2830 a(1) p Fo 955 2823 a([) p 999 2823 a(S) t(W) p Fl 1086 2830 a(2) p Fr 1106 2823 a(\);) p Fq 1147 2823 a(z) p Fl 1170 2830 a(min) p Fr 1230 2823 a(\() p Fn(W) p Fr 1296 2823 a(\)) p Fo 1332 2823 a(\024) p 1384 2823 a(\000) p Fq(l) q(=) p Fr(2) p Fo(g) p Fq(:) p Fr 927 2947 a(25) p 90 rotate dyy eop %%Page: 26 26 26 25 bop Fr 0 274 a(W) l(e) p 84 274 a(de\014ne) p Fo 127 373 a(S) t(W) p Fm 214 352 a(\016) p Fr 248 373 a(=) p Fo 300 373 a(f) p Fn(W) p Fo 388 373 a(2) p 435 373 a(S) t(W) p Fm 522 352 a(00) p Fo 544 373 a(n) p Fr(\() p Fo(S) t(W) p Fl 675 380 a(1) p Fo 705 373 a([) p 750 373 a(S) t(W) p Fl 837 380 a(2) p Fr 857 373 a(\);) p 898 373 a(for) p 972 373 a(an) o(y) p Fq 1064 373 a(W) p Fo 1131 373 a(2) p Fn 1178 373 a(W) p Fo 1225 373 a(nf) p Fq(W) p Fl 1321 380 a(0) p Fo 1343 373 a(g) p Fq(;) p 1406 373 a(W) p Fo 1470 373 a(\\) p Fq 1514 373 a(@) p Fr 1543 373 a(\003) p 1591 373 a(=) p Fo 1642 373 a(;g) p Fr 1778 446 a(\(4.36\)) 0 545 y(and) p Fo 95 545 a(S) t(W) p Fm 183 524 a(\016) p Fl 183 557 a(3) p Fr 217 545 a(=) p Fo 270 545 a(S) t(W) p Fl 357 552 a(3) p Fo 389 545 a(\\) p 433 545 a(S) t(W) p Fm 521 524 a(\016) p Fr 540 545 a(.) p 578 545 a(By) p 655 545 a(a) p 696 545 a(similar) p 857 545 a(argumen) o(t) p 1076 545 a(as) p 1136 545 a(in) p 1194 545 a(\(3.22\)-\(3.30\)) p 1476 545 a(together) p 1669 545 a(with) p 1781 545 a(\(ii) o(\)) p 1863 545 a(of) 0 605 y(Lemma) p 174 605 a(4.3) p 253 605 a(and) p 348 605 a(\(4.31\),) p 502 605 a(w) o(e) p 574 605 a(ha) o(v) o(e) p 686 605 a(that) p Fk 416 666 a(X) p Ff 385 772 a(W) p Fm 421 772 a(2) o(S) r(W) p Fj 503 777 a(3) p Fq 529 713 a(P) p Fp 567 692 a(\016) p Fl 560 725 a(\003) p Fr 587 713 a(\() p Fn(W) p Fr 652 713 a(\)) p Fo 304 855 a(\024) p Fk 385 800 a(\020) 447 808 y(X) p Ff 414 915 a(W) p Fm 451 915 a(2) o(S) r(W) p Fc 533 903 a(\016) p Fj 533 925 a(3) p Fq 559 855 a(P) p Fp 597 834 a(\016) p Fl 590 867 a(\003) p Fr 617 855 a(\() p Fn(W) p Fr 683 855 a(\)) p Fk 702 800 a(\021) p Fo 746 855 a(\002) p Fk 482 981 a(\020) p Fl 527 974 a(8) p Fp(L) p Fk 512 989 a(X) p Fp 516 1095 a(k) p Fl 535 1095 a(=1) p Fk 592 966 a(\022) p Fr 634 1002 a(4) p Fq(L) p Fl 691 984 a(2) p Fq 659 1070 a(k) p Fk 716 966 a(\023) 767 989 y(X) p Fp 761 1094 a(n) p Fj 782 1099 a(1) p Fm 800 1094 a(\025) p Fl(1) p Fo 853 1036 a(\001) p 875 1036 a(\001) p 897 1036 a(\001) p Fk 926 989 a(X) p Fp 920 1094 a(n) p Fe 941 1100 a(k) p Fm 960 1094 a(\025) p Fl(1) p Fq 1013 1036 a(\024) p Fp 1041 1016 a(n) p Fj 1062 1021 a(1) p Fl 1080 1016 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 1185 1022 a(k) p Fq 1207 1036 a(e) p Fm 1230 1016 a(\000) p Fl(\() p Fp(\014) r(=) p Fl(5) p Fm(\000) p Fp(c) p Fj 1371 1021 a(28) p Fl 1403 1016 a(\)\() p Fp(n) p Fj 1452 1021 a(1) p Fl 1469 1016 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 1574 1022 a(k) p Fl 1594 1016 a(\)) p Fk 1610 981 a(\021) p Fo 304 1174 a(\024) p Fq 385 1174 a(c) p Fl 406 1181 a(29) p Fr 451 1174 a(exp[) p Fq(c) p Fl 561 1181 a(30) p Fq 598 1174 a(L) p Fr 639 1174 a(log) p Fq 711 1174 a(L) p Fr(]) p Fk 798 1126 a(X) p Ff 766 1234 a(W) p Fm 802 1234 a(2) o(S) r(W) p Fc 884 1221 a(\016) p Fj 884 1243 a(3) p Fq 910 1174 a(P) p Fp 948 1153 a(\016) p Fl 941 1186 a(\003) p Fr 968 1174 a(\() p Fn(W) p Fr 1034 1174 a(\)) p Fq(:) p Fr 1778 1174 a(\(4.37\)) 73 1329 y(Let) p 157 1329 a(us) p 215 1329 a(\014x) p Fn 280 1329 a(W) p Fo 344 1329 a(2) p 391 1329 a(S) t(W) p Fm 478 1308 a(\016) p Fl 478 1341 a(3) p Fr 498 1329 a(.) p 532 1329 a(Let) p 615 1329 a(\000) p 660 1329 a(=) p 711 1329 a(\000\() p Fn(W) p Fr 808 1329 a(\)) p 842 1329 a(and) p Fq 933 1329 a(m) p Fr 989 1329 a(=) p Fq 1041 1329 a(z) p Fl 1064 1336 a(min) p Fr 1125 1329 a(\() p Fn(W) p Fr 1191 1329 a(\).) p 1246 1329 a(W) l(e) p 1326 1329 a(decomp) q(ose) p Fq 1568 1329 a(W) p Fl 1614 1336 a(0) p Fo 1634 1329 a(n) p Fr(cyl) o(\(\003) p Fq(;) p 1795 1329 a(m;) p Fr 1860 1329 a(0\)) 0 1389 y(in) o(to) p 98 1389 a(connected) p 324 1389 a(comp) q(onen) o(ts.) p 611 1389 a(By) p Fn 686 1389 a(F) p Fl 713 1371 a(1) p Fr 750 1389 a(=) p Fn 802 1389 a(F) p Fl 829 1371 a(1) p Fr 852 1389 a(\() p Fn(W) p Fr 918 1389 a(\),) p 968 1389 a(w) o(e) p 1039 1389 a(will) p 1130 1389 a(denote) p 1285 1389 a(the) p 1368 1389 a(collection) p 1584 1389 a(of) p 1638 1389 a(suc) o(h) p 1746 1389 a(comp) q(o-) 0 1449 y(nen) o(ts) p 128 1449 a(whic) o(h) p 267 1449 a(b) q(elong) p 421 1449 a(to) p Fn 480 1449 a(F) p Fr(\() p Fn(W) p Fr 576 1449 a(\)) p 613 1449 a(and) p 707 1449 a(are) p 788 1449 a(included) p 982 1449 a(in) p Fq 1038 1449 a(Q) p Fr(\(\003\() p Fq(m) p Fr 1200 1449 a(+) p 1247 1449 a(1) p Fq(;) p Fr 1293 1449 a(0\)\).) p 1390 1449 a(Note) p 1507 1449 a(that) p Fq 1612 1449 a(F) p Fo 1659 1449 a(\011) p Fq 1707 1449 a(@) p Fr 1736 1449 a(\002\() p Fq(F) p Fr 1832 1449 a(\)) p Fo 1863 1449 a(\032) p Fr 0 1509 a(cyl) o(\(\003) p Fq(;) p 136 1509 a(m) p Fr 189 1509 a(+) p 238 1509 a(1) p Fq(;) p Fr 284 1509 a(0\)) p 344 1509 a(for) p 419 1509 a(eac) o(h) p Fq 528 1509 a(F) p Fo 581 1509 a(2) p Fn 628 1509 a(F) p Fl 655 1491 a(1) p Fr 678 1509 a(.) p 713 1509 a(Let) p Fq 438 1609 a(F) p Fl 470 1616 a(0) p Fr 503 1609 a(=) p Fq 555 1609 a(F) p Fl 587 1616 a(0) p Fr 606 1609 a(\() p Fn(W) p Fr 672 1609 a(\)) p 708 1609 a(=) p 759 1609 a(cyl) o(\(\003) p Fq(;) p 895 1609 a(m;) p Fr 960 1609 a(0\)) p Fo 1014 1609 a(\011) p Fr 1064 1609 a(\() p Fo([) p Fp 1116 1617 a(F) p Fm 1143 1617 a(2) p Ff(F) p Fj 1188 1607 a(1) p Fq 1206 1609 a(@) p Fr 1235 1609 a(\002\() p Fq(F) p Fr 1331 1609 a(\)\)) p Fq(:) p Fr 1778 1609 a(\(4.38\)) 0 1708 y(F) l(rom) p 128 1708 a(\(4.36\)) p 269 1708 a(and) p 364 1708 a(\(4.38\),) p 518 1708 a(w) o(e) p 590 1708 a(can) p 679 1708 a(de\014ne) p 820 1708 a(the) p 904 1708 a(op) q(en) p 1022 1708 a(con) o(tour) p 1200 1708 a(\000) p Fm 1230 1690 a(0) p Fr 1242 1708 a(\() p Fn(W) p Fr 1308 1708 a(\)) p 1346 1708 a(whic) o(h) p 1485 1708 a(satis\014es) p Fn 352 1821 a(M) p Fl 396 1800 a(2) p Fk 419 1765 a(\020) p Fr 448 1821 a(\000) p Fm 478 1800 a(0) p Fr 490 1821 a(\() p Fn(W) p Fr 556 1821 a(\)) p Fo 589 1821 a(\011) p Fk 639 1780 a(\000) p Fq 662 1821 a(F) p Fl 694 1828 a(0) p Fr 713 1821 a(\() p Fn(W) p Fr 779 1821 a(\)) p Fo 812 1821 a([) p Fr 856 1821 a(shift\(\000\() p Fn(W) p Fo 1065 1821 a(nf) p Fq(W) p Fl 1161 1828 a(0) p Fo 1184 1821 a(g) p Fr(\)) p Fq(;) p 1250 1821 a(m) p Fr(\)) p Fk 1312 1780 a(\001) 1334 1765 y(\021) p Fr 1378 1821 a(=) p 1429 1821 a(0) p Fq(;) p Fr 1778 1821 a(\(4.39\)) 0 1931 y(and) p 95 1931 a(de\014ne) p Fn 623 2030 a(W) p Fm 670 2009 a(0) p Fr 698 2030 a(=) p Fn 750 2030 a(W) p Fm 797 2009 a(0) p Fr 812 2030 a(\() p Fn(W) p Fr 877 2030 a(\)) p 913 2030 a(=) p Fn 965 2030 a(W) p Fr 1012 2030 a(\(\000) p Fm 1061 2009 a(0) p Fr 1076 2030 a(\() p Fn(W) p Fr 1142 2030 a(\)\)) p Fq(:) p Fr 1778 2030 a(\(4.40\)) 0 2129 y(Note) p 118 2129 a(that) p 224 2129 a(\000) p Fm 254 2111 a(0) p Fr 266 2129 a(\() p Fn(W) p Fr 331 2129 a(\)) p 367 2129 a(=) p 419 2129 a(\000\() p Fn(W) p Fm 515 2111 a(0) p Fr 530 2129 a(\).) p 584 2129 a(W) l(e) p 668 2129 a(also) p 766 2129 a(de\014ne) p 123 2202 31 2 v 123 2242 a(\000) q(\() p Fn(W) p Fr 220 2242 a(\)) p 255 2242 a(=) p Fk 307 2186 a(\020) p Fr 337 2242 a(\000\() p Fo(f) p Fq(W) p Fl 457 2249 a(0) p Fo 477 2242 a(g) p Fr(\)) p Fo(n) p Fr(\() p Fo([) p Fp 598 2250 a(F) p Fm 625 2250 a(2) p Ff(F) p Fj 670 2241 a(1) p Fq 688 2242 a(@) p Fr 717 2242 a(\002\() p Fq(F) p Fr 813 2242 a(\)\)) p Fk 851 2186 a(\021) p Fo 891 2242 a([) p Fk 935 2186 a(\020) p Fo 965 2242 a([) p Fp 998 2250 a(F) p Fm 1025 2250 a(2) p Ff(F) p Fj 1070 2241 a(1) p Fr 1089 2242 a(\() p Fq(@) p Fr 1137 2242 a(\002\() p Fq(F) p Fr 1233 2242 a(\)) p Fo 1261 2242 a(\\) p Fr 1306 2242 a(cyl) o(\(\003) p Fq(;) p 1442 2242 a(m) p Fr 1495 2242 a(+) p 1544 2242 a(1) p Fq(;) p Fr 1590 2242 a(0\)\)) p Fk 1652 2186 a(\021) p Fq 1682 2242 a(:) p Fr 1778 2328 a(\(4.41\)) 0 2427 y(Let) p Fo 530 2526 a(f) p Fq(F) p Fl 594 2506 a(2) p Fp 587 2539 a(i) p Fo 613 2526 a(g) p Fp 638 2505 a(k) p Fj 656 2510 a(2) p Fp 638 2539 a(i) p Fl(=0) p Fr 711 2526 a(=) p Fo 763 2526 a(f) p Fq(F) p Fl 827 2506 a(2) p Fp 820 2539 a(i) p Fr 846 2526 a(\() p Fn(W) p Fr 911 2526 a(\)) p Fo(g) p Fp 955 2505 a(k) p Fj 974 2510 a(2) p Fp 955 2539 a(i) p Fl(=) q(0) p Fr 1031 2526 a(=) p Fn 1083 2526 a(W) p Fr 1130 2526 a(\() p 1149 2486 V(\000) s(\() p Fn(W) p Fr 1248 2526 a(\)\)) p 1778 2526 a(\(4.42\)) 0 2626 y(and) p 95 2626 a(let) p Fq 137 2734 a(F) p Fl 176 2714 a(2) 169 2747 y(0) p Fr 209 2734 a(=) p 260 2734 a(the) p 344 2734 a(unique) p 503 2734 a(maximal) p 702 2734 a(standard) p 906 2734 a(w) o(all) p 1007 2734 a(suc) o(h) p 1117 2734 a(that) p Fn 1223 2734 a(M) p Fl 1267 2714 a(2) p Fr 1290 2734 a(\() s(^) p Fq 1309 2734 a(\031) p Fr 1338 2734 a(\() p Fq(F) p Fl 1396 2714 a(2) 1389 2747 y(0) p Fr 1415 2734 a(\)\)) p Fo 1467 2734 a(\025) p Fr 1524 2701 a(3) p 1524 2723 25 2 v 1524 2769 a(4) 1554 2734 y(\(4) p Fq(L) p Fl 1630 2714 a(2) p Fr 1650 2734 a(\)) p Fq(:) p Fr 1778 2823 a(\(4.43\)) 927 2947 y(26) p 90 rotate dyy eop %%Page: 27 27 27 26 bop Fr 0 274 a(Then,) p 141 274 a(w) o(e) p 212 274 a(can) p 302 274 a(see) p 380 274 a(from) p 495 274 a(the) p 579 274 a(de\014nitions) p 815 274 a(of) p Fo 870 274 a(S) t(W) p Fl 957 281 a(3) p Fr 993 274 a(\() p Fo(S) t(W) p Fm 1099 253 a(0) p Fr 1111 274 a(\),) p 1160 274 a(\(standard\)) p 1401 274 a(w) o(alls,) p 1535 274 a(and) p Fo 1630 274 a(f) p Fq(F) p Fl 1694 256 a(2) p Fp 1687 286 a(i) p Fo 1713 274 a(g) p Fp 1738 252 a(k) p Fj 1756 257 a(2) p Fp 1738 287 a(i) p Fl(=1) p Fr 1813 274 a(that) 0 334 y(for) p 75 334 a(an) o(y) p 167 334 a(1) p Fo 205 334 a(\024) p Fq 257 334 a(i) p Fo 288 334 a(\024) p Fq 341 334 a(k) p Fl 366 341 a(2) p Fr 386 334 a(,) 375 430 y(^) p Fq 372 430 a(\031) p Fr 402 430 a(\() p Fq(F) p Fl 460 410 a(2) p Fp 453 443 a(i) p Fr 479 430 a(\)) p Fo 509 430 a(\\) p 553 430 a(f) p Fq(x) p Fo 619 430 a(2) p Fr 667 430 a(H\() p Fo(\000) p Fl 767 411 a(1) p 767 419 18 2 v 767 448 a(2) p Fr 788 430 a(\);) p 829 430 a(dist) p Fl 908 437 a(1) p Fr 928 430 a(\() p Fq(x;) p 997 430 a(@) p Fr 1026 430 a(\003\)) p Fo 1091 430 a(\024) p Fq 1144 430 a(K) p Fl 1185 437 a(4) p Fr 1214 430 a(log) p Fq 1285 430 a(L) p Fo(g) p 1357 430 a(6) p Fr(=) p Fo 1409 430 a(;) p Fq(:) p Fr 1778 430 a(\(4.44\)) 0 534 y(W) l(e) p 88 534 a(decomp) q(ose) p Fq 338 534 a(F) p Fl 377 516 a(2) 370 546 y(0) p Fo 396 534 a(n) p Fr(cyl) n(\(\003) p Fq(;) p 556 534 a(m;) p Fr 621 534 a(0\)) p 684 534 a(in) o(to) p 787 534 a(connected) p 1019 534 a(comp) q(onen) o(ts.) p 1319 534 a(W) l(e) p 1407 534 a(will) p 1503 534 a(denote) p 1664 534 a(b) o(y) p Fo 1736 534 a(f) p Fr 1772 521 a(~) p Fq 1761 534 a(F) p Fl 1800 516 a(3) p Fp 1793 546 a(i) p Fo 1819 534 a(g) p Fr 1864 534 a(=) p Fo 0 594 a(f) p Fr 36 581 a(~) p Fq 25 594 a(F) p Fl 64 576 a(3) p Fp 57 606 a(i) p Fr 83 594 a(\() p Fn(W) p Fr 149 594 a(\)) p Fo(g) p Fr 217 594 a(and) p Fo 316 594 a(f) p Fq(F) p Fl 380 576 a(4) p Fp 373 606 a(i) p Fo 399 594 a(g) p Fp 424 572 a(k) p Fj 442 577 a(4) p Fp 424 607 a(i) p Fl(=1) p Fr 505 594 a(=) p Fo 565 594 a(f) p Fq(F) p Fl 629 576 a(4) p Fp 622 606 a(i) p Fr 648 594 a(\() p Fn(W) p Fr 714 594 a(\)) p Fo(g) p Fp 758 572 a(k) p Fj 776 577 a(4) p Fp 758 607 a(i) p Fl(=1) p Fr 820 594 a(,) p 856 594 a(the) p 944 594 a(collections) p 1185 594 a(of) p 1245 594 a(suc) o(h) p 1360 594 a(comp) q(onen) o(ts) p 1633 594 a(b) q(elonging) p 1859 594 a(to) p Fn 0 654 a(F) p Fr(\() p Fn(W) p Fr 96 654 a(\)) p 134 654 a(and) p 229 654 a(not) p 316 654 a(b) q(elonging) p 537 654 a(to) p Fn 596 654 a(F) p Fr 624 654 a(\() p Fn(W) p Fr 693 654 a(\),) p 744 654 a(resp) q(ectiv) o(ely) l(.) p 1025 654 a(Note) p 1143 654 a(that) p 1249 654 a(0) p Fo 1287 654 a(\024) p Fq 1340 654 a(k) p Fl 1365 661 a(4) p Fo 1398 654 a(\024) p Fr 1451 654 a(8) p Fq(L) p Fr(.) p 1544 654 a(Let) p Fo 566 750 a(f) p Fq(x) p Fp 619 757 a(i) p Fo 633 750 a(g) p Fr 672 750 a(=) p Fo 723 750 a(f) p Fq(\031) p Fr 778 750 a(\() p Fq(x) p Fr(\);) p Fq 866 750 a(x) p Fo 907 750 a(2) p Fq 954 750 a(@) p Fp 980 757 a(in) p Fr 1015 750 a(\003) p 1065 750 a(and) p Fq 1160 750 a(x) p Fl 1188 730 a(3) p Fr 1221 750 a(=) p 1273 750 a(0) p Fo(g) p Fq(:) p Fr 0 847 a(W) l(e) p 84 847 a(de\014ne) p Fo 225 847 a(f) p Fq(F) p Fl 289 829 a(3) p Fp 282 859 a(i) p Fo 308 847 a(g) p Fp 333 825 a(k) p Fj 351 830 a(3) p Fp 333 859 a(i) p Fl(=1) p Fr 406 847 a(=) p Fo 458 847 a(f) p Fq(F) p Fl 522 829 a(3) p Fp 515 859 a(i) p Fr 541 847 a(\() p Fn(W) p Fr 606 847 a(\)) p Fo(g) p Fp 650 825 a(k) p Fj 669 830 a(3) p Fp 650 859 a(i) p Fl(=) q(1) p Fr 712 847 a(,) p 742 847 a(inductiv) o(ely) l(,) p 1002 847 a(b) o(y) p Fq 666 943 a(F) p Fl 705 922 a(3) 698 955 y(1) p Fr 738 943 a(=) p Fo 790 943 a([) p Fp 823 956 a(i) p Fl(;) p Fp(\031) p Fl 866 956 a(\() 888 948 y(~) p Fp 880 956 a(F) p Fj 907 945 a(3) p Fe 902 967 a(i) p Fl 925 956 a(\)) p Fm(\\f) p Fp(x) p Fj 1001 961 a(1) p Fm 1017 956 a(g6) p Fl(=) p Fm(;) p Fr 1092 930 a(~) p Fq 1081 943 a(F) p Fl 1120 922 a(3) p Fp 1113 955 a(i) p Fq 1139 943 a(;) p Fr 1778 943 a(\(4.45\)) 0 1039 y(and) p Fq 519 1136 a(F) p Fl 558 1115 a(3) p Fp 551 1148 a(j) p Fr 591 1136 a(=) p 643 1136 a(\() p Fo([) p Fp 695 1149 a(i) p Fl(;) p Fp(\031) p Fl 738 1149 a(\() 760 1141 y(~) p Fp 752 1149 a(F) p Fj 779 1138 a(3) p Fe 774 1160 a(i) p Fl 797 1149 a(\)) p Fm(\\f) p Fp(x) p Fe 873 1154 a(j) p Fm 888 1149 a(g6) p Fl(=) p Fm(;) p Fr 963 1123 a(~) p Fq 952 1136 a(F) p Fl 991 1115 a(3) p Fp 984 1148 a(i) p Fr 1011 1136 a(\)) p Fo(n) p Fr(\() p Fo([) p Fp 1107 1143 a(i) p Fm(\024) p Fp(j) p Fm 1162 1143 a(\000) p Fl(1) p Fq 1209 1136 a(F) p Fl 1248 1115 a(3) p Fp 1241 1148 a(i) p Fr 1267 1136 a(\)) p Fq(:) p Fr 1778 1136 a(\(4.46\)) 0 1232 y(Note) p 118 1232 a(that) p Fq 224 1232 a(k) p Fl 249 1239 a(3) p Fo 282 1232 a(\024) p Fr 335 1232 a(8) p Fq(L) p Fr(.) 73 1292 y(W) l(e) p 157 1292 a(will) p 249 1292 a(sho) o(w) p 370 1292 a(that) p 476 1292 a(the) p 560 1292 a(estimate) p Fq 305 1388 a(P) p Fp 343 1368 a(\016) p Fl 336 1401 a(\003) p Fr 363 1388 a(\() p Fn(W) p Fr 428 1388 a(\)) p Fk 447 1333 a(.) p Fq 491 1388 a(P) p Fp 529 1368 a(\016) p Fl 522 1401 a(\003) p Fr 549 1388 a(\() p Fn(W) p Fm 615 1368 a(0) p Fr 629 1388 a(\)) 225 1495 y(=) p Fk 305 1439 a(\020) p Fr 334 1495 a(\010) p Fp 369 1502 a(\016) p Fr 389 1495 a(\() p Fn(W) p Fr 454 1495 a(\)) p Fk 473 1439 a(.) p Fr 517 1495 a(\010) p Fp 552 1502 a(\016) p Fr 571 1495 a(\() p Fn(W) p Fm 637 1474 a(0) p Fr 651 1495 a(\)) p Fk 670 1439 a(\021) p Fo 711 1495 a(\002) p Fk 402 1546 a(\020) p Fr 432 1601 a(exp) o([) p Fo(\000) p Fk 592 1554 a(X) p Fp 567 1661 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 679 1661 a(\)) p Fg 698 1601 a(1) p Fp 726 1608 a(L) p Fc 750 1599 a(0) p Fp 761 1608 a(;) p Fl(2) p Fp(l) p Fr 802 1601 a(\() p Fq(C) p Fr 860 1601 a(\)\010) p Fl 914 1580 a(T) p Fp 914 1613 a(\016) p Fr 941 1601 a(\() p Fq(C) p Fr 999 1601 a(\)]) p Fk 1032 1546 a(.) p Fr 1080 1601 a(exp) o([) p Fo(\000) p Fk 1246 1554 a(X) p Fp 1215 1661 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 1327 1652 a(0) p Fl 1335 1661 a(\)) p Fg 1357 1601 a(1) p Fp 1385 1608 a(L) p Fc 1409 1599 a(0) p Fp 1420 1608 a(;) p Fl(2) p Fp(l) p Fr 1460 1601 a(\() p Fq(C) p Fr 1518 1601 a(\)\010) p Fl 1572 1580 a(T) p Fp 1572 1613 a(\016) p Fr 1600 1601 a(\() p Fq(C) p Fr 1658 1601 a(\)]) p Fk 1691 1546 a(\021) p Fo 224 1782 a(\024) p Fq 305 1782 a(c) p Fl 326 1789 a(31) p Fr 371 1782 a(exp) p Fk 446 1727 a(h) p Fo 469 1782 a(\000) p Fr(\() p Fq 532 1748 a(\014) p 532 1770 31 2 v Fr 535 1816 a(3) p Fo 578 1782 a(\000) p Fq 628 1782 a(c) p Fl 649 1789 a(32) p Fr 687 1782 a(\)) p Fk 706 1727 a(\020) p Fp 753 1719 a(k) p Fj 771 1724 a(2) p Fk 735 1735 a(X) p Fp 743 1840 a(i) p Fl(=1) p Fn 816 1782 a(M) p Fl 860 1761 a(2) p Fr 882 1782 a(\() p Fq(F) p Fl 940 1761 a(2) p Fp 933 1794 a(i) p Fr 959 1782 a(\)) p 989 1782 a(+) p Fp 1056 1719 a(k) p Fj 1074 1724 a(3) p Fk 1038 1735 a(X) p Fp 1046 1840 a(i) p Fl(=1) p Fn 1119 1782 a(M) p Fl 1163 1761 a(2) p Fr 1185 1782 a(\() p Fq(F) p Fl 1243 1761 a(3) p Fp 1236 1794 a(i) p Fr 1262 1782 a(\)) p 1292 1782 a(+) p Fp 1360 1719 a(k) p Fj 1378 1724 a(4) p Fk 1341 1735 a(X) p Fp 1349 1840 a(i) p Fl(=1) p Fn 1422 1782 a(M) p Fl 1466 1761 a(2) p Fr 1488 1782 a(\() p Fq(F) p Fl 1546 1761 a(4) p Fp 1539 1794 a(i) p Fr 1565 1782 a(\)) p Fk 1584 1727 a(\021i) p Fr 1778 1782 a(\(4.47\)) 0 1919 y(holds,) p 141 1919 a(as) p 201 1919 a(follo) o(ws.) 73 1980 y(W) l(e) p 157 1980 a(will) p 249 1980 a(\014rst) p 350 1980 a(b) q(ound) p 500 1980 a(\010) p Fp 535 1987 a(\016) p Fr 554 1980 a(\() p Fn(W) p Fr 620 1980 a(\)) p Fk 639 1939 a(\016) p Fr 671 1980 a(\010) p Fp 706 1987 a(\016) p Fr 725 1980 a(\() p Fn(W) p Fm 791 1961 a(0) p Fr 805 1980 a(\)) p 841 1980 a(from) p 956 1980 a(ab) q(o) o(v) o(e.) p 1113 1980 a(F) l(or) p Fq 1200 1980 a(j) p Fr 1237 1980 a(=) p 1289 1980 a(1) p 1330 1980 a(or) p 1389 1980 a(2,) p 1443 1980 a(let) p Fq 585 2076 a(S) p Fm 615 2083 a(\006) p Fp(j) p Fr 675 2076 a(=) p Fo 726 2076 a(f) p Fq(x) p Fo 793 2076 a(2) p Fq 840 2076 a(@) p Fr 869 2076 a(\003;) p Fq 925 2076 a(x) p Fp 953 2083 a(j) p Fr 984 2076 a(=) p Fo 1036 2076 a(\006) p Fq(L) p Fr 1119 2076 a(+) p 1168 2076 a(\(1) p Fq(=) p Fr(2\)) p Fo(g) p Fq(:) p Fr 0 2172 a(T) l(ak) o(e) p Fq 119 2172 a(i) p Fr 153 2172 a(with) p Fo 266 2172 a(\000) p Fr(1) p Fo 345 2172 a(\025) p Fq 400 2172 a(i) p Fo 433 2172 a(\025) p Fq 488 2172 a(m) p Fr(.) p 569 2172 a(If) p 620 2172 a(for) p 695 2172 a(ev) o(ery) p Fq 825 2172 a(B) p Fo 881 2172 a(2) p 930 2172 a(B) p Fr 965 2172 a(\() p Fq(W) p Fl 1030 2179 a(0) p Fq 1049 2172 a(;) p 1071 2172 a(i) p Fr(\),) p 1138 2172 a(there) p 1264 2172 a(exist) p 1381 2172 a(some) p Fq 1505 2172 a(j) p Fo 1544 2172 a(2) p 1593 2172 a(f\006) p Fr(1) p Fq(;) p Fo 1703 2172 a(\006) p Fr(2) p Fo(g) p Fr 1808 2172 a(suc) o(h) 0 2232 y(that) p Fq 106 2232 a(B) p Fo 156 2232 a(\\) p Fq 201 2232 a(S) p Fp 231 2239 a(j) p Fr 263 2232 a(=) p Fo 314 2232 a(;) p Fr(,) p 369 2232 a(then) p 480 2232 a(w) o(e) p 552 2232 a(can) p 642 2232 a(see) p 720 2232 a(from) p 836 2232 a(\(4.16\)) p 976 2232 a(and) p 1071 2232 a(\(4.26\)) p 1212 2232 a(that) p Fl 257 2319 a(4) p Fk 230 2334 a(X) p Fp 234 2439 a(p) p Fl(=2) p Fp 328 2315 a(k) p Fe 346 2319 a(p) p Fk 310 2334 a(X) p Fp 315 2439 a(j) p Fl 331 2439 a(=1) p Fn 390 2381 a(M) p Fl 434 2361 a(1) p Fr 457 2381 a(\() p Fq(F) p Fp 515 2358 a(p) 508 2394 y(j) p Fo 545 2381 a(\\) p Fr 590 2381 a(H\() p Fq(i) p Fr(\)\)) p Fo 741 2381 a(\025) p Fr 865 2381 a(inf) p Fp 821 2415 a(n) p Fm(2) p Ff(N) p Fm 893 2415 a([f) p Fl(0) p Fm 952 2415 a(g) p Fr 975 2381 a(max) p Fo 1066 2381 a(f) p Fr(2) p Fq(L;) p Fr 1191 2348 a(1) p 1191 2370 25 2 v 1191 2416 a(4) 1221 2381 y(\(2) p Fq(L) p Fo 1308 2381 a(\000) p Fq 1358 2381 a(nK) p Fl 1428 2388 a(4) p Fr 1457 2381 a(log) p Fq 1528 2381 a(L) p Fr(\)) p Fq(;) p 1618 2381 a(n) p Fo(g) 741 2535 y(\025) p Fr 927 2501 a(2) p Fq(L) p 826 2523 259 2 v Fr 826 2569 a(4) p 862 2569 a(+) p Fq 911 2569 a(K) p Fl 952 2576 a(4) p Fr 980 2569 a(log) p Fq 1052 2569 a(L) 1090 2535 y(:) p Fr 1778 2535 a(\(4.48\)) 0 2654 y(F) l(rom) p 128 2654 a(this) p 223 2654 a(together) p 416 2654 a(with) p Fn 190 2750 a(M) p Fl 234 2729 a(1) p Fk 257 2710 a(\000) p Fr 280 2750 a(\() p Fq(W) p Fl 345 2757 a(0) p Fo 364 2750 a(n) p Fq(@) p Fr 418 2750 a(\003\)) p Fo 482 2750 a(\\) p Fr 526 2750 a(H\() p Fq(i) p Fr(\)) p Fk 618 2710 a(\001) p Fo 651 2750 a(\000) p Fn 701 2750 a(M) p Fl 745 2729 a(1) p Fk 767 2710 a(\000) p Fr 790 2750 a(\() p Fq(F) p Fl 841 2757 a(0) p Fo 860 2750 a(n) p Fq(@) p Fr 914 2750 a(\003\)) p Fo 978 2750 a(\\) p Fr 1022 2750 a(H\() p Fq(i) p Fr(\)) p Fk 1114 2710 a(\001) p Fr 1150 2750 a(=) p Fn 1202 2750 a(M) p Fl 1246 2729 a(1) p Fk 1268 2710 a(\000) p Fr 1291 2750 a(\() p Fo([) p Fl 1343 2729 a(4) p Fp 1343 2762 a(p) p Fl(=2) p Fo 1419 2750 a([) p Fp 1452 2724 a(k) p Fe 1470 2728 a(p) p Fp 1452 2763 a(j) p Fl 1468 2763 a(=1) p Fq 1527 2750 a(F) p Fp 1566 2726 a(p) 1559 2763 y(j) p Fr 1585 2750 a(\)) p Fo 1615 2750 a(\\) p Fr 1659 2750 a(H\() p Fq(i) p Fr(\)) p Fk 1751 2710 a(\001) p Fq 1773 2750 a(;) p Fr 1778 2823 a(\(4.49\)) 927 2947 y(27) p 90 rotate dyy eop %%Page: 28 28 28 27 bop Fr 0 274 a(w) o(e) p 72 274 a(ha) o(v) o(e) p 184 274 a(that) p Fn 451 375 a(M) p Fl 495 354 a(1) p Fk 518 335 a(\000) p Fr 541 375 a(\() p Fq(W) p Fl 606 382 a(0) p Fo 625 375 a(n) p Fq(@) p Fr 679 375 a(\003\)) p Fo 743 375 a(\\) p Fr 787 375 a(H\() p Fq(i) p Fr(\)) p Fk 879 335 a(\001) p Fr 912 375 a(+) p Fq 961 375 a(\016) p Fn 985 375 a(M) p Fl 1029 354 a(1) p Fk 1051 335 a(\000) p Fr 1074 375 a(\() p Fq(W) p Fl 1139 382 a(0) p Fo 1170 375 a(\\) p Fq 1214 375 a(@) p Fr 1243 375 a(\003\)) p Fo 1306 375 a(\\) p Fr 1351 375 a(H\() p Fq(i) p Fr(\)) p Fk 1443 335 a(\001) p Fo 549 448 a(\000) p Fn(M) p Fl 631 427 a(1) p Fk 654 407 a(\000) p Fr 677 448 a(\() p Fq(F) p Fl 728 455 a(0) p Fo 747 448 a(n) p Fq(@) p Fr 801 448 a(\003\)) p Fo 864 448 a(\\) p Fr 909 448 a(H\() p Fq(i) p Fr(\)) p Fk 1001 407 a(\001) p Fo 1034 448 a(\000) p Fq 1084 448 a(\016) p Fn 1108 448 a(M) p Fl 1151 427 a(1) p Fk 1174 407 a(\000) p Fr 1197 448 a(\() p Fq(F) p Fl 1248 455 a(0) p Fo 1278 448 a(\\) p Fq 1322 448 a(@) p Fr 1351 448 a(\003\)) p Fo 1415 448 a(\\) p Fr 1459 448 a(H\() p Fq(i) p Fr(\)) p Fk 1551 407 a(\001) p Fo 371 549 a(\025) p Fr 456 516 a(1) p 456 538 25 2 v 456 583 a(2) p Fn 485 549 a(M) p Fl 529 529 a(1) p Fk 552 509 a(\000) p Fr 575 549 a(\() p Fo([) p Fl 627 529 a(4) p Fp 627 562 a(p) p Fl(=2) p Fo 703 549 a([) p Fp 736 523 a(k) p Fe 754 527 a(p) p Fp 736 562 a(j) p Fl 752 562 a(=1) p Fq 811 549 a(F) p Fp 850 526 a(p) 843 562 y(j) p Fr 869 549 a(\)) p Fo 899 549 a(\\) p Fr 943 549 a(H\() p Fq(i) p Fr(\)) p Fk 1035 509 a(\001) p Fr 1068 549 a(+) p Fq 1235 516 a(L) p 1122 538 259 2 v Fr 1122 583 a(4) p 1158 583 a(+) p Fq 1207 583 a(K) p Fl 1248 590 a(4) p Fr 1276 583 a(log) p Fq 1348 583 a(L) p Fo 1397 549 a(\000) p Fr 1447 549 a(8) p Fq(\016) r(L) p Fo 371 676 a(\025) p Fr 456 642 a(1) p 456 664 25 2 v 456 710 a(2) p Fn 485 676 a(M) p Fl 529 655 a(1) p Fk 552 635 a(\000) p Fr 575 676 a(\() p Fo([) p Fl 627 655 a(4) p Fp 627 688 a(p) p Fl(=2) p Fo 703 676 a([) p Fp 736 649 a(k) p Fe 754 653 a(p) p Fp 736 688 a(j) p Fl 752 688 a(=1) p Fq 811 676 a(F) p Fp 850 652 a(p) 843 688 y(j) p Fr 869 676 a(\)) p Fo 899 676 a(\\) p Fr 943 676 a(H\() p Fq(i) p Fr(\)) p Fk 1035 635 a(\001) p Fq 1057 676 a(:) p Fr 1778 676 a(\(4.50\)) 0 792 y(If) p 48 792 a(there) p 171 792 a(exists) p 305 792 a(a) p 344 792 a(unique) p Fq 502 792 a(B) p Fl 539 799 a(0) p Fo 572 792 a(2) p 619 792 a(B) p Fr 654 792 a(\() p Fq(W) p Fl 719 799 a(0) p Fq 738 792 a(;) p 760 792 a(i) p Fr(\)) p 811 792 a(suc) o(h) p 920 792 a(that) p Fq 1024 792 a(B) p Fl 1061 799 a(0) p Fo 1090 792 a(\\) p Fq 1132 792 a(S) p Fp 1162 799 a(j) p Fo 1194 792 a(6) p Fr(=) p Fo 1246 792 a(;) p Fr 1286 792 a(for) p 1359 792 a(all) p Fq 1426 792 a(j) p Fo 1463 792 a(2) p 1510 792 a(f\006) p Fr(1) p Fq(;) p Fo 1620 792 a(\006) p Fr(2) p Fo(g) p Fr(,) p 1737 792 a(then) p 1847 792 a(w) o(e) 0 852 y(can) p 89 852 a(see) p 168 852 a(that) p Fn 456 953 a(M) p Fl 500 932 a(1) p Fk 523 913 a(\000) p Fr 545 953 a(\() p Fo([) p Fl 597 932 a(4) p Fp 597 965 a(p) p Fl(=2) p Fo 674 953 a([) p Fp 707 927 a(k) p Fe 725 931 a(p) p Fp 707 966 a(j) p Fl 723 966 a(=1) p Fq 781 953 a(F) p Fp 820 929 a(p) 813 966 y(j) p Fr 839 953 a(\)) p Fo 870 953 a(\\) p Fr 914 953 a(H\() p Fq(i) p Fr(\)) p Fk 1006 913 a(\001) p Fr 1039 953 a(+) p Fn 1088 953 a(M) p Fl 1132 932 a(1) p Fk 1155 913 a(\000) p Fr 1177 953 a(\() p Fq(W) p Fl 1242 960 a(0) p Fo 1273 953 a(\\) p Fq 1318 953 a(@) p Fr 1347 953 a(\003\)) p Fo 1410 953 a(\\) p Fr 1454 953 a(H\() p Fq(i) p Fr(\)) p Fk 1546 913 a(\001) p Fo 376 1031 a(\025) p Fn 456 1031 a(M) p Fl 500 1011 a(1) p Fk 523 991 a(\000) p Fq 545 1031 a(B) p Fl 582 1038 a(0) p Fo 602 1031 a(n) p Fr(\() p Fo([) p Fp 679 1040 a(F) p Fm 706 1040 a(2) p Ff(F) p Fj 751 1030 a(1) p Fq 770 1031 a(F) p Fr 809 1031 a(\)) p Fk 828 991 a(\001) p Fo 376 1104 a(\025) p Fn 456 1104 a(M) p Fl 500 1083 a(1) p Fk 523 1063 a(\000) p Fq 545 1104 a(@) p Fr 574 1104 a(\003) p Fo 619 1104 a(\\) p Fr 663 1104 a(H\() p Fq(i) p Fr(\)) p Fk 755 1063 a(\001) p Fo 788 1104 a(\000) p Fn 838 1104 a(M) p Fl 882 1083 a(1) p Fk 905 1063 a(\000) p Fr 928 1104 a(\() p Fo([) p Fp 980 1112 a(F) p Fm 1007 1112 a(2) p Ff(F) p Fj 1052 1103 a(1) p Fr 1070 1104 a(\() p Fq(@) p Fr 1118 1104 a(\002\() p Fq(F) p Fr 1214 1104 a(\)) p Fo 1243 1104 a(\\) p Fq 1287 1104 a(@) p Fr 1316 1104 a(\003\)\)) p Fo 1398 1104 a(\\) p Fr 1443 1104 a(H\() p Fq(i) p Fr(\)) p Fk 1535 1063 a(\001) p Fr 376 1176 a(=) p Fn 456 1176 a(M) p Fl 500 1156 a(1) p Fk 523 1136 a(\000) p Fr 545 1176 a(\() p Fq(F) p Fl 596 1183 a(0) p Fo 627 1176 a(\\) p Fq 671 1176 a(@) p Fr 700 1176 a(\003\)) p Fo 763 1176 a(\\) p Fr 808 1176 a(H\() p Fq(i) p Fr(\)) p Fk 900 1136 a(\001) p Fq 922 1176 a(:) p Fr 1778 1176 a(\(4.51\)) 0 1277 y(F) l(rom) p 128 1277 a(this) p 223 1277 a(and) p 318 1277 a(\(4.49\),) p 472 1277 a(w) o(e) p 544 1277 a(ha) o(v) o(e) p 657 1277 a(that) 422 1384 y(LHS\(4) p Fq(:) p Fr(50\)) p Fo 682 1384 a(\025) p Fr 762 1384 a(\(1) p Fo 817 1384 a(\000) p Fq 866 1384 a(\016) p Fr 890 1384 a(\)) p Fn(M) p Fl 953 1363 a(1) p Fk 976 1344 a(\000) p Fr 998 1384 a(\() p Fo([) p Fl 1050 1363 a(4) p Fp 1050 1396 a(p) p Fl(=2) p Fo 1127 1384 a([) p Fp 1160 1358 a(k) p Fe 1178 1362 a(p) p Fp 1160 1397 a(j) p Fl 1176 1397 a(=1) p Fq 1234 1384 a(F) p Fp 1273 1360 a(p) 1266 1397 y(j) p Fr 1292 1384 a(\)) p Fo 1322 1384 a(\\) p Fr 1367 1384 a(H\() p Fq(i) p Fr(\)) p Fk 1459 1344 a(\001) p Fo 682 1486 a(\025) p Fr 767 1452 a(1) p 767 1474 V 767 1520 a(2) p Fn 796 1486 a(M) p Fl 841 1465 a(1) p Fk 863 1445 a(\000) p Fr 886 1486 a(\() p Fo([) p Fl 938 1465 a(4) p Fp 938 1498 a(p) p Fl(=2) p Fo 1014 1486 a([) p Fp 1047 1459 a(k) p Fe 1065 1463 a(p) p Fp 1047 1498 a(j) p Fl 1063 1498 a(=1) p Fq 1122 1486 a(F) p Fp 1161 1462 a(p) 1154 1498 y(j) p Fr 1180 1486 a(\)) p Fo 1210 1486 a(\\) p Fr 1254 1486 a(H\() p Fq(i) p Fr(\)) p Fk 1346 1445 a(\001) p Fq 1368 1486 a(:) p Fr 1778 1486 a(\(4.52\)) 0 1609 y(F) l(rom) p 127 1609 a(\(3.24\),) p 280 1609 a(\(4.50\),) p 434 1609 a(\(4.52\)) p 573 1609 a(and) p 667 1609 a(the) p 749 1609 a(de\014nitions) p 984 1609 a(of) p Fq 1038 1609 a(z) p Fl 1061 1616 a(min) p Fq 1122 1609 a(;) p Fo 1159 1609 a(f) p Fq(F) p Fl 1223 1591 a(2) p Fp 1216 1622 a(j) p Fo 1242 1609 a(g) p Fp 1267 1588 a(k) p Fj 1285 1593 a(2) p Fp 1267 1622 a(j) p Fl 1283 1622 a(=0) p Fq 1330 1609 a(;) p Fo 1367 1609 a(f) p Fq(F) p Fl 1431 1591 a(3) p Fp 1424 1622 a(j) p Fo 1450 1609 a(g) p Fp 1475 1588 a(k) p Fj 1493 1593 a(3) p Fp 1475 1622 a(j) p Fl 1491 1622 a(=1) p Fr 1553 1609 a(and) p Fo 1647 1609 a(f) p Fq(F) p Fl 1711 1591 a(4) p Fp 1704 1622 a(j) p Fo 1730 1609 a(g) p Fp 1755 1588 a(k) p Fj 1773 1593 a(4) p Fp 1755 1622 a(j) p Fl 1771 1622 a(=1) p Fr 1818 1609 a(,) p 1847 1609 a(w) o(e) 0 1670 y(ha) o(v) o(e) p 112 1670 a(that) 153 1805 y(\010) p Fp 188 1812 a(\016) p Fr 207 1805 a(\() p Fn(W) p Fr 273 1805 a(\)) p Fk 292 1765 a(\016) p Fr 324 1805 a(\010) p Fp 359 1812 a(\016) p Fr 378 1805 a(\() p Fn(W) p Fm 443 1784 a(0) p Fr 458 1805 a(\)) p Fo 491 1805 a(\024) p Fr 544 1805 a(exp) p Fk 618 1750 a(h) p Fo 642 1805 a(\000) p Fq 686 1771 a(\014) p 686 1793 31 2 v Fr 689 1839 a(3) p Fk 721 1750 a(\020) p Fp 768 1742 a(k) p Fj 786 1747 a(2) p Fk 750 1758 a(X) p Fp 756 1863 a(j) p Fl 772 1863 a(=1) p Fn 831 1805 a(M) p Fl 875 1784 a(2) p Fr 897 1805 a(\() p Fq(F) p Fl 955 1784 a(2) p Fp 948 1817 a(j) p Fr 974 1805 a(\)) p 1004 1805 a(+) p Fp 1072 1742 a(k) p Fj 1090 1747 a(3) p Fk 1053 1758 a(X) p Fp 1059 1863 a(j) p Fl 1075 1863 a(=1) p Fn 1134 1805 a(M) p Fl 1178 1784 a(2) p Fr 1200 1805 a(\() p Fq(F) p Fl 1258 1784 a(3) p Fp 1251 1817 a(j) p Fr 1277 1805 a(\)) p 1307 1805 a(+) p Fp 1375 1742 a(k) p Fj 1393 1747 a(4) p Fk 1357 1758 a(X) p Fp 1362 1863 a(j) p Fl 1378 1863 a(=1) p Fn 1437 1805 a(M) p Fl 1481 1784 a(2) p Fr 1504 1805 a(\() p Fq(F) p Fl 1562 1784 a(4) p Fp 1555 1817 a(j) p Fr 1581 1805 a(\)) p Fk 1600 1750 a(\021) o(i) p Fq 1653 1805 a(:) p Fr 1778 1928 a(\(4.53\)) 73 2029 y(In) p 134 2029 a(order) p 261 2029 a(to) p 321 2029 a(estimate) p 516 2029 a(the) p 600 2029 a(e\013ect) p 729 2029 a(of) p 785 2029 a(en) o(trop) o(y) l(,) p 972 2029 a(w) o(e) p 1043 2029 a(will) p 1136 2029 a(next) p 1245 2029 a(b) q(ound) p 1396 2029 a(from) p 1511 2029 a(ab) q(o) o(v) o(e) p Fk 441 2083 a(\014) 441 2113 y(\014) 441 2143 y(\014) 483 2093 y(X) p Fp 458 2201 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 570 2201 a(\)) p Fg 589 2141 a(1) p Fp 617 2148 a(L) p Fc 641 2139 a(0) p Fp 652 2148 a(;) p Fl(2) p Fp(l) p Fr 693 2141 a(\() p Fq(C) p Fr 751 2141 a(\)\010) p Fl 805 2120 a(T) p Fp 805 2153 a(\016) p Fr 832 2141 a(\() p Fq(C) p Fr 890 2141 a(\)) p Fo 919 2141 a(\000) p Fk 1000 2093 a(X) p Fp 969 2201 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 1081 2192 a(0) p Fl 1089 2201 a(\)) p Fg 1111 2141 a(1) p Fp 1139 2148 a(L) p Fc 1163 2139 a(0) p Fp 1175 2148 a(;) p Fl(2) p Fp(l) p Fr 1215 2141 a(\() p Fq(C) p Fr 1273 2141 a(\)\010) p Fl 1327 2120 a(T) p Fp 1327 2153 a(\016) p Fr 1354 2141 a(\() p Fq(C) p Fr 1412 2141 a(\)) p Fk 1431 2083 a(\014) 1431 2113 y(\014) 1431 2143 y(\014) p Fq 1447 2141 a(:) p Fr 0 2297 a(T) l(o) p 72 2297 a(do) p 140 2297 a(this,) p 248 2297 a(w) o(e) p 320 2297 a(ha) o(v) o(e) p 432 2297 a(only) p 540 2297 a(to) p 599 2297 a(lo) q(ok) p 705 2297 a(at) p 764 2297 a(standard) p 968 2297 a(w) o(alls) p Fq 1089 2297 a(W) p Fo 1155 2297 a(2) p Fn 1202 2297 a(W) p Fo 1249 2297 a(nf) p Fq(W) p Fl 1345 2304 a(0) p Fo 1368 2297 a(g) p Fr 1409 2297 a(suc) o(h) p 1519 2297 a(that) p 1625 2297 a(\(see) p 1723 2297 a(\(1.26\)\)) 724 2398 y(b\() p Fq(W) o(;) p Fn 837 2398 a(W) p Fr 884 2398 a(\)) p Fo 920 2398 a(6) p Fr(=) p 971 2398 a(b\() p Fq(W) o(;) p Fn 1084 2398 a(W) p Fm 1131 2377 a(0) p Fr 1145 2398 a(\)) p Fq(:) p Fr 0 2499 a(Note) p 118 2499 a(that) 758 2559 y(b\() p Fq(W) o(;) p Fn 871 2559 a(W) p Fm 917 2538 a(0) p Fr 932 2559 a(\)) p 965 2559 a(=) p Fq 1016 2559 a(m) p Fo 1070 2559 a(\000) p Fr 1120 2559 a(1) 0 2642 y(for) p 78 2642 a(all) p Fq 150 2642 a(W) p Fo 222 2642 a(2) p 276 2642 a(f) p Fq(W) p Fm 354 2624 a(0) p Fo 385 2642 a(2) p Fn 438 2642 a(W) p Fo 485 2642 a(nf) p Fq(W) p Fl 581 2649 a(0) p Fo 604 2642 a(g) p Fr(;) p Fq 651 2642 a(W) p Fm 704 2624 a(0) p Fr 735 2642 a(is) p 784 2642 a(a) p 824 2642 a(maximal) p 1024 2642 a(standard) p 1227 2642 a(w) o(all) p Fo 1312 2642 a(g) p Fr(.) p 1383 2642 a(Let) p Fq 1474 2642 a(v) p Fr 1500 2642 a(\() p Fq(W) p Fr 1572 2642 a(\)) p 1611 2642 a(=) p 1669 2642 a(b\() p Fq(W) o(;) p Fn 1782 2642 a(W) p Fr 1828 2642 a(\)) p Fo 1863 2642 a(\000) p Fr 0 2702 a(b\() p Fq(W) o(;) p Fn 113 2702 a(W) p Fm 159 2684 a(0) p Fr 174 2702 a(\).) p 235 2702 a(W) l(e) p 322 2702 a(will) p 416 2702 a(\014rst) p 519 2702 a(consider) p 711 2702 a(standard) p 917 2702 a(w) o(alls) p 1040 2702 a(suc) o(h) p 1153 2702 a(that) p 1263 2702 a(^) p Fq 1261 2702 a(\031) p Fr 1290 2702 a(\() p Fq(W) p Fr 1362 2702 a(\)) p Fo 1399 2702 a(\032) p Fr 1455 2702 a(\(H\() p Fo(\000) p Fl 1574 2683 a(1) p 1574 2691 18 2 v 1574 2719 a(2) p Fr 1596 2702 a(\)) p Fo(n) p Fr 1643 2702 a(^) p Fq 1640 2702 a(\031) p Fr 1670 2702 a(\() p Fq(W) p Fl 1735 2709 a(0) p Fr 1754 2702 a(\)\).) p 1834 2702 a(W) l(e) 0 2762 y(de\014ne) p Fn 488 2823 a(W) p Fp 535 2830 a(ex) p Fr 590 2823 a(=) p Fo 642 2823 a(f) p Fq(W) p Fo 733 2823 a(2) p Fn 780 2823 a(W) p Fr 827 2823 a(;) p 855 2823 a(^) p Fq 849 2823 a(\031) p Fr 882 2823 a(\() p Fq(W) p Fr 954 2823 a(\)) p Fo 986 2823 a(\032) p Fr 1039 2823 a(\(H\() p Fo(\000) p Fl 1158 2803 a(1) p 1158 2811 V 1158 2840 a(2) p Fr 1180 2823 a(\)) p Fo(n) p Fr 1227 2823 a(^) p Fq 1224 2823 a(\031) p Fr 1253 2823 a(\() p Fq(W) p Fl 1318 2830 a(0) p Fr 1338 2823 a(\)\)) p Fo(g) p Fq(:) p Fr 927 2947 a(28) p 90 rotate dyy eop %%Page: 29 29 29 28 bop Fr 0 274 a(Note) p 113 274 a(that) p Fq 213 274 a(v) p Fr 239 274 a(\() p Fq(W) p Fr 311 274 a(\)) p 343 274 a(=) p Fq 395 274 a(m) p 452 274 a(<) p Fr 503 274 a(0) p 539 274 a(for) p 608 274 a(an) o(y) p Fq 695 274 a(W) p Fo 762 274 a(2) p Fn 809 274 a(W) p Fp 856 281 a(ex) p Fr 897 274 a(.) p 931 274 a(W) l(e) p 1010 274 a(decomp) q(ose) p 1253 274 a(^) p Fq 1250 274 a(\031) p Fr 1279 274 a(\() p Fq(Q) p Fr(\(\003\)\)) p Fo(n) p Fr 1456 274 a(^) p Fq 1453 274 a(\031) p Fr 1482 274 a(\() p Fq(W) p Fl 1547 281 a(0) p Fr 1567 274 a(\)) p 1597 274 a(in) o(to) p 1691 274 a(connected) 0 334 y(comp) q(onen) o (ts) p Fo 271 334 a(f) p Fq(R) p Fp 333 341 a(k) p Fo 354 334 a(g) p Fp 379 316 a(r) 379 347 y(k) p Fl 398 347 a(=1) p Fr 445 334 a(.) p 487 334 a(F) l(or) p 577 334 a(eac) o(h) p Fq 689 334 a(k) p Fo 734 334 a(\024) p Fq 790 334 a(r) p Fr 832 334 a(and) p 929 334 a(an) o(y) p Fo 1023 334 a(\000) p Fr(1) p Fo 1104 334 a(\025) p Fq 1160 334 a(i) p Fo 1195 334 a(\025) p Fq 1251 334 a(m) p Fr(,) p 1326 334 a(there) p 1453 334 a(exist) p Fq 1571 334 a(D) p Fp 1611 341 a(k) p Fr 1633 334 a(\() p Fq(i) p Fr(\)) p Fo 1705 334 a(\032) p Fr 1761 334 a(H\() p Fo(\000) p Fl 1861 315 a(1) p 1861 323 18 2 v 1861 351 a(2) p Fr 1883 334 a(\)) 0 394 y(suc) o(h) p 110 394 a(that) p Fq 216 394 a(R) p Fp 253 401 a(k) p Fo 288 394 a(\032) p Fq 341 394 a(D) p Fp 381 401 a(k) p Fr 402 394 a(\() p Fq(i) p Fr(\)) p 473 394 a(and) p Fq 401 493 a(@) p Fl 430 473 a(2) p Fq 449 493 a(D) p Fp 489 500 a(k) p Fr 511 493 a(\() p Fq(i) p Fr(\)) p Fo 576 493 a(\011) p Fq 626 493 a(@) p Fl 655 473 a(2) p Fr 677 493 a(^) p Fq 674 493 a(\031) p Fr 704 493 a(\() p Fq(Q) p Fr(\(\003\)\)) p 863 493 a(+) p 912 493 a(\(0) p Fq(;) p Fr 977 493 a(0) p Fq(;) p 1023 493 a(i) p Fr 1051 493 a(+) p 1100 493 a(\(1) p Fq(=) p Fr(2\)\)) p Fo 1244 493 a(\032) p Fq 1297 493 a(F) p Fl 1336 473 a(4) p Fp 1329 506 a(j) p Fo 1366 493 a(\\) p Fr 1410 493 a(H\() p Fq(i) p Fr(\)) 0 593 y(for) p 75 593 a(some) p Fq 197 593 a(j) p Fr 234 593 a(=) p Fq 285 593 a(j) p Fr 308 593 a(\() p Fq(k) r(;) p 376 593 a(i) p Fr(\).) p 447 593 a(By) p 524 593 a(the) p 608 593 a(de\014nition) p 824 593 a(of) p Fq 880 593 a(W) p Fl 926 600 a(0) p Fr 946 593 a(,) p 975 593 a(w) o(e) p 1047 593 a(can) p 1137 593 a(see) p 1216 593 a(that) p Fn 568 692 a(M) p Fl 612 671 a(1) p Fr 635 692 a(\() p Fq(@) p Fl 683 671 a(2) p Fq 702 692 a(D) p Fp 742 699 a(k) p Fr 764 692 a(\() p Fq(i) p Fr(\)\)) p Fo 851 692 a(\024) p Fr 904 692 a(2) p Fn(M) p Fl 972 671 a(1) p Fr 995 692 a(\() p Fq(F) p Fl 1053 671 a(4) p Fp 1046 704 a(j) p Fo 1083 692 a(\\) p Fr 1127 692 a(H\() p Fq(i) p Fr(\)\)) p Fq(:) p Fr 1778 692 a(\(4.54\)) 0 791 y(It) p 53 791 a(ma) o(y) p 158 791 a(happ) q(en) p 330 791 a(that) p Fq 435 791 a(j) p Fr 458 791 a(\() p Fq(k) p Fl 502 798 a(1) p Fq 522 791 a(;) p 544 791 a(i) p Fr(\)) p 594 791 a(=) p Fq 645 791 a(j) p Fr 668 791 a(\() p Fq(k) p Fl 712 798 a(2) p Fq 732 791 a(;) p 754 791 a(i) p Fr(\)) p 806 791 a(ev) o(en) p 917 791 a(if) p Fq 961 791 a(k) p Fl 986 798 a(1) p Fo 1020 791 a(6) p Fr(=) p Fq 1072 791 a(k) p Fl 1097 798 a(2) p Fr 1117 791 a(.) p 1152 791 a(In) p 1213 791 a(this) p 1307 791 a(case,) p Fq 1424 791 a(D) p Fp 1464 798 a(k) p Fj 1482 803 a(1) p Fr 1502 791 a(\() p Fq(i) p Fr(\)) p 1571 791 a(=) p Fq 1623 791 a(D) p Fp 1663 798 a(k) p Fj 1681 803 a(2) p Fr 1701 791 a(\() p Fq(i) p Fr(\).) p 1790 791 a(F) l(rom) 0 851 y(this) p 95 851 a(and) p 190 851 a(\(4.54\),) p 344 851 a(w) o(e) p 416 851 a(can) p 506 851 a(see) p 584 851 a(that) p Fp 428 935 a(m) p Fk 408 950 a(X) p Fp 402 1055 a(i) p Fl(=) p Fm(\000) p Fl(1) p Fn 495 997 a(M) p Fl 539 976 a(1) p Fr 561 997 a(\() p Fo([) p Fp 613 976 a(r) 613 1009 y(k) p Fl 632 1009 a(=1) p Fq 680 997 a(@) p Fl 709 976 a(2) p Fq 728 997 a(D) p Fp 768 1004 a(k) p Fr 790 997 a(\() p Fq(i) p Fr(\)\)) p Fo 905 997 a(\024) p Fr 985 997 a(2) p Fp 1045 935 a(m) p Fk 1024 950 a(X) p Fp 1017 1055 a(i) p Fl(=) p Fm(\000) p Fl(1) p Fp 1129 934 a(k) p Fj 1147 939 a(4) p Fk 1111 950 a(X) p Fp 1116 1055 a(j) p Fl 1132 1055 a(=1) p Fn 1191 997 a(M) p Fl 1235 976 a(1) p Fr 1258 997 a(\() p Fq(F) p Fl 1316 976 a(4) p Fp 1309 1009 a(j) p Fo 1346 997 a(\\) p Fr 1390 997 a(H\() p Fq(i) p Fr(\)\)) p Fo 905 1173 a(\024) p Fr 985 1173 a(2) p Fp 1036 1111 a(k) p Fj 1054 1116 a(4) p Fk 1018 1126 a(X) p Fp 1023 1231 a(j) p Fl 1039 1231 a(=1) p Fn 1098 1173 a(M) p Fl 1142 1153 a(2) p Fr 1165 1173 a(\() p Fq(F) p Fl 1223 1153 a(4) p Fp 1216 1185 a(j) p Fr 1242 1173 a(\)) p Fq(:) p Fr 1778 1173 a(\(4.55\)) 0 1323 y(W) l(e) p 88 1323 a(will) p 184 1323 a(next) p 297 1323 a(consider) p 491 1323 a(standard) p 698 1323 a(w) o(alls) p Fq 822 1323 a(W) p Fr 895 1323 a(suc) o(h) p 1009 1323 a(that) p Fq 1118 1323 a(v) p Fr 1144 1323 a(\() p Fq(W) p Fr 1216 1323 a(\)) p Fo 1255 1323 a(6) p Fr(=) p 1313 1323 a(0) p 1357 1323 a(and) p 1458 1323 a(^) p Fq 1456 1323 a(\031) p Fr 1485 1323 a(\() p Fq(W) p Fr 1557 1323 a(\)) p Fo 1596 1323 a(\032) p Fr 1657 1323 a(^) p Fq 1655 1323 a(\031) p Fr 1684 1323 a(\() p Fq(W) p Fl 1749 1330 a(0) p Fr 1769 1323 a(\).) p 1834 1323 a(W) l(e) 0 1383 y(de\014ne) p Fn 369 1443 a(W) p Fm 416 1422 a(\000) p Fp 416 1456 a(in) p Fr 468 1443 a(=) p Fo 520 1443 a(f) p Fq(W) p Fo 612 1443 a(2) p Fn 659 1443 a(W) p Fo 706 1443 a(nf) p Fq(W) p Fl 802 1450 a(0) p Fo 824 1443 a(g) p Fr(;) p Fq 871 1443 a(v) p Fr 897 1443 a(\() p Fq(W) p Fr 969 1443 a(\)) p Fq 1001 1443 a(<) p Fr 1053 1443 a(0) p 1093 1443 a(and) p 1191 1443 a(^) p Fq 1188 1443 a(\031) p Fr 1218 1443 a(\() p Fq(W) p Fr 1290 1443 a(\)) p Fo 1322 1443 a(\032) p Fr 1377 1443 a(^) p Fq 1375 1443 a(\031) p Fr 1404 1443 a(\() p Fq(W) p Fl 1469 1450 a(0) p Fr 1489 1443 a(\)) p Fo(g) p Fr 0 1525 a(and) p Fn 363 1586 a(W) p Fl 409 1565 a(+) p Fp 409 1598 a(in) p Fr 462 1586 a(=) p Fo 513 1586 a(f) p Fq(W) p Fo 605 1586 a(2) p Fn 652 1586 a(W) p Fo 699 1586 a(nf) p Fq(W) p Fl 795 1593 a(0) p Fo 817 1586 a(g) p Fr(;) p Fq 864 1586 a(v) p Fr 890 1586 a(\() p Fq(W) p Fr 962 1586 a(\)) p Fq 994 1586 a(>) p Fr 1046 1586 a(0) p 1087 1586 a(and) p 1184 1586 a(^) p Fq 1181 1586 a(\031) p Fr 1211 1586 a(\() p Fq(W) p Fr 1283 1586 a(\)) p Fo 1315 1586 a(\032) p Fr 1371 1586 a(^) p Fq 1368 1586 a(\031) p Fr 1398 1586 a(\() p Fq(W) p Fl 1463 1593 a(0) p Fr 1482 1586 a(\)) p Fo(g) p Fq(:) p Fr 0 1668 a(F) l(or) p 86 1668 a(eac) o(h) p Fq 195 1668 a(W) p Fo 261 1668 a(2) p Fn 308 1668 a(W) p Fm 355 1648 a(\000) p Fp 355 1681 a(in) p Fr 409 1668 a(and) p 502 1668 a(an) o(y) p Fq 593 1668 a(m) p Fo 645 1668 a(\000) p Fr 692 1668 a(1) p Fo 730 1668 a(\025) p Fq 783 1668 a(i) p Fo 813 1668 a(\025) p Fq 866 1668 a(m) p Fr 917 1668 a(+) p Fq 964 1668 a(v) p Fr 990 1668 a(\() p Fq(W) p Fr 1062 1668 a(\),) p 1109 1668 a(there) p 1232 1668 a(exist) p Fq 1346 1668 a(D) p Fp 1386 1675 a(W) p Fr 1427 1668 a(\() p Fq(i) p Fr(\)) p Fo 1496 1668 a(\032) p Fr 1548 1668 a(H\() p Fo(\000) p Fl 1648 1649 a(1) p 1648 1657 V 1648 1685 a(2) p Fr 1670 1668 a(\)) p 1704 1668 a(suc) o(h) p 1813 1668 a(that) 3 1728 y(^) p Fq 0 1728 a(\031) p Fr 29 1728 a(\() p Fq(W) p Fr 101 1728 a(\)) p Fo 134 1728 a(\032) p Fq 187 1728 a(D) p Fp 227 1735 a(W) p Fr 267 1728 a(\() p Fq(i) p Fr(\)) p 338 1728 a(and) p Fq 418 1827 a(@) p Fl 447 1807 a(2) p Fq 466 1827 a(D) p Fp 506 1834 a(W) p Fr 546 1827 a(\() p Fq(i) p Fr(\)) p 612 1827 a(+) p 661 1827 a(\(0) p Fq(;) p Fr 726 1827 a(0) p Fq(;) p 772 1827 a(i) p Fr 800 1827 a(+) p 849 1827 a(\(1) p Fq(=) p Fr(2\)\)) p Fo 993 1827 a(\032) p Fr 1046 1827 a(\() p Fq(F) p Fl 1104 1807 a(2) p Fp 1097 1840 a(j) p Fo 1134 1827 a([) p Fq 1178 1827 a(F) p Fl 1217 1807 a(4) p Fp 1210 1840 a(k) p Fr 1236 1827 a(\)) p Fo 1266 1827 a(\\) p Fr 1311 1827 a(H\() p Fq(i) p Fr(\)) p 1778 1827 a(\(4.56\)) 0 1927 y(for) p 82 1927 a(some) p Fq 211 1927 a(j) p Fr 260 1927 a(=) p Fq 324 1927 a(j) p Fr 347 1927 a(\() p Fq(W) o(;) p 433 1927 a(i) p Fr(\)) p 491 1927 a(and) p Fq 593 1927 a(k) p Fr 646 1927 a(=) p Fq 710 1927 a(k) p Fr 737 1927 a(\() p Fq(W) o(;) p 823 1927 a(i) p Fr(\).) p 915 1927 a(It) p 975 1927 a(ma) o(y) p 1088 1927 a(happ) q(en) p 1267 1927 a(that) p Fq 1380 1927 a(j) p Fr 1403 1927 a(\() p Fq(W) p Fl 1468 1934 a(1) p Fq 1488 1927 a(;) p 1510 1927 a(i) p Fr(\)) p 1571 1927 a(=) p Fq 1635 1927 a(j) p Fr 1658 1927 a(\() p Fq(W) p Fl 1723 1934 a(2) p Fq 1743 1927 a(;) p 1765 1927 a(i) p Fr(\)) p 1824 1927 a(and) p Fq 0 1987 a(k) p Fr 27 1987 a(\() p Fq(W) p Fl 92 1994 a(1) p Fq 112 1987 a(;) p 134 1987 a(i) p Fr(\)) p 192 1987 a(=) p Fq 252 1987 a(k) p Fr 279 1987 a(\() p Fq(W) p Fl 344 1994 a(2) p Fq 364 1987 a(;) p 386 1987 a(i) p Fr(\)) p 442 1987 a(ev) o(en) p 559 1987 a(if) p Fq 608 1987 a(W) p Fl 654 1994 a(1) p Fo 696 1987 a(6) p Fr(=) p Fq 757 1987 a(W) p Fl 803 1994 a(2) p Fr 823 1987 a(.) p 873 1987 a(In) p 939 1987 a(this) p 1039 1987 a(case,) p Fq 1162 1987 a(D) p Fp 1202 1994 a(W) p Fj 1235 1999 a(1) p Fr 1255 1987 a(\() p Fq(i) p Fr(\)) p 1332 1987 a(=) p Fq 1392 1987 a(D) p Fp 1432 1994 a(W) p Fj 1465 1999 a(2) p Fr 1486 1987 a(\() p Fq(i) p Fr(\).) p 1590 1987 a(F) l(rom) p 1724 1987 a(this) p 1824 1987 a(and) 0 2047 y(\(4.56\),) p 154 2047 a(w) o(e) p 226 2047 a(can) p 316 2047 a(see) p 395 2047 a(that) p 500 2047 a(for) p 575 2047 a(an) o(y) p Fq 667 2047 a(i) p Fo 697 2047 a(\024) p Fq 750 2047 a(m) p Fo 804 2047 a(\000) p Fr 853 2047 a(1,) p Fn 225 2193 a(M) p Fl 269 2172 a(1) p Fr 291 2193 a(\() p Fo([) p Fp 343 2207 a(W) p Fm 381 2207 a(2) p Ff(W) p Fc 442 2192 a(\000) p Fe 442 2218 a(in) p Fq 473 2193 a(@) p Fl 502 2172 a(2) p Fq 521 2193 a(D) p Fp 561 2200 a(W) p Fr 602 2193 a(\() p Fq(i) p Fr(\)\)) p Fo 689 2193 a(\024) p Fp 760 2130 a(k) p Fj 778 2135 a(2) p Fk 742 2146 a(X) p Fp 747 2251 a(j) p Fl 763 2251 a(=1) p Fn 822 2193 a(M) p Fl 866 2172 a(1) p Fr 889 2193 a(\() p Fq(F) p Fl 947 2172 a(2) p Fp 940 2205 a(j) p Fo 977 2193 a(\\) p Fr 1021 2193 a(H\() p Fq(i) p Fr(\)\)) p 1142 2193 a(+) p Fp 1210 2130 a(k) p Fj 1228 2135 a(4) p Fk 1191 2146 a(X) p Fp 1197 2251 a(j) p Fl 1213 2251 a(=1) p Fn 1272 2193 a(M) p Fl 1316 2172 a(1) p Fr 1338 2193 a(\() p Fq(F) p Fl 1396 2172 a(4) p Fp 1389 2205 a(j) p Fo 1427 2193 a(\\) p Fr 1471 2193 a(H\() p Fq(i) p Fr(\)\)) p Fq(:) p Fr 1778 2193 a(\(4.57\)) 0 2342 y(Hence,) p 159 2342 a(w) o(e) p 230 2342 a(ha) o(v) o(e) p 343 2342 a(from) p 458 2342 a(\(4.57\)) p 599 2342 a(that) p Fk 331 2441 a(X) p Fp 309 2546 a(i) p Fm(\024) p Fp(m) p Fm(\000) p Fl(1) p Fn 433 2488 a(M) p Fl 477 2468 a(1) p Fr 500 2488 a(\() p Fo([) p Fp 552 2502 a(W) p Fm 590 2502 a(2) p Ff(W) p Fc 650 2487 a(\000) p Fe 650 2513 a(in) p Fq 681 2488 a(@) p Fl 710 2468 a(2) p Fq 730 2488 a(D) p Fp 770 2495 a(W) p Fr 810 2488 a(\() p Fq(i) p Fr(\)\)) p Fo 898 2488 a(\024) p Fp 969 2426 a(k) p Fj 987 2431 a(2) p Fk 950 2441 a(X) p Fp 956 2546 a(j) p Fl 972 2546 a(=1) p Fn 1031 2488 a(M) p Fl 1075 2468 a(2) p Fr 1097 2488 a(\() p Fq(F) p Fl 1155 2468 a(2) p Fp 1148 2501 a(j) p Fr 1174 2488 a(\)) p 1204 2488 a(+) p Fp 1272 2426 a(k) p Fj 1290 2431 a(4) p Fk 1253 2441 a(X) p Fp 1259 2546 a(j) p Fl 1275 2546 a(=1) p Fn 1334 2488 a(M) p Fl 1378 2468 a(2) p Fr 1401 2488 a(\() p Fq(F) p Fl 1459 2468 a(4) p Fp 1452 2501 a(j) p Fr 1478 2488 a(\)) p Fq(:) p Fr 1778 2488 a(\(4.58\)) 0 2635 y(Similarly) l(,) p 217 2635 a(w) o(e) p 289 2635 a(ha) o(v) o(e) p 401 2635 a(that) p Fk 331 2731 a(X) p Fp 309 2836 a(i) p Fm(\025) p Fp(m) p Fl(+1) p Fn 433 2778 a(M) p Fl 477 2758 a(1) p Fr 500 2778 a(\() p Fo([) p Fp 552 2792 a(W) p Fm 590 2792 a(2) p Ff(W) p Fj 650 2777 a(+) p Fe 650 2803 a(in) p Fq 681 2778 a(@) p Fl 710 2758 a(2) p Fq 730 2778 a(D) p Fp 770 2785 a(W) p Fr 810 2778 a(\() p Fq(i) p Fr(\)\)) p Fo 898 2778 a(\024) p Fp 969 2716 a(k) p Fj 987 2721 a(2) p Fk 950 2731 a(X) p Fp 956 2836 a(j) p Fl 972 2836 a(=1) p Fn 1031 2778 a(M) p Fl 1075 2758 a(2) p Fr 1097 2778 a(\() p Fq(F) p Fl 1155 2758 a(2) p Fp 1148 2791 a(j) p Fr 1174 2778 a(\)) p 1204 2778 a(+) p Fp 1272 2716 a(k) p Fj 1290 2721 a(4) p Fk 1253 2731 a(X) p Fp 1259 2836 a(j) p Fl 1275 2836 a(=1) p Fn 1334 2778 a(M) p Fl 1378 2758 a(2) p Fr 1401 2778 a(\() p Fq(F) p Fl 1459 2758 a(4) p Fp 1452 2791 a(j) p Fr 1478 2778 a(\)) p Fq(:) p Fr 1778 2778 a(\(4.59\)) 927 2947 y(29) p 90 rotate dyy eop %%Page: 30 30 30 29 bop Fr 0 274 a(Therefore,) p 236 274 a(in) p 295 274 a(a) p 337 274 a(similar) p 499 274 a(w) o(a) o(y) p 599 274 a(as) p 660 274 a(in) p 719 274 a(the) p 804 274 a(pro) q(of) p 933 274 a(of) p 990 274 a(Lemma) p 1166 274 a(4.4,) p 1260 274 a(w) o(e) p 1333 274 a(can) p 1424 274 a(see) p 1505 274 a(from) p 1621 274 a(\(4.55\),) p 1778 274 a(\(4.58\)) 0 334 y(and) p 95 334 a(\(4.59\)) p 236 334 a(that) p Fk 412 392 a(\014) 412 422 y(\014) 412 452 y(\014) 453 402 y(X) p Fp 428 510 a(C) r(\023) p Fl(\000\() p Ff(W) p Fl 540 510 a(\)) p Fg 559 449 a(1) p Fp 587 456 a(L) p Fc 611 447 a(0) p Fp 622 456 a(;) p Fl(2) p Fp(l) p Fr 663 449 a(\() p Fq(C) p Fr 721 449 a(\)\010) p Fl 775 428 a(T) p Fp 775 461 a(\016) p Fr 802 449 a(\() p Fq(C) p Fr 860 449 a(\)) p Fo 889 449 a(\000) p Fk 970 402 a(X) p Fp 939 510 a(C) r(\023) p Fl(\000\() p Ff(W) p Fc 1051 500 a(0) p Fl 1059 510 a(\)) p Fg 1081 449 a(1) p Fp 1109 456 a(L) p Fc 1133 447 a(0) p Fp 1145 456 a(;) p Fl(2) p Fp(l) p Fr 1185 449 a(\() p Fq(C) p Fr 1243 449 a(\)\010) p Fl 1297 428 a(T) p Fp 1297 461 a(\016) p Fr 1324 449 a(\() p Fq(C) p Fr 1382 449 a(\)) p Fk 1401 392 a(\014) 1401 422 y(\014) 1401 452 y(\014) p Fo 331 630 a(\024) p Fq 412 630 a(c) p Fl 433 637 a(22) p Fr 481 630 a(+) p 530 630 a(2) p Fq(c) p Fl 575 637 a(23) p Fk 613 575 a(\020) p Fp 661 568 a(k) p Fj 679 573 a(2) p Fk 642 583 a(X) p Fp 650 688 a(i) p Fl(=1) p Fn 723 630 a(M) p Fl 767 609 a(2) p Fr 789 630 a(\() p Fq(F) p Fl 847 609 a(2) p Fp 840 642 a(i) p Fr 867 630 a(\)) p 897 630 a(+) p Fp 964 568 a(k) p Fj 982 573 a(4) p Fk 946 583 a(X) p Fp 953 688 a(i) p Fl(=1) p Fn 1026 630 a(M) p Fl 1070 609 a(2) p Fr 1093 630 a(\() p Fq(F) p Fl 1151 609 a(4) p Fp 1144 642 a(i) p Fr 1170 630 a(\)) p Fk 1189 575 a(\021) p Fr 1229 630 a(+) p 1278 630 a(2) p Fq(c) p Fl 1323 637 a(23) p Fp 1388 568 a(k) p Fj 1406 573 a(4) p Fk 1369 583 a(X) p Fp 1377 688 a(i) p Fl(=1) p Fn 1450 630 a(M) p Fl 1494 609 a(2) p Fr 1516 630 a(\() p Fq(F) p Fl 1574 609 a(4) p Fp 1567 642 a(i) p Fr 1593 630 a(\)) p Fo 331 800 a(\024) p Fq 412 800 a(c) p Fl 433 807 a(33) p Fk 470 744 a(\020) p Fr 500 800 a(1) p 535 800 a(+) p Fp 602 737 a(k) p Fj 620 742 a(2) p Fk 584 752 a(X) p Fp 592 857 a(i) p Fl(=1) p Fn 664 800 a(M) p Fl 708 779 a(2) p Fr 731 800 a(\() p Fq(F) p Fl 789 779 a(2) p Fp 782 812 a(i) p Fr 808 800 a(\)) p 838 800 a(+) p Fp 905 737 a(k) p Fj 923 742 a(4) p Fk 887 752 a(X) p Fp 895 857 a(i) p Fl(=1) p Fn 967 800 a(M) p Fl 1011 779 a(2) p Fr 1034 800 a(\() p Fq(F) p Fl 1092 779 a(4) p Fp 1085 812 a(i) p Fr 1111 800 a(\)) p Fk 1130 744 a(\021) p Fr 1778 800 a(\(4.60\)) 0 947 y(in) p 54 947 a(this) p 146 947 a(time) p Fo 254 947 a([) p Fp 287 961 a(W) p Fc 325 951 a(0) p Fm 337 961 a(2) p Ff(W) p Fc 396 946 a(\000) p Fe 396 972 a(in) p Fm 426 961 a([) p Ff(W) p Fj 485 946 a(+) p Fe 485 972 a(in) p Fq 517 947 a(@) p Fl 546 929 a(2) p Fq 565 947 a(D) p Fp 605 954 a(W) p Fc 643 945 a(0) p Fr 657 947 a(\() p Fq(i) p Fr(\)) p 725 947 a(and) p Fo 817 947 a([) p Fp 850 929 a(r) 850 960 y(k) p Fl 869 960 a(=1) p Fq 916 947 a(@) p Fl 945 929 a(2) p Fq 964 947 a(D) p Fp 1004 954 a(k) p Fr 1026 947 a(\() p Fq(i) p Fr(\)) p 1094 947 a(pla) o(y) p 1197 947 a(the) p 1278 947 a(role) p 1369 947 a(of) p Fq 1422 947 a(W) p Fo 1479 947 a(\\) p Fr 1517 947 a(H\() p Fq(i) p Fr(\).) p 1643 947 a(Th) o(us,) p 1778 947 a(\(4.47\)) 0 1013 y(follo) o(ws) p 160 1013 a(from) p 275 1013 a(\(4.53\)) p 416 1013 a(and) p 511 1013 a(\(4.60\).) 73 1073 y(W) l(e) p 157 1073 a(will) p 249 1073 a(next) p 359 1073 a(sho) o(w) p 480 1073 a(that) p Fk 425 1127 a(X) p Ff 439 1234 a(W) p Fc 475 1224 a(0) p Fq 506 1175 a(P) p Fp 544 1154 a(\016) p Fl 537 1187 a(\003) p Fr 564 1175 a(\() p Fn(W) p Fm 629 1154 a(0) p Fr 644 1175 a(\)) p Fo 677 1175 a(\024) p Fq 729 1175 a(c) p Fl 750 1182 a(34) p Fr 796 1175 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 983 1175 a(\000) p Fq 1033 1175 a(c) p Fl 1054 1182 a(35) p Fr 1091 1175 a(\)) p Fq(K) p Fl 1151 1182 a(2) p Fq 1171 1175 a(L) p Fr(\(log) p Fq 1295 1175 a(L) p Fr(\)) p Fl 1347 1154 a(3) p Fr 1367 1175 a(]) p Fq(;) p Fr 1778 1175 a(\(4.61\)) 0 1336 y(where) p Fk 148 1289 a(X) p Ff 162 1395 a(W) p Fc 198 1385 a(0) p Fr 243 1336 a(stands) p 402 1336 a(for) p 484 1336 a(the) p 575 1336 a(summation) p 834 1336 a(o) o(v) o(er) p 945 1336 a(all) p 1020 1336 a(families) p 1204 1336 a(of) p 1267 1336 a(the) p 1358 1336 a(standard) p 1568 1336 a(w) o(alls) p 1696 1336 a(suc) o(h) p 1813 1336 a(that) p Fn 0 1441 a(W) p Fm 47 1423 a(0) p Fr 75 1441 a(=) p Fn 127 1441 a(W) p Fm 174 1423 a(0) p Fr 189 1441 a(\() p Fn(W) p Fr 254 1441 a(\)) p 293 1441 a(for) p 367 1441 a(some) p Fn 489 1441 a(W) p Fo 553 1441 a(2) p 600 1441 a(S) t(W) p Fm 687 1421 a(\016) p Fl 687 1454 a(3) p Fr 707 1441 a(.) p 742 1441 a(Let) p 829 1441 a(us) p 892 1441 a(\014x) p 961 1441 a(\000) p Fo 1005 1441 a(2) p 1053 1441 a(O) p Fr 1094 1441 a(\() p Fo(\000) p Fq(L) p Fm 1185 1423 a(0) p Fq 1196 1441 a(;) p Fr 1218 1441 a(2) p Fq(l) p Fr 1258 1441 a(\)) p 1293 1441 a(suc) o(h) p 1403 1441 a(that) p 1509 1441 a(for) p Fo 1583 1441 a(\003) p Fr 1622 1441 a(=) p 1674 1441 a(+) p 1728 1441 a(and) p Fo 1823 1441 a(\000) 683 1543 y(j) p Fr(h) p Fm 724 1522 a(\003) p Fr 743 1543 a(\(\000\)) p Fo(j) p Fq 839 1543 a(<) p Fr 891 1543 a(\() p Fq(K) p Fl 951 1550 a(5) p Fr 980 1543 a(log) p Fq 1051 1543 a(L) p Fr(\)) p Fl 1103 1522 a(2) p Fq 1123 1543 a(;) p Fr 1778 1543 a(\(4.62\)) 0 1644 y(and) p 95 1644 a(suc) o(h) p 205 1644 a(that) p Fo 575 1745 a(f) p Fq(W) p Fo 667 1745 a(2) p Fn 714 1745 a(W) p Fr 761 1745 a(\(\000\);) p Fq 851 1745 a(W) p Fo 918 1745 a(\\) p Fq 962 1745 a(@) p Fr 991 1745 a(\003) p Fo 1038 1745 a(6) p Fr(=) p Fo 1090 1745 a(;g) p Fr 1154 1745 a(=) p Fo 1205 1745 a(;) p Fq(:) p Fr 1778 1745 a(\(4.63\)) 0 1846 y(F) l(or) p 87 1846 a(eac) o(h) p Fq 197 1846 a(i) p Fo 227 1846 a(2) p Fn 274 1846 a(Z) p Fr 323 1846 a(suc) o(h) p 433 1846 a(that) p 538 1846 a(shift\(\000) p Fq(;) p 703 1846 a(i) p Fr(\)) p Fo 753 1846 a(\032) p Fq 805 1846 a(Q) p Fr(\(\003\),) p 945 1846 a(let) p 1016 1846 a(\000) p Fp 1046 1853 a(i) p Fr 1074 1846 a(=) p 1126 1846 a(shift) o(\(\000) p Fq(;) p 1290 1846 a(i) p Fr(\).) p 1361 1846 a(W) l(e) p 1445 1846 a(ha) o(v) o(e) p 1557 1846 a(from) p 1672 1846 a(\(4.63\)) p 1813 1846 a(that) 0 1906 y(for) p 75 1906 a(an) o(y) p 167 1906 a(negativ) o(e) p 359 1906 a(in) o(teger) p Fq 520 1906 a(i) p Fo 551 1906 a(\025) p 603 1906 a(\000) p Fq(L) p Fm 675 1888 a(00) p Fr 696 1906 a(,) p Fq 254 2008 a(\026) p Fp 283 1984 a(!) q(;) p Ff(J) p Fe 336 1990 a(\016) p Fl 283 2021 a(\003) p Fr 352 2008 a(\(\000) p Fp 401 1990 a(!) p Fl 401 2020 a(\003) p Fr 428 2008 a(\() p Fq(\033) p Fr 477 2008 a(\)) p Fo 509 2008 a(\033) p Fr 562 2008 a(\000) p Fp 592 2015 a(i) p Fr 607 2008 a(\)) p 254 2030 372 2 v Fq 261 2082 a(\026) p Fp 290 2059 a(!) q(;) p Ff(J) p Fe 343 2065 a(\016) p Fl 290 2096 a(\003) p Fr 360 2082 a(\(\000) p Fp 409 2065 a(!) p Fl 409 2096 a(\003) p Fr 436 2082 a(\() p Fq(\033) p Fr 485 2082 a(\)) p 517 2082 a(=) p 569 2082 a(\000\)) 644 2041 y(=) 701 2003 y(Z\() p Fq(R) p Fl 787 1983 a(+) 787 2017 y(\000) p Fe 809 2022 a(i) p Fq 824 2003 a(;) p Fr 846 2003 a(+) p Fq(;) p Fn 906 2003 a(J) p Fp 934 2010 a(\016) p Fr 950 2003 a(\)Z\() p Fq(R) p Fm 1055 1983 a(\000) p Fl 1055 2017 a(\000) p Fe 1077 2022 a(i) p Fq 1092 2003 a(;) p Fo 1114 2003 a(\000) p Fq(;) p Fn 1175 2003 a(J) p Fp 1202 2010 a(\016) p Fr 1218 2003 a(\)) p 701 2030 537 2 v 708 2077 a(Z\() p Fq(R) p Fl 794 2056 a(+) 794 2090 y(\000) p Fq 824 2077 a(;) p Fr 846 2077 a(+) p Fq(;) p Fn 906 2077 a(J) p Fp 934 2084 a(\016) p Fr 950 2077 a(\)Z\() p Fq(R) p Fm 1055 2056 a(\000) p Fl 1055 2090 a(\000) p Fq 1085 2077 a(;) p Fo 1107 2077 a(\000) p Fq(;) p Fn 1168 2077 a(J) p Fp 1195 2084 a(\016) p Fr 1211 2077 a(\)) p Fo 1253 2041 a(\001) p Fr 1286 2003 a(Z\() p Fq(R) p Fm 1372 1983 a(\000) p Fl 1372 2017 a(\000) p Fe 1394 2022 a(i) p Fq 1410 2003 a(;) p 1432 2003 a(!) r(;) p Fn 1486 2003 a(J) p Fp 1513 2010 a(\016) p Fr 1529 2003 a(\)) p 1283 2030 269 2 v 1283 2077 a(Z\() p Fq(R) p Fm 1369 2056 a(\000) p Fl 1369 2090 a(\000) p Fe 1391 2095 a(i) p Fq 1406 2077 a(;) p Fo 1428 2077 a(\000) p Fq(;) p Fn 1489 2077 a(J) p Fp 1517 2084 a(\016) p Fr 1533 2077 a(\)) p Fq 1557 2041 a(:) p Fr 1778 2150 a(\(4.64\)) 0 2251 y(W) l(e) p 84 2251 a(can) p 173 2251 a(see) p 252 2251 a(b) o(y) p 320 2251 a(Jensen's) p 511 2251 a(inequalit) o(y) p 737 2251 a(that) p Fk 196 2322 a(\022) p Fr 241 2355 a(Z\() p Fq(R) p Fm 327 2334 a(\000) p Fl 327 2368 a(\000) p Fe 349 2373 a(i) p Fq 364 2355 a(;) p 386 2355 a(!) r(;) p Fn 440 2355 a(J) p Fp 468 2362 a(\016) p Fr 484 2355 a(\)) p 238 2381 V 238 2428 a(Z\() p Fq(R) p Fm 324 2407 a(\000) p Fl 324 2441 a(\000) p Fe 346 2446 a(i) p Fq 361 2428 a(;) p Fo 383 2428 a(\000) p Fq(;) p Fn 444 2428 a(J) p Fp 471 2435 a(\016) p Fr 487 2428 a(\)) p Fk 511 2322 a(\023) p Fm 548 2327 a(\000) p Fl(1) p Fo 609 2393 a(\025) p Fr 662 2393 a(exp) p Fk 736 2337 a(h) p Fo 760 2393 a(\000) p Fr(2) p Fq(\014) s(\016) p Fk 1085 2345 a(X) p Fp 885 2459 a(x) p Fm(2) p Fp(@) p Fe 948 2464 a(in) p Fp 979 2459 a(R) p Fc 1006 2444 a(\000) p Fj 1006 2471 a(\000) p Fe 1025 2479 a(i) p Fm 1040 2459 a(\\) p Fp(@) p Fe 1083 2464 a(in) p Fl 1114 2459 a(\003;) p Fm(\000) p Fp(L) p Fc 1199 2450 a(00) p Fm 1220 2459 a(\024) p Fp(x) p Fj 1267 2450 a(3) p Fm 1285 2459 a(\024\000) p Fl(1) p Fq 1366 2393 a(\026) p Fp 1395 2369 a(!) q(;) p Ff(J) p Fe 1447 2375 a(\016) p Fp 1395 2414 a(R) p Fc 1422 2399 a(\000) p Fj 1422 2426 a(\000) p Fe 1441 2434 a(i) p Fr 1464 2393 a([) p Fq(\033) p Fr 1508 2393 a(\() p Fq(x) p Fr(\)]) p Fk 1588 2337 a(i) p Fq 1609 2393 a(:) p Fr 1778 2538 a(\(4.65\)) 0 2639 y(By) p 74 2639 a(a) p 112 2639 a(similar) p 270 2639 a(argumen) o(t) p 485 2639 a(as) p 543 2639 a(in) p 597 2639 a(\(4.14\)) p 735 2639 a(and) p 828 2639 a(\(4.15\),) p 980 2639 a(w) o(e) p 1049 2639 a(can) p 1136 2639 a(sho) o(w) p 1254 2639 a(that) p Fq 1357 2639 a(\026) p Fp 1386 2615 a(!) q(;) p Ff(J) p Fe 1439 2621 a(\016) p Fp 1386 2660 a(R) p Fc 1413 2646 a(\000) p Fj 1413 2672 a(\000) p Fe 1432 2680 a(i) p Fr 1455 2639 a([) p Fq(\033) p Fr 1499 2639 a(\() p Fq(x) p Fr(\)]) p Fo 1592 2639 a(\024) p 1644 2639 a(\000) p Fr(1) p Fq(=) p Fr(4.) p 1790 2639 a(F) l(rom) 0 2721 y(this) p 95 2721 a(and) p 190 2721 a(\(4.65\),) p 344 2721 a(w) o(e) p 416 2721 a(ha) o(v) o(e) p 529 2721 a(that) 442 2823 y(Z\() p Fq(R) p Fm 528 2802 a(\000) p Fl 528 2836 a(\000) p Fe 550 2841 a(i) p Fq 565 2823 a(;) p 587 2823 a(!) r(;) p Fn 641 2823 a(J) p Fp 669 2830 a(\016) p Fr 685 2823 a(\)) p Fk 704 2782 a(\016) p Fr 733 2823 a(Z\() p Fq(R) p Fm 819 2802 a(\000) p Fl 819 2836 a(\000) p Fe 841 2841 a(i) p Fq 856 2823 a(;) p Fo 878 2823 a(\000) p Fq(;) p Fn 939 2823 a(J) p Fp 966 2830 a(\016) p Fr 982 2823 a(\)) p Fo 1015 2823 a(\024) p Fr 1068 2823 a(exp) o([) p Fo(\000) p Fr(4) p Fq(\014) s(\016) r(L) p Fo(j) p Fq(i) p Fo(j) p Fr(]) p Fq(:) p Fr 1778 2823 a(\(4.66\)) 927 2947 y(30) p 90 rotate dyy eop %%Page: 31 31 31 30 bop Fr 0 274 a(By) p 77 274 a(the) p 161 274 a(de\014nition) p 377 274 a(of) p Fn 433 274 a(J) p Fp 461 281 a(\016) p Fr 477 274 a(,) p 507 274 a(w) o(e) p 578 274 a(can) p 668 274 a(see) p 747 274 a(that) 654 384 y(\010) p Fl 689 363 a(T) p Fp 689 396 a(\016) p Fr 717 384 a(\() p Fq(C) p Fr 775 384 a(\)) p 807 384 a(=) p 859 384 a(\010) p Fl 894 363 a(T) p Fp 894 396 a(\016) p Fr 921 384 a(\(shift\() p Fq(C) q(;) p 1111 384 a(i) p Fr(\)\)) p 1778 384 a(\(4.67\)) 0 494 y(if) p Fq 48 494 a(C) p Fo 100 494 a(\\) p Fq 146 494 a(@) p Fr 175 494 a(\003) p 228 494 a(=) p Fo 285 494 a(;) p Fr 329 494 a(and) p 427 494 a(shift\() p Fq(C) q(;) p 598 494 a(i) p Fr(\)) p Fo 647 494 a(\\) p Fq 693 494 a(@) p Fr 722 494 a(\003) p 775 494 a(=) p Fo 832 494 a(;) p Fr(.) p 902 494 a(W) l(e) p 989 494 a(can) p 1082 494 a(see) p 1164 494 a(from) p 1282 494 a(\(4.4\)) p 1402 494 a(\(see) p 1503 494 a(\(3.15\)) p 1647 494 a(and) p 1745 494 a(\(3.23\)\),) 0 554 y(\(4.62\)) p 141 554 a(and) p 236 554 a(\(4.67\)) p 377 554 a(that) p Fk 379 621 a(\014) 379 650 y(\014) 379 680 y(\014) 470 631 y(X) p Fp 395 738 a(C) p Fm 422 738 a(2) p Fb(C) p Fl(;) p Fp(C) p Fm 512 738 a(\\) p Fl(\000) p Fe 558 743 a(i) p Fm 572 738 a(6) p Fl(=) p Fm(;) p Fg 625 678 a(1) p Fp 653 685 a(L) p Fc 677 676 a(0) p Fp 688 685 a(;) p Fl(2) p Fp(l) p Fr 729 678 a(\() p Fq(C) p Fr 787 678 a(\)\010) p Fl 841 657 a(T) p Fp 841 690 a(\016) p Fr 868 678 a(\() p Fq(C) p Fr 926 678 a(\)) p Fo 955 678 a(\000) p Fk 1005 631 a(X) p Fp 1010 736 a(C) r(\023) p Fl(\000) p Fg 1085 678 a(1) p Fp 1113 685 a(L) p Fc 1137 676 a(0) p Fp 1149 685 a(;) p Fl(2) p Fp(l) p Fr 1189 678 a(\() p Fq(C) p Fr 1247 678 a(\)\010) p Fl 1301 657 a(T) p Fp 1301 690 a(\016) p Fr 1328 678 a(\() p Fq(C) p Fr 1386 678 a(\)) p Fk 1405 621 a(\014) 1405 650 y(\014) 1405 680 y(\014) p Fo 298 817 a(\024) p Fr 379 817 a(16) p Fq(L) p Fl 460 796 a(2) p Fq 480 817 a(c) p Fm 501 796 a(0) p Fl 501 829 a(1) p Fr 529 817 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 716 817 a(\000) p Fr 773 804 a(\026) p Fq 766 817 a(\014) p Fr 797 817 a(\)) p Fq(c) p Fl 837 824 a(36) p Fq 874 817 a(L) p Fj 912 783 a(2) p 912 789 16 2 v 912 809 a(3) p Fr 934 817 a(\(log) p Fq 1025 817 a(L) p Fr(\)) p Fl 1077 796 a(2) p Fr 1096 817 a(]) 476 889 y(+) p Fq(c) p Fl 535 896 a(37) p Fn 572 889 a(M) p Fl 616 869 a(2) p Fk 639 849 a(\000) p Fr 662 889 a(cyl) o(\(\003) p Fq(;) p Fo 798 889 a(\000) p Fr(\() p Fq(K) p Fl 897 896 a(5) p Fr 925 889 a(log) p Fq 996 889 a(L) p Fr(\)) p Fl 1048 869 a(2) p Fq 1068 889 a(;) p Fr 1090 889 a(\() p Fq(K) p Fl 1150 896 a(5) p Fr 1178 889 a(log) p Fq 1250 889 a(L) p Fr(\)) p Fl 1302 869 a(2) p Fr 1322 889 a(\)) p Fk 1341 849 a(\001) p Fr 476 962 a(+) p Fq(c) p Fl 535 969 a(37) p Fn 572 962 a(M) p Fl 616 941 a(2) p Fk 639 922 a(\000) p Fr 662 962 a(cyl) o(\(\003) p Fq(;) p Fo 798 962 a(\000) p Fq(L) p Fm 870 941 a(00) p Fo 902 962 a(\000) p Fr 952 962 a(\() p Fq(K) p Fl 1012 969 a(5) p Fr 1040 962 a(log) p Fq 1111 962 a(L) p Fr(\)) p Fl 1163 941 a(2) p Fq 1183 962 a(;) p Fo 1205 962 a(\000) p Fq(L) p Fm 1277 941 a(00) p Fr 1309 962 a(+) p 1358 962 a(\() p Fq(K) p Fl 1418 969 a(5) p Fr 1447 962 a(log) p Fq 1518 962 a(L) p Fr(\)) p Fl 1570 941 a(2) p Fr 1590 962 a(\)) p Fk 1609 922 a(\001) p Fq 1632 962 a(;) p Fr 1778 962 a(\(4.68\)) 0 1072 y(whic) o(h) p 140 1072 a(together) p 332 1072 a(with) p 443 1072 a(\(3.13\)) p 584 1072 a(implies) p 750 1072 a(that) 391 1179 y(Z\() p Fq(R) p Fl 477 1158 a(+) 477 1193 y(\000) p Fe 499 1198 a(i) p Fq 514 1179 a(;) p Fr 536 1179 a(+) p Fq(;) p Fn 596 1179 a(J) p Fp 623 1186 a(\016) p Fr 639 1179 a(\)Z\() p Fq(R) p Fm 744 1158 a(\000) p Fl 744 1193 a(\000) p Fe 766 1198 a(i) p Fq 781 1179 a(;) p Fo 803 1179 a(\000) p Fq(;) p Fn 864 1179 a(J) p Fp 892 1186 a(\016) p Fr 908 1179 a(\)) p 391 1206 537 2 v 398 1252 a(Z\() p Fq(R) p Fl 484 1232 a(+) 484 1266 y(\000) p Fq 514 1252 a(;) p Fr 536 1252 a(+) p Fq(;) p Fn 596 1252 a(J) p Fp 623 1259 a(\016) p Fr 639 1252 a(\)Z\() p Fq(R) p Fm 744 1232 a(\000) p Fl 744 1266 a(\000) p Fq 774 1252 a(;) p Fo 796 1252 a(\000) p Fq(;) p Fn 857 1252 a(J) p Fp 884 1259 a(\016) p Fr 900 1252 a(\)) p Fo 945 1217 a(\024) p Fq 998 1217 a(c) p Fl 1019 1224 a(38) p Fr 1065 1217 a(exp) o([) p Fq(c) p Fl 1174 1224 a(39) p Fq 1211 1217 a(L) p Fr(\(log) p Fq 1335 1217 a(L) p Fr(\)) p Fl 1387 1197 a(2) p Fr 1406 1217 a(]) p Fq(:) p Fr 1778 1217 a(\(4.69\)) 0 1357 y(Therefore,) p 234 1357 a(w) o(e) p 306 1357 a(ha) o(v) o(e) p 419 1357 a(from) p 534 1357 a(\(4.64\),) p 688 1357 a(\(4.66\)) p 829 1357 a(and) p 924 1357 a(\(4.69\)) p 1065 1357 a(that) p Fq 163 1467 a(\026) p Fp 192 1444 a(!) q(;) p Ff(J) p Fe 245 1450 a(\016) p Fl 192 1481 a(\003) p Fr 261 1467 a(\(\000) p Fp 310 1447 a(!) p Fl 310 1479 a(\003) p Fr 337 1467 a(\() p Fq(\033) p Fr 386 1467 a(\)) p Fo 419 1467 a(\033) p Fr 471 1467 a(\000) p Fp 501 1474 a(i) p Fr 516 1467 a(\)) p Fo 549 1467 a(\024) p Fq 601 1467 a(c) p Fl 622 1474 a(38) p Fr 668 1467 a(exp) o([) p Fo(\000) p Fr(4) p Fq(\014) s(\016) r(L) p Fo(j) p Fq(i) p Fo(j) p Fr 961 1467 a(+) p Fq 1010 1467 a(c) p Fl 1031 1474 a(39) p Fq 1069 1467 a(L) p Fr(\(log) p Fq 1192 1467 a(L) p Fr(\)) p Fl 1244 1447 a(2) p Fr 1264 1467 a(]) p Fq 1286 1467 a(\026) p Fp 1315 1444 a(!) q(;) p Ff(J) p Fe 1368 1450 a(\016) p Fl 1315 1481 a(\003) p Fr 1384 1467 a(\(\000) p Fp 1433 1447 a(!) p Fl 1433 1479 a(\003) p Fr 1460 1467 a(\() p Fq(\033) p Fr 1509 1467 a(\)) p 1541 1467 a(=) p 1593 1467 a(\000\)) p Fq(:) p Fr 1778 1540 a(\(4.70\)) 0 1650 y(Recall) p 150 1650 a(that) p 259 1650 a(w) o(e) p 333 1650 a(only) p 443 1650 a(consider) p 636 1650 a(the) p 723 1650 a(case) p 829 1650 a(where) p Fq 973 1650 a(i) p Fo 1009 1650 a(\024) p 1066 1650 a(\000) p Fq(l) q(=) p Fr(2.) p 1213 1650 a(Then,) p 1358 1650 a(w) o(e) p 1433 1650 a(can) p 1525 1650 a(pro) o(v) o(e) p 1659 1650 a(\(4.61\)) p 1803 1650 a(from) 0 1710 y(\(4.24\),) p 154 1710 a(\(4.39\),) p 309 1710 a(\(4.40\),) p 463 1710 a(\(4.62\)) p 604 1710 a(and) p 699 1710 a(\(4.70\).) 73 1770 y(Let) p Fq 161 1770 a(p) p Fr 199 1770 a(=) p 252 1770 a(2) p 292 1770 a(or) p 352 1770 a(4) p 393 1770 a(and) p 488 1770 a(let) p 559 1770 a(1) p Fo 597 1770 a(\024) p Fq 650 1770 a(i) p Fo 681 1770 a(\024) p Fq 734 1770 a(k) p Fp 759 1777 a(p) p Fr 779 1770 a(.) p 815 1770 a(Note) p 933 1770 a(that) p Fq 1039 1770 a(F) p Fp 1078 1747 a(p) 1071 1783 y(i) p Fr 1114 1770 a(is) p 1163 1770 a(connected,) p 1404 1770 a(and) p 1499 1770 a(that) p 1605 1770 a(w) o(e) p 1677 1770 a(can) p 1767 1770 a(regard) p Fq 0 1830 a(F) p Fp 39 1807 a(p) 32 1843 y(i) p Fr 73 1830 a(as) p 131 1830 a(the) p 213 1830 a(union) p 347 1830 a(of) p 401 1830 a(all) p 467 1830 a(faces) p Fq 584 1830 a(w) p Fr 635 1830 a(suc) o(h) p 743 1830 a(that) p Fn 847 1830 a(M) p Fl 891 1812 a(2) p Fr 914 1830 a(\() p Fq(w) p Fo 977 1830 a(\\) p Fq 1018 1830 a(F) p Fp 1057 1807 a(p) 1050 1843 y(i) p Fr 1076 1830 a(\)) p 1109 1830 a(=) p 1160 1830 a(1.) p 1219 1830 a(F) l(or) p 1305 1830 a(eac) o(h) p 1413 1830 a(1) p Fo 1452 1830 a(\024) p Fq 1504 1830 a(i) p Fo 1535 1830 a(\024) p Fq 1587 1830 a(k) p Fl 1612 1837 a(3) p Fr 1632 1830 a(,) p 1661 1830 a(there) p 1784 1830 a(exists) 0 1891 y(a) p 41 1891 a(union) p 176 1891 a(of) p 232 1891 a(faces) p Fq 350 1891 a(G) p Fp 388 1898 a(i) p Fo 416 1891 a(\033) p Fq 469 1891 a(F) p Fl 508 1872 a(3) p Fp 501 1903 a(i) p Fr 543 1891 a(suc) o(h) p 653 1891 a(that) p Fq 759 1891 a(G) p Fp 797 1898 a(i) p Fr 828 1891 a(is) p 877 1891 a(connected) p 1104 1891 a(and) p 1199 1891 a(that) p Fn 697 2001 a(M) p Fl 741 1980 a(2) p Fr 764 2001 a(\() p Fq(G) p Fp 821 2008 a(i) p Fr 836 2001 a(\)) p Fo 869 2001 a(\024) p Fr 921 2001 a(2) p Fn(M) p Fl 990 1980 a(2) p Fr 1012 2001 a(\() p Fq(F) p Fl 1070 1980 a(3) p Fp 1063 2013 a(i) p Fr 1089 2001 a(\)) p Fq(:) p Fr 1778 2001 a(\(4.71\)) 0 2111 y(W) l(e) p 86 2111 a(can) p 177 2111 a(see) p 258 2111 a(this,) p 369 2111 a(as) p 430 2111 a(follo) o(ws.) p 615 2111 a(By) p 694 2111 a(the) p 779 2111 a(de\014nition) p 998 2111 a(of) p Fo 1055 2111 a(f) p Fq(F) p Fl 1119 2092 a(3) p Fp 1112 2123 a(i) p Fo 1138 2111 a(g) p Fp 1163 2089 a(k) p Fj 1181 2094 a(3) p Fp 1163 2123 a(i) p Fl(=1) p Fr 1241 2111 a(\(see) p 1340 2111 a(\(4.45\)) p 1483 2111 a(and) p 1580 2111 a(\(4.46\)\),) p 1755 2111 a(w) o(e) p 1829 2111 a(can) 0 2171 y(connect) p 176 2171 a(all) p 240 2171 a(comp) q(onen) o(ts) p 506 2171 a(of) p Fq 558 2171 a(F) p Fl 597 2153 a(3) p Fp 590 2183 a(i) p Fr 630 2171 a(b) o(y) p 694 2171 a(using) p 819 2171 a(only) p 923 2171 a(faces) p 1038 2171 a(in) p 1092 2171 a(cyl) o(\() p Fq(@) p Fr 1201 2171 a(\003) p Fq(;) p Fo 1257 2171 a(\000) p Fq(m;) p Fr 1361 2171 a(0\).) p 1437 2171 a(Let) p Fq 1521 2171 a(G) p Fp 1559 2178 a(i) p Fr 1587 2171 a(b) q(e) p 1650 2171 a(the) p 1731 2171 a(smallest) 0 2231 y(one) p 93 2231 a(among) p 254 2231 a(suc) o(h) p 367 2231 a(connected) p 599 2231 a(sets) p 698 2231 a(con) o(taining) p Fq 938 2231 a(F) p Fl 977 2213 a(3) p Fp 970 2243 a(i) p Fr 996 2231 a(.) p 1042 2231 a(F) l(or) p 1133 2231 a(eac) o(h) p Fq 1247 2231 a(k) p Fl 1272 2238 a(2) p Fo 1312 2231 a(\025) p Fr 1370 2231 a(0,) p 1429 2231 a(eac) o(h) p Fq 1542 2231 a(k) p Fl 1567 2238 a(3) p Fo 1607 2231 a(\025) p Fr 1666 2231 a(1) p 1710 2231 a(and) p 1809 2231 a(eac) o(h) p Fq 0 2291 a(k) p Fl 25 2298 a(4) p Fo 59 2291 a(\025) p Fr 112 2291 a(0,) p 165 2291 a(w) o(e) p 236 2291 a(can) p 324 2291 a(see) p 402 2291 a(from) p 516 2291 a(\(4.44\)) p 656 2291 a(that) p 761 2291 a(the) p 844 2291 a(n) o(um) o(b) q(er) p 1020 2291 a(of) p 1075 2291 a(the) p 1158 2291 a(com) o(binations) p 1454 2291 a(of) p 1508 2291 a(the) p 1591 2291 a(starting) p 1772 2291 a(p) q(oin) o(ts) 0 2351 y(of) p Fo 56 2351 a(f) p Fq(F) p Fl 120 2333 a(2) p Fp 113 2364 a(i) p Fo 139 2351 a(g) p Fp 164 2330 a(k) p Fj 182 2335 a(2) p Fp 164 2364 a(i) p Fl(=1) p Fr 223 2351 a(,) p Fo 252 2351 a(f) p Fq(G) p Fp 315 2358 a(i) p Fo 330 2351 a(g) p Fp 355 2330 a(k) p Fj 373 2335 a(3) p Fp 355 2364 a(i) p Fl(=1) p Fr 430 2351 a(and) p Fo 525 2351 a(f) p Fq(F) p Fl 589 2333 a(4) p Fp 582 2364 a(i) p Fo 608 2351 a(g) p Fp 633 2330 a(k) p Fj 651 2335 a(4) p Fp 633 2364 a(i) p Fl(=1) p Fr 708 2351 a(is) p 757 2351 a(b) q(ounded) p 957 2351 a(from) p 1072 2351 a(ab) q(o) o(v) o(e,) p 1223 2351 a(b) o(y) p Fk 548 2421 a(\022) p Fr 590 2458 a(8) p Fq(K) p Fl 655 2465 a(4) p Fq 675 2458 a(L) p Fr 716 2458 a(log) p Fq 788 2458 a(L) 683 2525 y(k) p Fl 708 2532 a(2) p Fk 826 2421 a(\023) p 871 2421 a(\022) p Fr 913 2458 a(16) p Fq(L) p Fl 994 2439 a(2) p Fq 941 2525 a(k) p Fl 966 2532 a(3) p Fk 1019 2421 a(\023) p 1064 2421 a(\022) p Fr 1106 2458 a(16) p Fq(L) p Fl 1187 2439 a(2) p Fq 1134 2525 a(k) p Fl 1159 2532 a(4) p Fk 1213 2421 a(\023) p Fq 1258 2491 a(:) p Fr 1778 2491 a(\(4.72\)) 927 2947 y(31) p 90 rotate dyy eop %%Page: 32 32 32 31 bop Fr 0 274 a(Th) o(us,) p 137 274 a(w) o(e) p 209 274 a(ha) o(v) o(e) p 321 274 a(from) p 437 274 a(\(4.37\),) p 591 274 a(\(4.47\),) p 745 274 a(\(4.61\)) p 886 274 a(and) p 981 274 a(\(4.72\)) p 1122 274 a(that) p Fk 280 339 a(X) p Ff 248 445 a(W) p Fm 284 445 a(2S) r(W) p Fj 366 450 a(3) p Fq 392 386 a(P) p Fp 430 366 a(\016) p Fl 423 398 a(\003) p Fr 450 386 a(\() p Fn(W) p Fr 516 386 a(\)) p Fo 168 513 a(\024) p Fq 248 513 a(c) p Fl 269 520 a(40) p Fq 306 513 a(L) p Fr 347 513 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 535 513 a(\000) p Fq 585 513 a(c) p Fl 606 520 a(35) p Fr 643 513 a(\)) p Fq(K) p Fl 703 520 a(2) p Fq 723 513 a(L) p Fr(\(log) p Fq 847 513 a(L) p Fr(\)) p Fl 899 492 a(3) p Fr 930 513 a(+) p Fq 979 513 a(c) p Fl 1000 520 a(30) p Fq 1037 513 a(L) p Fr 1078 513 a(log) p Fq 1150 513 a(L) p Fr(]) p Fo 1208 513 a(\002) p Fk 297 579 a(\020) p Fl 327 570 a(8) p Fp(K) p Fj 375 575 a(4) p Fp 391 570 a(L) p Fl 421 570 a(log) p Fp 473 570 a(L) p Fk 376 587 a(X) p Fp 371 693 a(k) p Fj 389 698 a(2) p Fl 407 693 a(=1) 524 572 y(8) p Fp(L) p Fk 509 587 a(X) p Fp 505 693 a(k) p Fj 523 698 a(3) p Fl 541 693 a(=1) 613 572 y(8) p Fp(L) p Fk 598 587 a(X) p Fp 594 693 a(k) p Fj 612 698 a(4) p Fl 630 693 a(=1) p Fk 689 587 a(X) p Fp 683 692 a(n) p Fj 704 697 a(1) p Fm 722 692 a(\025) p Fl(1) p Fo 775 634 a(\001) p 797 634 a(\001) p 819 634 a(\001) p Fk 914 587 a(X) p Fp 841 692 a(n) p Fe 862 698 a(k) p Fj 878 705 a(2) 897 698 y(+) p Fe(k) p Fj 936 705 a(3) 954 698 y(+) p Fe(k) p Fj 993 705 a(4) p Fm 1013 692 a(\025) p Fl(1) p Fk 1066 564 a(\022) p Fr 1108 601 a(8) p Fq(K) p Fl 1173 608 a(4) p Fq 1193 601 a(L) p Fr 1234 601 a(log) p Fq 1306 601 a(L) 1201 668 y(k) p Fl 1226 675 a(2) p Fk 1344 564 a(\023) p 1389 564 a(\022) p Fr 1431 601 a(16) p Fq(L) p Fl 1512 583 a(2) p Fq 1459 668 a(k) p Fl 1484 675 a(3) p Fk 1538 564 a(\023) p 1583 564 a(\022) p Fr 1624 601 a(16) p Fq(L) p Fl 1705 583 a(2) p Fq 1653 668 a(k) p Fl 1678 675 a(4) p Fk 1731 564 a(\023) p Fq 394 784 a(\024) p Fp 422 764 a(n) p Fj 443 769 a(1) p Fl 461 764 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 566 770 a(k) p Fj 582 777 a(2) 601 770 y(+) p Fe(k) p Fj 640 777 a(3) 658 770 y(+) p Fe(k) p Fj 697 777 a(4) p Fq 719 784 a(e) p Fm 742 764 a(\000) p Fl(\() p Fp(\014) r(=) p Fl(3) p Fm(\000) p Fp(c) p Fj 883 769 a(32) p Fl 915 764 a(\)\() p Fp(n) p Fj 964 769 a(1) p Fl 981 764 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 1086 770 a(k) p Fj 1102 777 a(2) 1120 770 y(+) p Fe(k) p Fj 1159 777 a(3) 1177 770 y(+) p Fe(k) p Fj 1216 777 a(4) p Fl 1236 764 a(\)) p Fk 1252 729 a(\021) p Fo 168 875 a(\024) p Fq 248 875 a(c) p Fl 269 882 a(41) p Fr 315 875 a(exp) o([) p Fo(\000) p Fr(\() p Fq(\014) p Fo 502 875 a(\000) p Fq 552 875 a(c) p Fl 573 882 a(42) p Fr 610 875 a(\)) p Fq(K) p Fl 670 882 a(2) p Fq 690 875 a(L) p Fr(\(log) p Fq 814 875 a(L) p Fr(\)) p Fl 866 855 a(3) p Fr 885 875 a(]) p Fq(:) p Fr 1778 875 a(\(4.73\)) p Fq 73 979 a(C) t(ase) p Fr 199 979 a(4.) p 259 979 a(W) l(e) p 343 979 a(will) p 435 979 a(consider) p 625 979 a(the) p 709 979 a(case) p 812 979 a(where) p Fn 953 979 a(W) p Fo 1017 979 a(2) p 1064 979 a(S) t(W) p Fl 1151 986 a(4) p Fr 1171 979 a(.) p 1206 979 a(Recall) p 1353 979 a(that) p Fo 377 1082 a(S) t(W) p Fl 464 1089 a(4) p Fr 497 1082 a(=) p Fo 549 1082 a(f) p Fn(W) p Fo 638 1082 a(2) p 685 1082 a(S) t(W) p Fm 772 1061 a(00) p Fo 793 1082 a(n) p Fr(\() p Fo(S) t(W) p Fl 924 1089 a(1) p Fo 955 1082 a([) p 999 1082 a(S) t(W) p Fl 1087 1089 a(2) p Fr 1106 1082 a(\);) p Fq 1147 1082 a(z) p Fl 1170 1089 a(min) p Fr 1231 1082 a(\() p Fn(W) p Fr 1296 1082 a(\)) p Fq 1332 1082 a(>) p Fo 1384 1082 a(\000) p Fq(l) q(=) p Fr(2) p Fo(g) p Fq(:) p Fr 0 1186 a(W) l(e) p 88 1186 a(de\014ne) p 234 1146 31 2 v 234 1186 a(\000\() p Fn(W) p Fr 330 1186 a(\),) p Fo 387 1186 a(f) p Fq(F) p Fl 451 1168 a(2) p Fp 444 1198 a(i) p Fr 470 1186 a(\() p Fn(W) p Fr 536 1186 a(\)) p Fo(g) p Fp 580 1164 a(k) p Fj 598 1169 a(2) p Fp 580 1198 a(i) p Fl(=0) p Fr 642 1186 a(,) p Fo 677 1186 a(f) p Fq(F) p Fl 741 1168 a(3) p Fp 734 1198 a(i) p Fr 760 1186 a(\() p Fn(W) p Fr 826 1186 a(\)) p Fo(g) p Fp 870 1164 a(k) p Fj 888 1169 a(3) p Fp 870 1198 a(i) p Fl(=1) p Fr 953 1186 a(and) p Fo 1052 1186 a(f) p Fq(F) p Fl 1116 1168 a(4) p Fp 1109 1198 a(i) p Fr 1135 1186 a(\() p Fn(W) p Fr 1201 1186 a(\)) p Fo(g) p Fp 1245 1164 a(k) p Fj 1263 1169 a(4) p Fp 1245 1198 a(i) p Fl(=1) p Fr 1327 1186 a(for) p 1406 1186 a(eac) o(h) p Fn 1520 1186 a(W) p Fo 1591 1186 a(2) p 1646 1186 a(S) t(W) p Fl 1733 1193 a(4) p Fr 1773 1186 a(in) p 1834 1186 a(the) 0 1246 y(same) p 122 1246 a(w) o(a) o(y) p 221 1246 a(as) p 281 1246 a(in) p 338 1246 a(\(4.38\)-\(4.46\).) p 639 1246 a(Consider) p 842 1246 a(the) p 926 1246 a(set) p 1002 1246 a(\(see) p 1100 1246 a(\(1.27\)\)) p Fo 251 1379 a(S) t(W) p Fl 338 1386 a(41) p Fr 389 1379 a(=) p Fk 441 1309 a(\032) p Fn 478 1379 a(W) p Fo 542 1379 a(2) p 589 1379 a(S) t(W) p Fl 676 1386 a(4) p Fr 696 1379 a(;) 738 1348 y(for) p 813 1348 a(some) p Fq 935 1348 a(i) p Fo 966 1348 a(\025) p Fr 1018 1348 a(1) p Fq(;) p Fn 1081 1348 a(M) p Fl 1125 1330 a(2) p Fr 1147 1348 a(\() p Fq(F) p Fl 1205 1330 a(2) p Fp 1198 1360 a(i) p Fr 1224 1348 a(\() p Fn(W) p Fr 1290 1348 a(\)\)) p Fo 1345 1348 a(\025) p Fq 1398 1348 a(K) p Fl 1439 1355 a(5) p Fr 1467 1348 a(log) p Fq 1538 1348 a(L) p Fr 738 1410 a(and) p 833 1410 a(b\() p Fq(F) p Fl 918 1392 a(2) p Fp 911 1422 a(i) p Fr 937 1410 a(\() p Fn(W) p Fr 1003 1410 a(\)) p Fq(;) p 1044 1370 V Fr 1044 1410 a(\000) s(\() p Fn(W) p Fr 1143 1410 a(\)\)) p Fq 1198 1410 a(<) p 1250 1410 a(z) p Fl 1273 1417 a(min) p Fr 1333 1410 a(\() p Fn(W) p Fr 1399 1410 a(\)) p Fo 1432 1410 a(\000) p Fq 1482 1410 a(l) q(=) p Fr(8) p Fk 1592 1309 a(\033) p Fq 1638 1379 a(:) p Fr 0 1510 a(Then,) p 139 1510 a(b) o(y) p 205 1510 a(a) p 244 1510 a(similar) p 402 1510 a(argumen) o(t) p 618 1510 a(as) p 676 1510 a(in) p 731 1510 a(case) p 832 1510 a(1) p 871 1510 a(together) p 1061 1510 a(with) p 1170 1510 a(the) p 1252 1510 a(de\014nition) p 1467 1510 a(of) p Fq 1521 1510 a(z) p Fl 1544 1517 a(min) p Fr 1604 1510 a(,) p 1633 1510 a(w) o(e) p 1702 1510 a(ha) o(v) o(e) p 1813 1510 a(that) p Fk 467 1588 a(X) p Ff 428 1694 a(W) p Fm 464 1694 a(2S) r(W) p Fj 546 1699 a(41) p Fq 587 1635 a(P) p Fp 625 1615 a(\016) p Fl 618 1648 a(\003) p Fr 645 1635 a(\() p Fn(W) p Fr 711 1635 a(\)) p Fo 747 1635 a(\024) p Fq 799 1635 a(c) p Fl 820 1642 a(43) p Fr 866 1635 a(exp) o([) p Fo(\000) p Fr(\() p Fq 1017 1602 a(\014) p 1017 1624 V Fr 1020 1670 a(5) p Fo 1063 1635 a(\000) p Fq 1113 1635 a(c) p Fl 1134 1642 a(44) p Fr 1171 1635 a(\)) p Fq(K) p Fl 1231 1642 a(5) p Fr 1260 1635 a(log) p Fq 1331 1635 a(L) p Fr(]) p Fq(:) p Fr 1778 1635 a(\(4.74\)) 73 1788 y(Let) p Fn 164 1788 a(W) p Fo 234 1788 a(2) p 288 1788 a(S) t(W) p Fl 375 1795 a(4) p Fo 395 1788 a(nS) t(W) p Fl 507 1795 a(41) p Fr 564 1788 a(and) p 663 1788 a(let) p 737 1788 a(\000) p 788 1788 a(=) p 846 1788 a(\000\() p Fn(W) p Fr 942 1788 a(\).) p 1010 1788 a(W) l(e) p 1098 1788 a(can) p 1191 1788 a(see) p 1274 1788 a(b) o(y) p 1345 1788 a(the) p 1433 1788 a(de\014nition) p 1654 1788 a(of) p Fo 1713 1788 a(S) t(W) p Fl 1800 1795 a(4) p Fr 1840 1788 a(\(or) p Fo 0 1849 a(S) t(W) p Fr 87 1849 a(\)) p 121 1849 a(that) p 226 1849 a(\002\(\000\)) p Fo 346 1849 a(3) p Fq 393 1849 a(x) p Fr 436 1849 a(for) p 510 1849 a(some) p Fq 631 1849 a(x) p Fo 673 1849 a(2) p Fr 720 1849 a(\003) p 769 1849 a(with) p Fq 879 1849 a(x) p Fl 907 1830 a(3) p Fr 940 1849 a(=) p Fo 992 1849 a(\000) p Fq(l) p Fr 1047 1849 a(.) p 1081 1849 a(F) l(or) p 1168 1849 a(suc) o(h) p 1277 1849 a(a) p 1316 1849 a(p) q(oin) o(t) p Fq 1443 1849 a(x) p Fo 1484 1849 a(2) p Fr 1531 1849 a(\003) p 1581 1849 a(and) p 1674 1849 a(eac) o(h) p Fq 1783 1849 a(z) p Fo 1822 1849 a(2) p Fn 1869 1849 a(Z) p Fr 0 1909 a(with) p Fo 111 1909 a(\000) p Fr(3) p Fq(l) q(=) p Fr(4) p Fo 252 1909 a(\024) p Fq 305 1909 a(z) p Fo 344 1909 a(\024) p 396 1909 a(\000) p Fr(5) p Fq(l) q(=) p Fr(8,) p 554 1909 a(w) o(e) p 625 1909 a(de\014ne) 212 2012 y(\002\(\000) p Fq(;) p 321 2012 a(x;) p 371 2012 a(z) p Fr 396 2012 a(\)) p 429 2012 a(=) p Fo 481 2012 a(f) p Fq(y) p Fo 545 2012 a(2) p Fr 592 2012 a(\002) p Fp 630 2019 a(z) p Fr 650 2012 a(\(\000\);) p Fq 740 2012 a(y) p Fr 782 2012 a(is) p Fq 831 2012 a(l) p Fm 846 2019 a(1) p Fr 883 2012 a(-connected) p 1127 2012 a(to) p Fq 1186 2012 a(x) p Fr 1230 2012 a(in) p 1287 2012 a(\002) p Fp 1325 2019 a(z) p Fr 1345 2012 a(\(\000\)) p Fo 1414 2012 a(g) p 1450 2012 a(\\) p Fr 1494 2012 a(H\() p Fq(z) p Fr 1575 2012 a(\)) p Fq(;) p Fr 1778 2012 a(\(4.75\)) 0 2116 y(where) 606 2219 y(\002) p Fp 644 2226 a(z) p Fr 664 2219 a(\(\000\)) p 746 2219 a(=) p Fo 798 2219 a(f) p Fq(y) p Fo 863 2219 a(2) p Fr 910 2219 a(\002\(\000\);) p Fq 1038 2219 a(y) p Fl 1064 2199 a(3) p Fo 1097 2219 a(\024) p Fq 1149 2219 a(z) p Fo 1174 2219 a(g) p Fq(:) p Fr 1778 2219 a(\(4.76\)) 0 2323 y(W) l(e) p 87 2323 a(de\014ne) p 231 2323 a(\002\(\000) p Fq(;) p 340 2323 a(x;) p 390 2323 a(z) p Fr 415 2323 a(\)) p 453 2323 a(=) p Fo 510 2323 a(;) p Fr 554 2323 a(for) p 632 2323 a(all) p Fq 703 2323 a(z) p Fo 747 2323 a(2) p Fn 800 2323 a(Z) p Fr 852 2323 a(with) p Fo 966 2323 a(\000) p Fr(3) p Fq(l) q(=) p Fr(4) p Fo 1113 2323 a(\024) p Fq 1171 2323 a(z) p Fo 1215 2323 a(\024) p 1273 2323 a(\000) p Fr(5) p Fq(l) q(=) p Fr(8) p 1420 2323 a(if) p 1468 2323 a(\002\(\000\)) p Fo 1593 2323 a(63) p Fq 1646 2323 a(x) p Fr(.) p 1718 2323 a(F) l(or) p 1809 2323 a(eac) o(h) p Fq 0 2383 a(x) p Fo 42 2383 a(2) p Fr 89 2383 a(\003) p 139 2383 a(with) p Fq 250 2383 a(x) p Fl 278 2365 a(3) p Fr 311 2383 a(=) p Fo 363 2383 a(\000) p Fq(l) p Fr 418 2383 a(,) p 447 2383 a(w) o(e) p 519 2383 a(de\014ne) p Fo 198 2515 a(S) t(W) p Fl 286 2522 a(42) p Fr 323 2515 a(\() p Fq(x) p Fr(\)) p 403 2515 a(=) p Fk 454 2445 a(\032) p Fn 492 2515 a(W) p Fo 555 2515 a(2) p 602 2515 a(S) t(W) p Fl 690 2522 a(4) p Fo 709 2515 a(nS) t(W) p Fl 821 2522 a(41) p Fr 859 2515 a(;) p Fo 901 2488 a(j) p Fr(\002\(\000\() p Fn(W) p Fr 1068 2488 a(\)) p Fq(;) p 1109 2488 a(x;) p 1159 2488 a(z) p Fr 1184 2488 a(\)) p Fo(j) p 1233 2488 a(\025) p Fq 1286 2488 a(L) p Fj 1324 2456 a(2) p 1324 2462 16 2 v 1324 2482 a(3) p Fr 1363 2488 a(for) p 1437 2488 a(all) p Fq 1505 2488 a(z) p Fo 1544 2488 a(2) p Fn 1591 2488 a(Z) p Fr 901 2548 a(with) p Fo 1024 2548 a(\000) p Fr 1073 2548 a(3) p Fq(l) q(=) p Fr(4) p Fo 1176 2548 a(\024) p Fq 1229 2548 a(z) p Fo 1267 2548 a(\024) p 1320 2548 a(\000) p Fr(5) p Fq(l) q(=) p Fr(8) p Fk 1645 2445 a(\033) p Fq 1690 2515 a(:) p Fr 0 2651 a(F) l(or) p 85 2651 a(eac) o(h) p Fn 193 2651 a(W) p Fo 257 2651 a(2) p 304 2651 a(S) t(W) p Fl 391 2658 a(42) p Fr 429 2651 a(\() p Fq(x) p Fr(\),) p 523 2651 a(w) o(e) p 592 2651 a(can) p 680 2651 a(see) p 757 2651 a(b) o(y) p 823 2651 a(the) p 905 2651 a(de\014nition) p 1120 2651 a(of) p Fo 1174 2651 a(S) t(W) p Fl 1261 2658 a(42) p Fr 1298 2651 a(\() p Fq(x) p Fr(\)) p 1378 2651 a(that) p 1482 2651 a(for) p Fq 1555 2651 a(p) p Fr 1593 2651 a(=) p 1645 2651 a(2) p 1683 2651 a(or) p 1741 2651 a(4,) p 1794 2651 a(there) 0 2711 y(exists) p 135 2711 a(some) p 257 2711 a(1) p Fo 295 2711 a(\024) p Fq 348 2711 a(i) p Fo 378 2711 a(\024) p Fq 431 2711 a(k) p Fp 456 2718 a(p) p Fr 492 2711 a(suc) o(h) p 602 2711 a(that) p Fn 496 2823 a(M) p Fl 540 2802 a(2) p Fr 563 2823 a(\() p Fq(F) p Fp 621 2799 a(p) 614 2835 y(i) p Fr 640 2823 a(\() p Fn(W) p Fr 706 2823 a(\)\)) p Fo 760 2823 a(\025) p Fq 813 2823 a(L) p Fj 851 2788 a(1) p 851 2794 V 851 2815 a(3) p Fq 874 2823 a(l) q(=) p Fr(8) p Fo 952 2823 a(\025) p Fq 1004 2823 a(K) p Fl 1045 2830 a(2) p Fq 1066 2823 a(L) p Fr(\(log) p Fq 1189 2823 a(L) p Fr(\)) p Fl 1241 2802 a(2) p Fq 1261 2823 a(=) p Fr(8) p Fq(:) p Fr 1778 2823 a(\(4.77\)) 927 2947 y(32) p 90 rotate dyy eop %%Page: 33 33 33 32 bop Fr 0 274 a(W) l(e) p 84 274 a(de\014ne) p Fo 653 334 a(S) t(W) p Fl 740 341 a(42) p Fr 791 334 a(=) p Fo 843 334 a([) p Fp 876 343 a(x) p Fm(2) p Fl(\003;) p Fp(x) p Fj 974 333 a(3) p Fl 991 343 a(=) p Fm(\000) p Fp(l) p Fo 1059 334 a(S) t(W) p Fl 1146 341 a(42) p Fr 1184 334 a(\() p Fq(x) p Fr(\)) 0 421 y(and) p Fo 612 482 a(S) t(W) p Fl 699 489 a(43) p Fr 751 482 a(=) p Fo 802 482 a(S) t(W) p Fl 890 489 a(4) p Fo 909 482 a(n) p Fr(\() p Fo(S) t(W) p Fl 1040 489 a(41) p Fo 1089 482 a([) p 1133 482 a(S) t(W) p Fl 1220 489 a(42) p Fr 1258 482 a(\)) p Fq(:) p Fr 0 569 a(Then,) p 140 569 a(b) o(y) p 206 569 a(a) p 246 569 a(similar) p 405 569 a(argumen) o(t) p 622 569 a(as) p 680 569 a(in) p 736 569 a(case) p 838 569 a(3,) p 891 569 a(the) p 974 569 a(de\014nition) p 1190 569 a(of) p Fo 1244 569 a(S) t(W) p Fl 1331 576 a(42) p Fr 1384 569 a(and) p 1477 569 a(\(4.77\),) p 1631 569 a(w) o(e) p 1702 569 a(ha) o(v) o(e) p 1813 569 a(that) 0 629 y(for) p Fq 75 629 a(N) p Fr 133 629 a(=) p Fo 184 629 a(d) p Fq(K) p Fl 247 636 a(2) p Fq 268 629 a(L) p Fr(\(log) p Fq 391 629 a(L) p Fr(\)) p Fl 443 611 a(2) p Fq 463 629 a(=) p Fr(8) p Fo(e) p Fr 550 629 a(and) p Fq 645 629 a(N) p Fm 689 611 a(0) p Fr 715 629 a(=) p Fo 767 629 a(d) p Fr(8) p Fq(K) p Fl 854 636 a(4) p Fq 874 629 a(L) p Fr(\(log) p Fq 998 629 a(L) p Fr(\)) p Fo(e) p Fk 353 700 a(X) p Ff 313 806 a(W) p Fm 349 806 a(2S) r(W) p Fj 432 811 a(42) p Fq 472 748 a(P) p Fp 510 727 a(\016) p Fl 503 760 a(\003) p Fr 530 748 a(\() p Fn(W) p Fr 596 748 a(\)) p Fo 233 925 a(\024) p Fr 313 925 a(4) p Fq(L) p Fl 370 905 a(2) p Fk 391 870 a(\020) p Fp 439 863 a(N) p Fc 471 851 a(0) p Fk 425 878 a(X) p Fp 420 984 a(k) p Fj 438 989 a(2) p Fl 456 984 a(=1) 529 863 y(8) p Fp(L) p Fk 514 878 a(X) p Fp 509 984 a(k) p Fj 527 989 a(3) p Fl 545 984 a(=1) 618 863 y(8) p Fp(L) p Fk 603 878 a(X) p Fp 598 984 a(k) p Fj 616 989 a(4) p Fl 634 984 a(=1) p Fk 700 878 a(X) p Fp 687 984 a(n) p Fj 708 989 a(1) p Fm 726 984 a(\025) p Fp(N) p Fk 799 878 a(X) p Fp 793 983 a(n) p Fj 814 988 a(2) p Fm 832 983 a(\025) p Fl(1) p Fo 886 925 a(\001) p 908 925 a(\001) p 930 925 a(\001) p Fk 1024 878 a(X) p Fp 952 983 a(n) p Fe 973 989 a(k) p Fj 989 996 a(2) 1007 989 y(+) p Fe(k) p Fj 1046 996 a(3) 1064 989 y(+) p Fe(k) p Fj 1103 996 a(4) p Fm 1123 983 a(\025) p Fl(1) p Fk 1177 855 a(\022) p Fq 1218 891 a(N) p Fm 1262 873 a(0) p Fq 1224 959 a(k) p Fl 1249 966 a(2) p Fk 1279 855 a(\023) p 1324 855 a(\022) p Fr 1366 891 a(16) p Fq(L) p Fl 1447 873 a(2) p Fq 1394 959 a(k) p Fl 1419 966 a(3) p Fk 1472 855 a(\023) p 1517 855 a(\022) p Fr 1559 891 a(16) p Fq(L) p Fl 1640 873 a(2) p Fq 1587 959 a(k) p Fl 1612 966 a(4) p Fk 1666 855 a(\023) p Fq 508 1075 a(\024) p Fp 536 1055 a(n) p Fj 557 1060 a(1) p Fl 575 1055 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 680 1061 a(k) p Fj 696 1068 a(2) 715 1061 y(+) p Fe(k) p Fj 754 1068 a(3) 772 1061 y(+) p Fe(k) p Fj 811 1068 a(4) p Fq 833 1075 a(e) p Fm 856 1055 a(\000) p Fl(\() p Fp(\014) r(=) p Fl(3) p Fm(\000) p Fp(c) p Fj 997 1060 a(32) p Fl 1029 1055 a(\)\() p Fp(n) p Fj 1078 1060 a(1) p Fl 1095 1055 a(+) p Fm(\001\001\001) p Fl(+) p Fp(n) p Fe 1200 1061 a(k) p Fj 1216 1068 a(2) 1234 1061 y(+) p Fe(k) p Fj 1273 1068 a(3) 1291 1061 y(+) p Fe(k) p Fj 1330 1068 a(4) p Fl 1350 1055 a(\)) p Fk 1366 1020 a(\021) p Fo 233 1190 a(\024) p Fq 313 1190 a(c) p Fl 334 1197 a(45) p Fr 380 1190 a(exp) o([) p Fo(\000) p Fr 524 1156 a(1) p 512 1179 49 2 v 512 1224 a(24) 565 1190 y(\() p Fq(\014) p Fo 626 1190 a(\000) p Fq 676 1190 a(c) p Fl 697 1197 a(46) p Fr 734 1190 a(\)) p Fq(K) p Fl 794 1197 a(2) p Fq 814 1190 a(L) p Fr(\(log) p Fq 938 1190 a(L) p Fr(\)) p Fl 990 1170 a(2) p Fr 1009 1190 a(]) p Fq(:) p Fr 1778 1190 a(\(4.78\)) 73 1313 y(Finally) l(,) p 253 1313 a(w) o(e) p 329 1313 a(will) p 425 1313 a(consider) p 618 1313 a(the) p 706 1313 a(case) p 813 1313 a(where) p Fn 957 1313 a(W) p Fo 1027 1313 a(2) p 1081 1313 a(S) t(W) p Fl 1168 1320 a(43) p Fr 1205 1313 a(.) p 1252 1313 a(Let) p 1343 1313 a(us) p 1409 1313 a(\014x) p Fn 1482 1313 a(W) p Fo 1552 1313 a(2) p 1605 1313 a(S) t(W) p Fl 1692 1320 a(43) p Fr 1749 1313 a(and) p 1848 1313 a(let) 0 1373 y(\000) p 44 1373 a(=) p 96 1373 a(\000\() p Fn(W) p Fr 192 1373 a(\).) p 249 1373 a(In) p 310 1373 a(this) p 404 1373 a(case,) p 520 1373 a(there) p 644 1373 a(exists) p 778 1373 a(some) p Fq 900 1373 a(x) p Fo 941 1373 a(2) p Fr 989 1373 a(\003) p 1038 1373 a(with) p Fq 1148 1373 a(x) p Fl 1176 1355 a(3) p Fr 1210 1373 a(=) p Fo 1261 1373 a(\000) p Fq(l) p Fr 1331 1373 a(suc) o(h) p 1441 1373 a(that) p Fo 1546 1373 a(j) p Fr(\002\(\000) p Fq(;) p 1669 1373 a(x;) p 1719 1373 a(z) p Fr 1744 1373 a(\)) p Fo(j) p Fq 1790 1373 a(<) p 1842 1373 a(L) p Fj 1880 1341 a(2) p 1880 1347 16 2 v 1880 1368 a(3) p Fr 0 1433 a(for) p 77 1433 a(some) p Fq 201 1433 a(z) p Fo 244 1433 a(2) p Fn 295 1433 a(Z) p Fr 347 1433 a(with) p Fo 460 1433 a(\000) p Fr(3) p Fq(l) q(=) p Fr(4) p Fo 605 1433 a(\024) p Fq 662 1433 a(z) p Fo 704 1433 a(\024) p 761 1433 a(\000) p Fr(5) p Fq(l) q(=) p Fr(8.) p 930 1433 a(Let) p 1020 1433 a(us) p 1085 1433 a(\014x) p 1156 1433 a(suc) o(h) p 1269 1433 a(a) p 1312 1433 a(p) q(oin) o(t) p Fq 1441 1433 a(x) p Fo 1487 1433 a(2) p Fr 1538 1433 a(\003) p 1590 1433 a(and) p 1687 1433 a(an) p 1757 1433 a(in) o(teger) p Fq 0 1493 a(z) p Fo 39 1493 a(2) p Fn 86 1493 a(Z) p Fr 122 1493 a(.) p 154 1493 a(W) l(e) p 238 1493 a(de\014ne) p Fo 260 1622 a(A) p Fr(\(\002\(\000) p Fq(;) p 428 1622 a(x;) p 478 1622 a(z) p Fr 503 1622 a(\)\)) p 554 1622 a(=) p Fk 606 1552 a(\032) p Fq 643 1622 a(\033) p Fo 686 1622 a(2) p Fr 733 1622 a(\012) p Fl 768 1629 a(\003) p Fr 795 1622 a(;) p Fn 838 1591 a(W) p Fr 885 1591 a(\(\000) p Fp 934 1573 a(!) p Fl 934 1604 a(\003) p Fr 964 1591 a(\() p Fq(\033) p Fr 1013 1591 a(\)\)) p Fo 1064 1591 a(2) p 1111 1591 a(S) t(W) p Fl 1198 1598 a(43) p Fq 1235 1591 a(;) p Fr 1274 1591 a(\002\(\000) p Fp 1361 1573 a(!) p Fl 1361 1604 a(\003) p Fr 1388 1591 a(\() p Fq(\033) p Fr 1437 1591 a(\)\)) p Fo 1488 1591 a(3) p Fq 1535 1591 a(x) p Fr 838 1652 a(and) p 933 1652 a(\002\(\000) p Fp 1020 1634 a(!) p Fl 1020 1664 a(\003) p Fr 1047 1652 a(\() p Fq(\033) p Fr 1096 1652 a(\)) p Fq(;) p 1137 1652 a(x;) p 1187 1652 a(z) p Fr 1212 1652 a(\)) p 1243 1652 a(=) p 1295 1652 a(\002\(\000) p Fq(;) p 1404 1652 a(x;) p 1454 1652 a(z) p Fr 1479 1652 a(\)) p Fk 1583 1552 a(\033) p Fq 1629 1622 a(;) p Fo 139 1764 a(A) p Fm 179 1744 a(\006) p Fr 209 1764 a(\(\002\(\000) p Fq(;) p 337 1764 a(x;) p 387 1764 a(z) p Fr 412 1764 a(\)\)) p 463 1764 a(=) p Fo 515 1764 a(f) p Fq(\033) p Fo 583 1764 a(2) p Fr 630 1764 a(\012) p Fl 665 1771 a(\003) p Fr 692 1764 a(;) p 714 1764 a(for) p 788 1764 a(some) p Fq 911 1764 a(\021) p Fo 950 1764 a(2) p Fr 997 1764 a(\012) p Fl 1032 1772 a(\002\(\000) p Fp(;x;z) p Fl 1152 1772 a(\)) p Fq 1169 1764 a(;) p 1207 1764 a(\021) p Fl 1231 1772 a(\002\(\000) p Fp(;x;z) p Fl 1351 1772 a(\)) p Fq 1367 1764 a(\033) p Fo 1411 1764 a(2) p 1458 1764 a(A) p Fr(\(\002\(\000) p Fq(;) p 1626 1764 a(x;) p 1676 1764 a(z) p Fr 1701 1764 a(\)\)) p Fo(g) p Fr 0 1851 a(and) p Fo 186 1912 a(A) p Fl 226 1891 a(+) p Fr 256 1912 a(\(\002\(\000) p Fq(;) p 384 1912 a(x;) p 434 1912 a(z) p Fr 459 1912 a(\)\)) p 510 1912 a(=) p Fo 562 1912 a(f) p Fq(\033) p Fo 630 1912 a(2) p 677 1912 a(A) p Fm 717 1891 a(\006) p Fr 746 1912 a(\(\002\(\000) p Fq(;) p 874 1912 a(x;) p 924 1912 a(z) p Fr 949 1912 a(\)\);) p Fq 1009 1912 a(\033) p Fr 1039 1912 a(\() p Fq(y) p Fr 1084 1912 a(\)) p 1116 1912 a(=) p 1167 1912 a(+1) p 1246 1912 a(for) p 1321 1912 a(all) p Fq 1388 1912 a(y) p Fo 1428 1912 a(2) p Fr 1475 1912 a(\002\(\000) p Fq(;) p 1584 1912 a(x;) p 1634 1912 a(z) p Fr 1659 1912 a(\)) p Fo(g) p Fq(:) p Fr 0 1999 a(Then,) p 141 1999 a(w) o(e) p 213 1999 a(ha) o(v) o(e) p 325 1999 a(b) o(y) p 393 1999 a(the) p 477 1999 a(\014nite) p 602 1999 a(energy) p 757 1999 a(prop) q(ert) o(y) p 957 1999 a(that) p Fq 207 2120 a(\026) p Fp 236 2096 a(!) q(;) p Ff(J) p Fe 289 2102 a(\016) p Fl 236 2133 a(\003) p Fk 305 2064 a(\020) p Fo 335 2120 a(A) p Fr(\(\002\(\000) p Fq(;) p 503 2120 a(x;) p 553 2120 a(z) p Fr 578 2120 a(\)\)) p Fk 616 2064 a(\021) p Fo 659 2120 a(\024) p Fr 712 2120 a(exp) o([12) p Fq(\014) p Fo 879 2120 a(j) p Fr(\002\(\000) p Fq(;) p 1002 2120 a(x;) p 1052 2120 a(z) p Fr 1077 2120 a(\)) p Fo(j) p Fr(]) p Fq 1132 2120 a(\026) p Fp 1161 2096 a(!) q(;) p Ff(J) p Fe 1213 2102 a(\016) p Fl 1161 2133 a(\003) p Fk 1229 2064 a(\020) p Fo 1259 2120 a(A) p Fl 1299 2099 a(+) p Fr 1328 2120 a(\(\002\(\000) p Fq(;) p 1456 2120 a(x;) p 1506 2120 a(z) p Fr 1531 2120 a(\)\)) p Fk 1569 2064 a(\021) p Fq 1598 2120 a(:) p Fr 1778 2120 a(\(4.79\)) 0 2243 y(By) p 77 2243 a(\(A.6\)) p 205 2243 a(and) p 300 2243 a(standard) p 504 2243 a(P) o(eierls') p 674 2243 a(argumen) o(t,) p 906 2243 a(w) o(e) p 977 2243 a(ha) o(v) o(e) p 1090 2243 a(that) p Fq 448 2367 a(\026) p Fp 477 2344 a(!) q(;) p Ff(J) p Fe 530 2350 a(\016) p Fl 477 2381 a(\003) p Fk 546 2312 a(\020) p Fo 576 2367 a(A) p Fl 616 2347 a(+) p Fr 645 2367 a(\(\002\(\000) p Fq(;) p 773 2367 a(x;) p 823 2367 a(z) p Fr 848 2367 a(\)\)) p Fk 886 2312 a(\021) p Fo 929 2367 a(\024) p Fq 982 2367 a(c) p Fl 1003 2374 a(47) p Fr 1048 2367 a(exp[) p Fo(\000) p Fr(\() p Fq(\014) p Fo 1236 2367 a(\000) p Fq 1285 2367 a(c) p Fl 1306 2374 a(48) p Fr 1344 2367 a(\)) p Fq(l) q(=) p Fr(2]) p Fq(;) p Fr 0 2491 a(whic) o(h) p 140 2491 a(together) p 332 2491 a(with) p 443 2491 a(\(4.79\)) p 584 2491 a(implies) p 750 2491 a(that) p Fq 246 2626 a(\026) p Fp 275 2602 a(!) q(;) p Ff(J) p Fe 328 2608 a(\016) p Fl 275 2639 a(\003) p Fk 344 2570 a(\020) p Fo 374 2626 a(A) p Fr(\(\002\(\000) p Fq(;) p 542 2626 a(x;) p 592 2626 a(z) p Fr 617 2626 a(\)\)) p Fk 655 2570 a(\021) p Fo 726 2626 a(\024) p Fq 806 2626 a(c) p Fl 827 2633 a(47) p Fr 873 2626 a(exp) o([12) p Fq(\014) s(L) p Fj 1078 2591 a(2) p 1078 2597 V 1078 2618 a(3) p Fo 1111 2626 a(\000) p Fr 1161 2626 a(\() p Fq 1185 2592 a(\014) p 1185 2614 31 2 v Fr 1188 2660 a(2) p Fo 1231 2626 a(\000) p Fq 1281 2626 a(c) p Fl 1302 2633 a(49) p Fr 1340 2626 a(\)) p Fq(K) p Fl 1400 2633 a(2) p Fq 1420 2626 a(L) p Fj 1458 2591 a(2) p 1458 2597 16 2 v 1458 2618 a(3) p Fr 1480 2626 a(\(log) p Fq 1570 2626 a(L) p Fr(\)) p Fl 1622 2605 a(2) p Fr 1642 2626 a(]) p Fo 726 2745 a(\024) p Fq 806 2745 a(c) p Fl 827 2752 a(50) p Fr 873 2745 a(exp) o([) p Fo(\000) p Fr(\() p Fq 1024 2711 a(\014) p 1024 2733 31 2 v Fr 1027 2779 a(2) p Fo 1070 2745 a(\000) p Fq 1120 2745 a(c) p Fl 1141 2752 a(51) p Fr 1178 2745 a(\)) p Fq(K) p Fl 1238 2752 a(2) p Fq 1258 2745 a(L) p Fj 1296 2710 a(2) p 1296 2716 16 2 v 1296 2737 a(3) p Fr 1319 2745 a(\(log) p Fq 1409 2745 a(L) p Fr(\)) p Fl 1461 2724 a(2) p Fr 1481 2745 a(]) p Fq(:) p Fr 1778 2745 a(\(4.80\)) 927 2947 y(33) p 90 rotate dyy eop %%Page: 34 34 34 33 bop Fr 0 274 a(F) l(or) p 91 274 a(eac) o(h) p Fq 205 274 a(x) p Fo 253 274 a(2) p Fr 307 274 a(\003) p 361 274 a(with) p Fq 476 274 a(x) p Fl 504 256 a(3) p Fr 543 274 a(=) p Fo 602 274 a(\000) p Fq(l) p Fr 676 274 a(and) p 775 274 a(eac) o(h) p 889 274 a(collection) p 1109 274 a(\002\() p Fq(z) p Fr 1191 274 a(\)) p 1230 274 a(of) p Fq 1290 274 a(l) p Fm 1305 281 a(1) p Fr 1341 274 a(-connected) p 1589 274 a(comp) q(onen) o(ts) p 1862 274 a(in) 0 334 y(H\() p Fq(z) p Fr 81 334 a(\)) p Fo 110 334 a(\\) p Fr 155 334 a(\003,) p 218 334 a(w) o(e) p 290 334 a(de\014ne) p Fo 244 453 a(A) p Fr(\() p Fq(x;) p Fr 353 453 a(\002\() p Fq(z) p Fr 435 453 a(\)\)) p 486 453 a(=) p Fk 538 383 a(\032) p Fq 575 453 a(\033) p Fo 619 453 a(2) p Fr 666 453 a(\012) p Fl 701 460 a(\003) p Fr 728 453 a(;) p Fn 770 423 a(W) p Fr 817 423 a(\(\000) p Fp 866 405 a(!) p Fl 866 435 a(\003) p Fr 896 423 a(\() p Fq(\033) p Fr 945 423 a(\)\)) p Fo 996 423 a(2) p 1043 423 a(S) t(W) p Fl 1130 430 a(43) p Fq 1168 423 a(;) p Fr 1206 423 a(\002\(\000) p Fp 1293 405 a(!) p Fl 1293 435 a(\003) p Fr 1320 423 a(\() p Fq(\033) p Fr 1369 423 a(\)\)) p Fo 1420 423 a(3) p Fq 1467 423 a(x) p Fr 770 483 a(and) p 865 483 a(\002\(\000) p Fp 952 465 a(!) p Fl 952 495 a(\003) p Fr 979 483 a(\() p Fq(\033) p Fr 1028 483 a(\)) p Fq(;) p 1069 483 a(x;) p 1119 483 a(z) p Fr 1144 483 a(\)) p 1175 483 a(=) p 1227 483 a(\002\() p Fq(z) p Fr 1309 483 a(\)) p Fk 1516 383 a(\033) p Fq 1561 453 a(:) p Fr 0 572 a(W) l(e) p 84 572 a(ha) o(v) o(e) p 196 572 a(from) p 312 572 a(\(4.80\)) p 453 572 a(that) p Fk 222 628 a(X) p Ff 182 734 a(W) p Fm 219 734 a(2) o(S) r(W) p Fj 301 739 a(43) p Fq 341 676 a(P) p Fp 379 655 a(\016) p Fl 372 688 a(\003) p Fr 399 676 a(\() p Fn(W) p Fr 465 676 a(\)) p Fo 529 676 a(\024) p Fk 609 628 a(X) p Fp 635 733 a(x) p Fk 689 628 a(X) p Fp 716 733 a(z) p Fk 770 628 a(X) p Fl 769 736 a(\002\() p Fp(z) p Fl 827 736 a(\)) p Fq 851 676 a(\026) p Fp 880 652 a(!) q(;) p Ff(J) p Fe 932 658 a(\016) p Fl 880 689 a(\003) p Fk 948 620 a(\020) p Fo 978 676 a(A) p Fr(\() p Fq(x;) p Fr 1087 676 a(\002\() p Fq(z) p Fr 1169 676 a(\)\)) p Fk 1207 620 a(\021) p Fo 529 874 a(\024) p Fq 609 874 a(c) p Fl 630 881 a(50) p Fr 676 874 a(exp) o([) p Fo(\000) p Fr(\() p Fq 827 841 a(\014) p 827 863 31 2 v Fr 830 909 a(2) p Fo 873 874 a(\000) p Fq 923 874 a(c) p Fl 944 881 a(51) p Fr 981 874 a(\)) p Fq(K) p Fl 1041 881 a(2) p Fq 1061 874 a(L) p Fj 1099 840 a(2) p 1099 846 16 2 v 1099 867 a(3) p Fr 1122 874 a(\(log) p Fq 1212 874 a(L) p Fr(\)) p Fl 1264 854 a(2) p Fr 1284 874 a(]) p Fk 1306 827 a(X) p Fp 1332 932 a(x) p Fk 1386 827 a(X) p Fp 1413 932 a(z) 1479 812 y(L) p Fj 1508 787 a(2) p 1508 791 V 1508 809 a(3) p Fk 1468 827 a(X) p Fp 1466 933 a(N) p Fl 1498 933 a(=1) p Fk 1551 804 a(\022) p Fr 1593 841 a(4) p Fq(L) p Fl 1650 823 a(2) p Fq 1609 909 a(N) p Fk 1675 804 a(\023) p Fo 529 1023 a(\024) p Fq 609 1023 a(c) p Fl 630 1030 a(52) p Fr 676 1023 a(exp) o([) p Fo(\000) p Fr(\() p Fq 827 989 a(\014) p 827 1011 31 2 v Fr 830 1057 a(2) p Fo 873 1023 a(\000) p Fq 923 1023 a(c) p Fl 944 1030 a(53) p Fr 981 1023 a(\)) p Fq(K) p Fl 1041 1030 a(2) p Fq 1061 1023 a(L) p Fj 1099 989 a(2) p 1099 995 16 2 v 1099 1015 a(3) p Fr 1122 1023 a(\(log) p Fq 1212 1023 a(L) p Fr(\)) p Fl 1264 1002 a(2) p Fr 1284 1023 a(]) p Fq(;) p Fr 1778 1023 a(\(4.81\)) 0 1143 y(where) p Fk 148 1096 a(X) p Fp 174 1200 a(x) p Fr 243 1143 a(and) p Fk 345 1096 a(X) p Fp 372 1200 a(z) p Fr 440 1143 a(stand) p 580 1143 a(for) p Fk 662 1106 a(P) p Fp 714 1158 a(x) p Fm(2) p Fl(\003;) p Fp(x) p Fj 812 1148 a(3) p Fl 829 1158 a(=) p Fm(\000) p Fp(l) p Fr 920 1143 a(and) p Fk 1022 1106 a(P) p Fp 1074 1158 a(z) p Fm 1091 1158 a(2) p Ff(Z) p Fl 1141 1158 a(;) p Fm(\000) p Fl(3) p Fp(l) o(=) p Fl(4) p Fm(\024) p Fp(z) p Fm 1286 1158 a(\024\000) p Fl(5) p Fp(l=) p Fl(8) p Fr 1405 1143 a(,) p 1444 1143 a(resp) q(ectiv) o(ely) l(,) p 1728 1143 a(and) p Fk 1830 1096 a(X) p Fl 1830 1204 a(\002\() p Fp(z) p Fl 1888 1204 a(\)) p Fr 0 1258 a(stands) p 149 1258 a(for) p 220 1258 a(the) p 301 1258 a(summation) p 550 1258 a(o) o(v) o(er) p 651 1258 a(all) p 716 1258 a(collections) p 949 1258 a(\002\() p Fq(z) p Fr 1031 1258 a(\)) p 1063 1258 a(of) p Fq 1115 1258 a(l) p Fm 1130 1265 a(1) p Fr 1167 1258 a(-connected) p 1408 1258 a(comp) q(onen) o(ts) p 1673 1258 a(in) p 1727 1258 a(H\() p Fq(z) p Fr 1808 1258 a(\)) p Fo 1832 1258 a(\\) p Fr 1870 1258 a(\003) 0 1323 y(suc) o(h) p 110 1323 a(that) p Fo 216 1323 a(j) p Fr(\002\() p Fq(z) p Fr 312 1323 a(\)) p Fo(j) p Fq 358 1323 a(<) p 410 1323 a(L) p Fj 448 1291 a(2) p 448 1297 V 448 1318 a(3) p Fr 470 1323 a(.) 73 1412 y(Let) p 160 1412 a(us) p 223 1412 a(\014x) p Fq 292 1412 a(") p 328 1412 a(>) p Fr 380 1412 a(0.) p 440 1412 a(F) l(rom) p 568 1412 a(\(4.9\),) p 697 1412 a(\(4.10\),) p 852 1412 a(\(4.12\),) p 1006 1412 a(\(4.17\),) p 1160 1412 a(\(4.34\),) p 1315 1412 a(\(4.35\),) p 1469 1412 a(\(4.73\),) p 1623 1412 a(\(4.74\),) p 1778 1412 a(\(4.78\)) 0 1472 y(and) p 98 1472 a(\(4.81\),) p 256 1472 a(w) o(e) p 331 1472 a(ha) o(v) o(e) p 446 1472 a(that) p 555 1472 a(for) p 632 1472 a(some) p Fq 758 1472 a(K) p Fl 799 1479 a(3) p Fr 819 1472 a(,) p Fq 852 1472 a(K) p Fl 893 1479 a(4) p Fr 914 1472 a(,) p Fq 947 1472 a(K) p Fl 988 1479 a(5) p Fr 1028 1472 a(and) p Fq 1125 1472 a(K) p Fl 1166 1479 a(2) p Fr 1206 1472 a(large) p 1328 1472 a(enough) p 1499 1472 a(and) p 1597 1472 a(for) p 1674 1472 a(su\016cien) o(tly) 0 1533 y(large) p Fq 119 1533 a(L) p Fo 166 1533 a(2) p Fn 213 1533 a(N) p Fr(,) p Fq 731 1593 a(\026) p Fp 760 1569 a(!) q(;) p Ff(J) p Fe 813 1575 a(\016) p Fl 760 1606 a(\003) p Fr 829 1593 a(\(\() p Fo(A) p Fp 907 1572 a(!) p Fl 907 1605 a(\003) p Fr 933 1593 a(\)) p Fp 952 1572 a(c) p Fr 969 1593 a(\)) p Fo 1002 1593 a(\024) p Fq 1055 1593 a("L) p Fm 1111 1572 a(\000) p Fl(3) p Fq 1158 1593 a(;) p Fr 0 1671 a(and) p 95 1671 a(w) o(e) p 167 1671 a(\014nished) p 346 1671 a(the) p 430 1671 a(pro) q(of) p 557 1671 a(of) p 613 1671 a(Prop) q(osition) p 875 1671 a(2.2.) p Fs 0 1835 a(App) r(endix) p Fr 73 1944 a(In) p 133 1944 a(this) p 227 1944 a(app) q(endix,) p 452 1944 a(w) o(e) p 523 1944 a(will) p 614 1944 a(pro) o(v) o(e) p 745 1944 a(the) p 828 1944 a(claims) p 977 1944 a(whic) o(h) p 1116 1944 a(w) o(e) p 1187 1944 a(used) p 1298 1944 a(in) p 1354 1944 a(Section) p 1524 1944 a(4.) p 1584 1944 a(By) p Fq 1660 1944 a(@) p Fr 1689 1944 a(\002,) p 1755 1944 a(w) o(e) p 1826 1944 a(will) 0 2005 y(denote) p Fq 157 2005 a(@) s(Q) p Fr(\(\002\)) p 316 2005 a(if) p 361 2005 a(\002) p Fo 413 2005 a(\032) p Fn 465 2005 a(Z) p Fp 502 1986 a(d) p Fr 519 2005 a(.) p 554 2005 a(Let) p 641 2005 a(1) p Fo 260 2124 a(C) p Fr 289 2124 a(\() p Fq(L;) p 363 2124 a(d) p Fr(\)) p 421 2124 a(=) p Fk 473 2053 a(\032) p Fq 510 2124 a(\015) p Fr 538 2124 a(;) p Fq 581 2093 a(\015) p Fr 623 2093 a(=) p Fq 675 2093 a(@) p Fr 704 2093 a(\002) p 757 2093 a(for) p 832 2093 a(some) p Fq 954 2093 a(l) p Fm 969 2100 a(1) p Fr 1006 2093 a(-connected) p 1250 2093 a(\002) p Fo 1302 2093 a(\032) p Fr 1354 2093 a(\003) p Fp 1388 2100 a(d) p Fr 1408 2093 a(\() p Fq(L) p Fr(\)) 581 2153 y(whic) o(h) p 721 2153 a(satis\014es) p 900 2153 a(that) p 1006 2153 a(\002) p Fp 1044 2135 a(c) p Fr 1077 2153 a(is) p Fq 1126 2153 a(l) p Fm 1141 2160 a(1) p Fr 1178 2153 a(-connected) p Fk 1500 2053 a(\033) p Fq 1546 2124 a(:) p Fr 1790 2124 a(\(A.1\)) 0 2242 y(The) p 99 2242 a(set) p 175 2242 a(\002) p 228 2242 a(is) p 276 2242 a(uniquely) p 473 2242 a(determined) p 727 2242 a(b) o(y) p 794 2242 a(eac) o(h) p Fq 903 2242 a(\015) p Fo 945 2242 a(2) p 992 2242 a(C) p Fr 1021 2242 a(\() p Fq(L;) p 1095 2242 a(d) p Fr(\),) p 1168 2242 a(and) p 1262 2242 a(hence) p 1397 2242 a(is) p 1445 2242 a(denoted) p 1629 2242 a(b) o(y) p 1696 2242 a(\002\() p Fq(\015) p Fr 1781 2242 a(\).) p 1834 2242 a(W) l(e) 0 2303 y(de\014ne) p 141 2303 a(for) p 215 2303 a(eac) o(h) p Fq 325 2303 a(i) p Fo 356 2303 a(\024) p Fq 408 2303 a(d) p Fr(,) p Fo 342 2419 a(C) p Fp 368 2426 a(i) p Fr 382 2419 a(\() p Fq(L;) p 456 2419 a(d) p Fr(\)) p 514 2419 a(=) p Fk 566 2349 a(\032) p Fq 603 2419 a(\015) p Fo 645 2419 a(2) p 692 2419 a(C) p Fr 721 2419 a(\() p Fq(L;) p 795 2419 a(d) p Fr(\);) 882 2388 y(if) p Fq 927 2388 a(x) p Fo 968 2388 a(2) p Fr 1015 2388 a(\002\() p Fq(\015) p Fr 1100 2388 a(\)) p 1136 2388 a(and) p Fq 1230 2388 a(y) p Fo 1270 2388 a(2) p Fr 1317 2388 a(L) p Fp 1347 2370 a(i) p Fr 1361 2388 a(\() p Fq(x) p Fr(\)) 882 2449 y(with) p Fq 993 2449 a(y) p Fp 1019 2430 a(i) p Fo 1047 2449 a(\024) p Fq 1099 2449 a(x) p Fp 1127 2430 a(i) p Fq 1141 2449 a(;) p Fr 1179 2449 a(then) p Fq 1290 2449 a(y) p Fo 1330 2449 a(2) p Fr 1377 2449 a(\002\() p Fq(\015) p Fr 1462 2449 a(\)) p Fk 1501 2349 a(\033) p Fq 1547 2419 a(;) p Fr 0 2540 a(where) p 141 2540 a(L) p Fp 171 2522 a(i) p Fr 185 2540 a(\() p Fq(x) p Fr(\)) p 265 2540 a(=) p Fo 317 2540 a(f) p Fq(y) p Fo 381 2540 a(2) p Fr 428 2540 a(\003) p Fp 462 2547 a(d) p Fr 482 2540 a(\() p Fq(L) p Fr(\);) p Fq 575 2540 a(y) p Fp 601 2522 a(j) p Fr 633 2540 a(=) p Fq 685 2540 a(x) p Fp 713 2522 a(j) p Fr 747 2540 a(for) p 821 2540 a(an) o(y) p Fq 913 2540 a(j) p Fo 950 2540 a(6) p Fr(=) p Fq 1002 2540 a(i) p Fo(g) p Fr(.) p 1079 2540 a(W) l(e) p 1163 2540 a(also) p 1261 2540 a(de\014ne) p Fo 710 2630 a(S) p Fr 744 2630 a(\() p Fq(L;) p 818 2630 a(d) p Fr(\)) p 876 2630 a(=) p Fo 928 2630 a(\\) p Fp 961 2610 a(d) 961 2643 y(i) p Fl(=1) p Fo 1020 2630 a(C) p Fp 1046 2637 a(i) p Fr 1060 2630 a(\() p Fq(L;) p 1134 2630 a(d) p Fr(\)) p Fq(:) p Fr 0 2720 a(By) 83 2707 y(^) p Fq 77 2720 a(@) p Fr 105 2720 a(\003) p Fp 139 2727 a(d) p Fr 159 2720 a(\() p Fq(L) p Fr(\),) p 260 2720 a(w) o(e) p 332 2720 a(will) p 424 2720 a(denote) p Fq 417 2810 a(@) p Fr 446 2810 a(\003) p Fp 480 2817 a(d) p Fr 500 2810 a(\() p Fq(L) p Fr(\)) p Fo(nf) p Fq(x) p Fo 662 2810 a(2) p Fn 709 2810 a(R) p Fp 748 2790 a(d) p Fr 766 2810 a(;) p Fq 788 2810 a(x) p Fp 816 2790 a(d) p Fr 849 2810 a(=) p Fq 901 2810 a(L) p Fr 945 2810 a(+) p 994 2810 a(\(1) p Fq(=) p Fr(2\)) p 1122 2810 a(or) p Fo 1192 2810 a(\000) p Fq 1242 2810 a(L) p Fr 1286 2810 a(+) p 1335 2810 a(\(1) p Fq(=) p Fr(2\)) p Fo(g) p Fq(:) p Fr 927 2947 a(34) p 90 rotate dyy eop %%Page: 35 35 35 34 bop Fg 73 274 a(Lemma) p 275 274 a(A.1.) p Fd 399 274 a(Supp) n(ose) p 587 274 a(that) p Fq 689 274 a(d) p Fo 733 274 a(\025) p Fr 790 274 a(2) p Fd(.) p 859 274 a(F) l(or) p 953 274 a(e) n(ach) p Fq 1065 274 a(i) p Fo 1100 274 a(\024) p Fq 1157 274 a(d) p Fd(,) p 1218 274 a(c) n(onsider) p 1413 274 a(the) p 1497 274 a(map) p Fq 1606 274 a(') p Fp 1638 281 a(i) p Fr 1671 274 a(:) p Fo 1703 274 a(C) p Fr 1732 274 a(\() p Fq(L;) p 1806 274 a(d) p Fr(\)) p Fo 1869 274 a(3) p Fq 0 334 a(\015) p Fo 42 334 a(7!) p Fq 105 334 a(') p Fp 137 341 a(i) p Fr 152 334 a(\() p Fq(\015) p Fr 199 334 a(\)) p Fo 231 334 a(2) p 278 334 a(C) p Fp 304 341 a(i) p Fr 319 334 a(\() p Fq(L;) p 393 334 a(d) p Fr(\)) p Fd 454 334 a(which) p 591 334 a(satis\014es) p 774 334 a(that) p 874 334 a(for) p 952 334 a(any) p Fq 1045 334 a(x) p Fo 1087 334 a(2) p Fr 1134 334 a(\003) p Fp 1168 341 a(d) p Fr 1188 334 a(\() p Fq(L) p Fr(\)) p Fo 531 439 a(j) p Fr(\002\() p Fq(\015) p Fr 630 439 a(\)) p Fo 660 439 a(\\) p Fr 704 439 a(L) p Fp 734 418 a(i) p Fr 749 439 a(\() p Fq(x) p Fr(\)) p Fo(j) p Fr 842 439 a(=) p Fo 894 439 a(j) p Fr(\002\() p Fq(') p Fp 997 446 a(i) p Fr 1010 439 a(\() p Fq(\015) p Fr 1057 439 a(\)\)) p Fo 1106 439 a(\\) p Fr 1151 439 a(L) p Fp 1181 418 a(i) p Fr 1195 439 a(\() p Fq(x) p Fr(\)) p Fo(j) p Fq(:) p Fr 1790 439 a(\(A.2\)) p Fd 0 544 a(Then,) p 142 544 a(for) p 220 544 a(e) n(ach) p Fq 329 544 a(i) p Fo 360 544 a(\024) p Fq 412 544 a(d) p Fd 455 544 a(and) p 550 544 a(any) p Fq 643 544 a(\015) p Fo 685 544 a(2) p 732 544 a(C) p Fr 761 544 a(\() p Fq(L;) p 835 544 a(d) p Fr(\)) p Fn 656 649 a(M) p Fp 700 628 a(d) p Fm(\000) p Fl 746 628 a(1) p Fr 768 649 a(\() p Fq(\015) p Fr 815 649 a(\)) p Fo 848 649 a(\025) p Fn 901 649 a(M) p Fp 945 628 a(d) p Fm(\000) p Fl(1) p Fr 1013 649 a(\() p Fq(') p Fp 1064 656 a(i) p Fr 1078 649 a(\() p Fq(\015) p Fr 1125 649 a(\)\)) p 1790 649 a(\(A.3\)) p Fd 0 754 a(holds.) p 143 754 a(Mor) n(e) n(over,) p 369 754 a(for) p 443 754 a(e) n(ach) p Fq 549 754 a(i) p Fo 579 754 a(\024) p Fq 632 754 a(d) p Fd 671 754 a(and) p 762 754 a(any) p Fq 851 754 a(\015) p Fo 893 754 a(2) p 940 754 a(C) p Fr 969 754 a(\() p Fq(L;) p 1043 754 a(d) p Fr(\)) p Fd 1101 754 a(with) p Fn 1203 754 a(M) p Fp 1247 736 a(d) p Fm(\000) p Fl 1293 736 a(1) p Fr 1315 754 a(\() p Fq(\015) p Fo 1362 754 a(n) p Fr 1393 740 a(^) p Fq 1387 754 a(@) p Fr 1416 754 a(\003) p Fp 1450 761 a(d) p Fr 1470 754 a(\() p Fq(L) p Fr(\)\)) p Fq(=) p Fn(M) p Fp 1628 736 a(d) p Fm 1647 736 a(\000) p Fl(1) p Fr 1697 754 a(\() p Fq(\015) p Fr 1744 754 a(\)) p Fo 1776 754 a(\024) p Fr 1829 754 a(1) p Fq(=) p Fr(2) p Fn 473 856 a(M) p Fp 517 838 a(d) p Fm(\000) p Fl(1) p Fr 585 856 a(\() p Fq(\015) p Fo 632 856 a(n) p Fq(@) p Fr 686 856 a(\003) p Fp 720 863 a(d) p Fr 739 856 a(\() p Fq(L) p Fr(\)\)) p 473 878 357 2 v Fn 562 924 a(M) p Fp 606 910 a(d) p Fm(\000) p Fl(1) p Fr 674 924 a(\() p Fq(\015) p Fr 721 924 a(\)) p Fo 848 890 a(\025) p Fn 906 856 a(M) p Fp 950 838 a(d) p Fm(\000) p Fl(1) p Fr 1018 856 a(\() p Fq(') p Fp 1069 863 a(i) p Fr 1083 856 a(\() p Fq(\015) p Fr 1130 856 a(\)) p Fo(n) p Fq(@) p Fr 1203 856 a(\003) p Fp 1237 863 a(d) p Fr 1257 856 a(\() p Fq(L) p Fr(\)\)) p 906 878 441 2 v Fn 995 924 a(M) p Fp 1039 910 a(d) p Fm(\000) p Fl 1085 910 a(1) p Fr 1107 924 a(\() p Fq(') p Fp 1158 931 a(i) p Fr 1172 924 a(\() p Fq(\015) p Fr 1219 924 a(\)\)) 1790 890 y(\(A.4\)) p Fd 0 1020 a(and) p Fn 473 1116 a(M) p Fp 517 1098 a(d) p Fm(\000) p Fl(1) p Fr 585 1116 a(\() p Fq(\015) p Fo 632 1116 a(n) p Fr 663 1103 a(^) p Fq 657 1116 a(@) p Fr 685 1116 a(\003) p Fp 719 1123 a(d) p Fr 739 1116 a(\() p Fq(L) p Fr(\)\)) p 473 1139 357 2 v Fn 562 1184 a(M) p Fp 606 1170 a(d) p Fm(\000) p Fl(1) p Fr 674 1184 a(\() p Fq(\015) p Fr 721 1184 a(\)) p Fo 848 1150 a(\025) p Fn 906 1116 a(M) p Fp 950 1098 a(d) p Fm(\000) p Fl(1) p Fr 1018 1116 a(\() p Fq(') p Fp 1069 1123 a(i) p Fr 1083 1116 a(\() p Fq(\015) p Fr 1130 1116 a(\)) p Fo(n) p Fr 1180 1103 a(^) p Fq 1174 1116 a(@) p Fr 1202 1116 a(\003) p Fp 1236 1123 a(d) p Fr 1257 1116 a(\() p Fq(L) p Fr(\)\)) p 906 1139 441 2 v Fn 995 1184 a(M) p Fp 1039 1170 a(d) p Fm(\000) p Fl 1085 1170 a(1) p Fr 1107 1184 a(\() p Fq(') p Fp 1158 1191 a(i) p Fr 1172 1184 a(\() p Fq(\015) p Fr 1219 1184 a(\)\)) 1790 1150 y(\(A.5\)) p Fd 0 1280 a(hold.) p Fr 73 1406 a(See) p 159 1406 a(Section) p 329 1406 a(3) p 369 1406 a(of) p 424 1406 a([S,02]) p 556 1406 a(for) p 630 1406 a(the) p 713 1406 a(pro) q(of) p 840 1406 a(of) p 895 1406 a(\(A.3\)) p 1023 1406 a(and) p 1117 1406 a(\(A.4\).) p 1265 1406 a(T) l(o) p 1336 1406 a(obtain) p 1487 1406 a(\(A.5\),) p 1629 1406 a(w) o(e) p 1700 1406 a(ha) o(v) o(e) p 1811 1406 a(only) 0 1467 y(to) p 60 1467 a(replace) p Fq 225 1467 a(@) p Fr 270 1467 a(with) 387 1453 y(^) p Fq 381 1467 a(@) p Fr 425 1467 a(in) p 482 1467 a(Section) p 653 1467 a(3) p 694 1467 a(of) p 749 1467 a([S,02].) p Fg 73 1564 a(Corollary) p 323 1564 a(A.2.) p Fd 445 1564 a(Supp) n(ose) p 631 1564 a(that) p Fq 730 1564 a(d) p Fr 769 1564 a(=) p 821 1564 a(3) p Fd 863 1564 a(and) p Fq 958 1564 a(\015) p Fo 1000 1564 a(2) p 1047 1564 a(C) p Fr 1076 1564 a(\() p Fq(L;) p Fr 1150 1564 a(3\)) p Fd(.) p 1230 1564 a(Then,) p 1372 1564 a(it) p 1421 1564 a(holds) p 1546 1564 a(that) p Fn 631 1691 a(M) p Fl 675 1670 a(2) p Fr 697 1691 a(\() p Fq(\015) p Fo 744 1691 a(n) p Fr 775 1678 a(^) p Fq 769 1691 a(@) p Fr 798 1691 a(\003) p Fl 832 1698 a(3) p Fr 851 1691 a(\() p Fq(L) p Fr(\)\)) p Fo 955 1691 a(\025) p Fr 1013 1657 a(1) p 1013 1680 25 2 v 1013 1725 a(4) p Fn 1042 1691 a(M) p Fl 1086 1670 a(2) p Fr 1109 1691 a(\() p Fq(\015) p Fr 1156 1691 a(\)) p Fq(:) p Fr 1790 1691 a(\(A.6\)) p Fq 73 1811 a(P) p 111 1811 a(r) q(oof) p Fr 209 1811 a(.) p 258 1811 a(F) l(rom) p 391 1811 a(\(A.5\),) p 538 1811 a(w) o(e) p 614 1811 a(ha) o(v) o(e) p 730 1811 a(only) p 841 1811 a(to) p 905 1811 a(sho) o(w) p 1030 1811 a(\(A.6\)) p 1163 1811 a(for) p 1242 1811 a(all) p Fq 1313 1811 a(\015) p Fo 1362 1811 a(2) p 1416 1811 a(S) p Fr 1450 1811 a(\() p Fq(L;) p Fr 1524 1811 a(3\).) p 1615 1811 a(F) l(or) p 1706 1811 a(eac) o(h) p Fq 1820 1811 a(\015) p Fo 1869 1811 a(2) 0 1872 y(S) p Fr 34 1872 a(\() p Fq(L;) p Fr 108 1872 a(3\)) p 168 1872 a(and) p 262 1872 a(eac) o(h) p Fq 372 1872 a(i) p Fo 403 1872 a(\024) p Fr 455 1872 a(3,) p 509 1872 a(w) o(e) p 581 1872 a(set) p Fq 518 1976 a(S) p Fm 548 1983 a(\006) p Fp(i) p Fr 589 1976 a(\() p Fq(\015) p Fr 636 1976 a(\)) p 669 1976 a(=) p Fq 721 1976 a(\015) p Fo 760 1976 a(\\) p 804 1976 a(f) p Fq(x) p Fo 871 1976 a(2) p Fn 918 1976 a(R) p Fl 957 1956 a(3) p Fr 974 1976 a(;) p Fq 996 1976 a(x) p Fp 1024 1956 a(i) p Fr 1051 1976 a(=) p Fo 1103 1976 a(\006) p Fq(L) p Fr 1186 1976 a(+) p 1235 1976 a(\(1) p Fq(=) p Fr(2\)) p Fo(g) p Fq(:) p Fr 0 2081 a(Let) p Fq 90 2081 a(\025) p 138 2081 a(>) p Fr 194 2081 a(0) p 238 2081 a(b) q(e) p 307 2081 a(a) p 351 2081 a(constan) o(t) p 550 2081 a(to) p 613 2081 a(b) q(e) p 682 2081 a(sp) q(eci\014ed) p 882 2081 a(later.) p 1023 2081 a(Let) p 1114 2081 a(us) p 1179 2081 a(\014x) p Fq 1251 2081 a(\015) p Fo 1298 2081 a(2) p 1350 2081 a(S) p Fr 1384 2081 a(\() p Fq(L;) p Fr 1458 2081 a(3\).) p 1545 2081 a(If) p Fn 1597 2081 a(M) p Fl 1641 2063 a(2) p Fr 1664 2081 a(\() p Fq(S) p Fm 1713 2088 a(\000) p Fl(3) p Fr 1760 2081 a(\() p Fq(\015) p Fr 1807 2081 a(\)\)) p Fo 1863 2081 a(\025) p Fq 0 2141 a(\025) p Fn(M) p Fl 72 2123 a(2) p Fr 95 2141 a(\() p Fq(\015) p Fr 142 2141 a(\),) p 191 2141 a(then) p 302 2141 a(w) o(e) p 374 2141 a(ha) o(v) o(e) p 486 2141 a(that) p Fn 420 2250 a(M) p Fl 464 2232 a(2) p Fr 487 2250 a(\() p Fq(\015) p Fo 534 2250 a(n) p Fr 565 2237 a(^) p Fq 559 2250 a(@) p Fr 588 2250 a(\003) p Fl 622 2257 a(3) p Fr 641 2250 a(\() p Fq(L) p Fr(\)\)) p 420 2273 311 2 v Fn 509 2318 a(M) p Fl 553 2304 a(2) p Fr 576 2318 a(\() p Fq(\015) p Fr 623 2318 a(\)) 336 2436 y(=) 475 2402 y(1) p 420 2425 133 2 v Fn 420 2470 a(M) p Fl 464 2456 a(2) p Fr 487 2470 a(\() p Fq(\015) p Fr 534 2470 a(\)) p Fk 558 2381 a(\020) p Fr 588 2436 a(2) p Fn(M) p Fl 656 2415 a(2) p Fr 679 2436 a(\() p Fq(S) p Fm 728 2443 a(\000) p Fl(3) p Fr 775 2436 a(\() p Fq(\015) p Fr 822 2436 a(\)\)) p 871 2436 a(+) p Fl 947 2374 a(2) p Fk 920 2389 a(X) p Fp 928 2494 a(i) p Fl(=1) p Fk 992 2396 a(\002) p Fn 1013 2436 a(M) p Fl 1057 2415 a(2) p Fr 1080 2436 a(\() p Fq(S) p Fm 1129 2443 a(\000) p Fp(i) p Fr 1170 2436 a(\() p Fq(\015) p Fr 1217 2436 a(\)\)) p Fo 1266 2436 a(\000) p Fn 1316 2436 a(M) p Fl 1360 2415 a(2) p Fr 1383 2436 a(\() p Fq(S) p Fl 1432 2443 a(+) p Fp(i) p Fr 1473 2436 a(\() p Fq(\015) p Fr 1520 2436 a(\)\)) p Fk 1558 2396 a(\003) 1579 2381 y(\021) p Fo 335 2553 a(\025) p Fr 415 2553 a(2) p Fq(\025:) p Fr 1790 2553 a(\(A.7\)) 0 2658 y(Hence,) p 166 2658 a(w) o(e) p 245 2658 a(assume) p 420 2658 a(that) p Fn 532 2658 a(M) p Fl 576 2639 a(2) p Fr 598 2658 a(\() p Fq(S) p Fm 647 2665 a(\000) p Fl(3) p Fr 695 2658 a(\() p Fq(\015) p Fr 742 2658 a(\)\)) p Fq 804 2658 a(<) p 867 2658 a(\025) p Fn(M) p Fl 939 2639 a(2) p Fr 962 2658 a(\() p Fq(\015) p Fr 1009 2658 a(\).) p 1082 2658 a(Since) p 1216 2658 a(w) o(e) p 1294 2658 a(can) p 1390 2658 a(see) p 1475 2658 a(b) o(y) p 1549 2658 a(the) p 1640 2658 a(de\014nition) p 1863 2658 a(of) p Fo 0 2718 a(S) p Fr 34 2718 a(\() p Fq(L;) p Fr 108 2718 a(3\)) p 168 2718 a(that) p 273 2718 a(for) p 348 2718 a(an) o(y) p Fq 440 2718 a(i) p Fo 470 2718 a(\024) p Fr 523 2718 a(3,) 510 2823 y(2) p Fq(L) p Fn(M) p Fl 611 2802 a(2) p Fr 634 2823 a(\() p Fq(S) p Fl 683 2830 a(+) p Fp(i) p Fr 724 2823 a(\() p Fq(\015) p Fr 771 2823 a(\)\)) p Fo 823 2823 a(\024) p 876 2823 a(j) p Fr(\002\() p Fq(\015) p Fr 975 2823 a(\)) p Fo(j) p 1021 2823 a(\024) p Fr 1074 2823 a(2) p Fq(L) p Fn(M) p Fl 1175 2802 a(2) p Fr 1198 2823 a(\() p Fq(S) p Fm 1247 2830 a(\000) p Fl(3) p Fr 1294 2823 a(\() p Fq(\015) p Fr 1341 2823 a(\)\)) p Fq(;) p Fr 927 2947 a(35) p 90 rotate dyy eop %%Page: 36 36 36 35 bop Fr 0 274 a(w) o(e) p 72 274 a(ha) o(v) o(e) p 184 274 a(that) p 290 274 a(for) p 364 274 a(an) o(y) p Fq 457 274 a(i) p Fo 487 274 a(\024) p Fr 540 274 a(3,) p Fn 668 379 a(M) p Fl 712 358 a(2) p Fr 735 379 a(\() p Fq(S) p Fl 784 386 a(+) p Fp(i) p Fr 826 379 a(\() p Fq(\015) p Fr 873 379 a(\)\)) p Fq 924 379 a(<) p 976 379 a(\025) p Fn(M) p Fl 1049 358 a(2) p Fr 1071 379 a(\() p Fq(\015) p Fr 1118 379 a(\)) p Fq(:) p Fr 1790 379 a(\(A.8\)) 0 484 y(W) l(e) p 84 484 a(ha) o(v) o(e) p 196 484 a(from) p 312 484 a(\(A.8\)) p 440 484 a(that) p Fn 371 600 a(M) p Fl 415 582 a(2) p Fr 438 600 a(\() p Fq(\015) p Fo 485 600 a(n) p Fr 516 587 a(^) p Fq 510 600 a(@) p Fr 538 600 a(\003) p Fl 572 607 a(3) p Fr 591 600 a(\() p Fq(L) p Fr(\)\)) p 371 622 311 2 v Fn 460 668 a(M) p Fl 504 654 a(2) p Fr 527 668 a(\() p Fq(\015) p Fr 574 668 a(\)) p Fo 728 634 a(\025) p Fr 867 600 a(1) p 813 622 133 2 v Fn 813 668 a(M) p Fl 857 654 a(2) p Fr 880 668 a(\() p Fq(\015) p Fr 927 668 a(\)) p Fk 951 579 a(\020) p Fn 986 600 a(M) p Fl 1030 582 a(2) p Fr 1052 600 a(\() p Fq(\015) p Fr 1099 600 a(\)) p 986 622 V 1040 668 a(2) p Fo 1134 634 a(\000) p Fl 1211 572 a(2) p Fk 1184 587 a(X) p Fp 1192 692 a(i) p Fl(=1) p Fn 1265 634 a(M) p Fl 1309 613 a(2) p Fr 1331 634 a(\() p Fq(S) p Fl 1380 641 a(+) p Fp(i) p Fr 1422 634 a(\() p Fq(\015) p Fr 1469 634 a(\)\)) p Fk 1507 579 a(\021) p Fo 728 750 a(\025) p Fr 808 750 a(\(1) p Fo 863 750 a(\000) p Fr 913 750 a(4) p Fq(\025) p Fr(\)) p Fq(=) p Fr(2) p Fq(:) p Fr 1790 750 a(\(A.9\)) 0 855 y(Therefore,) p 234 855 a(from) p 350 855 a(\(A.7\),) p 492 855 a(\(A.9\)) p 620 855 a(and) p Fq 715 855 a(\025) p Fr 758 855 a(=) p 809 855 a(1) p Fq(=) p Fr(8,) p 912 855 a(w) o(e) p 984 855 a(obtained) p 1185 855 a(\(A.6\).) p Fg 73 953 a(Corollary) p 323 953 a(A.3.) p Fd 445 953 a(Supp) n(ose) p 631 953 a(that) p Fq 730 953 a(d) p Fr 769 953 a(=) p 821 953 a(2) p Fd 863 953 a(and) p Fq 958 953 a(\015) p Fo 1000 953 a(2) p 1047 953 a(C) p Fr 1076 953 a(\() p Fq(L;) p Fr 1150 953 a(2\)) p Fd(.) p 1230 953 a(If) p Fn 704 1054 a(M) p Fl 748 1036 a(1) p Fr 771 1054 a(\() p Fq(\015) p Fo 818 1054 a(n) p Fq(@) p Fr 872 1054 a(\003) p Fl 906 1061 a(2) p Fr 925 1054 a(\() p Fq(L) p Fr(\)\)) p 704 1076 311 2 v Fn 793 1122 a(M) p Fl 837 1107 a(1) p Fr 860 1122 a(\() p Fq(\015) p Fr 907 1122 a(\)) p Fq 1034 1087 a(<) p Fr 1091 1054 a(1) p 1091 1076 25 2 v 1091 1122 a(4) 1765 1087 y(\(A.10\)) p Fd 0 1217 a(holds,) p 139 1217 a(then) p 248 1217 a(we) p 320 1217 a(have) p 432 1217 a(that) p Fn 404 1322 a(M) p Fl 448 1302 a(1) p Fr 470 1322 a(\() p Fq(\015) p Fr 517 1322 a(\)) p Fo 550 1322 a(\025) p Fr 603 1322 a(8) p Fq(L) p Fd 760 1322 a(and) p Fn 937 1322 a(M) p Fl 981 1302 a(1) p Fr 1004 1322 a(\() p Fq(\015) p Fo 1062 1322 a(\\) p Fq 1106 1322 a(@) p Fr 1135 1322 a(\003) p Fl 1169 1329 a(2) p Fr 1188 1322 a(\() p Fq(L) p Fr(\)\)) p Fo 1292 1322 a(\025) p Fr 1344 1322 a(6) p Fq(L;) p Fr 1765 1322 a(\(A.11\)) p Fd 0 1427 a(and) p 95 1427 a(that) p Fo 710 1532 a(j) p Fr(\002\() p Fq(\015) p Fr 809 1532 a(\)) p Fo(j) p 855 1532 a(\025) p Fr 908 1532 a(3\(4) p Fq(L) p Fl 1008 1512 a(2) p Fr 1028 1532 a(\)) p Fq(=) p Fr(4) p Fq(:) p Fr 1765 1532 a(\(A.12\)) p Fq 73 1637 a(P) p 111 1637 a(r) q(oof) p Fr 209 1637 a(.) p 248 1637 a(Let) p 336 1637 a(us) p 400 1637 a(\014x) p Fq 469 1637 a(\015) p Fo 512 1637 a(2) p 561 1637 a(C) p Fr 590 1637 a(\() p Fq(L;) p Fr 664 1637 a(2\).) p 744 1637 a(Let) p Fq 832 1637 a(\015) p Fm 860 1619 a(0) p Fr 887 1637 a(=) p Fq 940 1637 a(') p Fl 972 1644 a(2) p Fo 1003 1637 a(\016) p Fq 1040 1637 a(') p Fl 1072 1644 a(1) p Fr 1091 1637 a(\() p Fq(\015) p Fr 1138 1637 a(\).) p 1194 1637 a(Assume) p 1376 1637 a(that) p Fn 1482 1637 a(M) p Fl 1526 1619 a(1) p Fr 1549 1637 a(\() p Fq(\015) p Fr 1596 1637 a(\)) p Fq 1630 1637 a(<) p Fr 1683 1637 a(8) p Fq(L) p Fr(.) p 1778 1637 a(Then,) 0 1697 y(w) o(e) p 72 1697 a(ha) o(v) o(e) p 184 1697 a(from) p 299 1697 a(\(A.3\)) p 428 1697 a(that) p Fn 534 1697 a(M) p Fl 578 1679 a(1) p Fr 601 1697 a(\() p Fq(\015) p Fm 648 1679 a(0) p Fr 659 1697 a(\)) p Fq 692 1697 a(<) p Fr 744 1697 a(8) p Fq(L) p Fr(.) p 837 1697 a(By) p 913 1697 a(this) p 1008 1697 a(and) p 1103 1697 a(the) p 1187 1697 a(de\014nition) p 1404 1697 a(of) p Fq 1459 1697 a(\015) p Fm 1487 1679 a(0) p Fr 1499 1697 a(,) p 1529 1697 a(w) o(e) p 1601 1697 a(can) p 1690 1697 a(see) p 1769 1697 a(that) p Fq 538 1802 a(S) p Fl 568 1809 a(+1) p Fr 615 1802 a(\() p Fq(\015) p Fm 662 1782 a(0) p Fr 674 1802 a(\)) p 707 1802 a(=) p Fo 759 1802 a(;) p Fr 881 1802 a(or) p Fq 1022 1802 a(S) p Fl 1052 1809 a(+2) p Fr 1099 1802 a(\() p Fq(\015) p Fm 1146 1782 a(0) p Fr 1158 1802 a(\)) p 1191 1802 a(=) p Fo 1242 1802 a(;) p Fq(;) p Fr 1765 1802 a(\(A.13\)) 0 1907 y(whic) o(h) p 140 1907 a(implies) p 305 1907 a(that) p Fn 585 2012 a(M) p Fl 629 1992 a(1) p Fr 652 2012 a(\() p Fq(\015) p Fm 699 1992 a(0) p Fo 711 2012 a(n) p Fq(@) p Fr 765 2012 a(\003) p Fl 799 2019 a(2) p Fr 818 2012 a(\() p Fq(L) p Fr(\)\)) p Fk 908 1972 a(\016) p Fn 936 2012 a(M) p Fl 981 1992 a(1) p Fr 1003 2012 a(\() p Fq(\015) p Fm 1050 1992 a(0) p Fr 1062 2012 a(\)) p Fo 1095 2012 a(\025) p Fr 1147 2012 a(1) p Fq(=) p Fr(4) p Fq(:) p Fr 1765 2012 a(\(A.14\)) 0 2117 y(F) l(rom) p 128 2117 a(this) p 223 2117 a(and) p 318 2117 a(\(A.4\),) p 460 2117 a(w) o(e) p 532 2117 a(ha) o(v) o(e) p 644 2117 a(that) p Fn 597 2222 a(M) p Fl 641 2202 a(1) p Fr 664 2222 a(\() p Fq(\015) p Fo 711 2222 a(n) p Fq(@) p Fr 765 2222 a(\003) p Fl 799 2229 a(2) p Fr 818 2222 a(\() p Fq(L) p Fr(\)\)) p Fk 908 2182 a(\016) p Fn 936 2222 a(M) p Fl 981 2202 a(1) p Fr 1003 2222 a(\() p Fq(\015) p Fr 1050 2222 a(\)) p Fo 1083 2222 a(\025) p Fr 1136 2222 a(1) p Fq(=) p Fr(4) p Fq(;) p Fr 1765 2222 a(\(A.15\)) 0 2327 y(whic) o(h) p 140 2327 a(con) o(tradicts) p 390 2327 a(\(A.10\).) p 563 2327 a(Th) o(us,) p 700 2327 a(w) o(e) p 771 2327 a(obtained) p 972 2327 a(the) p 1056 2327 a(\014rst) p 1156 2327 a(inequalit) o(y) p 1383 2327 a(in) p 1440 2327 a(\(A.11\).) p 1612 2327 a(Since) p Fn 381 2432 a(M) p Fl 425 2412 a(1) p Fr 448 2432 a(\() p Fq(\015) p Fo 495 2432 a(n) p Fq(@) p Fr 549 2432 a(\003) p Fl 583 2439 a(2) p Fr 602 2432 a(\() p Fq(L) p Fr(\)\)) p Fk 692 2392 a(\016) p Fn 721 2432 a(M) p Fl 765 2412 a(1) p Fr 787 2432 a(\() p Fq(\015) p Fr 834 2432 a(\)) p Fo 867 2432 a(\025) p Fr 920 2432 a(1) p Fo 955 2432 a(\000) p Fn 1005 2432 a(M) p Fl 1049 2412 a(1) p Fr 1072 2432 a(\() p Fq(\015) p Fo 1130 2432 a(\\) p Fq 1174 2432 a(@) p Fr 1203 2432 a(\003) p Fl 1237 2439 a(2) p Fr 1256 2432 a(\() p Fq(L) p Fr(\)\)) p Fk 1346 2392 a(\016) p Fn 1375 2432 a(M) p Fl 1419 2412 a(1) p Fr 1442 2432 a(\() p Fq(\015) p Fr 1489 2432 a(\)) p Fq(;) p Fr 0 2537 a(w) o(e) p 72 2537 a(can) p 161 2537 a(see) p 240 2537 a(that) p 346 2537 a(the) p 430 2537 a(second) p 587 2537 a(inequalit) o(y) p 813 2537 a(in) p 870 2537 a(\(A.11\)) p 1023 2537 a(is) p 1072 2537 a(also) p 1170 2537 a(true.) 73 2597 y(W) l(e) p 159 2597 a(will) p 254 2597 a(sho) o(w) p 377 2597 a(\(A.12\).) p 556 2597 a(Assume) p 739 2597 a(that) p Fo 847 2597 a(j) p Fr(\002\() p Fq(\015) p Fr 946 2597 a(\)) p Fo(j) p Fq 996 2597 a(<) p Fr 1051 2597 a(3\(4) p Fq(L) p Fl 1151 2579 a(2) p Fr 1172 2597 a(\)) p Fq(=) p Fr(4.) p 1282 2597 a(Then,) p 1426 2597 a(w) o(e) p 1500 2597 a(can) p 1591 2597 a(see) p 1672 2597 a(from) p 1790 2597 a(\(A.2\)) 0 2657 y(that) p Fo 114 2657 a(j) p Fr(\002\() p Fq(\015) p Fm 213 2639 a(0) p Fr 224 2657 a(\)) p Fo(j) p Fq 284 2657 a(<) p Fr 349 2657 a(3\(4) p Fq(L) p Fl 449 2639 a(2) p Fr 470 2657 a(\)) p Fq(=) p Fr(4,) p 577 2657 a(whic) o(h) p 725 2657 a(implies) p 898 2657 a(that) p Fn 1012 2657 a(M) p Fl 1056 2639 a(1) p Fr 1079 2657 a(\() p Fq(\015) p Fm 1126 2639 a(0) p Fo 1137 2657 a(n) p Fq(@) p Fr 1191 2657 a(\003) p Fl 1225 2664 a(2) p Fr 1244 2657 a(\() p Fq(L) p Fr(\)\)) p Fo 1362 2657 a(\025) p Fr 1428 2657 a(2) p Fq(L) p Fr(.) p 1544 2657 a(By) p 1629 2657 a(this) p 1732 2657 a(and) p 1834 2657 a(the) 0 2718 y(de\014nition) p 217 2718 a(of) p Fo 272 2718 a(S) p Fr 306 2718 a(\() p Fq(L;) p Fr 380 2718 a(2\),) p 453 2718 a(w) o(e) p 525 2718 a(ha) o(v) o(e) p 638 2718 a(that) p Fn 524 2823 a(M) p Fl 568 2802 a(1) p Fr 591 2823 a(\() p Fq(\015) p Fm 638 2802 a(0) p Fo 650 2823 a(n) p Fq(@) p Fr 704 2823 a(\003) p Fl 738 2830 a(2) p Fr 757 2823 a(\() p Fq(L) p Fr(\)\)) p Fk 847 2782 a(\016) p Fn 875 2823 a(M) p Fl 919 2802 a(1) p Fr 942 2823 a(\() p Fq(\015) p Fm 989 2802 a(0) p Fr 1001 2823 a(\)) p Fo 1034 2823 a(\025) p Fr 1086 2823 a(2) p Fq(L=) p Fr(8) p Fq(L) p Fr 1240 2823 a(=) p 1291 2823 a(1) p Fq(=) p Fr(4) p Fq(;) p Fr 927 2947 a(36) p 90 rotate dyy eop %%Page: 37 37 37 36 bop Fr 0 274 a(whic) o(h) p 140 274 a(together) p 332 274 a(with) p 443 274 a(\(A.4\)) p 572 274 a(con) o(tradicts) p 823 274 a(\(A.10\).) p 995 274 a(Th) o(us,) p 1132 274 a(w) o(e) p 1204 274 a(obtained) p 1404 274 a(\(A.12\).) p Fg 0 380 a(Added) p 178 380 a(in) p 240 380 a(pro) r(of.) p Fr 406 380 a(Let) p Fq 491 380 a(d) p Fr 530 380 a(=) p 582 380 a(3.) p 641 380 a(W) l(e) p 723 380 a(de\014ne) p 861 380 a(the) p 943 380 a(surface) p 1105 380 a(tension) p 1271 380 a(in) p 1326 380 a(\(0) p Fq(;) p Fr 1391 380 a(0) p Fq(;) p Fr 1437 380 a(1\)) p 1495 380 a(direction) p Fq 1696 380 a(\034) p Fp 1717 387 a(\014) p Fr 1755 380 a(b) o(y) p 1821 380 a(\(see) 0 440 y([MMR,92) o(]\)) p Fq 518 574 a(\034) p Fp 539 581 a(\014) p Fr 577 574 a(=) p Fo 628 574 a(\000) p Fr 689 574 a(lim) p Fp 675 605 a(L) p Fm(!1) p Fr 844 541 a(1) p 783 563 146 2 v Fq 783 609 a(\014) p Fr 814 609 a(\(2) p Fq(L) p Fr(\)) p Fl 909 594 a(2) p Fr 942 574 a(log) 1018 541 y(Z\(\003) p Fl 1101 548 a(3) p Fr 1121 541 a(\() p Fq(L) p Fr(\)) p Fq(;) p 1214 541 a(!) p Fl 1244 548 a(0) p Fr 1264 541 a(\)) p 1018 563 265 2 v 1024 609 a(Z\(\003) p Fl 1107 616 a(3) p Fr 1127 609 a(\() p Fq(L) p Fr(\)) p Fq(;) p Fr 1220 609 a(+\)) p Fq 1288 574 a(:) p Fr 1765 574 a(\(A.16\)) 0 709 y(Here,) p Fq 129 709 a(!) p Fl 159 716 a(0) p Fr 195 709 a(is) p 244 709 a(the) p 328 709 a(b) q(oundary) p 548 709 a(condition) p 762 709 a(de\014ned) p 930 709 a(in) p 987 709 a(\(1.15\).) p Fg 73 808 a(Theorem) p 307 808 a(A.4.) p Fd 428 808 a(L) n(et) p Fq 509 808 a(d) p Fr 548 808 a(=) p 600 808 a(3) p Fd(.) p 661 808 a(Consider) p 866 808 a(a) p 906 808 a(sto) n(chastic) p 1125 808 a(Ising) p 1243 808 a(mo) n(del) p 1380 808 a(on) p 1447 808 a(the) p 1525 808 a(squar) n(e) p Fr 1674 808 a(\003) p Fl 1708 815 a(3) p Fr 1728 808 a(\() p Fq(L) p Fr(\)) p Fd 1814 808 a(with) 0 869 y(the) p 82 869 a(fr) n(e) n(e) p 175 869 a(b) n(oundary) p 386 869 a(c) n(ondition.) p 622 869 a(Then,) p 765 869 a(ther) n(e) p 887 869 a(exists) p Fq 1021 869 a(\014) p Fl 1049 876 a(0) p Fq 1084 869 a(>) p Fr 1137 869 a(0) p Fd 1180 869 a(such) p 1292 869 a(that) p 1392 869 a(for) p 1471 869 a(any) p Fq 1565 869 a(\014) p Fo 1611 869 a(\025) p Fq 1665 869 a(\014) p Fl 1693 876 a(0) p Fd 1731 869 a(and) p 1826 869 a(any) p Fq 0 929 a(L) p Fo 47 929 a(2) p Fn 94 929 a(N) p Fr 376 1036 a(gap) q(\(\003) p Fl 505 1043 a(3) p Fr 525 1036 a(\() p Fq(L) p Fr(\)) p Fq(;) p 618 1036 a(\036) p Fr(\)) p Fo 679 1036 a(\025) p Fq 732 1036 a(B) p Fr 780 1036 a(exp) p Fk 854 995 a(\000) p Fo 877 1036 a(\000) p Fr(4) p Fq(\014) s(\034) p Fp 992 1043 a(\014) p Fq 1015 1036 a(L) p Fl 1048 1015 a(2) p Fo 1079 1036 a(\000) p Fq 1129 1036 a(\014) s(C) t(L) p Fj 1237 1002 a(5) p 1236 1008 16 2 v 1236 1028 a(3) p Fr 1258 1036 a(\(log) p Fq 1348 1036 a(L) p Fr(\)) p Fl 1400 1015 a(2) p Fk 1420 995 a(\001) p Fr 1765 1036 a(\(A.17\)) p Fd 0 1143 a(holds,) p 139 1143 a(wher) n(e) p Fq 277 1143 a(B) p Fr 330 1143 a(=) p Fq 382 1143 a(B) p Fr 422 1143 a(\() p Fq(c) p Fp 462 1150 a(m) p Fq 495 1143 a(;) p 517 1143 a(c) p Fp 538 1150 a(M) p Fr 577 1143 a(\)) p Fq 610 1143 a(>) p Fr 662 1143 a(0) p Fd 704 1143 a(and) p Fq 798 1143 a(C) p Fr 851 1143 a(=) p Fq 903 1143 a(C) p Fr 942 1143 a(\() p Fq(\014) p Fr 992 1143 a(\)) p Fq 1023 1143 a(>) p Fr 1075 1143 a(0) p Fd(.) p Fr 73 1242 a(F) l(rom) p 201 1242 a(the) p 284 1242 a(pro) q(of) p 411 1242 a(of) p 466 1242 a(Prop) q(osition) p 728 1242 a(2.2,) p 820 1242 a(w) o(e) p 891 1242 a(can) p 980 1242 a(see) p 1058 1242 a(under) p 1196 1242 a(the) p 1279 1242 a(same) p 1401 1242 a(h) o(yp) q(othesis) p 1641 1242 a(as) p 1700 1242 a(in) p 1757 1242 a(Prop) q(o-) 0 1302 y(sition) p 135 1302 a(2.2) p 216 1302 a(that) p 323 1302 a(for) p 400 1302 a(an) o(y) p Fq 494 1302 a(") p 534 1302 a(>) p Fr 589 1302 a(0) p 631 1302 a(and) p 728 1302 a(an) o(y) p Fq 822 1302 a(\024) p 868 1302 a(>) p Fr 923 1302 a(0) p 965 1302 a(there) p 1092 1302 a(exists) p Fq 1228 1302 a(K) p Fl 1269 1309 a(6) p Fr 1307 1302 a(=) p Fq 1362 1302 a(K) p Fl 1403 1309 a(6) p Fr 1423 1302 a(\() p Fq(\014) s(;) p 1495 1302 a(";) p 1540 1302 a(\024) p Fr(\)) p Fq 1603 1302 a(>) p Fr 1658 1302 a(0) p 1701 1302 a(suc) o(h) p 1813 1302 a(that) 0 1362 y(for) p 75 1362 a(su\016cien) o(tly) p 319 1362 a(large) p Fq 438 1362 a(L) p Fo 485 1362 a(2) p Fn 532 1362 a(N) p Fr 584 1362 a(and) p 679 1362 a(an) o(y) p Fq 771 1362 a(x) p Fo 813 1362 a(2) p Fr 860 1362 a(\003\() p Fo(\000) p Fq(L;) p Fo 1007 1362 a(\000) p Fq(L) p Fr 1089 1362 a(+) p Fq 1138 1362 a(M) p Fo 1202 1362 a(\000) p Fr 1252 1362 a(3) p Fq(l) p Fr 1292 1362 a(\),) p Fq 264 1481 a(\026) p Fl 293 1457 a(+) p Fp(;) p Fl 329 1448 a(^) p Ff 330 1457 a(J) p Fe 351 1463 a(\016) p Fl 293 1496 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 508 1496 a(\)) p Fr 525 1481 a(\() p Fq(\033) p Fr 574 1481 a(\() p Fq(x) p Fr(\)) p 653 1481 a(=) p 705 1481 a(+1\)) p Fo 797 1481 a(\000) p Fq 847 1481 a(\026) p Fp 876 1457 a(\021) q(;) p Fl 904 1448 a(^) p Ff 905 1457 a(J) p Fe 925 1463 a(\016) p Fl 876 1496 a(\003\() p Fm(\000) p Fp(L;) p Fm(\000) p Fp(L) p Fl(+) p Fp(M) p Fl 1091 1496 a(\)) p Fr 1108 1481 a(\() p Fq(\033) p Fr 1157 1481 a(\() p Fq(x) p Fr(\)) p 1236 1481 a(=) p 1288 1481 a(+1\)) p Fo 1383 1481 a(\024) p Fq 1435 1481 a("L) p Fm 1491 1460 a(\000) p Fp(\024) p Fq 1541 1481 a(:) p Fr 1765 1481 a(\(A.18\)) 0 1593 y(F) l(rom) p 128 1593 a(this) p 223 1593 a(and) p 317 1593 a(the) p 401 1593 a(same) p 523 1593 a(argumen) o(t) p 741 1593 a(as) p 800 1593 a(in) p 857 1593 a(Section) p 1027 1593 a(4) p 1068 1593 a(and) p 1162 1593 a(App) q(endix) p 1386 1593 a(in) p 1442 1593 a([Ma,94]) p 1617 1593 a(\(or) p 1695 1593 a(App) q(endix) 0 1653 y(in) p 57 1653 a([CGMS,96]\),) p 340 1653 a(w) o(e) p 412 1653 a(can) p 502 1653 a(obtain) p 653 1653 a(Theorem) p 859 1653 a(A.4.) p Fg 0 1742 a(Ac) n(kno) n (wledgmen) n(t.) p Fr 467 1742 a(The) p 572 1742 a(author) p 733 1742 a(w) o(ould) p 879 1742 a(lik) o(e) p 973 1742 a(to) p 1037 1742 a(thank) p 1181 1742 a(Professor) p 1396 1742 a(Y.) p 1467 1742 a(Higuc) o(hi) p 1650 1742 a(for) p 1728 1742 a(his) p 1809 1742 a(kind) 0 1803 y(helping) p 171 1803 a(and) p 266 1803 a(guidance) p 469 1803 a(in) p 526 1803 a(this) p 621 1803 a(w) o(ork.) p Fg 0 1884 a(Ac) n(kno) n(wledgmen) n(t) p Fr(.) p 466 1884 a(The) p 570 1884 a(author) p 732 1884 a(w) o(ould) p 878 1884 a(lik) o(e) p 972 1884 a(to) p 1036 1884 a(thank) p 1180 1884 a(Professor) p 1395 1884 a(Y.) p 1466 1884 a(Higuc) o(hi) p 1649 1884 a(for) p 1728 1884 a(his) p 1809 1884 a(kind) 0 1944 y(helping) p 171 1944 a(and) p 266 1944 a(guidance) p 469 1944 a(in) p 526 1944 a(this) p 621 1944 a(w) o(ork.) p Fs 0 2110 a(References) p Fr 0 2219 a([CGMS,96]) p 259 2219 a(Cesi,) p 381 2219 a(F.,) p 460 2219 a(Guadagni,) p 698 2219 a(G.,) p 783 2219 a(Martinelli,) p 1026 2219 a(F.) p 1090 2219 a(and) p 1187 2219 a(Sc) o(honmann,) p 1465 2219 a(R.) p 1533 2219 a(H.:) p 1623 2219 a(On) p 1706 2219 a(the) p 1792 2219 a(Tw) o(o-) 100 2279 y(Dimensional) p 374 2279 a(Sto) q(c) o(hastic) p 603 2279 a(Ising) p 716 2279 a(Mo) q(del) p 860 2279 a(in) p 912 2279 a(the) p 991 2279 a(Phase) p 1128 2279 a(Co) q(existence) p 1392 2279 a(Region) p 1550 2279 a(Near) p 1663 2279 a(the) p 1742 2279 a(Critical) 100 2340 y(P) o(oin) o(t.) p 245 2340 a(J.) p 299 2340 a(Stat.) p 419 2340 a(Ph) o(ys.,) p Fg 566 2340 a(85) p Fr(,) p 652 2340 a(Nos.1/2,) p 848 2340 a(55-102) p 1003 2340 a(\(1996\).) 0 2440 y([D,72]) p 151 2440 a(Dobrushin,) p 419 2440 a(R.) p 497 2440 a(L.:) p 602 2440 a(Gibbs) p 757 2440 a(state) p 889 2440 a(describing) p 1133 2440 a(co) q(existence) p 1400 2440 a(of) p 1469 2440 a(phases) p 1637 2440 a(for) p 1724 2440 a(a) p 1778 2440 a(three-) 100 2501 y(dimensional) p 369 2501 a(Ising) p 487 2501 a(mo) q(del.) p 645 2501 a(Theory) p 815 2501 a(Prob.) p 948 2501 a(Appl.,) p Fg 1096 2501 a(17) p Fr(,) p 1182 2501 a(No.4,) p 1310 2501 a(582-600) p 1489 2501 a(\(1972\).) 0 2601 y([D,73]) p 151 2601 a(Dobrushin,) p 410 2601 a(R.) p 482 2601 a(L.:) p 574 2601 a(In) o(v) o(estigation) p 870 2601 a(of) p 932 2601 a(Gibbsian) p 1145 2601 a(states) p 1289 2601 a(for) p 1370 2601 a(three-dimensional) p 1769 2601 a(lattice) 100 2662 y(systems.) p 295 2662 a(Theory) p 464 2662 a(Prob.) p 598 2662 a(Appl.,) p Fg 745 2662 a(18) p Fr(,) p 831 2662 a(No.2,) p 960 2662 a(253-271) p 1139 2662 a(\(1973\).) 0 2762 y([KP) l(,86]) p 181 2762 a(Kotec) o(k) q(\023) p 331 2762 a(y,) p 395 2762 a(R.) p 469 2762 a(and) p 571 2762 a(Preiss,) p 737 2762 a(D.:) p 838 2762 a(Cluster) p 1017 2762 a(expansion) p 1251 2762 a(for) p 1333 2762 a(Abstract) p 1543 2762 a(p) q(olymer) p 1741 2762 a(mo) q(dels.) 100 2823 y(Comm) o(un.) p 324 2823 a(Math.) p 469 2823 a(Ph) o(ys.,) p Fg 616 2823 a(103) p Fr(,) p 730 2823 a(491-498) p 909 2823 a(\(1986\).) 927 2947 y(37) p 90 rotate dyy eop %%Page: 38 38 38 37 bop Fr 0 274 a([L,85]) p 144 274 a(Liggett,) p 336 274 a(T.M.:) p 494 274 a(In) o(teracting) p 752 274 a(P) o(article) p 940 274 a(Systems.) p 1151 274 a(Springer-V) l (erlag,) p 1521 274 a(Berlin) p 1675 274 a(Heidelb) q(erg) 100 334 y(T) l(oky) o(o) p 247 334 a(\(1985\).) 0 436 y([Ma,94]) p 183 436 a(Martinelli,) p 422 436 a(F.:) p 502 436 a(On) p 582 436 a(the) p 665 436 a(t) o(w) o(o) p 756 436 a(dimensional) p 1023 436 a(dynamical) p 1257 436 a(Ising) p 1374 436 a(mo) q(del) p 1518 436 a(in) p 1574 436 a(the) p 1656 436 a(phase) p 1791 436 a(co) q(ex-) 100 496 y(istence) p 260 496 a(region.) p 420 496 a(J.) p 475 496 a(Stat.) p 594 496 a(Ph) o(ys.,) p Fg 742 496 a(76) p Fr(,) p 827 496 a(Mos.5/6,) p 1032 496 a(1179-1246) p 1260 496 a(\(1994\).) 0 598 y([Ma,99]) p 183 598 a(Martinelli,) p 427 598 a(F.:) p 514 598 a(Lectures) p 713 598 a(on) p 784 598 a(Glaub) q(er) p 976 598 a(dynamics) p 1194 598 a(for) p 1272 598 a(discrete) p 1454 598 a(spin) p 1561 598 a(mo) q(dels.) p 1742 598 a(Lecture) 100 658 y(Notes) p 237 658 a(in) p 294 658 a(Math.,) p 453 658 a(1717,) p 580 658 a(93-191,) p 748 658 a(Springer,) p 957 658 a(Berlin) p 1102 658 a(\(1999\).) 0 760 y([Sc) o(h,94]) p 188 760 a(Sc) o(honmann,) p 466 760 a(R.) p 534 760 a(H.:) p 623 760 a(Slo) o(w) p 740 760 a(droplet-driv) o(en) p 1059 760 a(relaxation) p 1290 760 a(of) p 1348 760 a(sto) q(c) o(hastic) p 1575 760 a(Ising) p 1695 760 a(mo) q(dels) p 1862 760 a(in) 100 820 y(the) p 182 820 a(vicinit) o(y) p 354 820 a(of) p 406 820 a(the) p 488 820 a(phase) p 621 820 a(co) q(existence) p 873 820 a(region.) p 1030 820 a(Comm) o(un.) p 1251 820 a(Math.) p 1393 820 a(Ph) o(ys.,) p Fg 1539 820 a(161) p Fr(,) p 1650 820 a(1-49) p 1753 820 a(\(1994\).) 0 922 y([S,01]) p 141 922 a(Sugimine,) p 373 922 a(N.:) p 470 922 a(Extension) p 703 922 a(of) p 764 922 a(Thomas') p 970 922 a(result) p 1112 922 a(upp) q(er) p 1257 922 a(b) q(ound) p 1413 922 a(on) p 1487 922 a(the) p 1576 922 a(sp) q(ectral) p 1765 922 a(gap) p 1863 922 a(of) 100 982 y(d\() p Fo(\025) p Fr 199 982 a(3\)-dimensional) p 527 982 a(Sto) q(c) o(hastic) p 760 982 a(Ising) p 878 982 a(mo) q(dels.) 0 1083 y([Tho,89]) p 201 1083 a(Thomas,) p 400 1083 a(L.) p 459 1083 a(E.:) p 540 1083 a(Bound) p 695 1083 a(on) p 761 1083 a(the) p 843 1083 a(mass) p 961 1083 a(gap) p 1052 1083 a(for) p 1125 1083 a(\014nite) p 1248 1083 a(v) o(olume) p 1414 1083 a(sto) q(c) o(hastic) p 1638 1083 a(Ising) p 1754 1083 a(mo) q(dels) 100 1144 y(at) p 160 1144 a(lo) o(w) p 248 1144 a(temp) q(erature.) p 539 1144 a(Comm) o(un.) p 763 1144 a(Math.) p 908 1144 a(Ph) o(ys.,) p Fg 1055 1144 a(126) p Fr(,) p 1169 1144 a(1-11) p 1275 1144 a(\(1989\).) 927 2947 y(38) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0210090005337--