%!PS-Adobe-2.0 %%Creator: dvips 5.76 (MiKTeX 1.10) Copyright 1997 Radical Eye Software (www.radicaleye.com) %%Title: Diracfinal.dvi %%CreationDate: Tue Jun 20 10:28:37 2000 %%Pages: 33 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: C:\LATEXX\TEXMF\MIKTEX\BIN\DVIPS.EXE Diracfinal %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2000.06.20:1028 %%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 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /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 600 600 (C:\Mes documents/Diracfinal.dvi) @start %DVIPSBitmapFont: Fa eufm8 8 1 /Fa 1 105 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fb eufm10 12 1 /Fb 1 105 df<0003C00000C007800000C00F000000C03E000000607C00000060F80000 0063F800000077F00000007FE00000007FE00000007FC00000007FC00000007FC0000000 7FC00000007F800000007F800000007F800000007F800000007F800000007F800000007F 800100007F8003C0007F800FE0007F801FF8007F803FFE007F80FFFF807F81FFFFE07F83 FFFFE07F8FFFFFF07F9F87FFF07FBE00FFF07FF8007FF07FE0001FF07FC0001FF07F8000 1FF07F80001FF07F80001FF07F80001FF07F80001FF07F80000FF07F80000FF07F80000F F07F80000FF07F80000FF07F80000FF07F80000FF07F80000FF07F80000FF07F80000FF0 FF80000FF0FF80000FF0FF80000FF0FF80000FF0FF80000FF0FF80000FF0FF80000FF0FF 80000FF0FFC0000FF0FFC0000FE0FFE0000FE0FFF0000FE0FFF0000FE07FF8001FE07FF8 001FE03FF0001FE03FE0001FE01FC0001FC00F80001FC00F00001FC00400001FC0000000 3F800000003F800000003F000000003E000000007E000000007C000000007800000000F0 00000000E000000001C0000000038000000007000000000E000000003C00000000780000 0000F000000001E000000000C00000245878C334>104 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmmi6 6 6 /Fc 6 117 df<03FFFFFC0FFFFFFC1FFFFFFC3FFFFFF878181800E0183800C030380000 30300000303000007030000060300000E0700000E0700000E0780001C0780001C0780003 C0780003807C0007803C0007803E000F003C00060018001E167D9424>25 D<000003E000003FC000003FC0000003C0000003C0000007800000078000000780000007 8000000F0000000F0000000F0000000F00001F1E0000FF9E0001E0DE0003807E0007007C 000F003C001E003C003E003C003C0078007C0078007C0078007C007800F800F000F800F0 00F800F040F800F060F801E0C07801E0C07803E0C03807E1801C1CF3000FF87F0007E03C 001B247EA220>100 D<0038007C007C0078007000000000000000000000000000000780 1FC038E030E060F0C1E0C1E0C1E003C003C003C0078007800F000F040F061E0C1E0C1E18 1C181E700FE007800F237DA116>105 D<00F800000FF000000FF0000000F0000000F000 0001E0000001E0000001E0000001E0000003C0000003C0000003C0000003C0000007801E 0007807F000781C300078387000F060F000F0C1F000F181F000F700E001FE000001FE000 001FFC00001E7E00003C0F00003C0F80003C0781003C078180780F0300780F0300780F02 0078070600F0078C00F003F8006000F00019247CA221>107 D<003F8000FFE001E0F003 80300300700700F00700F007804007C00007FE0003FF8001FFC0003FE00003F03000F078 00F0F800E0F800E0F000C06001C0780F803FFE0007F80014177D951D>115 D<00300000780000F00000F00000F00000F00001E00001E00001E00001E00003C000FFFF 80FFFF8003C0000780000780000780000780000F00000F00000F00000F00001E00001E00 001E01001E01803C03003C06003C06003C0C001C38000FF00007C00011217D9F18>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd lasy10 12 1 /Fd 1 51 df<3FFFFFFFFFFFFF00FFFFFFFFFFFFFF80FFFFFFFFFFFFFF80FFFFFFFFFFFF FF80F000000000000780F000000000000780F000000000000780F000000000000780F000 000000000780F000000000000780F000000000000780F000000000000780F00000000000 0780F000000000000780F000000000000780F000000000000780F000000000000780F000 000000000780F000000000000780F000000000000780F000000000000780F00000000000 0780F000000000000780F000000000000780F000000000000780F000000000000780F000 000000000780F000000000000780F000000000000780F000000000000780F00000000000 0780F000000000000780F000000000000780F000000000000780F000000000000780F000 000000000780F000000000000780F000000000000780F000000000000780F00000000000 0780F000000000000780F000000000000780F000000000000780F000000000000780F000 000000000780F000000000000780F000000000000780F000000000000780F00000000000 0780F000000000000780F000000000000780F000000000000780F000000000000780FFFF FFFFFFFFFF80FFFFFFFFFFFFFF80FFFFFFFFFFFFFF80FFFFFFFFFFFFFF80393977BE4A> 50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmti12 12 56 /Fe 56 128 df<0000000001FF0000FC00000000000FFFC003FF80000000003F81F00783 C0000000007C00781F01E000000000F800F83F03E000000001F001FC3E07F000000003F0 03FC7E0FF000000007E007FC7C1FF000000007E007FCFC1FF00000000FC007F8FC1FE000 00000FC003F0F80FC00000000FC001E1F807800000001FC00001F800000000001F800001 F800000000001F800003F800000000001F800003F000000000003F800003F00000000000 3F000003F000000000003F000003F000000000003F000007F000000000003F000007E000 000000007F000007E000000000007E000007E000000000007E000007E000000000007E00 000FE000000000007E00000FC00000000000FE00000FC000000000FFFFFFFFFFFFF00000 00FFFFFFFFFFFFF0000000FFFFFFFFFFFFF000000000FC00001F800000000001FC00001F 800000000001FC00001F800000000001F800001F800000000001F800003F800000000001 F800003F000000000001F800003F000000000003F800003F000000000003F000003F0000 00000003F000003F000000000003F000007F000000000003F000007E000000000007F000 007E000000000007E000007E000000000007E000007E000000000007E00000FE00000000 0007E00000FC00000000000FE00000FC00000000000FC00000FC00000000000FC00000FC 00000000000FC00001FC00000000000FC00001F800000000001FC00001F800000000001F 800001F800000000001F800001F800000000001F800003F800000000001F800003F00000 0000003F800003F000000000003F000003F000000000003F000003F000000000003F0000 07F000000000003F000007E000000000007F000007E000000000007E000007E000000000 007E000007E000000000007E00000FE000000000007E00000FC00000000000FE00000FC0 0000000000FC00000FC00000000000FC00000FC00000000000FC00001F800000000000FC 00001F800000000001F800001F800000000001F800001F000000000001F800003F000000 000001F000003F000000000003F000003E000000000003F000007E000000001C03E03800 7E000000007F03E0FE007C00000000FF07E1FE00FC00000000FF07C1FE00F800000000FF 07C1FE01F000000000FF0F81FE01F000000000FE0F01FC03E000000000F81F01F007C000 000000701E00E00F8000000000783C00F83E00000000001FF0003FF8000000000007C000 0FE000000000004C5A83C53C>11 D<00000000007FF8000000000007FFFF00000000001F C00FC0000000003E0001E000000000FC0000F000000001F80001F000000003F00007F000 000003E00007F000000007E0000FF000000007E0000FF00000000FC0000FF00000000FC0 000FE00000001FC00003800000001F800000000000001F800000000000001F8000000000 00003F800000000000003F000000000000003F000000000000003F000000000000003F00 0000000000007F000000000000007E000000000000007E000000000000007E0000000000 00007E00000000000000FE000000000000FFFFFFFFFF000000FFFFFFFFFF000000FFFFFF FFFE00000000FC00007E00000001FC0000FE00000001F80000FC00000001F80000FC0000 0001F80000FC00000001F80001FC00000001F80001F800000003F80001F800000003F000 01F800000003F00003F800000003F00003F000000003F00003F000000007F00003F00000 0007E00007F000000007E00007E000000007E00007E000000007E00007E00000000FE000 0FE00000000FC0000FC00000000FC0000FC00000000FC0000FC00000000FC0001FC00000 001FC0001F800000001F80001F800000001F80001F800000001F80003F80E000001F8000 3F01E000003F80003F01C000003F00003F01C000003F00003F01C000003F00007F03C000 003F00007E038000007F00007E038000007E00007E078000007E00007E070000007E0000 3E070000007E00003E0E000000FE00001E1E000000FC00001F1C000000FC000007F80000 00FC000001E0000000FC00000000000001F800000000000001F800000000000001F80000 0000000001F000000000000003F000000000000003F000000000001C03E000000000007F 03E00000000000FF07E00000000000FF07C00000000000FF07C00000000000FF0F800000 000000FE0F000000000000F81F000000000000701E000000000000783C0000000000001F F000000000000007C00000000000003C5A83C537>I<0000000000FFC00003FFE0000000 000007FFF8001FFFFE00000000001FC03E007F001F80000000003E000F01F80003C00000 0000FC001F03E00001E000000001F8003F87C00003E000000001F0007F8F80000FE00000 0003F000FF9F80000FE000000003E000FFBF00001FE000000007E000FF3F00001FE00000 0007E0007E7E00001FE00000000FC0003C7E00001FC00000000FC000007E000007000000 000FC00000FC000000000000001FC00000FC000000000000001F800000FC000000000000 001F800000FC000000000000001F800001FC000000000000001F800001F8000000000000 003F800001F8000000000000003F000001F8000000000000003F000001F8000000000000 003F000003F8000000000000003F000003F0000000000000007F000003F0000000000000 007E000003F0000000000000007E000003F0000000000000FFFFFFFFFFFFFFFFFE000000 FFFFFFFFFFFFFFFFFE000000FFFFFFFFFFFFFFFFFC00000000FC000007E00000FC000000 00FC000007E00001FC00000000FC00000FE00001F800000000FC00000FC00001F8000000 01FC00000FC00001F800000001F800000FC00003F800000001F800000FC00003F0000000 01F800001FC00003F000000001F800001F800003F000000003F800001F800007F0000000 03F000001F800007E000000003F000001F800007E000000003F000003F800007E0000000 03F000003F00000FE000000007F000003F00000FC000000007E000003F00000FC0000000 07E000003F00000FC000000007E000003F00001FC000000007E000007F00001F80000000 07E000007E00001F800000000FE000007E00001F800000000FC000007E00003F80000000 0FC000007E00003F000000000FC00000FE00003F000000000FC00000FC00003F00000000 1FC00000FC00007F01C000001F800000FC00007E03C000001F800000FC00007E03800000 1F800001FC00007E038000001F800001F800007E038000003F800001F80000FE07800000 3F000001F80000FC070000003F000001F80000FC070000003F000003F80000FC0F000000 3F000003F00000FC0E0000007F000003F000007C0E0000007E000003F000007C1C000000 7E000003F000003C3C0000007E000007E000003E380000007E000007E000000FF0000000 FC000007E0000003C0000000FC000007E000000000000000FC00000FC000000000000000 FC00000FC000000000000001F800000FC000000000000001F800000F8000000000000001 F800001F8000000000000001F000001F8000000000001C03F038001F0000000000007F03 F0FE003F000000000000FF03E1FE003E000000000000FF03E1FE007E000000000000FF07 C1FE007C000000000000FF0781FE00F8000000000000FE0F81FC01F0000000000000F80F 01F003E0000000000000701E00E007C0000000000000783C00781F000000000000001FF8 003FFC0000000000000007E00007F0000000000000005B5A83C556>14 D<00F003F807FC0FFC0FFC0FFC0FFC0FFC0FFC03CC001C00180018003800300030007000 E000C001C00180038007000E001C0038007000E000C0000E1D6BC41E>39 D<00F003FC07FC07FC0FFE0FFE0FFE0FFE07FC03CC000C001C0018001800380030007000 6000E001C00180038007000E001C0038007000E000C0000F1D7A891E>44 D<7FFFFFFFFFFFFFFFFFFFFFFEFFFFFE1805789723>I<0F003FC07FC07FC0FFC0FFC0FF C0FF807F003C000A0A76891E>I<000F00001FC0003FC0007FE000FFE000FFE000FFC000 7F80007F00001E0000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000F00003FC0007FC0007FC000FFC000FFC000FFC000FF80007F00003C000013 2B76AA1E>58 D<0000000000038000000000000007800000000000000780000000000000 0FC00000000000000FC00000000000001FC00000000000001FC00000000000003FC00000 000000007FC00000000000007FC0000000000000FFC0000000000000FFC0000000000001 FFC0000000000001FFC0000000000003BFC0000000000007BFC00000000000073FC00000 0000000F3FC000000000000E3FC000000000001C3FC000000000001C3FE0000000000038 3FE00000000000381FE00000000000701FE00000000000F01FE00000000000E01FE00000 000001C01FE00000000001C01FE00000000003801FE00000000003801FE0000000000700 1FE00000000007001FE0000000000E001FE0000000001E001FE0000000001C001FE00000 000038001FE00000000038001FF00000000070001FF00000000070000FF000000000E000 0FF000000001E0000FF000000001C0000FF000000003C0000FF00000000380000FF00000 000700000FF000000007FFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000001C0000 0FF00000003C00000FF00000003800000FF00000007000000FF00000007000000FF00000 00E000000FF8000000E000000FF8000001C0000007F8000001C0000007F8000003800000 07F800000780000007F800000700000007F800000E00000007F800001E00000007F80000 1E00000007F800003C00000007F800007C00000007F80000FC00000007F80001FC000000 0FFC0007FE0000001FFC00FFFFE00007FFFFF8FFFFE00007FFFFF8FFFFE00007FFFFF03D 477BC648>65 D<0000FFFFFFFFFC00000000FFFFFFFFFF80000000FFFFFFFFFFE0000000 01FF80001FF000000000FF000007F800000001FF000003FC00000001FF000001FE000000 01FE000001FF00000001FE000000FF00000001FE000000FF80000003FE0000007F800000 03FC0000007F80000003FC0000007F80000003FC0000007F80000007FC0000007F800000 07F80000007F80000007F8000000FF80000007F8000000FF8000000FF8000000FF000000 0FF0000001FF0000000FF0000001FE0000000FF0000003FE0000001FF0000003FC000000 1FE0000007F80000001FE000000FF80000001FE000001FF00000003FE000003FE0000000 3FC000007F800000003FC00000FF000000003FC00003FC000000007FC0000FF800000000 7F8000FFC0000000007FFFFFFF00000000007FFFFFFFE000000000FF800007F800000000 FF000001FC00000000FF000000FE00000000FF0000007F00000001FF0000007F80000001 FE0000003FC0000001FE0000003FC0000001FE0000003FC0000003FE0000003FE0000003 FC0000003FE0000003FC0000003FE0000003FC0000003FE0000007FC0000003FE0000007 F80000003FE0000007F80000003FE0000007F80000003FE000000FF80000003FC000000F F00000007FC000000FF00000007FC000000FF0000000FF8000001FF0000000FF8000001F E0000001FF0000001FE0000001FE0000001FE0000003FE0000003FE0000007FC0000003F C000000FF80000003FC000001FF00000007FC000003FE00000007FC000007FC00000007F 800001FF00000000FF80000FFE000000FFFFFFFFFFF8000000FFFFFFFFFFC0000000FFFF FFFFFE0000000041447AC345>I<000000000FF8000300000000FFFF000700000007FFFF C00F0000001FF803E01F0000007FC000F81E000000FF00007C3E000003FC00003C7E0000 0FF000001EFE00001FE000000FFC00003FC0000007FC00007F00000007FC0000FE000000 03FC0001FC00000003F80003FC00000003F80007F800000001F8000FF000000001F8001F E000000001F0003FC000000001F0007FC000000001F0007F8000000001F000FF80000000 01E001FF0000000001E001FF0000000001E003FE0000000001E003FE0000000001C007FC 0000000001C007FC0000000001C00FF80000000001C00FF80000000000001FF800000000 00001FF00000000000001FF00000000000003FF00000000000003FE00000000000003FE0 0000000000003FE00000000000007FE00000000000007FC00000000000007FC000000000 00007FC00000000000007FC0000000000000FF80000000000000FF80000000000000FF80 000000000000FF80000000000000FF80000000003800FF80000000003800FF8000000000 7800FF80000000007000FF80000000007000FF8000000000F0007F8000000000E0007F80 00000001E0007F8000000001C0007F8000000003C0003F800000000380003F8000000007 80003FC00000000F00001FC00000000E00001FC00000001E00000FE00000003C00000FF0 00000078000007F0000000F0000003F8000001E0000003FC000007C0000001FE00000F80 0000007F00003E000000003FC000FC000000001FF807F00000000007FFFFC00000000001 FFFF0000000000001FF000000000404872C546>I<0000FFFFFFFFF800000000FFFFFFFF FF00000000FFFFFFFFFFC000000001FF80003FF000000000FF00000FF800000001FF0000 03FC00000001FF000000FE00000001FE0000007F00000001FE0000007F00000001FE0000 003F80000003FE0000001FC0000003FC0000001FC0000003FC0000000FE0000003FC0000 000FE0000007FC0000000FE0000007F80000000FF0000007F800000007F0000007F80000 0007F000000FF800000007F000000FF000000007F000000FF000000007F800000FF00000 0007F800001FF000000007F800001FE000000007F800001FE000000007F800001FE00000 000FF800003FE00000000FF800003FC00000000FF800003FC00000000FF000003FC00000 000FF000007FC00000000FF000007F800000001FF000007F800000001FF000007F800000 001FF00000FF800000001FE00000FF000000003FE00000FF000000003FE00000FF000000 003FE00001FF000000003FC00001FE000000007FC00001FE000000007F800001FE000000 007F800003FE00000000FF800003FC00000000FF000003FC00000000FF000003FC000000 01FE000007FC00000001FE000007F800000003FC000007F800000003F8000007F8000000 07F800000FF800000007F000000FF00000000FE000000FF00000001FE000000FF0000000 1FC000001FF00000003F8000001FE00000007F0000001FE0000000FE0000001FE0000001 FC0000003FE0000003F80000003FC0000007F00000003FC000000FE00000007FC000003F C00000007FC00000FF000000007F800003FE00000000FF80001FF8000000FFFFFFFFFFE0 000000FFFFFFFFFF00000000FFFFFFFFF80000000045447AC34A>I<0000FFFFFFFFFFFF C00000FFFFFFFFFFFFC00000FFFFFFFFFFFFC0000001FF800003FF80000000FF0000007F 80000001FF0000003F80000001FF0000001F80000001FE0000000F80000001FE0000000F 80000001FE0000000F80000003FE0000000700000003FC0000000700000003FC00000007 00000003FC0000000700000007FC0000000700000007F80000000F00000007F80000000E 00000007F80000000E0000000FF80000000E0000000FF00007000E0000000FF00007000E 0000000FF0000F000E0000001FF0000E00000000001FE0000E00000000001FE0000E0000 0000001FE0001E00000000003FE0001C00000000003FC0003C00000000003FC0007C0000 0000003FC000FC00000000007FC003F800000000007FFFFFF800000000007FFFFFF80000 0000007FFFFFF80000000000FF8003F00000000000FF0001F00000000000FF0000F00000 000000FF0000F00000000001FF0000E00000000001FE0000E00000000001FE0000E00000 000001FE0001E00000000003FE0001C00070000003FC0001C00070000003FC0001C000F0 000003FC0001C000E0000007FC00000000E0000007F800000001E0000007F800000001C0 000007F800000003C000000FF8000000038000000FF0000000078000000FF00000000700 00000FF00000000F0000001FF00000000F0000001FE00000001E0000001FE00000003E00 00001FE00000003C0000003FE00000007C0000003FC0000000FC0000003FC0000001F800 00007FC0000003F80000007FC000000FF00000007F8000003FF0000000FF800003FFE000 00FFFFFFFFFFFFE00000FFFFFFFFFFFFE00000FFFFFFFFFFFFC0000042447AC342>I<00 00FFFFFFFFFFFF800000FFFFFFFFFFFF800000FFFFFFFFFFFF80000001FF800007FF0000 0000FF000000FF00000001FF0000003F00000001FF0000003F00000001FE0000001F0000 0001FE0000001F00000001FE0000001F00000003FE0000000E00000003FC0000000E0000 0003FC0000000E00000003FC0000000E00000007FC0000000E00000007F80000001E0000 0007F80000001C00000007F80000001C0000000FF80000001C0000000FF00000001C0000 000FF00007001C0000000FF0000F001C0000001FF0000E00000000001FE0000E00000000 001FE0000E00000000001FE0001E00000000003FE0001C00000000003FC0003C00000000 003FC0003C00000000003FC0007C00000000007FC000F800000000007F8003F800000000 007FFFFFF800000000007FFFFFF80000000000FFFFFFF00000000000FF0007F000000000 00FF0001F00000000000FF0001F00000000001FF0000E00000000001FE0000E000000000 01FE0000E00000000001FE0001E00000000003FE0001C00000000003FC0001C000000000 03FC0001C00000000003FC0003C00000000007FC0003800000000007F800000000000000 07F80000000000000007F8000000000000000FF8000000000000000FF000000000000000 0FF0000000000000000FF0000000000000001FF0000000000000001FE000000000000000 1FE0000000000000001FE0000000000000003FE0000000000000003FC000000000000000 3FC0000000000000007FC0000000000000007FC0000000000000007FC000000000000000 FFC0000000000000FFFFFFE00000000000FFFFFFE00000000000FFFFFFE0000000000041 447AC340>I<000000000FF8000600000000FFFE000E00000007FFFF801E0000001FF807 E03E0000007F8001F03C000001FE0000787C000003F800003CFC00000FF000001DFC0000 1FE000001FF800003F8000000FF800007F0000000FF80001FE00000007F80003FC000000 07F00003F800000007F00007F800000003F0000FF000000003F0001FE000000003E0003F C000000003E0007FC000000003E0007F8000000003E000FF8000000003C001FF00000000 03C001FE0000000003C003FE0000000003C003FE00000000038007FC00000000038007FC 0000000003800FF80000000003800FF80000000000001FF80000000000001FF000000000 00001FF00000000000003FF00000000000003FE00000000000003FE00000000000003FE0 0000000000007FE00000000000007FC00000000000007FC00000000000007FC000000000 00007FC0000000000000FF80000000000000FF8000003FFFFFE0FF8000003FFFFFE0FF80 00003FFFFFE0FF800000001FF800FF800000001FF000FF800000001FF000FF800000001F F000FF800000001FE000FF800000001FE0007F800000003FE0007F800000003FC0007F80 0000003FC0007F800000003FC0007F800000007FC0003F800000007F80003FC00000007F 80001FC00000007F80001FC0000000FF80001FE0000000FF00000FE0000001FF000007F0 000003FF000007F8000003FF000003FC000007FE000001FE00001F3E000000FF00003E3E 0000003FC000F81E0000001FF007F01C00000007FFFFC00C00000001FFFE000000000000 3FF0000000003F4872C54B>I<0000FFFFFF803FFFFFE00000FFFFFF803FFFFFE00000FF FFFF803FFFFFE0000001FF8000007FE000000000FF0000003FC000000001FF0000007FC0 00000001FF0000007FC000000001FE0000007F8000000001FE0000007F8000000001FE00 0000FF8000000003FE000000FF8000000003FC000000FF0000000003FC000000FF000000 0003FC000001FF0000000007FC000001FF0000000007F8000001FE0000000007F8000001 FE0000000007F8000003FE000000000FF8000003FE000000000FF0000003FC000000000F F0000003FC000000000FF0000007FC000000001FF0000007FC000000001FE0000007F800 0000001FE0000007F8000000001FE000000FF8000000003FE000000FF8000000003FC000 000FF0000000003FC000000FF0000000003FC000001FF0000000007FC000001FF0000000 007FFFFFFFFFE0000000007FFFFFFFFFE0000000007FFFFFFFFFE000000000FF8000003F E000000000FF0000003FC000000000FF0000003FC000000000FF0000007FC000000001FF 0000007FC000000001FE0000007F8000000001FE0000007F8000000001FE000000FF8000 000003FE000000FF8000000003FC000000FF0000000003FC000000FF0000000003FC0000 01FF0000000007FC000001FF0000000007F8000001FE0000000007F8000001FE00000000 07F8000003FE000000000FF8000003FE000000000FF0000003FC000000000FF0000003FC 000000000FF0000007FC000000001FF0000007FC000000001FE0000007F8000000001FE0 000007F8000000001FE000000FF8000000003FE000000FF8000000003FC000000FF00000 00003FC000000FF0000000007FC000001FF0000000007FC000001FF0000000007F800000 1FE000000000FFC000003FF0000000FFFFFF803FFFFFE00000FFFFFF803FFFFFE00000FF FFFF803FFFFFE000004B447AC348>I<00007FFFFFE00000FFFFFFE00000FFFFFFE00000 00FFE0000000007F8000000000FF8000000000FF8000000000FF0000000000FF00000000 00FF0000000001FF0000000001FE0000000001FE0000000001FE0000000003FE00000000 03FC0000000003FC0000000003FC0000000007FC0000000007F80000000007F800000000 07F8000000000FF8000000000FF0000000000FF0000000000FF0000000001FF000000000 1FE0000000001FE0000000001FE0000000003FE0000000003FC0000000003FC000000000 3FC0000000007FC0000000007F80000000007F80000000007F8000000000FF8000000000 FF0000000000FF0000000000FF0000000001FF0000000001FE0000000001FE0000000001 FE0000000003FE0000000003FC0000000003FC0000000003FC0000000007FC0000000007 F80000000007F80000000007F8000000000FF8000000000FF0000000000FF0000000000F F0000000001FF0000000001FE0000000001FE0000000003FE0000000003FE0000000003F C000000000FFE0000000FFFFFFE00000FFFFFFE00000FFFFFFC000002B447BC326>I<00 00FFFFFFF0000000FFFFFFF0000000FFFFFFE000000001FFC00000000000FF8000000000 01FF000000000001FF000000000001FE000000000001FE000000000001FE000000000003 FE000000000003FC000000000003FC000000000003FC000000000007FC000000000007F8 000000000007F8000000000007F800000000000FF800000000000FF000000000000FF000 000000000FF000000000001FF000000000001FE000000000001FE000000000001FE00000 0000003FE000000000003FC000000000003FC000000000003FC000000000007FC0000000 00007F8000000000007F8000000000007F800000000000FF800000000000FF0000000000 00FF000000000000FF000000000001FF000000000001FE000000000001FE000000000001 FE000000000003FE000000100003FC000000380003FC000000380003FC000000780007FC 000000700007F8000000700007F8000000F00007F8000000E0000FF8000001E0000FF000 0001E0000FF0000001C0000FF0000003C0001FF0000007C0001FE000000780001FE00000 0F80001FE000000F80003FE000001F00003FC000003F00003FC000007F00007FC00000FE 00007FC00003FE00007F80000FFE0000FF80007FFC00FFFFFFFFFFFC00FFFFFFFFFFFC00 FFFFFFFFFFF80035447AC33D>76 D<0000FFFF80000000007FFFC00000FFFFC000000000 7FFFC00000FFFFC000000000FFFFC0000001FFC000000001FFC000000000FFC000000001 FF8000000001FFC000000003FF8000000001FFC000000003FF8000000001DFC000000007 7F0000000001DFC00000000E7F0000000001DFC00000000EFF0000000003CFE00000001C FF00000000038FE00000001CFE00000000038FE000000038FE00000000038FE000000071 FE00000000078FE000000071FE00000000070FE0000000E1FC00000000070FE0000000E1 FC00000000070FE0000001C3FC000000000F0FE000000383FC000000000E0FE000000383 F8000000000E0FE000000703F8000000000E07F000000707F8000000001E07F000000E07 F8000000001C07F000000E07F0000000001C07F000001C07F0000000001C07F00000380F F0000000003C07F00000380FF0000000003807F00000700FE0000000003807F00000700F E0000000003807F00000E01FE0000000007807F00001C01FE0000000007003F80001C01F C0000000007003F80003801FC0000000007003F80003803FC000000000F003F80007003F C000000000E003F8000E003F8000000000E003F8000E003F8000000000E003F8001C007F 8000000001E003F8001C007F8000000001C003F80038007F0000000001C003F80070007F 0000000001C003F8007000FF0000000003C001FC00E000FF00000000038001FC00E000FE 00000000038001FC01C000FE00000000038001FC038001FE00000000078001FC038001FE 00000000070001FC070001FC00000000070001FC070001FC00000000070001FC0E0003FC 000000000F0001FC1C0003FC000000000E0001FC1C0003F8000000000E0000FE380003F8 000000000E0000FE380007F8000000001E0000FE700007F8000000001C0000FEE00007F0 000000001C0000FEE00007F0000000001C0000FFC0000FF0000000003C0000FFC0000FF0 00000000380000FF80000FE000000000780000FF00000FE000000000780000FF00001FE0 00000000F80000FE00001FE000000001FC00007E00001FC000000007FE00007C00003FE0 000000FFFFF00078003FFFFFC00000FFFFF00078003FFFFFC00000FFFFF00070003FFFFF C000005A447AC357>I<0000FFFF800001FFFFE00000FFFF800001FFFFE00000FFFFC000 01FFFFE0000000FFC000000FFC00000000FFC0000007F000000000FFE0000003E0000000 01FFE0000003C000000001DFE0000003C000000001DFF00000038000000001DFF0000007 8000000003CFF000000780000000038FF800000700000000038FF8000007000000000387 F800000F000000000787FC00000F000000000703FC00000E000000000703FC00000E0000 00000703FE00001E000000000F01FE00001E000000000E01FE00001C000000000E01FF00 001C000000000E00FF00003C000000001E00FF00003C000000001C00FF80003800000000 1C007F800038000000001C007F800078000000003C007FC000780000000038003FC00070 0000000038003FC000700000000038003FE000F00000000078001FE000F0000000007000 1FE000E00000000070001FF000E00000000070000FF001E000000000F0000FF801E00000 0000E0000FF801C000000000E00007F801C000000000E00007FC03C000000001E00007FC 03C000000001C00003FC038000000001C00003FE038000000001C00003FE078000000003 C00001FE078000000003800001FF070000000003800001FF070000000003800000FF0F00 00000007800000FF8F0000000007000000FF8E00000000070000007F8E00000000070000 007FDE000000000F0000007FDE000000000E0000003FDC000000000E0000003FFC000000 000E0000003FFC000000001E0000001FFC000000001C0000001FF8000000001C0000001F F8000000001C0000000FF8000000003C0000000FF8000000003800000007F00000000078 00000007F0000000007800000007F000000000F800000003F000000001FC00000003E000 000007FE00000003E0000000FFFFF0000001E0000000FFFFF0000001E0000000FFFFF000 0001C00000004B447AC348>I<000000001FF8000000000001FFFF000000000007F01FC0 000000001F8003F0000000007E0001F800000001F80000FC00000003E000007E0000000F C000003F0000001F8000001F8000003F0000001FC000007E0000000FC00000FC0000000F E00001F800000007E00003F000000007F00007F000000007F0000FE000000007F0001FC0 00000007F8003FC000000003F8003F8000000003F8007F8000000003F800FF0000000003 F800FE0000000003FC01FE0000000003FC03FE0000000003FC03FC0000000003FC07FC00 00000003FC07F80000000007FC0FF80000000007FC0FF80000000007FC0FF00000000007 FC1FF00000000007FC1FF00000000007F81FE0000000000FF83FE0000000000FF83FE000 0000000FF83FE0000000000FF87FC0000000001FF07FC0000000001FF07FC0000000001F F07FC0000000003FF07FC0000000003FE0FF80000000003FE0FF80000000003FC0FF8000 0000007FC0FF80000000007FC0FF8000000000FF80FF8000000000FF80FF8000000000FF 00FF8000000001FF00FF8000000001FE00FF8000000003FC00FF8000000003FC007F8000 000007F8007F800000000FF0007F800000000FF0007F800000001FE0003F800000001FC0 003F800000003F80003FC00000007F00001FC0000000FF00001FC0000001FE00000FE000 0001FC00000FE0000003F0000007F0000007E0000003F000001FC0000001F800003F8000 0000FC00007E000000007E0001F8000000003F8007F0000000000FE03F800000000003FF FE0000000000007FE0000000003E4872C54B>I<0000FFFFFFFFF0000000FFFFFFFFFE00 0000FFFFFFFFFF80000001FF80007FE0000000FF00001FF0000001FF000007F8000001FF 000003F8000001FE000003FC000001FE000001FE000003FE000001FE000003FE000001FE 000003FC000001FF000003FC000001FF000007FC000001FF000007FC000001FF000007F8 000001FF000007F8000001FF00000FF8000001FF00000FF8000003FE00000FF0000003FE 00000FF0000003FE00001FF0000003FC00001FF0000007FC00001FE0000007F800001FE0 00000FF800003FE000000FF000003FE000001FE000003FC000001FC000003FC000003F80 00007FC000007F0000007FC00000FE0000007F800003FC0000007F80000FF0000000FF80 007FC0000000FFFFFFFF00000000FFFFFFF800000000FF00000000000001FF0000000000 0001FF00000000000001FE00000000000001FE00000000000003FE00000000000003FE00 000000000003FC00000000000003FC00000000000007FC00000000000007FC0000000000 0007F800000000000007F80000000000000FF80000000000000FF80000000000000FF000 00000000000FF00000000000001FF00000000000001FF00000000000001FE00000000000 001FE00000000000003FE00000000000003FE00000000000003FC00000000000003FC000 00000000007FC00000000000007FC00000000000007F80000000000000FFC00000000000 FFFFFF8000000000FFFFFF8000000000FFFFFF800000000040447AC342>I<0000FFFFFF FF80000000FFFFFFFFF8000000FFFFFFFFFE00000001FF8001FF80000000FF00003FC000 0001FF00001FE0000001FF00000FF0000001FE000007F8000001FE000003F8000001FE00 0003FC000003FE000003FC000003FC000003FE000003FC000003FE000003FC000003FE00 0007FC000003FE000007F8000003FE000007F8000003FE000007F8000003FE00000FF800 0007FC00000FF0000007FC00000FF0000007FC00000FF000000FF800001FF000000FF800 001FE000000FF000001FE000001FE000001FE000003FC000003FE000003F8000003FC000 007F0000003FC00000FE0000003FC00003F80000007FC00007F00000007F80001FC00000 007F8001FF000000007FFFFFF800000000FFFFFFE000000000FF0003F800000000FF0000 FE00000000FF00007F00000001FF00003F80000001FE00001FC0000001FE00001FC00000 01FE00001FE0000003FE00001FE0000003FC00000FE0000003FC00000FE0000003FC0000 1FE0000007FC00001FE0000007F800001FE0000007F800001FE0000007F800003FE00000 0FF800003FE000000FF000003FE000000FF000003FE000000FF000007FC000001FF00000 7FC000001FE000007FC000001FE000007FC000001FE000007FC000003FE000007FC00E00 3FC000007FC00E003FC000007FC00E007FC000007F801E007FC000007F801C007F800000 7F803C00FFC000007F8038FFFFFF80003FC070FFFFFF80001FC0F0FFFFFF80000FE1E000 0000000003FF80000000000000FE003F467AC347>82 D<00000003FE000C0000000FFF80 1C0000007FFFE03C000000FE03F83C000003F0007C7C000007E0003EF800000FC0001FF8 00001F80000FF800003F00000FF800007E000007F00000FC000007F00000FC000003F000 01F8000003F00001F8000003E00003F0000003E00003F0000003E00007F0000003E00007 E0000003C00007E0000003C00007E0000003C0000FE0000003C0000FE000000380000FE0 00000380000FF000000380000FF000000000000FF000000000000FF800000000000FFC00 0000000007FE000000000007FFE00000000007FFFC0000000003FFFF8000000001FFFFF0 00000001FFFFFC00000000FFFFFF000000003FFFFF800000000FFFFFC000000003FFFFC0 000000003FFFE00000000007FFE00000000000FFF000000000003FF000000000001FF000 000000000FF000000000000FF0000000000007F0000000000007F0000000000007F00007 00000007F0000700000003F0000700000007F0000700000007F0000F00000007E0000F00 000007E0000E00000007E0000E0000000FE0001E0000000FC0001E0000000FC0001F0000 001F80001F0000001F80003F0000003F00003F8000003E00003F8000007E00003FC00000 FC00007FC00001F800007FE00003F000007CF00007E00000787C001F800000F03F807F00 0000F01FFFFC000000E007FFF0000000C0007F80000000364879C537>I<01FFFFFFFFFF FFF803FFFFFFFFFFFFF803FFFFFFFFFFFFF803FF0007FC001FF007F80007F80007F007E0 000FF80003F007C0000FF80001F00F80000FF00001F00F00000FF00000F00F00000FF000 00F01E00001FF00000E01E00001FE00000E01C00001FE00000E03C00001FE00000E03800 003FE00000E03800003FC00001E07800003FC00001C07000003FC00001C0F000007FC000 01C0E000007F800001C0E000007F800001C0E000007F800001C0000000FF800000000000 00FF00000000000000FF00000000000000FF00000000000001FF00000000000001FE0000 0000000001FE00000000000001FE00000000000003FE00000000000003FC000000000000 03FC00000000000003FC00000000000007FC00000000000007F800000000000007F80000 0000000007F80000000000000FF80000000000000FF00000000000000FF0000000000000 0FF00000000000001FF00000000000001FE00000000000001FE00000000000001FE00000 000000003FE00000000000003FC00000000000003FC00000000000003FC0000000000000 7FC00000000000007F800000000000007F800000000000007F80000000000000FF800000 00000000FF00000000000000FF00000000000000FF00000000000001FF00000000000001 FE00000000000001FE00000000000003FE00000000000003FE00000000000007FE000000 0000000FFF00000000007FFFFFFFC00000007FFFFFFFC00000007FFFFFFF800000003D44 6FC346>I<1FFFFFF0003FFFFC1FFFFFF0003FFFFC1FFFFFF0003FFFFC003FF0000001FF 80001FE0000000FE00003FE00000007C00003FE00000007800003FC00000007800003FC0 0000007000003FC0000000F000007FC0000000E000007F80000000E000007F80000000E0 00007F80000001E00000FF80000001C00000FF00000001C00000FF00000001C00000FF00 000003C00001FF00000003800001FE00000003800001FE00000003800001FE0000000780 0003FE00000007000003FC00000007000003FC00000007000003FC0000000F000007FC00 00000E000007F80000000E000007F80000000E000007F80000001E00000FF80000001E00 000FF00000001C00000FF00000001C00000FF00000003C00001FF00000003C00001FE000 00003800001FE00000003800001FE00000007800003FE00000007800003FC00000007000 003FC00000007000003FC0000000F000007FC0000000F000007F80000000E000007F8000 0000E000007F80000001E00000FF80000001C00000FF00000001C00000FF00000001C000 00FF00000003C00000FF00000003800000FF00000007800000FE00000007000000FE0000 000F000000FE0000000E000000FE0000001E000000FE0000003C0000007E000000380000 007F000000780000007F000000F00000003F000001E00000003F800003C00000001F8000 07800000001FC0000F000000000FE0003E0000000007F000F80000000003FC07F0000000 0000FFFFC000000000003FFF00000000000007F800000000003E466DC348>III<00001F80000000007FE000000001F07070000007C039F800000F801D F800001F001FF800003E000FF000007E000FF00000FC000FF00001F80007F00001F80007 E00003F00007E00007F00007E00007E0000FE0000FE0000FC0000FE0000FC0001FC0000F C0001FC0001FC0003FC0001F80003F80001F80003F80001F80003F80003F80007F80003F 00007F00003F00007F00003F00007F00007F00007F00007E0000FE00007E0000FE00007E 0000FE0000FE0380FE0000FC0780FE0000FC0700FE0000FC07007E0001FC07007E0001FC 0F007E0003F80E007E0007F80E003E000FF81E003E000FF81C001F001CF81C001F0038F8 38000F80F078780007C3E07C700001FF801FE000007E00078000292D76AB32>97 D<000FE0000007FFE0000007FFE0000007FFE00000001FC00000000FC00000001FC00000 001FC00000001F800000001F800000001F800000003F800000003F000000003F00000000 3F000000007F000000007E000000007E000000007E00000000FE00000000FC00000000FC 00000000FC00000001FC00000001F800000001F81F800001F87FE00003F9E0F80003F3C0 7C0003F7003E0003FE003E0007FC001F0007F8001F0007F8001F0007F0001F800FE0001F 800FE0001F800FC0001F800FC0001F801FC0001F801F80001F801F80001F801F80003F80 3F80003F803F00003F803F00003F803F00007F807F00007F007E00007F007E00007F007E 0000FF007E0000FE00FC0000FE00FC0000FE00FC0001FC00FC0001FC00FC0003F800FC00 03F8007C0003F0007C0007E0007C000FE0007C000FC0007C001F80003C003F00003E007E 00001E00FC00000F01F800000783E0000003FF80000000FE000000214676C42D>I<0000 0FE00000007FF8000001F81E000007E00F00000F800780001F000380007E0003C000FC00 1FC001FC003FC001F8003FC003F0007F8007F0007F800FE0007F800FE0003E001FC00000 001FC00000003F800000003F800000007F800000007F000000007F000000007F00000000 FF00000000FE00000000FE00000000FE00000000FE00000000FC00000000FC00000000FC 00000000FC00000000FC00000000FC00000180FC000003C0FC00000780FC000007807C00 000F007E00001E003E00007C003E0000F0001F0003E0000F800F800007C07E000001FFF8 0000007FC00000222D75AB2D>I<0000000007F000000003FFF000000003FFF000000003 FFF0000000000FE00000000007E0000000000FE0000000000FE0000000000FC000000000 0FC0000000001FC0000000001FC0000000001F80000000001F80000000003F8000000000 3F80000000003F00000000003F00000000007F00000000007F00000000007E0000000000 7E0000000000FE0000000000FE0000000000FC0000001F80FC0000007FE1FC000001F071 FC000007C039F800000F801DF800001F001FF800003E000FF800007E000FF00000FC000F F00001F80007F00001F80007F00003F00007E00007F00007E00007E0000FE0000FE0000F E0000FE0000FC0001FC0000FC0001FC0001FC0003FC0001FC0003F80001F80003F80001F 80003F80003F80007F80003F80007F00003F00007F00003F00007F00007F00007F00007F 0000FE00007E0000FE00007E0000FE0000FE0380FE0000FE0780FE0000FC0700FE0000FC 07007E0001FC07007E0001FC0F007E0003F80E007E0007F80E003E000FF81E003E000FF8 1C001F001CF81C001F0038F838000F80F078780007C3E07C700001FF801FE000007E0007 80002C4676C432>I<00000FE00000007FF8000001F83E000007C00F00001F800780003F 000780007E0007C000FC0003C001F80003C003F00007C007F000078007E00007800FE000 0F801FC0000F001FC0001F003F80003E003F8000FC003F8007F0007F80FFC0007FFFFE00 007FFFC000007F00000000FF00000000FE00000000FE00000000FE00000000FE00000000 FE00000000FC00000000FC00000000FC00000000FC00000000FC00000180FC000003C07C 000007807C000007807E00000F003E00001E003E00007C001F0000F0000F0003E0000780 0F800003C07E000001FFF80000003FC00000222D75AB2D>I<000000000F80000000003F E000000000F87000000001F03800000003E0F800000007E1FC00000007C3FC0000000FC7 FC0000000FC7FC0000000F87F80000001F83F00000001F81E00000001F80000000003F80 000000003F00000000003F00000000003F00000000003F00000000007F00000000007E00 000000007E00000000007E00000000007E0000000000FE0000000000FC0000000000FC00 00000000FC00000001FFFFFE000001FFFFFE000001FFFFFE00000001F80000000001F800 00000001F80000000003F80000000003F00000000003F00000000003F00000000003F000 00000007F00000000007E00000000007E00000000007E00000000007E0000000000FE000 0000000FC0000000000FC0000000000FC0000000000FC0000000001FC0000000001F8000 0000001F80000000001F80000000001F80000000003F80000000003F00000000003F0000 0000003F00000000003F00000000003F00000000007F00000000007E00000000007E0000 0000007E0000000000FE0000000000FC0000000000FC0000000000FC0000000000FC0000 000001FC0000000001F80000000001F80000000001F80000000001F80000000003F00000 000003F00000000003F00000000003E00000000007E00000001C07E00000007F07C00000 00FF07C0000000FF0F80000000FF0F80000000FF0F00000000FE1F00000000F81E000000 00F03C000000007878000000001FF00000000007C0000000002E5A83C51E>I<000000FC 0000000003FF000000000F83838000003E01CFC000007C00EFC00000F800FFC00001F000 7FC00003F0007F800007E0003F80000FC0003F80001FC0003F80001F80003F00003F8000 3F00003F00007F00007F00007F00007F00007E0000FE00007E0000FE0000FE0001FE0000 FE0001FC0000FC0001FC0000FC0001FC0001FC0003FC0001FC0003F80001F80003F80001 F80003F80003F80003F80003F80003F00003F00003F00003F00003F00007F00003F00007 F00003F00007E00003F00007E00003F0000FE00003F0001FE00003F0001FC00001F0003F C00001F0007FC00000F800FFC00000F801DF8000007C039F8000003E0F3F8000000FFC3F 80000003F03F00000000003F00000000007F00000000007F00000000007E00000000007E 0000000000FE0000000000FE0000000000FC0000000000FC00001C0001F800007F0001F8 0000FF0003F00000FF0007F00000FF000FE00000FE000FC00000FE003F000000F8007E00 00007C01F80000001FFFE000000003FF000000002A407BAB2D>I<0000FE000000007FFE 000000007FFE000000007FFE0000000001FC0000000000FC0000000001FC0000000001FC 0000000001F80000000001F80000000003F80000000003F80000000003F00000000003F0 0000000007F00000000007F00000000007E00000000007E0000000000FE0000000000FE0 000000000FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F80 7F0000003F83FFC000003F8F81F000003F1E00F800003F3800FC00007F70007C00007FE0 007C00007FC0007E00007FC0007E0000FF80007E0000FF00007E0000FF00007E0000FE00 007E0001FC0000FE0001FC0000FC0001F80000FC0001F80000FC0003F80001FC0003F800 01F80003F00001F80003F00001F80007F00003F80007F00003F00007E00003F00007E000 07F0000FE00007E0000FE00007E0000FC0000FE0000FC0000FC0001FC0000FC0781FC000 1FC0701F80001F80701F80001F80703F80003F80F03F80003F00E03F00003F00E03F0000 3F01E07F00003E01C07F00003E03C07E00003E03807E00003E0700FE00001E0F00FE0000 1F1E00FC00000FF80038000003E0002D467AC432>I<00003C00007E0000FE0001FE0001 FE0001FE0000FC0000700000000000000000000000000000000000000000000000000000 00000000000000000000000000000000007C0001FF0003C7800703C00F03E00E03E01C03 E01C07E03807E03807E07807E0700FE0700FC0701FC0F01F80E01F80003F80003F00003F 00007F00007E00007E0000FE0000FC0001FC0001F80001F80003F80003F00003F01E07F0 1C07E01C07E01C0FE03C0FC0380FC0380FC0780F80700F80F00F80E00F81C00783C007C7 8003FE0000F800174378C11E>I<00000000F000000003F800000003F800000007F80000 0007F800000007F800000007F000000001C0000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000001F000000007FC0000001E1E000000380F00 0000700F800000E00F800001E00F800001C00F800003800F800007801F800007001F8000 07001F80000E001F80000E003F80001E003F80001C003F000000003F000000007F000000 007F000000007E000000007E00000000FE00000000FE00000000FC00000000FC00000001 FC00000001FC00000001F800000001F800000003F800000003F800000003F000000003F0 00000007F000000007F000000007E000000007E00000000FE00000000FE00000000FC000 00000FC00000001FC00000001FC00000001F800000001F800000003F800000003F800000 003F000000003F000000007F000000007E000000007E00000000FE00001C00FC00007F00 FC0000FF01F80000FF03F00000FF03F00000FE07E00000FE0FC00000F81F000000707E00 00003FF80000000FC0000000255683C11E>I<0000FE000000007FFE000000007FFE0000 00007FFE0000000001FC0000000000FC0000000001FC0000000001FC0000000001F80000 000001F80000000003F80000000003F80000000003F00000000003F00000000007F00000 000007F00000000007E00000000007E0000000000FE0000000000FE0000000000FC00000 00000FC0000000001FC0000000001FC0000000001F80000000001F80007E00003F8001FF 00003F800783C0003F000E07C0003F003C1FC0007F00701FC0007F00603FC0007E00E03F C0007E01C03FC000FE03803F8000FE07000E0000FC0E00000000FC1C00000001FC380000 0001FC7000000001F8E000000001F9C000000003FB8000000003FF0000000003FF000000 0003FFF000000007F3FC00000007F07F00000007E01FC0000007E00FE000000FE007E000 000FE007F000000FC003F000000FC003F000001FC003F00F001FC003F00F001F8003F00E 001F8003F00E003F8003F01E003F8003F01C003F0003E01C003F0003E01C007F0003E038 007F0003E038007E0003E078007E0003E07000FE0001E0E000FE0001F1E000FC00007F80 003800001F00002A467AC42D>I<0003F801FFF801FFF801FFF80007F00003F00007F000 07F00007E00007E0000FE0000FE0000FC0000FC0001FC0001FC0001F80001F80003F8000 3F80003F00003F00007F00007F00007E00007E0000FE0000FE0000FC0000FC0001FC0001 FC0001F80001F80003F80003F80003F00003F00007F00007F00007E00007E0000FE0000F E0000FC0000FC0001FC0001FC0001F80001F80003F80003F80003F00003F00007F01C07F 03C07E03807E03807E0780FE0700FC0700FC0700FC0F00FC0E007C1E007C1C003C3C003E 78001FF00007C000154678C419>I<01F0000FE00007F0000003FC007FF8003FFC000007 1E01F03E00F81F00000E1F03C01F01E00F80001E0F87001F83800FC0001C0F8E000F8700 07C0003C0F9C000F8E0007C000380FB8000FDC0007E000380FF8000FFC0007E000781FF0 000FF80007E000701FE0000FF00007E000701FE0000FF00007E000701FC0000FE00007E0 00F01F80001FC0000FE000E03F80001FC0000FC000E03F00001F80000FC000003F00001F 80000FC000003F00003F80001FC000007F00003F80001F8000007E00003F00001F800000 7E00003F00001F8000007E00007F00003F800000FE00007F00003F000000FC00007E0000 3F000000FC00007E00007F000000FC0000FE00007E000001FC0000FE00007E000001F800 00FC0000FE000001F80000FC0000FC000001F80001FC0000FC078003F80001FC0001FC07 0003F00001F80001F8070003F00001F80001F8070003F00003F80003F80F0007F00003F8 0003F00E0007E00003F00003F00E0007E00003F00003F01E0007E00007F00003E01C000F E00007F00003E03C000FC00007E00003E038000FC00007E00003E070000FC0000FE00001 E0F0001FC0000FE00001F1E0001F80000FC00000FF8000070000038000003E0000492D78 AB50>I<01F0000FE00003FC007FF800071E01F03E000E0F03C01F001E0F87001F801C0F 8E000F803C0F9C000F80380FB8000FC0380FF8000FC0781FF0000FC0701FE0000FC0701F E0000FC0701FC0000FC0F01F80001FC0E03F80001F80E03F00001F80003F00001F80003F 00003F80007F00003F00007E00003F00007E00003F00007E00007F0000FE00007E0000FC 00007E0000FC0000FE0000FC0000FC0001FC0000FC0001F80001FC0001F80001F80001F8 0001F80F03F80003F80E03F00003F00E03F00003F00E03F00007F01E07F00007E01C07E0 0007E01C07E00007E03C07E00007C0380FE00007C0780FC00007C0700FC00007C0E00FC0 0003C1E01FC00003E3C01F800001FF00070000007C00302D78AB37>I<00000FE0000000 7FFC000001F83E000007E00F80000F8007C0001F0007C0007E0003E000FC0003F000FC00 03F001F80001F003F00001F807F00001F80FE00001F80FE00001F81FC00001F81FC00001 F83F800001F83F800003F87F800003F87F000003F87F000003F87F000007F8FF000007F0 FE000007F0FE000007F0FE00000FF0FE00000FE0FC00000FE0FC00001FC0FC00001FC0FC 00001F80FC00003F80FC00003F00FC00007F00FC00007E00FC0000FC007C0001F8007E00 03F0003E0003E0003E0007C0001F001F80000F803E000007C0FC000001FFF00000003F80 0000252D75AB32>I<0003E0007E000007F801FF80000E3C0783E0001C1E0F01F0003C1F 1C00F800381F3800F800781F70007C00701FE0007C00701FE0007C00703FC0007E00E03F 80007E00E03F80007E00E03F00007E01E07F00007E01C07F00007E01C07E00007E00007E 00007E0000FE0000FE0000FE0000FE0000FC0000FE0000FC0000FE0001FC0001FE0001FC 0001FC0001F80001FC0001F80001FC0003F80003FC0003F80003F80003F00003F80003F0 0003F80007F00007F00007F00007F00007E0000FE00007E0000FE0000FE0000FC0000FE0 001F80000FE0003F80000FE0003F00001FF0007E00001FF000FC00001FF001F800001FB8 03F000003F9C07E000003F9E0F8000003F07FE0000003F01F80000007F00000000007F00 000000007E00000000007E0000000000FE0000000000FE0000000000FC0000000000FC00 00000001FC0000000001FC0000000001F80000000001F80000000003F80000000003F800 00000007F800000000FFFFF0000000FFFFF0000000FFFFE00000002F3F7FAB32>I<0000 1F800C00007FE01C0001F0703C0007C03878000F801CF8001F001DF8003E000FF8007E00 0FF000FC000FF001F80007F001F80007F003F00007E007F00007E007E00007E00FE0000F E00FE0000FC01FC0000FC01FC0000FC03FC0001FC03F80001F803F80001F803F80001F80 7F80003F807F00003F007F00003F007F00003F007F00007F00FE00007E00FE00007E00FE 00007E00FE0000FE00FE0000FC00FE0000FC007E0001FC007E0001FC007E0003F8007E00 07F8003E000FF8003E000FF8001F001FF0001F003BF0000F80F3F00007C3E7F00001FF87 E000007E07E000000007E00000000FE00000000FC00000000FC00000000FC00000001FC0 0000001F800000001F800000001F800000003F800000003F000000003F000000007F0000 00007F00000000FF0000007FFFFE00007FFFFE00007FFFFC00263F76AB2D>I<01F0003F 8003FC01FFF0071E03C0F80E0F0F007C1E0F9E01FC1C0F9C01FC1C0FB803FC380FF003FC 380FF003FC381FE003F8781FE000E0701FC00000701FC00000F01F800000E03F800000E0 3F000000003F000000003F000000007F000000007E000000007E000000007E00000000FE 00000000FC00000000FC00000000FC00000001FC00000001F800000001F800000001F800 000003F800000003F000000003F000000003F000000007F000000007E000000007E00000 0007E00000000FE00000000FC00000000FC00000000FC00000001FC00000001F80000000 0700000000262D78AB29>I<00000FE00000007FF8000001F01E000003C00F0000078007 80000F000380001E0003C0001E0007C0003C001FC0003C001FC0007C003F800078003F80 007C003F80007C000E00007C000000007E000000007F000000007FF00000007FFF000000 3FFFC000001FFFF000000FFFF8000007FFFC000000FFFC0000000FFE00000001FE000000 00FE000000007F000000003F000E00003F003F00001E007F80001E007F80001E007F8000 3E00FF00003C00FF00003C00FC000078007000007800700000F000780001E0003C0003C0 001E000F80000F803E000003FFF80000007FC00000222D7AAB28>I<000070000001F800 0001F8000001F8000003F8000003F0000003F0000003F0000007F0000007E0000007E000 0007E000000FE000000FC000000FC000000FC000001FC000001F8000001F80007FFFFFE0 FFFFFFE0FFFFFFC0003F0000003F0000007F0000007E0000007E0000007E000000FE0000 00FC000000FC000000FC000001FC000001F8000001F8000001F8000003F8000003F00000 03F0000003F0000007F0000007E0000007E0000007E000000FE000000FC000000FC00000 0FC007801FC007001F8007001F800F001F800E003F801E003F001C003F003C003F003800 3F0070001F00F0001F01E0000F03C0000F87800007FE000001F800001B3F78BD20>I<00 7C0000000001FF0000070003C780001F800703C0001F800F03E0001F800E03E0003F801C 03E0003F801C07E0003F003807E0003F003807E0007F007807E0007F00700FE0007E0070 0FC0007E00701FC000FE00F01F8000FE00E01F8000FC00003F8000FC00003F0001FC0000 3F0001FC00007F0001F800007E0001F800007E0003F80000FE0003F80000FC0003F00000 FC0003F00000FC0007F00001FC0007F00001F80007E00001F80007E00001F8000FE03803 F8000FE07803F0000FC07003F0000FC07003F0000FC07003F0001FC0F003F0001F80E003 F0003F80E001F0003F81E001F0007F81C001F800EF83C000F801EF8380007C03C7878000 3E0F07C700001FFE01FE000003F00078002D2D78AB34>I<007C00003801FF0000FC03C7 8001FE0703C001FE0F03E001FE0E03E001FE1C03E000FE1C07E0007E3807E0007E3807E0 003E7807E0003E700FE0001E700FC0001E701FC0001EF01F80001CE01F80001C003F8000 1C003F00003C003F000038007F000038007E000038007E00007800FE00007000FC000070 00FC00007000FC0000F001FC0000E001F80000E001F80001E001F80001C001F80001C003 F000038003F000038003F000070003F000070003F0000E0001F0000E0001F0001C0001F8 00380000F800780000FC00F000007C01E000003F078000000FFF00000003F80000272D78 AB2D>I<007C00000000038001FF00000E000FC003C780003F001FE00703C0003F001FE0 0E03E0003F001FE00E03E0007F001FE01C03E0007E000FE01C07E0007E0007E03807E000 7E0007E03807E000FE0003E07807E000FC0003E0700FE000FC0003E0700FC000FC0001E0 701FC001FC0001E0F01F8001F80001C0E01F8001F80001C0003F8001F80001C0003F0003 F80003C0003F0003F0000380007F0003F0000380007E0003F0000380007E0007F0000780 00FE0007F000070000FC0007E000070000FC0007E000070000FC000FE0000F0001FC000F E0000E0001F8000FC0000E0001F8000FC0000E0001F8000FC0001C0001F8000FC0001C00 03F0001F80001C0003F0001F8000380003F0001F8000380003F0001F8000700001F0001F 8000700001F0003F8000E00001F8003F8000E00001F8007FC001C00000F800F7C003C000 00FC00E7E0078000007E01C3E00F0000001F0781F81E0000000FFF007FF800000001FC00 0FE000003B2D78AB41>I<0000F8003F000007FE00FFE0000F0F83C0F0001C07C780F800 3803CF03F8007003EE03F800E003FC07F801E003FC07F801C003F807F803C003F807F003 8003F801C0078003F00000070003F00000070007F000000F0007E000000E0007E0000000 0007E0000000000FE0000000000FC0000000000FC0000000000FC0000000001FC0000000 001F80000000001F80000000001F80000000003F80000000003F00000000003F00000000 003F00000000007F0003C000007F00038000007E00038000007E0003800000FE0007001E 00FE0007003F00FE000F007F81FC000E007F81FE001C00FF83FE003C00FF03BE007800FE 079E00F0007C0F1F01E0003C1E0F83C0001FF803FF000007E000FC00002D2D7CAB2D>I< 007C0000000001FF0000070003C780001F800703C0001F800F03E0001F800E03E0003F80 1C03E0003F001C07E0003F003807E0003F003807E0007F007807E0007E00700FE0007E00 700FC0007E00701FC000FE00F01F8000FC00E01F8000FC00003F8000FC00003F0001FC00 003F0001F800007F0001F800007E0001F800007E0003F80000FE0003F00000FC0003F000 00FC0003F00000FC0007F00001FC0007E00001F80007E00001F80007E00001F8000FE000 03F8000FC00003F0000FC00003F0000FC00003F0001FC00003F0001F800003F0001F8000 03F0003F800001F0003F800001F0007F000001F800FF000000F801FF0000007C03FF0000 003E0F7E0000001FFE7E00000003F07E0000000000FE0000000000FC0000000000FC0000 000001FC0000000001F800001F0001F800007F8003F000007F8003F000007F8007E00000 FF000FC00000FF000F800000FE001F800000F0003F00000070007E0000007800F8000000 3801F00000001E07C00000000FFF0000000001FC00000000294078AB2F>I<00007C0007 0001FF000F0003FF800E000FFF801E001FFFC03C001FFFE038003F03F078007C00FDF000 78003FE000700003C000F000038000E00007800000000F000000001E000000003C000000 007800000000F000000001E000000003C000000007800000000F000000001E000000003C 000000007800000000F000000001E000000003C000000007800000000F000000001E0000 F0003C0000E000780000E000F00001E001E00001E003C00003C007B00007C007FE000F80 0FCF801F801F07E07F003E03FFFE003C01FFFC007800FFF8007000FFF000F0007FC000E0 001F0000282D7BAB28>II<0F0007803F801F C07FC03FE0FFC07FE0FFC07FE0FFC07FE0FFC07FE0FF807FC07F003F803C001E001B0A66 C232>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmsy6 6 3 /Ff 3 8 df0 D<0000300000000038000000003800000000380000000038000000003800000000380000 000038000000003800000000380000000038000000003800000000380000000038000000 00380000000038000000003800000000380000FFFFFFFFFCFFFFFFFFFCFFFFFFFFFC0000 380000000038000000003800000000380000000038000000003800000000380000000038 000000003800000000380000000038000000003800000000380000000038000000003800 00FFFFFFFFFCFFFFFFFFFCFFFFFFFFFC26277CA430>6 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg msbm8 8 1 /Fg 1 83 df 82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh msbm10 12 3 /Fh 3 83 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmex10 12 20 /Fi 20 113 df<000001C0000003C00000078000000F0000001E0000003C0000007C0000 00F8000001F0000003F0000003E0000007C000000FC000000F8000001F8000003F000000 3F0000007E0000007E000000FC000000FC000001F8000001F8000001F8000003F0000003 F0000007F0000007E0000007E000000FE000000FC000000FC000001FC000001FC000001F 8000001F8000003F8000003F8000003F8000003F8000003F0000007F0000007F0000007F 0000007F0000007F0000007F0000007F000000FE000000FE000000FE000000FE000000FE 000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE 000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE 0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000003F0000003F 8000003F8000003F8000003F8000001F8000001F8000001FC000001FC000000FC000000F C000000FE0000007E0000007E0000007F0000003F0000003F0000001F8000001F8000001 F8000000FC000000FC0000007E0000007E0000003F0000003F0000001F8000000F800000 0FC0000007C0000003E0000003F0000001F0000000F80000007C0000003C0000001E0000 000F0000000780000003C0000001C01A7771832E>0 DI 12 D<00000000F000000001F000000003E000000007C00000000F800000001F00000000 3F000000007E00000000FC00000000F800000001F800000003F000000007E00000000FC0 0000000FC00000001F800000003F800000003F000000007E000000007E00000000FC0000 0001FC00000001F800000003F800000003F000000007F000000007E00000000FE0000000 0FC00000001FC00000001FC00000003F800000003F800000003F800000007F000000007F 00000000FE00000000FE00000000FE00000001FE00000001FC00000001FC00000003FC00 000003F800000003F800000007F800000007F800000007F000000007F00000000FF00000 000FF00000000FE00000000FE00000001FE00000001FE00000001FE00000001FE0000000 1FC00000001FC00000003FC00000003FC00000003FC00000003FC00000003FC00000003F 800000007F800000007F800000007F800000007F800000007F800000007F800000007F80 0000007F800000007F800000007F00000000FF00000000FF00000000FF00000000FF0000 0000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF000000 00FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000 FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF 00000000FF00000000FF000000007F000000007F800000007F800000007F800000007F80 0000007F800000007F800000007F800000007F800000007F800000003F800000003FC000 00003FC00000003FC00000003FC00000003FC00000001FC00000001FC00000001FE00000 001FE00000001FE00000001FE00000000FE00000000FE00000000FF00000000FF0000000 07F000000007F000000007F800000007F800000003F800000003F800000003FC00000001 FC00000001FC00000001FE00000000FE00000000FE00000000FE000000007F000000007F 000000003F800000003F800000003F800000001FC00000001FC00000000FC00000000FE0 00000007E000000007F000000003F000000003F800000001F800000001FC00000000FC00 0000007E000000007E000000003F000000003F800000001F800000000FC00000000FC000 000007E000000003F000000001F800000000F800000000FC000000007E000000003F0000 00001F000000000F8000000007C000000003E000000001F000000000F024B26E833B>16 DI20 DI<00000000000F00000000003F0000000000FF0000000003FF000000 000FFC000000001FF0000000007FE000000000FF8000000001FF0000000003FE00000000 07FC000000000FF8000000001FF0000000003FE0000000007FC000000000FFC000000000 FF8000000001FF8000000001FF0000000003FF0000000003FE0000000007FE0000000007 FC0000000007FC0000000007FC000000000FFC000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000001F F0000000001FF0000000001FF0000000003FF0000000003FE0000000003FE0000000007F C0000000007FC000000000FF8000000000FF8000000001FF0000000003FE0000000003FE 0000000007FC000000000FF8000000001FF0000000003FE0000000007FC000000000FF00 00000001FE0000000007FC000000000FF0000000003FC000000000FF0000000000FC0000 000000FC0000000000FF00000000003FC0000000000FF00000000007FC0000000001FE00 00000000FF00000000007FC0000000003FE0000000001FF0000000000FF80000000007FC 0000000003FE0000000003FE0000000001FF0000000000FF8000000000FF80000000007F C0000000007FC0000000003FE0000000003FE0000000003FF0000000001FF0000000001F F0000000001FF0000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000F F8000000000FF8000000000FF8000000000FF8000000000FFC0000000007FC0000000007 FC0000000007FC0000000007FE0000000003FE0000000003FF0000000001FF0000000001 FF8000000000FF8000000000FFC0000000007FC0000000003FE0000000001FF000000000 0FF80000000007FC0000000003FE0000000001FF0000000000FF80000000007FE0000000 001FF0000000000FFC0000000003FF0000000000FF00000000003F00000000000F30EE73 834B>26 DI[< 000000000003E0000000000007E000000000000FC000000000001F8000000000003F8000 000000003F0000000000007E000000000000FC000000000001FC000000000003F8000000 000003F0000000000007E000000000000FE000000000001FC000000000001F8000000000 003F8000000000007F000000000000FE000000000000FE000000000001FC000000000003 FC000000000003F8000000000007F0000000000007F000000000000FE000000000001FE0 00000000001FC000000000003FC000000000003F8000000000007F8000000000007F0000 00000000FF000000000001FE000000000001FE000000000003FC000000000003FC000000 000007F8000000000007F800000000000FF000000000000FF000000000000FF000000000 001FE000000000001FE000000000003FC000000000003FC000000000007FC00000000000 7F8000000000007F800000000000FF800000000000FF000000000001FF000000000001FE 000000000001FE000000000003FE000000000003FC000000000003FC000000000007FC00 0000000007F800000000000FF800000000000FF800000000000FF800000000000FF00000 0000001FF000000000001FF000000000001FE000000000003FE000000000003FE0000000 00003FE000000000007FC000000000007FC000000000007FC000000000007FC000000000 00FF800000000000FF800000000000FF800000000000FF800000000001FF800000000001 FF000000000001FF000000000001FF000000000001FF000000000003FF000000000003FE 000000000003FE000000000003FE000000000007FE000000000007FE000000000007FE00 0000000007FC000000000007FC000000000007FC00000000000FFC00000000000FFC0000 0000000FFC00000000000FF800000000000FF800000000000FF800000000001FF8000000 00001FF800000000001FF800000000001FF800000000001FF800000000001FF000000000 001FF000000000003FF000000000003FF000000000003FF000000000003FF00000000000 3FF000000000003FF000000000003FF000000000003FF000000000003FE000000000003F E000000000007FE000000000007FE000000000007FE000000000007FE000000000007FE0 00000000007FE000000000007FE000000000007FE000000000007FE000000000007FE000 000000007FE000000000007FE000000000007FE000000000007FC00000000000FFC00000 000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC0000000 0000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC000000000 00FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000 FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FF C00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC0 0000000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC000 00000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC00000 000000FFC00000000000FFC00000000000FFC00000000000FFC00000000000FFC0000000 00007FC000000000007FE000000000007FE000000000007FE000000000007FE000000000 007FE000000000007FE000000000007FE000000000007FE000000000007FE00000000000 7FE000000000007FE000000000007FE000000000007FE000000000003FE000000000003F E000000000003FF000000000003FF000000000003FF000000000003FF000000000003FF0 00000000003FF000000000003FF000000000003FF000000000001FF000000000001FF000 000000001FF800000000001FF800000000001FF800000000001FF800000000001FF80000 0000000FF800000000000FF800000000000FF800000000000FFC00000000000FFC000000 00000FFC000000000007FC000000000007FC000000000007FC000000000007FE00000000 0007FE000000000007FE000000000003FE000000000003FE000000000003FE0000000000 03FF000000000001FF000000000001FF000000000001FF000000000001FF000000000001 FF800000000000FF800000000000FF800000000000FF800000000000FF8000000000007F C000000000007FC000000000007FC000000000007FC000000000003FE000000000003FE0 00000000003FE000000000001FE000000000001FF000000000001FF000000000000FF000 000000000FF800000000000FF800000000000FF8000000000007F8000000000007FC0000 00000003FC000000000003FC000000000003FE000000000001FE000000000001FE000000 000001FF000000000000FF000000000000FF8000000000007F8000000000007F80000000 00007FC000000000003FC000000000003FC000000000001FE000000000001FE000000000 000FF000000000000FF000000000000FF0000000000007F8000000000007F80000000000 03FC000000000003FC000000000001FE000000000001FE000000000000FF000000000000 7F0000000000007F8000000000003F8000000000003FC000000000001FC000000000001F E000000000000FE0000000000007F0000000000007F0000000000003F8000000000003FC 000000000001FC000000000000FE000000000000FE0000000000007F0000000000003F80 00000000001F8000000000001FC000000000000FE0000000000007E0000000000003F000 0000000003F8000000000001FC000000000000FC0000000000007E0000000000003F0000 000000003F8000000000001F8000000000000FC0000000000007E0000000000003E0>51 298 104 131 79 32 D[51 298 125 131 79 I<0000000000007C000000000000FC0000 00000001F8000000000001F8000000000003F0000000000007E000000000000FC0000000 00001FC000000000001F8000000000003F0000000000007F0000000000007E0000000000 00FE000000000001FC000000000001F8000000000003F8000000000007F0000000000007 F000000000000FE000000000001FC000000000001FC000000000003F8000000000007F80 00000000007F000000000000FF000000000000FE000000000001FE000000000001FC0000 00000003FC000000000007F8000000000007F800000000000FF000000000000FF0000000 00001FE000000000001FE000000000003FC000000000003FC000000000007FC000000000 007F800000000000FF800000000000FF000000000000FF000000000001FE000000000001 FE000000000003FE000000000003FC000000000007FC000000000007F8000000000007F8 00000000000FF800000000000FF000000000001FF000000000001FF000000000001FE000 000000003FE000000000003FE000000000007FC000000000007FC000000000007FC00000 000000FF800000000000FF800000000000FF800000000001FF000000000001FF00000000 0001FF000000000003FF000000000003FE000000000003FE000000000007FE0000000000 07FC000000000007FC000000000007FC00000000000FFC00000000000FF800000000000F F800000000001FF800000000001FF800000000001FF000000000001FF000000000003FF0 00000000003FF000000000003FF000000000003FE000000000007FE000000000007FE000 000000007FE000000000007FE00000000000FFC00000000000FFC00000000000FFC00000 000000FFC00000000000FFC00000000001FF800000000001FF800000000001FF80000000 0001FF800000000001FF800000000003FF800000000003FF000000000003FF0000000000 03FF000000000003FF000000000003FF000000000007FF000000000007FE000000000007 FE000000000007FE000000000007FE000000000007FE00000000000FFE00000000000FFE 00000000000FFE00000000000FFC00000000000FFC00000000000FFC00000000000FFC00 000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0000 0000001FF800000000001FF800000000001FF800000000001FF800000000003FF8000000 00003FF800000000003FF800000000003FF800000000003FF800000000003FF800000000 003FF800000000003FF000000000003FF000000000003FF000000000003FF00000000000 7FF000000000007FF000000000007FF000000000007FF000000000007FF000000000007F F000000000007FF000000000007FF000000000007FF000000000007FF000000000007FF0 00000000007FF000000000007FF000000000007FF000000000007FF000000000007FE000 000000007FE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000 000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE0000000 0000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE000000000 00FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000 FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FF E00000000000FFE0000000000036B3638257>48 DI64 D<00000000001FFC00000000001FFC 00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00 000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0000 0000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC000000 00001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000 001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FF80000000000 1FF800000000003FF800000000003FF800000000003FF800000000003FF800000000003F F800000000003FF800000000003FF800000000003FF800000000003FF800000000003FF8 00000000003FF800000000003FF800000000003FF800000000003FF800000000003FF800 000000003FF000000000003FF000000000003FF000000000003FF000000000007FF00000 0000007FF000000000007FF000000000007FF000000000007FF000000000007FF0000000 00007FF000000000007FE000000000007FE000000000007FE000000000007FE000000000 00FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000 FFC00000000000FFC00000000000FFC00000000000FFC00000000001FFC00000000001FF C00000000001FFC00000000001FF800000000001FF800000000001FF800000000001FF80 0000000001FF800000000003FF800000000003FF000000000003FF000000000003FF0000 00000003FF000000000003FF000000000007FF000000000007FE000000000007FE000000 000007FE000000000007FE000000000007FE00000000000FFC00000000000FFC00000000 000FFC00000000000FFC00000000000FFC00000000001FF800000000001FF80000000000 1FF800000000001FF800000000001FF000000000003FF000000000003FF000000000003F F000000000003FE000000000003FE000000000007FE000000000007FE000000000007FC0 00000000007FC00000000000FFC00000000000FF800000000000FF800000000000FF8000 00000001FF800000000001FF000000000001FF000000000003FF000000000003FE000000 000003FE000000000003FE000000000007FC000000000007FC000000000007FC00000000 000FF800000000000FF800000000000FF800000000001FF000000000001FF00000000000 1FE000000000003FE000000000003FE000000000003FC000000000007FC000000000007F 8000000000007F800000000000FF800000000000FF000000000001FF000000000001FE00 0000000001FE000000000003FC000000000003FC000000000007FC000000000007F80000 0000000FF800000000000FF000000000000FF000000000001FE000000000001FE0000000 00003FC000000000003FC000000000007F8000000000007F800000000000FF0000000000 00FE000000000001FE000000000001FC000000000003FC000000000003F8000000000007 F8000000000007F000000000000FE000000000000FE000000000001FC000000000003F80 00000000003F8000000000007F0000000000007E000000000000FE000000000001FC0000 00000001F8000000000003F8000000000003F0000000000007E000000000000FE0000000 00000FC000000000001F8000000000003F0000000000007E0000000000007E0000000000 00FC000000000000F800000000000036B37D8457>I80 D88 D<0000000000000000003F00000000000000000000FFC0000000000000000003E0F00000 00000000000007C03800000000000000000F801C00000000000000001F807E0000000000 0000003F01FE00000000000000003F03FF00000000000000007E03FF0000000000000000 FE03FF0000000000000000FC03FF0000000000000001FC03FF0000000000000001FC03FF 0000000000000003F801FE0000000000000003F800780000000000000003F80000000000 0000000007F000000000000000000007F00000000000000000000FF00000000000000000 000FF00000000000000000000FE00000000000000000001FE00000000000000000001FE0 0000000000000000001FE00000000000000000003FC00000000000000000003FC0000000 0000000000003FC00000000000000000003FC00000000000000000007F80000000000000 0000007F800000000000000000007F80000000000000000000FF80000000000000000000 FF00000000000000000000FF00000000000000000000FF00000000000000000001FF0000 0000000000000001FF00000000000000000001FE00000000000000000001FE0000000000 0000000003FE00000000000000000003FE00000000000000000003FE0000000000000000 0003FC00000000000000000007FC00000000000000000007FC00000000000000000007FC 00000000000000000007FC00000000000000000007F80000000000000000000FF8000000 0000000000000FF80000000000000000000FF80000000000000000000FF8000000000000 0000001FF00000000000000000001FF00000000000000000001FF0000000000000000000 1FF00000000000000000003FF00000000000000000003FF00000000000000000003FE000 00000000000000003FE00000000000000000007FE00000000000000000007FE000000000 00000000007FE00000000000000000007FC00000000000000000007FC000000000000000 0000FFC0000000000000000000FFC0000000000000000000FFC0000000000000000000FF C0000000000000000001FF80000000000000000001FF80000000000000000001FF800000 00000000000001FF80000000000000000001FF80000000000000000003FF800000000000 00000003FF00000000000000000003FF00000000000000000003FF000000000000000000 07FF00000000000000000007FF00000000000000000007FF00000000000000000007FE00 000000000000000007FE0000000000000000000FFE0000000000000000000FFE00000000 00000000000FFE0000000000000000000FFE0000000000000000000FFC00000000000000 00001FFC0000000000000000001FFC0000000000000000001FFC0000000000000000001F FC0000000000000000001FF80000000000000000003FF80000000000000000003FF80000 000000000000003FF80000000000000000003FF80000000000000000003FF80000000000 000000007FF00000000000000000007FF00000000000000000007FF00000000000000000 007FF00000000000000000007FF0000000000000000000FFE0000000000000000000FFE0 000000000000000000FFE0000000000000000000FFE0000000000000000001FFE0000000 000000000001FFC0000000000000000001FFC0000000000000000001FFC0000000000000 000001FFC0000000000000000001FFC0000000000000000003FFC0000000000000000003 FF80000000000000000003FF80000000000000000003FF80000000000000000003FF8000 0000000000000007FF00000000000000000007FF00000000000000000007FF0000000000 0000000007FF00000000000000000007FF0000000000000000000FFE0000000000000000 000FFE0000000000000000000FFE0000000000000000000FFE0000000000000000000FFE 0000000000000000000FFC0000000000000000001FFC0000000000000000001FFC000000 0000000000001FFC0000000000000000001FFC0000000000000000001FF8000000000000 0000003FF80000000000000000003FF80000000000000000003FF8000000000000000000 3FF80000000000000000003FF00000000000000000003FF00000000000000000007FF000 00000000000000007FF00000000000000000007FF00000000000000000007FE000000000 00000000007FE00000000000000000007FE0000000000000000000FFE000000000000000 0000FFC0000000000000000000FFC0000000000000000000FFC0000000000000000000FF C0000000000000000000FFC0000000000000000001FF80000000000000000001FF800000 00000000000001FF80000000000000000001FF80000000000000000001FF000000000000 00000001FF00000000000000000003FF00000000000000000003FF000000000000000000 03FF00000000000000000003FE00000000000000000003FE00000000000000000007FE00 000000000000000007FE00000000000000000007FC00000000000000000007FC00000000 000000000007FC00000000000000000007FC0000000000000000000FF800000000000000 00000FF80000000000000000000FF80000000000000000000FF80000000000000000000F F00000000000000000001FF00000000000000000001FF00000000000000000001FF00000 000000000000001FF00000000000000000001FE00000000000000000003FE00000000000 000000003FE00000000000000000003FE00000000000000000003FC00000000000000000 003FC00000000000000000007FC00000000000000000007FC00000000000000000007F80 0000000000000000007F800000000000000000007F80000000000000000000FF80000000 000000000000FF00000000000000000000FF00000000000000000000FF00000000000000 000001FE00000000000000000001FE00000000000000000001FE00000000000000000001 FE00000000000000000003FC00000000000000000003FC00000000000000000003FC0000 0000000000000003F800000000000000000007F800000000000000000007F00000000000 0000000007F00000000000000000000FF00000000000000000000FE0000000000000001E 000FE0000000000000007F801FC000000000000000FFC01FC000000000000000FFC01F80 00000000000000FFC03F8000000000000000FFC03F0000000000000000FFC07F00000000 00000000FFC07E00000000000000007F80FC00000000000000007E00FC00000000000000 003801F800000000000000001C03F000000000000000000F07C0000000000000000003FF 80000000000000000000FC00000000000000000058DD7B7F37>90 D<000000000000000007C0000000000000000000000000000000007FFC00000000000000 000000000000000007FFFFC000000000000000000000000000007FFFFFFC000000000000 0000000000000007FFFFFFFFC0000000000000000000000000FFFFFFFFFFFE0000000000 0000000000000FFFFFFC7FFFFFE000000000000000000000FFFFFF8003FFFFFE00000000 00000000000FFFFFF000001FFFFFE00000000000000000FFFFFC000000007FFFFE000000 000000001FFFFF800000000003FFFFF0000000000001FFFFF00000000000001FFFFF0000 0000001FFFFE0000000000000000FFFFF000000001FFFFC0000000000000000007FFFF00 00001FFFF8000000000000000000003FFFF00003FFFF000000000000000000000001FFFF 803FFFC000000000000000000000000007FFF8FFF800000000000000000000000000003F FEFF00000000000000000000000000000001FEE000000000000000000000000000000000 0E8F1480CC90>100 D<0000000000000000000000C00000000000000000000001E00000 000000000000000003E00000000000000000000003E00000000000000000000007C00000 000000000000000007C0000000000000000000000F80000000000000000000000F800000 00000000000000001F00000000000000000000001F00000000000000000000003E000000 00000000000000003E00000000000000000000007C00000000000000000000007C000000 0000000000000000F80000000000000000000000F80000000000000000000000F0000000 0000000000000001F00000000000000000000001F00000000000000000000003E0000000 0000000000000003E00000000000000000000007C00000000000000000000007C0000000 000000000000000F80000000000000000000000F80000000000000000000001F00000000 000000000000001F00000000000000000000003E00000000000000000000003E00000000 000000000000007C00000000000000000000007C0000000000000000000000F800000000 00000000000000F80000000000000000000001F00000000000000000000001F000000000 00000000000003E00000000000000000000003E00000000000000000000007C000000000 00000000000007C0000000000000000000000F80000000000000000000000F8000000000 0000000000001F00000000000000000000001F00000000000000000000003E0000000000 0000000000003E00000000000000000000003C00000000000000000000007C0000000000 0000000000007C0000000000000000000000F80000000000000000000000F80000000000 000000000001F00000000000000000000001F00000000000000000000003E00000000000 000000000003E00000000000000000000007C00000000000000000000007C00000000000 00000000000F80000000000000000000000F80000000000000000000001F000000000000 00000000001F00000000000400000000003E00000000000E00000000003E00000000001E 00000000007C00000000007F00000000007C0000000000FF0000000000F80000000001FF 0000000000F80000000003FF8000000001F0000000000FFF8000000001F0000000001C7F C000000003E000000000387FC000000003E000000000F03FE000000007C000000000403F E000000007C000000000003FE00000000F8000000000001FF00000000F8000000000001F F00000000F0000000000000FF80000001F0000000000000FF80000001F00000000000007 FC0000003E00000000000007FC0000003E00000000000007FC0000007C00000000000003 FE0000007C00000000000003FE000000F800000000000001FF000000F800000000000001 FF000001F000000000000000FF800001F000000000000000FF800003E000000000000000 FF800003E0000000000000007FC00007C0000000000000007FC00007C000000000000000 3FE0000F80000000000000003FE0000F80000000000000001FF0001F0000000000000000 1FF0001F00000000000000000FF8003E00000000000000000FF8003E0000000000000000 0FF8007C000000000000000007FC007C000000000000000007FC00F80000000000000000 03FE00F8000000000000000003FE01F0000000000000000001FF01F00000000000000000 01FF03E0000000000000000001FF03E0000000000000000000FF83C00000000000000000 00FF87C00000000000000000007FC7C00000000000000000007FCF800000000000000000 003FEF800000000000000000003FFF000000000000000000003FFF000000000000000000 001FFE000000000000000000001FFE000000000000000000000FFC000000000000000000 000FFC0000000000000000000007F80000000000000000000007F8000000000000000000 0007F00000000000000000000003F00000000000000000000003E0000000000000000000 0001C0000000000000005B78758364>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr8 8 21 /Fj 21 127 df<003FFFFF0000003FFFFF000000007F80000000003F00000000003F0000 0000003F00000000003F00000000003F00000000003F0000000001FFE00000001FFFFE00 00007F3F3F800001F83F07E00007E03F01F8000FC03F00FC001F803F007E003F003F003F 007F003F003F807F003F003F807E003F001F80FE003F001FC0FE003F001FC0FE003F001F C0FE003F001FC0FE003F001FC07E003F001F807F003F003F807F003F003F803F003F003F 001F803F007E000FC03F00FC0007E03F01F80001F83F07E000007F3F3F8000001FFFFE00 000001FFE0000000003F00000000003F00000000003F00000000003F00000000003F0000 0000003F00000000007F800000003FFFFF0000003FFFFF00002A2D7CAC33>8 D<00007FE000000007FFFE0000001FC03F8000007E0007E00001FC0003F80003F80001FC 0007F00000FE000FE000007F001FC000003F801FC000003F803F8000001FC03F8000001F C07F0000000FE07F0000000FE07F0000000FE07F0000000FE07F0000000FE07F0000000F E07F0000000FE07F0000000FE03F8000001FC03F8000001FC03F8000001FC01F8000001F 801FC000003F800FC000003F000FC000003F0007E000007E0007E000007E0003E000007C 0001F00000F80001F00000F80000F00000F00000780001E00000780001E00000380001C0 00C03C0003C030C01C00038030601C00038060600C00030060600E00070060700E000700 E07FFE0007FFE03FFE0007FFC03FFE0007FFC03FFE0007FFC02C2E7DAD33>10 D<00030007000E001C0038007000F001E001C003C0078007800F000F001E001E001E003C 003C003C003C0078007800780078007800F800F800F000F000F000F000F000F000F000F0 00F000F000F000F800F800780078007800780078003C003C003C003C001E001E001E000F 000F000780078003C001C001E000F000700038001C000E0007000310437AB11B>40 DI<0000 038000000000038000000000038000000000038000000000038000000000038000000000 038000000000038000000000038000000000038000000000038000000000038000000000 038000000000038000000000038000000000038000000000038000000000038000000000 03800000000003800000000003800000000003800000FFFFFFFFFFFCFFFFFFFFFFFCFFFF FFFFFFFC0000038000000000038000000000038000000000038000000000038000000000 038000000000038000000000038000000000038000000000038000000000038000000000 038000000000038000000000038000000000038000000000038000000000038000000000 038000000000038000000000038000000000038000000000038000002E2F7CA737>43 D<003FC00000FFF00003E07C0007C03E000F801F000F000F001E0007801E0007803E0007 C03E0007C07C0003E07C0003E07C0003E07C0003E07C0003E0FC0003F0FC0003F0FC0003 F0FC0003F0FC0003F0FC0003F0FC0003F0FC0003F0FC0003F0FC0003F0FC0003F0FC0003 F0FC0003F0FC0003F0FC0003F0FC0003F07C0003E07C0003E07C0003E07E0007E03E0007 C03E0007C03E0007C01F000F800F000F000F801F0007C03E0003F0FC0000FFF000003FC0 001C2D7DAB23>48 D<000C00003C00007C0003FC00FFFC00FC7C00007C00007C00007C00 007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00 007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00007C00 007C00007C00007C00007C00007C00007C00007C00007C0000FE007FFFFE7FFFFE172C7A AB23>I<007F800001FFF0000780FC000E003F001C001F8038000FC070000FC0600007E0 F00007E0FC0007F0FE0007F0FE0003F0FE0003F0FE0003F07C0007F0000007F0000007F0 000007E000000FE000000FC000001FC000001F8000003F0000007E0000007C000000F800 0001F0000003E0000007C000000F8000001E0000003C00000078000000F0003000E00030 01C0003003800060070000600E0000E01FFFFFE03FFFFFE07FFFFFC0FFFFFFC0FFFFFFC0 1C2C7DAB23>I<003FC00001FFF00007C0FC000E007E001C003F001C001F803F001FC03F 001FC03F800FC03F000FC03F000FC00C001FC000001FC000001F8000001F8000003F0000 003E0000007C000000F8000003F00000FFC00000FFF0000000FC0000003F0000001F8000 001FC000000FC000000FE000000FE0000007F0000007F0380007F07C0007F0FE0007F0FE 0007F0FE0007F0FE000FE0F8000FE060000FC070001FC038001F801E003F000780FC0001 FFF000007FC0001C2D7DAB23>I<00000E0000000E0000001E0000003E0000003E000000 7E000000FE000000FE000001BE000003BE0000033E0000063E00000E3E00000C3E000018 3E0000383E0000303E0000603E0000E03E0000C03E0001803E0003803E0003003E000600 3E000E003E000C003E0018003E0038003E0030003E0060003E00E0003E00FFFFFFFCFFFF FFFC00003E0000003E0000003E0000003E0000003E0000003E0000003E0000003E000000 3E0000007F00001FFFFC001FFFFC1E2D7EAC23>I<0C0001800FC01F800FFFFF000FFFFE 000FFFFC000FFFF0000FFFC0000C7E00000C0000000C0000000C0000000C0000000C0000 000C0000000C0000000C0000000C1FC0000C7FF8000DE07C000F801F000F001F800E000F 800C0007C0000007E0000007E0000003E0000003F0000003F0000003F0000003F0780003 F0FC0003F0FC0003F0FC0003F0FC0003F0F80007E0E00007E0600007C070000FC038000F 801C001F000E003E000780F80001FFE000007F80001C2D7DAB23>I<0003F800000FFE00 003E078000F8018001F007C003E00FC007C00FC00F800FC00F800FC01F0007801F000000 3E0000003E0000007E0000007E0000007C0000007C0FC000FC3FF000FCF07C00FDC01E00 FF800F00FF000F80FF0007C0FE0007E0FE0007E0FE0003E0FC0003F0FC0003F0FC0003F0 FC0003F07C0003F07C0003F07C0003F07E0003F07E0003F03E0003E03E0007E01E0007E0 1F0007C00F000F8007801F0003C03E0001E07C00007FF000001FC0001C2D7DAB23>I61 D73 D82 D<001F800000FFF00003E0780007C03E000F801E001F001F001F000F80 3E000F807E0007807E0007C07C0007C0FC0007C0FC0007C0FC0007C0FFFFFFC0FFFFFFC0 FC000000FC000000FC000000FC000000FC0000007E0000007E0000003E0000C03F0000C0 1F0001C00F8003800FC0030003E00F0001F03C00007FF800001FC0001A207E9E1F>101 D<003F00F800FFC3FE03E1FF1E07807C1E0F807C0C1F003E001F003E003E001F003E001F 003E001F003E001F003E001F003E001F003E001F001F003E001F003E000F807C00078078 000FE1F0000CFFC0001C3F00001C0000001C0000001C0000001E0000001F0000000FFFF8 000FFFFF0007FFFFC00FFFFFF01E0007F83C0000F87800007CF800007CF000003CF00000 3CF000003CF000003CF800007C7C0000F83E0001F01F0003E007E01F8001FFFE00003FF0 001F2D7E9D23>103 D<07C07F0007F000FFC3FFC03FFC00FFC783F0783F000FCE01F8E0 1F8007DC00F9C00F8007F800FF800FC007F0007F0007C007E0007E0007C007E0007E0007 C007C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C0 07C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C007 C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C007C0007C0007C007C0 007C0007C007C0007C0007C007C0007C0007C00FE000FE000FE0FFFE0FFFE0FFFEFFFE0F FFE0FFFE371E7E9D3C>109 D<07C0FE0000FFC3FF8000FFC703E0000FDE01F00007F801 F00007F000F80007F000F80007E000F80007E000F80007C000F80007C000F80007C000F8 0007C000F80007C000F80007C000F80007C000F80007C000F80007C000F80007C000F800 07C000F80007C000F80007C000F80007C000F80007C000F80007C000F80007C000F80007 C000F8000FE001FC00FFFE1FFFC0FFFE1FFFC0221E7E9D27>I<01FE1807FFB81E01F83C 00F8780078F00038F00038F00018F00018F80018FC0018FF00007FF0003FFF001FFFC00F FFF001FFF8001FFC0001FCC0007EC0003EC0003EE0001EE0001EF0001EF0001EF8003CF8 003CFC0078FF01F0E3FFC0C0FF0017207E9E1C>115 D<0780080FE01C1FF8383FFFF070 7FE0E01FC040078016077AAC23>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmsy10 12 33 /Fk 33 115 df<7FFFFFFFFFFFFFE0FFFFFFFFFFFFFFF0FFFFFFFFFFFFFFF07FFFFFFFFF FFFFE03C04789A4D>0 D<1F003F807FC0FFE0FFE0FFE0FFE0FFE07FC03F801F000B0B78 9E1C>I<600000000006F8000000000FFC000000001F7E000000003F3F000000007E1F80 000000FC0FC0000001F807E0000003F003F0000007E001F800000FC000FC00001F80007E 00003F00003F00007E00001F8000FC00000FC001F8000007E003F0000003F007E0000001 F80FC0000000FC1F800000007E3F000000003F7E000000001FFC000000000FF800000000 07F00000000007F0000000000FF8000000001FFC000000003F7E000000007E3F00000000 FC1F80000001F80FC0000003F007E0000007E003F000000FC001F800001F8000FC00003F 00007E00007E00003F0000FC00001F8001F800000FC003F0000007E007E0000003F00FC0 000001F81F80000000FC3F000000007E7E000000003FFC000000001FF8000000000F6000 00000006303072B04D>I<00000000C00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 00007FFFFFFFFFFFFFFF80FFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFC07FFFFFFFFFFFFF FF8000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E00000000000000001E00000 000000000001E00000000000000001E00000000000000001E0000000007FFFFFFFFFFFFF FF80FFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFC07FFFFFFFFFFFFFFF8042427BC14D>6 D<7FFFFFFFFFFFFFFF80FFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFC07FFFFFFFFFFFFFFF 8000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E0000000007FFFFFFFFFFFFFFF 80FFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFC07FFFFFFFFFFFFFFF8000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000001E00000000000000001E00000000000000001E0000000 0000000001E00000000000000000C00000000042427BB14D>I<0000001FFE0000000000 0001FFFFE000000000000FFFFFFC00000000003FF003FF0000000000FF00003FC0000000 01F8000007E000000007E0000001F80000000F800000007C0000001F000000003E000000 3C000000000F000000780000000007800000F00000000003C00001E00000000001E00003 C00000000000F0000380000000000070000780000000000078000F0000000000003C000E 0000000000001C001E0000000000001E001C0000000000000E003C0000000000000F0038 000000000000070038000000000000070078000000000000078070000000000000038070 0000000000000380700000000000000380F000000000000003C0E000000000000001C0E0 00000000000001C0E000000000000001C0FFFFFFFFFFFFFFFFC0FFFFFFFFFFFFFFFFC0FF FFFFFFFFFFFFFFC0E000000000000001C0E000000000000001C0E000000000000001C0E0 00000000000001C0F000000000000003C070000000000000038070000000000000038070 00000000000003807800000000000007803800000000000007003800000000000007003C 0000000000000F001C0000000000000E001E0000000000001E000E0000000000001C000F 0000000000003C0007800000000000780003800000000000700003C00000000000F00001 E00000000001E00000F00000000003C000007800000000078000003C000000000F000000 1F000000003E0000000F800000007C00000007E0000001F800000001F8000007E0000000 00FF00003FC0000000003FF003FF00000000000FFFFFFC000000000001FFFFE000000000 00001FFE0000000042427BB94D>9 D<00000000000000E000000000000003F000000000 00000FF00000000000003FE0000000000000FF80000000000003FE0000000000000FF800 00000000003FE0000000000000FF80000000000003FE0000000000000FF8000000000000 3FE0000000000000FF80000000000003FE0000000000001FF80000000000007FE0000000 000001FF80000000000007FE0000000000001FF00000000000007FC0000000000001FF00 000000000007FC0000000000001FF00000000000007FC0000000000001FF000000000000 07FC0000000000001FF00000000000007FC0000000000000FF00000000000000FF000000 000000007FC00000000000001FF000000000000007FC00000000000001FF000000000000 007FC00000000000001FF000000000000007FC00000000000001FF000000000000007FC0 0000000000001FF000000000000007FC00000000000001FF800000000000007FE0000000 0000001FF800000000000007FE00000000000000FF800000000000003FE0000000000000 0FF800000000000003FE00000000000000FF800000000000003FE00000000000000FF800 000000000003FE00000000000000FF800000000000003FE00000000000000FF000000000 000003F000000000000000E0000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000007FFFFFFF FFFFFFE0FFFFFFFFFFFFFFF0FFFFFFFFFFFFFFF07FFFFFFFFFFFFFE03C4E78BE4D>20 D<7000000000000000FC00000000000000FF000000000000007FC00000000000001FF000 000000000007FC00000000000001FF000000000000007FC00000000000001FF000000000 000007FC00000000000001FF000000000000007FC00000000000001FF000000000000007 FC00000000000001FF800000000000007FE00000000000001FF800000000000007FE0000 0000000000FF800000000000003FE00000000000000FF800000000000003FE0000000000 0000FF800000000000003FE00000000000000FF800000000000003FE00000000000000FF 800000000000003FE00000000000000FF00000000000000FF00000000000003FE0000000 000000FF80000000000003FE0000000000000FF80000000000003FE0000000000000FF80 000000000003FE0000000000000FF80000000000003FE0000000000000FF800000000000 03FE0000000000001FF80000000000007FE0000000000001FF80000000000007FE000000 0000001FF00000000000007FC0000000000001FF00000000000007FC0000000000001FF0 0000000000007FC0000000000001FF00000000000007FC0000000000001FF00000000000 007FC0000000000000FF00000000000000FC000000000000007000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000007FFFFFFFFFFFFFE0FFFFFFFFFFFFFFF0FFFFFF FFFFFFFFF07FFFFFFFFFFFFFE03C4E78BE4D>I<0000007FFFFFFFE0000007FFFFFFFFF0 00003FFFFFFFFFF00000FFFFFFFFFFE00003FFC0000000000007FC0000000000000FE000 00000000003F800000000000007F00000000000000FC00000000000001F8000000000000 03F000000000000007E000000000000007C00000000000000F800000000000001F800000 000000001F000000000000003E000000000000003E000000000000003C00000000000000 7C000000000000007C000000000000007800000000000000F800000000000000F8000000 00000000F000000000000000F000000000000000F000000000000000F000000000000000 F000000000000000F000000000000000F000000000000000F000000000000000F8000000 00000000F80000000000000078000000000000007C000000000000007C00000000000000 3C000000000000003E000000000000003E000000000000001F000000000000001F800000 000000000F8000000000000007C000000000000007E000000000000003F0000000000000 01F800000000000000FC000000000000007E000000000000003F800000000000001FE000 000000000007FC00000000000003FF80000000000000FFFFFFFFFFE000003FFFFFFFFFF0 000007FFFFFFFFF0000000FFFFFFFFE03C3A78B54D>26 D<0000000000000000F0000000 0000000000000000F00000000000000000000000F00000000000000000000000F8000000 00000000000000007800000000000000000000007800000000000000000000007C000000 00000000000000003C00000000000000000000003C00000000000000000000003E000000 00000000000000001E00000000000000000000001F00000000000000000000000F800000 00000000000000000F800000000000000000000007C00000000000000000000003E00000 000000000000000003F00000000000000000000001F80000000000000000000000FC0000 0000000000000000007E00000000000000000000003F00000000000000000000001F8000 0000000000000000000FE00000000000000000000003F8007FFFFFFFFFFFFFFFFFFFFE00 FFFFFFFFFFFFFFFFFFFFFF80FFFFFFFFFFFFFFFFFFFFFF807FFFFFFFFFFFFFFFFFFFFE00 00000000000000000003F8000000000000000000000FE0000000000000000000001F8000 0000000000000000003F00000000000000000000007E0000000000000000000000FC0000 000000000000000001F80000000000000000000003F00000000000000000000003E00000 000000000000000007C0000000000000000000000F80000000000000000000000F800000 00000000000000001F00000000000000000000001E00000000000000000000003E000000 00000000000000003C00000000000000000000003C00000000000000000000007C000000 0000000000000000780000000000000000000000780000000000000000000000F8000000 0000000000000000F00000000000000000000000F00000000000000000000000F0000000 59347BB264>33 D<0001FF00000000003FC00000000FFFE000000003FFF80000003FFFFC 0000000FFFFE0000007FFFFF0000003FE01F000001FFFFFF8000007E0007C00003F803FF E00001F80001E00007E0007FF00003F00000F0000780003FF80007C0000070000F00001F FC000F80000038001E000007FE001F0000001C001C000003FF003E0000000C0038000001 FF807C0000000E0038000001FFC0F8000000060070000000FFE0F8000000070070000000 7FF1F00000000700600000003FF3E00000000300600000001FFBC00000000300E0000000 1FFFC00000000380C00000000FFF800000000180C000000007FF000000000180C0000000 03FF000000000180C000000001FF800000000180C000000001FFC00000000180C0000000 00FFC00000000180C0000000007FE00000000180C0000000007FF00000000180C0000000 00FFF80000000180E000000001FFFC00000003806000000001EFFC000000030060000000 03E7FE00000003007000000007C7FF0000000700700000000F83FF800000070030000000 0F81FFC000000E00380000001F00FFC000000E00180000003E007FE000001C001C000000 7C003FF000003C000E000000F8001FFC0000780007000001F0000FFE0000F00007800007 E00007FF0003F00003C0000FC00003FFE00FE00001F0003F000000FFFFFFC000007C03FE 0000007FFFFF0000003FFFF80000001FFFFE0000000FFFE000000003FFF800000001FE00 000000007FC00000592D7BAB64>49 D<000000FFFFFF00000007FFFFFF8000003FFFFFFF 800000FFFFFFFF000003FF800000000007FC00000000001FE000000000003F8000000000 007E000000000000FC000000000001F8000000000003F0000000000007E0000000000007 C000000000000F8000000000001F8000000000001F0000000000003E0000000000003E00 00000000003C0000000000007C0000000000007C00000000000078000000000000F80000 00000000F8000000000000F0000000000000F0000000000000FFFFFFFFFFFF00FFFFFFFF FFFF80FFFFFFFFFFFF80FFFFFFFFFFFF00F0000000000000F0000000000000F800000000 0000F8000000000000780000000000007C0000000000007C0000000000003C0000000000 003E0000000000003E0000000000001F0000000000001F8000000000000F800000000000 07C0000000000007E0000000000003F0000000000001F8000000000000FC000000000000 7E0000000000003F8000000000001FE0000000000007FC000000000003FF800000000000 FFFFFFFF0000003FFFFFFF80000007FFFFFF80000000FFFFFF00313A78B542>I<600000 00000018F000000000003CF800000000007CF800000000007C780000000000787C000000 0000F87C0000000000F83C0000000000F03E0000000001F03E0000000001F01F00000000 03E01F0000000003E00F0000000003C00F8000000007C00F8000000007C0078000000007 8007C00000000F8007C00000000F8003E00000001F0003E00000001F0001E00000001E00 01F00000003E0001F00000003E0000F00000003C0000FFFFFFFFFC0000FFFFFFFFFC0000 7FFFFFFFF800007FFFFFFFF800003C000000F000003E000001F000003E000001F000001E 000001E000001F000003E000001F000003E000000F000003C000000F800007C000000F80 0007C0000007C0000F80000007C0000F80000003C0000F00000003E0001F00000003E000 1F00000001E0001E00000001F0003E00000001F0003E00000000F8007C00000000F8007C 00000000780078000000007C00F8000000007C00F8000000003C00F0000000003E01F000 0000003E01F0000000001F03E0000000001F03E0000000000F03C0000000000F87C00000 00000F87C0000000000787800000000007CF800000000007CF800000000003FF00000000 0003FF000000000001FE000000000001FE000000000001FE000000000000FC0000000000 00FC000000000000FC0000000000007800000000000030000000364780C437>56 D<00000001800000000003C00000000003C00000000007C00000000007C0000000000780 000000FF8F80000003FFEF8000000F80FF0000003E003F0000007C001F000000F8001F80 0001F0001FC00003E0003FE00003C0003FE00007C0003DF0000780003CF0000F80007CF8 000F80007CF8001F0000787C001F0000F87C003F0000F87E003F0000F07E003F0000F07E 003F0001F07E007F0001F07F007E0001E03F007E0003E03F007E0003E03F007E0003C03F 007E0003C03F00FE0007C03F80FE0007C03F80FE0007803F80FE000F803F80FE000F803F 80FE000F003F80FE000F003F80FE001F003F80FE001F003F80FE001E003F80FE003E003F 80FE003E003F80FE003C003F80FE003C003F80FE007C003F80FE007C003F80FE0078003F 80FE0078003F80FE00F8003F80FE00F8003F80FE00F0003F80FE01F0003F80FE01F0003F 807E01E0003F007E01E0003F007E03E0003F007E03E0003F007F03C0007F007F07C0007F 003F07C0007E003F0780007E003F0780007E003F0F80007E001F0F80007C001F8F0000FC 000F9F0000F8000F9F0000F8000FDE0001F80007DE0001F00003FE0003E00003FE0003E0 0001FC0007C00000FC000F8000007C001F0000007E003E0000007F80F8000000FBFFE000 0000F8FF80000000F00000000001F00000000001F00000000001E00000000001E0000000 0000C00000000029557CCC32>59 D<000001C00001FE00000007C0001FFF8000001FC000 FFFFE000007F8003FFFFF00001FF800FFFFFF80007FF803FFFFFF8000FFF807F01FFFC00 1FFF81F8007FFC003CFF83E0001FFE0020FF87C0000FFE0000FF0F800007FE0000FF1F00 0007FE0000FF3E000003FE0000FF7E000003FE0001FFFC000003FC0001FFF8000003FC00 01FFF8000003F80001FFF0000003F80001FFF0000007F00001FFE0000007E00003FFC000 000FC00003FFC000000F800003FF8000001F000003FF8000007E000003FF800000F80000 03FF000003F0000007FF00001FC0000007FE00007F80000007FE0003FE00000007FC001F F800000007FC00FFFF0000000FFC03FFFFC000000FF807FFFFF000000FF80FFFFFF80000 0FF81FFFFFFC00000FF01007FFFE00001FF00000FFFF00001FF000003FFF00001FE00000 0FFF80001FE0000007FF80003FE0000003FFC0003FC0000001FFC0003FC0000000FFE000 3FC0000000FFE0003FC00000007FE0007F800000007FE0007F800000003FE0007F800000 003FE0007F800000003FE000FF000000003FE000FF000000003FC000FF000000003FC000 FE000000003FC001FE000000003F8001FE000000007F8001FC000000007F0003FC000000 007F0003FC00000000FE0003F800000000FC0007F800000001F80007F020000001F00007 F1F0000003E0000FF7F8000007C0000FEFFE00001F80001FFFFF80007E00001FDFFFF007 FC00001FDFFFFFFFF000003F8FFFFFFFC000003F07FFFFFF0000007E01FFFFF800000078 007FFFC0000000E0000FFC000000003F487DC541>66 D<0000000003FE00000000003FFF 8000000001FFFFC000000007FFFFC00000001FFFFFE00000007FFFFFE0000001FE01FFE0 000003F0007FE000000FC0003FE000001F00003FE000003E00003FC000007C00003FC000 00F800003F800001F000003F800003F000007F800007E000007F00000FC00000FF00001F 800000FE00001F800000FE00003F000001FC00007F000001FC0000FE000003F80000FE00 0003F00001FC000007C00001FC000007000003F8000000000003F8000000000007F80000 00000007F000000000000FF000000000000FF000000000000FE000000000001FE0000000 00001FE000000000001FC000000000003FC000000000003FC000000000003FC000000000 007FC000000000007F8000000000007F8000000000007F8000000000007F800000000000 FF800000000000FF800000000000FF800000000000FF800000000000FF800000000000FF 800000000000FF800000000000FF800000000000FF800000000000FFC00000000000FFC0 0000000200FFC00000001E00FFC00000003E007FE0000000FC007FE0000001F8007FF000 0003F0007FF0000003E0003FF8000007C0003FFC00000F80001FFE00001F00001FFF0000 3E00000FFFC000FC00000FFFF803F0000007FFFFFFE0000003FFFFFF80000001FFFFFE00 000000FFFFF8000000003FFFC00000000007FE0000000033487FC534>I<0000001FFFFF C0000000000003FFFFFFFF00000000001FFFFFFFFFE000000000FFFFFFFFFFF800000003 FFFFFFFFFFFE0000000FFFFFFFFFFFFF8000003FF07FC03FFFFFC00000FE007FC000FFFF E00001F8007FC0001FFFF00003E0007F800007FFF80007C0007F800001FFF8000FC0007F 8000007FFC001F80007F8000003FFE003F8000FF8000001FFE007F8000FF8000000FFE00 7F0000FF80000007FF00FE0000FF00000007FF00FC0000FF00000003FF00F00000FF0000 0003FF80C00000FF00000001FF80000001FF00000001FF80000001FF00000001FF800000 01FE00000000FF80000001FE00000000FF80000001FE00000000FF80000001FE00000000 FF80000003FE00000000FF80000003FC00000000FF80000003FC00000000FF80000003FC 00000000FF00000003FC00000000FF00000007F800000000FF00000007F800000000FF00 000007F800000001FE00000007F800000001FE0000000FF000000001FE0000000FF00000 0001FC0000000FF000000003FC0000000FF000000003F80000001FE000000003F8000000 1FE000000007F00000001FE000000007F00000001FC00000000FE00000003FC00000000F C00000003FC00000001FC00000003F800000001F800000007F800000003F000000007F80 0000007E000000007F000000007C00000000FF00000000F800000000FF00000001F00000 0000FE00000003E000000001FE00000007C000000001FE0000001F8000000001FC000000 3E0000000003FC0000007C0000000003F8000001F80000000003F8000007E00000000007 F800001FC00000000007F00000FF00000000000FF00007FC00000000000FE001FFF00000 0000000FFFFFFFC000000000007FFFFFFE000000000000FFFFFFF0000000000001FFFFFF 80000000000003FFFFFC00000000000007FFFF0000000000000049447EC34D>I<000000 0007FFFFFFFFF8000000003FFFFFFFFFFE00000001FFFFFFFFFFFF00000007FFFFFFFFFF FF0000001FFFFFFFFFFFFF0000007FFFFFFFFFFFFF000001FC00FF000007FE000003F001 FF000001FC000007C001FE000001F000000F8001FE0000008000001F8001FE0000000000 003F0001FE0000000000007F0003FC000000000000FF0003FC000000000000FE0003FC00 0000000001FC0003FC000000000001F80007F8000000000001F00007F8000000000003E0 0007F8000000000001000007F800000000000000000FF000000000000000000FF0000000 00000000000FF000000000000000000FE000000000000000001FE000000000000000001F E000000000000000001FE000000000000000003FC000000000000000003FC00000000000 0000003FC000000000000000003F8000000000000000007F8000000000000000007FFFFF FFC000000000007FFFFFFFC00000000000FFFFFFFFC00000000000FFFFFFFF8000000000 01FFFFFFFF000000000001FFFFFFFC000000000001FC000070000000000003FC00000000 0000000003F8000000000000000003F8000000000000000007F0000000000000000007F0 00000000000000000FF000000000000000000FE000000000000000001FE0000000000000 00001FC000000000000000001FC000000000000000003F8000000000000000003F800000 0000000000007F0000000000000000007F000000000000000000FE000000000000000000 FE000000000000000001FC000000000000000001FC000000000000000003F80000000000 00018003F80000000000000F8007F00000000000001FC007F00000000000003FE00FE000 00000000007FF00FC0000000000000FFFC1F800000000000007FFF1F000000000000007F FFFE000000000000003FFFFC000000000000001FFFF0000000000000000FFFE000000000 00000003FF800000000000000000FC000000000000000050477EC348>70 D<0000007FC00000000060000007FFE000000001E000003FFFF000000007E00000FFFFF0 0000000FE00003FFFFF80000001FC0000FFFFFF80000003FC0001FC03FF80000003F8000 7E001FF80000003F8000F8000FF80000007F8001F0000FF80000007F0003E0000FF80000 00FF0007E0000FF0000000FF000FC0000FF0000000FE001F80000FF0000001FE003F8000 0FF0000001FE003F00001FF0000001FC007E00001FF0000003FC00FC00001FF0000003FC 00F000001FE0000003F800C000001FE0000007F8000000001FE0000007F8000000001FE0 000007F0000000003FE000000FF0000000003FC000000FF0000000003FC000000FE00000 00003FC000001FE0000000003FC000001FE0000000007F8000001FC0000000007F800000 3FC0000000007F8000003FC0000000007F8000003FC000000000FF0000007F8000000000 FF0000007F8000000000FF0000007F800000001FFFFFFFFFFF00000000FFFFFFFFFFFF00 000001FFFFFFFFFFFF00000003FFFFFFFFFFFF00000007FFFFFFFFFFFE0000000FFFFFFF FFF9FE0000000003FC000001FE0000000003F8000001FE0000000007F8000003FC000000 0007F8000003FC0000000007F8000003FC000000000FF0000003FC000000000FF0000007 F8000000000FF0000007F8000000000FE0000007F8000000001FE0000007F8000000001F E000000FF8000000001FC000000FF0000000003FC000000FF0000000003FC000000FF000 0000003F8000000FF0000000007F8000001FF0000000007F0000001FF0000000007F0000 001FF000000000FF0000001FE000000000FE0000001FE000000001FE0000001FE0001800 01FE0000001FE000F80001FC0000003FE001F80003FC0000003FE003F00003F80000003F E007E00003F80000003FF00FC00007F80000003FF80F800007F00000003FFFFF00000FE0 0000003FFFFE00000FC00000001FFFF800000F800000001FFFE000000C000000000FFF00 0000000000000007F800004D497EC354>72 D<00000007FFFFFFFFC0000001FFFFFFFFFF C000000FFFFFFFFFFF8000003FFFFFFFFFFF000001FFFFFFFFFFFC000003FFFFFFFFFFF0 00000FFC0000FC000000001F800001F8000000003F000003F8000000007E000007F00000 0000FE000007F000000001FE00000FE000000001FC00000FE000000003F800001FC00000 0003E000001FC000000003C000003FC0000000020000003F80000000000000007F800000 00000000007F80000000000000007F0000000000000000FF0000000000000000FF000000 0000000000FF0000000000000001FE0000000000000001FE0000000000000001FE000000 0000000001FC0000000000000003FC0000000000000003FC0000000000000003FC000000 0000000007F80000000000000007F80000000000000007F80000000000000007F8000000 000000000FF0000000000000000FF0000000000000000FF0000000000000000FF0000000 000000001FE0000000000000001FE0000000000000001FE0000000000000001FE0000000 000000003FC0000000000000003FC0000000000000003FC0000000000000003F80000000 000000007F80000000000000007F80000000000000007F0000000000000000FF00000000 00000000FF0000000000000000FE0000000000000001FE0000000000000001FC00000000 00000001FC0000000000000003F80000070000000003F000001F0000000007F000003F00 00000007E000007E000000000FC00000FC000000001F800001F8000000001F000001F000 0001FFFFFFFFFFE000000FFFFFFFFFFF8000001FFFFFFFFFFF0000003FFFFFFFFFFC0000 007FFFFFFFFFE0000000FFFFFFFFFF00000000424483C336>I<00000000007FF0000000 000007FFFE00000000003FFFFF8000000000FFFFFFE000000003FFFFFFF00000000FFFFF FFF80000001FC00FFFF80000007E0001FFFC000000F800007FFC000001F000001FFC0000 03F000000FFC000007E0000007FC00000FE0000007F800001FE0000007F800001FC00000 07F000003FC0000007E000003FC000000FC000003FC000000F0000007FC0000008000000 7FC00000000000007FC00000000000007FE00000000000007FE00000000000007FF00000 000000007FF80000000000003FFC0000000000003FFE0000000000001FFF800000000000 1FFFE000000000000FFFF8000000000007FFFE000000000003FFFFC00000000001FFFFF0 00000000007FFFFC00000000001FFFFE000000000007FFFF800000000001FFFFC0000000 00003FFFE000000000000FFFF0000000000003FFF8000000000001FFF80000000000007F FC0000000000003FFC00000E0000001FFC00007C0000000FFE0001F800000007FE0003F0 00000007FE0007E000000007FE000FC000000003FE001FC000000003FE003F8000000003 FE003F8000000003FC007F8000000003FC007F8000000003FC00FF8000000003F800FF80 00000007F000FF8000000007F000FFC000000007E000FFC00000000FC000FFE00000001F 8000FFF00000001F00007FF80000003E00007FFC0000007C00003FFF000001F800003FFF C00007E000001FFFFC007FC000000FFFFFFFFF00000007FFFFFFFC00000003FFFFFFF000 000000FFFFFF80000000003FFFFC000000000003FFC0000000003E487EC53C>83 D<0000FE0000000000180007FF0000000000F8001FFF0000000001F8007FFF8000000003 F801FFFF8000000007F007FFFF800000000FF00FC1FF800000000FF01F00FF800000001F E03C00FF800000001FE00000FF000000001FC00000FF000000003FC00000FF000000003F C00000FE000000003F800001FE000000007F800001FE000000007F800001FC00000000FF 000003FC00000000FF000003FC00000000FF000003F800000001FE000007F800000001FE 000007F000000003FE000007F000000003FC00000FF000000007FC00000FE000000007FC 00001FE00000000FFC00001FC00000001FF800001FC00000001FF800003F800000003FF8 00003F800000003FF000007F800000007FF000007F000000007FF00000FF00000000FFE0 0000FE00000001FFE00000FE00000001FFE00001FC00000003FFE00001FC00000007FFC0 0003FC00000007FFC00003F80000000FFFC00007F80000001FFFC00007F00000001FFF80 0007F00000003F7F80000FF00000007E7F80000FE00000007E7F80001FE0000000FCFF00 001FE0000001F8FF00001FC0000003F0FF00003FC0000003E0FF00003FC0000007E1FE00 003FC000000FC1FE00007F8000001F81FE00007F8000003F01FE00007F8000003E03FC00 007F8000007C03FC0000FF800000F803FC0000FF800001F003FC0000FF800003E007FC00 00FF800007C007FC0000FF80000F8007F80000FFC0001F0007F80000FFC0003E0007F800 00FFC000FC0007F80000FFE001F0000FF800007FF007E0000FF800007FFC0FC0000FF830 007FFFFF00000FFDF0003FFFFC00000FFFE0003FFFF800000FFFC0001FFFE000000FFF00 000FFF00000007FE000003F800000007F80000000000000003C00000454781C33E>85 D<07F00000000000700000001E001FFC0000000001F00000001F803FFF0000000007F800 00003FC07FFF800000000FF80000003FE0FFFFC00000000FF80000007FE007FFE0000000 0FFC0000007FF001FFE000000007FC0000007FF0007FF00000000FFC0000007FF0003FF8 0000000FFE0000007FF0001FF80000001FFE0000001FF0001FF80000003FFE00000007F0 000FFC0000003FFF00000003F00007FC00000079FF00000001F00007FC00000079FF0000 0001F00007FE000000F1FF00000000F00003FE000000F0FF80000000F00003FE000001E0 FF80000000F00003FE000001C0FF80000000E00001FE000003C0FFC0000000E00001FE00 0007807FC0000001E00001FF000007807FC0000001C00001FF00000F007FC0000001C000 01FF00000F003FC0000003C00001FF00001E003FE0000003800000FF00003E003FE00000 03800000FF00003C003FE0000007000000FF000078003FE0000007000000FF000078001F F000000F000000FF0000F0001FF000000E000000FF0001F0001FF000001E000000FF0001 E0001FF000001C000000FF0003C0000FF000003C000000FF0007C0000FF8000078000000 FF000780000FF8000078000000FF000F80000FF80000F0000000FF000F00000FF80000F0 000000FF001E000007F80001E0000000FF003E000007F80003E0000000FF007C000007FC 0003C0000000FF0078000007FC000780000000FF00F8000007FC000F80000000FE01F000 0007FC000F00000000FE01F0000003FC001F00000000FE03E0000003FC003E00000000FE 07C0000003FC003C00000001FE0780000003FE007C00000001FE0F80000003FE00F80000 0001FE1F00000003FE00F000000001FE3E00000003FE01F000000001FE3E00000001FE03 E000000001FC7C00000001FE07C000000001FCF800000001FE07C000000001FDF8000000 01FE0F8000000001FDF000000001FE1F0000000003FFE000000001FE3F0000000003FFC0 00000001FE7E0000000003FFC000000001FF7C0000000003FF8000000001FFF800000000 03FF0000000001FFF80000000003FE0000000001FFF00000000003FE0000000000FFE000 00000007FC0000000000FFC00000000007F80000000000FF800000000007F00000000000 FF800000000007E00000000000FF000000000007E00000000000FE00000000000FC00000 000000FC00000000000F800000000000F800000000000F000000000000F800000000000E 000000000000F000000000000E000000000000E000000000000C000000000000C0000000 0064487DC362>87 D<6000000000000CF000000000001EF000000000001EF00000000000 1EF000000000001EF000000000001EF000000000001EF000000000001EF000000000001E F000000000001EF000000000001EF000000000001EF000000000001EF000000000001EF0 00000000001EF000000000001EF000000000001EF000000000001EF000000000001EF000 000000001EF000000000001EF000000000001EF000000000001EF000000000001EF00000 0000001EF000000000001EF000000000001EF000000000001EF000000000001EF0000000 00001EF000000000001EF000000000001EF000000000001EF000000000001EF000000000 001EF000000000001EF000000000001EF000000000001EF000000000001EF00000000000 1EF000000000001EF000000000001EF000000000001EF800000000003EF800000000003E 7800000000003C7C00000000007C7E0000000000FC3E0000000000F81F0000000001F01F 8000000003F00FC000000007E007E00000000FC003F80000003F8001FE000000FF00007F C00007FC00003FFC007FF800000FFFFFFFE0000003FFFFFF800000007FFFFC0000000007 FFC00000373D7BBA42>91 D<000007FFC0000000007FFFFC00000003FFFFFF8000000FFF FFFFE000003FFC007FF800007FC00007FC0001FE000000FF0003F80000003F8007E00000 000FC00FC000000007E01F8000000003F01F0000000001F03E0000000000F87E00000000 00FC7C00000000007C7800000000003CF800000000003EF800000000003EF00000000000 1EF000000000001EF000000000001EF000000000001EF000000000001EF000000000001E F000000000001EF000000000001EF000000000001EF000000000001EF000000000001EF0 00000000001EF000000000001EF000000000001EF000000000001EF000000000001EF000 000000001EF000000000001EF000000000001EF000000000001EF000000000001EF00000 0000001EF000000000001EF000000000001EF000000000001EF000000000001EF0000000 00001EF000000000001EF000000000001EF000000000001EF000000000001EF000000000 001EF000000000001EF000000000001EF000000000001EF000000000001EF00000000000 1EF000000000001EF000000000001EF000000000001EF000000000001EF000000000001E 6000000000000C373D7BBA42>I<0000000FE0000000FFE0000003FC0000000FE0000000 3FC00000007F80000000FF00000000FE00000001FC00000001FC00000003F800000003F8 00000003F800000003F800000003F800000003F800000003F800000003F800000003F800 000003F800000003F800000003F800000003F800000003F800000003F800000003F80000 0003F800000003F800000003F800000003F800000003F800000003F800000003F8000000 03F800000003F800000003F800000003F800000003F800000003F800000003F800000003 F800000007F000000007F00000000FE00000001FE00000003FC00000007F80000000FE00 000007F8000000FFE0000000FFE000000007F800000000FE000000007F800000003FC000 00001FE00000000FE000000007F000000007F000000003F800000003F800000003F80000 0003F800000003F800000003F800000003F800000003F800000003F800000003F8000000 03F800000003F800000003F800000003F800000003F800000003F800000003F800000003 F800000003F800000003F800000003F800000003F800000003F800000003F800000003F8 00000003F800000003F800000003F800000003F800000003F800000003F800000001FC00 000001FC00000000FE00000000FF000000007F800000003FC00000000FE000000003FC00 000000FFE00000000FE0236479CA32>102 DI<00000C00001E00003E00003E0000 3C00007C00007C0000F80000F80000F00001F00001F00003E00003E00003C00007C00007 C0000F80000F80000F00001F00001F00003E00003E00003C00007C00007C0000780000F8 0000F80001F00001F00001E00003E00003E00007C00007C0000780000F80000F80001F00 001F00001E00003E00003E00007C00007C0000780000F80000F80000F80000F800007800 007C00007C00003E00003E00001E00001F00001F00000F80000F800007800007C00007C0 0003E00003E00001E00001F00001F00000F80000F800007800007C00007C00003C00003E 00003E00001F00001F00000F00000F80000F800007C00007C00003C00003E00003E00001 F00001F00000F00000F80000F800007C00007C00003C00003E00003E00001E00000C1764 76CA27>I<600000F00000F80000F800007800007C00007C00003E00003E00001E00001F 00001F00000F80000F800007800007C00007C00003E00003E00001E00001F00001F00000 F80000F800007800007C00007C00003C00003E00003E00001F00001F00000F00000F8000 0F800007C00007C00003C00003E00003E00001F00001F00000F00000F80000F800007C00 007C00003C00003E00003E00003E00003E00003C00007C00007C0000F80000F80000F000 01F00001F00003E00003E00003C00007C00007C0000F80000F80000F00001F00001F0000 3E00003E00003C00007C00007C0000780000F80000F80001F00001F00001E00003E00003 E00007C00007C0000780000F80000F80001F00001F00001E00003E00003E00007C00007C 0000780000F80000F80000F0000060000017647BCA27>I<60F0F0F0F0F0F0F0F0F0F0F0 F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0 F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0F0 F0F0F0F0F0F0F0F0F0F0F0F0F0F0F060046474CA1C>I<70000700F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0000780F0 000780F0000780F0000780F0000780F0000780F000078070000700196474CA32>I<6000 000000F000000000F800000000F80000000078000000007C000000007C000000003C0000 00003E000000003E000000001E000000001F000000001F000000000F800000000F800000 00078000000007C000000007C000000003C000000003E000000003E000000001E0000000 01F000000001F000000000F800000000F80000000078000000007C000000007C00000000 3C000000003E000000003E000000001E000000001F000000001F000000000F800000000F 80000000078000000007C000000007C000000003C000000003E000000003E000000001E0 00000001F000000001F000000000F800000000F80000000078000000007C000000007C00 0000003C000000003E000000003E000000001F000000001F000000000F000000000F8000 00000F80000000078000000007C000000007C000000003C000000003E000000003E00000 0001F000000001F000000000F000000000F800000000F80000000078000000007C000000 007C000000003C000000003E000000003E000000001F000000001F000000000F00000000 0F800000000F80000000078000000007C000000007C000000003C000000003E000000003 E000000001F000000001F000000000F000000000F800000000F80000000078000000007C 000000007C000000003C000000003E000000003E000000001E000000000C27647BCA32> 110 D 114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmr6 6 7 /Fl 7 53 df<000C0038007000E001C00380030007000E000E001C001C00380038003800 7800700070007000F000F000F000F000F000F000F000F000F000F000F000700070007000 78003800380038001C001C000E000E0007000300038001C000E000700038000C0E317AA4 18>40 D I<00FF0003FFC00781E00F00F01E00783C003C3C003C78001E78001E78001E78001EF800 1FF8001FF8001FF8001FF8001FF8001FF8001FF8001FF8001FF8001FF8001FF8001FF800 1F78001E78001E7C003E3C003C3C003C1E00780F00F00781E003FFC000FF0018227DA01E >48 D<00E00001E00007E000FFE000F9E00001E00001E00001E00001E00001E00001E000 01E00001E00001E00001E00001E00001E00001E00001E00001E00001E00001E00001E000 01E00001E00001E00001E00001E00001E00001E00003F000FFFFC0FFFFC012217AA01E> I<01FC0007FF801C0FC03003E06001F06000F8F800F8FC00FCFC00FCFC007C78007C3000 FC0000FC0000F80000F80001F00003E00003C0000780000F00001E0000380000700000E0 0001C00C03800C0600180C00181800183FFFF87FFFF8FFFFF0FFFFF016217CA01E>I<00 FF0003FFC00F03E01C00F01C00F83E00FC3E007C3E007C1E00FC0C00FC0000F80000F800 01F00003E0000FC001FF0001FF000003E00000F000007800007C00003E00003F30003F78 003FFC003FFC003FFC003EF8007E60007C3800F81E03F00FFFC001FF0018227DA01E>I< 0000E00001E00001E00003E00007E00007E0000DE0001DE00039E00031E00061E000E1E0 00C1E00181E00381E00701E00601E00C01E01C01E01801E03001E07001E0E001E0FFFFFF FFFFFF0001E00001E00001E00001E00001E00001E00003F0003FFF003FFF18227DA11E> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmmi8 8 37 /Fm 37 123 df<0001FC0000000FFF0000003F07C000007C03E00001F801F00C03F001F0 0C07E000F80C0FC000F81C0F8000FC181F80007C183F00007C383F00007C307F00007C70 7E00007C607E00007CE07E00007CC0FE00007DC0FC00007F80FC00007F00FC00007E00FC 00007E00FC00007C00FC00007C007C00007C007C0000FE007C0003FE0C3E00073E0C1F00 1E3E1C0F81F81F3803FFE00FF000FE0003C0261F7D9D2D>11 D<0000007E00000001FFC0 00000781E000001E00F000003800F000007000F80000E000780001C0007800038000F800 030000F800070000F800060000F8000E0001F8000C0001F0001C0001F000180003E00018 0007C0003800078000301FEF0000303FFE0000703FFE0000601FEF000060000F80006000 07C000E00007C000C00007E000C00007E000C00007E001C00007E001800007E001800007 E001800007E00380000FE00300000FC00300000FC00300000FC00700001F800700001F80 0700003F000700003F000F80007E000D80007C000DC000F8000CE001F0001C7003E00018 3C0F8000181FFE00001803F8000038000000003000000000300000000030000000007000 000000600000000060000000006000000000E000000000C000000000C000000000C00000 0000253C7EAE28>I<0003FE00000FFFE0000E3FF0001C0FF0001803E0001800C0001800 00001C0000001C0000001E0000001F0000000F8000000F8000000FC0000007E0000007F0 000003F0000001F800000FFC00003EFE000078FE0001F07E0003E07F0007C03F000F803F 000F803F001F001F003F001F003E001F007E001F007C001F007C001F007C001F00FC001E 00F8003E00F8003E00F8003E00F8003C00F8007C00F8007C00780078007800F0007C00F0 003C01E0001E03C0000F07800007FF000000FC00001C307DAE1F>14 D<0003FE001FFE007E0000F80003F00007E0000FC0001F80001F80003F00003F00007F00 007FFFF07FFFF07E00007E0000FC0000FC0000FC00007C00007C00007C00007C00003E00 003E00001F00080F801C07C0F801FFE0007F00171E7D9C1D>I<07C007E00FE03FF81CF8 783E3879E01E307B801F707F001F607F001F60FE001FE0FC001FC0FC001FC0F8001F81F8 003F01F8003F01F0003E01F0003E03F0007E03F0007E03E0007C03E0007C07E000FC07E0 00FC07C000F807C000F80FC001F80FC001F80F8001F00F8001F01F8003F01F8003F01F00 03E00E0003E0000007E0000007E0000007C0000007C000000FC000000FC000000F800000 0F8000001F8000001F8000001F0000001F0000000E00202C7E9D23>17 D<00FC00000000FF000000001FC00000000FC000000007E000000007E000000007E00000 0003F000000003F000000001F000000001F800000001F800000000FC00000000FC000000 00FC000000007E000000007E000000003F000000003F000000003F000000001F80000000 1F800000000F800000000FC00000000FC00000001FE00000003FE00000007FE0000000F3 F0000001E3F0000003C1F000000781F800000F81F800001F00FC00003E00FC00007C00FC 0000F8007E0001F0007E0003E0003F0007E0003F000FC0003F001F80001F803F00001F80 7E00001F80FC00000FC0F8000007E070000003E0232F7DAD29>21 D<01F00007003FF0000F803FF0000F8003F0001F8003F0001F0003E0001F0003E0003F00 07E0003E0007E0003E0007C0007C0007C0007C000FC000F8000FC001F8000F8001F0000F 8003E0001F8007E0001F8007C0001F000F80001F001F00003F003E00003F007C00003E00 F000003E03E000007E07C000007E0F0000007C3E0000007CF8000000FFE0000000FF0000 0000F800000000211E7D9D23>23 D<0000C0000000C0000000C0000000C0000000C00000 00FFE00001FFF80007FFF8001F9FE0007F000000FE000000FC000001F8000003F8000003 F0000007F0000007F0000007E0000007E0000007E0000003E0000003F0000003F0000001 FBFE00007FFF00007FFF0000F7FE0003C00000078000000F0000001E0000001E0000003C 0000007C0000007800000078000000F8000000F0000000F8000000F8000000F8000000FC 000000FF0000007FC000003FF800001FFE00000FFFC00003FFF000007FFC00001FFE0000 03FF000000FF0000001F0000000F0000000F0000000F0000701E00003C1C00001FF80000 03E0001D3C7EAD1F>I<00FFFFFFF803FFFFFFF807FFFFFFF80FFFFFFFF01E0380C0003C 0300C000700301C000700701C000E007018000C006018000000E038000000E038000000E 038000001C038000001C038000003C038000003C07800000380780000078078000007807 800000F007C00000F007C00001F007C00001F007C00003E007E00003E007E00007E003E0 0007C003E00007C003E000038001C000251E7E9C29>I<00001F8000007FF00001F0F800 03E07C0007803E000F003E001F001F003E001F007C001F007C001F00F8001F00F8003F01 F8003F01F0003F01F0003F03F0007F03F0007E03E0007E03E0007E07E000FC07E000FC07 C000F807C001F80FC003F00FC003E00FE007C00FE00F801FF01F001FB83E001F1FF8001F 07C0003F0000003F0000003E0000003E0000007E0000007E0000007C0000007C000000FC 000000FC000000F8000000F800000070000000202C7E9D24>I<0003FFFFF0001FFFFFF0 007FFFFFF000FFFFFFE001FC1F800003F00FC00007C007C0000F8003E0001F8003E0001F 0003E0003E0003E0003E0003E0007C0003E0007C0003E0007C0007E000FC0007C000F800 07C000F80007C000F8000FC000F8000F8000F8001F8000F8001F0000F8003E000078003C 000078007C00007C00F800003C01E000001F07C0000007FF00000001F8000000241E7D9C 28>I<00FFFFFF8003FFFFFF8007FFFFFF800FFFFFFF001E00E000003C00E000007000C0 00007001C00000E001C00000C001C000000003C000000003C00000000380000000038000 00000780000000078000000007800000000F000000000F000000000F000000001F000000 001F000000001E000000003E000000003E000000003E000000003E000000007C00000000 7C0000000038000000211E7E9C1F>I<0003F800003FFF0000FFFFC001F807E007C001E0 070000000E0000000C0000001C000000180000001C0000000C0000000E3FC00007FFE000 07FFE0000E7F80001C000000380000007000000060000000E0000000C0000000C0000000 C0000200E0000600E0000E0070001C003E00F8001FFFF00007FFC00001FE00001B1F7E9D 21>34 D<0000000FC00300003FE0070000FFF80E0001FFF80C0003E07C1C0007803C3800 07001C30000E000E30001C000E70001C000E600038000E600030000EE00030000CC00060 000CC00060000CC000C0001CC000C00018C000C00038C001800030C001800070E0018000 E0E0038001E070038003C078030007803C07001F001F87007E000FF703FC0007FFFFF000 01FFFFC000007FFF0000001FF80000001E000000001E000000001E000000003C00000000 3C000000003C000000007C000000007C000000007C00000000F800000000F800000000F8 0000000070000000272C7C9D2E>39 D<3C007E00FF00FF00FF80FF807F803D8001800180 0180038003000300070006000E001C0038007000600009157A8714>59 D<0000000001C00000000007C0000000001FC0000000007F0000000001FC0000000007F0 000000001FC0000000007F0000000001FC0000000007F0000000000FC0000000003F0000 000000FC0000000003F8000000000FE0000000003F8000000000FE0000000003F8000000 000FE0000000003F8000000000FE0000000000F80000000000FE00000000003F80000000 000FE00000000003F80000000000FE00000000003F80000000000FE00000000003F80000 000000FC00000000003F00000000000FC00000000007F00000000001FC00000000007F00 000000001FC00000000007F00000000001FC00000000007F00000000001FC00000000007 C00000000001C02A2B7AA537>I<000000C0000001C0000003C000000380000003800000 0780000007000000070000000F0000000E0000000E0000001E0000001C0000001C000000 3C00000038000000780000007000000070000000F0000000E0000000E0000001E0000001 C0000001C0000003C00000038000000780000007000000070000000F0000000E0000000E 0000001E0000001C0000001C0000003C00000038000000380000007800000070000000F0 000000E0000000E0000001E0000001C0000001C0000003C0000003800000038000000780 0000070000000F0000000E0000000E0000001E0000001C0000001C0000003C0000003800 000038000000780000007000000070000000F0000000E0000000E00000001A437CB123> II<003FFFFC0FFFFF003FFFFC0FFFFF0000FE00003F8000 00FE00003F800000FC00003F000000FC00003F000001FC00007F000001FC00007E000001 F800007E000001F800007E000003F80000FE000003F80000FC000003F00000FC000003F0 0000FC000007F00001FC000007F00001F8000007E00001F8000007E00001F800000FE000 03F800000FE00003F000000FC00003F000000FFFFFFFF000001FFFFFFFF000001FC00007 E000001F800007E000001F800007E000003F80000FE000003F80000FC000003F00000FC0 00003F00000FC000007F00001FC000007F00001F8000007E00001F8000007E00001F8000 00FE00003F800000FE00003F000000FC00003F000000FC00003F000001FC00007F000001 FC00007E000001F800007E000001F800007E000003F80000FE0000FFFFE03FFFF800FFFF E03FFFF800382D7CAC3A>72 D<003FFFFE0000003FFFFE00000000FF0000000000FE0000 000000FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F80000 000003F80000000003F80000000003F00000000003F00000000007F00000000007F00000 000007E00000000007E0000000000FE0000000000FE0000000000FC0000000000FC00000 00001FC0000000001FC0000000001F80000000001F80000000003F80000000003F800000 00003F00000180003F00000180007F00000380007F00000300007E00000700007E000006 0000FE00000E0000FE00000E0000FC00001C0000FC00003C0001FC00003C0001FC000078 0001F80001F80001F80003F00003F8001FF000FFFFFFFFF000FFFFFFFFE000292D7DAC30 >76 D<003FFE0000FFFF003FFE0000FFFF0000FF000007E00000FF000007C00000FF8000 03800000DF800003000001DFC00007000001CFC000060000018FE0000600000187E00006 00000387F0000E00000387F0000C00000303F0000C00000303F8000C00000701F8001C00 000701FC001800000600FC001800000600FE001800000E007E003800000E007F00300000 0C003F003000000C003F003000001C003F807000001C001F8060000018001FC060000018 000FC060000038000FE0E00000380007E0C00000300007F0C00000300003F0C000007000 03F1C00000700003F9800000600001F9800000600001FD800000E00000FF800000E00000 FF000000C000007F000000C000007F000001C000003F000001C000003E0000018000003E 000003C000001E00000FE000001E0000FFFE00000C0000FFFE00000C0000382D7CAC38> 78 D<000007F00600003FFE0E0000F80F9E0003E001FE00078000FE000F00007C001E00 007C003C00003C003C00003C00780000380078000038007800003800F800003800F80000 3000F800003000FC00000000FC00000000FE000000007F800000007FF80000003FFF8000 003FFFF000001FFFFC000007FFFE000000FFFF0000001FFF00000001FF800000003F8000 00001F800000000F800000000F8000000007801800000780180000078018000007801800 000F803800000F003800000F003800001E003800001E007C00003C007E000078007F0000 F0007B8003E000F1F00F8000E07FFE0000C00FF00000272F7CAD2B>83 D<000FFFFC007FFF000FFFFC007FFF00007FC0000FF000003F80000F8000003F80000F00 00001FC0001E0000001FC000180000000FC000300000000FE0006000000007E000C00000 0007F0018000000003F0030000000003F8060000000003F80C0000000001FC1800000000 01FC300000000000FE600000000000FEC000000000007F8000000000007F000000000000 3F8000000000003F8000000000001FC000000000003FC000000000006FC00000000000CF E0000000000187E0000000000307F0000000000703F0000000000E03F8000000001C03F8 000000003801FC000000007001FC00000000E000FE00000001C000FE0000000380007F00 00000700007F0000000E00003F8000001C00003F8000003800001FC000007000001FC000 01F000001FE00007F800003FE000FFFE0003FFFF00FFFE0003FFFF00382D7EAC3A>88 DI<00 07E000001FF800007C1CE000F80DE001F00FE003E007E007C007E00FC007E01F8007C01F 8007C03F0007C03F000FC07F000F807E000F807E000F807E001F80FE001F00FC001F00FC 001F00FC003F02FC003E06FC003E06F8003E06F8007E0E7C00FE0C7C00FC0C7C01FC1C3E 07BE181F0E1E380FFC0FF003F003C01F1F7D9D25>97 D<0000007C00000001FF00000007 C38000000F878000000F0F8000001F1F8000001F1F8000001F1F8000003E0E0000003E00 0000003E000000003E000000007E000000007C000000007C000000007C000000007C0000 0000FC0000003FFFF800003FFFF8000000F800000000F800000000F800000001F8000000 01F000000001F000000001F000000001F000000003F000000003E000000003E000000003 E000000003E000000007E000000007C000000007C000000007C000000007C000000007C0 0000000FC00000000F800000000F800000000F800000000F800000001F800000001F0000 00001F000000001F000000001F000000003E000000003E000000003E000000383C000000 FC3C000000FC78000000FC78000000FCF0000000F0F0000000E1E00000007FC00000001F 00000000213D7CAE22>102 D<000700000F80001FC0001FC0000F800007000000000000 0000000000000000000000000000000000000000000001E00007F8000E3C001C3E00383E 00303E00703E00607E00E07C00C07C00C0FC0080F80000F80001F80001F00003F00003E0 0003E00007E00007C04007C0C00FC0C00F80C00F81C01F01801F03801F07000F06000F1E 0007F80001F000122E7EAC18>105 D<000000E0000001F0000003F0000003F0000003F0 000001C00000000000000000000000000000000000000000000000000000000000000000 0000000000007C000003FE0000078F80000E0780001C0780003807C0003007C000700FC0 00600F8000E00F8000C00F8000801F8000001F8000001F0000001F0000003F0000003F00 00003E0000003E0000007E0000007E0000007C0000007C000000FC000000FC000000F800 0000F8000001F8000001F8000001F0000001F0000003F0000003F0000003E0000003E000 0007E0003807C000FC0FC000FC0F8000FC1F0000F83E0000F0F800007FF000001F800000 1C3B81AC1D>I<001F000003FF000003FF0000003F0000003F0000003E0000003E000000 7E0000007E0000007C0000007C000000FC000000FC000000F8000000F8000001F8000001 F800F801F003FC01F00F0E03F01C1E03F0387E03E0707E03E0E07E07E1C07E07E3803807 C7000007CE00000FDC00000FF800000FF800000FFF80001F9FE0001F83F0001F01F8001F 00F8003F00F8043F00F80C3E00F80C3E00F80C7E00F81C7E00F8187C00F0387C00F830FC 00F870FC0078E0F8003FC070000F801F2F7DAD25>I<078007F0007E00001FE01FFC03FF 800018F0781F0783E0003878E00F1E01E0003079C00FB801F000707F800FB001F000607F 000FF001F00060FE000FE001F000E0FE000FC001F000C0FC000FC001F000C0F8000F8001 F00081F8001F8003F00001F8001F8003E00001F0001F0003E00001F0001F0003E00003F0 003F0007E00003F0003F0007C00003E0003E0007C00003E0003E000FC00007E0007E000F 808007E0007E000F818007C0007C001F818007C0007C001F01800FC000FC003F03800FC0 00FC003E03000F8000F8003E07000F8000F8003E0E001F8001F8001E0C001F8001F8001E 3C001F0001F0000FF0000E0000E00003E000391F7E9D3E>109 D<07C007E0001FE03FF8 0018F8783E003879E01E00307B801F00707F001F00607F001F0060FE001F00E0FC001F00 C0FC001F00C0F8001F0081F8003F0001F8003E0001F0003E0001F0003E0003F0007E0003 F0007C0003E0007C0003E000FC0007E000F80807E000F81807C001F81807C001F0180FC0 01F0380FC003E0300F8003E0700F8003E0E01F8001E0C01F8001E3C01F0000FF000E0000 3E00251F7E9D2B>I<007C01F80000FE07FE0001CF8E0F0003879C07800307B807C00707 F007C00607E003E0060FC003E00E0F8003E00C0F8003E00C0F8003E0081F8007E0001F80 07E0001F0007E0001F0007E0003F000FE0003F000FC0003E000FC0003E000FC0007E001F 80007E001F80007C001F00007C003F0000FC003E0000FC007C0000FC00FC0000FE01F800 01FF03E00001FB87C00001F1FF000001F0FC000003F000000003F000000003E000000003 E000000007E000000007E000000007C000000007C00000000FC00000000FC0000000FFFC 000000FFFC000000232B829D24>112 D<07C01F000FF07FC01CF8E0E03879C1E0307B87 E0707F07E0607E07E060FC07E0E0FC0380C0F80000C0F8000081F8000001F8000001F000 0001F0000003F0000003F0000003E0000003E0000007E0000007E0000007C0000007C000 000FC000000FC000000F8000000F8000001F8000001F8000001F0000000E0000001B1F7E 9D20>114 D<0007E0003FF800781E00F00601E00703C00F03C01F03C01F07C01E07C00C 07E00007F80007FF8003FFE001FFF000FFF8003FFC0001FC0000FC00007C78003CFC003C FC003CFC007CF80078E000F8E000F06001E07807C01FFF0007F800181F7C9D21>I<000E 00001F00001F00003F00003F00003E00003E00007E00007E00007C00007C0000FC0000FC 00FFFFF8FFFFF801F80001F80001F00001F00003F00003F00003E00003E00007E00007E0 0007C00007C0000FC0000FC0000F80000F80001F80101F80301F00301F00701F00601F00 E01E01C01E03801F07000F0E0007FC0001F000152B7EA919>I<003F007C0000FFC1FF00 01C1E383800380F703C00700F60FC00E00FE0FC01C00FC0FC01800FC0FC03800FC070030 00F800003000F800002001F800000001F000000001F000000001F000000003F000000003 E000000003E000000003E000000007E001000007E003000007C003003807C007007C0FC0 0600FC0FC00E00FC1FC00C00FC1BC01C00F03BE038007071E0F0003FE0FFC0000F803F00 00221F7E9D28>120 D<001E0030003F803000FFC07001FFE0E001FFF1C003C0FFC00380 3F800300070007000E0000001C0000003800000070000000E0000001C000000380000007 0000001E0000003800000070000000E0004001C000C0038000C0070001C00E0003800FE0 07801FF81F00387FFF00703FFE00601FFC00E00FF000C003C0001C1F7D9D21>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmsy8 8 15 /Fn 15 107 df0 D<000C0000001E0000001E0000001E0000001E0000001E0000601E0180781E0780FC0C0F C07F0C3F803F8C7F0007CCF80001FFE000007F8000001E0000007F800001FFE00007CCF8 003F8C7F007F0C3F80FC0C0FC0781E0780601E0180001E0000001E0000001E0000001E00 00001E0000000C00001A1D7C9E23>3 D<00000300000000000380000000000380000000 000380000000000380000000000380000000000380000000000380000000000380000000 000380000000000380000000000380000000000380000000000380000000000380000000 000380000000000380000000000380000000000380000000000380000000000380000000 0003800000FFFFFFFFFFFCFFFFFFFFFFFCFFFFFFFFFFFC00000380000000000380000000 000380000000000380000000000380000000000380000000000380000000000380000000 000380000000000380000000000380000000000380000000000380000000000380000000 0003800000000003800000000003800000000003800000000003800000FFFFFFFFFFFCFF FFFFFFFFFCFFFFFFFFFFFC2E2F7CAD37>6 DI<0000000001C00000000007C000000000 1FC0000000007F0000000001FC0000000007F0000000001FC0000000007F0000000001FC 0000000007F0000000000FC0000000003F0000000000FC0000000003F8000000000FE000 0000003F8000000000FE0000000003F8000000000FE0000000003F8000000000FE000000 0000F80000000000FE00000000003F80000000000FE00000000003F80000000000FE0000 0000003F80000000000FE00000000003F80000000000FC00000000003F00000000000FC0 0000000007F00000000001FC00000000007F00000000001FC00000000007F00000000001 FC00000000007F00000000001FC00000000007C00000000001C000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000007FFFFFFF FF80FFFFFFFFFFC0FFFFFFFFFFC02A3B7AAB37>20 D<0000FFFFFFC00007FFFFFFC0001F FFFFFFC0007F8000000000FC0000000001F00000000003C0000000000780000000000F00 000000001E00000000001C00000000003C00000000003800000000007800000000007000 00000000700000000000F00000000000E00000000000E00000000000E00000000000E000 00000000E00000000000E00000000000E00000000000E00000000000E00000000000F000 000000007000000000007000000000007800000000003800000000003C00000000001C00 000000001E00000000000F000000000007800000000003C00000000001F00000000000FC 00000000007F80000000001FFFFFFFC00007FFFFFFC00000FFFFFFC02A2B7AA537>26 D<00000000000E000000000000000E000000000000000E000000000000000F0000000000 000007000000000000000780000000000000038000000000000003C000000000000001C0 00000000000001E000000000000000F00000000000000078000000000000007C00000000 0000003E000000000000000F0000000000000007C0FFFFFFFFFFFFFFF8FFFFFFFFFFFFFF FCFFFFFFFFFFFFFFF800000000000007C00000000000000F000000000000003E00000000 0000007C000000000000007800000000000000F000000000000001E000000000000001C0 00000000000003C000000000000003800000000000000780000000000000070000000000 00000F000000000000000E000000000000000E000000000000000E00003E237CA147>33 D<007800FE01FE01FE01FE03FE03FC03FC03FC07F807F807F807F007F00FE00FE00FE00F C01FC01F801F801F803F003F003F003E007E007C007C007C00F800F800F800F0000F227E A413>48 D<003F80000007F00000FFF000003FFC0003FFFC0000FFFF0007FFFF0001F807 800F80FF8007C001C01E003FC00F8000E03C001FE01F00007038000FF03E000030700007 F83C000038700003FC78000018600001FEF0000018E00000FFE000001CC000007FE00000 0CC000007FC000000CC000003FC000000CC000001FE000000CC000000FF000000CC00000 0FF800000CC000001FF800000CE000001FFC00001C6000003DFE00001860000078FF0000 38700000F07F800038300001F03FC00070380003E01FE000F01C0007C00FF001E00E000F 8007FC07C007807E0003FFFF8003FFFC0000FFFF0000FFF000003FFC00003F80000007F0 003E1F7C9D47>I<0000FFFFC00007FFFFC0001FFFFFC0007F80000000FC00000001F000 000003C000000007800000000F000000000E000000001E000000003C0000000038000000 00780000000070000000007000000000F000000000E000000000E000000000E000000000 FFFFFFFFC0FFFFFFFFC0FFFFFFFFC0E000000000E000000000E000000000F00000000070 000000007000000000780000000038000000003C000000001E000000000E000000000F00 000000078000000003C000000001F000000000FC000000007F800000001FFFFFC00007FF FFC00000FFFFC0222B7AA52F>I<00000180000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 000000000380000000000380000000000380000000000380000000000380000000000380 00000000038000000000038000000000038000007FFFFFFFFFFEFFFFFFFFFFFE7FFFFFFF FFFE2F2E7CAD38>63 D<00003FFFF000000007FFFFFF0000001FFFFFFFE000007FFFFFFF F00001F83E03FFFC0003C03E003FFE000F003E0007FF001E007E0003FF803C007E0000FF 807C007E00007FC078007E00003FC0F0007E00001FE0E0007C00001FE000007C00000FE0 00007C00000FE00000FC000007E00000FC000007E00000F8000007E00000F8000007E000 00F8000007E00001F8000007C00001F0000007C00001F0000007C00001F000000F800003 F000000F800003E000000F000003E000001F000003E000001E000007C000003C000007C0 00007C000007C000007800000F800000F000000F800001E000000F800003C000001F0000 078000001F00000E0000001F00003C0000003E0000F00000003E0003E00000003C000F80 0000007C00FE000000007FFFF800000001FFFFE000000003FFFE0000000007FFE0000000 00332D7EAC37>68 D<00030007000F000E000E001E001C003C003800380078007000F000 E000E001E001C003C003800780070007000F000E001E001C001C003C0038007800700070 00F000E000F00070007000780038003C001C001C001E000E000F00070007000780038003 C001C001E000E000E000F00070007800380038003C001C001E000E000E000F0007000310 437AB11B>104 DII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmmi12 12 74 /Fo 74 123 df<000003FC00000000001FFF0000000000FE07C000000003F001F0000000 07E000F80000001FC000FC000E003F80007C000E007F00003E000C00FE00003F000C01FC 00003F001C03F800001F001807F800001F801807F000001F80380FF000001F80301FE000 001F80701FE000001FC0603FC000001FC0603FC000001FC0E03FC000000FC0C07F800000 0FC1C07F8000000FC1807F8000000FC380FF8000000FC700FF0000000FC600FF0000000F CE00FF0000000FDC00FF0000001FD800FE0000001FF800FE0000001FF000FE0000001FE0 00FE0000001FC000FE0000001FC000FE0000001FC000FE0000001FC000FE0000001FC000 7E0000003FC0007E0000007FC0003F000000EFC0383F000003CFC0381F80000F07C0300F C0001C07C07007E000F803E0E001F00FE001E1C0007FFF0000FF80001FF000003E00372D 7CAB3E>11 D<0000000003F800000000001FFF00000000007C0F8000000001E003E00000 00078001F00000000E0001F00000001C0000F8000000380000F8000000700000FC000000 E00000FC000001C00000FC000001800000FC000003800000FC000007000000FC00000600 0000FC00000E000001FC00000C000001FC00001C000001F8000018000001F80000380000 03F0000030000003F0000070000007E0000060000007E000006000000FC00000E000000F 800000C000001F000000C000003E000001C007FE7C000001801FFFF8000001801807E000 0001801FFFF80000038007FCFC0000030000007E0000030000007E0000030000003F0000 070000003F0000060000003F8000060000001F8000060000001FC0000E0000001FC0000C 0000001FC0000C0000001FC0000C0000003FC0001C0000003FC000180000003FC0001800 00003FC000180000003FC000380000007FC000300000007F8000300000007F8000300000 007F800070000000FF800070000000FF000070000000FF000070000001FE0000F0000001 FE0000F0000001FC0000F0000003FC0000F0000003F80001F0000007F80001B8000007F0 00019800000FE000019800001FC000039C00003F8000030E00007F000003060000FE0000 03078001F800000701C003F000000600F01FC0000006003FFF00000006000FF00000000E 0000000000000C0000000000000C0000000000000C0000000000001C0000000000001800 000000000018000000000000180000000000003800000000000030000000000000300000 000000003000000000000070000000000000600000000000006000000000000060000000 000000E0000000000000E000000000000036597DC537>I<0001FC000000000007FF0000 00E0001FFFC00000E0007FFFE00001C000FFFFF000018001FFFFF800038003FE07F80003 0007F000FC00070007C0007C0006000F00003E000E001E00001E000C001C00000F000C00 3C000007001C003800000700180070000003003800700000038030006000000180700060 000001806000E000000180E00000000001C0C00000000000C0C00000000000C1C0000000 0000C1800000000000C3800000000000C3000000000000E3000000000000E70000000000 00660000000000006E0000000000006C0000000000006C0000000000007C000000000000 78000000000000780000000000007800000000000070000000000000F0000000000000E0 000000000000E0000000000000E0000000000000C0000000000000C0000000000000C000 0000000001C0000000000001C00000000000018000000000000380000000000003800000 000000038000000000000380000000000007000000000000070000000000000700000000 00000F0000000000000E0000000000000E0000000000000E0000000000000E0000000000 001C0000000000001C0000000000001C0000000000001C00000000000038000000000000 380000000000003800000033417EAB33>I<0000007800000007FFE000001FFFFC00003C 7FFE00007007FE00006003FE0000E000FE0000C000380000C000000000C000000000E000 000000E000000000E000000000F000000000F000000000F8000000007C000000007C0000 00007E000000003E000000003F000000003F800000001FC00000001FC00000000FE00000 000FF000000007F000000007F80000003FFC000000FFFC000003E1FE000007C1FE00001F 00FF00003E00FF00007C007F8000F8007F8001F8003F8003F0003F8007E0003FC007C000 1FC00FC0001FC01F80001FC01F80001FC03F00001FC03F00000FC07F00000FC07E00000F C07E00000FC07E00000FC0FE00001F80FC00001F80FC00001F80FC00001F80FC00001F00 F800001F00F800003F00F800003F00F800003E00F800007E00F800007C00F800007C00FC 0000F8007C0000F8007C0001F0003E0003E0003E0003E0001F0007C0000F800F800007C0 1F000003E07C000000FFF00000001FC0000027487CC62B>I<000007FE00007FFF0001FF FE0007F800001FE000003F8000007F000000FE000001FC000003F8000007F800000FF000 000FE000001FE000003FE000003FC000003FC000007FFFFFC07FFFFFE07FFFFFE07F8000 00FF800000FF000000FF000000FF000000FF000000FF000000FF000000FE000000FE0000 007E0000007F0000007F0000003F0000003F0000003F8000001F8000000FC0000007C000 0C03E0003C01F000F000FC07C0003FFF000007F800202C7CAA27>I<0000003000000000 003000000000003000000000003000000000003000000000003000000000003000000000 0033FF000000003FFFC00000007C00C0000000FFFFC0000003C3FF000000078000000000 0F00000000001C0000000000780000000000F00000000001E00000000001C00000000003 80000000000780000000000F00000000001E00000000001C00000000003C000000000078 0000000000F00000000000F00000000001E00000000001E00000000003C00000000003C0 000000000780000000000780000000000F00000000000F00000000001F00000000001E00 000000001E00000000003E00000000003C00000000003C00000000003C00000000007C00 00000000780000000000780000000000780000000000780000000000F80000000000F800 00000000F80000000000F80000000000F80000000000F80000000000FC0000000000FC00 000000007C00000000007E00000000007E00000000007F00000000003F80000000003FC0 000000001FE0000000001FF8000000000FFE0000000007FFC000000003FFF800000001FF FF000000007FFFE00000001FFFF000000003FFFC000000007FFE000000001FFF00000000 03FF00000000007F80000000003F80000000001F80000000001F80000000000F80000000 000F80000000000F80000000000F00000000000F00000002001E00000007001E00000003 803C00000001E078000000007FE0000000001F8000002A597CC42B>I<00F80003FC0003 FE001FFF00071F007C0FC00E0F80E007E01C0FC3C003E01807C70003F01807CE0001F038 07DC0001F83007D80001F8300FF80001F8700FF00001F8600FE00001F8600FE00001F8E0 0FC00003F8C01FC00003F0C01F800003F0001F800003F0001F800007F0003F800007F000 3F000007E0003F000007E0003F00000FE0007F00000FE0007E00000FC0007E00000FC000 7E00001FC000FE00001FC000FC00001F8000FC00001F8000FC00003F8001FC00003F8001 F800003F0001F800003F0001F800007F0003F800007F0003F000007E0003F000007E0003 F00000FE0007F00000FE0007E00000FC0007E00000FC0007E00001FC000FE00001FC000F C00001F80003800001F80000000003F80000000003F80000000003F00000000003F00000 000007F00000000007F00000000007E00000000007E0000000000FE0000000000FE00000 00000FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F800000 00003F80000000003F80000000003F00000000000E00002D417DAB30>I<0007C0000000 0007F80000000000FE00000000007F00000000003F80000000001FC0000000001FC00000 00001FC0000000000FE0000000000FE0000000000FE00000000007F00000000007F00000 000007F00000000003F80000000003F80000000003F80000000001FC0000000001FC0000 000001FC0000000000FE0000000000FE0000000000FE00000000007F00000000007F0000 0000007F00000000003F80000000003F80000000003F80000000001FC0000000001FC000 0000001FC0000000000FE0000000000FE0000000000FE00000000007F00000000007F000 00000007F0000000000FF8000000001FF8000000003BF80000000071FC00000000F1FC00 000001E1FC00000003C0FE0000000780FE0000000F00FE0000001E007F0000003E007F00 00007C007F000000F8003F800001F0003F800003E0003F800007C0001FC0000FC0001FC0 001F80001FC0003F00000FC0007E00000FE000FC00000FE001F8000007E003F8000007F0 07F0000007F00FE0000003F01FC0000003F83F80000003F87F00000001FCFF00000001FC FE00000001FEFC00000000FE78000000007E2F467BC439>21 D<000070000000000000F8 00000E000001F800003F000001F800003F000001F800003F000003F800007F000003F800 007F000003F000007E000003F000007E000007F00000FE000007F00000FE000007E00000 FC000007E00000FC00000FE00001FC00000FE00001FC00000FC00001F800000FC00001F8 00001FC00003F800001FC00003F800001F800003F000001F800003F000003F800007F000 003F800007F000003F000007E000003F000007E000007F00000FE000007F00000FE00000 7E00000FC000007E00000FC00000FE00001FC01800FE00001FC03800FC00001F803000FC 00001F803001FC00003F807001FC00003F806001FC00007F006001FC0000FF006003FE00 00FF00E003FE0001DF00C003FE00039F01C003FF00071F018007FF801E0F838007F7C078 07870007E1FFE003FE0007E07F8000F8000FE000000000000FE000000000000FC0000000 00000FC000000000001FC000000000001FC000000000001F8000000000001F8000000000 003F8000000000003F8000000000003F0000000000003F0000000000007F000000000000 7F0000000000007E0000000000007E000000000000FE000000000000FE000000000000FC 0000000000003800000000000035417DAB3B>I<003F800000701FFF800000F83FFF8000 01F83FFF000001F8007F000001F8007F000003F8007F000003F0007E000003F0007E0000 07F000FE000007E000FE000007E000FC00000FC000FC00000FC001FC00001FC001FC0000 1F8001F800003F8001F800003F0003F800007E0003F800007E0003F00000FC0003F00001 F80007F00001F80007F00003F00007E00007E00007E00007C0000FE0000FC0000FE0001F 80000FC0003F00000FC0007E00001FC000FC00001FC001F800001F8003F000001F8007C0 00003F800F8000003F801F0000003F003C0000003F00F80000007F01E00000007F07C000 00007E1F000000007EFC00000000FFE000000000FF8000000000F800000000002D2C7BAB 30>I<000000600000000000600000000000600000000000600000000000600000000000 6000000000006000000000007FFF00000000FFFFC0000007F801C000001FDFFFC000007F 87FE000000FF0000000003FC0000000007F8000000000FF8000000000FF0000000001FE0 000000003FE0000000003FC0000000007FC0000000007F8000000000FF8000000000FF80 00000000FF0000000000FF0000000000FF0000000000FF0000000000FF00000000007F00 000000007F80000000007F80000000003F80000000001FC0000000000FE3FF80000007FF FFE0000001FC0060000003FFFFE000000F8FFF8000001E00000000003C0000000000F800 00000001F00000000001E00000000003C0000000000780000000000F00000000000F0000 0000001E00000000003E00000000003C00000000007C0000000000780000000000780000 000000780000000000F80000000000F80000000000F80000000000F80000000000FC0000 000000FC0000000000FE00000000007F00000000007F80000000003FE0000000003FF800 0000001FFF000000000FFFC000000003FFF800000001FFFE000000007FFFC00000000FFF F000000003FFFC000000007FFF000000001FFF8000000003FFC000000000FFC000000000 1FC0000000000FC00000000007C00000000007C00000000007C00000000007C000000200 0780000003800F80000001C00F00000000F83E000000003FF80000000007E000002A597E C42B>I<000FFFFFFFFFE0003FFFFFFFFFF0007FFFFFFFFFF001FFFFFFFFFFE003FFFFFF FFFFC007E0060030000007800E003000000F000E003000001E000C007000003C000C0070 000038001C0060000070001C0060000060001800E00000E0003800E0000040003800E000 0000003800E0000000007000E0000000007001C0000000007001C000000000F001C00000 0000E001C000000001E001C000000001E003C000000001C003C000000003C003C0000000 03C003C000000003C003C0000000078003C0000000078003E00000000F8003E00000000F 8003E00000001F0003E00000001F0003E00000001F0003E00000003F0003F00000003E00 03F00000007E0003F00000007E0003F0000000FC0003F8000000FC0003F8000001FC0001 F8000001F80001F8000001F80001F8000000F00000E00000342C7EAA37>I<00000007F0 000000001FFE000000007C1F00000001F00FC0000007C007E000000F8003E000001F0003 F000003E0001F800007E0001F80000FC0001F80000F80001FC0001F80001FC0003F00001 FC0003F00001FC0007E00001FC0007E00001FC000FC00001FC000FC00003FC001FC00003 FC001F800003FC001F800003FC001F800007FC003F800007F8003F000007F8003F000007 F8007F00000FF8007F00000FF0007E00000FF0007E00000FE000FE00001FE000FE00001F C000FC00003FC000FC00003F8001FC00007F8001FC00007F0001FC0000FE0001FC0000FC 0003FE0001F80003FE0003F00003F70007E00003F3800FC00007F1C01F000007F0E07E00 0007E07FF8000007E01FC000000FE0000000000FE0000000000FC0000000000FC0000000 001FC0000000001FC0000000001F80000000001F80000000003F80000000003F80000000 003F00000000003F00000000007F00000000007F00000000007E00000000007E00000000 00FE0000000000FE0000000000FC00000000003800000000002E417DAB32>I<000003FF FFFFE000001FFFFFFFF00000FFFFFFFFF00001FFFFFFFFE00007FFFFFFFFC0000FF80FF8 0000001FC003F80000003F8001FC0000007E0000FC000000FC00007E000001F800007E00 0003F000003E000007F000003F000007E000003F00000FC000003F00000FC000003F0000 1F8000003F00001F8000003F00003F8000003F00003F0000003F00003F0000007F00007F 0000007E00007E0000007E00007E0000007E00007E000000FE0000FE000000FC0000FC00 0000FC0000FC000001FC0000FC000001F80000FC000001F80000FC000003F000007C0000 03E000007C000007E000007C00000FC000007C00000F8000003E00001F0000003E00003E 0000001F00007C0000001F0000F80000000F8003F000000007C007C000000001F03F0000 0000007FFC00000000001FE000000000342C7DAA37>I<000FFFFFFFFC003FFFFFFFFE00 7FFFFFFFFE01FFFFFFFFFC03FFFFFFFFF807E001C000000780018000000F00038000001E 00038000001C0003800000380003800000700007000000600007000000E0000700000040 000F00000000000F00000000000E00000000001E00000000001E00000000001E00000000 001E00000000003C00000000003C00000000003C00000000007C00000000007C00000000 00780000000000F80000000000F80000000000F80000000000F80000000001F000000000 01F00000000001F00000000003F00000000003F00000000003E00000000007E000000000 07E00000000007E0000000000FE0000000000FE0000000000FC00000000007800000002F 2C7EAA2A>I<000000001C0000000000001C000000000000180000000000001800000000 000038000000000000380000000000003000000000000030000000000000700000000000 00700000000000006000000000000060000000000000E0000000000000E0000000000000 C0000000000000C0000000000001C0000000000001C00000000000018000000000000180 000000000003800000000000038000000000000300000000000003000000000000070000 000000007FE00000000007FFFE000000001FC63F80000000FE0E07C0000001F80E03F000 0007E00C00F800001FC00C00FC00003F001C007E00007E001C003F0000FC0018003F0001 F80018001F8003F80038001F8007F00038001F800FE00030001FC00FE00030001FC01FC0 0070001FC01FC00070001FC03F800060001FC03F800060001FC07F0000E0001FC07F0000 E0001FC07F0000C0003FC0FF0000C0003F80FE0001C0003F80FE0001C0003F80FE000180 007F80FE000180007F00FE000380007F00FC00038000FE00FC00030000FE00FC00030001 FC00FE00070003F800FE00070003F8007E00060007F0007E0006000FE0003F000E001FC0 003F000E003F80001F800C007F00000F800C00FC000007C01C01F8000003E01C07E00000 01F8181F800000007E18FE000000001FFFF80000000001FF800000000000300000000000 003000000000000070000000000000700000000000006000000000000060000000000000 E0000000000000E0000000000000C0000000000000C0000000000001C0000000000001C0 000000000001800000000000018000000000000380000000000003800000000000030000 000000000300000000000003000000000032597BC43A>30 D<0000000000300000000000 000030000000000000003000000000000000700000000000000060000000000000006000 0000000000006000000000000000E000000000000000C000000000000000C00000000000 0000C000000000000001C000000000000001800000000000000180000000000000018000 000000000003800000000000000300000000000000030000000000000003000000000000 0007000000000000000600000000000000060000000000000006000000000000000E0000 00000000000C000000003E00000C00070000FF80000C001F8003C3C0001C003FC00703E0 0018003FC00601F00018007FC00E01F00018003FC01C01F00038003FC01803F00030001F C03803F00030000FC03003F000300007C07003F000700007C06007F000600003C06007E0 00600003C06007E000600003C0E00FE000E0000380C00FC000C0000180001FC000C00001 80001F8000C0000380001F8001C0000300003F800180000300003F000180000300003F00 0180000700007F000380000600007E000300000600007E000300000E00007E000300000C 0000FE000700001C0000FC00060000180000FC00060000380000FC00060000700000FC00 0E0000600000FC000C0000E00000FC000C0001C00000FC000C0003800000FC001C000700 0000FC0018000E0000007E0018001C0000007E001800380000003F003800700000001F80 3000E00000000FC03003C000000007F0300F0000000001FE707C00000000003FFFF00000 00000003FF800000000000006000000000000000E000000000000000C000000000000000 C000000000000000C000000000000001C000000000000001800000000000000180000000 000000018000000000000003800000000000000300000000000000030000000000000003 000000000000000700000000000000060000000000000006000000000000000600000000 0000000E000000000000000C00000000003A597DC43F>32 D<000007FE0000007FFFC000 01FFFFF00007FFFFF8001FF003FE003F00007E007800003E00E000000801C00000000380 000000030000000007000000000600000000060000000006000000000600000000070000 0000030000000003803E000001E7FFC000007FC1E000007FFFE00001E7FFC00003800000 0007000000000E000000001C000000003800000000700000000060000000006000000000 E000000000C000000000C000000000C000000000C000000000C000000180E000000380F0 0000030070000007007800000E003E00003C001FC003F8000FFFFFE00003FFFFC00000FF FE0000001FF00000272F7EAC2E>34 D<00000000007F000030000003FFC0007000000FFF E000E000001FFFF001C000003FFFF8038000007F01F803000000F8007C07000001F0003C 06000003E0001C0E000003C0001E0C00000780000E1C00000700000E1800000E00000E18 00000C00000E3800001C00000630000018000006300000300000063000003000000E7000 006000000C6000006000000C6000004000000C600000C000001CE00000C0000018E00001 80000018C0000180000038E0000180000030E0000300000070E00003000000E060000300 0000E0700007000001C0700007000003807800060000078038000600000F003C000E0000 1E001E000E00007C001F800E0000F8000FC01C0003F00007F01C000FE00003FE1C003FC0 0001FFFC03FF0000007FFFFFFE0000003FFFFFF80000000FFFFFE000000001FFFF800000 00007FF80000000000F8000000000000F8000000000000F0000000000000F00000000000 01F0000000000001F0000000000001F0000000000003E0000000000003E0000000000003 E0000000000007E0000000000007E0000000000007C000000000000FC000000000000FC0 00000000000FC000000000000FC000000000001FC000000000001F8000000000000F0000 00000037417BAB40>39 D<1E007F807F80FFC0FFC0FFC0FFC07F807F801E000A0A78891B >58 D<1E007F80FF80FFC0FFC0FFE0FFE0FFE07FE01E60006000600060006000E000C000 C000C001C0018003800300070006000E001C003800700060000B1D78891B>I<00000000 000001C000000000000007E00000000000001FE00000000000007FC0000000000001FF00 000000000007FC0000000000001FF00000000000007FC0000000000001FF000000000000 0FFC0000000000003FF0000000000000FFC0000000000003FF0000000000000FF8000000 0000003FE0000000000000FF80000000000003FE0000000000001FF80000000000007FE0 000000000001FF80000000000007FE0000000000001FF00000000000007FC00000000000 01FF00000000000007FC0000000000001FF00000000000007FC0000000000000FF000000 00000000FF000000000000007FC00000000000001FF000000000000007FC000000000000 01FF000000000000007FC00000000000001FF000000000000007FE00000000000001FF80 0000000000007FE00000000000001FF800000000000003FE00000000000000FF80000000 0000003FE00000000000000FF800000000000003FF00000000000000FFC0000000000000 3FF00000000000000FFC00000000000001FF000000000000007FC00000000000001FF000 000000000007FC00000000000001FF000000000000007FC00000000000001FE000000000 000007E000000000000001C03B3878B44C>I<0000000018000000003C000000007C0000 00007C000000007800000000F800000000F800000000F000000001F000000001F0000000 01E000000003E000000003E000000003C000000007C000000007C000000007800000000F 800000000F800000001F000000001F000000001E000000003E000000003E000000003C00 0000007C000000007C000000007800000000F800000000F800000000F000000001F00000 0001F000000003E000000003E000000003C000000007C000000007C00000000780000000 0F800000000F800000000F000000001F000000001F000000001E000000003E000000003E 000000003C000000007C000000007C00000000F800000000F800000000F000000001F000 000001F000000001E000000003E000000003E000000003C000000007C000000007C00000 0007800000000F800000000F800000000F000000001F000000001F000000003E00000000 3E000000003C000000007C000000007C000000007800000000F800000000F800000000F0 00000001F000000001F000000001E000000003E000000003E000000007C000000007C000 000007800000000F800000000F800000000F000000001F000000001F000000001E000000 003E000000003E000000003C000000007C000000007C000000007800000000F800000000 F800000000F000000000600000000026647BCA31>I<7000000000000000FC0000000000 0000FF000000000000007FC00000000000001FF000000000000007FC00000000000001FF 000000000000007FC00000000000001FF000000000000007FE00000000000001FF800000 000000007FE00000000000001FF800000000000003FE00000000000000FF800000000000 003FE00000000000000FF800000000000003FF00000000000000FFC00000000000003FF0 0000000000000FFC00000000000001FF000000000000007FC00000000000001FF0000000 00000007FC00000000000001FF000000000000007FC00000000000001FE0000000000000 1FE00000000000007FC0000000000001FF00000000000007FC0000000000001FF0000000 0000007FC0000000000001FF0000000000000FFC0000000000003FF0000000000000FFC0 000000000003FF0000000000000FF80000000000003FE0000000000000FF800000000000 03FE0000000000001FF80000000000007FE0000000000001FF80000000000007FE000000 0000001FF00000000000007FC0000000000001FF00000000000007FC0000000000001FF0 0000000000007FC0000000000000FF00000000000000FC00000000000000700000000000 00003B3878B44C>I<0000007FC00000000003FFF8000000000FFFFE000000003F807F80 00000078000FC0000000F00007E0000001C00003F0000003800001F8000007000000FC00 0006000000FC00000FC000007E00000FE000007E00000FE000003F00001FE000003F0000 1FE000003F80001FE000001F80001FC000001F8000070000001F8000000000001FC00000 0000001FC000000000001FC000000000001FC000000000001FC000000000001FC0000000 00001FC000000000001FC0000001FF001FC000000FFFC03FC000007F00F03FC00001F800 383FC00003F0001C3FC0000FC0000C3FC0001F80000E7FC0003F0000067F80007E000007 7F8000FC0000037F8001FC000003FF8003F8000003FF0007F0000003FF000FF0000003FF 000FE0000001FF001FE0000001FE001FE0000003FE003FC0000003FE003FC0000003FC00 7FC0000003FC007F80000003FC007F80000003F8007F80000007F800FF80000007F800FF 00000007F000FF0000000FF000FF0000000FE000FF0000001FE000FE0000001FC000FE00 00001FC000FE0000003F8000FE0000003F8000FE0000007F0000FE0000007E0000FE0000 00FE0000FE000001FC00007E000001F800007F000003F000003F000007E000003F80000F C000001F80001F8000000FC0007F00000007E000FC00000003F807F800000000FFFFE000 0000007FFF80000000000FFC0000000032497CC633>64 D<000000000000300000000000 000000700000000000000000F00000000000000000F00000000000000001F00000000000 000003F00000000000000003F00000000000000007F80000000000000007F80000000000 00000FF8000000000000001FF8000000000000001FF80000000000000037F80000000000 000037F80000000000000067F800000000000000E7F800000000000000C7F80000000000 000187FC0000000000000187FC0000000000000307FC0000000000000703FC0000000000 000603FC0000000000000C03FC0000000000000C03FC0000000000001803FC0000000000 003803FC0000000000003003FC0000000000006003FE0000000000006003FE0000000000 00C003FE000000000001C001FE0000000000018001FE0000000000030001FE0000000000 030001FE0000000000060001FE00000000000E0001FE00000000000C0001FE0000000000 180001FE0000000000180001FF0000000000300001FF0000000000700000FF0000000000 600000FF0000000000C00000FF0000000000C00000FF0000000001800000FF0000000003 FFFFFFFF0000000003FFFFFFFF0000000007FFFFFFFF0000000006000000FF800000000C 000000FF800000001C0000007F80000000180000007F80000000300000007F8000000030 0000007F80000000600000007F80000000E00000007F80000000C00000007F8000000180 0000007F80000001800000007FC0000003000000007FC0000007000000003FC000000600 0000003FC000000E000000003FC000001C000000003FC000003C000000003FC000007C00 0000003FC00000FE000000007FE00007FF00000001FFE0007FFFF000007FFFFFC0FFFFF0 00007FFFFFC0FFFFE000007FFFFFC042477DC649>I<0000FFFFFFFFFF80000000FFFFFF FFFFF0000000FFFFFFFFFFFC00000000FFC00003FF000000007F800000FF80000000FF80 00003FC0000000FF8000003FE0000000FF0000001FE0000000FF0000000FF0000000FF00 00000FF0000001FF0000000FF8000001FE00000007F8000001FE00000007F8000001FE00 000007F8000003FE00000007F8000003FC00000007F8000003FC0000000FF8000003FC00 00000FF8000007FC0000000FF0000007F80000001FF0000007F80000001FE0000007F800 00003FE000000FF80000003FC000000FF00000007F8000000FF0000000FF0000000FF000 0001FE0000001FF0000003FC0000001FE0000007F80000001FE000001FF00000001FE000 003FC00000003FE00001FF000000003FC0001FFC000000003FFFFFFFF0000000003FFFFF FFFE000000007FC000007F800000007F8000001FC00000007F8000000FF00000007F8000 0007F8000000FF80000003FC000000FF00000003FC000000FF00000001FE000000FF0000 0001FE000001FF00000001FF000001FE00000001FF000001FE00000001FF000001FE0000 0001FF000003FE00000001FF000003FC00000001FF000003FC00000001FF000003FC0000 0001FF000007FC00000001FE000007F800000003FE000007F800000003FE000007F80000 0007FC00000FF800000007FC00000FF00000000FF800000FF00000001FF000000FF00000 001FF000001FF00000003FE000001FE00000007FC000001FE0000001FF8000003FE00000 03FE0000003FE000000FFC0000003FC000003FF8000000FFC00001FFE00000FFFFFFFFFF FF800000FFFFFFFFFFFC000000FFFFFFFFFFC000000045447CC34A>I<0000000001FF80 0018000000003FFFF0003800000001FFFFFC003800000007FF007E00780000001FF0000F 80F00000007F800003C1F0000001FE000001C3F0000003FC000000E7F000000FF0000000 7FE000001FE00000003FE000003FC00000003FE00000FF000000001FE00001FE00000000 1FC00003FC000000000FC00007F8000000000FC0000FF8000000000FC0000FF000000000 0F80001FE0000000000780003FC0000000000780007FC000000000078000FF8000000000 070000FF0000000000070001FF0000000000070003FE0000000000070003FE0000000000 060007FC0000000000060007FC000000000006000FF8000000000006000FF80000000000 00001FF8000000000000001FF0000000000000001FF0000000000000003FF00000000000 00003FE0000000000000003FE0000000000000003FE0000000000000007FE00000000000 00007FC0000000000000007FC0000000000000007FC0000000000000007FC00000000000 0000FF8000000000000000FF8000000000000000FF8000000000000000FF800000000000 0000FF800000000000C000FF800000000000C000FF800000000001C000FF800000000001 80007F80000000000180007F80000000000380007F80000000000300007F800000000007 00007F80000000000600003FC0000000000E00003FC0000000001C00003FC00000000018 00001FC0000000003800001FE0000000007000000FE000000000E000000FF000000001C0 000007F80000000380000003F80000000700000001FC0000000E00000000FE0000003C00 0000007F00000078000000003FC00001E0000000001FF0000FC00000000007FE007F0000 00000001FFFFFC0000000000003FFFE000000000000007FF000000000045487CC546>I< 0000FFFFFFFFFF8000000000FFFFFFFFFFF000000000FFFFFFFFFFFC0000000000FFC000 07FF00000000007F8000007FC000000000FF8000001FE000000000FF8000000FF0000000 00FF00000007F800000000FF00000003FC00000000FF00000001FC00000001FF00000000 FE00000001FE00000000FE00000001FE000000007F00000001FE000000007F00000003FE 000000003F80000003FC000000003F80000003FC000000003F80000003FC000000003FC0 000007FC000000003FC0000007F8000000003FC0000007F8000000003FC0000007F80000 00003FC000000FF8000000003FC000000FF0000000003FE000000FF0000000003FE00000 0FF0000000003FE000001FF0000000003FE000001FE0000000003FC000001FE000000000 3FC000001FE0000000003FC000003FE0000000003FC000003FC0000000007FC000003FC0 000000007FC000003FC0000000007FC000007FC0000000007F8000007F8000000000FF80 00007F8000000000FF8000007F8000000000FF800000FF8000000000FF000000FF000000 0001FF000000FF0000000001FE000000FF0000000001FE000001FF0000000003FE000001 FE0000000003FC000001FE0000000007FC000001FE0000000007F8000003FE000000000F F0000003FC000000000FF0000003FC000000001FE0000003FC000000001FC0000007FC00 0000003FC0000007F8000000003F80000007F8000000007F00000007F800000000FE0000 000FF800000001FC0000000FF000000003FC0000000FF000000007F80000000FF0000000 0FE00000001FF00000001FC00000001FE00000003F800000001FE0000000FF000000003F E0000001FC000000003FE000000FF8000000003FC000003FE000000000FFC00003FF8000 0000FFFFFFFFFFFE00000000FFFFFFFFFFF000000000FFFFFFFFFF00000000004B447CC3 51>I<0000FFFFFFFFFFFFFC0000FFFFFFFFFFFFFC0000FFFFFFFFFFFFFC000000FFC000 003FFC0000007F80000003F8000000FF80000001F8000000FF80000000F8000000FF0000 000078000000FF0000000078000000FF0000000038000001FF0000000038000001FE0000 000038000001FE0000000038000001FE0000000038000003FE0000000030000003FC0000 000030000003FC0000000030000003FC0000000030000007FC0000000030000007F80000 600030000007F80000600030000007F80000E0003000000FF80000C0000000000FF00000 C0000000000FF00000C0000000000FF00001C0000000001FF0000180000000001FE00003 80000000001FE0000780000000001FE0000F80000000003FE0007F00000000003FFFFFFF 00000000003FFFFFFF00000000003FFFFFFF00000000007FC0007E00000000007F80001E 00000000007F80001E00000000007F80000E0000000000FF80000C0000000000FF00000C 0000000000FF00000C0000000000FF00001C0000000001FF0000180003000001FE000018 0003000001FE0000180007000001FE0000180006000003FE0000000006000003FC000000 000E000003FC000000000C000003FC000000001C000007FC0000000018000007F8000000 0038000007F80000000030000007F8000000007000000FF8000000007000000FF0000000 00E000000FF000000001E000000FF000000001C000001FF000000003C000001FE0000000 07C000001FE00000000F8000003FE00000003F8000003FE00000007F0000003FC0000003 FF000000FFC000003FFE0000FFFFFFFFFFFFFE0000FFFFFFFFFFFFFE0000FFFFFFFFFFFF FC000046447CC348>I<0000FFFFFFFFFFFFF80000FFFFFFFFFFFFF80000FFFFFFFFFFFF F8000000FFC000003FF80000007F80000007F0000000FF80000003F0000000FF80000001 F0000000FF00000000F0000000FF00000000F0000000FF0000000070000001FF00000000 70000001FE0000000070000001FE0000000070000001FE0000000070000003FE00000000 60000003FC0000000060000003FC0000000060000003FC0000000060000007FC00000000 60000007F80000000060000007F80000C00060000007F80001C0006000000FF800018000 0000000FF0000180000000000FF0000180000000000FF0000380000000001FF000030000 0000001FE0000700000000001FE0000700000000001FE0000F00000000003FE0001E0000 0000003FC000FE00000000003FFFFFFE00000000003FFFFFFE00000000007FFFFFFC0000 0000007F8000FC00000000007F80003C00000000007F80003C0000000000FF8000180000 000000FF0000180000000000FF0000180000000000FF0000380000000001FF0000300000 000001FE0000300000000001FE0000300000000001FE0000700000000003FE0000600000 000003FC0000000000000003FC0000000000000003FC0000000000000007FC0000000000 000007F80000000000000007F80000000000000007F8000000000000000FF80000000000 00000FF0000000000000000FF0000000000000000FF0000000000000001FF00000000000 00001FE0000000000000001FE0000000000000003FE0000000000000003FE00000000000 00003FE000000000000000FFE0000000000000FFFFFFF80000000000FFFFFFF800000000 00FFFFFFF8000000000045447CC33F>I<0000000001FF800018000000003FFFF0003800 000001FFFFFC003800000007FF007E00780000001FF0000F80F00000007F800003C1F000 0001FE000001C3F0000003FC000000E7F000000FF00000007FE000001FE00000003FE000 003FC00000003FE00000FF000000001FE00001FE000000001FC00003FC000000000FC000 07F8000000000FC0000FF8000000000FC0000FF0000000000F80001FE000000000078000 3FC0000000000780007FC000000000078000FF8000000000070000FF0000000000070001 FF0000000000070003FE0000000000070003FE0000000000060007FC0000000000060007 FC000000000006000FF8000000000006000FF8000000000000001FF8000000000000001F F0000000000000001FF0000000000000003FF0000000000000003FE0000000000000003F E0000000000000003FE0000000000000007FE0000000000000007FC0000000000000007F C0000000000000007FC0000000000000007FC000000000000000FF8000000000000000FF 80000001FFFFFF80FF80000003FFFFFF80FF80000003FFFFFF80FF8000000000FFE000FF 80000000007FC000FF80000000007FC000FF80000000007FC0007F80000000007F80007F 80000000007F80007F8000000000FF80007F8000000000FF00007F8000000000FF00003F C000000000FF00003FC000000001FF00003FC000000001FE00001FE000000001FE00001F E000000001FE00000FE000000003FE00000FF000000003FC000007F800000007FC000003 F80000000FFC000001FC0000001FFC000000FE0000003DF80000007F80000078F8000000 3FC00001E0F80000001FF00007C07800000007FE007F007000000001FFFFFC0030000000 003FFFF000000000000007FF000000000045487CC54D>I<0000FFFFFFE003FFFFFF8000 00FFFFFFE003FFFFFF800000FFFFFFE003FFFFFF80000000FFE0000003FF80000000007F 80000001FE0000000000FF80000003FE0000000000FF80000003FE0000000000FF000000 03FC0000000000FF00000003FC0000000000FF00000007FC0000000001FF00000007FC00 00000001FE00000007F80000000001FE00000007F80000000001FE0000000FF800000000 03FE0000000FF80000000003FC0000000FF00000000003FC0000000FF00000000003FC00 00001FF00000000007FC0000001FF00000000007F80000001FE00000000007F80000001F E00000000007F80000003FE0000000000FF80000003FE0000000000FF00000003FC00000 00000FF00000003FC0000000000FF00000007FC0000000001FF00000007FC0000000001F E00000007F80000000001FE00000007F80000000001FE0000000FF80000000003FE00000 00FF80000000003FFFFFFFFFFF00000000003FFFFFFFFFFF00000000003FFFFFFFFFFF00 000000007FC0000001FF00000000007F80000001FE00000000007F80000001FE00000000 007F80000003FE0000000000FF80000003FE0000000000FF00000003FC0000000000FF00 000003FC0000000000FF00000007FC0000000001FF00000007FC0000000001FE00000007 F80000000001FE00000007F80000000001FE0000000FF80000000003FE0000000FF80000 000003FC0000000FF00000000003FC0000000FF00000000003FC0000001FF00000000007 FC0000001FF00000000007F80000001FE00000000007F80000001FE00000000007F80000 003FE0000000000FF80000003FE0000000000FF00000003FC0000000000FF00000003FC0 000000000FF00000007FC0000000001FF00000007FC0000000001FE00000007F80000000 001FE00000007F80000000003FE0000000FF80000000003FE0000000FF80000000003FC0 000000FF0000000000FFE0000003FF80000000FFFFFFE003FFFFFF800000FFFFFFE003FF FFFF800000FFFFFFE003FFFFFF80000051447CC351>I<00007FFFFFF800007FFFFFF800 007FFFFFF00000007FF0000000003FC0000000007FC0000000007FC0000000007F800000 00007F80000000007F8000000000FF8000000000FF0000000000FF0000000000FF000000 0001FF0000000001FE0000000001FE0000000001FE0000000003FE0000000003FC000000 0003FC0000000003FC0000000007FC0000000007F80000000007F80000000007F8000000 000FF8000000000FF0000000000FF0000000000FF0000000001FF0000000001FE0000000 001FE0000000001FE0000000003FE0000000003FC0000000003FC0000000003FC0000000 007FC0000000007F80000000007F80000000007F8000000000FF8000000000FF00000000 00FF0000000000FF0000000001FF0000000001FE0000000001FE0000000001FE00000000 03FE0000000003FC0000000003FC0000000003FC0000000007FC0000000007F800000000 07F80000000007F8000000000FF8000000000FF0000000000FF0000000001FF000000000 1FF0000000001FE0000000007FF00000007FFFFFF00000FFFFFFF00000FFFFFFF000002D 447DC32B>I<0000001FFFFFFC0000003FFFFFFC0000003FFFFFF8000000000FFE000000 000007FC000000000007FC000000000007FC000000000007F8000000000007F800000000 000FF800000000000FF800000000000FF000000000000FF000000000001FF00000000000 1FF000000000001FE000000000001FE000000000003FE000000000003FE000000000003F C000000000003FC000000000007FC000000000007FC000000000007F8000000000007F80 0000000000FF800000000000FF800000000000FF000000000000FF000000000001FF0000 00000001FF000000000001FE000000000001FE000000000003FE000000000003FE000000 000003FC000000000003FC000000000007FC000000000007FC000000000007F800000000 0007F800000000000FF800000000000FF800000000000FF000000000000FF00000000000 1FF000000000001FF000000000001FE000000000001FE000000000003FE000000000003F E000000000003FC000000F80003FC000003FE0007FC000003FE0007F8000007FE0007F80 00007FE0007F8000007FE000FF000000FFC000FF000000FFC001FE000000FF0001FE0000 006C0003FC000000600007F800000070000FF000000030001FE000000038003F80000000 1C007F000000000F81FC0000000003FFF000000000007F8000000000364679C336>I<00 00FFFFFFE00001FFFFC00000FFFFFFE00001FFFFC00000FFFFFFE00001FFFFC0000000FF E00000003FF8000000007F800000001FE000000000FF800000001F0000000000FF800000 003E0000000000FF00000000780000000000FF00000000F00000000000FF00000001C000 00000001FF00000003800000000001FE00000007000000000001FE0000001C0000000000 01FE00000038000000000003FE00000070000000000003FC000000E0000000000003FC00 000380000000000003FC00000700000000000007FC00000E00000000000007F800003800 000000000007F800007000000000000007F80000E00000000000000FF80001C000000000 00000FF00007000000000000000FF0000E000000000000000FF0001C000000000000001F F00078000000000000001FE000F8000000000000001FE001FC000000000000001FE003FC 000000000000003FE00FFC000000000000003FC01FFE000000000000003FC03BFE000000 000000003FC0E1FF000000000000007FC1C1FF000000000000007F8380FF800000000000 007F8700FF800000000000007F9C00FF80000000000000FFB8007FC0000000000000FF70 007FC0000000000000FFC0003FE0000000000000FF80003FE0000000000001FF00003FE0 000000000001FE00001FF0000000000001FE00001FF0000000000001FE00000FF8000000 000003FE00000FF8000000000003FC00000FFC000000000003FC000007FC000000000003 FC000007FC000000000007FC000003FE000000000007F8000003FE000000000007F80000 01FF000000000007F8000001FF00000000000FF8000001FF00000000000FF0000000FF80 000000000FF0000000FF80000000000FF00000007FC0000000001FF00000007FC0000000 001FE00000007FC0000000001FE00000003FE0000000003FE00000003FE0000000003FE0 0000003FF0000000003FC00000003FF800000000FFE00000007FFC000000FFFFFFE0000F FFFFE00000FFFFFFE0001FFFFFE00000FFFFFFE0001FFFFFE0000052447CC353>I<0000 FFFFFFF800000000FFFFFFF800000000FFFFFFF80000000000FFE00000000000007FC000 0000000000FF80000000000000FF80000000000000FF00000000000000FF000000000000 00FF00000000000001FF00000000000001FE00000000000001FE00000000000001FE0000 0000000003FE00000000000003FC00000000000003FC00000000000003FC000000000000 07FC00000000000007F800000000000007F800000000000007F80000000000000FF80000 000000000FF00000000000000FF00000000000000FF00000000000001FF0000000000000 1FE00000000000001FE00000000000001FE00000000000003FE00000000000003FC00000 000000003FC00000000000003FC00000000000007FC00000000000007F80000000000000 7F800000000000007F80000000000000FF80000000000000FF00000000000000FF000000 00000000FF00000000000001FF00000000000001FE00000000C00001FE00000000C00001 FE00000001C00003FE00000001800003FC00000003800003FC00000003000003FC000000 03000007FC00000007000007F800000006000007F80000000E000007F80000001E00000F F80000001C00000FF00000003C00000FF00000003800000FF00000007800001FF0000000 F800001FE0000001F000001FE0000003F000003FE000000FF000003FE000001FE000003F C00000FFE00000FFC00007FFC000FFFFFFFFFFFFC000FFFFFFFFFFFFC000FFFFFFFFFFFF 80003A447CC342>I<0000FFFFC00000000003FFFE0000FFFFC00000000007FFFE0000FF FFC0000000000FFFFE000000FFC0000000000FFE000000006FE0000000001BF800000000 EFE0000000001FF800000000EFE00000000037F800000000CFE00000000067F000000000 CFE00000000067F000000000CFE000000000CFF000000001CFE0000000018FF000000001 8FE0000000018FE00000000187F0000000030FE00000000187F0000000031FE000000003 87F0000000061FE00000000307F00000000C1FC00000000307F00000000C1FC000000003 07F0000000183FC00000000707F0000000303FC00000000607F0000000303F8000000006 03F8000000603F800000000603F8000000607F800000000E03F8000000C07F800000000C 03F8000001807F000000000C03F8000001807F000000000C03F800000300FF000000001C 03F800000600FF000000001803F800000600FE000000001801FC00000C00FE0000000018 01FC00000C01FE000000003801FC00001801FE000000003001FC00003001FC0000000030 01FC00003001FC000000003001FC00006003FC000000007001FC0000C003FC0000000060 01FC0000C003F8000000006000FE00018003F8000000006000FE00018007F800000000E0 00FE00030007F800000000C000FE00060007F000000000C000FE00060007F000000000C0 00FE000C000FF000000001C000FE0018000FF0000000018000FE0018000FE00000000180 007F0030000FE00000000180007F0030001FE00000000380007F0060001FE00000000300 007F00C0001FC00000000300007F00C0001FC00000000300007F0180003FC00000000700 007F0300003FC00000000600007F0300003F800000000600003F8600003F800000000600 003F8600007F800000000E00003F8C00007F800000000C00003F9800007F000000000C00 003F9800007F000000000C00003FB00000FF000000001C00003FE00000FF000000001800 003FE00000FE000000003800001FC00000FE000000003800001FC00001FE000000007800 001F800001FE00000000FC00001F000001FC00000003FF00001F000007FE000000FFFFF8 001E0007FFFFFE0000FFFFF8001C0007FFFFFE0000FFFFF8000C0007FFFFFE00005F447B C35E>I<0000FFFFC000000FFFFF800000FFFFE000000FFFFF800000FFFFE000000FFFFF 800000007FE00000007FE0000000007FF00000001F80000000007FF00000000F00000000 00EFF80000000E0000000000CFF80000000E0000000000C7F80000000C0000000000C7FC 0000001C0000000001C7FC0000001C000000000183FE00000018000000000183FE000000 18000000000181FF00000038000000000381FF00000038000000000300FF000000300000 00000300FF80000030000000000300FF800000700000000007007FC00000700000000006 007FC00000600000000006003FC00000600000000006003FE00000E0000000000E003FE0 0000E0000000000C001FF00000C0000000000C001FF00000C0000000000C000FF80001C0 000000001C000FF80001C000000000180007F800018000000000180007FC000180000000 00180007FC00038000000000380003FE00038000000000300003FE000300000000003000 01FE00030000000000300001FF00070000000000700001FF00070000000000600000FF80 060000000000600000FF800600000000006000007FC00E0000000000E000007FC00E0000 000000C000003FC00C0000000000C000003FE00C0000000000C000003FE01C0000000001 C000001FF01C00000000018000001FF01800000000018000000FF0180000000001800000 0FF83800000000038000000FF838000000000300000007FC30000000000300000007FC30 000000000300000003FE70000000000700000003FE70000000000600000001FE60000000 000600000001FF60000000000600000001FFE0000000000E00000000FFE0000000000C00 000000FFC0000000000C000000007FC0000000000C000000007FC0000000001C00000000 7FC00000000018000000003F800000000038000000003F800000000038000000001F8000 00000078000000001F8000000000FC000000000F0000000003FF000000000F00000000FF FFF80000000F00000000FFFFF80000000700000000FFFFF8000000060000000051447CC3 4E>I<0000000003FF000000000000007FFFF0000000000001FC01FC00000000000FE000 7F00000000003F00001FC000000000FE000007E000000001F8000003F000000007F00000 01F80000000FC0000000FC0000001F80000000FE0000007F000000007E000000FE000000 007F000001FC000000003F000003F8000000003F800007F0000000003F80000FF0000000 001FC0000FE0000000001FC0001FC0000000001FC0003F80000000001FE0007F80000000 001FE0007F00000000001FE000FF00000000001FE001FE00000000000FE001FE00000000 001FF003FC00000000001FF003FC00000000001FF007F800000000001FF007F800000000 001FF00FF800000000001FF00FF000000000001FF01FF000000000001FE01FF000000000 001FE01FE000000000003FE03FE000000000003FE03FE000000000003FE03FE000000000 003FE07FC000000000007FC07FC000000000007FC07FC000000000007FC07FC000000000 00FF807FC00000000000FF80FF800000000000FF80FF800000000001FF00FF8000000000 01FF00FF800000000001FF00FF800000000003FE00FF800000000003FE00FF8000000000 07FC00FF800000000007F800FF80000000000FF8007F80000000000FF0007F8000000000 1FF0007F80000000001FE0007F80000000003FC0007F80000000007F80003FC000000000 7F80003FC000000000FF00003FC000000001FE00001FC000000003FC00001FE000000007 F800000FE000000007F0000007F00000000FE0000007F00000003F80000003F80000007F 00000001FC000000FE00000000FE000001F8000000007F000007F0000000003F80001FC0 000000000FE0007F000000000003F803FC000000000000FFFFE00000000000000FFE0000 00000044487CC54B>I<0000FFFFFFFFFE00000000FFFFFFFFFFE0000000FFFFFFFFFFF8 00000000FFC0000FFE000000007F800001FF00000000FF8000007F80000000FF8000003F C0000000FF0000001FE0000000FF0000001FE0000001FF0000000FF0000001FF0000000F F0000001FE0000000FF0000001FE0000000FF8000003FE0000000FF8000003FE0000000F F8000003FC0000000FF8000003FC0000000FF8000007FC0000000FF8000007FC0000001F F0000007F80000001FF0000007F80000001FF000000FF80000003FE000000FF80000003F E000000FF00000003FC000000FF00000007FC000001FF00000007F8000001FF0000000FF 0000001FE0000001FE0000001FE0000003FC0000003FE0000007F80000003FE000000FF0 0000003FC000003FC00000003FC00000FF000000007FC00007FC000000007FFFFFFFF000 0000007FFFFFFF80000000007F8000000000000000FF8000000000000000FF8000000000 000000FF0000000000000000FF0000000000000001FF0000000000000001FF0000000000 000001FE0000000000000001FE0000000000000003FE0000000000000003FE0000000000 000003FC0000000000000003FC0000000000000007FC0000000000000007FC0000000000 000007F80000000000000007F8000000000000000FF8000000000000000FF80000000000 00000FF0000000000000000FF0000000000000001FF0000000000000001FF00000000000 00001FE0000000000000001FE0000000000000003FE0000000000000003FE00000000000 00003FC000000000000000FFE0000000000000FFFFFFE00000000000FFFFFFE000000000 00FFFFFFE0000000000045447CC33F>I<0000000003FF000000000000007FFFF0000000 000001FC01FC00000000000FE0007F00000000003F80001FC000000000FE00000FE00000 0001F8000003F000000007F0000003F80000000FE0000001FC0000001F80000000FE0000 007F00000000FE000000FE000000007F000001FC000000007F000003F8000000003F8000 07F8000000003F80000FF0000000003FC0000FE0000000001FC0001FC0000000001FC000 3FC0000000001FE0007F80000000001FE0007F80000000001FE000FF00000000001FE001 FE00000000001FE001FE00000000001FF003FE00000000001FF003FC00000000001FF007 FC00000000001FF007F800000000001FF00FF800000000001FF00FF000000000001FF01F F000000000001FE01FF000000000003FE01FE000000000003FE03FE000000000003FE03F E000000000003FE03FE000000000003FE07FC000000000007FC07FC000000000007FC07F C000000000007FC07FC000000000007F807FC00000000000FF80FF800000000000FF80FF 800000000000FF00FF800000000001FF00FF800000000001FF00FF800000000003FE00FF 800000000003FE00FF800000000003FC00FF800000000007F800FF800000000007F8007F 80000000000FF0007F80000000000FF0007F80000000001FE0007F80000000003FC0007F 80000000003F80003F80001F00007F80003FC000FFC000FF00003FC001E0E001FE00001F C003807001FC00001FC007003003F800000FE006003807F0000007E00E00180FE0000007 F00C00181F80000003F80C00183F00000001F81C001CFE00000000FC18001DF800000000 7E18001FF0000000003F9C001FC0000000000FEC007F000000000003FE03FC0000600000 00FFFFFC0000600000000FFE1C0000E000000000001E0000C000000000001E0001C00000 0000001E0001C000000000001E00038000000000003F00078000000000003F000F800000 0000003F803F0000000000003FC0FF0000000000003FFFFE0000000000001FFFFC000000 0000001FFFFC0000000000001FFFF80000000000001FFFF00000000000000FFFE0000000 0000000FFFC000000000000003FF0000000000000000FC00000044597CC54D>I<0000FF FFFFFFF000000000FFFFFFFFFF00000000FFFFFFFFFFE000000000FFC0003FF800000000 7F800007FC00000000FF800001FE00000000FF8000007F00000000FF0000003F80000000 FF0000003FC0000000FF0000001FE0000001FF0000001FE0000001FE0000001FE0000001 FE0000001FF0000001FE0000001FF0000003FE0000001FF0000003FC0000001FF0000003 FC0000001FF0000003FC0000001FF0000007FC0000003FE0000007F80000003FE0000007 F80000003FE0000007F80000007FC000000FF80000007F8000000FF0000000FF8000000F F0000000FF0000000FF0000001FE0000001FF0000003FC0000001FE0000007F80000001F E000000FE00000001FE000001FC00000003FE000007F000000003FC00003FC000000003F C0001FF0000000003FFFFFFF80000000007FFFFFFE00000000007F80007F80000000007F 80000FC0000000007F800007F000000000FF800003F800000000FF000003FC00000000FF 000001FC00000000FF000001FE00000001FF000001FE00000001FE000000FE00000001FE 000000FE00000001FE000001FE00000003FE000001FE00000003FC000001FE00000003FC 000001FE00000003FC000003FE00000007FC000003FE00000007F8000003FE00000007F8 000003FE00000007F8000007FC0000000FF8000007FC0000000FF0000007FC0000000FF0 000007FC0000000FF0000007FC0000001FF0000007FC0018001FE0000007FC0018001FE0 000007FC0018003FE0000007F80038003FE0000007F80030003FC0000007FC007000FFE0 000003FC00E0FFFFFFE00003FC01C0FFFFFFE00001FC0380FFFFFFE00000FE0F00000000 0000003FFE0000000000000007F00045467CC34A>I<00000000FF80018000000007FFF0 03800000003FFFFC0380000000FF007E0780000001F8000F0F80000007E000079F000000 0FC00003FF0000001F000001FF0000003E000000FF0000007C000000FE0000007C000000 7E000000F80000007E000001F00000007E000001F00000003C000003E00000003C000003 E00000003C000007E00000003C000007C000000038000007C000000038000007C0000000 3800000FC00000003800000FC00000003000000FE00000003000000FE00000003000000F E00000000000000FF000000000000007F800000000000007FC00000000000007FF000000 00000003FFE0000000000003FFFC000000000001FFFFC00000000000FFFFFC0000000000 7FFFFF00000000003FFFFFC0000000000FFFFFE00000000003FFFFF800000000003FFFF8 000000000007FFFC0000000000007FFE0000000000000FFE00000000000003FE00000000 000001FF00000000000000FF000000000000007F000000000000007F000000000000003F 000000000000003F000006000000003F000006000000003F000006000000003F00000600 0000003F00000E000000003E00000E000000003E00000C000000003E00000C000000007E 00001E000000007C00001E000000007C00001E00000000F800001E00000000F000003F00 000001F000003F00000003E000003F80000007C000003F8000000F8000007FC000001F00 00007FE000003E0000007CF800007C000000787E0001F8000000F01FC00FE0000000E007 FFFF80000000E001FFFE00000000C0003FF00000000039487BC53C>I<01FFFFFFFFFFFF FFC003FFFFFFFFFFFFFFC003FFFFFFFFFFFFFFC003FF0000FF8000FF8007F00000FF0000 1F8007E00001FF00000F8007800001FF000007800F000001FE000007800F000001FE0000 03800E000001FE000003801C000003FE000003001C000003FC0000030018000003FC0000 030038000003FC0000030030000007FC0000030030000007F80000070070000007F80000 060060000007F800000600E000000FF800000600C000000FF000000600C000000FF00000 0600C000000FF0000006000000001FF0000000000000001FE0000000000000001FE00000 00000000001FE0000000000000003FE0000000000000003FC0000000000000003FC00000 00000000003FC0000000000000007FC0000000000000007F80000000000000007F800000 00000000007F8000000000000000FF8000000000000000FF0000000000000000FF000000 0000000000FF0000000000000001FF0000000000000001FE0000000000000001FE000000 0000000001FE0000000000000003FE0000000000000003FC0000000000000003FC000000 0000000003FC0000000000000007FC0000000000000007F80000000000000007F8000000 0000000007F8000000000000000FF8000000000000000FF0000000000000000FF0000000 000000000FF0000000000000001FF0000000000000001FE0000000000000001FE0000000 000000001FE0000000000000003FE0000000000000003FC0000000000000003FC0000000 000000007FC0000000000000007FC000000000000000FFC000000000000003FFE0000000 00001FFFFFFFFC000000001FFFFFFFFC000000001FFFFFFFF80000000042447EC339>I< 3FFFFFF80003FFFFE03FFFFFF80003FFFFE03FFFFFF80003FFFFE0003FF80000001FF800 001FE000000007E000003FE000000003C000003FE0000000038000003FC0000000038000 003FC0000000030000003FC0000000070000007FC0000000060000007F80000000060000 007F80000000060000007F800000000E000000FF800000000C000000FF000000000C0000 00FF000000000C000000FF000000001C000001FF0000000018000001FE00000000180000 01FE0000000018000001FE0000000038000003FE0000000030000003FC00000000300000 03FC0000000030000003FC0000000070000007FC0000000060000007F800000000600000 07F80000000060000007F800000000E000000FF800000000E000000FF000000000C00000 0FF000000000C000000FF000000001C000001FF000000001C000001FE000000001800000 1FE0000000018000001FE0000000038000003FE0000000038000003FC000000003000000 3FC0000000030000003FC0000000070000007FC0000000070000007F8000000006000000 7F80000000060000007F800000000E000000FF800000000C000000FF000000000C000000 FF000000001C000000FF000000001C000000FF0000000018000000FF0000000038000000 FF0000000030000000FE0000000070000000FE00000000E0000000FF00000000C0000000 7F00000001C00000007F00000003800000007F00000007000000003F0000000E00000000 3F8000001E000000001F8000003C000000001FC0000078000000000FE00001E000000000 07F00003C00000000003F8001F800000000000FF00FE0000000000007FFFF80000000000 001FFFE000000000000001FF00000000000043467AC342>I<7FFFFF8000001FFFF8FFFF FF8000003FFFF8FFFFFF8000003FFFF801FFE000000003FF0000FF8000000001FC0000FF 8000000000F00000FF8000000000E00000FF8000000001C00000FF8000000001C000007F 80000000038000007F80000000030000007F80000000060000007F80000000060000007F 800000000C0000007FC0000000180000007FC0000000180000003FC0000000300000003F C0000000700000003FC0000000600000003FC0000000C00000003FC0000000C00000003F C0000001800000003FE0000003000000003FE0000003000000001FE0000006000000001F E000000E000000001FE000000C000000001FE0000018000000001FE0000018000000001F F0000030000000001FF0000060000000001FF0000060000000000FF00000C0000000000F F00001C0000000000FF0000180000000000FF0000300000000000FF0000300000000000F F8000600000000000FF8000C00000000000FF8000C000000000007F80018000000000007 F80030000000000007F80030000000000007F80060000000000007F800E0000000000007 FC00C0000000000007FC0180000000000003FC0180000000000003FC0300000000000003 FC0600000000000003FC0600000000000003FC0C00000000000003FC1C00000000000003 FE1800000000000003FE3000000000000001FE3000000000000001FE6000000000000001 FEC000000000000001FEC000000000000001FF8000000000000001FF8000000000000001 FF0000000000000001FE0000000000000000FE0000000000000000FC0000000000000000 F80000000000000000F80000000000000000F00000000000000000F00000000000000000 E000000000000045467BC339>II<00003F FFFFE0001FFFFF00003FFFFFE0001FFFFF00003FFFFFE0001FFFFF0000007FFE000003FF E00000003FF8000001FE000000001FF0000000FC000000001FF0000000F0000000000FF8 000001E0000000000FF8000001C00000000007FC000003800000000007FC000006000000 000007FC00000E000000000003FE00001C000000000003FE000038000000000001FF0000 70000000000001FF0000E0000000000001FF8001C0000000000000FF8001800000000000 00FF8003000000000000007FC006000000000000007FC00C000000000000003FE0180000 00000000003FE030000000000000003FE060000000000000001FF0C0000000000000001F F1C0000000000000000FFB80000000000000000FFF00000000000000000FFE0000000000 00000007FC000000000000000007FC000000000000000003FE000000000000000003FE00 0000000000000003FE000000000000000001FF000000000000000003FF00000000000000 0006FF80000000000000000CFF80000000000000001C7FC000000000000000387FC00000 0000000000707FC000000000000000E03FE000000000000001C03FE00000000000000380 1FF000000000000003001FF000000000000006001FF00000000000000C000FF800000000 000018000FF8000000000000300007FC000000000000600007FC000000000000C00007FC 000000000001800003FE000000000003800003FE000000000007000001FF00000000000E 000001FF00000000001C000001FF000000000038000000FF800000000030000000FF8000 000000E00000007FC000000001C00000007FC000000003C00000003FE000000007800000 003FE00000001F800000003FE00000003FC00000007FF0000003FFE0000001FFF800007F FFFC00001FFFFFF000FFFFFC00001FFFFFF000FFFFFC00001FFFFFF00050447EC351>I< FFFFFF8000001FFFFCFFFFFF8000001FFFFCFFFFFF8000001FFFF801FFE000000003FF80 00FFC000000001FC0000FF8000000001F000007FC000000001E000007FC000000003C000 007FC0000000038000003FE0000000070000003FE00000000E0000003FE00000001C0000 001FF0000000180000001FF0000000300000001FF8000000600000000FF8000000C00000 000FF80000018000000007FC0000038000000007FC0000070000000007FC000006000000 0003FE00000C0000000003FE0000180000000003FE0000300000000001FF000060000000 0001FF0000E00000000001FF0001C00000000000FF8001800000000000FF800300000000 0000FFC0060000000000007FC00C0000000000007FC0180000000000007FE03800000000 00003FE0700000000000003FE0600000000000001FF0C00000000000001FF18000000000 00001FF3000000000000000FFE000000000000000FFE000000000000000FFC0000000000 000007F80000000000000007F0000000000000000FF0000000000000000FF00000000000 00000FF0000000000000000FE0000000000000001FE0000000000000001FE00000000000 00001FE0000000000000001FC0000000000000003FC0000000000000003FC00000000000 00003FC0000000000000003F80000000000000007F80000000000000007F800000000000 00007F80000000000000007F0000000000000000FF0000000000000000FF000000000000 0000FF0000000000000001FE0000000000000001FE0000000000000001FE000000000000 0007FF00000000000007FFFFFF000000000007FFFFFF000000000007FFFFFE0000000000 46447CC339>I<00000FC0000000007FF000000001F8381C000007E01C7E00000FC00E7E 00003F0007FE00007F0003FC0000FE0003FC0001FC0003FC0001F80001FC0003F80001F8 0007F00001F8000FF00001F8000FE00003F8001FE00003F0001FE00003F0003FC00003F0 003FC00007F0007FC00007E0007F800007E0007F800007E0007F80000FE000FF80000FC0 00FF00000FC000FF00000FC000FF00001FC000FF00001F8000FE00001F8000FE00001F80 00FE00003F8030FE00003F0070FE00003F0060FE00003F0060FE00007F00E0FE00007F00 C0FE0000FE00C07E0001FE00C07E0003FE01C03E00073E01803F000E3E03801F001C3E03 000F80381F070007C0F00F0E0001FFC007FC00007F0001F0002C2D7CAB33>97 D<000FE0000007FFE0000007FFE0000007FFE00000001FC00000000FC00000001FC00000 001FC00000001F800000001F800000001F800000003F800000003F000000003F00000000 3F000000007F000000007E000000007E000000007E00000000FE00000000FC00000000FC 00000000FC00000001FC00000001F800000001F80FC00001F83FF00003F8F07C0003F3C0 3E0003F7001F0003FE001F8007FC000F8007F8000FC007F0000FC007F0000FE00FE0000F E00FC0000FE00FC0000FE00FC0000FE01FC0000FE01F80000FE01F80000FE01F80001FE0 3F80001FE03F00001FE03F00001FE03F00003FE07F00003FC07E00003FC07E00003FC07E 00007FC07E00007F80FC00007F80FC00007F00FC0000FF00FC0000FF00FC0001FE007C00 01FC007C0001FC007C0003F8007C0007F0007C0007E0003C000FE0003E001FC0001E003F 80001F007E00000F00FC000007C1F0000001FFC00000007F00000023467CC429>I<0000 07F80000003FFF000000FC07C00003F000E00007E00070001F800030003F000070007E00 03F800FE0007F801FC0007F803F8000FF007F8000FF007F0000FF00FF00007C01FE00000 001FE00000003FC00000003FC00000007FC00000007F800000007F800000007F80000000 FF80000000FF00000000FF00000000FF00000000FF00000000FE00000000FE00000000FE 00000000FE00000000FE00000000FE00000018FE00000038FE000000707E000000E07E00 0001C03F000003803F000007001F80001E000F8000380007C001F00003F00FC00000FFFE 0000001FF00000252D7CAB2A>I<0000000001FC00000000FFFC00000000FFFC00000000 FFFC0000000003F80000000001F80000000003F80000000003F80000000003F000000000 03F00000000007F00000000007F00000000007E00000000007E0000000000FE000000000 0FE0000000000FC0000000000FC0000000001FC0000000001FC0000000001F8000000000 1F80000000003F80000000003F80000000003F0000000FC03F0000007FF07F000001F838 7F000007E01C7E00000FC00E7E00003F0007FE00007F0003FE0000FE0003FC0001FC0003 FC0001F80001FC0003F80001FC0007F00001F8000FF00001F8000FE00003F8001FE00003 F8001FE00003F0003FC00003F0003FC00007F0007FC00007F0007F800007E0007F800007 E0007F80000FE000FF80000FE000FF00000FC000FF00000FC000FF00001FC000FF00001F C000FE00001F8000FE00001F8000FE00003F8030FE00003F8070FE00003F0060FE00003F 0060FE00007F00E0FE00007F00C0FE0000FE00C07E0001FE00C07E0003FE01C03E00073E 01803F000E3E03801F001C3E03000F80381F070007C0F00F0E0001FFC007FC00007F0001 F0002E467CC433>I<000007F80000003FFE000001FC07800003F003C0000FC001E0001F 8000E0007F0000E000FE00007001FC00007003F80000F007F80000E007F00000E00FF000 01E01FE00001C01FE00003C03FC00007803FC0001F003FC000FC007FC01FF0007FFFFF80 007FFFF000007F80000000FF80000000FF00000000FF00000000FF00000000FF00000000 FF00000000FE00000000FE00000000FE00000000FE00000000FE000000187E000000387E 000000707F000000E03F000001C03F000003801F000007000F80001E000FC000380007E0 01F00001F00FC000007FFE0000001FF00000252D7CAB2D>I<0000000007E0000000001F F8000000007C1C00000000F80E00000001F03E00000003E07F00000003E0FF00000007E1 FF00000007C1FF00000007C1FE0000000FC0FC0000000FC0780000000FC0000000001F80 000000001F80000000001F80000000001F80000000003F80000000003F00000000003F00 000000003F00000000003F00000000007F00000000007E00000000007E00000000007E00 000000007E00000000FFFFFF800000FFFFFF800000FFFFFF80000000FC0000000000FC00 00000000FC0000000001FC0000000001F80000000001F80000000001F80000000001F800 00000003F80000000003F00000000003F00000000003F00000000003F00000000007F000 00000007E00000000007E00000000007E00000000007E0000000000FE0000000000FC000 0000000FC0000000000FC0000000000FC0000000000FC0000000001FC0000000001F8000 0000001F80000000001F80000000001F80000000003F80000000003F00000000003F0000 0000003F00000000003F00000000007F00000000007E00000000007E00000000007E0000 0000007E0000000000FC0000000000FC0000000000FC0000000000FC0000000000F80000 000001F80000000001F80000000001F00000000001F00000001C03F00000007F03E00000 00FF03E0000000FF03C0000000FF07C0000000FF0780000000FE0F00000000F80F000000 00601E00000000783C000000001FF00000000007C000000000305A7BC530>I<0000007E 0000000003FF800000000FC1E0E000001F0073F000007E0033F00000FC003FF00001F800 1FF00003F8001FE00007F0000FE0000FE0000FE0000FE0000FE0001FC0000FC0003FC000 0FC0003F80001FC0007F80001FC0007F00001F8000FF00001F8000FF00003F8001FF0000 3F8001FE00003F0001FE00003F0001FE00007F0003FE00007F0003FC00007E0003FC0000 7E0003FC0000FE0003FC0000FE0003F80000FC0003F80000FC0003F80001FC0003F80001 FC0003F80001F80003F80001F80003F80003F80003F80007F80001F80007F00001F8000F F00000F8001FF00000FC003FF000007C0077E000003E01E7E000001F078FE0000007FE0F E0000001F80FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F 80000000003F80000000003F80000000003F00000000003F00001C00007E00007F0000FE 0000FF0000FC0000FF0001F80000FF0003F80000FE0007F00000FE000FC00000F8001F80 00007C00FE0000001FFFF800000003FFC00000002C407EAB2F>I<0000FE000000007FFE 000000007FFE000000007FFE0000000001FC0000000000FC0000000001FC0000000001FC 0000000001F80000000001F80000000003F80000000003F80000000003F00000000003F0 0000000007F00000000007F00000000007E00000000007E0000000000FE0000000000FE0 000000000FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F80 3FC000003F81FFF000003F87C0FC00003F0E007E00003F3C003E00007F70003F00007FE0 001F00007FC0001F80007F80001F8000FF80001F8000FF00001F8000FE00001F8000FE00 001F8001FC00003F8001FC00003F0001F800003F0001F800003F0003F800007F0003F800 007E0003F000007E0003F000007E0007F00000FE0007F00000FC0007E00000FC0007E000 01FC000FE00001F8000FE00001F8000FC00003F8000FC00003F0001FC00003F0071FC000 07F0061F800007E0061F80000FE0063F80000FC00E3F80000FC00C3F00000FC01C3F0000 0F80187F00000F80387F00000F80307E00000F80707E00000F80E0FE00000781C0FE0000 07C380FC000001FF00380000007C0030467BC438>I<00001E0000003F0000007F000000 FF000000FF000000FF0000007E0000003800000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 0000003E000000FF800001C3C0000781E0000601F0000E01F0001C01F0001803F0003803 F0003003F0003003F0007007F0006007E0006007E000E00FE000C00FC000001FC000001F 8000001F8000003F8000003F0000003F0000007F0000007E000000FE000000FC000000FC 000001FC000001F8000001F8038003F8030003F0030007F0030007E0070007E0060007E0 0E0007E00C0007C01C0007C0180007C0380007C0700003C0E00003E1C00000FF8000003E 000019437DC121>I<000000003C00000000FE00000000FE00000001FE00000001FE0000 0001FE00000001FC00000000700000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000FC00000003FF0000000F078000001C07C000003803E0 00007003E00000E003E00000C003E00001C003E000018007E000038007E000030007E000 070007E00006000FE0000E000FE0000C000FC00000000FC00000001FC00000001FC00000 001F800000001F800000003F800000003F800000003F000000003F000000007F00000000 7F000000007E000000007E00000000FE00000000FE00000000FC00000000FC00000001FC 00000001FC00000001F800000001F800000003F800000003F800000003F000000003F000 000007F000000007F000000007E000000007E00000000FE00000000FE00000000FC00000 000FC00000001FC00000001F800000001F800000003F80001C003F00007F003F0000FF00 7E0000FF00FC0000FF00FC0000FE01F80000FE03E00000F807C00000781F8000003FFE00 000007F0000000275681C128>I<0000FE000000007FFE000000007FFE000000007FFE00 00000001FC0000000000FC0000000001FC0000000001FC0000000001F80000000001F800 00000003F80000000003F80000000003F00000000003F00000000007F00000000007F000 00000007E00000000007E0000000000FE0000000000FE0000000000FC0000000000FC000 0000001FC0000000001FC0000000001F80000000001F80003F00003F8000FFC0003F8003 C0E0003F000703E0003F001E0FE0007F00380FE0007F00701FE0007E00E01FE0007E01C0 1FE000FE01801FC000FE0380070000FC0700000000FC0E00000001FC1C00000001FC3800 000001F87000000001F8E000000003FBC000000003FF0000000003FF8000000003FFF800 000007F1FE00000007F03F80000007E00FE0000007E007F000000FE003F000000FE003F8 00000FC001F800000FC001F800001FC001F801C01FC001F801801F8001F801801F8001F8 01803F8001F803803F8001F803003F0001F003003F0001F007007F0001F006007F0001F0 0E007E0001F00C007E0001F01C00FE0000F03800FE0000787000FC00003FE0003800000F 80002B467BC433>I<00F80003FC00007F800003FE001FFF0003FFE000071F007C0FC00F 81F8000E0F80E007E01C00FC001C0FC3C003E078007C001807C70003F0E0007E001807CE 0001F1C0003E003807DC0001FB80003F003007D80001FB00003F00300FF80001FF00003F 00700FF00001FE00003F00600FE00001FC00003F00600FE00001FC00003F00E00FC00003 F800007F00C01FC00003F800007E00C01F800003F000007E00001F800003F000007E0000 1F800007F00000FE00003F800007F00000FC00003F000007E00000FC00003F000007E000 00FC00003F00000FE00001FC00007F00000FE00001F800007E00000FC00001F800007E00 000FC00003F800007E00001FC00003F00000FE00001FC00003F00000FC00001F800007F0 0000FC00001F800007E00000FC00003F800007E00E01FC00003F80000FE00C01F800003F 00000FC00C01F800003F00001FC00C01F800007F00001F801C03F800007F00001F801803 F000007E00001F803803F000007E00001F003003F00000FE00001F007007F00000FE0000 1F006007E00000FC00001F00E007E00000FC00001F01C007E00001FC00000F03800FE000 01FC00000F87000FC00001F8000003FE000380000070000000F8004F2D7DAB55>109 D<00F80003FC000003FE001FFF0000071F007C0FC0000E0F80E007E0000C07C3C003E000 1C07C70003F0001807CE0001F0003807DC0001F8003007D80001F800300FF80001F80070 0FF00001F800600FE00001F800600FE00001F800E00FC00003F800C01FC00003F000C01F 800003F000001F800003F000001F800007F000003F800007E000003F000007E000003F00 0007E000003F00000FE000007F00000FC000007E00000FC000007E00001FC000007E0000 1F800000FE00001F800000FC00003F800000FC00003F000000FC00003F007001FC00007F 006001F800007E006001F80000FE006001F80000FC00E003F80000FC00C003F00000FC01 C003F00000F8018003F00000F8038007F00000F8030007E00000F8070007E00000F80E00 07E00000781C000FE000007C38000FC000001FF0000380000007C000342D7DAB3A>I<00 0003FC000000003FFF00000000FE07C0000003F003F0000007E001F800001FC000FC0000 3F00007C00007F00007E0000FE00007F0001FC00003F0003F800003F0007F800003F8007 F000003F800FF000003F801FE000003F801FE000003F803FC000003F803FC000007F807F C000007F807F8000007F807F8000007F807F800000FF80FF800000FF00FF000000FF00FF 000000FF00FF000001FF00FF000001FE00FE000001FE00FE000003FC00FE000003FC00FE 000003F800FE000007F800FE000007F000FE00000FE000FE00001FE0007E00001FC0007E 00003F80003F00007F00003F0000FE00001F8001F800000FC003F0000007E00FC0000001 F03F80000000FFFC000000001FE0000000292D7CAB2F>I<0003E0003F8000000FF800FF E000001C7C03C0F80000383E07007C0000703F1E007E0000601F38003F0000601F70003F 0000E01F60001F8000C01FE0001F8000C03FC0001F8001C03F80001FC001803F00001FC0 01803F00001FC003807F00001FC003007F00001FC003007E00001FC000007E00001FC000 00FE00003FC00000FE00003FC00000FC00003FC00000FC00003FC00001FC00007FC00001 FC00007F800001F800007F800001F800007F800003F80000FF800003F80000FF000003F0 0000FF000003F00000FE000007F00001FE000007F00001FC000007E00003FC000007E000 03F800000FE00007F800000FE00007F000000FE0000FE000000FE0000FC000001FF0001F 8000001FF0003F0000001FB8007E0000001F9800FC0000003F9C01F80000003F8F07E000 00003F03FF800000003F00FC000000007F0000000000007F0000000000007E0000000000 007E000000000000FE000000000000FE000000000000FC000000000000FC000000000001 FC000000000001FC000000000001F8000000000001F8000000000003F8000000000003F8 000000000007F80000000000FFFFF000000000FFFFF000000000FFFFE000000000323F83 AB31>I<00000FC00300003FF0070000F83C0F0003E00E1E000FC0063E001F80073E003F 00037E007F0003FC00FE0001FC01FC0001FC01FC0001FC03F80001F807F80001F807F000 01F80FF00003F80FF00003F01FE00003F01FE00003F03FE00007F03FC00007E03FC00007 E03FC00007E07FC0000FE07F80000FC07F80000FC07F80000FC07F80001FC07F00001F80 FF00001F80FF00001F80FF00003F807F00003F007F00003F007E00003F007E00007F007F 0000FE003F0001FE003F0001FE003F0003FE001F8007FC000F801EFC0007C038FC0003E0 F1FC0001FFC1F800003F01F800000001F800000003F800000003F000000003F000000003 F000000007F000000007E000000007E000000007E00000000FE00000000FC00000000FC0 0000001FC00000001FC00000003FC000001FFFFF80001FFFFF80001FFFFF00283F7DAB2B >I<00F8000FC003FE007FF0070F00F0380E0F83C07C0C07C701FC1C07CE01FC1807DC03 FC3807D803FC3007F803FC300FF003F8700FE000E0600FE00000600FC00000E00FC00000 C01FC00000C01F800000001F800000001F800000003F800000003F000000003F00000000 3F000000007F000000007E000000007E000000007E00000000FE00000000FC00000000FC 00000000FC00000001FC00000001F800000001F800000001F800000003F800000003F000 000003F000000003F000000007F000000007E000000007E000000007E00000000FE00000 000FC00000000380000000262D7DAB2C>I<00000FF00000007FFE000001F00F80000780 01C0000F0000E0001E000060003C000060003C0001F000780007F000780007F000F8000F E000F0000FE000F8000FE000F800038000FC00000000FE00000000FF00000000FFF80000 007FFF8000007FFFE000003FFFF800001FFFFC000007FFFE000000FFFE00000007FF0000 0000FF000000007F000000003F800000001F800E00001F803F00000F007F80000F007F80 000F007F80001F00FF00001E00FF00001E00FC00003C006000003C006000007800700000 F000380001E0001C0007C0000F803F000003FFFC0000007FE00000242D7BAB2E>I<0000 1C0000007E0000007E0000007E000000FE000000FC000000FC000000FC000001FC000001 F8000001F8000001F8000003F8000003F0000003F0000003F0000007F0000007E0000007 E0007FFFFFFCFFFFFFFCFFFFFFF8000FC000000FC000001FC000001F8000001F8000001F 8000003F8000003F0000003F0000003F0000007F0000007E0000007E0000007E000000FE 000000FC000000FC000000FC000001FC000001F8000001F8000001F8000003F8000003F0 000003F0000003F0007007F0006007E0006007E000E007E000C00FE001C00FC001800FC0 03800FC0070007C0060007C00E0007C01C0003E0380001E0F00000FFC000003F00001E3F 7EBD23>I<003E000000000000FF800000E00003C3C00003F0000703E00003F0000601F0 0003F0000E01F00007F0001C01F00007F0001803F00007E0003803F00007E0003003F000 0FE0003003F0000FE0007007F0000FC0006007E0000FC0006007E0001FC000E00FE0001F C000C00FC0001F8000001FC0001F8000001F80003F8000001F80003F8000003F80003F00 00003F00003F0000003F00007F0000007F00007F0000007E00007E0000007E00007E0000 007E0000FE000000FE0000FE000000FC0000FC000000FC0000FC000000FC0001FC018000 FC0001FC038001F80001F8030001F80001F8030001F80001F8070001F80003F8060001F8 0003F0060000F80007F0060000F8000FF00E0000FC000DF00C00007C001DF01C00007C00 39F01800003E00F0F83800001F03C07870000007FF803FE0000001FC000F8000312D7DAB 38>I<003E00000E0000FF80003F8003C3C0007F800703E0007F800601F0007F800E01F0 007F801C01F0007F801803F0003F803803F0001F803003F0000F803003F0000F807007F0 0007806007E00007806007E0000780E00FE0000700C00FC0000300001FC0000300001F80 000700001F80000600003F80000600003F00000600003F00000E00007F00000C00007E00 000C00007E00000C00007E00001C0000FE0000180000FC0000180000FC0000380000FC00 00300000FC0000700001F80000600001F80000E00001F80000C00001F80001C00000F800 01800000F80003800000FC0007000000FC00060000007C000E0000007E001C0000003F00 780000000F81E000000007FFC000000000FE000000292D7DAB2F>I<003E000000000038 00FF800001C000FC03C3C00007E001FE0703E00007E001FE0601F00007E001FE0E01F000 0FE001FE1C01F0000FC001FE1803F0000FC000FE3803F0000FC0007E3003F0001FC0003E 7003F0001F80003E6007F0001F80001E6007E0001F80001E6007E0003F80001EE00FE000 3F00001CC00FC0003F00000C001FC0003F00000C001F80007F00001C001F80007E000018 003F80007E000018003F00007E000018003F0000FE000038007F0000FE000030007E0000 FC000030007E0000FC000030007E0001FC00007000FE0001FC00006000FC0001F8000060 00FC0001F80000E000FC0001F80000C000FC0001F80000C000F80003F00001C000F80003 F000018000F80003F000038000F80003F000030000F80003F000070000FC0007F0000600 00FC0007F8000E00007C000FF8001C00007E000CF8001800003E001CFC003800001F0038 7E00F000000FC0F01F01C0000003FFC00FFF800000007F0001FE00003F2D7DAB46>I<00 00FC0007E00003FF801FFC000F07C0781E001C03E0E01F003801F1C07F007000F1807F00 E000FB80FF01C000FF00FF018000FE00FF038000FE00FE030000FE0038070000FC000006 0000FC0000060001FC00000E0001F800000C0001F80000000001F80000000003F8000000 0003F00000000003F00000000003F00000000007F00000000007E00000000007E0000000 0007E0000000000FE0000000000FC0000000000FC0000000000FC0000000001FC0003800 001FC0003000001F80003000001F80007000003F8000601E003F8000603F003F8000E07F 807F8001C07F806F800180FF80EF800380FF01CF800700FE0187C00E007C0383C01C003C 0F01E078001FFC00FFE00003F0003F8000302D7EAB37>I<00007C0001800001FF000380 0003FF800300000FFFC00700001FFFE00E00001FFFF01C00003F03F838000078007EF800 0070001FF00000600001E00000E00001C00000C0000380000000000700000000000E0000 0000001C0000000000380000000000700000000000E00000000001C00000000003800000 00000700000000000E00000000001C0000000000380000000000700000000000E0000000 0003C0000000000700000000000E00000000001C00001C00003800001800007000001800 00E00000380001C00000300001800000700003900000F00007FF0001E0000FEFC007C000 1E03F01FC0001C01FFFF80003800FFFF00007000FFFE000060007FFC0000E0003FF00000 C0000FC00000292D7CAB2D>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr12 12 85 /Fp 85 128 df<000000001800000000000000003C00000000000000003C000000000000 00007E00000000000000007E0000000000000000FF0000000000000000FF000000000000 0001FF8000000000000001FF80000000000000037FC0000000000000037FC00000000000 00063FE0000000000000063FE00000000000000C1FF00000000000000C1FF00000000000 00180FF8000000000000180FF80000000000003807FC0000000000003007FC0000000000 007003FE0000000000006003FE000000000000E001FF000000000000C001FF0000000000 01C000FF8000000000018000FF80000000000380007FC0000000000300007FC000000000 0700003FE0000000000600003FE0000000000E00001FF0000000000C00001FF000000000 1C00000FF8000000001800000FF80000000038000007FC0000000030000007FC00000000 70000003FE0000000060000003FE00000000E0000001FF00000000C0000001FF00000001 C0000000FF8000000180000000FF80000003800000007FC0000003000000007FC0000003 000000003FC0000006000000003FE0000006000000001FE000000C000000001FF000000C 000000000FF0000018000000000FF80000180000000007F80000300000000007FC000030 0000000003FC0000600000000003FE0000600000000003FE0000C00000000001FF0000C0 0000000001FF0001800000000000FF8001800000000000FF80030000000000007FC00300 00000000007FC0060000000000003FE0060000000000003FE00C0000000000001FF00C00 00000000001FF01FFFFFFFFFFFFFFFF81FFFFFFFFFFFFFFFF83FFFFFFFFFFFFFFFFC3FFF FFFFFFFFFFFFFC7FFFFFFFFFFFFFFFFE7FFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFF4847 7CC651>1 D<0000001FFC00000000000001FFFFC0000000000007F007F000000000001F 8000FC00000000007E00003F0000000001FC00001FC000000003F0000007E000000007E0 000003F00000000FC0000001F80000001F80000000FC0000003F000000007E0000007F00 0000007F000000FE000000003F800001FC000000001FC00003FC000000001FE00003F800 0000000FE00007F8000000000FF00007F00000000007F0000FF00000000007F8000FF000 00000007F8001FE00000000003FC001FE00000000003FC003FE00000000003FE003FC000 00000001FE003FC00000000001FE007FC00000000001FF007FC00000000001FF007FC000 00000001FF007F800000000000FF007F8180000000C0FF00FF8180000000C0FF80FF8180 000000C0FF80FF81FFFFFFFFC0FF80FF81FFFFFFFFC0FF80FF81FFFFFFFFC0FF80FF81FF FFFFFFC0FF80FF81FFFFFFFFC0FF80FF81FFFFFFFFC0FF80FF81FFFFFFFFC0FF80FF8180 000000C0FF80FF8180000000C0FF80FF8180000000C0FF80FF800000000000FF807F8000 00000000FF007FC00000000001FF007FC00000000001FF007FC00000000001FF003FC000 00000001FE003FC00000000001FE003FE00000000003FE001FE00000000003FC001FE000 00000003FC000FE00000000003F8000FF00000000007F80007F00000000007F00007F800 0000000FF00003F8000000000FE00003FC000000001FE00001FC000000001FC00000FE00 0000003F8000007F000000007F0000007F000000007F0000003F80000000FE0000001FC0 000001FC00000007E0000003F000000003F0000007E000000001FC00001FC0000000007E 00003F00000000001F8000FC000000000007F007F0000000000001FFFFC0000000000000 1FFC0000000041487BC54C>I<0000000700000000000000070000000000000007000000 000000000F800000000000000F800000000000000F800000000000001FC0000000000000 1FC00000000000001FC00000000000003FE00000000000003FE00000000000003FE00000 000000007FF00000000000006FF00000000000006FF0000000000000EFF8000000000000 C7F8000000000000C7F8000000000001C7FC00000000000187FC00000000000183FC0000 0000000383FE00000000000303FE00000000000301FE00000000000701FF000000000006 01FF00000000000600FF00000000000E00FF80000000000C00FF80000000000C007F8000 0000000C007F800000000018007FC00000000018003FC00000000018003FC00000000030 003FE00000000030001FE00000000030001FE00000000060001FF00000000060000FF000 00000060000FF000000000C0000FF800000000C00007F800000000C00007F80000000180 0007FC00000001800003FC00000001800003FC00000003000003FE00000003000001FE00 000003000001FE00000006000001FF00000006000000FF00000006000000FF0000000C00 0000FF8000000C0000007F8000000C0000007F800000180000007FC00000180000003FC0 0000180000003FC00000300000003FE00000300000001FE00000300000001FE000007000 00001FF00000600000001FF00000E00000000FF00000F00000000FF80001F00000000FF8 0003F80000000FFC000FFE0000003FFE00FFFFC00007FFFFF8FFFFC00007FFFFF8FFFFC0 0007FFFFF83D477DC644>I<0003FFFFFFFC00000003FFFFFFFC00000003FFFFFFFC0000 000000FFF00000000000007FE00000000000003FC00000000000003FC00000000000003F C00000000000003FC00000000000003FC00000000000003FC00000000000003FC0000000 0000003FC0000000000001FFF000000000003FFFFF8000000001FF3FDFF000000007F03F C1FC0000001FC03FC07F0000003F003FC01F800000FE003FC00FE00001FC003FC007F000 03F8003FC003F80007F0003FC001FC000FE0003FC000FE001FE0003FC000FF001FC0003F C0007F003FC0003FC0007F807FC0003FC0007FC07FC0003FC0007FC07F80003FC0003FC0 FF80003FC0003FE0FF80003FC0003FE0FF80003FC0003FE0FF80003FC0003FE0FF80003F C0003FE0FF80003FC0003FE0FF80003FC0003FE0FF80003FC0003FE07F80003FC0003FC0 7FC0003FC0007FC07FC0003FC0007FC03FC0003FC0007F801FC0003FC0007F001FE0003F C000FF000FE0003FC000FE0007F0003FC001FC0003F8003FC003F80001FC003FC007F000 00FE003FC00FE000003F003FC01F8000001FC03FC07F00000007F03FC1FC00000001FF3F DFF0000000003FFFFF800000000001FFF00000000000003FC00000000000003FC0000000 0000003FC00000000000003FC00000000000003FC00000000000003FC00000000000003F C00000000000003FC00000000000007FE0000000000000FFF00000000003FFFFFFFC0000 0003FFFFFFFC00000003FFFFFFFC00003B447BC346>8 D<0000007FF000000000000FFF FF80000000003FC01FE000000000FE0003F800000003F80000FE0000000FE000003F8000 001FC000001FC000007F8000000FF00000FF00000007F80001FE00000003FC0003FC0000 0001FE0007FC00000001FF0007F800000000FF000FF0000000007F800FF0000000007F80 1FF0000000007FC01FE0000000003FC03FE0000000003FE03FE0000000003FE03FE00000 00003FE07FC0000000001FF07FC0000000001FF07FC0000000001FF07FC0000000001FF0 7FC0000000001FF07FC0000000001FF07FC0000000001FF07FC0000000001FF07FC00000 00001FF07FC0000000001FF03FE0000000003FE03FE0000000003FE03FE0000000003FE0 3FE0000000003FE01FE0000000003FC01FF0000000007FC00FF0000000007F800FF00000 00007F8007F800000000FF0007F800000000FF0003F800000000FE0003FC00000001FE00 01FC00000001FC0000FC00000001F80000FE00000003F800007E00000003F000007F0000 0007F000003F00000007E000001F00000007C000001F8000000FC000000F8000000F8000 00078000000F00000007C000001F00000003C000001E0000C003C000001E0018C001E000 003C0018C001E000003C00186000E000003800306000F000007800306000700000700030 6000700000700030700030000060007030003000006000603800380000E000E03FFFF800 00FFFFE03FFFF80000FFFFE03FFFF80000FFFFE01FFFF80000FFFFC01FFFF80000FFFFC0 1FFFF80000FFFFC03D467CC546>10 D<000000FFC001FC0000000FFFF80FFF0000003F80 3E3F03C00000FC00077E07E00003F8000FFC0FF00007F0003FF81FF0000FE0007FF01FF0 001FC0007FF01FF0003F80007FE01FF0007F00007FE01FF0007F00007FE00FE000FF0000 3FC0038000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE0000 1FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC00000FFFFFFFFFFFFF000FFFFFFFFFFFFF000FFFFFFFF FFFFF00000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE0000 1FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE0000 1FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE0000 1FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC00000 00FE00001FC0000000FE00001FC0000000FE00001FC0000000FE00001FC0000000FE0000 1FC0000001FF00003FF000007FFFFC0FFFFFE0007FFFFC0FFFFFE0007FFFFC0FFFFFE000 3C467EC539>I<000001FF000000000FFFE00000007F80F8000001FC001C000003F8000E 000007E0000F00000FC0007F00001FC000FF80003F8000FF80007F0000FF80007F0000FF 8000FF0000FF8000FE00007F0000FE00003E0000FE0000000000FE0000000000FE000000 0000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE000000 0000FE0000000000FE0000000000FE0000000000FE00003F80FFFFFFFFFF80FFFFFFFFFF 80FFFFFFFFFF8000FE0000FF8000FE00007F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F8000FE00003F 8000FE00003F8001FF00007FC07FFFFC1FFFFF7FFFFC1FFFFF7FFFFC1FFFFF30467EC536 >I<000000FF80003FE0000000000FFFF001FFFC000000003F807C0FF01F00000000FC00 0E3F800380000003F800077F0001C0000007F0000FFC0001E000000FE0003FF8000FE000 001FC0007FF8001FF000003F80007FF0001FF000007F00007FE0001FF000007F00007FE0 001FF00000FF00007FE0001FF00000FE00007FC0000FE00000FE00001FC00007C00000FE 00001FC00000000000FE00001FC00000000000FE00001FC00000000000FE00001FC00000 000000FE00001FC00000000000FE00001FC00000000000FE00001FC00000000000FE0000 1FC00000000000FE00001FC00000000000FE00001FC00000000000FE00001FC000000000 00FE00001FC00000000000FE00001FC00007F000FFFFFFFFFFFFFFFFF000FFFFFFFFFFFF FFFFF000FFFFFFFFFFFFFFFFF00000FE00001FC0001FF00000FE00001FC0000FF00000FE 00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007 F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE0000 1FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F000 00FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC0 0007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE 00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007 F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE0000 1FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F000 00FE00001FC00007F00000FE00001FC00007F00000FE00001FC00007F00000FE00001FC0 0007F00000FE00001FC00007F00001FF00003FE0000FF8007FFFFC0FFFFF83FFFFE07FFF FC0FFFFF83FFFFE07FFFFC0FFFFF83FFFFE04B467EC551>14 D<001F00001F80003F8000 7F80007F8000FF0001FE0003FC0003F80007F0000FE0000F80001F00003E00003C000078 0000E0000040000011126CC431>19 D<1E0003C07F800FF0FF801FF0FFC01FF8FFC01FF8 FFE01FFCFFE01FFCFFE01FFC7FE00FFC1E6003CC0060000C0060000C0060000C0060000C 00E0001C00C0001800C0001800C0001801C00038018000300380007003000060070000E0 060000C00E0001C01C0003803800070070000E0060000C001E1D7DC431>34 D<00000C00001C0000380000700000E00001C00003C0000780000F00000F00001E00003C 00003C0000780000F80000F00001F00001E00003E00003E00007C00007C00007C0000F80 000F80000F80001F00001F00001F00003F00003F00003E00003E00007E00007E00007E00 007E00007C00007C00007C0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC00 00FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC00 007C00007C00007C00007E00007E00007E00007E00003E00003E00003F00003F00001F00 001F00001F00000F80000F80000F800007C00007C00007C00003E00003E00001E00001F0 0000F00000F800007800003C00003C00001E00000F00000F000007800003C00001C00000 E000007000003800001C00000C166476CA26>40 DI<00000000C00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E0000000007FFFFFFFFFFFFFFF00FFFFFFFFFF FFFFFF80FFFFFFFFFFFFFFFF807FFFFFFFFFFFFFFF0000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000001E0 0000000000000001E00000000000000001E00000000000000001E00000000000000000C0 0000000041407BB84C>43 D<1E007F80FF80FFC0FFC0FFE0FFE0FFE07FE01E6000600060 0060006000E000C000C000C001C0018003800300070006000E001C003800700060000B1D 78891B>II<1E 007F807F80FFC0FFC0FFC0FFC07F807F801E000A0A78891B>I<0000FF00000007FFE000 001F81F800003E007C0000FC003F0001F8001F8001F0000F8003E00007C007C00003E007 C00003E00FC00003F00F800001F01F800001F81F800001F83F800001FC3F800001FC3F80 0001FC3F000000FC7F000000FE7F000000FE7F000000FE7F000000FE7F000000FEFF0000 00FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000 FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FF FF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FF7F 000000FE7F000000FE7F000000FE7F000000FE7F000000FE7F800001FE3F800001FC3F80 0001FC3F800001FC1F800001F81F800001F80FC00003F00FC00003F00FC00003F007E000 07E003E00007C003F0000FC001F8001F8000FC003F00003E007C00001F81F8000007FFE0 000000FF000028447CC131>48 D<000030000000F0000001F0000003F000001FF00000FF F000FFFFF000FFE7F000FF07F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007F0000007 F0000007F000000FF800001FFC007FFFFFFF7FFFFFFF7FFFFFFF204278C131>I<0003FE 0000001FFFC000007FFFF00001F80FFC0003C001FE00078000FF000E00007F801C00003F C01C00001FE03800001FF03000000FF07000000FF860000007F86C000007F8FF000007FC FF800007FCFFC00007FCFFC00003FCFFC00003FCFFC00003FCFFC00003FC7F800007FC3F 000007FC00000007FC00000007F800000007F80000000FF80000000FF00000001FF00000 001FE00000001FE00000003FC00000007F800000007F00000000FF00000000FE00000001 FC00000003F800000007F000000007E00000000FC00000001F800000003F000000007C00 000000F800000000F000000001E000000003C000000007800000000F00000C001E00000C 003C00000C0038000018007000001800E000001801C0000018038000003807000000300E 000000701FFFFFFFF01FFFFFFFF03FFFFFFFF07FFFFFFFF0FFFFFFFFE0FFFFFFFFE0FFFF FFFFE026427BC131>I<0001FF0000000FFFE000003FFFFC0000FE01FE0001F0007F8003 C0003FC00700001FE00E00001FE00E00000FF00FE0000FF01FF0000FF81FF0000FF81FF0 0007F81FF80007F81FF00007F81FF00007F80FE0000FF803C0000FF80000000FF0000000 0FF00000000FF00000001FE00000001FE00000003FC00000003F800000007F00000000FE 00000001FC00000003F00000001FC000000FFF0000000FFFF000000001FC000000007F00 0000003F800000001FC00000000FE00000000FF000000007F800000007FC00000003FC00 000003FE00000003FE00000001FE00000001FF00000001FF00000001FF1E000001FF7F80 0001FFFFC00001FFFFC00001FFFFC00001FFFFC00001FFFFC00001FEFF800003FEFF8000 03FE7E000003FC70000007FC30000007F83800000FF81C00000FF00E00001FE00780003F C003E0007F8001FE01FE00007FFFF800000FFFE0000001FF000028447CC131>I<000000 0380000000000380000000000780000000000F80000000000F80000000001F8000000000 3F80000000003F80000000007F8000000000FF8000000000FF8000000001FF8000000003 BF80000000033F80000000073F80000000063F800000000C3F800000001C3F8000000018 3F80000000303F80000000703F80000000603F80000000C03F80000001C03F8000000180 3F80000003003F80000007003F80000006003F8000000C003F8000001C003F8000001800 3F80000030003F80000070003F80000060003F800000E0003F800001C0003F8000018000 3F80000380003F80000300003F80000600003F80000E00003F80000C00003F8000180000 3F80003800003F80003000003F80006000003F8000E000003F8000FFFFFFFFFFC0FFFFFF FFFFC0FFFFFFFFFFC00000003F80000000003F80000000003F80000000003F8000000000 3F80000000003F80000000003F80000000003F80000000003F80000000003F8000000000 3F80000000003F80000000003F8000000000FFE00000007FFFFFC000007FFFFFC000007F FFFFC02A437DC231>I<06000000C007C00007C007FC007F8007FFFFFF0007FFFFFE0007 FFFFFC0007FFFFF80007FFFFE00007FFFF8000063FFC0000060000000006000000000600 000000060000000006000000000600000000060000000006000000000600000000060000 000006000000000600000000060000000006000000000600FF00000607FFC000061F01F0 00063800FC0006F0007E0007C0003F000780001F800780001FC00700000FC00600000FE0 00000007F000000007F000000007F000000007F800000003F800000003F800000003FC00 000003FC00000003FC00000003FC00000003FC3E000003FC7F000003FCFF800003FCFF80 0003FCFF800003FCFF800003FCFF800003F8FF000007F8FE000007F860000007F0600000 07F07000000FF03000000FE03800001FC01C00001FC01E00003F800F00007F00078000FE 0003C001FC0001F807F000007FFFE000001FFF00000007F8000026447BC131>I<000007 FC0000003FFF000000FFFFC00003FC03E00007E000F0001FC00038003F000058007E0001 FC00FE0003FC00FC0007FC01F80007FC03F00007FC03F00007FC07E00003F80FE00001F0 0FE00000001FC00000001FC00000001FC00000003F800000003F800000003F800000007F 800000007F800000007F007F80007F01FFF0007F0780FC00FF0E003E00FF1C001F80FF38 000FC0FF700007E0FF600007E0FFE00003F0FFC00003F8FFC00001F8FFC00001FCFF8000 01FCFF800000FEFF800000FEFF800000FEFF000000FFFF000000FFFF000000FFFF000000 FF7F000000FF7F000000FF7F000000FF7F000000FF7F000000FF7F800000FF3F800000FF 3F800000FF3F800000FE1F800000FE1F800001FE1FC00001FC0FC00001FC0FC00003F807 E00003F807E00007F003F00007E001F8000FC000FC001F80007E003F00003F80FE00000F FFF8000003FFE0000000FF800028447CC131>I<1C00000000001C00000000001F800000 00001FFFFFFFFFC01FFFFFFFFFC01FFFFFFFFFC03FFFFFFFFF803FFFFFFFFF803FFFFFFF FF003FFFFFFFFE00380000000C00300000001C0070000000380060000000300060000000 700060000000E00060000000C000C0000001C000C00000038000C0000007000000000006 00000000000E00000000001C000000000018000000000038000000000070000000000060 0000000000E00000000001C00000000001C0000000000380000000000780000000000700 000000000F00000000000F00000000001F00000000001E00000000003E00000000003E00 000000007E00000000007C00000000007C0000000000FC0000000000FC0000000001FC00 00000001FC0000000001FC0000000003F80000000003F80000000003F80000000003F800 00000007F80000000007F80000000007F80000000007F80000000007F80000000007F800 0000000FF8000000000FF8000000000FF8000000000FF8000000000FF8000000000FF800 0000000FF8000000000FF8000000000FF8000000000FF80000000007F00000000001C000 00002A457BC231>I<0000FF00000007FFE000001FFFF800007F00FE0000FC003F0001F0 001F8003E0000FC003C00007E007C00003F00F800001F00F800001F00F000001F81F0000 00F81F000000F81F000000F81F000000F81F800000F81F800000F81FC00001F81FC00001 F01FE00001F00FF00003E00FFC0003E007FE0007C007FF800F8003FFC01F0001FFF03E00 01FFF87800007FFEF000003FFFC000001FFFC0000007FFE0000003FFF8000007FFFC0000 1E7FFF00007C1FFF8000F80FFFC001E003FFE003C001FFF007C0007FF80F80003FFC1F00 000FFC3E000007FE3E000001FE7C000000FE7C000000FF7C0000007FF80000003FF80000 003FF80000001FF80000001FF80000001FF80000001FF80000001FFC0000001E7C000000 3E7C0000003E7E0000003C3E0000007C1F000000F81F800001F00FC00003E007E00007C0 03F8001F8000FF00FF00003FFFFC00000FFFF0000001FF800028447CC131>I<0000FF00 000007FFE000001FFFF800007F80FC0000FC007E0001F8003F0003F0001F8007E0000FC0 0FE00007E01FC00007E01FC00003F03F800003F03F800003F87F800001F87F000001FC7F 000001FCFF000001FCFF000001FCFF000001FEFF000000FEFF000000FEFF000000FEFF00 0000FEFF000000FEFF000000FFFF000000FFFF000000FFFF000000FF7F000001FF7F0000 01FF7F000001FF3F800001FF3F800003FF1F800003FF1FC00003FF0FC00007FF07E00006 FF07E0000EFF03F0001CFF01F80038FF007C0070FF003F01E0FF000FFF80FE0001FE00FE 00000000FE00000001FE00000001FC00000001FC00000001FC00000001FC00000003F800 000003F800000003F00F800007F01FC00007E03FE0000FE03FE0000FC03FE0001F803FE0 001F803FC0003F003F80007E001E0000FC001C0001F8000F0003F00007E01FE00003FFFF 800000FFFE0000001FF0000028447CC131>I<1E007F807F80FFC0FFC0FFC0FFC07F807F 801E00000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000001E007F807F80FFC0FFC0FFC0FFC07F807F801E000A2B78 AA1B>I<1E007F807F80FFC0FFC0FFC0FFC07F807F801E00000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000001E00 7F00FF80FF80FFC0FFC0FFC0FFC07FC01EC000C000C000C000C000C001C0018001800180 03800300070006000E000C001C003800700060000A3E78AA1B>I<7FFFFFFFFFFFFFFF00 FFFFFFFFFFFFFFFF80FFFFFFFFFFFFFFFF807FFFFFFFFFFFFFFF00000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000007FFFFFFFFFFFFFFF00 FFFFFFFFFFFFFFFF80FFFFFFFFFFFFFFFF807FFFFFFFFFFFFFFF0041187BA44C>61 D<00000000C00000000000000001E00000000000000001E00000000000000001E0000000 0000000003F00000000000000003F00000000000000003F00000000000000007F8000000 0000000007F80000000000000007F8000000000000000FFC000000000000000FFC000000 000000000FFC0000000000000019FE0000000000000019FE0000000000000019FE000000 0000000030FF0000000000000030FF0000000000000070FF80000000000000607F800000 00000000607F80000000000000E07FC0000000000000C03FC0000000000000C03FC00000 00000001C03FE0000000000001801FE0000000000001801FE0000000000003001FF00000 00000003000FF0000000000003000FF0000000000006000FF80000000000060007F80000 000000060007F800000000000C0003FC00000000000C0003FC00000000000C0003FC0000 000000180001FE0000000000180001FE0000000000180001FE0000000000300000FF0000 000000300000FF0000000000700000FF80000000006000007F80000000006000007F8000 000000E000007FC000000000FFFFFFFFC000000000FFFFFFFFC000000001FFFFFFFFE000 0000018000001FE0000000018000001FE0000000030000001FF0000000030000000FF000 0000030000000FF0000000060000000FF80000000600000007F80000000600000007F800 00000C00000003FC0000000C00000003FC0000000C00000003FC0000001800000001FE00 00001800000001FE0000001800000001FE0000003000000000FF0000003000000000FF00 00007800000000FF800000F800000000FF800001FC00000000FFC0000FFF00000003FFE0 00FFFFE000007FFFFFC0FFFFE000007FFFFFC0FFFFE000007FFFFFC042477DC649>65 DI<0000000FFE000060000000FFFFC000E0000003FFFFF000E0 00000FFC01FC01E000003FC0003E01E00000FF00000F83E00003FC000003C7E00007F800 0001E7E0000FF0000000FFE0001FE00000007FE0003FC00000003FE0007F800000001FE0 00FF000000000FE001FE000000000FE001FC0000000007E003FC0000000007E007F80000 000003E007F80000000003E00FF00000000001E00FF00000000001E01FE00000000000E0 1FE00000000000E03FE00000000000E03FE00000000000E03FC00000000000607FC00000 000000607FC00000000000607FC00000000000607FC0000000000000FF80000000000000 FF80000000000000FF80000000000000FF80000000000000FF80000000000000FF800000 00000000FF80000000000000FF80000000000000FF80000000000000FF80000000000000 FF80000000000000FF80000000000000FF80000000000000FF800000000000007FC00000 000000007FC00000000000007FC00000000000607FC00000000000603FC0000000000060 3FE00000000000603FE00000000000601FE00000000000E01FF00000000000E00FF00000 000000C00FF00000000000C007F80000000001C007F800000000018003FC000000000380 01FC00000000038001FE00000000070000FF000000000600007F800000000E00003FC000 00001C00001FE00000003800000FF000000078000007F8000000F0000003FC000001E000 0000FF000007800000003FC0001F000000000FFC00FC0000000003FFFFF00000000000FF FFC000000000000FFE0000003B487BC546>II II<0000000FFE00006000000000FFFFC000E0000000 03FFFFF000E00000000FFC01FC01E00000003FC0003E01E0000000FF00000F83E0000003 FC000003C7E0000007F8000001E7E000000FF0000000FFE000001FE00000007FE000003F C00000003FE000007F800000001FE00000FF000000000FE00001FE000000000FE00001FC 0000000007E00003FC0000000007E00007F80000000003E00007F80000000003E0000FF0 0000000001E0000FF00000000001E0001FE00000000000E0001FE00000000000E0003FE0 0000000000E0003FE00000000000E0003FC0000000000060007FC0000000000060007FC0 000000000060007FC0000000000060007FC000000000000000FF8000000000000000FF80 00000000000000FF8000000000000000FF8000000000000000FF8000000000000000FF80 00000000000000FF8000000000000000FF8000000000000000FF8000000000000000FF80 00000000000000FF8000000000000000FF8000000000000000FF8000000000000000FF80 000001FFFFFFC07FC0000001FFFFFFC07FC0000001FFFFFFC07FC0000000007FF0007FC0 000000003FE0003FC0000000001FE0003FE0000000001FE0003FE0000000001FE0001FE0 000000001FE0001FF0000000001FE0000FF0000000001FE0000FF0000000001FE00007F8 000000001FE00007F8000000001FE00003FC000000001FE00001FE000000001FE00001FE 000000001FE00000FF000000001FE000007F800000001FE000003FC00000003FE000001F E00000003FE000000FF00000007FE0000007F8000000E7E0000003FE000001C7E0000000 FF00000383E00000003FE0000F01E00000000FFC00FE00E000000003FFFFF80060000000 00FFFFE00000000000000FFE0000000042487BC54D>III<000FFFFFFE000FFFFFFE00 0FFFFFFE000003FF80000001FF00000000FF00000000FF00000000FF00000000FF000000 00FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000 FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF 00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00 000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF0000 0000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF000000 00FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF003F0000 FF007F8000FF00FFC000FF00FFC000FF00FFC000FF00FFC000FF00FFC001FE00FF8001FE 00FF0001FE006C0003FC00700003F800380007F8001C0007F0000E000FE00007001F8000 03E07F000000FFFC0000001FE0000027467BC332>IIIII<0000001FFC00000000000001FFFF C0000000000007F007F000000000001F8000FC00000000007E00003F0000000001F80000 0FC000000003F0000007E000000007E0000003F00000000FC0000001F80000001F800000 00FC0000003F000000007E0000007E000000003F000000FE000000003F800001FC000000 001FC00003F8000000000FE00003F8000000000FE00007F00000000007F00007F0000000 0007F0000FF00000000007F8000FE00000000003F8001FE00000000003FC001FE0000000 0003FC003FC00000000001FE003FC00000000001FE003FC00000000001FE007FC0000000 0001FF007FC00000000001FF007F800000000000FF007F800000000000FF007F80000000 0000FF00FF800000000000FF80FF800000000000FF80FF800000000000FF80FF80000000 0000FF80FF800000000000FF80FF800000000000FF80FF800000000000FF80FF80000000 0000FF80FF800000000000FF80FF800000000000FF80FF800000000000FF80FF80000000 0000FF80FF800000000000FF807FC00000000001FF007FC00000000001FF007FC0000000 0001FF007FC00000000001FF003FC00000000001FE003FE00000000003FE003FE0000000 0003FE001FE00000000003FC001FE00000000003FC000FF00000000007F8000FF0000000 0007F80007F8000000000FF00007F8000000000FF00003F8000000000FE00003FC000000 001FE00001FE000000003FC00000FE000000003F8000007F000000007F0000007F800000 00FF0000003F80000000FE0000001FC0000001FC00000007E0000003F000000003F00000 07E000000001FC00001FC0000000007E00003F00000000001F8000FC000000000007F007 F0000000000001FFFFC00000000000001FFC0000000041487BC54C>II82 D<0001FF000300000FFFE00700003FFFF8070000FE00FE0F0001F8001F0F0007E000079F 0007C00003DF000F800001FF001F000000FF003F0000007F003E0000003F007E0000003F 007E0000001F007C0000001F00FC0000000F00FC0000000F00FC0000000700FC00000007 00FC0000000700FE0000000700FE0000000300FE0000000300FF0000000300FF00000003 007F80000000007FC0000000007FE0000000003FF8000000003FFE000000001FFFE00000 000FFFFE00000007FFFFE0000003FFFFFC000001FFFFFF000000FFFFFFC000003FFFFFF0 00000FFFFFF8000001FFFFFC0000001FFFFE00000001FFFE000000001FFF0000000003FF 8000000001FF8000000000FFC0000000007FC0000000003FC0000000001FC0000000001F E0C00000000FE0C00000000FE0C00000000FE0C000000007E0C000000007E0C000000007 E0E000000007E0E000000007E0E000000007E0F000000007C0F00000000FC0F80000000F C0F80000000F80FC0000001F80FE0000001F00FF0000003F00FF8000007E00FBC00000FC 00F9F00001F800F07C0003F000F03FC00FE000E00FFFFF8000E001FFFE0000C0003FF000 002B487BC536>I<3FFFFFFFFFFFFFF83FFFFFFFFFFFFFF83FFFFFFFFFFFFFF83FF0001F F8001FF83F80000FF00003F83E00000FF00000F87C00000FF000007C7800000FF000003C 7800000FF000003C7000000FF000001C7000000FF000001C7000000FF000001C6000000F F000000C6000000FF000000C6000000FF000000C6000000FF000000C6000000FF000000C C000000FF0000006C000000FF0000006C000000FF0000006C000000FF0000006C000000F F00000060000000FF00000000000000FF00000000000000FF00000000000000FF0000000 0000000FF00000000000000FF00000000000000FF00000000000000FF00000000000000F F00000000000000FF00000000000000FF00000000000000FF00000000000000FF0000000 0000000FF00000000000000FF00000000000000FF00000000000000FF00000000000000F F00000000000000FF00000000000000FF00000000000000FF00000000000000FF0000000 0000000FF00000000000000FF00000000000000FF00000000000000FF00000000000000F F00000000000000FF00000000000000FF00000000000000FF00000000000000FF0000000 0000000FF00000000000000FF00000000000000FF00000000000000FF00000000000000F F00000000000000FF00000000000000FF00000000000000FF00000000000000FF0000000 0000000FF00000000000001FF80000000000007FFE0000000001FFFFFFFF80000001FFFF FFFF80000001FFFFFFFF80003F447DC346>IIII89 D91 D<00C0001801C0003803800070070000E00E00 01C00C0001801C00038018000300380007003000060070000E0060000C0060000C006000 0C00E0001C00C0001800C0001800C0001800C0001800CF0019E0FFC01FF8FFE01FFCFFE0 1FFCFFE01FFC7FE00FFC7FE00FFC3FE007FC3FC007F80F0001E01E1D71C431>II<000C0000001E0000003F0000 007F800000F3C00001E1E00003C0F000078078000F003C001E001E003C000F0070000380 E00001C0400000801A0E75C331>I<0007FC000000003FFF80000000F80FE0000003C003 F00000070001F800000E0000FC00000FC0007E00001FE0007F00001FF0003F80001FF000 3F80001FF0003F80001FF0001FC0001FF0001FC0000FE0001FC0000380001FC000000000 1FC0000000001FC0000000001FC0000000001FC00000000FFFC0000001FFFFC000000FFE 1FC000003FC01FC00000FF001FC00003FC001FC00007F8001FC0000FF0001FC0001FE000 1FC0003FC0001FC0007FC0001FC0007F80001FC0007F80001FC060FF00001FC060FF0000 1FC060FF00001FC060FF00003FC060FF00003FC060FF00003FC060FF80007FC0607F8000 EFC0607FC000C7E0C03FC001C7E0C01FE00783F1C007F81E03FF8001FFFC01FF00001FE0 007C002B2E7CAC31>97 D<01FC00000000FFFC00000000FFFC00000000FFFC0000000007 FC0000000003FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC03FC000001FC0FFF800001FC3C07E00001 FC7001F80001FDE0007E0001FD80003F0001FF80001F8001FF00001FC001FE00000FE001 FC000007E001FC000007F001FC000007F001FC000003F801FC000003F801FC000003FC01 FC000003FC01FC000001FC01FC000001FE01FC000001FE01FC000001FE01FC000001FE01 FC000001FE01FC000001FE01FC000001FE01FC000001FE01FC000001FE01FC000001FE01 FC000001FE01FC000001FC01FC000003FC01FC000003FC01FC000003F801FC000003F801 FC000007F001FC000007F001FE00000FE001FE00000FC001FF00001FC001FB00003F8001 F380007E0001E1C000FC0001E0F001F80001C03C07E00001801FFF8000000003FC00002F 467DC436>I<00007F80000003FFF000000FC07C00003F000F0000FC00038001F80001C0 03F8000FC007F0001FE007E0003FE00FE0003FE01FC0003FE01FC0003FE03F80003FE03F 80001FC07F800007007F800000007F800000007F00000000FF00000000FF00000000FF00 000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF0000 0000FF000000007F000000007F800000007F800000003F800000003F800000303FC00000 301FC00000700FE00000600FE00000E007F00000C003F80001C001F800038000FC000700 003F001E00001FC078000007FFF0000000FF8000242E7DAC2B>I<000000007F00000000 3FFF000000003FFF000000003FFF0000000001FF0000000000FF00000000007F00000000 007F00000000007F00000000007F00000000007F00000000007F00000000007F00000000 007F00000000007F00000000007F00000000007F00000000007F00000000007F00000000 007F00000000007F00000000007F00000000007F00000000007F00000000007F0000007F 807F000003FFF07F00000FC07C7F00003F000E7F00007E00077F0000FC0003FF0003F800 01FF0007F00000FF0007E00000FF000FE000007F001FC000007F001FC000007F003F8000 007F003F8000007F007F8000007F007F8000007F007F0000007F00FF0000007F00FF0000 007F00FF0000007F00FF0000007F00FF0000007F00FF0000007F00FF0000007F00FF0000 007F00FF0000007F00FF0000007F00FF0000007F007F0000007F007F8000007F007F8000 007F003F8000007F003F8000007F001FC000007F001FC000007F000FC00000FF000FE000 00FF0007F00001FF0003F00003FF0001F800077F8000FC000E7FC0003F001C7FFE000FC0 F87FFE0003FFE07FFE00007F007F002F467DC436>I<0001FE00000007FFC000001F03F0 00007E00FC0000FC007E0001F8003F0003F0003F0007E0001F800FE0001FC00FC0000FC0 1FC0000FC03F80000FE03F800007E03F800007E07F800007F07F000007F07F000007F0FF 000007F0FF000007F0FF000007F0FFFFFFFFF0FFFFFFFFF0FF00000000FF00000000FF00 000000FF00000000FF00000000FF000000007F000000007F000000007F800000007F8000 00003F800000003F800000301FC00000301FC00000700FC00000600FE00000E007F00000 C003F00001C001F800038000FC000700003E001E00001F80F8000003FFE0000000FF0000 242E7DAC2B>I<00000FE00000007FF8000001F81E000003F03F00000FE07F80001FC0FF 80001F80FF80003F80FF80007F00FF80007F00FF80007F007F0000FE001C0000FE000000 00FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000 FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE000000FFFF FF8000FFFFFF8000FFFFFF800000FE00000000FE00000000FE00000000FE00000000FE00 000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE0000 0000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE000000 00FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000 FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE00000000FE 00000000FE00000000FE00000001FF8000007FFFFF00007FFFFF00007FFFFF000021467E C51E>I<000000000F800001FC007FE0000FFF81F0F0003F07E381F000FC01FF03F001F8 00FE01F003F0007E01E007F0007F000007E0003F00000FE0003F80000FC0001F80001FC0 001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0 001FC0001FC0001FC0001FC0001FC0000FC0001F80000FE0003F800007E0003F000007F0 007F000003F0007E000001F800FC000001FC01F8000003BF07E00000030FFF8000000701 FC0000000700000000000700000000000F00000000000F00000000000F00000000000F80 0000000007C00000000007E00000000007FFFFF8000003FFFFFF000003FFFFFFE00001FF FFFFF800007FFFFFFC0001FFFFFFFE0007C0000FFF000F800000FF003F0000003F803E00 00001F807C0000000FC07C0000000FC0F800000007C0F800000007C0F800000007C0F800 000007C0F800000007C0FC0000000FC07C0000000F807E0000001F803E0000001F001F00 00003E000F8000007C0007E00001F80001F80007E000007F003F8000001FFFFE00000001 FFE000002C427DAC31>I<01FC00000000FFFC00000000FFFC00000000FFFC0000000007 FC0000000003FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC01FE000001FC07FFC00001FC1E07F00001 FC3801F80001FC7001FC0001FCE000FC0001FDC000FE0001FD8000FE0001FF80007F0001 FF00007F0001FF00007F0001FE00007F0001FE00007F0001FE00007F0001FC00007F0001 FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001 FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001 FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001 FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001 FC00007F0003FE0000FF80FFFFF83FFFFEFFFFF83FFFFEFFFFF83FFFFE2F457DC436>I< 01E00007F80007F8000FFC000FFC000FFC000FFC0007F80007F80001E000000000000000 00000000000000000000000000000000000000000000000000000000000000000001FC00 FFFC00FFFC00FFFC0007FC0003FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0003FE00FFFFF8FFFFF8FFFFF815437DC21C>I<00003C000000FF00 0000FF000001FF800001FF800001FF800001FF800000FF000000FF0000003C0000000000 000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000007F80003FFF80003FFF80003FFF800000FF8000007F80 00003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F80 00003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F80 00003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F80 00003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F80 00003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F8000003F80 00003F803E003F807F003F80FF807F00FF807F00FF807E00FF807E00FF80FC007F00F800 3C01F0001E03E00007FF800001FE0000195785C21E>I<01FC00000000FFFC00000000FF FC00000000FFFC0000000007FC0000000003FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC001FFFE001FC001FFFE001FC001FFFE001FC000FFF0001FC0007F80001FC0007E00001 FC0007C00001FC0007800001FC000E000001FC001C000001FC0038000001FC0070000001 FC00E0000001FC01C0000001FC0380000001FC0700000001FC0F00000001FC3F80000001 FC7FC0000001FCFFC0000001FDCFE0000001FF8FF0000001FF07F0000001FE03F8000001 FC03FC000001FC01FC000001FC00FE000001FC00FF000001FC007F000001FC003F800001 FC003FC00001FC001FC00001FC000FE00001FC000FF00001FC0007F00001FC0007F80001 FC0003FC0001FC0003FE0001FC0003FF0003FE0007FF80FFFFF81FFFF8FFFFF81FFFF8FF FFF81FFFF82D457DC433>I<01FC00FFFC00FFFC00FFFC0007FC0003FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0003FE00FFFFF8FFFFF8 FFFFF815457DC41C>I<01FC00FF00001FE00000FFFC07FFE000FFFC0000FFFC0F03F801 E07F0000FFFC3C01FC07803F800007FC7000FE0E001FC00003FCE0007E1C000FC00001FD C0007F38000FE00001FD80007F30000FE00001FF80003FF00007F00001FF00003FE00007 F00001FF00003FE00007F00001FE00003FC00007F00001FE00003FC00007F00001FE0000 3FC00007F00001FC00003F800007F00001FC00003F800007F00001FC00003F800007F000 01FC00003F800007F00001FC00003F800007F00001FC00003F800007F00001FC00003F80 0007F00001FC00003F800007F00001FC00003F800007F00001FC00003F800007F00001FC 00003F800007F00001FC00003F800007F00001FC00003F800007F00001FC00003F800007 F00001FC00003F800007F00001FC00003F800007F00001FC00003F800007F00001FC0000 3F800007F00001FC00003F800007F00001FC00003F800007F00001FC00003F800007F000 01FC00003F800007F00001FC00003F800007F00001FC00003F800007F00001FC00003F80 0007F00001FC00003F800007F00003FE00007FC0000FF800FFFFF81FFFFF03FFFFE0FFFF F81FFFFF03FFFFE0FFFFF81FFFFF03FFFFE04B2C7DAB52>I<01FC01FE0000FFFC07FFC0 00FFFC1E07F000FFFC3801F80007FC7001FC0003FCE000FC0001FDC000FE0001FD8000FE 0001FF80007F0001FF00007F0001FF00007F0001FE00007F0001FE00007F0001FE00007F 0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F 0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F 0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F 0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F 0001FC00007F0001FC00007F0003FE0000FF80FFFFF83FFFFEFFFFF83FFFFEFFFFF83FFF FE2F2C7DAB36>I<00007F8000000003FFF00000000FC0FC0000003E001F0000007C000F 800000F80007C00001F00003E00003E00001F00007C00000F8000FC00000FC000FC00000 FC001F8000007E003F8000007F003F8000007F003F0000003F007F0000003F807F000000 3F807F0000003F807F0000003F80FF0000003FC0FF0000003FC0FF0000003FC0FF000000 3FC0FF0000003FC0FF0000003FC0FF0000003FC0FF0000003FC0FF0000003FC0FF000000 3FC07F0000003F807F0000003F807F8000007F803F8000007F003F8000007F001F800000 7E001FC00000FE000FC00000FC000FE00001FC0007E00001F80003F00003F00001F80007 E00000FC000FC000003E001F0000001FC0FE00000007FFF8000000007F8000002A2E7DAC 31>I<01FC03FC0000FFFC0FFF8000FFFC3C07E000FFFC7001F80007FDE000FE0001FD80 007F0001FF80003F8001FF00001FC001FE00001FE001FC00000FE001FC00000FF001FC00 0007F001FC000007F801FC000003F801FC000003FC01FC000003FC01FC000003FC01FC00 0001FE01FC000001FE01FC000001FE01FC000001FE01FC000001FE01FC000001FE01FC00 0001FE01FC000001FE01FC000001FE01FC000001FE01FC000001FE01FC000003FC01FC00 0003FC01FC000003FC01FC000007F801FC000007F801FC000007F001FC00000FF001FE00 000FE001FE00001FC001FF00003FC001FF00003F8001FF80007E0001FDC000FC0001FCF0 03F80001FC3C0FE00001FC1FFF800001FC03FC000001FC0000000001FC0000000001FC00 00000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC00 00000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000003FE00 000000FFFFF8000000FFFFF8000000FFFFF80000002F3F7DAB36>I<00007F8003000003 FFE00700000FE0780700003F801C0F00007E000E0F0000FC00071F0003F800039F0007F8 0001BF0007F00001FF000FE00000FF001FE00000FF001FC00000FF003FC000007F003FC0 00007F007F8000007F007F8000007F007F8000007F00FF0000007F00FF0000007F00FF00 00007F00FF0000007F00FF0000007F00FF0000007F00FF0000007F00FF0000007F00FF00 00007F00FF0000007F00FF0000007F007F8000007F007F8000007F007F8000007F003F80 00007F003FC000007F001FC000007F001FE00000FF000FE00000FF000FF00001FF0007F0 0001FF0003F80003FF0001FC00077F0000FE000E7F00003F001C7F00000FC0F87F000003 FFE07F0000007F007F00000000007F00000000007F00000000007F00000000007F000000 00007F00000000007F00000000007F00000000007F00000000007F00000000007F000000 00007F00000000007F00000000007F00000000007F0000000000FF800000003FFFFE0000 003FFFFE0000003FFFFE2F3F7DAB33>I<03F803F0FFF81FFCFFF83C3EFFF8707F07F8E0 FF03F9C0FF01F980FF01FB80FF01FB007E01FB003C01FF000001FE000001FE000001FE00 0001FE000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC00 0001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC00 0001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000003FF00 00FFFFFE00FFFFFE00FFFFFE00202C7DAB26>I<003FE01801FFFC3807E01F780F0003F8 1E0001F83C0000F87C00007878000078F8000038F8000038F8000018F8000018FC000018 FC000018FE000018FF8000007FC000007FFC00003FFFE0001FFFFC000FFFFF0007FFFFC0 03FFFFE000FFFFF0001FFFF80000FFF800000FFC000003FCC00001FEC00000FEC000007E E000007EE000003EE000003EF000003EF000003EF000003EF800003CFC00007CFC000078 FE0000F8FF0001F0F38003E0F1F00F80E07FFE00C00FF0001F2E7DAC26>I<0006000000 060000000600000006000000060000000E0000000E0000000E0000000E0000001E000000 1E0000001E0000003E0000007E0000007E000000FE000001FE000007FE00001FFFFFF0FF FFFFF0FFFFFFF000FE000000FE000000FE000000FE000000FE000000FE000000FE000000 FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000 FE000000FE000000FE000000FE000000FE000000FE000000FE000C00FE000C00FE000C00 FE000C00FE000C00FE000C00FE000C00FE000C00FE000C00FE000C007E001C007F001800 7F0018003F0038001F8030001FC0700007E0E00001FFC000007F001E3E7EBC26>I<01FC 00007F00FFFC003FFF00FFFC003FFF00FFFC003FFF0007FC0001FF0003FC0000FF0001FC 00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC 00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC 00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC 00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC00007F0001FC 00007F0001FC00007F0001FC0000FF0001FC0000FF0001FC0000FF0001FC0001FF0001FC 0001FF0000FC0001FF0000FE0003FF00007E00077F80007F000E7FC0003F001C7FFE000F C0787FFE0003FFF07FFE00007F807F002F2D7DAB36>IIIII<3FFFFFFFE03FFFFFFFE03FC0003FE03F00003FC03C 00007F80380000FF00380000FF00300001FE00700003FC00700003FC00700007F8006000 0FF00060000FF00060001FE00060003FC00060003FC00000007F80000000FF00000001FF 00000001FE00000003FC00000007FC00000007F80000000FF00000001FF00000001FE000 60003FC00060007F800060007F80006000FF0000C001FE0000C001FE0000C003FC0000C0 07F80000C007F80001C00FF00001C01FE00003C01FE00003C03FC00007807F80001F80FF 8000FF80FFFFFFFF80FFFFFFFF80232B7DAA2B>II<00F8000203FE000707FF800E0FFFE01C1F1FF8F83807FFF07001FFE0E0007FC0 40001F00200978C131>126 D<1E0007807F000FE0FF801FF0FFC03FF0FFC03FF0FFC03F F0FFC03FF0FF801FF07F000FE01E0007801C0A76C231>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmmi10 10.95 5 /Fq 5 121 df<1E007F80FF80FFC0FFC0FFE0FFE0FFE07FE01E60006000600060006000 E000C000C000C001C001800380030007000E001C001800380030000B1C798919>59 D86 D<000070000000FC000001FC000001FC000001F8 000001F8000003F8000003F8000003F0000003F0000007F0000007F0000007E0000007E0 00000FE000000FE000000FC000000FC0007FFFFFF0FFFFFFF0FFFFFFE0001F8000003F80 00003F8000003F0000003F0000007F0000007F0000007E0000007E000000FE000000FE00 0000FC000000FC000001FC000001FC000001F8000001F8000003F8000003F8000003F000 0003F0000007F0000007F001C007E001C007E003C00FE003800FE003800FC007800FC007 000FC00E000FC01E000FC03C0007C0380007C0700003E1E00001FF8000003E00001C3A7E B821>116 D<007C0000000001FF0000038003C7C0000FC00703C0000FC00F03E0000FC0 0E03E0001FC01C03E0001FC01C07E0001F803807E0001F803807E0003F80780FE0003F80 700FC0003F00700FC0003F00F01FC0007F00F01F80007F00001F80007E00003F80007E00 003F0000FE00003F0000FE00007F0000FC00007E0000FC00007E0001FC0000FE0001FC00 00FC0001F80000FC0001F80000FC0003F80001FC0003F81C01F80003F01C01F80003F01C 01F80007F01C01F80007F03C01F80007E03801F8000FE03801F8001FE07800F8001FE070 00FC003FE070007C0073E0F0007E00E3E0E0003F03C1F1C0000FFF007F800001FC001F00 2E297EA734>I<0001F8003F000007FE00FFE0001E0F83C0F0003807C780F8007003CF03 F800E003FE03F801C003FC07F803C003FC07F8038003F807F8070003F807F0070003F801 C00E0003F000000E0003F000001E0007F000001E0007F00000000007E00000000007E000 0000000FE0000000000FC0000000000FC0000000000FC0000000001FC0000000001F8000 0000001F80000000001F80000000003F80000000003F0001C000003F0001C000003F0001 C000007F0003C01E007F0003803F007E0007807F80FE0007007F80FE000F00FF81FE001E 00FF01DF001C00FE03DF0038007C078F80F0003C0F07C1E0001FFC03FF800007F0007E00 002D297EA734>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr10 10.95 36 /Fr 36 122 df<000001FF000FE00000001FFFE03FFC0000007F00F8FC1E000001FC003F F03F000007F0007FE07F80000FE000FFE0FF80001FC001FFC0FF80003F8001FF80FF8000 7F8001FF80FF80007F0001FF807F00007F0001FF003E0000FE0000FF00000000FE00007F 00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000 FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F 00000000FE00007F00000000FE00007F00000000FE00007F000000FFFFFFFFFFFF8000FF FFFFFFFFFF8000FFFFFFFFFFFF800000FE00007F00000000FE00007F00000000FE00007F 00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000 FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F 00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000 FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F 00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000 FE00007F00000000FE00007F00000000FE00007F00000000FE00007F00000000FE00007F 00000000FE00007F00000000FE00007F00000001FF0000FF8000007FFFFC3FFFFF80007F FFFC3FFFFF80007FFFFC3FFFFF800039407FBF35>11 D<000001FF000000001FFFC00000 007F01F0000001FC0078000007F0001C00000FE0003E00001FC000FF00003F8001FF0000 7F8001FF00007F0001FF00007F0001FF0000FE0001FF0000FE0000FE0000FE0000380000 FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000FE0000000000 FE0000000000FE0000000000FE0000000000FE0000000000FE00007F00FFFFFFFFFF00FF FFFFFFFF00FFFFFFFFFF0000FE0001FF0000FE0000FF0000FE00007F0000FE00007F0000 FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000 FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000 FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000 FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000FE00007F0000 FE00007F0000FE00007F0000FE00007F0000FE00007F0001FF0000FF807FFFFC3FFFFE7F FFFC3FFFFE7FFFFC3FFFFE2F407FBF33>I<0000300000700000E00001C0000380000780 000F00001E00003E00003C0000780000F80000F00001F00001E00003E00003E00007C000 07C0000FC0000F80000F80001F80001F00001F00003F00003F00003F00003E00007E0000 7E00007E00007E00007E00007E00007C0000FC0000FC0000FC0000FC0000FC0000FC0000 FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000FC0000 7C00007E00007E00007E00007E00007E00007E00003E00003F00003F00003F00001F0000 1F00001F80000F80000F80000FC00007C00007C00003E00003E00001E00001F00000F000 00F800007800003C00003E00001E00000F000007800003800001C00000E0000070000030 145A77C323>40 DI<1E007F 80FF80FFC0FFC0FFE0FFE0FFE07FE01E60006000600060006000E000C000C000C001C001 800380030007000E001C001800380030000B1C798919>44 DI<1E007F807F80FFC0FFC0FFC0FFC07F807F801E000A0A 798919>I68 D70 D<0007FC000C001FFF801C007FFFF03C01FC03F83C03 F0007E7C07C0001FFC0F80000FFC1F800007FC3F000003FC3E000001FC7E000000FC7E00 0000FC7C0000007CFC0000007CFC0000007CFC0000003CFC0000003CFC0000003CFE0000 001CFE0000001CFF0000001CFF0000001C7F800000007FC00000007FE00000003FF80000 003FFF8000001FFFF800000FFFFF800007FFFFF00003FFFFFC0001FFFFFF0000FFFFFFC0 003FFFFFE00007FFFFF000007FFFF0000007FFF80000007FFC0000000FFC00000007FE00 000003FE00000001FE00000000FF00000000FFE00000007FE00000007FE00000007FE000 00003FE00000003FF00000003FF00000003FF00000003FF00000003EF80000003EF80000 007EFC0000007CFE000000FCFF000000F8FF800001F8FFC00003F0FFE00007E0F9FC000F C0F07F803F80F01FFFFE00E007FFF800C0007FC00028427BBF33>83 D<3FFFFFFFFFFFFF803FFFFFFFFFFFFF803FFFFFFFFFFFFF803FF0007FE001FF803F8000 3FC0003F807F00003FC0001FC07E00003FC00007C07C00003FC00007C07800003FC00003 C07800003FC00003C07800003FC00003C07000003FC00001C07000003FC00001C0700000 3FC00001C07000003FC00001C07000003FC00001C0E000003FC00000E0E000003FC00000 E0E000003FC00000E0E000003FC00000E0E000003FC00000E00000003FC0000000000000 3FC00000000000003FC00000000000003FC00000000000003FC00000000000003FC00000 000000003FC00000000000003FC00000000000003FC00000000000003FC0000000000000 3FC00000000000003FC00000000000003FC00000000000003FC00000000000003FC00000 000000003FC00000000000003FC00000000000003FC00000000000003FC0000000000000 3FC00000000000003FC00000000000003FC00000000000003FC00000000000003FC00000 000000003FC00000000000003FC00000000000003FC00000000000003FC0000000000000 3FC00000000000003FC00000000000003FC00000000000003FC00000000000003FC00000 000000003FC00000000000003FC00000000000007FE0000000000000FFF00000000007FF FFFFFE00000007FFFFFFFE00000007FFFFFFFE00003B3D7DBC42>I87 D<000FF800000000FFFE00000003F01F80 0000078007E000000F8003F000000FE001F800001FF001FC00001FF000FE00001FF000FE 00001FF000FE00001FF0007F00000FE0007F00000380007F00000000007F00000000007F 00000000007F00000000007F000000001FFF00000003FFFF0000001FF87F0000007F807F 000001FC007F000007F8007F00000FE0007F00001FC0007F00003F80007F00003F80007F 00007F00007F00007F00007F0380FE00007F0380FE00007F0380FE00007F0380FE0000FF 0380FE0000FF0380FE0000FF03807F0001FF03807F0003BF03803F80071F87001FC00E1F CF0007F03C0FFE0001FFF807FC00003FC001F000292A7DA82D>97 D<01FC00000000FFFC00000000FFFC00000000FFFC0000000007FC0000000003FC000000 0001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC000000 0001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC000000 0001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC03FC00 0001FC1FFF800001FC7C07E00001FDE001F00001FFC000FC0001FF80007E0001FF00003F 0001FE00003F8001FC00001F8001FC00001FC001FC00000FE001FC00000FE001FC00000F F001FC00000FF001FC000007F001FC000007F801FC000007F801FC000007F801FC000007 F801FC000007F801FC000007F801FC000007F801FC000007F801FC000007F801FC000007 F801FC000007F001FC000007F001FC00000FF001FC00000FF001FC00000FE001FC00001F E001FC00001FC001FE00001F8001FE00003F0001FF00007F0001FF8000FE0001F3C001F8 0001F1E003F00001E0780FC00001C03FFF0000000007F800002D407EBE33>I<0001FF00 00000FFFE000003F00F800007C001E0001F8001F0003F0007F0007F000FF800FE000FF80 0FC000FF801FC000FF801FC000FF803F80007F003F80001C007F800000007F800000007F 00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00000000FF00 000000FF00000000FF00000000FF00000000FF000000007F800000007F800000007F8000 00003F800001C03FC00001C01FC00003C01FC00003800FE000078007F000070003F0000E 0001F8001E0000FC007800003F01F000000FFFC0000001FE0000222A7DA828>I<000000 01FC00000000FFFC00000000FFFC00000000FFFC0000000007FC0000000003FC00000000 01FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC00000000 01FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC00000000 01FC0000000001FC0000000001FC0000000001FC0000000001FC000000FF01FC000007FF E1FC00001F80F9FC00007E003DFC0000FC001FFC0003F80007FC0007F00007FC0007E000 03FC000FC00001FC001FC00001FC003FC00001FC003F800001FC007F800001FC007F8000 01FC007F000001FC007F000001FC00FF000001FC00FF000001FC00FF000001FC00FF0000 01FC00FF000001FC00FF000001FC00FF000001FC00FF000001FC00FF000001FC00FF0000 01FC007F000001FC007F800001FC007F800001FC003F800001FC003F800001FC001FC000 01FC000FC00003FC000FE00003FC0007E00007FC0003F0000FFE0001F8001FFF00007C00 79FFF8003F01F1FFF8000FFFC1FFF80001FE01FC002D407DBE33>I<0001FE0000000FFF C000003F03F00000FC01F80001F800FC0003F0007E0007E0003F000FE0003F800FC0001F 801FC0001FC03F80000FC03F80000FC07F80000FC07F80000FE07F00000FE07F00000FE0 FF00000FE0FF00000FE0FFFFFFFFE0FFFFFFFFE0FF00000000FF00000000FF00000000FF 00000000FF00000000FF000000007F000000007F000000007F800000003F800000003F80 0000E01FC00000E01FC00001E00FC00001C007E00003C007F000078003F800070000FC00 1E00007E003C00001F80F8000007FFE0000000FF0000232A7EA828>I<00001FC000007F F80001F83C0007E07E000FC0FF001FC1FF003F81FF003F01FF007F01FF007F00FE00FE00 7C00FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00 0000FE000000FE000000FE000000FE000000FE0000FFFFFF00FFFFFF00FFFFFF0000FE00 0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00 0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00 0000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE000000FE00 0000FE000000FE000000FE000000FE000001FF00007FFFFF007FFFFF007FFFFF0020407E BF1C>I<000000007C000003F801FF00001FFF078F80007E0FDE1F8000F803F81F8003F0 01F81F8003F001F81F8007E000FC06000FE000FE00000FC0007E00001FC0007F00001FC0 007F00001FC0007F00001FC0007F00001FC0007F00001FC0007F00001FC0007F00001FC0 007F00000FC0007E00000FE000FE000007E000FC000003F001F8000003F001F8000001F8 03E0000003FE0FC00000071FFF0000000703F80000000600000000000E00000000000E00 000000000E00000000000F00000000000F00000000000F80000000000FC00000000007FF FFE0000007FFFFFE000003FFFFFF800001FFFFFFE00000FFFFFFF00003FFFFFFF8000FC0 001FFC001F000001FE003E000000FE007C0000007E007C0000003F00F80000003F00F800 00001F00F80000001F00F80000001F00F80000001F00FC0000003F007C0000003E007E00 00007E003F000000FC001F800001F8000FC00003F00003F0000FC00000FE007F0000003F FFFC00000003FFC00000293D7EA82D>I<01FC00000000FFFC00000000FFFC00000000FF FC0000000007FC0000000003FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC01FE000001FC07FFC00001FC1E07E00001FC7803F00001 FCE001F80001FDC001FC0001FD8001FC0001FF8000FE0001FF0000FE0001FF0000FE0001 FE0000FE0001FE0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001 FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001 FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001 FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001 FC0000FE0001FC0000FE0003FE0001FF00FFFFF87FFFFCFFFFF87FFFFCFFFFF87FFFFC2E 3F7DBE33>I<01E00007F80007F8000FFC000FFC000FFC000FFC0007F80007F80001E000 000000000000000000000000000000000000000000000000000000000000000000000000 01FC007FFC007FFC007FFC0007FC0003FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 01FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC00 03FE00FFFFF0FFFFF0FFFFF0143E7DBD1A>I<01FC00000000FFFC00000000FFFC000000 00FFFC0000000007FC0000000003FC0000000001FC0000000001FC0000000001FC000000 0001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC000000 0001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC000000 0001FC0000000001FC0000000001FC0000000001FC00FFFF8001FC00FFFF8001FC00FFFF 8001FC003FFC0001FC003FE00001FC003F800001FC003F000001FC003C000001FC007800 0001FC00F0000001FC01E0000001FC07C0000001FC0F80000001FC1F00000001FC3E0000 0001FC7F00000001FCFF80000001FDFF80000001FFDFC0000001FF9FE0000001FF0FE000 0001FE07F0000001FC07F8000001F803FC000001F801FC000001F801FE000001F800FF00 0001F8007F000001F8007F800001F8003FC00001F8001FC00001F8001FE00001F8000FF0 0001F8000FF00001F8000FF80003FC000FFE00FFFFF07FFFE0FFFFF07FFFE0FFFFF07FFF E02B3F7EBE30>107 D<01FC00FFFC00FFFC00FFFC0007FC0003FC0001FC0001FC0001FC 0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC 0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC 0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC 0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC0001FC 0001FC0001FC0003FE00FFFFF8FFFFF8FFFFF8153F7DBE1A>I<01F801FE0000FF0000FF F807FFC003FFE000FFF81E07E00F03F000FFF87803F03C01F80007F8E001F87000FC0003 F9C001FCE000FE0001F98001FCC000FE0001FB8000FFC0007F0001FB0000FF80007F0001 FF0000FF80007F0001FE0000FF00007F0001FE0000FF00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0001 FC0000FE00007F0001FC0000FE00007F0001FC0000FE00007F0003FE0001FF0000FF80FF FFF87FFFFC3FFFFEFFFFF87FFFFC3FFFFEFFFFF87FFFFC3FFFFE47287DA74C>I<01F801 FE0000FFF807FFC000FFF81E07E000FFF87803F00007F8E001F80003F9C001FC0001F980 01FC0001FB8000FE0001FB0000FE0001FF0000FE0001FE0000FE0001FE0000FE0001FC00 00FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC00 00FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC00 00FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC00 00FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0003FE00 01FF00FFFFF87FFFFCFFFFF87FFFFCFFFFF87FFFFC2E287DA733>I<0000FF00000007FF E000001F81F800007E007E0000F8001F0001F0000F8003E00007C007C00003E00FC00003 F01F800001F81F800001F83F800001FC3F800001FC7F000000FE7F000000FE7F000000FE 7F000000FEFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF000000FFFF 000000FFFF000000FFFF000000FF7F000000FE7F000000FE7F000000FE3F800001FC3F80 0001FC3F800001FC1F800001F80FC00003F00FC00003F007E00007E003F0000FC001F800 1F80007E007E00003F81FC00000FFFF0000000FF0000282A7EA82D>I<01FC03FC0000FF FC1FFF8000FFFC7C0FE000FFFDE003F00003FFC001FC0001FF8000FE0001FF00007F0001 FE00003F8001FC00003F8001FC00001FC001FC00001FE001FC00001FE001FC00000FF001 FC00000FF001FC00000FF001FC000007F801FC000007F801FC000007F801FC000007F801 FC000007F801FC000007F801FC000007F801FC000007F801FC000007F801FC000007F801 FC00000FF001FC00000FF001FC00000FF001FC00000FF001FC00001FE001FC00001FE001 FC00003FC001FE00003F8001FE00007F0001FF00007F0001FF8000FE0001FFC001F80001 FDE007F00001FC780FC00001FC3FFF000001FC07F8000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001 FC0000000001FC0000000001FC0000000001FC0000000001FC0000000003FE00000000FF FFF8000000FFFFF8000000FFFFF80000002D3A7EA733>I<0000FF001C000007FFC03C00 001F80F03C00007F00387C0000FC001C7C0003F8000E7C0007F0000FFC0007F00007FC00 0FE00003FC001FE00003FC003FC00003FC003FC00001FC007F800001FC007F800001FC00 7F800001FC007F800001FC00FF000001FC00FF000001FC00FF000001FC00FF000001FC00 FF000001FC00FF000001FC00FF000001FC00FF000001FC00FF000001FC00FF000001FC00 7F800001FC007F800001FC007F800001FC003FC00001FC003FC00001FC001FC00003FC00 0FE00003FC000FE00007FC0007F0000FFC0003F8000FFC0001FC003DFC00007E0079FC00 003F81F1FC00000FFFC1FC000001FE01FC0000000001FC0000000001FC0000000001FC00 00000001FC0000000001FC0000000001FC0000000001FC0000000001FC0000000001FC00 00000001FC0000000001FC0000000001FC0000000001FC0000000003FE00000000FFFFF8 000000FFFFF8000000FFFFF82D3A7DA730>I<01F807E0FFF81FF8FFF8787CFFF8E1FE07 F9C1FE03F981FE01FB81FE01FB01FE01FB00FC01FF003001FE000001FE000001FE000001 FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001 FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001 FC000001FC000001FC000001FC000001FC000003FE0000FFFFFE00FFFFFE00FFFFFE001F 287EA724>I<003FC06001FFF8E007C03FE01F000FE03E0007E03C0003E07C0003E07800 01E0F80001E0F80000E0F80000E0FC0000E0FE0000E0FF0000E0FF8000007FF800007FFF C0003FFFF8001FFFFE000FFFFF0007FFFF8001FFFFC0003FFFE00003FFF000001FF00000 0FF8E00003F8E00003F8E00001F8F00001F8F00000F8F00000F8F80000F8F80000F0FC00 00F0FC0001F0FE0001E0FF0003C0FF800780F3E01F00E0FFFC00C01FE0001D2A7DA824> I<001C0000001C0000001C0000001C0000001C0000001C0000003C0000003C0000003C00 00003C0000007C0000007C000000FC000000FC000001FC000003FC000007FC00001FFFFF C0FFFFFFC0FFFFFFC001FC000001FC000001FC000001FC000001FC000001FC000001FC00 0001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC000001FC00 0001FC000001FC000001FC000001FC000001FC00E001FC00E001FC00E001FC00E001FC00 E001FC00E001FC00E001FC00E001FC00E000FC00E000FE01C000FE01C0007F03C0003F03 80001F87000007FE000001F8001B397EB723>I<01FC0000FE00FFFC007FFE00FFFC007F FE00FFFC007FFE0007FC0003FE0003FC0001FE0001FC0000FE0001FC0000FE0001FC0000 FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000 FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000 FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000FE0001FC0000 FE0001FC0000FE0001FC0000FE0001FC0001FE0001FC0001FE0001FC0001FE0001FC0003 FE0000FC0003FE0000FC0007FE0000FE0006FF00007E000EFF80003F001CFFFC001FC078 FFFC0007FFE0FFFC0000FF80FE002E297DA733>IIIII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmbx10 10.95 7 /Fs 7 117 df<00000000FC0000000000000000FC0000000000000001FE000000000000 0001FE0000000000000003FF0000000000000003FF0000000000000003FF000000000000 0007FF8000000000000007FF800000000000000FFFC00000000000000FFFC00000000000 000FFFC00000000000001FFFE00000000000001FFFE00000000000003FFFF00000000000 003FFFF00000000000003FFFF00000000000007FFFF80000000000007CFFF80000000000 00FCFFFC000000000000F87FFC000000000000F87FFC000000000001F87FFE0000000000 01F03FFE000000000003F03FFF000000000003E01FFF000000000007E01FFF8000000000 07C01FFF800000000007C00FFF80000000000FC00FFFC0000000000F8007FFC000000000 1F8007FFE0000000001F0007FFE0000000001F0003FFE0000000003F0003FFF000000000 3E0001FFF0000000007E0001FFF8000000007C0000FFF8000000007C0000FFF800000000 FC0000FFFC00000000F800007FFC00000001FFFFFFFFFE00000001FFFFFFFFFE00000001 FFFFFFFFFE00000003FFFFFFFFFF00000003FFFFFFFFFF00000007E000001FFF80000007 C000000FFF8000000FC000000FFFC000000F8000000FFFC000000F80000007FFC000001F 80000007FFE000001F00000003FFE000003F00000003FFF000003E00000003FFF000003E 00000001FFF000007E00000001FFF800007C00000000FFF800FFFFFC0000FFFFFFFCFFFF FC0000FFFFFFFCFFFFFC0000FFFFFFFCFFFFFC0000FFFFFFFCFFFFFC0000FFFFFFFC463F 7CBE4F>65 D<0007FFC00000003FFFF8000001FFFFFF000003FFFFFF800007FE03FFC000 0FF800FFE0000FFC003FF0001FFE003FF8001FFE001FFC001FFE001FFC001FFE001FFC00 1FFE000FFE001FFE000FFE000FFC000FFE0007F8000FFE0001E0000FFE000000000FFE00 0000003FFE000000FFFFFE00000FFFFFFE00007FFFFFFE0001FFFE0FFE0003FFE00FFE00 0FFF800FFE001FFE000FFE003FFC000FFE003FF8000FFE007FF0000FFE00FFF0000FFE00 FFE0000FFE00FFE0000FFE00FFE0000FFE00FFE0000FFE00FFE0001FFE00FFF0001FFE00 7FF0003FFE007FF8007BFF803FFC00FBFFFE1FFF07F3FFFE0FFFFFE1FFFE03FFFF80FFFE 00FFFF003FFE001FF80000002F2B7DA933>97 D<00FF0000000000FFFF0000000000FFFF 0000000000FFFF0000000000FFFF0000000000FFFF000000000007FF000000000003FF00 0000000003FF000000000003FF000000000003FF000000000003FF000000000003FF0000 00000003FF000000000003FF000000000003FF000000000003FF000000000003FF000000 000003FF000000000003FF000000000003FF000000000003FF000000000003FF00FFE000 0003FF07FFFC000003FF1FFFFF800003FF7FFFFFC00003FFFF81FFF00003FFFC003FF800 03FFF0001FFC0003FFE0000FFE0003FFC00007FE0003FF800007FF0003FF800003FF8003 FF800003FF8003FF800003FFC003FF800001FFC003FF800001FFC003FF800001FFC003FF 800001FFE003FF800001FFE003FF800001FFE003FF800001FFE003FF800001FFE003FF80 0001FFE003FF800001FFE003FF800001FFE003FF800001FFE003FF800001FFE003FF8000 01FFC003FF800001FFC003FF800003FFC003FF800003FF8003FF800003FF8003FF800003 FF0003FF800007FF0003FFC00007FE0003FFE0000FFC0003FFF0001FF80003FFFC007FF0 0003FCFF01FFE00003F87FFFFFC00003F01FFFFF000003E007FFFC0000000001FFC00000 33407DBE3A>I<00007FF0000007FFFF00001FFFFFC0007FFFFFE000FFF01FF001FF800F F803FF001FF807FE003FFC0FFE003FFC1FFC003FFC1FFC003FFC3FF8003FFC3FF8003FFC 7FF8001FF87FF0000FF07FF00003C0FFF0000000FFF0000000FFF0000000FFF0000000FF F0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF00000007FF0 0000007FF80000007FF80000007FF80000003FF800003E3FFC00003E1FFC00007E0FFE00 007C07FF0000FC07FF8001F803FFC003F000FFF81FE0007FFFFFC0001FFFFF800007FFFE 0000007FF000272B7DA92E>I<01FE01FE00FFFE07FF80FFFE0FFFE0FFFE1FFFF0FFFE3F 1FF0FFFE7C3FF807FEF83FF803FEF03FF803FFE03FF803FFE03FF803FFC01FF003FFC00F E003FF8007C003FF80000003FF80000003FF80000003FF00000003FF00000003FF000000 03FF00000003FF00000003FF00000003FF00000003FF00000003FF00000003FF00000003 FF00000003FF00000003FF00000003FF00000003FF00000003FF00000003FF00000003FF 00000003FF00000003FF000000FFFFFF0000FFFFFF0000FFFFFF0000FFFFFF0000FFFFFF 000025297DA82B>114 D<003FFC1E0001FFFFBE0007FFFFFE000FFFFFFE001FF00FFE00 3F8001FE007F0000FE007E00007E007E00007E00FE00003E00FE00003E00FF00003E00FF 80003E00FFC0000000FFF8000000FFFFE000007FFFFF00007FFFFFC0003FFFFFF0001FFF FFF8000FFFFFFC0007FFFFFE0003FFFFFF0000FFFFFF80001FFFFF800000FFFF80000007 FFC0000000FFC07800007FC0F800003FC0F800001FC0FC00001FC0FC00001FC0FE00001F C0FE00001F80FF00003F80FF80003F00FFE000FF00FFF803FE00FFFFFFFC00FFFFFFF000 F87FFFC000E00FFE0000222B7DA929>I<0007C0000007C0000007C0000007C0000007C0 00000FC000000FC000000FC000000FC000001FC000001FC000001FC000003FC000007FC0 00007FC00000FFC00001FFC00007FFC0001FFFFFFEFFFFFFFEFFFFFFFEFFFFFFFEFFFFFF FE01FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC01F01FFC01F01FFC01F01FFC01F01FFC01F01FFC01F01FFC01F01FFC0 1F01FFC01F00FFE03E00FFE03E007FE07E007FF8FC003FFFF8001FFFF00007FFE00000FF 80203B7EB929>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmbx12 12 62 /Ft 62 122 df<0000000FFF0000000001FFFFC00000000FFFFFF00000007FFFFFF80000 01FFF803FC000003FFC000FE00000FFF0003FE00001FFE0007FF00003FFC000FFF00003F F8000FFF00007FF0000FFF00007FF0001FFF8000FFF0000FFF0000FFE0000FFF0000FFE0 000FFF0000FFE0000FFF0000FFE00007FE0000FFE00001F80000FFE00000000000FFE000 00000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000 000000FFE001FFFF80FFFFFFFFFFFF80FFFFFFFFFFFF80FFFFFFFFFFFF80FFFFFFFFFFFF 80FFFFFFFFFFFF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF80 00FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000 FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FF E00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE0 0003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE000 03FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003 FF8000FFE00003FF8000FFE00003FF8000FFE00003FF8000FFE00003FF807FFFFFC1FFFF FF7FFFFFC1FFFFFF7FFFFFC1FFFFFF7FFFFFC1FFFFFF7FFFFFC1FFFFFF38467EC53E>12 D<0007C0000FE0001FF0003FF8007FF800FFF800FFF801FFF803FFF007FFF00FFFC00FFF 801FFE003FF8007FE000FF8000FE00007C0000300000151369C538>19 D<07C01FF03FF87FFCFFFCFFFEFFFEFFFFFFFFFFFFFFFF7FFF3FFF1FFF07CF000F000F00 1F001E001E003E003E003C007C00F800F801F003F003E007C01F801F001E000C00102278 8E1F>44 DI<07C01FF03FF87FFCFFFEFFFEFFFEFFFEFFFEFFFEFFFE7FFC 3FF81FF007C00F0F788E1F>I<00003FF800000001FFFF0000000FFFFFE000003FFFFFF8 00007FF01FFC0000FFC007FE0001FF0001FF0003FE0000FF8007FE0000FFC007FC00007F C00FFC00007FE00FF800003FE01FF800003FF01FF800003FF03FF800003FF83FF800003F F83FF000001FF87FF000001FFC7FF000001FFC7FF000001FFC7FF000001FFC7FF000001F FC7FF000001FFCFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001F FEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001F FEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001F FEFFF000001FFEFFF000001FFEFFF000001FFEFFF000001FFE7FF000001FFC7FF000001F FC7FF000001FFC7FF000001FFC7FF000001FFC3FF800003FF83FF800003FF83FF800003F F81FF800003FF01FF800003FF00FF800003FE00FFC00007FE007FC00007FC007FE0000FF C003FF0001FF8001FF8003FF0000FFC007FE00007FF01FFC00003FFFFFF800000FFFFFE0 000003FFFF800000003FF800002F427CC038>48 D<000003C000000007C00000001FC000 00007FC0000003FFC000003FFFC000FFFFFFC000FFFFFFC000FFFFFFC000FFFFFFC000FF C3FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003 FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FF C0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0 000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC000 0003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC00000 03FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003 FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC0000003FFC000FFFFFF FFFCFFFFFFFFFCFFFFFFFFFCFFFFFFFFFCFFFFFFFFFC264177C038>I<0000FFE0000000 0FFFFE0000003FFFFF800000FFFFFFE00003FFFFFFF80007FC03FFFE000FE0007FFF001F 80003FFF803F00000FFFC07F000007FFC07FC00007FFE07FF00003FFE0FFF00001FFF0FF F80001FFF0FFF80001FFF8FFF80000FFF8FFF80000FFF8FFF80000FFF8FFF80000FFF87F F00000FFF83FE00000FFF81FC00000FFF800000000FFF800000000FFF000000001FFF000 000001FFF000000001FFE000000003FFE000000003FFC000000007FF800000000FFF0000 00000FFF000000001FFC000000003FF8000000003FF0000000007FE000000000FFC00000 0001FF0000000003FE0000000007FC000000000FF0000000001FE0000000003F80000000 007F0000780000FE0000780001FC0000780003F80000F80007E00000F0000FC00000F000 1F800000F0003F000000F0007C000001F000F8000003F001FFFFFFFFF003FFFFFFFFE007 FFFFFFFFE00FFFFFFFFFE01FFFFFFFFFE03FFFFFFFFFE07FFFFFFFFFE0FFFFFFFFFFE0FF FFFFFFFFC0FFFFFFFFFFC0FFFFFFFFFFC0FFFFFFFFFFC02D417BC038>I<0000FFF00000 0007FFFF0000001FFFFFC000007FFFFFF00000FF007FF80003F8003FFE0007E0001FFF00 07E0000FFF000FF80007FF800FFE0007FF801FFE0007FFC01FFF0007FFC01FFF0007FFC0 1FFF0007FFC01FFF0007FFC01FFF0007FFC01FFF0007FFC00FFE0007FFC007FC0007FF80 03F8000FFF800000000FFF000000001FFF000000001FFE000000003FFC000000007FF800 000000FFF000000001FFE00000000FFF80000007FFFE00000007FFF800000007FFFF0000 0007FFFFC000000000FFF0000000003FFC000000000FFE000000000FFF8000000007FF80 00000003FFC000000003FFE000000003FFE000000001FFF000000001FFF000000001FFF8 00000001FFF800000001FFF80FC00001FFF83FF00001FFF87FF80001FFF87FF80001FFF8 FFFC0001FFF8FFFC0001FFF8FFFC0001FFF0FFFC0001FFF0FFFC0003FFF0FFFC0003FFE0 7FF80003FFE07FF00007FFC07FE00007FFC03F80000FFF801FF0001FFF000FFE00FFFE00 07FFFFFFF80001FFFFFFF000007FFFFFC000001FFFFE00000001FFE000002D427BC038> I<000000003F0000000000003F0000000000007F000000000000FF000000000001FF0000 00000003FF000000000003FF000000000007FF00000000000FFF00000000001FFF000000 00003FFF00000000003FFF00000000007FFF0000000000FFFF0000000001F7FF00000000 03E7FF0000000007E7FF0000000007C7FF000000000F87FF000000001F07FF000000003E 07FF000000007E07FF000000007C07FF00000000F807FF00000001F007FF00000003E007 FF00000007E007FF00000007C007FF0000000F8007FF0000001F0007FF0000003E0007FF 0000007C0007FF0000007C0007FF000000F80007FF000001F00007FF000003E00007FF00 0007C00007FF00000FC00007FF00000F800007FF00001F000007FF00003E000007FF0000 7C000007FF0000FC000007FF0000FFFFFFFFFFFF80FFFFFFFFFFFF80FFFFFFFFFFFF80FF FFFFFFFFFF80FFFFFFFFFFFF800000000FFF00000000000FFF00000000000FFF00000000 000FFF00000000000FFF00000000000FFF00000000000FFF00000000000FFF0000000000 0FFF00000000000FFF00000000000FFF00000000000FFF000000007FFFFFFF8000007FFF FFFF8000007FFFFFFF8000007FFFFFFF8000007FFFFFFF8031417DC038>I<0700000003 0007E000003F0007FF0007FF0007FFFFFFFF0007FFFFFFFE0007FFFFFFFC0007FFFFFFF8 0007FFFFFFF00007FFFFFFE00007FFFFFF800007FFFFFE000007FFFFFC000007FFFFE000 0007FFFF00000007C00000000007C00000000007C00000000007C00000000007C0000000 0007C00000000007C00000000007C00000000007C00000000007C00000000007C03FF000 0007C1FFFF000007C7FFFFC00007DFFFFFF00007FFE03FFC0007FF000FFE0007FC0007FF 0007F00003FF8007E00003FFC007C00001FFC003800001FFE000000001FFE000000000FF F000000000FFF000000000FFF000000000FFF800000000FFF800000000FFF800000000FF F80F800000FFF83FE00000FFF87FF00000FFF8FFF00000FFF8FFF80000FFF8FFF80000FF F8FFF80000FFF8FFF80000FFF0FFF00000FFF0FFF00001FFF07FE00001FFE07FC00001FF E07E000003FFC03E000003FFC03F000007FF801FC0000FFF000FF0001FFE0007FE00FFFC 0003FFFFFFF00000FFFFFFE000003FFFFF8000000FFFFC00000001FFC000002D427BC038 >I<000001FF800000001FFFF00000007FFFFC000001FFFFFF000007FF807F80000FFC00 1F80003FF0001FC0007FE0007FC000FFC000FFE001FF8001FFE003FF8001FFE003FF0001 FFE007FE0001FFE00FFE0001FFE00FFE0001FFE01FFC0000FFC01FFC00007F801FFC0000 1E003FFC000000003FFC000000003FF8000000007FF8000000007FF8000000007FF807FC 00007FF81FFF8000FFF87FFFE000FFF8FFFFF800FFF9F01FFC00FFFBC007FE00FFFF8003 FF00FFFF8003FF80FFFF0001FFC0FFFE0001FFC0FFFE0000FFE0FFFE0000FFE0FFFC0000 FFF0FFFC0000FFF0FFFC0000FFF0FFFC0000FFF8FFF80000FFF8FFF80000FFF8FFF80000 FFF8FFF80000FFF87FF80000FFF87FF80000FFF87FF80000FFF87FF80000FFF87FF80000 FFF83FF80000FFF83FF80000FFF83FF80000FFF03FFC0000FFF01FFC0000FFF01FFC0000 FFF00FFC0001FFE00FFC0001FFE007FE0001FFC007FF0003FF8003FF8003FF0001FFC007 FE0000FFE01FFC00007FFFFFF800001FFFFFF0000007FFFFC0000001FFFF000000003FF0 00002D427BC038>I<1E00000000001F00000000001FFC000000001FFFFFFFFFFE1FFFFF FFFFFE1FFFFFFFFFFE1FFFFFFFFFFE3FFFFFFFFFFE3FFFFFFFFFFC3FFFFFFFFFF83FFFFF FFFFF03FFFFFFFFFE03FFFFFFFFFC03FFFFFFFFFC07FFFFFFFFF807E0000003F007C0000 007E007C000000FC0078000000F80078000001F80078000003F000F8000007E000F00000 0FC000F000000F8000F000001F80000000003F00000000007E0000000000FC0000000000 FC0000000001F80000000003F80000000003F00000000007F0000000000FE0000000000F E0000000001FE0000000001FC0000000003FC0000000003FC0000000007FC0000000007F 8000000000FF8000000000FF8000000001FF8000000001FF8000000001FF8000000003FF 8000000003FF0000000003FF0000000003FF0000000007FF0000000007FF0000000007FF 0000000007FF0000000007FF000000000FFF000000000FFF000000000FFF000000000FFF 000000000FFF000000000FFF000000000FFF000000000FFF000000000FFF000000000FFF 0000000007FE0000000003FC0000000001F80000002F447AC238>I<00007FF000000003 FFFF0000000FFFFFC000003FFFFFF000007F801FFC0001FC0003FE0003F80001FF0003F0 0000FF0007E000007F8007E000003F800FC000003FC00FC000003FC01FC000001FC01FC0 00001FC01FE000001FC01FE000001FC01FF000001FC01FF800001FC01FFE00003FC01FFF 00003F801FFFC0007F801FFFF0007F000FFFFC00FF000FFFFE01FE0007FFFF83FC0007FF FFE7F80003FFFFFFE00001FFFFFFC00000FFFFFF0000007FFFFFC000003FFFFFE000000F FFFFF800000FFFFFFC00003FFFFFFE0000FFFFFFFF0001FF3FFFFF8007FC0FFFFFC00FF8 03FFFFE01FF000FFFFE01FE0007FFFF03FE0001FFFF07FC00007FFF07F800003FFF87F80 0000FFF8FF8000007FF8FF0000003FF8FF0000001FF8FF0000000FF8FF0000000FF8FF00 000007F8FF00000007F8FF00000007F8FF80000007F07F80000007F07F8000000FF07FC0 00000FE03FE000001FE03FF000003FC01FF800007F800FFE0001FF0007FFC00FFE0003FF FFFFFC0000FFFFFFF000003FFFFFC000000FFFFF00000000FFF000002D427BC038>I<00 007FF000000007FFFE0000001FFFFF8000007FFFFFE00000FFE03FF00001FF800FF80003 FF0007FC0007FE0007FE000FFC0003FF001FFC0001FF003FFC0001FF803FFC0001FF807F F80001FFC07FF80000FFC07FF80000FFE07FF80000FFE0FFF80000FFE0FFF80000FFF0FF F80000FFF0FFF80000FFF0FFF80000FFF0FFF80000FFF0FFF80000FFF0FFF80000FFF8FF F80000FFF8FFF80000FFF8FFF80000FFF8FFF80001FFF87FF80001FFF87FF80001FFF87F F80001FFF83FF80003FFF83FF80003FFF81FFC0003FFF81FFC0007FFF80FFE000FFFF807 FE000FFFF803FF001EFFF801FFC07CFFF800FFFFF8FFF8003FFFF0FFF8000FFFC0FFF000 01FF00FFF000000000FFF000000000FFF000000000FFE000000001FFE000000001FFE003 C00001FFE00FF00001FFC01FF80001FFC03FFC0003FF803FFC0003FF803FFC0003FF003F FC0007FE003FFC000FFE003FFC000FFC003FF8001FF8001FF0003FF0001FC000FFE0000F F003FFC00007FFFFFF800003FFFFFE000001FFFFF80000007FFFE000000007FE0000002D 427BC038>I<000000001F8000000000000000001F8000000000000000003FC000000000 000000003FC000000000000000007FE000000000000000007FE000000000000000007FE0 0000000000000000FFF00000000000000000FFF00000000000000001FFF8000000000000 0001FFF80000000000000001FFF80000000000000003FFFC0000000000000003FFFC0000 000000000007FFFE0000000000000007FFFE0000000000000007FFFE000000000000000F FFFF000000000000000F9FFF000000000000001F9FFF800000000000001F1FFF80000000 0000001F0FFF800000000000003F0FFFC00000000000003E07FFC00000000000007E07FF E00000000000007C07FFE00000000000007C03FFE0000000000000FC03FFF00000000000 00F801FFF0000000000001F801FFF8000000000001F001FFF8000000000001F000FFF800 0000000003F000FFFC000000000003E0007FFC000000000007E0007FFE000000000007C0 007FFE000000000007C0003FFE00000000000FC0003FFF00000000000F80001FFF000000 00001F80001FFF80000000001F00000FFF80000000001F00000FFF80000000003F00000F FFC0000000003E000007FFC0000000007E000007FFE0000000007FFFFFFFFFE000000000 7FFFFFFFFFE000000000FFFFFFFFFFF000000000FFFFFFFFFFF000000001FFFFFFFFFFF8 00000001F0000000FFF800000001F0000000FFF800000003F0000000FFFC00000003E000 00007FFC00000007E00000007FFE00000007C00000003FFE00000007C00000003FFE0000 000F800000003FFF0000000F800000001FFF0000001F800000001FFF8000001F00000000 0FFF8000003F000000000FFFC000003E000000000FFFC000007E0000000007FFC000FFFF FF00000FFFFFFFF0FFFFFF00000FFFFFFFF0FFFFFF00000FFFFFFFF0FFFFFF00000FFFFF FFF0FFFFFF00000FFFFFFFF04C457CC455>65 DI<00000000FFF0000070 0000001FFFFF0000F0000001FFFFFFE001F0000007FFFFFFF803F000003FFFFFFFFE07F0 0000FFFFE001FF0FF00001FFFE00003F9FF00007FFF000000FFFF0000FFFC0000007FFF0 001FFF00000003FFF0003FFE00000001FFF0007FFC00000000FFF000FFF8000000007FF0 01FFF0000000003FF003FFE0000000001FF007FFE0000000001FF007FFC0000000000FF0 0FFF80000000000FF00FFF800000000007F01FFF000000000007F01FFF000000000003F0 3FFF000000000003F03FFE000000000003F03FFE000000000003F07FFE000000000001F0 7FFE000000000001F07FFE000000000001F07FFC00000000000000FFFC00000000000000 FFFC00000000000000FFFC00000000000000FFFC00000000000000FFFC00000000000000 FFFC00000000000000FFFC00000000000000FFFC00000000000000FFFC00000000000000 FFFC00000000000000FFFC00000000000000FFFC00000000000000FFFC00000000000000 FFFC000000000000007FFC000000000000007FFE000000000000007FFE000000000000F0 7FFE000000000000F03FFE000000000000F03FFE000000000000F03FFF000000000000F0 1FFF000000000001F01FFF000000000001E00FFF800000000001E00FFF800000000003E0 07FFC00000000003C007FFE00000000007C003FFE00000000007C001FFF0000000000F80 00FFF8000000001F00007FFC000000003F00003FFE000000007E00001FFF80000000FC00 000FFFC0000001F8000007FFF0000007F0000001FFFE00001FE0000000FFFFF001FF8000 00003FFFFFFFFF0000000007FFFFFFFC0000000001FFFFFFF000000000001FFFFF800000 00000000FFF800000044467AC451>III I<00000000FFF0000070000000001FFFFF0000F000000001FFFFFFE001F000000007FFFF FFF803F00000003FFFFFFFFE07F0000000FFFFE001FF0FF0000001FFFE00003F9FF00000 07FFF000000FFFF000000FFFC0000007FFF000001FFF00000003FFF000003FFE00000001 FFF000007FFC00000000FFF00000FFF8000000007FF00001FFF0000000003FF00003FFE0 000000001FF00007FFE0000000001FF00007FFC0000000000FF0000FFF80000000000FF0 000FFF800000000007F0001FFF000000000007F0001FFF000000000003F0003FFF000000 000003F0003FFE000000000003F0003FFE000000000003F0007FFE000000000001F0007F FE000000000001F0007FFE000000000001F0007FFC0000000000000000FFFC0000000000 000000FFFC0000000000000000FFFC0000000000000000FFFC0000000000000000FFFC00 00000000000000FFFC0000000000000000FFFC0000000000000000FFFC00000000000000 00FFFC0000000000000000FFFC0000000000000000FFFC0000000000000000FFFC000000 0000000000FFFC0000000000000000FFFC0000007FFFFFFFF07FFC0000007FFFFFFFF07F FE0000007FFFFFFFF07FFE0000007FFFFFFFF07FFE0000007FFFFFFFF03FFE0000000001 FFF0003FFE0000000001FFF0003FFF0000000001FFF0001FFF0000000001FFF0001FFF00 00000001FFF0000FFF8000000001FFF0000FFF8000000001FFF00007FFC000000001FFF0 0007FFE000000001FFF00003FFE000000001FFF00001FFF000000001FFF00000FFF80000 0001FFF000007FFC00000001FFF000003FFE00000003FFF000001FFF80000003FFF00000 0FFFC0000007FFF0000007FFF000000FFFF0000001FFFE00003FFFF0000000FFFFF001FF 9FF00000003FFFFFFFFF0FF000000007FFFFFFFC03F000000001FFFFFFF000F000000000 1FFFFFC000300000000000FFFC000000004C467AC458>III<0007FFFFFFFF0007FFFFFFFF0007FFFFFFFF0007FFFF FFFF0007FFFFFFFF0000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF000000001FFF000000001F FF000000001FFF000000001FFF000000001FFF000000001FFF001FE0001FFF003FF0001F FF007FF8001FFF007FF8001FFF00FFFC001FFF00FFFC001FFF00FFFC001FFF00FFFC001F FF00FFFC003FFE00FFFC003FFE007FF8007FFC007FF0007FF8003FE000FFF8001FC001FF F0000FFC07FFC00007FFFFFF800003FFFFFE0000007FFFF80000000FFF80000030457DC3 3A>IIIII<00000007FFC0000000000000FFFFFE000000000007FFFFFFC0 000000001FFFFFFFF0000000007FFE00FFFC00000001FFF0001FFF00000007FF800003FF C000000FFF000001FFE000001FFC0000007FF000003FF80000003FF800007FF00000001F FC0000FFF00000001FFE0001FFE00000000FFF0003FFC000000007FF8003FFC000000007 FF8007FF8000000003FFC007FF8000000003FFC00FFF0000000001FFE00FFF0000000001 FFE01FFF0000000001FFF01FFE0000000000FFF03FFE0000000000FFF83FFE0000000000 FFF83FFE0000000000FFF87FFE0000000000FFFC7FFC00000000007FFC7FFC0000000000 7FFC7FFC00000000007FFC7FFC00000000007FFCFFFC00000000007FFEFFFC0000000000 7FFEFFFC00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC0000000000 7FFEFFFC00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC0000000000 7FFEFFFC00000000007FFEFFFC00000000007FFEFFFC00000000007FFE7FFC0000000000 7FFC7FFE0000000000FFFC7FFE0000000000FFFC7FFE0000000000FFFC3FFE0000000000 FFF83FFE0000000000FFF83FFF0000000001FFF81FFF0000000001FFF01FFF0000000001 FFF01FFF8000000003FFF00FFF8000000003FFE00FFF8000000003FFE007FFC000000007 FFC003FFC000000007FF8003FFE00000000FFF8001FFF00000001FFF0000FFF80000003F FE00007FFC0000007FFC00003FFE000000FFF800001FFF000001FFF000000FFFC00007FF E0000007FFF0001FFFC0000001FFFE00FFFF00000000FFFFFFFFFE000000003FFFFFFFF8 0000000007FFFFFFC00000000000FFFFFE00000000000007FFC000000047467AC454>I< FFFFFFFFFFFF000000FFFFFFFFFFFFF00000FFFFFFFFFFFFFE0000FFFFFFFFFFFFFF8000 FFFFFFFFFFFFFFE000001FFF00000FFFF000001FFF000001FFF800001FFF0000007FFC00 001FFF0000003FFE00001FFF0000001FFF00001FFF0000000FFF80001FFF0000000FFF80 001FFF0000000FFFC0001FFF00000007FFC0001FFF00000007FFC0001FFF00000007FFE0 001FFF00000007FFE0001FFF00000007FFE0001FFF00000007FFE0001FFF00000007FFE0 001FFF00000007FFE0001FFF00000007FFE0001FFF00000007FFE0001FFF00000007FFE0 001FFF00000007FFC0001FFF00000007FFC0001FFF0000000FFF80001FFF0000000FFF80 001FFF0000000FFF00001FFF0000001FFF00001FFF0000003FFE00001FFF0000007FFC00 001FFF000001FFF800001FFF00000FFFF000001FFFFFFFFFFFC000001FFFFFFFFFFF0000 001FFFFFFFFFFC0000001FFFFFFFFFC00000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000001FFF000000000000 001FFF000000000000001FFF000000000000001FFF000000000000FFFFFFFFE000000000 FFFFFFFFE000000000FFFFFFFFE000000000FFFFFFFFE000000000FFFFFFFFE000000000 43447DC34D>I<00000007FFC0000000000000FFFFFE000000000007FFFFFFC000000000 1FFFFFFFF0000000007FFE00FFFC00000001FFF0001FFF00000007FFC00007FFC000000F FF000001FFE000001FFE000000FFF000003FFC0000007FF800007FF80000003FFC0000FF F00000001FFE0001FFE00000000FFF0003FFC000000007FF8003FFC000000007FF8007FF 8000000003FFC007FF8000000003FFC00FFF8000000003FFE00FFF0000000001FFE01FFF 0000000001FFF01FFF0000000001FFF03FFE0000000000FFF83FFE0000000000FFF83FFE 0000000000FFF87FFE0000000000FFFC7FFE0000000000FFFC7FFC00000000007FFC7FFC 00000000007FFC7FFC00000000007FFCFFFC00000000007FFEFFFC00000000007FFEFFFC 00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC 00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC00000000007FFEFFFC 00000000007FFEFFFC00000000007FFEFFFC00000000007FFE7FFC00000000007FFC7FFC 00000000007FFC7FFC00000000007FFC7FFE0000000000FFFC3FFE0000000000FFF83FFE 0000000000FFF83FFE0000000000FFF81FFE0000000000FFF01FFF0000000001FFF01FFF 0000000001FFF00FFF0000000001FFE00FFF8000FE0003FFE007FF8003FF8003FFC003FF C007FFC007FF8003FFC00FFFE007FF8001FFE01F83F00FFF0000FFF01E00F81FFE00007F F83E007C3FFC00003FFC3C003E7FF800001FFE3C001EFFF000000FFF3C001FFFE0000007 FFFE001FFFC0000001FFFE001FFF00000000FFFF80FFFE000000003FFFFFFFF800000000 07FFFFFFE00002000000FFFFFFF0000700000007FFC7F00007000000000007F800070000 00000003FC000F000000000003FE001F000000000003FF80FF000000000003FFFFFF0000 00000001FFFFFE000000000001FFFFFE000000000001FFFFFE000000000000FFFFFE0000 00000000FFFFFC000000000000FFFFFC0000000000007FFFF80000000000007FFFF00000 000000003FFFF00000000000001FFFE00000000000000FFFC000000000000007FF000000 0000000001FC0048587AC454>II<0000FFE0001C000007 FFFE003C00003FFFFF807C0000FFFFFFE0FC0001FFFFFFF9FC0003FF801FFFFC0007FC00 01FFFC000FF800007FFC001FF000003FFC003FE000000FFC003FC0000007FC007FC00000 03FC007F80000003FC007F80000001FC007F80000000FC00FF80000000FC00FF80000000 7C00FF800000007C00FFC00000007C00FFC00000007C00FFE00000003C00FFF00000003C 00FFF80000003C00FFFC00000000007FFE00000000007FFFE0000000007FFFFE00000000 3FFFFFF00000003FFFFFFF0000001FFFFFFFE000001FFFFFFFFC00000FFFFFFFFE000007 FFFFFFFF800003FFFFFFFFC00001FFFFFFFFE000007FFFFFFFF000001FFFFFFFF8000007 FFFFFFFC000000FFFFFFFC0000000FFFFFFE00000000FFFFFE0000000007FFFF00000000 007FFF00000000003FFF00000000000FFF800000000007FF800000000003FF80F0000000 03FF80F000000001FF80F000000001FF80F000000000FF80F000000000FF80F800000000 FF80F800000000FF80F800000000FF00FC00000000FF00FC00000000FF00FE00000001FF 00FF00000001FE00FF80000003FE00FFC0000003FC00FFE0000007FC00FFF800000FF800 FFFF00003FF000FFFFF800FFE000FE7FFFFFFFC000FC1FFFFFFF0000F807FFFFFC0000F0 00FFFFF00000E00007FF80000031467AC43E>I<3FFFFFFFFFFFFFFFE03FFFFFFFFFFFFF FFE03FFFFFFFFFFFFFFFE03FFFFFFFFFFFFFFFE03FFFFFFFFFFFFFFFE03FFE000FFF8003 FFE07FE0000FFF80003FF07FC0000FFF80001FF07F00000FFF800007F07F00000FFF8000 07F07E00000FFF800003F07C00000FFF800001F07C00000FFF800001F07C00000FFF8000 01F07800000FFF800000F07800000FFF800000F07800000FFF800000F07800000FFF8000 00F0F800000FFF800000F8F000000FFF80000078F000000FFF80000078F000000FFF8000 0078F000000FFF80000078F000000FFF800000780000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000000000FFF800000000000000FFF800000000000000FFF800000000000000FFF8000 00000007FFFFFFFFFF00000007FFFFFFFFFF00000007FFFFFFFFFF00000007FFFFFFFFFF 00000007FFFFFFFFFF000045437CC24E>IIII<7FFFFFFFC003FFFFFF807FFFFFFFC003FFFFFF807FFFFFFFC003FF FFFF807FFFFFFFC003FFFFFF807FFFFFFFC003FFFFFF80000FFFE0000001F800000007FF E0000003F000000007FFF0000007F000000003FFF8000007E000000001FFFC00000FC000 000001FFFC00001F8000000000FFFE00003F80000000007FFF00003F00000000003FFF00 007E00000000003FFF8000FC00000000001FFFC001FC00000000000FFFE001F800000000 000FFFE003F0000000000007FFF007E0000000000003FFF80FE0000000000001FFFC0FC0 000000000001FFFC1F80000000000000FFFE3F000000000000007FFF7F00000000000000 3FFF7E000000000000003FFFFC000000000000001FFFF8000000000000000FFFF8000000 000000000FFFF00000000000000007FFF00000000000000003FFF80000000000000001FF F80000000000000001FFFC0000000000000000FFFE00000000000000007FFF0000000000 000000FFFF0000000000000000FFFF8000000000000001FFFFC000000000000003FFFFC0 00000000000007FFFFE000000000000007E7FFF00000000000000FC3FFF8000000000000 1F83FFF80000000000003F81FFFC0000000000003F00FFFE0000000000007E007FFE0000 00000000FC007FFF000000000001FC003FFF800000000001F8001FFFC00000000003F000 1FFFC00000000007E0000FFFE0000000000FE00007FFF0000000000FC00003FFF0000000 001F800003FFF8000000003F000001FFFC000000003F000000FFFE000000007E000000FF FE00000000FC0000007FFF00000001FC0000003FFF80000001F80000001FFF80000003F0 0000001FFFC0000007E00000000FFFE000000FE000000007FFF000FFFFFFE00003FFFFFF FCFFFFFFE00003FFFFFFFCFFFFFFE00003FFFFFFFCFFFFFFE00003FFFFFFFCFFFFFFE000 03FFFFFFFC4E447DC355>II<0002000000070000000F8000001FC000007FF00000 FFF80001FFFC0003FFFE0007FDFF000FF07F801FE03FC07F800FF0FF0007F8FC0001F878 0000F0200000201D1073C438>94 D<0001FFE0000000001FFFFE000000007FFFFF800000 01FFFFFFE0000003FE007FF8000007FC001FFC000007FE000FFE00000FFF0007FF00000F FF0007FF00000FFF0003FF80000FFF0003FF80000FFF0003FF80000FFF0001FFC00007FE 0001FFC00003FC0001FFC00000F00001FFC00000000001FFC00000000001FFC000000000 01FFC00000000001FFC000000003FFFFC0000000FFFFFFC0000007FFFFFFC000003FFFF1 FFC00000FFFC01FFC00003FFE001FFC0000FFF8001FFC0001FFE0001FFC0003FFC0001FF C0003FF80001FFC0007FF80001FFC0007FF00001FFC000FFF00001FFC000FFE00001FFC0 00FFE00001FFC000FFE00001FFC000FFE00003FFC000FFE00003FFC000FFF00007FFC000 7FF8000FFFC0007FF8001FFFF0003FFE003EFFFFC01FFF80FC7FFFC007FFFFF87FFFC003 FFFFE01FFFC0007FFF8007FFC0000FFC00000000322F7DAD36>97 D<007FC000000000FFFFC000000000FFFFC000000000FFFFC000000000FFFFC000000000 FFFFC00000000003FFC00000000001FFC00000000001FFC00000000001FFC00000000001 FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FF C00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0 0000000001FFC00000000001FFC00000000001FFC00000000001FFC00FF8000001FFC0FF FF800001FFC3FFFFE00001FFCFFFFFF80001FFDFC03FFC0001FFFF000FFE0001FFFC0003 FF0001FFF80001FF8001FFF00001FFC001FFE00000FFE001FFC00000FFE001FFC000007F F001FFC000007FF001FFC000007FF801FFC000003FF801FFC000003FF801FFC000003FF8 01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01 FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01FF C000003FFC01FFC000003FFC01FFC000003FF801FFC000003FF801FFC000007FF801FFC0 00007FF001FFC000007FF001FFC000007FF001FFC00000FFE001FFE00000FFC001FFF000 01FFC001FFF80003FF8001FF7C0007FF0001FE3E000FFE0001FC1FC07FFC0001F80FFFFF F00001F003FFFFC00001E000FFFF00000000001FF0000036467DC43E>I<0000000003FE 0000000007FFFE0000000007FFFE0000000007FFFE0000000007FFFE0000000007FFFE00 000000001FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE0000 0000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE000000 00000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000 000FFE00000000000FFE00000000000FFE0000003FE00FFE000003FFFC0FFE00000FFFFF 8FFE00003FFFFFCFFE0000FFF807FFFE0001FFC001FFFE0003FF80007FFE0007FF00003F FE000FFE00001FFE000FFC00000FFE001FFC00000FFE003FF800000FFE003FF800000FFE 003FF800000FFE007FF800000FFE007FF000000FFE007FF000000FFE00FFF000000FFE00 FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FF F000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF0 00000FFE007FF000000FFE007FF000000FFE007FF000000FFE007FF800000FFE003FF800 000FFE003FF800000FFE001FFC00001FFE001FFC00001FFE000FFE00003FFE0007FE0000 7FFE0003FF0000FFFF0001FFC003FFFFFC00FFF01FEFFFFC007FFFFF8FFFFC001FFFFE0F FFFC0007FFF80FFFFC00007FC00FF80036467CC43E>100 D<00003FF800000003FFFF80 00000FFFFFE000003FFFFFF000007FF83FF80000FFC007FC0001FF8003FE0003FF0001FF 0007FE0000FF800FFC0000FF801FFC00007FC01FF800007FC03FF800003FE03FF800003F E07FF800003FE07FF000003FE07FF000003FF07FF000001FF0FFF000001FF0FFF000001F F0FFFFFFFFFFF0FFFFFFFFFFF0FFFFFFFFFFF0FFFFFFFFFFF0FFF000000000FFF0000000 00FFF000000000FFF000000000FFF0000000007FF0000000007FF0000000007FF8000000 007FF8000000003FF8000000003FF8000000F01FFC000000F01FFC000001F00FFE000001 E007FF000003E003FF800007C001FFC0000F8000FFF0003F00007FFE01FE00001FFFFFFC 000007FFFFF0000001FFFFC00000001FFE00002C2F7DAD33>I<000000FF8000000FFFE0 00007FFFF00001FFFFF80003FF8FFC000FFE0FFE001FFC1FFE001FF81FFE003FF81FFE00 7FF01FFE007FF01FFE007FF00FFC00FFE00FFC00FFE003F000FFE000C000FFE0000000FF E0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0 000000FFE0000000FFE00000FFFFFFF800FFFFFFF800FFFFFFF800FFFFFFF800FFFFFFF8 0000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE00000 00FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000 FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FF E0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0 000000FFE0000000FFE0000000FFE0000000FFE0000000FFE000007FFFFFE0007FFFFFE0 007FFFFFE0007FFFFFE0007FFFFFE00027467DC522>I<007FC000000000FFFFC0000000 00FFFFC000000000FFFFC000000000FFFFC000000000FFFFC00000000003FFC000000000 01FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001 FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FF C00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0 0000000001FFC00000000001FFC007FE000001FFC03FFF800001FFC0FFFFE00001FFC1FF FFF80001FFC7F03FFC0001FFCF801FFC0001FFDF000FFE0001FFDE000FFE0001FFFC000F FE0001FFF80007FF0001FFF00007FF0001FFF00007FF0001FFE00007FF0001FFE00007FF 0001FFE00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF00 01FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001 FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FF C00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC0 0007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC000 07FF00FFFFFF83FFFFFEFFFFFF83FFFFFEFFFFFF83FFFFFEFFFFFF83FFFFFEFFFFFF83FF FFFE37457CC43E>104 D<007C0001FF0003FF8007FFC007FFC00FFFE00FFFE00FFFE00F FFE00FFFE007FFC007FFC003FF8001FF00007C0000000000000000000000000000000000 0000000000000000000000000000007FC07FFFC07FFFC07FFFC07FFFC07FFFC003FFC001 FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001 FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001 FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC001FFC0FFFFFFFFFFFFFFFFFFFF FFFFFFFFFF18467CC520>I<007FC000000000FFFFC000000000FFFFC000000000FFFFC0 00000000FFFFC000000000FFFFC00000000003FFC00000000001FFC00000000001FFC000 00000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC00000 000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0000000 0001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC000000000 01FFC00000000001FFC0007FFFE001FFC0007FFFE001FFC0007FFFE001FFC0007FFFE001 FFC0007FFFE001FFC0000FE00001FFC0001FC00001FFC0003F000001FFC0007E000001FF C000FC000001FFC003F8000001FFC007E0000001FFC00FC0000001FFC01F80000001FFC0 7F00000001FFC0FE00000001FFC1FC00000001FFC3FE00000001FFC7FE00000001FFDFFF 00000001FFFFFF80000001FFFFFFC0000001FFFFFFC0000001FFF9FFE0000001FFE1FFF0 000001FFC0FFF8000001FF807FF8000001FF803FFC000001FF803FFE000001FF801FFF00 0001FF800FFF000001FF8007FF800001FF8007FFC00001FF8003FFE00001FF8001FFE000 01FF8000FFF00001FF8000FFF80001FF80007FFC0001FF80003FFC00FFFFFF03FFFFF8FF FFFF03FFFFF8FFFFFF03FFFFF8FFFFFF03FFFFF8FFFFFF03FFFFF835457DC43B>107 D<007FC000FFFFC000FFFFC000FFFFC000FFFFC000FFFFC00003FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC00001FFC0 0001FFC000FFFFFF80FFFFFF80FFFFFF80FFFFFF80FFFFFF8019457CC420>I<007F8007 FE00000FFC0000FFFF803FFFC0007FFF8000FFFF80FFFFF001FFFFE000FFFF81FFFFF803 FFFFF000FFFF87F01FFC0FE03FF800FFFF8FC00FFE1F801FFC0003FF9F000FFF3E001FFE 0001FF9E0007FF3C000FFE0001FFBC0007FF78000FFE0001FFF80003FFF00007FF0001FF F80003FFF00007FF0001FFF00003FFE00007FF0001FFE00003FFC00007FF0001FFE00003 FFC00007FF0001FFE00003FFC00007FF0001FFC00003FF800007FF0001FFC00003FF8000 07FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF00 01FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC0 0003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF 800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007 FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001 FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC000 03FF800007FF0001FFC00003FF800007FF0001FFC00003FF800007FF0001FFC00003FF80 0007FF00FFFFFF81FFFFFF03FFFFFEFFFFFF81FFFFFF03FFFFFEFFFFFF81FFFFFF03FFFF FEFFFFFF81FFFFFF03FFFFFEFFFFFF81FFFFFF03FFFFFE572D7CAC5E>I<007F8007FE00 00FFFF803FFF8000FFFF80FFFFE000FFFF81FFFFF800FFFF87F03FFC00FFFF8F801FFC00 03FF9F000FFE0001FF9E000FFE0001FFBC000FFE0001FFF80007FF0001FFF00007FF0001 FFF00007FF0001FFE00007FF0001FFE00007FF0001FFE00007FF0001FFC00007FF0001FF C00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC0 0007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC000 07FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007 FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF 0001FFC00007FF0001FFC00007FF0001FFC00007FF00FFFFFF83FFFFFEFFFFFF83FFFFFE FFFFFF83FFFFFEFFFFFF83FFFFFEFFFFFF83FFFFFE372D7CAC3E>I<00001FFC00000000 01FFFFC000000007FFFFF00000001FFFFFFC0000007FF80FFF000000FFC001FF800001FF 8000FFC00003FE00003FE00007FE00003FF0000FFC00001FF8000FF800000FF8001FF800 000FFC001FF800000FFC003FF800000FFE003FF0000007FE007FF0000007FF007FF00000 07FF007FF0000007FF007FF0000007FF00FFF0000007FF80FFF0000007FF80FFF0000007 FF80FFF0000007FF80FFF0000007FF80FFF0000007FF80FFF0000007FF80FFF0000007FF 80FFF0000007FF80FFF0000007FF807FF0000007FF007FF0000007FF007FF0000007FF00 7FF0000007FF003FF800000FFE003FF800000FFE001FF800000FFC001FFC00001FFC000F FC00001FF80007FE00003FF00007FE00003FF00003FF8000FFE00001FFC001FFC000007F F80FFF0000003FFFFFFE0000000FFFFFF800000001FFFFC0000000001FFC000000312F7D AD38>I<007FC00FF80000FFFFC0FFFF8000FFFFC3FFFFE000FFFFCFFFFFF800FFFFDFC0 3FFC00FFFFFF001FFE0003FFFC0007FF0001FFF80003FF8001FFF00003FFC001FFE00001 FFE001FFC00001FFE001FFC00000FFF001FFC00000FFF001FFC000007FF801FFC000007F F801FFC000007FF801FFC000007FF801FFC000003FFC01FFC000003FFC01FFC000003FFC 01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01 FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000003FFC01FFC000007FF801FF C000007FF801FFC000007FF801FFC000007FF001FFC00000FFF001FFC00000FFF001FFC0 0001FFE001FFE00001FFC001FFF00003FFC001FFF80007FF8001FFFC000FFF0001FFFE00 1FFE0001FFDFC07FFC0001FFCFFFFFF00001FFC3FFFFC00001FFC0FFFF000001FFC01FF0 000001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC0000000 0001FFC00000000001FFC00000000001FFC00000000001FFC00000000001FFC000000000 01FFC00000000001FFC00000000001FFC000000000FFFFFF80000000FFFFFF80000000FF FFFF80000000FFFFFF80000000FFFFFF8000000036407DAC3E>I<00003FE0001E000003 FFFC003E00000FFFFF007E00003FFFFF807E0000FFF80FE0FE0001FFE003F1FE0003FFC0 01F1FE0007FF8000FBFE000FFF00007FFE000FFE00003FFE001FFE00001FFE003FFC0000 1FFE003FFC00000FFE003FF800000FFE007FF800000FFE007FF800000FFE007FF800000F FE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE 00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00FFF000000FFE00 FFF000000FFE00FFF000000FFE007FF800000FFE007FF800000FFE007FF800000FFE007F F800000FFE003FFC00000FFE003FFC00000FFE001FFE00001FFE001FFE00003FFE000FFF 00007FFE0007FF0000FFFE0003FF8001FFFE0001FFE003EFFE0000FFF01FCFFE00007FFF FF8FFE00001FFFFE0FFE000003FFF80FFE0000007FC00FFE00000000000FFE0000000000 0FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000F FE00000000000FFE00000000000FFE00000000000FFE00000000000FFE00000000000FFE 00000000000FFE0000000007FFFFFC00000007FFFFFC00000007FFFFFC00000007FFFFFC 00000007FFFFFC36407CAC3B>I<007F807F00FFFF81FFE0FFFF83FFF0FFFF8FFFF8FFFF 8F8FFCFFFF9F1FFE03FFBE1FFE01FFBC1FFE01FFF81FFE01FFF81FFE01FFF01FFE01FFF0 0FFC01FFE007F801FFE001E001FFE0000001FFE0000001FFE0000001FFC0000001FFC000 0001FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC00000 01FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001 FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC0000001FFC00000FFFF FFE000FFFFFFE000FFFFFFE000FFFFFFE000FFFFFFE000272D7DAC2E>I<001FFC038000 FFFF878003FFFFFF800FFFFFFF801FF003FF803FC000FF803F80003F807F00001F807E00 001F80FE00000F80FE00000F80FE00000780FF00000780FF00000780FF80000780FFE000 0000FFFE0000007FFFF000007FFFFF00003FFFFFC0003FFFFFF0001FFFFFFC000FFFFFFE 0003FFFFFF0001FFFFFF80007FFFFF80000FFFFFC000003FFFC0000003FFE0000000FFE0 F000003FE0F000003FE0F800001FE0F800000FE0F800000FE0FC00000FE0FC00000FE0FE 00000FC0FF00001FC0FF00001FC0FF80003F80FFE0007F00FFF803FE00FFFFFFFC00FCFF FFF800F03FFFE000E007FE0000232F7CAD2C>I<0001E000000001E000000001E0000000 01E000000001E000000003E000000003E000000003E000000003E000000007E000000007 E00000000FE00000000FE00000001FE00000001FE00000003FE00000007FE0000000FFE0 000003FFE000000FFFFFFF80FFFFFFFF80FFFFFFFF80FFFFFFFF80FFFFFFFF8000FFE000 0000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE00000 00FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000 FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE0000000FFE001E000FF E001E000FFE001E000FFE001E000FFE001E000FFE001E000FFE001E000FFE001E000FFE0 01E000FFE003E000FFF003C0007FF003C0007FF007C0003FF80F80001FFC1F00000FFFFF 000007FFFC000001FFF80000003FE00023407EBE2C>I<007FC00001FF00FFFFC003FFFF 00FFFFC003FFFF00FFFFC003FFFF00FFFFC003FFFF00FFFFC003FFFF0003FFC0000FFF00 01FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001 FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FF C00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC0 0007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC000 07FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007FF0001FFC00007 FF0001FFC0000FFF0001FFC0000FFF0001FFC0001FFF0001FFC0001FFF0001FFC0003FFF 0000FFC0003FFF0000FFE0007FFF80007FE001F7FFFE007FF807E7FFFE003FFFFFC7FFFE 000FFFFF07FFFE0003FFFE07FFFE00007FF007FC00372E7CAC3E>II120 DI E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 166 408 a Ft(SCA)-9 b(TTERING)35 b(THEOR)-9 b(Y)35 b(F)m(OR)j(THE)e(DIRA)m(C)h(OPERA)-9 b(TOR)35 b(WITH)h(A)507 529 y(LONG-RANGE)h(ELECTR)m(OMA)m(GNETIC)e(POTENTIAL)1317 785 y(Y.G)o(^)-55 b(atel)37 b(and)h(D.Y)-9 b(afaev)1063 906 y(IRMAR,)36 b(Univ)m(ersit)n(\023)-54 b(e)36 b(de)i(Rennes)g(I)813 1026 y(Campus)g(de)g(Beaulieu,)f(35042)g(Rennes)h(Cedex)1659 1636 y Fs(Abstract)373 1838 y Fr(W)-8 b(e)47 b(consider)e(the)h(Dirac)g (op)s(erator)h(with)d(a)j(long-range)f(p)s(oten)m(tial)f Fq(V)21 b Fr(\()p Fq(x)p Fr(\).)88 b(Scalar,)237 1951 y(pseudo-scalar)25 b(and)h(v)m(ector)h(comp)s(onen)m(ts)f(of)g Fq(V)20 b Fr(\()p Fq(x)p Fr(\))27 b(ma)m(y)f(ha)m(v)m(e)h(arbitrary)e (p)s(o)m(w)m(er-lik)m(e)g(deca)m(y)237 2064 y(at)32 b(in\014nit)m(y)-8 b(.)43 b(W)-8 b(e)33 b(in)m(tro)s(duce)e(w)m(a)m(v)m(e)i(op)s(erators)f (with)f(time-indep)s(enden)m(t)e(mo)s(di\014ers.)43 b(These)237 2177 y(mo)s(di\014ers)34 b(are)i(pseudo-di\013eren)m(tial)e(op)s (erators)j(whose)f(sym)m(b)s(ols)e(are,)39 b(roughly)34 b(sp)s(eaking,)237 2290 y(constructed)27 b(in)e(terms)h(of)h(appro)m (ximate)f(eigenfunctions)f(of)i(the)g(stationary)f(problem.)38 b(W)-8 b(e)237 2403 y(deriv)m(e)30 b(and)g(solv)m(e)h(eik)m(onal)g(and) f(transp)s(ort)f(equations)i(for)f(the)h(corresp)s(onding)e(phase)h (and)237 2516 y(amplitude)25 b(functions.)38 b(F)-8 b(rom)28 b(analytical)e(p)s(oin)m(t)g(of)i(view,)f(our)f(pro)s(of)h(of)g(the)g (existence)h(and)237 2628 y(completeness)h(of)h(the)f(w)m(a)m(v)m(e)i (op)s(erators)f(relies)e(on)h(the)h(limiting)c(absorption)i(principle)e (and)237 2741 y(radiation)32 b(estimates)i(established)e(in)g(the)i (pap)s(er.)49 b(This)31 b(allo)m(ws)i(us)g(to)h(\014t)f(the)h (long-range)237 2854 y(scattering)h(theory)f(for)g(the)g(Dirac)g(op)s (erator)g(in)m(to)g(the)h(framew)m(ork)f(of)g(smo)s(oth)g(p)s(erturba-) 237 2967 y(tions.)45 b(Finally)-8 b(,)30 b(w)m(e)j(\014nd)d(the)i (asymptotics)g(for)g(large)g(times)f Fq(t)h Fr(of)g(solutions)e Fq(u)p Fr(\()p Fq(x;)15 b(t)p Fr(\))33 b(of)f(the)237 3080 y(time-dep)s(enden)m(t)d(Dirac)i(equation.)-7 3846 y Ft(1.)112 b(INTR)m(ODUCTION)-7 4107 y(1.1.)89 b Fp(F)-8 b(or)26 b(short-range)h(in)m(teractions)f Fo(V)48 b Fp(\(deca)m(ying)27 b(faster)g(than)g(the)g(Coulom)m(b)f(p)s(oten)m(tial\),)g(scat-)-7 4227 y(tering)31 b(theory)h(for)f(the)h(Dirac)f(op)s(erator)g Fo(H)39 b Fp(is)31 b(completely)g(analogous)f(to)h(the)h(Sc)m(hr\177) -49 b(odinger)32 b(case.)-7 4347 y(The)g(situation)c(is)i(more)g (complicated)f(for)h(long-range)f(in)m(teractions)h(\(deca)m(ying)h(as) f(the)h(Coulom)m(b)-7 4468 y(p)s(oten)m(tial)23 b(or)g(slo)m(w)m(er\))i (when)g(the)g(free)g(dynamics)f Fo(e)1883 4432 y Fn(\000)p Fm(iH)2020 4441 y Fl(0)2054 4432 y Fm(t)2108 4468 y Fp(cannot)g(b)s(e)h (used)g(as)g(an)f(appro)m(ximation)e(to)-7 4588 y Fo(e)38 4552 y Fn(\000)p Fm(iH)5 b(t)210 4588 y Fp(.)43 b(An)30 b(appropriate)f(mo)s(di\014cation)f(of)h Fo(e)1672 4552 y Fn(\000)p Fm(iH)1809 4561 y Fl(0)1844 4552 y Fm(t)1903 4588 y Fp(relies)h(alw)m(a)m(ys)g(on)g(solutions)g(of)f(an)h(eik)m (onal)f(and)-7 4708 y(a)d(transp)s(ort)f(equation)h(for)f(the)h(phase)h (and)f(the)g(amplitude)e(functions)h(determining)f(the)j(mo)s(di\014ed) -7 4829 y(dynamics.)64 b(In)40 b(general,)h(in)e(the)h(case)g(of)g (systems)h(these)f(equations)g(are)g(not)f(e\016cien)m(t)i(and)e(are)-7 4949 y(di\016cult)28 b(to)h(handle.)42 b(Nev)m(ertheless)31 b(for)e(the)g(Dirac)e(op)s(erator)i(w)m(e)h(deriv)m(e)f(an)g(eik)m (onal)f(equation)h(for)-7 5070 y(the)k(phase)h(function)e(whic)m(h)i (is)e(quite)h(similar)d(to)i(the)h(Sc)m(hr\177)-49 b(odinger)33 b(case.)46 b(Moreo)m(v)m(er,)34 b(w)m(e)g(\014nd)f(an)-7 5190 y(explicit)c(solution)h(of)g(the)h(corresp)s(onding)g(transp)s (ort)f(equation)h(\(whic)m(h)g(can)g(b)s(e)g(neglected)g(in)f(the)-7 5310 y(Sc)m(hr\177)-49 b(odinger)33 b(case\))g(for)f(the)h(amplitude)e (function.)p eop %%Page: 2 2 2 1 bop 134 52 a Fp(The)42 b(existing)f(pap)s(ers)h(on)f(scattering)g (theory)h(for)e(the)i(Dirac)e(op)s(erator)g(with)h(a)g(long-range)-7 172 y(p)s(erturbation)27 b(rely)g(mainly)f(on)h(the)h(Enss)h(metho)s(d) e(whic)m(h)i(is)e(in)m(trinsically)d(time-dep)s(enden)m(t.)42 b(The)-7 293 y(results)48 b(on)f(the)h(existence)h(and)e(completeness)h (of)f(mo)s(di\014ed)f(w)m(a)m(v)m(e)k(op)s(erators)d(are)g(somewhat)-7 413 y(patc)m(h)m(y)-8 b(.)53 b(In)36 b(the)g(Coulom)m(b)e(case)j(mo)s (di\014ed)d(w)m(a)m(v)m(e)j(op)s(erators)e(w)m(ere)i(constructed)g(in)e ([5])g(basically)-7 533 y(in)i(the)i(same)e(w)m(a)m(y)j(as)e(in)f([4].) 60 b(F)-8 b(ollo)m(wing)35 b(the)j(ideas)g(of)f([3])h(for)g(the)g(Sc)m (hr\177)-49 b(odinger)38 b(op)s(erator,)h(the)-7 654 y(construction)29 b(\(without)g(pro)s(of)7 b(\))28 b(for)g(a)h(general) f(class)h(of)g(long-range)e(electrostatic)i(p)s(erturbations)-7 774 y(w)m(as)39 b(giv)m(en)e(in)g([22].)58 b(The)38 b(more)f (di\016cult)g(problem)f(of)h(completeness)i(w)m(as)f(\014rst)g(studied) g(in)f([10)o(])-7 895 y(where)j(a)f(purely)g(electrostatic)f(p)s(oten)m (tial)f(with)i(an)g(arbitrary)f(deca)m(y)i(w)m(as)g(considered.)63 b(In)40 b([15)o(])-7 1015 y(detailed)30 b(results)i(on)f(the)h (asymptotic)f(b)s(eha)m(viour)g(of)g(observ)-5 b(ables)32 b(suc)m(h)h(as)f(p)s(osition,)d(v)m(elo)s(cit)m(y)j(or)-7 1135 y(pro)5 b(jections)29 b(on)f(the)h(p)s(ositiv)m(e)f(and)h(negativ) m(e)f(energy)i(states)f(w)m(ere)h(obtained.)42 b(These)30 b(results)f(w)m(ere)-7 1256 y(used)k(in)f([11])g(to)g(study)h(a)f (general)g(electromagnetic)e(p)s(oten)m(tial)h(deca)m(ying)i(as)f Fk(j)p Fo(x)p Fk(j)3058 1220 y Fn(\000)p Fj(1)3184 1256 y Fp(for)g Fk(j)p Fo(x)p Fk(j)27 b(!)h(1)p Fp(.)134 1418 y(Our)k(goal)f(here)h(is)g(to)g(dev)m(elop)g(a)g(consisten)m(t)h (stationary)e(approac)m(h)i(to)e(scattering)h(theory)h(for)-7 1538 y(the)39 b(Dirac)f(op)s(erator)g(with)h(a)f(general)g(long-range)g (electromagnetic)f(p)s(oten)m(tial.)61 b(In)39 b(particular,)-7 1658 y(w)m(e)32 b(pro)m(v)m(e)g(the)g(existence)g(and)f(completeness)h (of)e(w)m(a)m(v)m(e)j(op)s(erators)e(for)f(an)h(arbitrary)f(\(p)s(o)m (w)m(er-lik)m(e\))-7 1779 y(deca)m(y)47 b(of)e(p)s(erturbation)g(at)g (in\014nit)m(y)-8 b(.)82 b(W)-8 b(e)46 b(mo)s(dify)d(the)j(free)g (dynamics)g(in)e(the)i(co)s(ordinate)f Fo(x)-7 1899 y Fp(and)33 b(momen)m(tum)f Fo(\030)38 b Fp(v)-5 b(ariables)32 b(whic)m(h)i(amoun)m(ts)f(to)g(in)m(tro)s(duction)f(of)g(a)h(mo)s (di\014er)f(\(called)g(also)g(an)-7 2020 y(\\iden)m(ti\014cation"\))d Fo(J)769 2035 y Fn(\006)859 2020 y Fp(in)m(tert)m(wining)h(appro)m (ximately)g(the)h(op)s(erators)g Fo(H)2723 2035 y Fj(0)2793 2020 y Fp(and)g Fo(H)39 b Fp(and)31 b(dep)s(ending)-7 2140 y(on)45 b(the)h(sign)f(of)g(the)h(time)e Fo(t)p Fp(.)82 b(The)46 b(op)s(erators)f Fo(J)1931 2155 y Fn(\006)2036 2140 y Fp(emerge)g(naturally)f(as)h(pseudo-di\013eren)m(tial)-7 2260 y(op)s(erators)35 b(with)f(sym)m(b)s(ols)h Fo(j)1066 2275 y Fn(\006)1125 2260 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))35 b(constructed)h(\(up)f(to)g(di\013eren)m(t)g(cut-o\013)f (functions\))h(in)f(terms)-7 2381 y(of)j(appro)m(ximate)f (eigenfunctions)g(of)h(the)g(op)s(erator)g Fo(H)8 b Fp(.)56 b(In)37 b(the)g(Sc)m(hr\177)-49 b(odinger)38 b(case,)h(the)e(sc)m(heme) -7 2501 y(adopted)e(here)g(w)m(as)h(dev)m(elop)s(ed)f(in)f([19)o(])h (and)g(the)f(construction)h(of)f(the)h(op)s(erators)f Fo(J)3220 2516 y Fn(\006)3314 2501 y Fp(go)s(es)g(bac)m(k)-7 2621 y(to)e([7].)134 2783 y Ft(1.2.)94 b Fp(Let)817 2969 y Fo(H)898 2984 y Fj(0)965 2969 y Fp(=)1123 2844 y Fj(3)1069 2874 y Fi(X)1077 3086 y Fm(k)r Fj(=1)1229 2969 y Fo(\013)1291 2984 y Fm(k)1334 2969 y Fo(D)1415 2984 y Fm(k)1480 2969 y Fp(+)22 b Fo(m\013)1725 2984 y Fj(0)1765 2969 y Fo(;)81 b(m)28 b(>)g Fp(0)p Fo(;)82 b(D)2329 2984 y Fm(k)2399 2969 y Fp(=)27 b Fk(\000)p Fo(i@)5 b(=@)g(x)2828 2984 y Fm(k)2874 2969 y Fo(;)624 b Fp(\(1.1\))-7 3238 y(b)s(e)34 b(the)f(self-adjoin)m(t)f(op)s(erator)h(in)f(the)i(Hilb)s(ert)e(space)j Fk(H)30 b Fp(=)f Fo(L)2359 3201 y Fj(2)2398 3238 y Fp(\()p Fh(R)2502 3201 y Fj(3)2548 3238 y Fo(;)17 b Fh(C)2657 3201 y Fj(4)2703 3238 y Fp(\))33 b(with)g(domain)f Fk(D)s Fp(\()p Fo(H)3544 3253 y Fj(0)3583 3238 y Fp(\))c(=)-7 3358 y Ft(H)81 3316 y Fj(1)120 3358 y Fp(\()p Fh(R)224 3322 y Fj(3)269 3358 y Fo(;)17 b Fh(C)379 3322 y Fj(4)425 3358 y Fp(\))35 b(\(the)i(Sob)s(olev)e(class\).)54 b(Recall)34 b(that)h(the)i(\(4)24 b Fk(\002)h Fp(4\)-Dirac)34 b(matrices)h Fo(\013)3128 3373 y Fm(k)3204 3358 y Fp(=)e Fo(\013)3376 3322 y Fn(\003)3375 3384 y Fm(k)3453 3358 y Fp(satisfy)-7 3478 y(the)g(an)m(ticomm)m(utation)d(relations)1056 3698 y Fo(\013)1118 3713 y Fm(j)1154 3698 y Fo(\013)1216 3713 y Fm(k)1281 3698 y Fp(+)22 b Fo(\013)1441 3713 y Fm(k)1484 3698 y Fo(\013)1546 3713 y Fm(j)1610 3698 y Fp(=)27 b(2)p Fo(\016)1805 3713 y Fm(j)t(k)1880 3698 y Fo(I)8 b(;)82 b(j;)17 b(k)31 b Fp(=)d(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3)p Fo(:)860 b Fp(\(1.2\))-7 3918 y(They)34 b(ma)m(y)e(b)s(e)h(c)m(hosen)h(as)654 4191 y Fo(\013)716 4206 y Fj(0)783 4191 y Fp(=)887 4051 y Fi(\024)981 4130 y Fo(I)1024 4145 y Fj(2)1202 4130 y Fp(0)998 4250 y(0)99 b Fk(\000)p Fo(I)1266 4265 y Fj(2)1348 4051 y Fi(\025)1482 4191 y Fp(and)65 b Fo(\013)1766 4206 y Fm(k)1837 4191 y Fp(=)1940 4051 y Fi(\024)2059 4130 y Fp(0)107 b Fo(\033)2270 4145 y Fm(k)2034 4250 y Fo(\033)2089 4265 y Fm(k)2240 4250 y Fp(0)2355 4051 y Fi(\025)2489 4191 y Fp(if)71 b Fo(k)31 b Fp(=)c(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)-7 4464 y Fp(where)770 4617 y Fo(\033)825 4632 y Fj(1)893 4617 y Fp(=)997 4477 y Fi(\024)1091 4556 y Fp(0)82 b(1)1091 4677 y(1)g(0)1313 4477 y Fi(\025)1382 4617 y Fo(;)h(\033)1547 4632 y Fj(2)1615 4617 y Fp(=)1718 4477 y Fi(\024)1812 4556 y Fp(0)g Fk(\000)p Fo(i)1820 4677 y(i)122 b Fp(0)2096 4477 y Fi(\025)2166 4617 y Fo(;)83 b(\033)2331 4632 y Fj(3)2398 4617 y Fp(=)2502 4477 y Fi(\024)2596 4556 y Fp(1)121 b(0)2596 4677 y(0)83 b Fk(\000)p Fp(1)2895 4477 y Fi(\025)-7 4844 y Fp(are)33 b(the)g(P)m(auli)e (matrices.)134 5006 y(The)j(free)f(Dirac)e(op)s(erator)h Fo(H)1260 5021 y Fj(0)1332 5006 y Fp(can)g(b)s(e)h(easily)f (diagonalized)e(b)m(y)k(the)f(F)-8 b(ourier)31 b(transform)h Fk(F)10 b Fp(,)892 5269 y(\()p Fk(F)g Fo(f)h Fp(\)\()p Fo(\030)5 b Fp(\))26 b(=)i(\(2)p Fo(\031)t Fp(\))1547 5228 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1728 5133 y Fi(Z)1783 5359 y Fg(R)1831 5340 y Fl(3)1887 5269 y Fo(e)1932 5228 y Fn(\000)p Fm(i)p Fn(h)p Fm(\030)s(;x)p Fn(i)2163 5269 y Fo(f)11 b Fp(\()p Fo(x)p Fp(\))p Fo(dx)27 b Fp(=:)2638 5243 y(^)2617 5269 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(:)1835 5634 y Fp(2)p eop %%Page: 3 3 3 2 bop -7 52 a Fp(Actually)-8 b(,)32 b Fk(F)10 b Fo(H)571 67 y Fj(0)609 52 y Fk(F)691 16 y Fn(\003)763 52 y Fp(acts)33 b(as)g(m)m(ultiplication)28 b(b)m(y)33 b(the)g(matrix)1355 356 y Fo(h)1411 371 y Fj(0)1451 356 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)1760 232 y Fj(3)1706 262 y Fi(X)1713 474 y Fm(k)r Fj(=1)1866 356 y Fo(\013)1928 371 y Fm(k)1971 356 y Fo(\030)2014 371 y Fm(k)2078 356 y Fp(+)22 b Fo(m\013)2323 371 y Fj(0)3525 356 y Fp(\(1.3\))-7 661 y(called)31 b(the)i(sym)m(b)s (ol)f(of)g Fo(H)963 676 y Fj(0)1003 661 y Fp(.)43 b(A)33 b(straigh)m(tforw)m(ard)f(calculation)e(sho)m(ws)k(that)732 881 y Fo(h)788 896 y Fj(0)828 881 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(p)1309 840 y Fj(+)1309 906 y(0)1368 881 y Fp(\()p Fo(\030)g Fp(\))21 b Fk(\000)i Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(p)1840 840 y Fn(\000)1840 906 y Fj(0)1899 881 y Fp(\()p Fo(\030)g Fp(\))p Fo(;)113 b(\027)6 b Fp(\()p Fo(\030)f Fp(\))28 b(=)2472 791 y Fi(p)p 2572 791 388 4 v 90 x Fk(j)p Fo(\030)5 b Fk(j)2676 852 y Fj(2)2736 881 y Fp(+)22 b Fo(m)2919 852 y Fj(2)2959 881 y Fo(;)539 b Fp(\(1.4\))-7 1101 y(where)930 1287 y Fo(p)979 1246 y Fn(\006)979 1311 y Fj(0)1038 1287 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)h(2)1342 1246 y Fn(\000)p Fj(1)1452 1116 y Fi( )1531 1287 y Fo(I)i Fk(\006)23 b Fo(\027)1758 1246 y Fn(\000)p Fj(1)1853 1287 y Fp(\()p Fo(\030)5 b Fp(\)\()2068 1162 y Fj(3)2015 1192 y Fi(X)2023 1404 y Fm(k)r Fj(=1)2174 1287 y Fo(\013)2236 1302 y Fm(k)2279 1287 y Fo(\030)2322 1302 y Fm(k)2387 1287 y Fp(+)22 b Fo(m\013)2632 1302 y Fj(0)2671 1287 y Fp(\))2709 1116 y Fi(!)3525 1287 y Fp(\(1.5\))-7 1551 y(are)37 b(orthogonal)d(pro)5 b(jections)37 b(on)g(the)g(eigenspaces)h(of)e Fo(h)2160 1566 y Fj(0)2200 1551 y Fp(\()p Fo(\030)5 b Fp(\))35 b(corresp)s(onding)i(to)f(its)g (eigen)m(v)-5 b(alues)-7 1672 y Fk(\006)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\).)66 b(In)41 b(particular,)f(the)h(sp)s(ectrum)f (of)g Fo(H)1766 1687 y Fj(0)1845 1672 y Fp(is)g(absolutely)g(con)m(tin) m(uous)g(and)h(coincides)f(with)-7 1792 y(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(])k Fk([)g Fp([)p Fo(m;)c Fk(1)p Fp(\).)42 b(Let)32 b Fk(I)1147 1756 y Fj(+)1235 1792 y Fp(=)27 b(\()p Fo(m;)17 b Fk(1)p Fp(\),)32 b Fk(I)1763 1756 y Fn(\000)1850 1792 y Fp(=)27 b(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))33 b(and)e(denote)i(b)m(y)f Fo(E)3153 1807 y Fj(0)3224 1792 y Fp(the)h(sp)s(ectral)-7 1912 y(family)d(of)i(the)h(op)s(erator)f Fo(H)1044 1927 y Fj(0)1083 1912 y Fp(.)44 b(Equation)32 b(\(1.4\))g(implies)e(that)984 2132 y(\()p Fk(F)10 b Fo(E)1176 2147 y Fj(0)1215 2132 y Fp(\()p Fk(I)1314 2091 y Fn(\006)1373 2132 y Fp(\))p Fo(f)h Fp(\)\()p Fo(\030)5 b Fp(\))27 b(=)h Fo(p)1812 2091 y Fn(\006)1812 2157 y Fj(0)1871 2132 y Fp(\()p Fo(\030)5 b Fp(\)\()p Fk(F)10 b Fo(f)h Fp(\)\()p Fo(\030)5 b Fp(\))p Fo(;)79 b(f)38 b Fk(2)28 b(H)q Fo(:)-7 2352 y Fp(Ob)m(viously)-8 b(,)49 b(functions)c Fo(u)976 2311 y Fn(\006)976 2377 y Fj(0)1035 2352 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))48 b(=)i Fo(p)1481 2311 y Fn(\006)1481 2377 y Fj(0)1540 2352 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(e)1709 2316 y Fm(i)p Fn(h)p Fm(x;\030)s Fn(i)1930 2352 y Fp(\(actually)-8 b(,)47 b(instead)e(of)g(v)m(ectors,)51 b(w)m(e)46 b(consider)-7 2473 y(matrices)e(whose)i(columns)e(are)g(eigenfunctions)g(of)h Fo(H)2116 2488 y Fj(0)2155 2473 y Fp(\))f(satisfy)h(the)g(equation)f Fo(H)3225 2488 y Fj(0)3264 2473 y Fo(u)3320 2431 y Fn(\006)3320 2497 y Fj(0)3379 2473 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))47 b(=)-7 2593 y Fk(\006)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(u)304 2552 y Fn(\006)304 2618 y Fj(0)363 2593 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\).)42 b(Belo)m(w)31 b(w)m(e)g(consider)g(p)s(ositiv)m(e)f(energies)h(and)g(omit)d(the)j (upp)s(er)g(index)g(\\)18 b(+)g(".)42 b(F)-8 b(or)-7 2713 y(negativ)m(e)33 b(energies,)g(considerations)f(are)h(quite)f (similar)e(and)i(w)m(e)i(indicate)d(necessary)k(c)m(hanges.)134 2875 y(Let)49 b(us)f(no)m(w)h(consider)g(the)g(Dirac)d(op)s(erator)i Fo(H)62 b Fp(=)54 b Fo(H)2306 2890 y Fj(0)2378 2875 y Fp(+)33 b Fo(V)69 b Fp(with)48 b(a)g(long-range)f(matrix)-7 2996 y(in)m(teraction)1268 3181 y Fo(V)21 b Fp(\()p Fo(x)p Fp(\))28 b(=)g Fo(v)t Fp(\()p Fo(x)p Fp(\))22 b(+)1965 3057 y Fj(3)1911 3087 y Fi(X)1919 3299 y Fm(k)r Fj(=0)2072 3181 y Fo(\013)2134 3196 y Fm(k)2176 3181 y Fo(A)2249 3196 y Fm(k)2292 3181 y Fp(\()p Fo(x)p Fp(\))p Fo(:)1075 b Fp(\(1.6\))-7 3446 y(Of)37 b(course,)i Fo(H)44 b Fp(is)36 b(self-adjoin)m(t)g(in)g(the)h(space)h Fk(H)g Fp(on)f(the)g(domain)e Fk(D)s Fp(\()p Fo(H)8 b Fp(\))34 b(=)h Fk(D)s Fp(\()p Fo(H)3130 3461 y Fj(0)3169 3446 y Fp(\))i(if)e(functions)-7 3566 y Fo(v)t(;)17 b(A)161 3581 y Fm(k)203 3566 y Fo(;)g(k)56 b Fp(=)e(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3)45 b(are)j(real)f(and,)k(sa)m(y)-8 b(,)53 b(b)s(ounded.)89 b(W)-8 b(e)48 b(recall)f(that)g Fo(v)k Fp(is)c(an)h(electrostatic)-7 3687 y(p)s(oten)m(tial,)29 b(and)i(\()p Fo(A)729 3702 y Fj(1)768 3687 y Fo(;)17 b(A)885 3702 y Fj(2)924 3687 y Fo(;)g(A)1041 3702 y Fj(3)1081 3687 y Fp(\))30 b(is)g(a)g(magnetic)f (p)s(oten)m(tial.)41 b(Our)30 b(\014rst)h(goal)e(is)g(to)h(\014nd)h (appro)m(ximate)-7 3807 y(eigenfunctions)h(of)h(the)g(con)m(tin)m(uous) g(sp)s(ectrum)g(of)f(the)h(op)s(erator)f Fo(H)8 b Fp(.)134 3969 y(Recall)28 b(that)i(in)e(the)j(Sc)m(hr\177)-49 b(odinger)29 b(case)i(one)f(constructs)h(appro)m(ximate)e (eigenfunctions)g(in)g(the)-7 4089 y(form)1372 4210 y Fo(u)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))26 b(=)i Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(e)2098 4168 y Fm(i')p Fj(\()p Fm(x;\030)s Fj(\))2320 4210 y Fo(;)1178 b Fp(\(1.7\))-7 4384 y(where)38 b Fo(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))24 b Fk(\000)h(h)p Fo(x;)17 b(\030)5 b Fk(i)34 b Fp(=)g Fo(o)p Fp(\()p Fk(j)p Fo(x)p Fk(j)p Fp(\))i(and)h Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))24 b Fk(\000)h Fp(1)34 b(=)h Fo(o)p Fp(\(1\))h(as)g Fk(j)p Fo(x)p Fk(j)e(!)h(1)p Fp(.)54 b(Substitution)36 b(in)g(the)-7 4504 y(equation)41 b Fk(\000)p Fp(\001)p Fo(u)28 b Fp(+)f Fo(V)22 b(u)41 b Fp(=)h Fk(j)p Fo(\030)5 b Fk(j)1143 4468 y Fj(2)1181 4504 y Fo(u)40 b Fp(leads)h(to)f(the)i(eik)m(onal)d (equation)i Fk(jr)p Fo(')p Fk(j)2782 4468 y Fj(2)2848 4504 y Fp(+)28 b Fo(V)22 b Fp(\()p Fo(x)p Fp(\))42 b(=)f Fk(j)p Fo(\030)5 b Fk(j)3425 4468 y Fj(2)3504 4504 y Fp(for)40 b Fo(')-7 4625 y Fp(and)f(the)g(transp)s(ort)f(equation)g (for)g Fo(p)p Fp(.)62 b(Moreo)m(v)m(er,)41 b(one)e(can)g(set)g Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))37 b(=)h(1)g(and)h(th)m(us)g (a)m(v)m(oid)g(a)-7 4745 y(consideration)d(of)g(the)h(transp)s(ort)f (equation.)56 b(Indeed,)39 b(the)e(function)f Fo(u)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))33 b(=)i Fo(e)3140 4709 y Fm(i')p Fj(\()p Fm(x;\030)s Fj(\))3399 4745 y Fp(satis\014es)-7 4865 y(already)26 b(the)g(Sc)m(hr\177)-49 b(odinger)26 b(equation)g(up)g(to)f(a)h(term)f Fk(\000)p Fo(i)p Fp(\001)p Fo(')i Fp(whic)m(h)f(is)g(short-range.)41 b(Note)26 b(ho)m(w)m(ev)m(er)-7 4986 y(that)32 b(Ansatz)i(\(1.7\))e (seems)h(to)g(fail)d(for)i(the)h(Sc)m(hr\177)-49 b(odinger)33 b(op)s(erator)f(with)g(a)g(matrix)f(p)s(oten)m(tial.)134 5148 y(In)46 b(the)g(Dirac)d(case,)50 b(it)44 b(is)h(natural)f(to)h (seek)i(appro)m(ximate)d(eigenfunctions)h(corresp)s(onding)-7 5268 y(to)d(the)h(\\eigen)m(v)-5 b(alues")43 b Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))42 b(in)g(the)h(form)e(\(1.7\))i(where)g (again)f Fo(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b Fk(\000)h(h)p Fo(x;)17 b(\030)5 b Fk(i)44 b Fp(=)h Fo(o)p Fp(\()p Fk(j)p Fo(x)p Fk(j)p Fp(\))d(and)1835 5634 y(3)p eop %%Page: 4 4 4 3 bop -7 52 a Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))20 b Fk(\000)i Fo(p)433 67 y Fj(0)472 52 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)g Fo(o)p Fp(\(1\))32 b(as)g Fk(j)p Fo(x)p Fk(j)27 b(!)h(1)p Fp(.)43 b(Substituting)31 b(\(1.7\))g(in)g(the)i (Dirac)d(equation)i Fo(H)8 b(u)27 b Fp(=)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(u)-7 172 y Fp(and)33 b(setting)258 462 y Fo(B)5 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)745 338 y Fj(3)691 368 y Fi(X)702 578 y Fm(j)t Fj(=1)835 462 y Fp(\()p Fo(@)5 b(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(=@)g(x)1376 477 y Fm(j)1436 462 y Fp(+)22 b Fo(A)1607 477 y Fm(j)1643 462 y Fp(\()p Fo(x)p Fp(\)\))p Fo(\013)1874 477 y Fm(j)1933 462 y Fp(+)g Fo(m)p Fp(\()p Fo(\013)2216 477 y Fj(0)2278 462 y Fp(+)g Fo(A)2449 477 y Fj(0)2489 462 y Fp(\()p Fo(x)p Fp(\)\))g(+)g Fo(v)t Fp(\()p Fo(x)p Fp(\))g Fk(\000)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))265 b(\(1.8\))-7 773 y(w)m(e)35 b(obtain)f(the)g (equation)g Fo(B)5 b(p)31 b Fp(=)f(0)k(\(for)g(\014xed)h Fo(x;)17 b(\030)5 b Fp(\).)48 b(This)35 b(implies)c(that)k Fo(B)2897 736 y Fj(2)2936 773 y Fo(p)c Fp(=)f(0.)48 b(Then)36 b(using)-7 893 y(the)i(algebra)f(of)h(Dirac)e(matrices)i(w)m(e)h (deduce)g(from)e(the)h(equations)h Fo(B)5 b(p)36 b Fp(=)h(0)h(and)g Fo(B)3265 857 y Fj(2)3305 893 y Fo(p)e Fp(=)h(0)h(the)-7 1013 y(eik)m(onal)32 b(equation)397 1219 y Fk(jr)p Fo(')22 b Fp(+)g Fo(A)p Fk(j)793 1178 y Fj(2)855 1219 y Fp(+)g(\()p Fo(m)g Fp(+)g Fo(A)1269 1234 y Fj(0)1309 1219 y Fp(\))1347 1178 y Fj(2)1408 1219 y Fk(\000)h Fp(\()p Fo(\027)28 b Fk(\000)23 b Fo(v)t Fp(\))1811 1178 y Fj(2)1878 1219 y Fp(=)k(0)p Fo(;)82 b Fk(r)27 b Fp(=)h Fk(r)2436 1234 y Fm(x)2480 1219 y Fo(;)82 b(A)27 b Fp(=)h(\()p Fo(A)2904 1234 y Fj(1)2943 1219 y Fo(;)17 b(A)3060 1234 y Fj(2)3100 1219 y Fo(;)g(A)3217 1234 y Fj(3)3256 1219 y Fp(\))p Fo(;)204 b Fp(\(1.9\))-7 1424 y(for)32 b(the)h(phase-function)g Fo(')p Fp(.)134 1582 y(The)k(next)g(step)g(is)f(to)f(c)m(ho)s(ose)i (the)g(matrix-function)c Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\).)53 b(W)-8 b(e)37 b(note)f(that)g(in)f(con)m(trast)i(to)-7 1702 y(the)c(Sc)m(hr\177)-49 b(odinger)33 b(case)g(the)g(c)m(hoice)g Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(p)1811 1717 y Fj(0)1850 1702 y Fp(\()p Fo(\030)5 b Fp(\))32 b(is)g(not)h(su\016cien)m(t,)g(and)g(the)g(relation)801 1908 y(\()p Fo(H)c Fk(\000)23 b Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\)\))p Fo(u)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))26 b(=)i Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)1901 1866 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)2078 1908 y Fp(\))p Fo(;)81 b(\017)28 b(>)g Fp(0)p Fo(;)81 b Fk(j)p Fo(x)p Fk(j)28 b(!)f(1)558 b Fp(\(1.10\))-7 2113 y(is)43 b(satis\014ed)g(only)f(if)g Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))42 b(is)h(a)f(solution)g(of)g (the)i(corresp)s(onding)f(transp)s(ort)f(equation.)75 b(F)-8 b(or-)-7 2233 y(tunately)g(,)37 b(this)f(equation)g(turns)g(out) g(to)g(b)s(e)h(degenerate)g(and)f(admits)f(an)h(explicit)f(solution)f (\(see)-7 2354 y(Prop)s(osition)j(3.2\).)60 b(Of)38 b(course,)j(to)d (satisfy)g(\(1.10\))g(it)f(su\016ces)k(to)d(solv)m(e)g(eik)m(onal)g (equation)g(\(1.9\))-7 2474 y(also)32 b(up)h(to)f(a)g(short-range)h (term)f(only)-8 b(.)134 2632 y(Equation)27 b(\(1.9\))g(seems)i(to)e(b)s (e)g(new.)43 b(It)28 b(is)f(con)m(v)m(enien)m(t)i(to)e(rewrite)g(it)g (in)g(terms)g(of)g(the)h(function)1318 2837 y(\010\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b Fk(\000)i(h)p Fo(x;)17 b(\030)5 b Fk(i)p Fo(:)1074 b Fp(\(1.11\))-7 3043 y(Let)33 b(us)g(in)m(tro)s (duce)g(the)g(e\013ectiv)m(e)g(\(momen)m(tum)e(dep)s(enden)m(t\))k (scalar)d(p)s(oten)m(tial)1055 3248 y Ft(v)r Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fk(h)p Fo(\030)5 b(;)17 b(A)p Fp(\()p Fo(x)p Fp(\))p Fk(i)22 b Fp(+)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(v)t Fp(\()p Fo(x)p Fp(\))22 b(+)g Ft(b)p Fp(\()p Fo(x)p Fp(\))p Fo(;)813 b Fp(\(1.12\))-7 3453 y(where)846 3574 y Ft(b)p Fp(\()p Fo(x)p Fp(\))28 b(=)g Fo(mA)1329 3589 y Fj(0)1369 3574 y Fp(\()p Fo(x)p Fp(\))22 b(+)g(2)1669 3532 y Fn(\000)p Fj(1)1763 3574 y Fp(\()p Fk(j)p Fo(A)p Fp(\()p Fo(x)p Fp(\))p Fk(j)2061 3532 y Fj(2)2122 3574 y Fp(+)g Fo(A)2293 3532 y Fj(2)2293 3598 y(0)2333 3574 y Fp(\()p Fo(x)p Fp(\))g Fk(\000)h Fo(v)2637 3532 y Fj(2)2676 3574 y Fp(\()p Fo(x)p Fp(\)\))p Fo(:)604 b Fp(\(1.13\))-7 3742 y(Then)34 b(\(1.9\))e(is)g(equiv)-5 b(alen)m(t)32 b(to)h(the)g(equation)504 3947 y Fk(h)p Fo(\030)5 b(;)17 b Fk(r)p Fp(\010\()p Fo(x;)g(\030)5 b Fp(\))p Fk(i)21 b Fp(+)h Fk(h)p Fo(A)p Fp(\()p Fo(x)p Fp(\))p Fo(;)17 b Fk(r)p Fp(\010\()p Fo(x;)g(\030)5 b Fp(\))p Fk(i)21 b Fp(+)h(2)2039 3906 y Fn(\000)p Fj(1)2133 3947 y Fk(jr)p Fp(\010\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)2565 3906 y Fj(2)2626 3947 y Fp(+)22 b Ft(v)r Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(0)p Fo(;)261 b Fp(\(1.14\))-7 4152 y(whic)m(h)33 b(w)m(e)h(use)f(b)s(elo)m(w.)134 4310 y(As)46 b(is)e(w)m(ell)g(kno)m(wn,)50 b(equation)45 b(\(1.14\))f(do)s (es)h(not)g(ha)m(v)m(e)i(global)42 b(solutions)i(and)h(w)m(e)h(ha)m(v)m (e)h(to)-7 4431 y(remo)m(v)m(e)37 b(either)e(a)h(neigh)m(b)s(ourho)s(o) s(d)f(of)g(the)i(inciden)m(t)e Fk(\000)p Fo(\030)41 b Fp(or)35 b(of)h(the)g(outgoing)f(direction)f Fo(\030)5 b Fp(.)53 b(This)-7 4551 y(leads)42 b(to)g(t)m(w)m(o)g(solutions)g (\010)1057 4566 y Fn(\006)1116 4551 y Fp(,)i(t)m(w)m(o)f(appro)m (ximate)e(eigenfunctions)h Fo(u)2657 4566 y Fn(\006)2716 4551 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))41 b(and)h(t)m(w)m(o)h (di\013eren)m(t)-7 4671 y(iden)m(ti\014cations)32 b Fo(J)674 4686 y Fn(\006)765 4671 y Fp(de\014ned)i(as)f(PDO)319 4922 y(\()p Fo(J)411 4937 y Fn(\006)470 4922 y Fo(f)11 b Fp(\)\()p Fo(x)p Fp(\))27 b(=)h(\(2)p Fo(\031)t Fp(\))1013 4881 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1194 4786 y Fi(Z)1249 5012 y Fg(R)1297 4993 y Fl(3)1353 4922 y Fo(e)1398 4881 y Fm(i)p Fn(h)p Fm(x;\030)s Fn(i)p Fj(+)p Fm(i)p Fj(\010)1700 4890 y Ff(\006)1752 4881 y Fj(\()p Fm(x;\030)s Fj(\))1904 4922 y Fo(p)1953 4937 y Fn(\006)2012 4922 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\020)2278 4937 y Fn(\006)2336 4922 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)2768 4881 y Fj(2)2805 4922 y Fp(\))2864 4896 y(^)2843 4922 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)g(:)324 b Fp(\(1.15\))-7 5180 y(Here)33 b Fo( )f Fk(2)c Fo(C)489 5144 y Fn(1)482 5205 y Fj(0)564 5180 y Fp(\(0)p Fo(;)17 b Fk(1)p Fp(\))31 b(and)i(the)g(cut-o\013)f (function)g Fo(\020)1953 5195 y Fn(\006)2044 5180 y Fp(is)g(supp)s (orted)i(in)e(a)g(cone)694 5385 y Fk(C)746 5400 y Fn(\006)806 5385 y Fp(\()p Fo(\016)t Fp(\))27 b(=)h Fk(f)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(2)h Fh(R)1520 5344 y Fj(6)1593 5385 y Fp(:)g Fk(\006h)p Fo(x;)17 b(\030)5 b Fk(i)27 b(\025)h Fo(\016)t Fk(j)p Fo(x)p Fk(jj)p Fo(\030)5 b Fk(jg)p Fo(;)113 b(\016)31 b Fk(2)d Fp(\()p Fk(\000)p Fp(1)p Fo(;)17 b Fp(1\))p Fo(;)452 b Fp(\(1.16\))1835 5634 y(4)p eop %%Page: 5 5 5 4 bop -7 52 a Fp(so)44 b Fo(\020)167 67 y Fj(+)270 52 y Fp(\()p Fo(\020)351 67 y Fn(\000)409 52 y Fp(\))g(remo)m(v)m(es)i (a)d(neigh)m(b)s(ourho)s(o)s(d)g(of)h(the)g(inciden)m(t)g Fk(\000)p Fo(\030)49 b Fp(\(outgoing)42 b Fo(\030)5 b Fp(\))44 b(direction.)76 b(The)-7 172 y(function)37 b Fo(\020)423 187 y Fn(\006)519 172 y Fp(lo)s(calizes)e Fo(u)962 187 y Fn(\006)1058 172 y Fp(on)j(the)g(part)f(of)g(the)h (phase)g(space)g(where)h(\(1.10\))e(is)g(satis\014ed.)58 b(Note)-7 293 y(ho)m(w)m(ev)m(er)35 b(that)d(due)i(to)e Fo(\020)925 308 y Fn(\006)984 293 y Fp(,)g(the)h(\\e\013ectiv)m(e")g(p) s(erturbation)1457 494 y Fo(T)1514 509 y Fn(\006)1601 494 y Fp(=)28 b Fo(H)8 b(J)1848 509 y Fn(\006)1928 494 y Fk(\000)23 b Fo(J)2082 509 y Fn(\006)2141 494 y Fo(H)2222 509 y Fj(0)3476 494 y Fp(\(1.17\))-7 696 y(is)32 b(a)g (pseudo-di\013eren)m(tial)g(op)s(erator)g(with)g(sym)m(b)s(ol)g(v)-5 b(anishing)31 b(as)i Fk(j)p Fo(x)p Fk(j)2597 660 y Fn(\000)p Fj(1)2724 696 y Fp(only)f(at)g(in\014nit)m(y)-8 b(.)134 853 y(T)g(o)35 b(use)g(freely)g(the)g(pseudo-di\013eren)m(tial)e (calculus,)i(w)m(e)h(require)e(that)h Fo(v)t(;)17 b(A)2959 868 y Fm(k)3001 853 y Fo(;)g(k)34 b Fp(=)d(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3,)33 b(b)s(e)-7 973 y Fo(C)70 937 y Fn(1)145 973 y Fp(-functions)f(suc)m(h)i(that)e(for)g (all)f Fo(\013)d Fk(2)g Fh(N)1564 937 y Fj(3)259 1244 y Fk(j)p Fo(D)371 1203 y Fm(\013)420 1244 y Fo(v)t Fp(\()p Fo(x)p Fp(\))p Fk(j)22 b Fp(+)804 1120 y Fj(3)750 1149 y Fi(X)758 1362 y Fm(k)r Fj(=0)911 1244 y Fk(j)p Fo(D)1023 1203 y Fm(\013)1071 1244 y Fo(A)1144 1259 y Fm(k)1187 1244 y Fp(\()p Fo(x)p Fp(\))p Fk(j)28 b(\024)g Fo(C)1549 1259 y Fm(\013)1598 1244 y Fk(h)p Fo(x)p Fk(i)1731 1203 y Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)1966 1244 y Fo(;)82 b(\032)28 b(>)f Fp(0)p Fo(;)82 b Fk(h)p Fo(x)p Fk(i)27 b Fp(=)h(\(1)22 b(+)g Fk(j)p Fo(x)p Fk(j)2996 1203 y Fj(2)3035 1244 y Fp(\))3073 1203 y Fj(1)p Fm(=)p Fj(2)3183 1244 y Fo(:)266 b Fp(\(1.18\))134 1572 y Ft(1.3.)49 b Fp(Similarly)25 b(to)k(the)h(Sc)m(hr\177)-49 b(odinger)30 b(case)g([19)o(],)g(our)g(approac)m(h)f(to)g(scattering)g(theory)h(for) f(the)-7 1693 y(Dirac)38 b(op)s(erator)h(relies)g(on)g(the)h(limiting) 35 b(absorption)k(principle)f(and)h(the)h(radiation)e(estimates.)-7 1813 y(The)32 b(\014rst)g(of)f(these)h(results)g(means)f(that)g(the)h (op)s(erator)e(of)h(m)m(ultiplication)c(b)m(y)32 b Fk(h)p Fo(x)p Fk(i)3126 1777 y Fn(\000)p Fm(r)3219 1813 y Fp(,)f Fo(r)f(>)e Fp(1)p Fo(=)p Fp(2,)j(is)-7 1933 y(lo)s(cally)h Fo(H)8 b Fp(-smo)s(oth)33 b(in)g(the)i(sense)h(of)e(T.)h(Kato)f(\(see)i (De\014nition)d(2.1\).)48 b(The)36 b(second)g(is)e(related)g(to)-7 2054 y(the)f(critical)d(case)k Fo(r)c Fp(=)e(1)p Fo(=)p Fp(2.)42 b(Set)195 2346 y(\()p Fk(r)316 2305 y Fn(?)316 2370 y Fm(j)375 2346 y Fo(u)p Fp(\)\()p Fo(x)p Fp(\))27 b(=)h(\()p Fo(@)820 2361 y Fm(j)857 2346 y Fo(u)p Fp(\)\()p Fo(x)p Fp(\))22 b Fk(\000)g(j)p Fo(x)p Fk(j)1314 2305 y Fn(\000)p Fj(2)1409 2346 y Fo(x)1464 2361 y Fm(j)1571 2221 y Fj(3)1517 2251 y Fi(X)1525 2463 y Fm(k)r Fj(=1)1678 2346 y Fo(x)1733 2361 y Fm(k)1776 2346 y Fp(\()p Fo(@)1865 2361 y Fm(k)1908 2346 y Fo(u)p Fp(\)\()p Fo(x)p Fp(\))p Fo(;)81 b(j)34 b Fp(=)28 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)80 b(@)2812 2361 y Fm(k)2883 2346 y Fp(=)27 b Fo(@)5 b(=@)g(x)3202 2361 y Fm(k)3247 2346 y Fo(;)202 b Fp(\(1.19\))-7 2649 y(\(so)37 b Fk(h)p Fo(x;)17 b Fp(\()p Fk(r)414 2613 y Fn(?)473 2649 y Fo(u)p Fp(\)\()p Fo(x)p Fp(\))p Fk(i)35 b Fp(=)g(0\).)57 b(Then)38 b(the)f(op)s(erators)g Fk(h)p Fo(x)p Fk(i)2054 2613 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2219 2649 y Fk(r)2302 2613 y Fn(?)2302 2673 y Fm(j)2398 2649 y Fp(are)g(lo)s(cally)e Fo(H)8 b Fp(-smo)s(oth.)55 b(W)-8 b(e)37 b(em-)-7 2769 y(phasize)25 b(that)g(radiation)e (estimates)h(are)h(necessary)j(to)c(treat)h(the)g(part)g(of)g(the)g(p)s (erturbation)f(\(1.17\))-7 2890 y(deca)m(ying)33 b(as)g Fk(j)p Fo(x)p Fk(j)625 2853 y Fn(\000)p Fj(1)752 2890 y Fp(at)f(in\014nit)m(y)-8 b(.)134 3046 y(These)37 b(results)f(allo)m (w)e(us)i(to)f(factorize)f Fo(T)1689 3061 y Fn(\006)1784 3046 y Fp(in)m(to)g(a)h(sum)h(of)e(pro)s(ducts)i(of)f(lo)s(cally)e Fo(H)8 b Fp(-)34 b(and)i Fo(H)3654 3061 y Fj(0)3693 3046 y Fp(-)-7 3167 y(smo)s(oth)29 b(op)s(erators.)42 b(Th)m(us)31 b(the)e(theory)h(of)f(smo)s(oth)g(p)s(erturbations)g(can)g(b)s(e)h (applied)e(to)h(pro)m(v)m(e)i(the)-7 3287 y(existence)j(of)e(w)m(a)m(v) m(e)j(op)s(erators)1031 3489 y Fo(W)1123 3504 y Fn(\006)1182 3489 y Fp(\()p Fo(H)r(;)17 b(H)1428 3504 y Fj(0)1467 3489 y Fp(;)g Fo(J)1565 3504 y Fm(\034)1608 3489 y Fp(\))27 b(=)h Fo(s)22 b Fk(\000)65 b Fp(lim)1944 3549 y Fm(t)p Fn(!\0061)2182 3489 y Fo(e)2227 3448 y Fm(iH)5 b(t)2344 3489 y Fo(J)2398 3504 y Fm(\034)2442 3489 y Fo(e)2487 3448 y Fn(\000)p Fm(iH)2624 3457 y Fl(0)2658 3448 y Fm(t)3476 3489 y Fp(\(1.20\))-7 3724 y(for)32 b Fo(\034)39 b Fp(=)28 b(\\)22 b(+)g(")32 b(and)h Fo(\034)39 b Fp(=)27 b(\\)22 b Fk(\000)h Fp(")32 b(as)h(w)m(ell)f(as)h(\\in)m(v)m(erse")g(w)m(a)m(v) m(e)i(op)s(erators)976 3926 y Fo(W)1068 3941 y Fn(\006)1127 3926 y Fp(\()p Fo(H)1246 3941 y Fj(0)1285 3926 y Fo(;)17 b(H)8 b Fp(;)17 b Fo(J)1525 3885 y Fn(\003)1516 3951 y Fm(\034)1564 3926 y Fp(\))27 b(=)h Fo(s)22 b Fk(\000)66 b Fp(lim)1901 3986 y Fm(t)p Fn(!\0061)2139 3926 y Fo(e)2184 3885 y Fm(iH)2266 3894 y Fl(0)2301 3885 y Fm(t)2330 3926 y Fo(J)2393 3885 y Fn(\003)2384 3951 y Fm(\034)2433 3926 y Fo(e)2478 3885 y Fn(\000)p Fm(iH)5 b(t)2650 3926 y Fo(P)s(:)733 b Fp(\(1.21\))-7 4162 y(Here)27 b(the)g(limits)c(are)k (strong,)h(and)e Fo(P)40 b Fp(is)26 b(the)h(pro)5 b(jection)26 b(on)h(the)f(absolutely)g(con)m(tin)m(uous)h(subspace)-7 4282 y(of)39 b Fo(H)8 b Fp(.)62 b(Under)40 b(assumption)f(of)f(their)h (existence,)j(op)s(erators)d(\(1.20\))g(and)g(\(1.21\))f(are)i(adjoin)m (t)e(to)-7 4402 y(eac)m(h)c(other.)43 b(One)33 b(can)g(replace)g Fo(J)1275 4417 y Fn(\006)1366 4402 y Fp(b)m(y)h(a)e(simpler)f(op)s (erator)501 4649 y(\()p Ft(J)597 4664 y Fn(\006)656 4649 y Fo(f)11 b Fp(\)\()p Fo(x)p Fp(\))27 b(=)h(\(2)p Fo(\031)t Fp(\))1199 4608 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1380 4514 y Fi(Z)1435 4739 y Fg(R)1483 4720 y Fl(3)1539 4649 y Fo(e)1584 4608 y Fm(i)p Fn(h)p Fm(x;\030)s Fn(i)p Fj(+)p Fm(i)p Fj(\010)1886 4617 y Ff(\006)1938 4608 y Fj(\()p Fm(x;\030)s Fj(\))2090 4649 y Fo(p)2139 4664 y Fj(0)2178 4649 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(\020)2345 4664 y Fn(\006)2403 4649 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)2835 4608 y Fj(2)2872 4649 y Fp(\))2932 4623 y(^)2910 4649 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)g(;)257 b Fp(\(1.22\))-7 4904 y(constructed)31 b(in)d(terms)g(of)h(solutions)e(\010)1474 4919 y Fn(\006)1563 4904 y Fp(of)h(the)h(eik)m(onal)f(equation)h (\(1.14\))f(only)-8 b(.)41 b(Indeed,)32 b(the)d(dif-)-7 5024 y(ference)d Fo(J)367 5039 y Fn(\006)433 5024 y Fk(\000)7 b Ft(J)575 5039 y Fn(\006)660 5024 y Fp(is)24 b(compact.)41 b(Therefore)26 b Fo(W)1702 5039 y Fn(\006)1761 5024 y Fp(\()p Fo(H)r(;)17 b(H)2007 5039 y Fj(0)2046 5024 y Fp(;)g Fo(J)2144 5039 y Fm(\034)2187 5024 y Fp(\))28 b(=)f Fo(W)2448 5039 y Fn(\006)2507 5024 y Fp(\()p Fo(H)r(;)17 b(H)2753 5039 y Fj(0)2792 5024 y Fp(;)g Ft(J)2894 5039 y Fm(\034)2937 5024 y Fp(\))25 b(and)g(the)h(existence)-7 5145 y(of)h(one)h(of)f(these)i(op)s(erators)e(implies)e(the)j (existence)i(of)d(another.)42 b(Ho)m(w)m(ev)m(er,)31 b(the)d(preliminary)d(con-)-7 5265 y(sideration)37 b(of)h(the)h(more)f (complicated)f(iden)m(ti\014cation)f Fo(J)2185 5280 y Fn(\006)2283 5265 y Fp(is)i(necessary)i(b)s(ecause)g(the)f(op)s(erator) -7 5385 y Fo(H)8 b Ft(J)140 5400 y Fn(\006)221 5385 y Fk(\000)22 b Ft(J)378 5400 y Fn(\006)437 5385 y Fo(H)518 5400 y Fj(0)590 5385 y Fp(do)s(es)33 b(not)f(factorize)g(in)m(to)g(a)g (pro)s(duct)h(of)f(lo)s(cally)e Fo(H)8 b Fp(-)32 b(and)h Fo(H)2866 5400 y Fj(0)2905 5385 y Fp(-smo)s(oth)e(op)s(erators.)1835 5634 y(5)p eop %%Page: 6 6 6 5 bop 134 52 a Fp(Note)52 b(that)e(a)h(classical)f(particle)g (propagates)h(as)g Fo(t)60 b Fk(!)f(\0061)51 b Fp(in)f(the)i(cone)g Fk(C)3227 67 y Fn(\006)3286 52 y Fp(\()p Fo(\016)t Fp(\))f(of)g(the)-7 172 y(phase)i(space.)101 b(The)53 b(corresp)s(onding)f(quan)m(tum)f (argumen)m(ts)h(sho)m(w)h(that)e(the)h(w)m(a)m(v)m(e)i(op)s(erator)-7 293 y Fo(W)85 308 y Fn(\006)144 293 y Fp(\()p Fo(H)r(;)17 b(H)390 308 y Fj(0)429 293 y Fp(;)g Ft(J)531 308 y Fn(\006)590 293 y Fp(\))43 b(are)g(isometric)e(on)i(the)g(subspace)i Fo(E)2086 308 y Fj(0)2126 293 y Fp(\(\003\))p Fk(H)e Fp(if)f Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)2706 256 y Fj(2)2744 293 y Fp(\))46 b(=)f(1)d(for)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))45 b Fk(2)h Fp(\003)f Fk(\032)-7 413 y Fp(\()p Fo(m;)17 b Fk(1)p Fp(\).)77 b(Similarly)-8 b(,)42 b Fo(W)941 428 y Fn(\006)1000 413 y Fp(\()p Fo(H)r(;)17 b(H)1246 428 y Fj(0)1285 413 y Fp(;)g Ft(J)1387 428 y Fn(\007)1446 413 y Fp(\))47 b(=)f(0.)77 b(These)46 b(w)m(a)m(v)m(e)f (op)s(erators)f(pla)m(y)g(an)f(auxiliary)f(but)-7 533 y(imp)s(ortan)m(t)34 b(role)g(in)h(our)g(construction)h(of)f (scattering)g(theory)-8 b(.)53 b(Actually)-8 b(,)35 b(using)g(the)h (results)g(for-)-7 654 y(m)m(ulated)c(ab)s(o)m(v)m(e)h(and)g(c)m(ho)s (osing)f(the)h(cut-o\013)f(functions)h Fo(\020)2170 669 y Fn(\006)2261 654 y Fp(in)f(suc)m(h)i(a)e(w)m(a)m(y)i(that)e(the)h(op) s(erator)1330 874 y(\()p Ft(J)1426 889 y Fj(+)1485 874 y Ft(J)1543 833 y Fn(\003)1543 898 y Fj(+)1624 874 y Fp(+)22 b Ft(J)1780 889 y Fn(\000)1839 874 y Ft(J)1897 833 y Fn(\003)1897 898 y(\000)1978 874 y Fk(\000)h Fo(I)8 b Fp(\))p Fo(E)e Fp(\(\003\))-7 1094 y(is)32 b(compact,)g(w)m(e)i(pro)m (v)m(e)g(that)e(the)h(op)s(erators)g Fo(W)1818 1109 y Fn(\006)1877 1094 y Fp(\()p Fo(H)r(;)17 b(H)2123 1109 y Fj(0)2162 1094 y Fp(;)g Ft(J)2264 1109 y Fn(\006)2322 1094 y Fp(\))33 b(are)f(complete,)g(that)h(is)f(the)h(range)1018 1314 y(Ran\()p Fo(W)1323 1329 y Fn(\006)1382 1314 y Fp(\()p Fo(H)r(;)17 b(H)1628 1329 y Fj(0)1667 1314 y Fp(;)g Ft(J)1769 1329 y Fn(\006)1828 1314 y Fp(\))p Fo(E)1938 1329 y Fj(0)1977 1314 y Fp(\(\003\)\))27 b(=)h Fo(E)6 b Fp(\(\003\))p Fo(P)14 b Fk(H)q Fo(:)775 b Fp(\(1.23\))134 1575 y(The)34 b(stationary)e(approac)m(h)h(dev)m(elop)s(ed)h(here)f(allo)m(ws)f(one)h (to)f(write)g(do)m(wn)i(form)m(ulas)d(for)h(scat-)-7 1696 y(tering)38 b(matrix)g(and)h(to)g(study)h(the)f(diagonal)e (singularit)m(y)g(of)i(its)f(k)m(ernel.)64 b(Giv)m(en)39 b(the)g(results)h(of)-7 1816 y(this)28 b(pap)s(er,)h(this)f(is)g(essen) m(tially)f(similar)e(to)j(the)h(Sc)m(hr\177)-49 b(odinger)28 b(case)h([19])f(and)g(therefore)h(w)m(e)g(do)f(not)-7 1936 y(dw)m(ell)k(up)s(on)h(it)e(here.)-7 2249 y Ft(2.)112 b(LIMITING)37 b(ABSORPTION)f(PRINCIPLE)f(AND)i(RADIA)-9 b(TION)192 2369 y(ESTIMA)g(TES)-7 2629 y(2.1.)68 b Fp(Let)41 b(us)g(recall)f(some)g(basic)h(notions)f(of)g(the)h(theory)h(of)e(smo)s (oth)g(p)s(erturbations)g(\(see)i(e.g.)-7 2750 y([13],)f([18])e(for)g (details\).)64 b(Belo)m(w)39 b(w)m(e)i(denote)f(b)m(y)h Fo(c)e Fp(and)h Fo(C)46 b Fp(di\013eren)m(t)40 b(p)s(ositiv)m(e)f (constan)m(ts)i(whose)-7 2870 y(precise)30 b(v)-5 b(alues)30 b(are)f(of)g(no)h(imp)s(ortance)e(for)h(us.)43 b(The)30 b(class)g(of)f(b)s(ounded)h(op)s(erators)f(is)g(denoted)i Fk(B)s Fp(.)-7 3032 y Ft(De\014nition)36 b(2.1)49 b Fe(L)-5 b(et)47 b Fo(H)54 b Fe(b)-5 b(e)47 b(a)f(self-adjoint)f(op)-5 b(er)g(ator)47 b(in)f(a)h(Hilb)-5 b(ert)47 b(sp)-5 b(ac)g(e)45 b Fk(H)q Fe(,)50 b(and)c(let)h Fo(K)54 b Fe(b)-5 b(e)-7 3152 y(an)37 b Fo(H)8 b Fe(-b)-5 b(ounde)g(d)36 b(op)-5 b(er)g(ator.)53 b(It)38 b(is)f(c)-5 b(al)5 b(le)-5 b(d)37 b Fo(H)8 b Fe(-smo)-5 b(oth)36 b(if)h(one)g(of)h(the)f(fol)5 b(lowing)36 b(thr)-5 b(e)g(e)38 b Fp(\()p Fe(e)-5 b(quivalent)p Fp(\))-7 3273 y Fe(r)g(elations)34 b(is)h(satis\014e)-5 b(d:)134 3435 y Fp(\()p Fe(i)p Fp(\))808 3606 y Fo(\015)864 3565 y Fj(2)859 3630 y(1)931 3606 y Fp(=)27 b(\(2)p Fo(\031)t Fp(\))1218 3565 y Fn(\000)p Fj(1)1507 3606 y Fp(sup)1329 3692 y Fn(jj)p Fm(f)7 b Fn(jj)p Fj(=1)p Fm(;)j(f)d Fn(2D)r Fj(\()p Fm(H)e Fj(\))1849 3470 y Fi(Z)1949 3497 y Fn(1)1905 3696 y(\0001)2051 3606 y Fk(jj)p Fo(K)i(e)2242 3565 y Fn(\000)p Fm(iH)e(t)2413 3606 y Fo(f)11 b Fk(jj)2528 3565 y Fj(2)2567 3606 y Fo(dt)27 b(<)h Fk(1)p Fo(;)614 b Fp(\(2.1\))134 3897 y(\()p Fe(ii)p Fp(\))1031 4017 y Fo(\015)1087 3976 y Fj(2)1082 4042 y(2)1154 4017 y Fp(=)28 b Fo(\031)1317 3976 y Fn(\000)p Fj(1)1500 4017 y Fp(sup)1428 4099 y Fm(">)p Fj(0)p Fm(;)11 b(\025)p Fn(2)p Fg(R)1735 4017 y Fo(")p Fk(jj)p Fo(K)c(R)q Fp(\()p Fo(\025)21 b Fk(\006)i Fo(i")p Fp(\))p Fk(jj)2391 3976 y Fj(2)2457 4017 y Fo(<)k Fk(1)p Fo(;)838 b Fp(\(2.2\))134 4301 y(\()p Fe(iii)p Fp(\))1165 4421 y Fo(\015)1221 4380 y Fj(2)1216 4446 y(3)1288 4421 y Fp(=)37 b(sup)1392 4503 y Fm(X)5 b Fn(\032)p Fg(R)1574 4421 y Fk(j)p Fo(X)j Fk(j)1719 4380 y Fn(\000)p Fj(1)1813 4421 y Fk(jj)p Fo(K)f(E)f Fp(\()p Fo(X)i Fp(\))p Fk(jj)2258 4380 y Fj(2)2323 4421 y Fo(<)28 b Fk(1)p Fo(:)971 b Fp(\(2.3\))-7 4648 y Fe(In)34 b(this)h(c)-5 b(ase,)34 b Fo(\015)597 4663 y Fj(1)664 4648 y Fp(=)27 b Fo(\015)818 4663 y Fj(2)885 4648 y Fp(=)h Fo(\015)1040 4663 y Fj(3)1079 4648 y Fe(.)134 4810 y(The)34 b(op)-5 b(er)g(ator)35 b Fo(K)42 b Fe(is)35 b(said)f(to)h(b)-5 b(e)35 b Fo(H)8 b Fe(-smo)-5 b(oth)33 b(on)i(a)f(Bor)-5 b(el)34 b(set)h Fp(\003)g Fe(if)g Fo(K)7 b(E)f Fp(\(\003\))34 b Fe(is)h Fo(H)8 b Fe(-smo)-5 b(oth.)134 4972 y Fp(The)34 b(follo)m(wing)c(assertion)i(is)g(almost)f(ob)m(vious.)-7 5159 y Ft(Prop)s(osition)36 b(2.2)49 b Fe(L)-5 b(et)34 b Fo(K)42 b Fe(b)-5 b(e)34 b(an)g Fo(H)8 b Fe(-b)-5 b(ounde)g(d)33 b(op)-5 b(er)g(ator)34 b(and)f(let)i Fp(\003)27 b Fk(\032)h Fh(R)2809 5123 y Fj(+)2909 5159 y Fe(b)-5 b(e)34 b(a)g(c)-5 b(omp)g(act)34 b(inter-)-7 5279 y(val.)44 b(Then)34 b Fo(K)42 b Fe(is)35 b Fo(H)8 b Fe(-smo)-5 b(oth)34 b(on)g Fp(\003)h Fe(and)f Fk(\000)p Fp(\003)h Fe(if)g(and)f(only)h(if)f(it)i (is)e Fo(H)2618 5243 y Fj(2)2657 5279 y Fe(-smo)-5 b(oth)34 b(on)h Fp(\003)3231 5243 y Fj(2)3270 5279 y Fe(.)1835 5634 y Fp(6)p eop %%Page: 7 7 7 6 bop -7 52 a Fe(Pr)-5 b(o)g(of)35 b({)67 b Fp(It)33 b(su\016ces)h(to)e(tak)m(e)i(in)m(to)e(accoun)m(t)h(the)g(ob)m(vious)g (iden)m(tit)m(y)541 272 y Fk(jj)p Fo(E)669 288 y Fm(H)732 269 y Fl(2)770 272 y Fp(\()p Fo(X)897 230 y Fj(2)936 272 y Fp(\))p Fo(K)7 b(f)k Fk(jj)1179 230 y Fj(2)1245 272 y Fp(=)28 b Fk(jj)p Fo(E)1477 287 y Fm(H)1544 272 y Fp(\()p Fo(X)8 b Fp(\))p Fo(K)f(f)k Fk(jj)1914 230 y Fj(2)1974 272 y Fp(+)22 b Fk(jj)p Fo(E)2200 287 y Fm(H)2267 272 y Fp(\()p Fk(\000)p Fo(X)8 b Fp(\))p Fo(K)f(f)k Fk(jj)2714 230 y Fj(2)2753 272 y Fo(;)81 b(X)36 b Fk(\032)28 b Fp(\003)p Fo(;)-7 491 y Fp(and)33 b(use)g(de\014nition)f(\(2.3\).)43 b Fd(2)134 703 y Fp(The)31 b(next)f(w)m(ell)f(kno)m(wn)i(assertion)e (allo)m(ws)g(to)g(construct)h(new)h Fo(H)8 b Fp(-smo)s(oth)27 b(op)s(erators)j(giv)m(en)f(an)-7 823 y Fo(H)8 b Fp(-smo)s(oth)33 b(op)s(erator)h Fo(K)42 b Fp(\(see,)36 b(e.g.,)g([20])f(for)f(its)g (pro)s(of)7 b(\),)35 b(but)g(it)e(is)i(also)f(of)g(in)m(terest)h(in)f (the)h(case)-7 944 y Fo(K)g Fp(=)27 b(0.)-7 1105 y Ft(Prop)s(osition)36 b(2.3)49 b Fe(L)-5 b(et)27 b Ft(M)h Fe(b)-5 b(e)27 b(an)g Fo(H)8 b Fe(-b)-5 b(ounde)g(d)26 b(op)-5 b(er)g(ator)27 b(and)g(let)g Fo(K)35 b Fe(b)-5 b(e)27 b Fo(H)8 b Fe(-smo)-5 b(oth)26 b(on)h(a)g(b)-5 b(ounde)g(d)-7 1226 y(interval)34 b Fp(\003)p Fe(.)45 b(Supp)-5 b(ose)34 b(that)h(for)g(any)g Fo(u)27 b Fp(=)g Fo(E)1664 1241 y Fm(H)1732 1226 y Fp(\(\003\))p Fo(u)1154 1445 y Fk(jj)p Fo(Gu)p Fk(jj)1399 1404 y Fj(2)1465 1445 y Fk(\024)h Fp(\()p Fo(i)p Fp([)p Fo(H)r(;)17 b Ft(M)p Fp(])p Fo(u;)g(u)p Fp(\))k(+)h Fk(jj)p Fo(K)7 b(u)p Fk(jj)2499 1404 y Fj(2)2537 1445 y Fo(:)-7 1665 y Fe(Then)34 b Fo(G)h Fe(is)g(also)f Fo(H)8 b Fe(-smo)-5 b(oth)33 b(on)i Fp(\003)p Fe(.)134 1827 y Fp(The)42 b(theory)g(of)f (smo)s(oth)f(p)s(erturbations)g(giv)m(es)i(a)f(con)m(v)m(enien)m(t)i (su\016cien)m(t)f(condition)d(for)i(the)-7 1947 y(existence)34 b(of)e(w)m(a)m(v)m(e)j(op)s(erators)d(\(it)g(can)g(b)s(e)h(easily)f (deduced)i(from)e(de\014nition)f(\(2.1\)\).)-7 2109 y Ft(Prop)s(osition)36 b(2.4)49 b Fe(L)-5 b(et)38 b Fo(H)1043 2124 y Fj(1)1082 2109 y Fo(;)17 b(H)1207 2124 y Fj(2)1284 2109 y Fe(b)-5 b(e)37 b(a)g(c)-5 b(ouple)38 b(of)f(self-adjoint)f(op)-5 b(er)g(ators)38 b(in)f Fk(H)q Fe(,)h(and)g(let)f Fo(J)47 b Fe(b)-5 b(e)38 b(a)-7 2229 y(b)-5 b(ounde)g(d)34 b(op)-5 b(er)g(ator.)45 b(Supp)-5 b(ose)34 b(that)h(the)g(op)-5 b(er)g(ator)34 b Fo(T)42 b Fp(=)27 b Fo(H)2186 2244 y Fj(2)2226 2229 y Fo(J)k Fk(\000)23 b Fo(J)9 b(H)2555 2244 y Fj(1)2629 2229 y Fe(admits)34 b(a)h(factorization)1498 2536 y Fo(T)42 b Fp(=)1741 2412 y Fm(N)1700 2442 y Fi(X)1715 2652 y Fm(i)p Fj(=1)1861 2536 y Fo(K)1951 2495 y Fn(\003)1944 2561 y Fj(2)p Fm(;i)2027 2536 y Fo(K)2110 2551 y Fj(1)p Fm(;i)2193 2536 y Fo(;)-7 2838 y Fe(wher)-5 b(e)38 b Fo(K)355 2853 y Fm(j;i)431 2838 y Fo(;)17 b(i)34 b Fp(=)g(1)p Fo(;)17 b(:)g(:)g(:)f(;)h(N)10 b Fe(,)39 b(ar)-5 b(e)38 b Fo(H)1327 2853 y Fm(j)1363 2838 y Fe(-smo)-5 b(oth,)39 b Fo(j)h Fp(=)34 b(1)p Fo(;)17 b Fp(2)p Fe(,)38 b(on)g(a)g(c)-5 b(omp)g(act)38 b(interval)g Fp(\003)c Fk(\032)g Fh(R)5 b Fe(.)61 b(Then)-7 2959 y(the)35 b(wave)f(op)-5 b(er)g(ators)802 3178 y Fo(W)894 3193 y Fn(\006)953 3178 y Fp(\()p Fo(H)1072 3193 y Fj(2)1111 3178 y Fo(;)17 b(H)1236 3193 y Fj(1)1275 3178 y Fp(;)g Fo(J)n(;)g Fp(\003\))27 b(=)h Fo(s)22 b Fk(\000)66 b Fp(lim)1820 3238 y Fm(t)p Fn(!\0061)2058 3178 y Fo(e)2103 3137 y Fm(iH)2185 3146 y Fl(2)2220 3137 y Fm(t)2249 3178 y Fo(J)9 b(e)2357 3137 y Fn(\000)p Fm(iH)2494 3146 y Fl(1)2529 3137 y Fm(t)2559 3178 y Fo(E)2631 3193 y Fj(1)2670 3178 y Fp(\(\003\))p Fo(P)2877 3193 y Fj(1)-7 3437 y Fp(\()p Fo(P)94 3452 y Fj(1)177 3437 y Fe(is)44 b(the)g(ortho)-5 b(gonal)43 b(pr)-5 b(oje)g(ction)43 b(on)g(the)h(absolutely)g(c)-5 b(ontinuous)43 b(subsp)-5 b(ac)g(e)43 b(of)h(the)g(op)-5 b(er)g(ator)-7 3558 y Fo(H)74 3573 y Fj(1)113 3558 y Fp(\))35 b Fe(and)f Fo(W)467 3573 y Fn(\006)527 3558 y Fp(\()p Fo(H)646 3573 y Fj(1)685 3558 y Fo(;)17 b(H)810 3573 y Fj(2)849 3558 y Fp(;)g Fo(J)956 3522 y Fn(\003)995 3558 y Fo(;)g Fp(\003\))34 b Fe(exist.)134 3720 y Ft(2.2.)47 b Fp(Let)24 b(us)g(return)h(to)e(the) h(Dirac)f(op)s(erator)g Fo(H)35 b Fp(=)28 b Fo(H)2137 3735 y Fj(0)2180 3720 y Fp(+)t Fo(V)46 b Fp(de\014ned)25 b(b)m(y)g(equations)f(\(1.1\),)h(\(1.6\).)-7 3840 y(With)33 b(the)h(help)g(of)f(the)h(Mourre)h(comm)m(utator)d(metho)s(d,)h(the)h (limiting)c(absorption)j(principle)f(for)-7 3960 y(the)42 b(op)s(erator)f Fo(H)49 b Fp(\(cf.)70 b([2],)44 b([16]\))d(can)h(b)s(e) g(obtained)f(practically)e(in)i(the)h(same)f(w)m(a)m(y)i(as)f(for)f (the)-7 4081 y(Sc)m(hr\177)-49 b(odinger)33 b(op)s(erator)f(\(see)i ([9],)f([12]\).)45 b(Actually)-8 b(,)32 b(it)g(can)h(b)s(e)g(reduced)h (to)f(the)g(Sc)m(hr\177)-49 b(odinger)33 b(case)-7 4201 y(but)g(w)m(e)h(prefer)f(a)f(direct)g(w)m(a)m(y)-8 b(.)45 b(Let)33 b(us)g(set)1266 4505 y Ft(A)27 b Fp(=)h(2)1531 4464 y Fn(\000)p Fj(1)1696 4381 y(3)1642 4411 y Fi(X)1649 4623 y Fm(k)r Fj(=1)1786 4505 y Fp(\()p Fo(x)1879 4520 y Fm(k)1922 4505 y Fo(D)2003 4520 y Fm(k)2067 4505 y Fp(+)22 b Fo(D)2246 4520 y Fm(k)2289 4505 y Fo(x)2344 4520 y Fm(k)2387 4505 y Fp(\))p Fo(:)-7 4809 y Fp(Since)1398 4929 y Fo(i)p Fp([)p Fo(H)1539 4944 y Fj(0)1578 4929 y Fo(;)17 b Ft(A)p Fp(])27 b(=)h Fo(H)1946 4944 y Fj(0)2007 4929 y Fk(\000)23 b Fo(m\013)2254 4944 y Fj(0)2294 4929 y Fo(;)1204 b Fp(\(2.4\))-7 5103 y(the)29 b(op)s(erator)f Ft(A)g Fp(\(in)f(con)m(trast)i(to)f([2])h(where)g(the)g(Mourre)g(metho) s(d)f(w)m(as)h(also)f(used\))h(can)g(b)s(e)f(tak)m(en)-7 5224 y(for)k(the)h(conjugate)g(op)s(erator)f(to)g Fo(H)8 b Fp(.)134 5385 y(The)34 b(Mourre)f(estimate)f(is)g(in)m(tro)s(duced)g (in)g(the)h(follo)m(wing)1835 5634 y(7)p eop %%Page: 8 8 8 7 bop -7 52 a Ft(Theorem)37 b(2.5)49 b Fe(Supp)-5 b(ose)34 b(that)i Fo(V)21 b Fp(\()p Fo(x)p Fp(\))28 b(=)g Fo(V)1629 67 y Fm(L)1681 52 y Fp(\()p Fo(x)p Fp(\))22 b(+)g Fo(V)1989 67 y Fm(S)2040 52 y Fp(\()p Fo(x)p Fp(\))35 b Fe(wher)-5 b(e)905 272 y Fk(j)p Fo(V)990 287 y Fm(L)1042 272 y Fp(\()p Fo(x)p Fp(\))p Fk(j)22 b Fp(+)g Fk(h)p Fo(x)p Fk(i)17 b(j)o Fo(@)5 b(V)1611 287 y Fm(L)1664 272 y Fp(\()p Fo(x)p Fp(\))p Fo(=@)g Fk(j)p Fo(x)p Fk(jj)28 b(\024)g Fo(C)7 b Fk(h)p Fo(x)p Fk(i)2382 231 y Fn(\000)p Fm(\032)2477 272 y Fo(;)52 b(\032)28 b(>)f Fp(0)p Fo(;)712 b Fp(\(2.5\))1434 492 y Fk(j)p Fo(V)1519 507 y Fm(S)1570 492 y Fp(\()p Fo(x)p Fp(\))p Fk(j)27 b(\024)i Fo(C)7 b Fk(h)p Fo(x)p Fk(i)2072 451 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\032)2257 492 y Fo(:)1241 b Fp(\(2.6\))-7 666 y Fe(Then)39 b(eigenvalues)g(of)h Fo(H)48 b Fe(ar)-5 b(e)40 b(of)g(\014nite)g(multiplicity)g Fp(\()p Fe(exc)-5 b(ept,)41 b(p)-5 b(ossibly,)41 b(the)f(eigenvalues)f Fk(\006)p Fo(m)p Fp(\))-7 787 y Fe(and)e(may)f(ac)-5 b(cumulate)37 b(at)g(the)g(p)-5 b(oints)37 b Fk(\006)p Fo(m)h Fe(only.)51 b(F)-7 b(or)36 b(any)h Fk(\006)p Fo(\025)32 b(>)f(m)p Fe(,)38 b Fo(\025)43 b(=)-60 b Fk(2)32 b Fo(\033)2977 802 y Fm(p)3017 787 y Fp(\()p Fo(H)8 b Fp(\))p Fe(,)37 b(ther)-5 b(e)37 b(exists)-7 907 y(a)e(su\016ciently)g(smal)5 b(l)34 b Fo(\021)d(>)d Fp(0)34 b Fe(such)h(that)g(the)g Fp(\()p Fe(Mourr)-5 b(e)p Fp(\))35 b Fe(estimate)493 1127 y Fk(\006)p Fo(E)6 b Fp(\()p Fo(X)767 1142 y Fm(\021)809 1127 y Fp(\))p Fo(i)p Fp([)p Fo(H)r(;)17 b Ft(A)p Fp(])p Fo(E)6 b Fp(\()p Fo(X)1343 1142 y Fm(\021)1385 1127 y Fp(\))27 b Fk(\025)i Fo(cE)6 b Fp(\()p Fo(X)1795 1142 y Fm(\021)1836 1127 y Fp(\))p Fo(;)122 b(c)27 b(>)h Fp(0)p Fo(;)121 b(X)2474 1142 y Fm(\021)2544 1127 y Fp(=)27 b(\()p Fo(\025)22 b Fk(\000)h Fo(\021)t(;)17 b(\025)k Fp(+)h Fo(\021)t Fp(\))299 b(\(2.7\))-7 1347 y Fe(holds.)-7 1509 y(Pr)-5 b(o)g(of)43 b({)84 b Fp(Consider,)45 b(for)c(example,)i (the)f(p)s(ositiv)m(e)f(sp)s(ectrum)h(of)f Fo(H)8 b Fp(.)70 b(Let)42 b(\003)g(=)h(\()p Fo(\025)3217 1524 y Fj(0)3257 1509 y Fo(;)17 b(\025)3358 1524 y Fj(1)3397 1509 y Fp(\))41 b(where)-7 1629 y Fo(m)28 b(<)g(\025)267 1644 y Fj(0)334 1629 y Fo(<)f(\025)494 1644 y Fj(1)561 1629 y Fo(<)h Fk(1)p Fp(.)43 b(It)32 b(follo)m(ws)g(from)f(\(2.4\))h(that)1095 1849 y Fo(i)p Fp([)p Fo(H)r(;)17 b Ft(A)p Fp(])27 b(=)h(\()p Fo(H)i Fk(\000)22 b Fo(m\013)1920 1864 y Fj(0)1960 1849 y Fp(\))g Fk(\000)h Fo(V)43 b Fp(+)22 b Fo(i)p Fp([)p Fo(V)5 b(;)17 b Ft(A)p Fp(])p Fo(:)902 b Fp(\(2.8\))-7 2069 y(Since)33 b Fo(\013)310 2084 y Fj(0)377 2069 y Fk(\024)28 b Fo(I)8 b Fp(,)33 b(w)m(e)g(ha)m(v)m(e)h(that)1021 2289 y Fo(E)6 b Fp(\(\003\)\()p Fo(H)29 b Fk(\000)23 b Fo(m\013)1638 2304 y Fj(0)1677 2289 y Fp(\))p Fo(E)6 b Fp(\(\003\))28 b Fk(\025)g Fp(\()p Fo(\025)2165 2304 y Fj(0)2226 2289 y Fk(\000)23 b Fo(m)p Fp(\))p Fo(E)6 b Fp(\(\003\))p Fo(:)827 b Fp(\(2.9\))-7 2509 y(The)30 b(op)s(erator)f Fo(V)21 b Fp(\()p Fo(H)777 2524 y Fj(0)832 2509 y Fp(+)15 b Fo(i)p Fp(\))994 2473 y Fn(\000)p Fj(1)1117 2509 y Fp(is)29 b(compact)g(b)s(ecause)h Fo(V)22 b Fp(\()p Fo(x)p Fp(\))28 b Fk(!)f Fp(0)i(as)g Fk(j)p Fo(x)p Fk(j)f(!)f(1)p Fp(.)42 b(Under)30 b(assumption)-7 2630 y(\(2.5\))40 b(the)i(op)s(erator)e([)p Fo(V)896 2645 y Fm(L)948 2630 y Fo(;)17 b Ft(A)p Fp(])40 b(is)g(m)m(ultiplication)c(b)m(y)42 b(the)f(matrix-function)e Fo(i)p Fk(j)p Fo(x)p Fk(j)p Fo(@)5 b(V)3169 2645 y Fm(L)3222 2630 y Fo(=@)g Fk(j)p Fo(x)p Fk(j)41 b Fp(whic)m(h)-7 2750 y(tends)26 b(to)f(zero.)42 b(Therefore)26 b(the)f(op)s(erator)g([)p Fo(V)1664 2765 y Fm(L)1716 2750 y Fo(;)17 b Ft(A)p Fp(]\()p Fo(H)1991 2765 y Fj(0)2037 2750 y Fp(+)7 b Fo(i)p Fp(\))2191 2714 y Fn(\000)p Fj(1)2310 2750 y Fp(is)25 b(also)f(compact.)41 b(The)26 b(comm)m(utator)673 3060 y([)p Fo(V)757 3075 y Fm(S)807 3060 y Fo(;)17 b Ft(A)p Fp(])27 b(=)h Fo(V)1151 3075 y Fm(S)1202 3060 y Ft(A)21 b Fk(\000)i Ft(A)p Fo(V)1550 3075 y Fm(S)1628 3060 y Fp(=)1786 2936 y Fj(3)1732 2966 y Fi(X)1742 3176 y Fm(j)t Fj(=1)1875 3060 y Fp(\()p Fo(V)1970 3075 y Fm(S)2021 3060 y Fo(x)2076 3075 y Fm(j)2113 3060 y Fo(D)2194 3075 y Fm(j)2253 3060 y Fk(\000)f Fo(D)2433 3075 y Fm(j)2470 3060 y Fo(x)2525 3075 y Fm(j)2562 3060 y Fo(V)2619 3075 y Fm(S)2669 3060 y Fp(\))g Fk(\000)h Fp(3)p Fo(iV)2968 3075 y Fm(S)3019 3060 y Fo(;)430 b Fp(\(2.10\))-7 3385 y(so)32 b(under)g(assumption)e(\(2.6\))h(the)h(op)s (erator)e(\()p Fo(H)1810 3400 y Fj(0)1869 3385 y Fp(+)19 b Fo(i)p Fp(\))2035 3349 y Fn(\000)p Fj(1)2130 3385 y Fp([)p Fo(V)2214 3400 y Fm(S)2265 3385 y Fo(;)e Ft(A)p Fp(]\()p Fo(H)2540 3400 y Fj(0)2598 3385 y Fp(+)i Fo(i)p Fp(\))2764 3349 y Fn(\000)p Fj(1)2890 3385 y Fp(is)31 b(compact.)42 b(Th)m(us)33 b(it)-7 3506 y(follo)m(ws)e(from)h(\(2.8\),) g(\(2.9\))g(that)1016 3726 y Fo(E)6 b Fp(\(\003\))p Fo(i)p Fp([)p Fo(H)r(;)17 b Ft(A)p Fp(])p Fo(E)6 b Fp(\(\003\))27 b Fk(\025)h Fp(\()p Fo(\025)1986 3741 y Fj(0)2048 3726 y Fk(\000)22 b Fo(m)p Fp(\))p Fo(E)6 b Fp(\(\003\))22 b(+)g Fo(K)781 b Fp(\(2.11\))-7 3946 y(with)32 b(a)h(compact)f(op)s (erator)g Fo(K)7 b Fp(.)134 4108 y(Similarly)34 b(to)j(the)h(Sc)m (hr\177)-49 b(odinger)38 b(case)h(\(see,)h(e.g.,)f([12]\),)g(it)d(is)h (easy)i(to)e(c)m(hec)m(k)j(that)e(the)g(virial)-7 4228 y(theorem)d(holds)g(for)g(eigenfunctions)g(of)g Fo(H)8 b Fp(.)51 b(This)36 b(means)f(that)g(\([)p Fo(H)r(;)17 b Ft(A)p Fp(])p Fo( )t(;)g( )t Fp(\))32 b(=)g(0)j(if)f Fo( )j Fk(2)32 b(D)s Fp(\()p Fo(H)8 b Fp(\))-7 4348 y(and)31 b Fo(H)8 b( )31 b Fp(=)d Fo(\025 )t Fp(.)43 b(Com)m(bined)31 b(with)f(estimate)g(\(2.11\),)h(this)g(standardly)g(implies)e(that)h (eigen)m(v)-5 b(alues)-7 4469 y Fo(\025)28 b(>)f(m)h Fp(are)g(of)g(\014nite)g(m)m(ultiplicit)m(y)c(and)k(they)h(cannot)f (accum)m(ulate)g(at)f(in)m(terior)g(p)s(oin)m(ts)g(of)h(\()p Fo(m;)17 b Fk(1)p Fp(\).)134 4631 y(Let)37 b(us)h(\014x)g(the)f(p)s (oin)m(t)g Fo(\025)e Fk(2)h Fp(\003,)i Fo(\025)46 b(=)-60 b Fk(2)36 b Fo(\033)1594 4646 y Fm(p)1634 4631 y Fp(\()p Fo(H)8 b Fp(\),)37 b(and)h(m)m(ultiply)c(\(2.11\))j(b)m(y)h(the)f(op)s (erator)g Fo(E)6 b Fp(\()p Fo(X)3646 4646 y Fm(\021)3687 4631 y Fp(\))-7 4751 y(from)34 b(the)h(left)g(and)g(from)f(the)h(righ)m (t.)51 b(Since)35 b Fo(E)6 b Fp(\()p Fo(X)1901 4766 y Fm(\021)1943 4751 y Fp(\))35 b(con)m(v)m(erges)i(strongly)e(to)g(zero)g (as)g Fo(\021)h Fk(!)c Fp(0,)j(w)m(e)-7 4871 y(ha)m(v)m(e)f(that)e Fk(jj)p Fo(K)7 b(E)f Fp(\()p Fo(X)772 4886 y Fm(\021)814 4871 y Fp(\))p Fk(jj)27 b(!)g Fp(0)32 b(as)h Fo(\021)e Fk(!)d Fp(0.)43 b(Th)m(us)34 b(\(2.11\))e(implies)e(\(2.7\))i(if)f Fo(\021)37 b Fp(is)32 b(small)e(enough.)44 b Fd(2)-7 5108 y Ft(Remark)37 b(2.6)49 b Fp(W)-8 b(e)34 b(ha)m(v)m(e)g(sho)m(wn)h (that)e(under)h(the)g(assumptions)f(of)g(Theorem)g(2.5)g(the)h(op)s (erator)-7 5228 y(\()p Fo(H)112 5243 y Fj(0)173 5228 y Fp(+)22 b Fo(i)p Fp(\))342 5192 y Fn(\000)p Fj(1)437 5228 y Fp([)p Fo(H)r(;)17 b Ft(A)p Fp(]\()p Fo(H)822 5243 y Fj(0)883 5228 y Fp(+)22 b Fo(i)p Fp(\))1052 5192 y Fn(\000)p Fj(1)1179 5228 y Fp(is)32 b(b)s(ounded.)1835 5634 y(8)p eop %%Page: 9 9 9 8 bop 134 52 a Fp(T)-8 b(o)37 b(deduce)g(the)g(limiting)32 b(absorption)j(principle)g(from)g(estimate)g(\(2.7\))h(one)h(needs)g (some)g(as-)-7 172 y(sumptions)44 b(on)h(the)g(double)f(comm)m(utator)f ([[)p Fo(V)5 b(;)17 b Ft(A)p Fp(])p Fo(;)g Ft(A)p Fp(].)79 b(As)45 b(sho)m(wn)h(in)e([9],)j([12])d(it)g(su\016ces)j(to)-7 293 y(require)32 b(that)f(this)h(op)s(erator)f(b)s(e)h(b)s(ounded.)44 b(It)31 b(is)g(easy)i(to)e(see)i(that)f(this)f(condition)f(is)h (satis\014ed)h(if)-7 413 y Fo(V)54 b Fp(is)32 b(su\016cien)m(tly)i (regular,)d(that)i(is)886 633 y Fk(j)p Fo(@)970 592 y Fm(\013)1020 633 y Fo(V)22 b Fp(\()p Fo(x)p Fp(\))p Fk(j)27 b(\024)i Fo(C)7 b Fp(\(1)21 b(+)h Fk(j)p Fo(x)p Fk(j)p Fp(\))1823 592 y Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)2058 633 y Fo(;)81 b(\032)28 b(>)g Fp(0)p Fo(;)82 b Fk(j)p Fo(\013)q Fk(j)26 b(\024)i Fp(2)p Fo(:)644 b Fp(\(2.12\))-7 853 y(Th)m(us)34 b(w)m(e)g(obtain)-7 1040 y Ft(Theorem)j(2.7)49 b Fe(L)-5 b(et)27 b(assumptions)e Fp(\(2)p Fo(:)p Fp(12\))h Fe(hold.)41 b(Then)25 b(the)i(op)-5 b(er)g(ator-function)25 b Fk(h)p Fo(x)p Fk(i)3176 1004 y Fn(\000)p Fm(r)3269 1040 y Fo(R)q Fp(\()p Fo(z)t Fp(\))p Fk(h)p Fo(x)p Fk(i)3602 1004 y Fn(\000)p Fm(r)3695 1040 y Fe(,)-7 1160 y Fo(r)44 b(>)c Fp(1)p Fo(=)p Fp(2)p Fe(,)j(is)f(c)-5 b(ontinuous)42 b(in)g(norm)f(with)h(r)-5 b(esp)g(e)g(ct)41 b(to)i(the)f(p)-5 b(ar)g(ameter)41 b(z)h(in)g(the)g(close)-5 b(d)41 b(c)-5 b(omplex)-7 1281 y(plane)38 b(cut)i(along)f Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(])26 b Fk([)f Fp([)p Fo(m;)17 b Fk(1)p Fp(\))39 b Fe(with)g(exc)-5 b(eption)38 b(of)h(eigenvalues)f(of)h Fo(H)47 b Fe(and)39 b(the)g(p)-5 b(oints)-7 1401 y Fk(\006)p Fo(m)p Fe(.)45 b(In)33 b(p)-5 b(articular,)34 b(the)g(op)-5 b(er)g(ator)34 b Fk(h)p Fo(x)p Fk(i)1508 1365 y Fn(\000)p Fm(r)1634 1401 y Fe(for)g Fo(r)c(>)e Fp(1)p Fo(=)p Fp(2)33 b Fe(is)g Fo(H)8 b Fe(-smo)-5 b(oth)33 b(on)g(any)h(c)-5 b(omp)g(act)33 b(interval)-7 1521 y Fp(\003)40 b Fk(\032)i Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))27 b Fk([)h Fp(\()p Fo(m;)17 b Fk(1)p Fp(\))42 b Fe(such)f(that)i Fp(\003)27 b Fk(\\)g Fo(\033)1825 1536 y Fm(p)1866 1521 y Fp(\()p Fo(H)8 b Fp(\))40 b(=)g Fk(;)p Fe(.)66 b(The)41 b(op)-5 b(er)g(ator)42 b Fo(H)49 b Fe(has)41 b(no)h(singular)-7 1642 y(c)-5 b(ontinuous)35 b(sp)-5 b(e)g(ctrum.)134 1878 y Ft(2.3.)60 b Fp(Theorem)35 b(2.7)g(remains)g(true)g(under)h (assumptions)g(of)e(Theorem)i(2.5)f(although)f(in)h(this)-7 1999 y(case)29 b(the)f(double)g(comm)m(utator)e([[)p Fo(V)5 b(;)17 b Ft(A)p Fp(])p Fo(;)g Ft(A)p Fp(])27 b(is)h(no)f(longer) g(b)s(ounded.)43 b(Ho)m(w)m(ev)m(er,)31 b(as)d(sho)m(wn)h(in)f([17)o (],)-7 2119 y(it)k(su\016ces)i(to)f(c)m(hec)m(k)h(that)314 2339 y Fk(h)p Fo(x)p Fk(i)447 2298 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)758 2339 y Fp(\()p Fo(H)877 2354 y Fj(0)938 2339 y Fp(+)22 b Fo(i)p Fp(\))1107 2298 y Fn(\000)p Fj(1)1202 2339 y Fp([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(V)d(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(]\()p Fo(H)2197 2354 y Fj(0)2256 2339 y Fk(\000)22 b Fo(i)p Fp(\))2426 2298 y Fn(\000)p Fj(1)2521 2339 y Fk(h)p Fo(x)p Fk(i)2654 2298 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2992 2339 y Fk(2)28 b(B)325 b Fp(\(2.13\))-7 2559 y(for)28 b(an)m(y)i Fo(f)38 b Fk(2)29 b Fo(C)577 2523 y Fn(1)570 2584 y Fj(0)651 2559 y Fp(\()p Fh(R)5 b Fp(\).)48 b(T)-8 b(o)29 b(b)s(e)g(more)g(precise,)h(in)e([17])h(the)g (Sc)m(hr\177)-49 b(odinger)29 b(op)s(erator)g(w)m(as)g(considered)-7 2680 y(and)k(the)g(ab)s(o)m(v)m(e)g(result)g(w)m(as)g(hidden)g(in)f (the)h(pro)s(of.)42 b(Therefore)34 b(w)m(e)g(discuss)f(it)f(in)g(App)s (endix)h(A.)134 2841 y(Let)f(us)g(pro)m(v)m(e)h(\(2.13\).)42 b(Di\013eren)m(t)32 b(tec)m(hnical)f(estimates)g(needed)i(for)e(this)g (are)h(collected)f(in)g(the)-7 2962 y(t)m(w)m(o)i(follo)m(wing)d (lemmas.)-7 3124 y Ft(Lemma)37 b(2.8)49 b Fe(Supp)-5 b(ose)46 b(that)i(functions)f Fo(v)j Fe(and)d Fo(A)1985 3139 y Fm(k)2028 3124 y Fe(,)j Fo(k)j Fp(=)d(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3)p Fe(,)48 b(ar)-5 b(e)47 b(b)-5 b(ounde)g(d.)81 b(L)-5 b(et)47 b Fo(f)61 b Fk(2)-7 3244 y Fo(C)70 3208 y Fn(1)63 3269 y Fj(0)145 3244 y Fp(\()p Fh(R)5 b Fp(\))40 b Fe(and)35 b Fo(r)30 b Fk(2)e Fp([0)p Fo(;)17 b Fp(1])p Fe(.)44 b(Then)189 3464 y Fp(\()p Fo(H)308 3479 y Fj(0)369 3464 y Fp(+)22 b Fo(i)p Fp(\)[\()p Fo(H)30 b Fp(+)22 b Fo(i)p Fp(\))883 3423 y Fn(\000)p Fj(1)977 3464 y Fo(;)17 b Fk(h)p Fo(x)p Fk(i)1154 3423 y Fm(r)1192 3464 y Fp(]\()p Fo(H)1338 3479 y Fj(0)1399 3464 y Fp(+)22 b Fo(i)p Fp(\))28 b Fk(2)g(B)s Fo(;)87 b Fp(\()p Fo(H)1991 3479 y Fj(0)2053 3464 y Fp(+)22 b Fo(i)p Fp(\)[)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Fk(h)p Fo(x)p Fk(i)2650 3423 y Fm(r)2687 3464 y Fp(]\()p Fo(H)2833 3479 y Fj(0)2894 3464 y Fp(+)22 b Fo(i)p Fp(\))28 b Fk(2)g(B)s Fo(:)196 b Fp(\(2.14\))-7 3726 y Fe(Pr)-5 b(o)g(of)35 b({)67 b Fp(Indeed,)509 3946 y(\()p Fo(H)30 b Fp(+)22 b Fo(i)p Fp(\))827 3904 y Fn(\000)p Fj(1)921 3946 y Fk(h)p Fo(x)p Fk(i)1054 3904 y Fm(r)1114 3946 y Fk(\000)h(h)p Fo(x)p Fk(i)1347 3904 y Fm(r)1385 3946 y Fp(\()p Fo(H)30 b Fp(+)22 b Fo(i)p Fp(\))1703 3904 y Fn(\000)p Fj(1)1825 3946 y Fp(=)27 b Fk(\000)p Fp(\()p Fo(H)j Fp(+)22 b Fo(i)p Fp(\))2323 3904 y Fn(\000)p Fj(1)2418 3946 y Fp([)p Fo(H)r(;)17 b Fk(h)p Fo(x)p Fk(i)2705 3904 y Fm(r)2743 3946 y Fp(]\()p Fo(H)29 b Fp(+)22 b Fo(i)p Fp(\))3087 3904 y Fn(\000)p Fj(1)3182 3946 y Fo(;)-7 4166 y Fp(where)34 b(the)f(op)s(erator)964 4470 y([)p Fo(H)r(;)17 b Fk(h)p Fo(x)p Fk(i)1251 4429 y Fm(r)1289 4470 y Fp(])28 b(=)g([)p Fo(H)1556 4485 y Fj(0)1595 4470 y Fo(;)17 b Fk(h)p Fo(x)p Fk(i)1772 4429 y Fm(r)1810 4470 y Fp(])27 b(=)h Fk(\000)p Fo(ir)s Fk(h)p Fo(x)p Fk(i)2258 4429 y Fm(r)r Fn(\000)p Fj(2)2457 4346 y(3)2403 4376 y Fi(X)2414 4586 y Fm(j)t Fj(=1)2563 4470 y Fo(\013)2625 4485 y Fm(j)2662 4470 y Fo(x)2717 4485 y Fm(j)3476 4470 y Fp(\(2.15\))-7 4791 y(is)39 b(b)s(ounded.)66 b(Since)40 b Fk(D)s Fp(\()p Fo(H)8 b Fp(\))38 b(=)i Fk(D)s Fp(\()p Fo(H)1416 4806 y Fj(0)1455 4791 y Fp(\),)h(this)f(implies)d(the)j (\014rst)g(inclusion)e(\(2.14\).)64 b(The)41 b(second)-7 4911 y(follo)m(ws)33 b(from)g(the)i(\014rst)f(in)g(a)f(standard)i(w)m (a)m(y)h(\(see)f(Lemma)e(7.4)g(of)h([12])g(for)g(a)f(similar)e (assertion\).)-7 5032 y Fd(2)134 5244 y Fp(Lemma)h(2)p Fo(:)p Fp(8)h(allo)m(ws)f(us)i(to)f(comm)m(ute)g(the)h(op)s(erators)f (\()p Fo(H)d Fk(\006)23 b Fo(i)p Fp(\))2520 5207 y Fn(\000)p Fj(1)2648 5244 y Fp(or)33 b Fo(f)11 b Fp(\()p Fo(H)d Fp(\))32 b(with)h Fk(h)p Fo(x)p Fk(i)3380 5207 y Fm(r)3418 5244 y Fp(,)h(whic)m(h)-7 5364 y(leads)e(to)1835 5634 y(9)p eop %%Page: 10 10 10 9 bop -7 52 a Ft(Lemma)37 b(2.9)49 b Fe(Under)35 b(the)g (assumptions)f(of)g(L)-5 b(emma)34 b Fp(2)p Fo(:)p Fp(8)p Fe(,)h(the)g(op)-5 b(er)g(ators)658 228 y Fk(h)p Fo(x)p Fk(i)791 186 y Fn(\000)p Fm(r)883 228 y Fp(\()p Fo(H)30 b Fk(\006)23 b Fo(i)p Fp(\))1203 186 y Fn(\000)p Fj(1)1297 228 y Fk(h)p Fo(x)p Fk(i)1430 186 y Fm(r)1468 228 y Fo(;)86 b Fk(h)p Fo(x)p Fk(i)1714 186 y Fn(\000)p Fm(r)1807 228 y Fo(D)1888 243 y Fm(j)1925 228 y Fp(\()p Fo(H)29 b Fk(\006)23 b Fo(i)p Fp(\))2244 186 y Fn(\000)p Fj(1)2338 228 y Fk(h)p Fo(x)p Fk(i)2471 186 y Fm(r)2509 228 y Fo(;)87 b(j)33 b Fp(=)28 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)414 b Fp(\(2.16\))-7 403 y Fe(and)1047 524 y Fk(h)p Fo(x)p Fk(i)1180 482 y Fn(\000)p Fm(r)1273 524 y Fp(\()p Fo(H)1392 539 y Fj(0)1453 524 y Fk(\006)23 b Fo(i)p Fp(\))1624 482 y Fm(n)1671 524 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)2028 482 y Fm(r)2065 524 y Fo(;)52 b(n)27 b Fp(=)h Fk(\000)p Fp(1)p Fo(;)17 b Fp(0)p Fo(;)g Fp(1)p Fo(;)804 b Fp(\(2.17\))-7 679 y Fe(ar)-5 b(e)35 b(b)-5 b(ounde)g(d.)-7 840 y Ft(Prop)s(osition)36 b(2.10)49 b Fe(L)-5 b(et)41 b(assumption)f Fp(\(2)p Fo(:)p Fp(5\))p Fe(,)h Fp(\(2)p Fo(:)p Fp(6\))g Fe(b)-5 b(e)40 b(satis\014e)-5 b(d)40 b(and)g Fo(f)50 b Fk(2)39 b Fo(C)3031 804 y Fn(1)3024 865 y Fj(0)3106 840 y Fp(\()p Fh(R)t Fp(\))p Fe(.)69 b(Then)40 b(in-)-7 961 y(clusion)34 b Fp(\(2)p Fo(:)p Fp(13\))h Fe(holds.)-7 1122 y(Pr)-5 b(o)g(of)35 b({)67 b Fp(Let)33 b(us)g(consider)g(\014rst)g(the)g(long-range)e(part)h Fo(V)2166 1137 y Fm(L)2218 1122 y Fp(.)44 b(The)33 b(comm)m(utator)710 1298 y Fk(U)38 b Fp(=)27 b([)p Fo(V)997 1313 y Fm(L)1050 1298 y Fo(;)17 b Ft(A)p Fp(])27 b(=)g Fo(i)p Fp(\()p Fk(j)p Fo(x)p Fk(j)p Fo(@)5 b(V)1631 1313 y Fm(L)1684 1298 y Fo(=@)g Fk(j)p Fo(x)p Fk(j)p Fp(\))28 b(=)g Fk(h)p Fo(x)p Fk(i)2203 1257 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2459 1298 y Fo(B)5 b Fk(h)p Fo(x)p Fk(i)2671 1257 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2981 1298 y Fo(;)-7 1473 y Fp(where)34 b Fo(B)f Fk(2)28 b(B)s Fp(.)44 b(The)33 b(double)g(comm)m(utator)669 1649 y([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(V)1004 1664 y Fm(L)1056 1649 y Fo(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])25 b(=)j Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(U)i Fo(f)h Fp(\()p Fo(H)d Fp(\))p Ft(A)20 b Fk(\000)j Ft(A)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(U)i Fo(f)h Fp(\()p Fo(H)d Fp(\))-7 1825 y(consists)41 b(of)e(t)m(w)m(o)i(terms)f(whic)m(h)g(are)g(adjoin)m (t)f(to)h(one)g(another.)66 b(F)-8 b(or)39 b(example,)i(for)e(the)i (\014rst)f(w)m(e)-7 1945 y(ha)m(v)m(e)34 b(that)193 2121 y Fk(h)p Fo(x)p Fk(i)326 2080 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)637 2121 y Fp(\()p Fo(H)756 2136 y Fj(0)817 2121 y Fp(+)22 b Fo(i)p Fp(\))986 2080 y Fn(\000)p Fj(1)1081 2121 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(U)i Fo(f)h Fp(\()p Fo(H)d Fp(\))p Ft(A)p Fp(\()p Fo(H)1805 2136 y Fj(0)1864 2121 y Fk(\000)23 b Fo(i)p Fp(\))2035 2080 y Fn(\000)p Fj(1)2129 2121 y Fk(h)p Fo(x)p Fk(i)2262 2080 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2601 2121 y Fp(=)573 2266 y(\()p Fk(h)p Fo(x)p Fk(i)744 2225 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1055 2266 y Fp(\()p Fo(H)1174 2281 y Fj(0)1235 2266 y Fp(+)f Fo(i)p Fp(\))1404 2225 y Fn(\000)p Fj(1)1499 2266 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)1856 2225 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2111 2266 y Fp(\))p Fo(B)d Fp(\()p Fk(h)p Fo(x)p Fk(i)2399 2225 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2709 2266 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)3066 2225 y Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3321 2266 y Fp(\))1761 2411 y Fk(\002)p Fp(\()p Fk(h)p Fo(x)p Fk(i)2009 2370 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2320 2411 y Ft(A)p Fp(\()p Fo(H)2524 2426 y Fj(0)2585 2411 y Fk(\000)23 b Fo(i)p Fp(\))2756 2370 y Fn(\000)p Fj(1)2851 2411 y Fk(h)p Fo(x)p Fk(i)2984 2370 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3294 2411 y Fp(\))p Fo(:)-7 2587 y Fp(Ev)m(ery)35 b(factor)d(here)h(is)f(a)g(b)s(ounded)i (op)s(erator)e(according)g(to)g(Lemma)f(2.9.)134 2736 y(T)-8 b(o)33 b(consider)g(the)g(short-range)f(part)g Fo(V)1609 2751 y Fm(S)1693 2736 y Fp(w)m(e)h(are)g(obliged)e(to)h(op)s (en)h(the)g(double)f(comm)m(utator)481 2912 y([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(V)816 2927 y Fm(S)866 2912 y Fo(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])82 b(=)i Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(V)1925 2927 y Fm(S)1974 2912 y Ft(A)p Fo(f)j Fp(\()p Fo(H)d Fp(\))p Ft(A)21 b Fk(\000)i Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Ft(A)p Fo(V)2855 2927 y Fm(S)2904 2912 y Fo(f)j Fp(\()p Fo(H)d Fp(\))p Ft(A)1483 3057 y Fk(\000)84 b Ft(A)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(V)2010 3072 y Fm(S)2059 3057 y Ft(A)p Fo(f)j Fp(\()p Fo(H)d Fp(\))21 b(+)h Ft(A)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Ft(A)p Fo(V)2938 3072 y Fm(S)2987 3057 y Fo(f)j Fp(\()p Fo(H)d Fp(\))p Fo(:)-7 3233 y Fp(Here)29 b(the)g(\014rst)g(and) g(the)g(fourth)f(terms)h(as)g(w)m(ell)f(as)g(the)h(second)h(and)f(the)g (third)f(are)g(adjoin)m(t)g(to)g(one)-7 3353 y(another.)44 b(Th)m(us)34 b(w)m(e)f(ha)m(v)m(e)h(to)f(pro)m(v)m(e)g(that)561 3529 y Fk(h)p Fo(x)p Fk(i)694 3488 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1005 3529 y Fp(\()p Fo(H)1124 3544 y Fj(0)1185 3529 y Fp(+)22 b Fo(i)p Fp(\))1354 3488 y Fn(\000)p Fj(1)1449 3529 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(T)14 b(f)d Fp(\()p Fo(H)d Fp(\))p Ft(A)p Fp(\()p Fo(H)2172 3544 y Fj(0)2231 3529 y Fk(\000)23 b Fo(i)p Fp(\))2402 3488 y Fn(\000)p Fj(1)2496 3529 y Fk(h)p Fo(x)p Fk(i)2629 3488 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2967 3529 y Fk(2)29 b(B)s Fo(;)319 b Fp(\(2.18\))-7 3704 y(where)42 b Fo(T)55 b Fp(is)40 b(one)h(of)g(the)g(op)s(erators)g Fo(V)1481 3719 y Fm(S)1531 3704 y Ft(A)g Fp(or)f Ft(A)p Fo(V)1926 3719 y Fm(S)1977 3704 y Fp(.)68 b(If)41 b Fo(T)55 b Fp(=)42 b Fo(V)2465 3719 y Fm(S)2516 3704 y Ft(A)p Fp(,)g(w)m(e)g(factorize)e Fo(V)3280 3719 y Fm(S)3372 3704 y Fp(as)h Fo(V)3557 3719 y Fm(S)3649 3704 y Fp(=)-7 3825 y Fk(h)p Fo(x)p Fk(i)126 3788 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)382 3825 y Fo(B)5 b Fk(h)p Fo(x)p Fk(i)594 3788 y Fn(\000)p Fj(1)p Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1043 3825 y Fp(with)48 b(a)h(b)s(ounded)g(op)s(erator)e Fo(B)5 b Fp(.)92 b(Therefore)49 b(op)s(erator)f(\(2.18\))g(is)g(a)-7 3945 y(pro)s(duct)33 b(of)f(op)s(erators)316 4121 y Fk(h)p Fo(x)p Fk(i)449 4080 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)760 4121 y Fp(\()p Fo(H)879 4136 y Fj(0)940 4121 y Fp(+)22 b Fo(i)p Fp(\))1109 4080 y Fn(\000)p Fj(1)1204 4121 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)1561 4080 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1815 4121 y Fo(;)82 b Fk(h)p Fo(x)p Fk(i)2057 4080 y Fn(\000)p Fj(1)p Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2458 4121 y Ft(A)p Fp(\()p Fo(H)2662 4136 y Fj(0)2723 4121 y Fp(+)22 b Fo(i)p Fp(\))2892 4080 y Fn(\000)p Fj(1)2987 4121 y Fk(h)p Fo(x)p Fk(i)3120 4080 y Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3375 4121 y Fo(;)380 4296 y Fk(h)p Fo(x)p Fk(i)513 4255 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)824 4296 y Fp(\()p Fo(H)943 4311 y Fj(0)1004 4296 y Fp(+)g Fo(i)p Fp(\))p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)1530 4255 y Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1785 4296 y Fo(;)82 b Fk(h)p Fo(x)p Fk(i)2027 4255 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2338 4296 y Ft(A)p Fp(\()p Fo(H)2542 4311 y Fj(0)2603 4296 y Fk(\000)22 b Fo(i)p Fp(\))2773 4255 y Fn(\000)p Fj(1)2868 4296 y Fk(h)p Fo(x)p Fk(i)3001 4255 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3311 4296 y Fo(:)-7 4452 y Fp(All)44 b(of)i(them)g(are)g(b)s(ounded)h(b)m(y)g(Lemma)d(2.9.)84 b(Similarly)-8 b(,)45 b(if)g Fo(T)64 b Fp(=)51 b Ft(A)p Fo(V)2831 4467 y Fm(S)2927 4452 y Fp(w)m(e)c(use)g(that)f Fo(V)3548 4467 y Fm(S)3649 4452 y Fp(=)-7 4572 y Fk(h)p Fo(x)p Fk(i)126 4536 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)437 4572 y Fo(B)5 b Fk(h)p Fo(x)p Fk(i)649 4536 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)990 4572 y Fp(with)31 b Fo(B)i Fk(2)28 b(B)s Fp(.)43 b(Therefore)32 b(op)s(erator)e(\(2.18\))g(factorizes)h(in)f(a)h (pro)s(duct)g(of)-7 4692 y(op)s(erators)555 4868 y Fk(h)p Fo(x)p Fk(i)688 4827 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)999 4868 y Fp(\()p Fo(H)1118 4883 y Fj(0)1180 4868 y Fp(+)22 b Fo(i)p Fp(\))1349 4827 y Fn(\000)p Fj(1)1443 4868 y Fk(h)p Fo(x)p Fk(i)1576 4827 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1832 4868 y Fo(;)82 b Fk(h)p Fo(x)p Fk(i)2074 4827 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2384 4868 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Ft(A)p Fk(h)p Fo(x)p Fk(i)2826 4827 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3136 4868 y Fo(;)555 5044 y Fk(h)p Fo(x)p Fk(i)688 5003 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)998 5044 y Fo(f)j Fp(\()p Fo(H)d Fp(\))p Fk(h)p Fo(x)p Fk(i)1355 5003 y Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)1610 5044 y Fo(;)82 b Fk(h)p Fo(x)p Fk(i)1852 5003 y Fn(\000)p Fj(\(1+)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2163 5044 y Ft(A)p Fp(\()p Fo(H)2367 5059 y Fj(0)2428 5044 y Fk(\000)22 b Fo(i)p Fp(\))2598 5003 y Fn(\000)p Fj(1)2693 5044 y Fk(h)p Fo(x)p Fk(i)2826 5003 y Fn(\000)p Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3137 5044 y Fo(:)-7 5199 y Fp(All)31 b(of)h(them)g(are)h (again)e(b)s(ounded)i(b)m(y)h(Lemma)d(2.9.)43 b Fd(2)134 5385 y Fp(As)33 b(w)m(as)h(already)e(men)m(tioned)g(\(see)i(App)s (endix)f(A)g(for)f(details\),)f(Prop)s(osition)g(2.10)h(implies)1810 5634 y(10)p eop %%Page: 11 11 11 10 bop -7 52 a Ft(Theorem)37 b(2.11)49 b Fe(Under)34 b(the)g(assumptions)e(of)i(The)-5 b(or)g(em)32 b Fp(2)p Fo(:)p Fp(5)p Fe(,)i(al)5 b(l)33 b(c)-5 b(onclusions)33 b(of)g(The)-5 b(or)g(em)33 b Fp(2)p Fo(:)p Fp(7)-7 172 y Fe(r)-5 b(emain)34 b(true.)-7 359 y Ft(Corollary)i(2.12)49 b Fe(L)-5 b(et)27 b Fp(\003)g Fk(\032)i Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))t Fk([)t Fp(\()p Fo(m;)g Fk(1)p Fp(\))27 b Fe(b)-5 b(e)27 b(a)f(c)-5 b(omp)g(act)26 b(interval)h(disjoint)f(fr)-5 b(om)26 b Fo(\033)3491 374 y Fm(p)3531 359 y Fp(\()p Fo(H)8 b Fp(\))p Fe(.)-7 479 y(Under)44 b(the)f(assumptions)g(of)g(The)-5 b(or)g(em)42 b Fp(2)p Fo(:)p Fp(5)p Fe(,)j(for)f(any)f Fo(r)k(>)c Fp(1)p Fo(=)p Fp(2)g Fe(the)h(op)-5 b(er)g(ators)43 b Fk(h)p Fo(x)p Fk(i)3264 443 y Fn(\000)p Fm(r)3356 479 y Fo(D)3437 494 y Fm(j)3474 479 y Fo(E)6 b Fp(\(\003\))p Fe(,)-7 600 y Fo(j)34 b Fp(=)27 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)34 b Fe(ar)-5 b(e)35 b Fo(H)8 b Fe(-smo)-5 b(oth.)-7 787 y(Pr)g(o)g(of)35 b({)67 b Fp(Using)32 b(the)h(Hilb)s(ert) e(iden)m(tit)m(y)-8 b(,)32 b(w)m(e)i(get)253 1007 y Fk(jjh)p Fo(x)p Fk(i)442 965 y Fn(\000)p Fm(r)534 1007 y Fo(D)615 1022 y Fm(j)652 1007 y Fo(R)q Fp(\()p Fo(z)t Fp(\))p Fk(jj)27 b(\024)h(jjh)p Fo(x)p Fk(i)1229 965 y Fn(\000)p Fm(r)1322 1007 y Fo(D)1403 1022 y Fm(j)1439 1007 y Fo(R)q Fp(\()p Fo(i)p Fp(\))p Fk(jj)22 b Fp(+)g Fk(j)p Fo(z)k Fk(\000)d Fo(i)p Fk(j)17 b(jjh)p Fo(x)p Fk(i)2265 965 y Fn(\000)p Fm(r)2357 1007 y Fo(D)2438 1022 y Fm(j)2474 1007 y Fo(R)q Fp(\()p Fo(i)p Fp(\))p Fk(h)p Fo(x)p Fk(i)2791 965 y Fm(r)2829 1007 y Fk(jj)g(jjh)p Fo(x)p Fk(i)3091 965 y Fn(\000)p Fm(r)3182 1007 y Fo(R)q Fp(\()p Fo(z)t Fp(\))p Fk(jj)p Fo(:)-7 1227 y Fp(Since,)36 b(b)m(y)g(\(2.16\),)f(the)h (op)s(erator)f Fk(h)p Fo(x)p Fk(i)1428 1190 y Fn(\000)p Fm(r)1520 1227 y Fo(D)1601 1242 y Fm(j)1638 1227 y Fo(R)q Fp(\()p Fo(i)p Fp(\))p Fk(h)p Fo(x)p Fk(i)1955 1190 y Fm(r)2028 1227 y Fp(is)g(b)s(ounded,)h(the)g(pro)s(of)e(follo)m(ws)g (from)g(de\014-)-7 1347 y(nition)d(\(2.2\))h(of)g Fo(H)8 b Fp(-smo)s(othness.)43 b Fd(2)-7 1584 y Ft(Corollary)36 b(2.13)49 b Fe(Under)36 b(the)g(assumptions)e(of)i(The)-5 b(or)g(em)35 b Fp(2)p Fo(:)p Fp(5)p Fe(,)g(for)h(any)f Fo(r)e(>)c Fp(1)p Fo(=)p Fp(2)35 b Fe(the)h(op)-5 b(er)g(ators)-7 1704 y Fk(h)p Fo(x)p Fk(i)126 1668 y Fn(\000)p Fm(r)268 1704 y Fe(and)49 b Fk(h)p Fo(x)p Fk(i)605 1668 y Fn(\000)p Fm(r)698 1704 y Fo(D)779 1719 y Fm(j)815 1704 y Fe(,)k Fo(j)61 b Fp(=)54 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fe(,)52 b(ar)-5 b(e)49 b Fo(H)1715 1668 y Fj(2)1754 1704 y Fe(-smo)-5 b(oth)48 b(on)h(any)h(c)-5 b(omp)g(act)48 b(interval)h(of)g Fp(\()p Fo(m)3504 1668 y Fj(2)3544 1704 y Fo(;)17 b Fk(1)p Fp(\))-7 1824 y Fe(disjoint)34 b(fr)-5 b(om)35 b Fo(\033)630 1839 y Fm(p)670 1824 y Fp(\()p Fo(H)797 1788 y Fj(2)836 1824 y Fp(\))p Fe(.)-7 2011 y(Pr)-5 b(o)g(of)33 b({)d Fp(It)g(su\016ces)j(to)d(put)h(together) f(Prop)s(osition)f(2.2,)i(Theorem)f(2.11)g(and)h(Corollary)d(2.12.)43 b Fd(2)134 2223 y Fp(Results)28 b(on)g(the)f(absence)j(of)d(eigen)m(v) -5 b(alues)27 b(em)m(b)s(edded)i(in)e(the)h(con)m(tin)m(uous)g(sp)s (ectrum)g(of)f Fo(H)35 b Fp(can)-7 2343 y(b)s(e)e(found)g(in)e([1],)i (but)g(w)m(e)g(do)g(not)f(need)i(them.)134 2505 y Ft(2.4.)49 b Fp(Our)28 b(pro)s(of)g(of)g(the)g(radiation)f(estimates)h(for)g(the)g (Dirac)f(op)s(erator)h(relies)g(on)g(a)g(reduction)-7 2626 y(to)j(the)g(Sc)m(hr\177)-49 b(odinger)31 b(case.)44 b(Then)32 b(the)g(approac)m(h)f(of)g([20)o(])g(can)h(b)s(e)f(directly)f (applied.)42 b(Let)31 b Ft(m)p Fp(\()p Fo(x)p Fp(\))c(=)-7 2746 y Fk(j)p Fo(x)p Fk(j)d Fp(for)f Fk(j)p Fo(x)p Fk(j)k(\025)i Fp(1,)c Ft(m)p Fp(\()p Fo(x)p Fp(\))e(b)s(eing)g Fo(C)1192 2710 y Fn(1)1291 2746 y Fp(ev)m(erywhere.)44 b(Let)24 b(us)g(also)f(in)m(tro)s(duce)h(the)g(di\013eren)m(tial)e(op)s(erator) 901 3056 y Ft(M)28 b Fp(=)1193 2932 y Fj(3)1139 2961 y Fi(X)1150 3171 y Fm(j)t Fj(=1)1300 3056 y Fp(\()o Ft(m)1431 3071 y Fm(j)1467 3056 y Fo(D)1548 3071 y Fm(j)1607 3056 y Fp(+)22 b Fo(D)1786 3071 y Fm(j)1823 3056 y Ft(m)1917 3071 y Fm(j)1952 3056 y Fp(\))17 b Fo(;)147 b Ft(m)2275 3071 y Fm(j)2338 3056 y Fp(=)28 b Fo(@)5 b Ft(m)p Fo(=@)g(x)2752 3071 y Fm(j)2790 3056 y Fo(:)-7 3377 y Fp(Note)33 b(that)f(for)g Fk(j)p Fo(x)p Fk(j)c(\025)g Fp(1,)k Ft(m)1035 3392 y Fm(j)1071 3377 y Fp(\()p Fo(x)p Fp(\))c(=)g Fo(x)1389 3392 y Fm(j)1426 3377 y Fo(=)p Fk(j)p Fo(x)p Fk(j)k Fp(and)808 3597 y Ft(m)902 3612 y Fm(j)t(k)976 3597 y Fp(\()p Fo(x)p Fp(\))c(=)g Fo(@)1295 3556 y Fj(2)1335 3597 y Ft(m)p Fp(\()p Fo(x)p Fp(\))p Fo(=@)5 b(x)1720 3612 y Fm(j)1757 3597 y Fo(@)g(x)1868 3612 y Fm(k)1940 3597 y Fp(=)27 b Fk(j)p Fo(x)p Fk(j)2154 3556 y Fn(\000)p Fj(1)2249 3597 y Fo(\016)2292 3612 y Fm(j)t(k)2389 3597 y Fk(\000)c(j)p Fo(x)p Fk(j)2600 3556 y Fn(\000)p Fj(3)2694 3597 y Fo(x)2749 3612 y Fm(j)2786 3597 y Fo(x)2841 3612 y Fm(k)2884 3597 y Fo(;)565 b Fp(\(2.19\))-7 3817 y(where)34 b Fo(\016)318 3832 y Fm(j)t(k)426 3817 y Fp(is)e(the)h(Kronec)m(k)m(er)h(sym)m(b)s (ol.)134 3979 y(The)g(case)f(of)f(regular)g(p)s(erturbations)g(is)g (quite)h(easy)-8 b(.)-7 4166 y Ft(Theorem)37 b(2.14)49 b Fe(L)-5 b(et)32 b(assumption)e Fp(\(2)p Fo(:)p Fp(12\))g Fe(b)-5 b(e)31 b(satis\014e)-5 b(d,)31 b(and)g(let)g(the)g(op)-5 b(er)g(ators)31 b Fk(r)3164 4129 y Fn(?)3164 4190 y Fm(j)3223 4166 y Fe(,)h Fo(j)h Fp(=)28 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fe(,)-7 4297 y(b)-5 b(e)33 b(de\014ne)-5 b(d)33 b(by)h Fp(\(1)p Fo(:)p Fp(19\))p Fe(.)43 b(Then)33 b(the)h(op)-5 b(er)g(ators)33 b Fo(G)1801 4312 y Fm(j)1865 4297 y Fp(=)28 b Fk(h)p Fo(x)p Fk(i)2102 4261 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2267 4297 y Fk(r)2350 4261 y Fn(?)2350 4322 y Fm(j)2442 4297 y Fe(ar)-5 b(e)34 b Fo(H)8 b Fe(-smo)-5 b(oth)32 b(on)i(any)f(c)-5 b(omp)g(act)-7 4418 y(interval)34 b Fp(\003)28 b Fk(\032)g Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))23 b Fk([)f Fp(\()p Fo(m;)17 b Fk(1)p Fp(\))35 b Fe(such)f(that)i Fp(\003)21 b Fk(\\)i Fo(\033)2115 4433 y Fm(p)2155 4418 y Fp(\()p Fo(H)8 b Fp(\))27 b(=)h Fk(;)p Fe(.)-7 4605 y(Pr)-5 b(o)g(of)35 b({)67 b Fp(Let)33 b(us)g(consider)1063 4825 y Fo(H)1152 4783 y Fj(2)1218 4825 y Fp(=)28 b(\()p Fo(H)1441 4840 y Fj(0)1502 4825 y Fp(+)22 b Fo(V)g Fp(\()p Fo(x)p Fp(\)\))1848 4783 y Fj(2)1915 4825 y Fp(=)28 b Fk(\000)p Fp(\001)23 b(+)f Fo(m)2383 4783 y Fj(2)2444 4825 y Fp(+)g Ft(V)r Fo(;)-7 5045 y Fp(where)862 5230 y Ft(V)29 b Fp(=)e Fo(V)22 b(H)1239 5245 y Fj(0)1300 5230 y Fp(+)g Fo(H)1479 5245 y Fj(0)1518 5230 y Fo(V)44 b Fp(+)22 b Fo(V)1796 5189 y Fj(2)1863 5230 y Fp(=:)27 b Fo(N)2071 5245 y Fj(0)2111 5230 y Fp(\()p Fo(x)p Fp(\))22 b(+)2417 5106 y Fj(3)2362 5136 y Fi(X)2373 5346 y Fm(j)t Fj(=1)2523 5230 y Fo(N)2601 5245 y Fm(j)2637 5230 y Fp(\()p Fo(x)p Fp(\))p Fo(@)2819 5245 y Fm(j)3476 5230 y Fp(\(2.20\))1810 5634 y(11)p eop %%Page: 12 12 12 11 bop -7 52 a Fp(and)33 b(the)g(matrices)f Fo(N)820 67 y Fm(k)862 52 y Fp(\()p Fo(x)p Fp(\))h(satisfy)g(the)g(conditions) 836 272 y Fk(j)p Fo(@)920 231 y Fm(\013)970 272 y Fo(N)1048 287 y Fm(k)1091 272 y Fp(\()p Fo(x)p Fp(\))p Fk(j)27 b(\024)h Fo(C)7 b Fk(h)p Fo(x)p Fk(i)1592 231 y Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)1827 272 y Fo(;)82 b Fk(j)p Fo(\013)q Fk(j)26 b(\024)j Fp(1)p Fo(;)81 b(k)31 b Fp(=)c(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3)p Fo(:)592 b Fp(\(2.21\))-7 492 y(The)41 b(op)s(erator)d Fo(H)689 456 y Fj(2)768 492 y Fp(is)h(selfadjoin)m(t)f(on)i(the)g (domain)e Ft(H)2109 456 y Fj(2)2148 492 y Fp(\()p Fh(R)2252 456 y Fj(3)2297 492 y Fo(;)17 b Fh(C)2407 456 y Fj(4)2452 492 y Fp(\).)65 b(A)39 b(direct)h(calculation)d(sho)m(ws)-7 612 y(that)1042 798 y Fo(i)p Fp([)p Fk(\000)p Fp(\001)p Fo(;)17 b Ft(M)p Fp(])29 b(=)e(4)1705 673 y Fj(3)1651 703 y Fi(X)1635 915 y Fm(j;k)r Fj(=1)1828 798 y Fo(D)1909 813 y Fm(j)1946 798 y Ft(m)2040 813 y Fm(j)t(k)2114 798 y Fo(D)2195 813 y Fm(k)2260 798 y Fk(\000)22 b Fp(\(\001)2478 757 y Fj(2)2518 798 y Ft(m)p Fp(\))p Fo(:)799 b Fp(\(2.22\))-7 1075 y(By)33 b(\(2.19\),)f(for)g Fk(j)p Fo(x)p Fk(j)c(\025)g Fp(1)1157 1261 y Fj(3)1102 1291 y Fi(X)1086 1503 y Fm(j;k)r Fj(=1)1279 1385 y Ft(m)1373 1400 y Fm(j)t(k)1448 1385 y Fo(D)1529 1400 y Fm(k)1571 1385 y Fo(u)p 1627 1305 174 4 v(D)1708 1400 y Fm(j)1744 1385 y Fo(u)f Fp(=)h Fk(j)p Fo(x)p Fk(j)2042 1344 y Fn(\000)p Fj(1)2207 1261 y(3)2153 1291 y Fi(X)2163 1501 y Fm(j)t Fj(=1)2313 1385 y Fk(jr)2424 1344 y Fn(?)2424 1410 y Fm(j)2483 1385 y Fo(u)p Fk(j)2567 1344 y Fj(2)2606 1385 y Fo(;)843 b Fp(\(2.23\))-7 1713 y(and)33 b(\(\001)302 1677 y Fj(2)341 1713 y Ft(m)p Fp(\)\()p Fo(x)p Fp(\))28 b(=)f Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)962 1677 y Fn(\000)p Fj(3)1056 1713 y Fp(\).)43 b(By)33 b(\(2.20\),)f(\(2.21\),)1194 2023 y([)p Ft(V)r Fo(;)17 b Ft(M)p Fp(])27 b(=)g Ft(N)1703 2038 y Fj(0)1742 2023 y Fp(\()p Fo(x)p Fp(\))c(+)2048 1898 y Fj(3)1994 1928 y Fi(X)2004 2138 y Fm(j)t Fj(=1)2154 2023 y Ft(N)2242 2038 y Fm(j)2278 2023 y Fp(\()p Fo(x)p Fp(\))p Fo(@)2460 2038 y Fm(j)2498 2023 y Fo(;)951 b Fp(\(2.24\))-7 2348 y(where)34 b Ft(N)363 2363 y Fm(k)405 2348 y Fp(\()p Fo(x)p Fp(\))28 b(=)g Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)895 2312 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\032)1079 2348 y Fp(\),)33 b Fo(k)d Fp(=)e(0)p Fo(;)17 b Fp(1)p Fo(;)g Fp(2)p Fo(;)g Fp(3.)42 b(Com)m(bining)30 b(\(2.22\))i({)h(\(2.24\),)e (w)m(e)j(get)f(that)527 2658 y(4)p Fk(jj)p Fo(G)709 2673 y Fm(k)751 2658 y Fo(u)p Fk(jj)863 2617 y Fj(2)929 2658 y Fk(\024)28 b Fo(i)p Fp(\([)p Fo(H)1221 2617 y Fj(2)1260 2658 y Fo(;)17 b Ft(M)p Fp(])p Fo(u;)g(u)p Fp(\))k(+)h Fo(C)7 b Fp(\()p Fk(jjh)p Fo(x)p Fk(i)2054 2617 y Fn(\000)p Fm(r)2146 2658 y Fo(u)p Fk(jj)2258 2617 y Fj(2)2319 2658 y Fp(+)2471 2533 y Fj(3)2417 2563 y Fi(X)2427 2773 y Fm(j)t Fj(=1)2577 2658 y Fk(jjh)p Fo(x)p Fk(i)2766 2617 y Fn(\000)p Fm(r)2858 2658 y Fo(D)2939 2673 y Fm(j)2976 2658 y Fo(u)p Fk(jj)3088 2617 y Fj(2)3126 2658 y Fp(\))p Fo(;)285 b Fp(\(2.25\))-7 2979 y(where)35 b Fo(r)f Fp(=)c(\(1)23 b(+)g Fo(\032)p Fp(\))p Fo(=)p Fp(2)p Fo(;)17 b(k)33 b Fp(=)d(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3.)47 b(By)35 b(Prop)s(osition)d(2.3,)j(this)e(implies)f(that)i(the)h(op)s(erators)f Fo(G)3683 2994 y Fm(k)-7 3099 y Fp(are)f Fo(H)245 3063 y Fj(2)284 3099 y Fp(-smo)s(oth)e(on)h(\003)864 3063 y Fj(2)903 3099 y Fp(.)44 b(Prop)s(osition)31 b(2.2)h(concludes)h(the)g (pro)s(of.)43 b Fd(2)134 3311 y Fp(The)34 b(radiation)c(estimates)i (are)h(still)d(true)j(in)f(the)h(general)f(case.)-7 3473 y Ft(Theorem)37 b(2.15)49 b Fe(Under)27 b(the)f(assumptions)g(of)g(The) -5 b(or)g(em)25 b Fp(2)p Fo(:)p Fp(5)p Fe(,)j(the)e(c)-5 b(onclusions)25 b(of)i(The)-5 b(or)g(em)25 b Fp(2)p Fo(:)p Fp(14)-7 3593 y Fe(r)-5 b(emain)34 b(true.)134 3755 y Fp(The)50 b(pro)s(of)e(of)g(Theorem)h(2.15)f(is)g(tec)m(hnically)g (rather)h(complicated,)i(and)e(therefore)g(it)f(is)-7 3875 y(p)s(ostp)s(oned)33 b(up)f(to)g(the)h(App)s(endix)f(B.)h (Although)e(con)m(v)m(enien)m(t,)j(Theorem)f(2.15)e(is)h(not)g (absolutely)-7 3996 y(necessary)38 b(for)d(construction)h(of)f (scattering)h(theory)g(\(see)h(subsection)g(4.4\).)52 b(Probably)35 b(it)g(is)g(also)-7 4116 y(of)d(in)m(terest)h(in)f(its)g (o)m(wn)h(sak)m(e.)-7 4428 y Ft(3.)112 b(THE)37 b(EIK)m(ONAL)f(AND)g (TRANSPOR)-9 b(T)36 b(EQUA)-9 b(TIONS)-7 4689 y(3.1.)111 b Fp(Our)35 b(aim)e(here)j(is)f(to)g(construct)h(\\appro)m(ximate")e (eigenfunctions)h(\(1.7\))g(of)f(the)i(op)s(erator)-7 4809 y Fo(H)8 b Fp(.)42 b(This)28 b(will)e(lead)i(to)f(the)i(eik)m (onal)e(equation)h(\(1.14\))g(for)f(the)i(phase)g(\(1.11\).)42 b(W)-8 b(e)28 b(emphasize)h(that)-7 4930 y(all)i(our)h(estimates)g(b)s (elo)m(w)h(are)f(uniform)f(in)h Fo(\030)37 b Fp(for)32 b(0)27 b Fo(<)h(c)f Fk(\024)i(j)p Fo(\030)5 b Fk(j)26 b(\024)i Fo(C)35 b(<)27 b Fk(1)p Fp(.)134 5091 y(Let)33 b(us)g(in)m(tro)s(duce)g(the)g(\\remainder")944 5311 y Ft(q)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(e)1402 5270 y Fn(\000)p Fm(i')p Fj(\()p Fm(x;\030)s Fj(\))1679 5311 y Fp(\(\()p Fo(H)8 b(u)p Fp(\)\()p Fo(x;)17 b(\030)5 b Fp(\))20 b Fk(\000)j Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(u)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))749 b(\(3.1\))1810 5634 y(12)p eop %%Page: 13 13 13 12 bop -7 52 a Fp(in)32 b(the)h(Dirac)e(equation)h Fo(H)8 b(u)27 b Fp(=)h Fo(\027)6 b(u)p Fp(.)43 b(Plugging)31 b(\(1.7\))h(in)m(to)g(\(3.1\),)g(w)m(e)i(see)f(that)1103 346 y Ft(q)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)g Fo(i)2011 221 y Fj(3)1957 251 y Fi(X)1965 463 y Fm(k)r Fj(=1)2118 346 y Fo(\013)2180 361 y Fm(k)2222 346 y Fo(@)2273 361 y Fm(k)2317 346 y Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)909 b Fp(\(3.2\))-7 634 y(where)594 820 y Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))26 b(=)994 650 y Fi( )1127 695 y Fj(3)1073 725 y Fi(X)1080 937 y Fm(k)r Fj(=1)1233 820 y Fo(\013)1295 835 y Fm(k)1338 820 y Fp(\()p Fo(@)1427 835 y Fm(k)1470 820 y Fo(')p Fp(\)\()p Fo(x;)17 b(\030)5 b Fp(\))22 b(+)g Fo(m\013)2062 835 y Fj(0)2124 820 y Fp(+)g Fo(V)f Fp(\()p Fo(x)p Fp(\))i Fk(\000)f Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))2731 650 y Fi(!)2826 820 y Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(:)400 b Fp(\(3.3\))-7 1077 y(W)-8 b(e)36 b(will)d(construct) j(functions)f Fo(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))34 b(and)i Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))34 b(in)h(suc)m(h)h(a) f(w)m(a)m(y)i(that,)e(for)g(all)e(m)m(ulti-indices)-7 1198 y Fo(\013)q(;)17 b(\014)6 b Fp(,)1026 1318 y Fk(j)p Fo(@)1110 1277 y Fm(\013)1105 1343 y(x)1160 1318 y Fo(@)1216 1271 y Fm(\014)1211 1346 y(\030)1264 1318 y Ft(q)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1776 1333 y Fm(\013;\014)1888 1318 y Fk(h)p Fo(x)p Fk(i)2021 1277 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)p Fn(\000j)p Fm(\013)p Fn(j)2338 1318 y Fo(;)81 b(\017)29 b(>)e Fp(0)p Fo(;)832 b Fp(\(3.4\))-7 1486 y(in)34 b(one)h(of)g(the)g(cones)h Fk(C)6 b Fp(\()p Fo(\016)t Fp(\))32 b(=)g Fk(C)1210 1501 y Fn(\006)1269 1486 y Fp(\()p Fo(\016)t Fp(\))j(de\014ned)h(b)m(y)g (\(1.16\).)50 b(In)35 b(particular,)f(this)g(implies)f(\(1.10\))h(in)-7 1606 y(the)39 b(same)f(cone)g Fk(C)6 b Fp(\()p Fo(\016)t Fp(\).)60 b(Of)38 b(course,)j(\(3.4\))c(is)h(satis\014ed)h(if)d(b)s (oth)i(functions)g Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))38 b(and)g Fk(r)p Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))-7 1726 y(satisfy)37 b(these)h(estimates.)57 b(The)38 b(condition)e(on)h Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))36 b(\\couples")h Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))36 b(and)i(\010\()p Fo(x;)17 b(\030)5 b Fp(\).)56 b(So)37 b(our)-7 1847 y(\014rst)c(goal)e(is)h(to)g(obtain)g(an)g (equation)h(for)f(the)h(function)f(\010\()p Fo(x;)17 b(\030)5 b Fp(\))32 b(alone.)134 2004 y(Actually)-8 b(,)24 b(the)g(function)f(\010\()p Fo(x;)17 b(\030)5 b Fp(\))23 b(will)f(b)s(e)h(de\014ned)i(as)f(an)f(appro)m(ximate)g(solution)e(of)i (the)h(eik)m(onal)-7 2124 y(equation)32 b(\(1.14\).)43 b(Let)33 b(us)g(set)292 2328 y Ft(r)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(2)p Fk(h)p Fo(\030)5 b(;)17 b Fk(r)p Fp(\010\()p Fo(x;)g(\030)5 b Fp(\))p Fk(i)20 b Fp(+)i(2)p Fk(h)p Fo(A)p Fp(\()p Fo(x)p Fp(\))p Fo(;)17 b Fk(r)p Fp(\010\()p Fo(x;)g(\030)5 b Fp(\))p Fk(i)22 b Fp(+)g Fk(jr)p Fp(\010\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)2708 2287 y Fj(2)2769 2328 y Fp(+)22 b(2)p Ft(v)r Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)298 b Fp(\(3.5\))-7 2532 y(where)34 b Ft(v)r Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))32 b(is)g(e\013ectiv)m(e)h(p)s(oten)m(tial)e(\(1.12\).)43 b(W)-8 b(e)33 b(will)d(construct)k(\010\()p Fo(x;)17 b(\030)5 b Fp(\))32 b(suc)m(h)i(that)974 2736 y Fk(j)p Fo(@)1058 2695 y Fm(\013)1053 2761 y(x)1108 2736 y Fo(@)1164 2689 y Fm(\014)1159 2764 y(\030)1212 2736 y Fp(\010\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)i Fo(C)1736 2751 y Fm(\013;\014)1847 2736 y Fk(h)p Fo(x)p Fk(i)1980 2695 y Fj(1)p Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)2250 2736 y Fo(;)82 b(x)28 b Fk(2)g(C)6 b Fp(\()p Fo(\016)t Fp(\))p Fo(;)781 b Fp(\(3.6\))-7 2940 y(and)799 3060 y Fk(j)p Fo(@)883 3019 y Fm(\013)878 3085 y(x)933 3060 y Fo(@)989 3013 y Fm(\014)984 3088 y(\030)1037 3060 y Ft(r)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)26 b(\024)j Fo(C)1536 3075 y Fm(\013;\014)1647 3060 y Fk(h)p Fo(x)p Fk(i)1780 3019 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)p Fn(\000j)p Fm(\013)p Fn(j)2098 3060 y Fo(;)81 b(x)28 b Fk(2)g(C)6 b Fp(\()p Fo(\016)t Fp(\))p Fo(;)82 b(\017)28 b(>)g Fp(0)p Fo(;)605 b Fp(\(3.7\))-7 3228 y(for)32 b(all)f(m)m (ulti-indices)e Fo(\013)q(;)17 b(\014)6 b Fp(.)134 3385 y(Then)34 b(the)f(matrix-function)d Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))32 b(is)g(de\014ned)i(b)m(y)g(the)f(follo)m(wing)c (explicit)j(form)m(ula.)41 b(Put)61 3679 y Fo(K)7 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(K)587 3694 y Fj(\010)642 3679 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f(\(2)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\)\))1299 3638 y Fn(\000)p Fj(1)1409 3509 y Fi( )1488 3679 y Fo(v)t Fp(\()p Fo(x)p Fp(\))23 b(+)f Fo(A)1864 3694 y Fj(0)1903 3679 y Fp(\()p Fo(x)p Fp(\))p Fo(\013)2096 3694 y Fj(0)2158 3679 y Fp(+)2310 3554 y Fj(3)2256 3584 y Fi(X)2264 3797 y Fm(k)r Fj(=1)2400 3679 y Fp(\()p Fo(A)2511 3694 y Fm(k)2554 3679 y Fp(\()p Fo(x)p Fp(\))g(+)g Fo(@)2856 3694 y Fm(k)2899 3679 y Fp(\010\()p Fo(x;)17 b(\030)5 b Fp(\)\))p Fo(\013)3292 3694 y Fm(k)3335 3509 y Fi(!)3430 3679 y Fo(:)68 b Fp(\(3.8\))-7 3967 y(Clearly)-8 b(,)1063 4088 y Fo(K)7 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(!)g Fp(0)65 b(as)g Fk(j)p Fo(x)p Fk(j)28 b(!)f(1)p Fo(;)81 b(x)29 b Fk(2)f(C)6 b Fp(\()p Fo(\016)t Fp(\))p Fo(;)-7 4255 y Fp(pro)m(vided)46 b Fo(V)21 b Fp(\()p Fo(x)p Fp(\))49 b Fk(!)g Fp(0)44 b(and)h Fk(r)p Fp(\010\()p Fo(x;)17 b(\030)5 b Fp(\))49 b Fk(!)g Fp(0)44 b(as)h Fk(j)p Fo(x)p Fk(j)k(!)f(1)p Fp(.)81 b(Th)m(us)46 b(the)g(in)m(v)m(erse)g(matrix)d(\()p Fo(I)c Fk(\000)-7 4376 y Fo(K)7 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))344 4340 y Fn(\000)p Fj(1)470 4376 y Fp(is)33 b(w)m(ell-de\014ned)f(for)g Fo(x)c Fk(2)h(C)6 b Fp(\()p Fo(\016)t Fp(\))32 b(with)g Fk(j)p Fo(x)p Fk(j)h Fp(large)e(enough,)i(and)g(w)m(e)h(can)e(set)1211 4580 y Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g(\()p Fo(I)j Fk(\000)23 b Fo(K)7 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))2175 4538 y Fn(\000)p Fj(1)2269 4580 y Fo(p)2318 4595 y Fj(0)2357 4580 y Fp(\()p Fo(\030)g Fp(\))p Fo(;)1017 b Fp(\(3.9\))-7 4783 y(where)36 b Fo(p)326 4798 y Fj(0)365 4783 y Fp(\()p Fo(\030)5 b Fp(\))34 b(is)h(matrix)e(\(1.5\).)49 b(The)36 b(v)-5 b(alues)34 b(of)g Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))34 b(for)h Fo(x)g Fp(from)e(a)h(compact)h(domain)e (remain)-7 4904 y(arbitrary)-8 b(.)134 5061 y(Let)31 b(us)h(\014nd)g(an)f(explicit)e(relation)g(b)s(et)m(w)m(een)34 b(the)d(remainders)g Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))30 b(and)h Ft(r)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\).)42 b(W)-8 b(e)32 b(in)m(tro-)-7 5181 y(duce)i(auxiliary)c (functions)515 5385 y Fo(s)561 5400 y Fj(0)600 5385 y Fp(\()p Fo(x)p Fp(\))e(=)f Fo(A)935 5400 y Fj(0)975 5385 y Fp(\()p Fo(x)p Fp(\))22 b(+)g Fo(m;)115 b(s)1499 5400 y Fm(j)1536 5385 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(A)1962 5400 y Fm(j)1999 5385 y Fp(\()p Fo(x)p Fp(\))22 b(+)g Fo(@)2301 5400 y Fm(j)2338 5385 y Fo(')p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)114 b(j)34 b Fp(=)27 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)1810 5634 y Fp(13)p eop %%Page: 14 14 14 13 bop 1405 52 a Fo(s)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(v)t Fp(\()p Fo(x)p Fp(\))22 b Fk(\000)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(:)1163 b Fp(\(3.10\))-7 226 y(Then)34 b(function)e(\(3.5\))g(equals)1195 536 y Ft(r)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1649 412 y Fj(3)1595 442 y Fi(X)1602 654 y Fm(k)r Fj(=0)1755 536 y Fo(s)1801 495 y Fj(2)1801 561 y Fm(k)1844 536 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)g Fo(s)2234 495 y Fj(2)2274 536 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(:)952 b Fp(\(3.11\))-7 841 y(W)-8 b(e)33 b(in)m(tro)s(duce)g(also)e (the)i(auxiliary)e(matrix-function)919 1146 y Fo(B)5 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(B)1426 1161 y Fj(\010)1481 1146 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1889 1021 y Fj(3)1835 1051 y Fi(X)1842 1263 y Fm(k)r Fj(=0)1995 1146 y Fo(s)2041 1161 y Fm(k)2084 1146 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\013)2369 1161 y Fm(k)2433 1146 y Fp(+)22 b Fo(s)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))676 b(\(3.12\))-7 1456 y(\(this)32 b(matrix)f(is)h(of) g(course)i(the)f(same)f(as)h(\(1.8\)\))f(whic)m(h)h(allo)m(ws)f(us)h (to)f(rewrite)h(\(3.3\))f(as)1359 1676 y Fo(q)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(B)5 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(:)1116 b Fp(\(3.13\))-7 1896 y(Note)33 b(the)g(iden)m(tit)m (y)603 2200 y Fo(B)682 2159 y Fj(2)721 2200 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))83 b(=)1240 2076 y Fj(3)1186 2106 y Fi(X)1193 2318 y Fm(k)r Fj(=0)1346 2200 y Fo(s)1392 2159 y Fj(2)1392 2225 y Fm(k)1435 2200 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b(+)g Fo(s)1824 2159 y Fj(2)1863 2200 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)i(2)p Fo(s)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2594 2076 y Fj(3)2539 2106 y Fi(X)2547 2318 y Fm(k)r Fj(=0)2700 2200 y Fo(s)2746 2215 y Fm(k)2788 2200 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\013)3073 2215 y Fm(k)1027 2436 y Fp(=)83 b Ft(r)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h(2)p Fo(s)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(B)g Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)1255 b Fp(\(3.14\))-7 2656 y(follo)m(wing)30 b(directly)i(from)f(\(1.2\).) 134 2818 y(No)m(w)40 b(w)m(e)f(are)g(able)g(to)f(obtain)g(a)g(con)m(v)m (enien)m(t)j(expression)f(for)e Fo(q)43 b Fp(via)38 b(\010)h(and)g Ft(r)p Fp(.)62 b(The)40 b(in)m(v)m(erse)-7 2938 y(matrix)e(\()p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(K)i Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b Fk(\000)g Fo(s)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))1284 2902 y Fn(\000)p Fj(1)1417 2938 y Fp(app)s(earing)39 b(b)s(elo)m(w)h(is)f(w)m(ell-de\014ned)h(for) f Fo(x)h Fk(2)g(C)6 b Fp(\()p Fo(\016)t Fp(\))40 b(with)g Fk(j)p Fo(x)p Fk(j)-7 3058 y Fp(large)32 b(enough.)-7 3220 y Ft(Prop)s(osition)k(3.1)49 b Fe(L)-5 b(et)28 b(the)g(functions)g Fo(q)t(;)17 b Ft(r)p Fo(;)g(s)27 b Fe(and)h(the)g(matrix-function)f Fo(K)36 b Fe(b)-5 b(e)27 b(de\014ne)-5 b(d)27 b(by)i(e)-5 b(qual-)-7 3341 y(ities)35 b Fp(\(3)p Fo(:)p Fp(3\))p Fe(,)f Fp(\(3)p Fo(:)p Fp(5\))p Fe(,)g Fp(\(3)p Fo(:)p Fp(10\))h Fe(and)f Fp(\(3)p Fo(:)p Fp(8\))p Fe(,)g(r)-5 b(esp)g(e)g(ctively.)44 b(Then)1160 3561 y Fo(q)32 b Fp(=)27 b(2)1387 3520 y Fn(\000)p Fj(1)1481 3561 y Ft(r)p Fp(\()p Fo(\027)6 b(K)30 b Fk(\000)23 b Fo(s)p Fp(\))1916 3520 y Fn(\000)p Fj(1)2010 3561 y Fp(\()p Fo(I)30 b Fk(\000)22 b Fo(K)7 b Fp(\))2348 3520 y Fn(\000)p Fj(1)2443 3561 y Fo(p)2492 3576 y Fj(0)2531 3561 y Fo(:)918 b Fp(\(3.15\))-7 3822 y Fe(Pr)-5 b(o)g(of)35 b({)67 b Fp(Clearly)-8 b(,)32 b(matrix)f(\(3.12\))g(equals)1181 4042 y Fo(B)5 b Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(B)1688 4057 y Fj(0)1728 4042 y Fp(\()p Fo(\030)5 b Fp(\))21 b(+)h(2)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(K)i Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)938 b Fp(\(3.16\))-7 4262 y(where)1183 4448 y Fo(B)1257 4463 y Fj(0)1297 4448 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)1606 4323 y Fj(3)1551 4353 y Fi(X)1559 4565 y Fm(k)r Fj(=1)1712 4448 y Fo(\013)1774 4463 y Fm(k)1816 4448 y Fo(\030)1859 4463 y Fm(k)1924 4448 y Fp(+)22 b Fo(m\013)2169 4463 y Fj(0)2231 4448 y Fk(\000)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(:)-7 4712 y Fp(It)33 b(follo)m(ws)e (from)g(\(3.16\))h(that)1252 4932 y Fo(B)1331 4891 y Fj(2)1398 4932 y Fp(=)27 b Fo(B)1580 4891 y Fj(2)1575 4957 y(0)1642 4932 y Fp(+)22 b(2)p Fo(\027)6 b(B)1917 4947 y Fj(0)1957 4932 y Fo(K)29 b Fp(+)22 b(2)p Fo(\027)6 b(K)h(B)e(:)-7 5152 y Fp(Using)32 b(iden)m(tities)g Fo(B)767 5116 y Fj(2)762 5177 y(0)834 5152 y Fp(=)c Fk(\000)p Fp(2)p Fo(\027)6 b(B)1192 5167 y Fj(0)1264 5152 y Fp(and)33 b(\(3.14\),)f(w)m(e)i(deduce)g(from)d(it)h(that)1161 5372 y(2\()p Fo(\027)6 b(K)30 b Fk(\000)22 b Fo(s)p Fp(\))p Fo(B)33 b Fp(=)28 b(2)p Fo(\027)6 b(B)1986 5387 y Fj(0)2025 5372 y Fp(\()p Fo(I)30 b Fk(\000)23 b Fo(K)7 b Fp(\))22 b(+)g Ft(r)p Fo(:)1810 5634 y Fp(14)p eop %%Page: 15 15 15 14 bop -7 52 a Fp(Therefore)586 257 y Fo(B)5 b Fp(\()p Fo(I)31 b Fk(\000)22 b Fo(K)7 b Fp(\))1004 216 y Fn(\000)p Fj(1)1126 257 y Fp(=)28 b Fo(\027)6 b Fp(\()p Fo(\027)g(K)30 b Fk(\000)23 b Fo(s)p Fp(\))1673 216 y Fn(\000)p Fj(1)1767 257 y Fo(B)1841 272 y Fj(0)1902 257 y Fp(+)f(2)2049 216 y Fn(\000)p Fj(1)2144 257 y Ft(r)p Fp(\()p Fo(\027)6 b(K)29 b Fk(\000)23 b Fo(s)p Fp(\))2578 216 y Fn(\000)p Fj(1)2672 257 y Fp(\()p Fo(I)30 b Fk(\000)22 b Fo(K)7 b Fp(\))3010 216 y Fn(\000)p Fj(1)3105 257 y Fo(:)-7 463 y Fp(T)-8 b(aking)32 b(in)m(to)g(accoun)m(t)h(equalit)m(y)g Fo(B)1322 478 y Fj(0)1361 463 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(p)1534 478 y Fj(0)1573 463 y Fp(\()p Fo(\030)g Fp(\))27 b(=)g(0,)33 b(w)m(e)g(\014nd)h(that)883 668 y Fo(B)5 b Fp(\()p Fo(I)30 b Fk(\000)23 b Fo(K)7 b Fp(\))1301 627 y Fn(\000)p Fj(1)1396 668 y Fo(p)1445 683 y Fj(0)1512 668 y Fp(=)27 b(2)1664 627 y Fn(\000)p Fj(1)1758 668 y Ft(r)p Fp(\()p Fo(\027)6 b(K)30 b Fk(\000)22 b Fo(s)p Fp(\))2192 627 y Fn(\000)p Fj(1)2287 668 y Fp(\()p Fo(I)29 b Fk(\000)23 b Fo(K)7 b Fp(\))2625 627 y Fn(\000)p Fj(1)2720 668 y Fo(p)2769 683 y Fj(0)2808 668 y Fo(:)-7 874 y Fp(By)33 b(virtue)g(of)f(\(3.9\),)g(\(3.13\),)g(this)g(implies)e(\(3.15\).)43 b Fd(2)134 1077 y Fp(In)32 b(particular,)e(if)h(eik)m(onal)f(equation)i (\(1.14\))e(is)i(satis\014ed)g(\(for)f(example,)g(in)g(some)g(cone\),)i (then)-7 1198 y Ft(r)28 b Fp(=)f(0)k(and,)g(b)m(y)h(\(3.15\),)e Fo(q)i Fp(=)27 b(0.)43 b(In)31 b(this)f(case)i(function)e(\(3.3\))h (equals)g(zero,)g(and)g(the)g(remainder)f Ft(q)-7 1318 y Fp(in)i(the)h(Dirac)e(equation)h(reduces)j(to)d(the)h(second)h(term)e (in)g(the)h(righ)m(t-hand)e(side)i(of)f(\(3.2\).)134 1476 y(The)37 b(function)e(\010)h(will)e(b)s(e)i(constructed)h(in)e (the)i(next)f(subsection.)54 b(Let)36 b(us)h(form)m(ulate)d(here)j(a)-7 1596 y(conditional)30 b(result)j(follo)m(wing)c(directly)j(from)g(Prop) s(osition)f(3.1.)-7 1754 y Ft(Prop)s(osition)36 b(3.2)49 b Fe(L)-5 b(et)31 b(assumption)f Fp(\(1)p Fo(:)p Fp(18\))g Fe(with)h(some)f Fo(\032)e Fk(2)g Fp(\(0)p Fo(;)17 b Fp(1\))31 b Fe(b)-5 b(e)30 b(ful\014l)5 b(le)-5 b(d.)43 b(Supp)-5 b(ose)30 b(that)i(a)-7 1874 y(function)38 b Fp(\010)g Fe(satis\014es)f(estimates)h Fp(\(3)p Fo(:)p Fp(6\))f Fe(and)g(c)-5 b(orr)g(esp)g(onding)37 b(function)g Fp(\(3)p Fo(:)p Fp(5\))h Fe(satis\014es)f(estimates)-7 1995 y Fp(\(3)p Fo(:)p Fp(7\))p Fe(.)44 b(De\014ne)34 b(the)h(matrix)f Fo(p)h Fe(by)g(formulas)g Fp(\(3)p Fo(:)p Fp(8\))p Fe(,)f Fp(\(3)p Fo(:)p Fp(9\))p Fe(,)g(set)1364 2200 y Fp(~)-58 b Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)f Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)g Fo(p)2200 2215 y Fj(0)2240 2200 y Fp(\()p Fo(\030)5 b Fp(\))1112 b(\(3.17\))-7 2406 y Fe(and)34 b(let)h Fo(u)g Fe(b)-5 b(e)34 b(function)h Fp(\(1)p Fo(:)p Fp(7\))p Fe(.)44 b(Then)34 b(for)h(al)5 b(l)34 b(multi-indic)-5 b(es)34 b Fo(\013)q(;)17 b(\014)1000 2611 y Fk(j)p Fo(@)1084 2570 y Fm(\013)1079 2636 y(x)1134 2611 y Fo(@)1190 2564 y Fm(\014)1185 2639 y(\030)1246 2611 y Fp(~)-57 b Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1740 2626 y Fm(\013;\014)1852 2611 y Fk(h)p Fo(x)p Fk(i)1985 2570 y Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)2220 2611 y Fo(;)86 b(x)28 b Fk(2)g(C)6 b Fp(\()p Fo(\016)t Fp(\))p Fo(;)758 b Fp(\(3.18\))-7 2817 y Fe(and)34 b(r)-5 b(emainder)34 b Fp(\(3)p Fo(:)p Fp(1\))h Fe(in)f(the)h(Dir)-5 b(ac)34 b(e)-5 b(quation)35 b(satis\014es)f(estimates)g Fp(\(3)p Fo(:)p Fp(4\))p Fe(.)134 2974 y Ft(3.2.)115 b Fp(T)-8 b(o)35 b(construct)i(a)f(function)f(\010)f(=)f(\010)1754 2989 y Fn(\006)1849 2974 y Fp(satisfying)i(conditions)g(of)g(Prop)s (osition)f(3.2)i(in)f(a)-7 3095 y(cone)e Fk(C)267 3110 y Fn(\006)327 3095 y Fp(\()p Fo(\016)t Fp(\),)f(w)m(e)i(consider)f (\014rst)g(the)g(auxiliary)d(linear)h(equation)1251 3300 y Fk(h)p Fo(\030)5 b(;)17 b Fk(r)p Fo(\036)1523 3315 y Fn(\006)1580 3300 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))p Fk(i)22 b Fp(+)g Fo(F)14 b Fp(\()p Fo(x;)j(\030)5 b Fp(\))26 b(=)i(0)p Fo(:)1008 b Fp(\(3.19\))-7 3506 y Ft(Lemma)37 b(3.3)49 b Fe(Supp)-5 b(ose)34 b(that)i(for)e(al)5 b(l)35 b(multi-indic)-5 b(es)34 b Fo(\013)q(;)17 b(\014)708 3711 y Fk(j)p Fo(@)792 3670 y Fm(\013)787 3736 y(x)842 3711 y Fo(@)898 3664 y Fm(\014)893 3739 y(\030)946 3711 y Fo(F)d Fp(\()p Fo(x;)j(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1476 3726 y Fm(\013;\014)1588 3711 y Fk(h)p Fo(x)p Fk(i)1721 3670 y Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)1955 3711 y Fo(;)87 b(\032)28 b Fk(2)g Fp(\(0)p Fo(;)17 b Fp(1\))p Fo(;)86 b(x)28 b Fk(2)g(C)2801 3726 y Fn(\006)2860 3711 y Fp(\()p Fo(\016)t Fp(\))p Fo(:)-7 3917 y Fe(Then)34 b(the)h(function)543 4167 y Fo(\036)601 4182 y Fn(\006)660 4167 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fk(\006)1108 4032 y Fi(Z)1208 4058 y Fn(1)1163 4257 y Fj(0)1282 4167 y Fp(\()p Fo(F)14 b Fp(\()p Fo(x)22 b Fk(\006)h Fo(t\030)5 b(;)17 b(\030)5 b Fp(\))21 b Fk(\000)i Fo(F)14 b Fp(\()p Fk(\006)p Fo(t\030)5 b(;)17 b(\030)5 b Fp(\)\))p Fo(dt)26 b Fp(=:)i(\()p Fo(Q)2747 4182 y Fn(\006)2806 4167 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(F)14 b Fp(\)\()p Fo(x)p Fp(\))300 b(\(3.20\))-7 4426 y Fe(satis\014es)34 b(e)-5 b(quation)35 b Fp(\(3)p Fo(:)p Fp(19\))f Fe(and)754 4631 y Fk(j)p Fo(@)838 4590 y Fm(\013)833 4656 y(x)888 4631 y Fo(@)944 4584 y Fm(\014)939 4659 y(\030)992 4631 y Fo(\036)1050 4646 y Fn(\006)1109 4631 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1562 4646 y Fm(\013;\014)1674 4631 y Fk(h)p Fo(x)p Fk(i)1807 4590 y Fj(1)p Fn(\000)p Fm(\032)p Fn(\000j)p Fm(\013)p Fn(j)2077 4631 y Fo(;)86 b(x)28 b Fk(2)g(C)2419 4646 y Fn(\006)2479 4631 y Fp(\()p Fo(\016)t Fp(\))p Fo(;)51 b Fk(8)35 b Fo(\013)q(;)17 b(\014)6 b(:)134 4874 y Fp(The)34 b(pro)s(of)d(can)i(b)s (e)g(obtained)f(b)m(y)i(a)e(direct)g(di\013eren)m(tiation)f(\(see)j ([19)o(],)f(for)f(details\).)134 5032 y(Lemma)k(3.3)h(allo)m(ws)f(us)i (to)f(construct)h(\010)1701 5047 y Fn(\006)1798 5032 y Fp(b)m(y)g(the)g(metho)s(d)e(of)h(successiv)m(e)j(appro)m(ximations.) -7 5163 y(W)-8 b(e)33 b(de\014ne)h(inductiv)m(ely)e(functions)h(\010) 1435 5112 y Fj(\()p Fm(n)p Fj(\))1435 5184 y Fn(\006)1570 5163 y Fp(b)m(y)g(the)g(equalities)1239 5385 y(\010)1309 5334 y Fj(\()p Fm(n)p Fj(+1\))1309 5407 y Fn(\006)1529 5385 y Fp(=)28 b Fo(Q)1710 5400 y Fn(\006)1769 5385 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(F)1970 5334 y Fj(\()p Fm(n)p Fj(\))1956 5407 y Fn(\006)2071 5385 y Fo(;)114 b(n)28 b Fk(\025)g Fp(0)p Fo(;)997 b Fp(\(3.21\))1810 5634 y(15)p eop %%Page: 16 16 16 15 bop 918 53 a Fo(F)995 2 y Fj(\(0\))981 75 y Fn(\006)1117 53 y Fp(=)28 b Ft(v)r Fo(;)114 b(F)1500 2 y Fj(\(1\))1486 75 y Fn(\006)1621 53 y Fp(=)28 b Fk(h)p Fo(A;)17 b Fk(r)p Fp(\010)2034 2 y Fj(\(1\))2034 75 y Fn(\006)2128 53 y Fk(i)22 b Fp(+)g(2)2336 12 y Fn(\000)p Fj(1)2430 53 y Fk(jr)p Fp(\010)2611 2 y Fj(\(1\))2611 75 y Fn(\006)2706 53 y Fk(j)2734 12 y Fj(2)2773 53 y Fo(;)676 b Fp(\(3.22\))-7 209 y(and)33 b(for)f Fo(n)c Fk(\025)g Fp(2,)697 470 y Fo(F)774 419 y Fj(\()p Fm(n)p Fj(\))760 492 y Fn(\006)903 470 y Fp(=)g Fk(h)p Fo(A;)17 b Fk(r)p Fp(\010)1316 419 y Fj(\()p Fm(n)p Fj(\))1316 492 y Fn(\006)1418 470 y Fk(i)22 b Fp(+)1587 345 y Fm(n)p Fn(\000)p Fj(1)1581 375 y Fi(X)1577 584 y Fm(m)p Fj(=1)1729 470 y Fk(hr)p Fp(\010)1921 419 y Fj(\()p Fm(m)p Fj(\))1921 492 y Fn(\006)2043 470 y Fo(;)17 b Fk(r)p Fp(\010)2240 419 y Fj(\()p Fm(n)p Fj(\))2240 492 y Fn(\006)2342 470 y Fk(i)22 b Fp(+)g(2)2550 429 y Fn(\000)p Fj(1)2644 470 y Fk(jr)p Fp(\010)2825 419 y Fj(\()p Fm(n)p Fj(\))2825 492 y Fn(\006)2927 470 y Fk(j)2955 429 y Fj(2)2994 470 y Fo(:)455 b Fp(\(3.23\))-7 728 y(Then)1056 848 y Fk(h)p Fo(\030)5 b(;)17 b Fk(r)p Fp(\010)1340 797 y Fj(\()p Fm(n)p Fj(+1\))1340 870 y Fn(\006)1531 848 y Fk(i)22 b Fp(+)g Fo(F)1767 797 y Fj(\()p Fm(n)p Fj(\))1753 870 y Fn(\006)1896 848 y Fp(=)28 b(0)p Fo(;)81 b(n)28 b Fp(=)g(0)p Fo(;)17 b Fp(1)g Fo(:)g(:)g(:)e(:)813 b Fp(\(3.24\))-7 1004 y(Using)32 b(Lemma)f(3.3,)i(w)m(e)g(obtain)f(b)m (y)h(induction)f(that)866 1181 y Fk(j)p Fo(@)950 1139 y Fm(\013)945 1205 y(x)1000 1181 y Fo(@)1051 1196 y Fm(\030)1090 1181 y Fp(\010)1160 1130 y Fj(\()p Fm(n)p Fj(\))1160 1202 y Fn(\006)1262 1181 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1715 1196 y Fm(\013;\014)1827 1181 y Fk(h)p Fo(x)p Fk(i)1960 1139 y Fj(1)p Fn(\000)p Fm(n\032)p Fn(\000j)p Fm(\013)p Fn(j)2272 1181 y Fo(;)115 b(x)28 b Fk(2)g(C)2643 1196 y Fn(\006)2702 1181 y Fp(\()p Fo(\016)t Fp(\))p Fo(:)624 b Fp(\(3.25\))134 1386 y(F)-8 b(or)32 b(\()p Fo(N)h Fp(+)22 b(1\))p Fo(\032)27 b(>)h Fp(1,)k(w)m(e)i(set)1326 1655 y(\010)1396 1670 y Fn(\006)1456 1655 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1850 1531 y Fm(N)1810 1561 y Fi(X)1815 1770 y Fm(n)p Fj(=1)1970 1655 y Fp(\010)2040 1605 y Fj(\()p Fm(n)p Fj(\))2040 1677 y Fn(\006)2142 1655 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(:)1084 b Fp(\(3.26\))-7 1919 y(Then)34 b(it)d(follo)m(ws)h (from)f(\(3.22\))h({)g(\(3.24\))g(that)g(function)g(\(3.5\))g(equals) 582 2188 y Ft(r)628 2203 y Fn(\006)714 2188 y Fp(=)c Ft(r)864 2137 y Fj(\()p Fm(N)7 b Fj(\))864 2210 y Fn(\006)1013 2188 y Fp(=)28 b(2)p Fk(h)p Fo(A;)17 b Fk(r)p Fp(\010)1475 2137 y Fj(\()p Fm(N)7 b Fj(\))1475 2210 y Fn(\006)1597 2188 y Fk(i)22 b Fp(+)g(2)1822 2064 y Fm(N)7 b Fn(\000)p Fj(1)1826 2094 y Fi(X)1821 2303 y Fm(m)p Fj(=1)1974 2188 y Fk(hr)p Fp(\010)2166 2137 y Fj(\()p Fm(m)p Fj(\))2166 2210 y Fn(\006)2288 2188 y Fo(;)17 b Fk(r)p Fp(\010)2485 2137 y Fj(\()p Fm(N)7 b Fj(\))2485 2210 y Fn(\006)2607 2188 y Fk(i)22 b Fp(+)g Fk(jr)p Fp(\010)2947 2137 y Fj(\()p Fm(N)7 b Fj(\))2947 2210 y Fn(\006)3070 2188 y Fk(j)3098 2147 y Fj(2)-7 2452 y Fp(\(if)31 b Fo(N)38 b Fp(=)28 b(1)k(the)h(sum)f(in)g(the)g(righ)m(t-hand)g(side)g(is)g(absen)m(t\).) 45 b(Therefore)33 b(the)g(follo)m(wing)c(assertion)k(is)-7 2572 y(a)f(direct)h(consequence)i(of)d(estimates)h(\(3.25\).)-7 2734 y Ft(Prop)s(osition)j(3.4)49 b Fe(L)-5 b(et)45 b(assumption)f Fp(\(1)p Fo(:)p Fp(18\))g Fe(with)h(some)g Fo(\032)h Fk(2)h Fp(\(0)p Fo(;)17 b Fp(1\))44 b Fe(b)-5 b(e)45 b(ful\014l)5 b(le)-5 b(d.)75 b(De\014ne)43 b(the)-7 2855 y(function)38 b Fp(\010)450 2870 y Fn(\006)510 2855 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))37 b Fe(by)i(e)-5 b(qualities)37 b Fp(\(3)p Fo(:)p Fp(20\))p Fe(,)i Fp(\(3)p Fo(:)p Fp(21\))e Fe({)h Fp(\(3)p Fo(:)p Fp(23\))p Fe(,)h Fp(\(3)p Fo(:)p Fp(26\))e Fe(and)h Ft(r)2866 2870 y Fn(\006)2925 2855 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))38 b Fe({)g(by)g(e)-5 b(quality)-7 2975 y Fp(\(3)p Fo(:)p Fp(5\))p Fe(.)71 b(Then)43 b(for)g(al)5 b(l)43 b(multi-indic)-5 b(es)43 b Fo(\013)q(;)17 b(\014)49 b Fe(estimates)43 b Fp(\(3)p Fo(:)p Fp(6\))g Fe(and)g Fp(\(3)p Fo(:)p Fp(7\))g Fe(ar)-5 b(e)44 b(satis\014e)-5 b(d)43 b(with)g Fo(\017)h Fp(=)-7 3096 y(\()p Fo(N)33 b Fp(+)22 b(1\))p Fo(\032)g Fk(\000)g Fp(1)35 b Fe(in)g Fk(C)754 3111 y Fn(\006)813 3096 y Fp(\()p Fo(\016)t Fp(\))p Fe(.)134 3258 y Fp(In)e(particular,)e(w)m(e)j (can)e(set)i Fo(N)k Fp(=)28 b(1)k(if)f Fo(\032)d(>)g Fp(1)p Fo(=)p Fp(2)k(and)g(hence)887 3485 y(\010)957 3500 y Fn(\006)1017 3485 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fk(\006)1464 3349 y Fi(Z)1564 3375 y Fn(1)1520 3575 y Fj(0)1656 3485 y Fp(\()o Ft(v)r Fp(\()p Fo(x)c Fk(\006)f Fo(t\030)5 b(;)17 b(\030)5 b Fp(\))21 b Fk(\000)i Ft(v)r Fp(\()p Fk(\006)p Fo(t\030)5 b(;)17 b(\030)5 b Fp(\)\))15 b Fo(dt)645 b Fp(\(3.27\))-7 3714 y(where)32 b Ft(v)h Fp(is)e(de\014ned)h(b)m(y)g(\(1)p Fo(:)p Fp(12\),)f(\(1)p Fo(:)p Fp(13\).)42 b(Moreo)m(v)m(er,)33 b(w)m(e)f(can)f(neglect)g(quadratic)g(terms)g(in)f(\(1)p Fo(:)p Fp(13\))-7 3834 y(whic)m(h)j(giv)m(es)g(the)g(expression)237 4056 y(\010)307 4071 y Fn(\006)367 4056 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))82 b(=)h Fk(\006)925 3920 y Fi(Z)1025 3947 y Fn(1)980 4146 y Fj(0)1116 4056 y Fp(\()p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(v)t Fp(\()p Fo(x)22 b Fk(\006)h Fo(t\030)5 b Fp(\))21 b Fk(\000)i Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(v)t Fp(\()p Fk(\006)p Fo(t\030)g Fp(\))994 4254 y(+)26 b Fk(h)p Fo(\030)5 b(;)17 b(A)p Fp(\()p Fo(x)k Fk(\006)i Fo(t\030)5 b Fp(\))22 b Fk(\000)g Fo(A)p Fp(\()p Fk(\006)p Fo(t\030)5 b Fp(\))p Fk(i)22 b Fp(+)g Fo(mA)2382 4269 y Fj(0)2422 4254 y Fp(\()p Fo(x)h Fk(\006)g Fo(t\030)5 b Fp(\))21 b Fk(\000)i Fo(mA)3038 4269 y Fj(0)3078 4254 y Fp(\()p Fk(\006)p Fo(t\030)5 b Fp(\)\))16 b Fo(dt:)134 4460 y Fp(Com)m(bining)31 b(Prop)s(ositions)g (3.2)i(and)f(3.4,)h(w)m(e)g(arriv)m(e)g(at)f(the)h(main)e(result)h(of)g (this)g(section.)-7 4621 y Ft(Theorem)37 b(3.5)49 b Fe(L)-5 b(et)36 b(assumption)f Fp(\(1)p Fo(:)p Fp(18\))g Fe(with)g(some)g Fo(\032)29 b Fk(2)g Fp(\(0)p Fo(;)17 b Fp(1\))35 b Fe(b)-5 b(e)35 b(ful\014l)5 b(le)-5 b(d.)46 b(De\014ne)35 b(the)g(phase)-7 4742 y(function)41 b Fp(\010)453 4757 y Fn(\006)512 4742 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))41 b Fe(by)g(e)-5 b(qualities)40 b Fp(\(3)p Fo(:)p Fp(20\))p Fe(,)i Fp(\(3)p Fo(:)p Fp(21\))e Fe({)h Fp(\(3)p Fo(:)p Fp(23\))p Fe(,)h Fp(\(3)p Fo(:)p Fp(26\))p Fe(,)f(the)g(matrix)g Fo(p)3220 4757 y Fn(\006)3279 4742 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))40 b Fe({)h(by)-7 4862 y(formulas)f Fp(\(3)p Fo(:)p Fp(8\))p Fe(,)i Fp(\(3)p Fo(:)p Fp(9\))p Fe(,)g(and)e(let)h Fo(u)1341 4877 y Fn(\006)1399 4862 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))40 b Fe(b)-5 b(e)41 b(function)f Fp(\(1)p Fo(:)p Fp(7\))p Fe(.)62 b(Then)40 b Fp(\010)2800 4877 y Fn(\006)2860 4862 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))40 b Fe(satis\014es)g Fp(\(3)p Fo(:)p Fp(6\))p Fe(,)-7 4983 y(matrix-function)c Fp(\(3)p Fo(:)p Fp(17\))h Fe(satis\014es)f Fp(\(3)p Fo(:)p Fp(18\))g Fe(and)g(for)h(the)g(function)g Ft(q)2590 4998 y Fn(\006)2649 4983 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))36 b Fe(de\014ne)-5 b(d)36 b(by)h Fp(\(3)p Fo(:)p Fp(1\))g Fe(es-)-7 5103 y(timate)e Fp(\(3)p Fo(:)p Fp(4\))f Fe(holds.)134 5265 y Fp(The)41 b(construction)f(ab)s(o)m(v)m (e)h(w)m(orks)h(for)d(p)s(ositiv)m(e)h(energies.)66 b(T)-8 b(o)40 b(consider)g(negativ)m(e)h(energies,)-7 5385 y(w)m(e)34 b(should)e(replace)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))32 b(b)m(y)i Fk(\000)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))32 b(in)g(all)f(form)m(ulas.)1810 5634 y(16)p eop %%Page: 17 17 17 16 bop -7 52 a Ft(4.)112 b(W)-12 b(A)g(VE)35 b(OPERA)-9 b(TORS)-7 311 y Fp(Here)25 b(w)m(e)g(pro)m(v)m(e)g(the)f(existence)i (and)e(completeness)g(of)g(w)m(a)m(v)m(e)i(op)s(erators)d(\(1.20\))g (with)h(iden)m(ti\014cation)-7 432 y(\(1.15\).)134 593 y Ft(4.1.)43 b Fp(In)32 b(this)f(subsection)h(w)m(e)g(collect)f (necessary)i(facts)f(ab)s(out)e(pseudo-di\013eren)m(tial)g(op)s (erators)-7 713 y(\(PDO\))i(de\014ned)i(b)m(y)961 882 y(\()p Fo(Af)11 b Fp(\)\()p Fo(x)p Fp(\))28 b(=)f(\(2)p Fo(\031)t Fp(\))1615 841 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1797 746 y Fi(Z)1852 972 y Fg(R)1900 953 y Fl(3)1955 882 y Fo(e)2000 841 y Fm(i)p Fn(h)p Fm(\030)s(;x)p Fn(i)2176 882 y Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))2471 856 y(^)2450 882 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)g(;)766 b Fp(\(4.1\))-7 1112 y(where)43 b Fo(f)54 b Fk(2)43 b(S)7 b Fp(\()p Fh(R)667 1075 y Fj(3)713 1112 y Fo(;)17 b Fh(C)822 1075 y Fj(4)868 1112 y Fp(\).)70 b(With)41 b(resp)s(ect)i(to)f(\(4)28 b Fk(\002)g Fp(4\)-matrix)40 b(sym)m(b)s(ols)h Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))41 b(w)m(e)i(ev)m(erywhere)-7 1232 y(assume)31 b(that)f Fo(a)e Fk(2)g Fo(C)787 1196 y Fn(1)862 1232 y Fp(\()p Fh(R)965 1196 y Fj(3)1028 1232 y Fk(\002)18 b Fh(R)1189 1196 y Fj(3)1235 1232 y Fp(\))30 b(and)g Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h(0)i(for)g Fk(j)p Fo(\030)5 b Fk(j)28 b Fp(large)i(enough.)43 b(Recall)28 b(that)i(the)h(class)-7 1352 y Fo(S)59 1316 y Fm(m)53 1378 y(\032;\016)147 1352 y Fp(,)h Fo(\032)c(>)g Fp(0)p Fo(;)17 b(\016)31 b(<)c Fp(1,)33 b(of)f(sym)m(b)s(ols)g(is)g (distinguished)g(b)m(y)i(the)f(condition)1146 1589 y Fk(j)p Fo(@)1230 1548 y Fm(\013)1225 1614 y(x)1280 1589 y Fo(@)1336 1542 y Fm(\014)1331 1617 y(\030)1384 1589 y Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1888 1604 y Fm(\013;\014)2000 1589 y Fk(h)p Fo(x)p Fk(i)2133 1548 y Fm(m)p Fn(\000)p Fm(\032)p Fn(j)p Fm(\013)p Fn(j)p Fj(+)p Fm(\016)r Fn(j)p Fm(\014)s Fn(j)2546 1589 y Fo(:)952 b Fp(\(4.2\))-7 1806 y(W)-8 b(e)35 b(need)h(also)e(a)h (more)f(sp)s(ecial)g(class)h(of)g(oscillating)c(sym)m(b)s(ols)k Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))35 b(satisfying)f(the)h (represen-)-7 1926 y(tation)475 2046 y Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(e)925 2005 y Fm(i)p Fj(\010\()p Fm(x;\030)s Fj(\))1152 2046 y Fo(b)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))32 b(for)g(\010)d Fk(2)f Fo(S)1856 2005 y Fm(r)1850 2071 y Fj(1)p Fm(;)p Fj(0)1944 2046 y Fo(;)49 b Fp(where)34 b Fo(r)c Fk(2)e Fp([0)p Fo(;)17 b Fp(1\))32 b(and)h Fo(b)28 b Fk(2)g Fo(S)3128 2005 y Fm(m)3122 2071 y Fj(1)p Fm(;)p Fj(0)3216 2046 y Fo(:)282 b Fp(\(4.3\))-7 2219 y(This)34 b(class)g(will)e(b)s(e)i(denoted)h Fo(C)1214 2183 y Fm(m)1281 2219 y Fp(\(\010\).)48 b(Clearly)-8 b(,)34 b Fo(C)1939 2183 y Fm(m)2005 2219 y Fp(\(\010\))d Fk(\032)g Fo(S)2356 2183 y Fm(m)2350 2244 y Fj(1)p Fn(\000)p Fm(r)n(;r)2527 2219 y Fp(.)48 b(W)-8 b(e)34 b(consider)h(PDO)f(\(4.1\)) f(as)-7 2340 y(op)s(erators)f(in)g(the)h(space)h Fk(H)29 b Fp(=)e Fo(L)1249 2303 y Fj(2)1289 2340 y Fp(\()p Fh(R)1393 2303 y Fj(3)1438 2340 y Fo(;)17 b Fh(C)1548 2303 y Fj(4)1593 2340 y Fp(\).)44 b(The)33 b(adjoin)m(t)f(to)g Fo(A)h Fp(op)s(erator)f Fo(A)2924 2303 y Fn(\003)2996 2340 y Fp(is)g(giv)m(en)h(b)m(y)924 2605 y(\()976 2578 y Fi(d)962 2605 y Fo(A)1035 2576 y Fn(\003)1074 2605 y Fo(f)11 b Fp(\)\()p Fo(\030)5 b Fp(\))27 b(=)g(\(2)p Fo(\031)t Fp(\))1609 2563 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1790 2469 y Fi(Z)1846 2695 y Fg(R)1894 2676 y Fl(3)1949 2605 y Fo(e)1994 2563 y Fn(\000)p Fm(i)p Fn(h)p Fm(\030)s(;x)p Fn(i)p 2225 2518 274 4 v 2225 2605 a Fo(a)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(f)11 b Fp(\()p Fo(x)p Fp(\))p Fo(dx)730 b Fp(\(4.4\))-7 2874 y(and)31 b(th)m(us)h(\014ts)g(in)m(to)e(the)h (usual)g(framew)m(ork)g(of)g(the)g(PDO)g(theory)g(\(note)g(ho)m(w)m(ev) m(er)j(that)c(compared)-7 2994 y(to)k(this)h(theory)g(the)g(roles)g(of) f(the)h(v)-5 b(ariables)34 b Fo(x)h Fp(and)g Fo(\030)k Fp(in)34 b(\(4.4\))g(are)h(in)m(terc)m(hanged\).)50 b(This)35 b(allo)m(ws)-7 3115 y(us)e(to)f(reco)m(v)m(er)j(all)30 b(the)j(results)g(of)f(the)h(theory)h(for)e(the)h(op)s(erator)f Fo(A)g Fp(itself.)134 3275 y(The)i(follo)m(wing)c(assertions)j(are)f (tak)m(en)i(from)d(the)i(pap)s(er)g([21)o(].)-7 3460 y Ft(Prop)s(osition)j(4.1)49 b Fe(Supp)-5 b(ose)33 b(that)h Fo(A)f Fe(is)h(a)f(PDO)g(with)h(symb)-5 b(ol)33 b Fo(a)28 b Fk(2)g Fo(C)2676 3424 y Fm(m)2742 3460 y Fp(\(\010\))p Fe(.)45 b(Then)33 b(the)h(op)-5 b(er)g(ator)-7 3581 y Fo(A)p Fk(h)p Fo(x)p Fk(i)199 3545 y Fn(\000)p Fm(m)355 3581 y Fe(is)35 b(b)-5 b(ounde)g(d)34 b(and)g Fo(A)p Fk(h)p Fo(x)p Fk(i)1226 3545 y Fn(\000)p Fm(m)1343 3554 y Fl(1)1383 3581 y Fo(;)51 b(m)1546 3596 y Fj(1)1614 3581 y Fo(>)27 b(m)p Fe(,)35 b(is)g(c)-5 b(omp)g(act)34 b(in)g(the)h(sp)-5 b(ac)g(e)34 b Fk(H)q Fe(.)-7 3765 y Ft(Prop)s(osition)i(4.2)49 b Fe(L)-5 b(et)37 b Fo(A)1034 3780 y Fm(j)1070 3765 y Fo(;)54 b(j)38 b Fp(=)31 b(1)p Fo(;)17 b Fp(2)p Fe(,)36 b(b)-5 b(e)37 b(PDO)f(with)h(symb)-5 b(ols)36 b Fo(a)2540 3780 y Fm(j)2608 3765 y Fk(2)c Fo(C)2783 3729 y Fj(0)2823 3765 y Fp(\(\010\))p Fe(,)37 b(and)g(let)g Fo(A)g Fe(b)-5 b(e)36 b(the)-7 3886 y(PDO)e(with)h(symb)-5 b(ol)p 770 3831 91 4 v 34 w Fo(a)821 3901 y Fj(1)861 3886 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(a)1135 3901 y Fj(2)1174 3886 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fe(.)44 b(Then)34 b(the)h(op)-5 b(er)g(ator)35 b Fo(A)2344 3850 y Fn(\003)2344 3911 y Fj(1)2383 3886 y Fo(A)2456 3901 y Fj(2)2518 3886 y Fk(\000)23 b Fo(A)35 b Fe(is)f(c)-5 b(omp)g(act.)-7 4071 y Ft(Prop)s(osition)36 b(4.3)49 b Fe(L)-5 b(et)37 b Fo(A)1034 4086 y Fm(j)1070 4071 y Fo(;)54 b(j)38 b Fp(=)31 b(1)p Fo(;)17 b Fp(2)p Fe(,)36 b(b)-5 b(e)37 b(PDO)f(with)h(symb)-5 b(ols)36 b Fo(a)2540 4086 y Fm(j)2608 4071 y Fk(2)c Fo(C)2783 4035 y Fj(0)2823 4071 y Fp(\(\010\))p Fe(,)37 b(and)g(let)g Fo(A)g Fe(b)-5 b(e)36 b(the)-7 4191 y(PDO)e(with)h(symb)-5 b(ol)34 b Fo(a)821 4206 y Fj(1)861 4191 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p 1084 4136 V Fo(a)1135 4206 y Fj(2)1174 4191 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fe(.)44 b(Then)34 b(the)h(op)-5 b(er)g(ator)35 b Fo(A)2344 4206 y Fj(1)2383 4191 y Fo(A)2456 4155 y Fn(\003)2456 4216 y Fj(2)2518 4191 y Fk(\000)23 b Fo(A)35 b Fe(is)f(c)-5 b(omp)g(act.)-7 4376 y Fp(If)34 b(\010)c Fk(2)h Fo(S)355 4340 y Fm(r)349 4401 y Fj(1)p Fm(;)p Fj(0)477 4376 y Fp(for)i Fo(r)g(<)c Fp(1)p Fo(=)p Fp(2,)34 b(then)h Fo(C)1318 4340 y Fm(m)1384 4376 y Fp(\(\010\))30 b Fk(\032)h Fo(S)1734 4340 y Fm(m)1728 4402 y(\032;\016)1855 4376 y Fp(where)k Fo(\032)c Fp(=)e(1)23 b Fk(\000)h Fo(r)32 b(>)e Fp(1)p Fo(=)p Fp(2)j(and)h Fo(\016)g Fp(=)c Fo(r)i(<)e Fp(1)p Fo(=)p Fp(2.)47 b(In)-7 4496 y(this)30 b(case)h(Prop)s(ositions)f(4.1)g({)g(4.3)g(reduce)h(to)f (standard)h(assertions)g(of)f(PDO)g(calculus)g(\(see,)i(e.g.,)-7 4617 y(the)h(b)s(o)s(ok)f([14]\).)134 4778 y(W)-8 b(e)33 b(note)g(also)f(the)h(follo)m(wing)c(elemen)m(tary)-7 4939 y Ft(Prop)s(osition)36 b(4.4)49 b Fe(Supp)-5 b(ose)42 b(that)i Fo(B)k Fe(is)43 b(a)g(PDO)f(with)h(symb)-5 b(ol)43 b Fo(b)g Fk(2)h Fo(C)2779 4902 y Fm(m)2845 4939 y Fp(\(\010\))g Fe(wher)-5 b(e)42 b Fp(\010)i Fk(2)f Fo(S)3607 4902 y Fm(r)3601 4963 y Fj(1)p Fm(;)p Fj(0)3695 4939 y Fe(.)-7 5059 y(Supp)-5 b(ose)34 b(that)h(c)-5 b(o)g(e\016cients)34 b(of)h(di\013er)-5 b(ential)34 b(op)-5 b(er)g(ators)1220 5287 y Fo(G)1297 5302 y Fm(i)1353 5287 y Fp(=)1481 5193 y Fi(X)1456 5409 y Fn(j)p Fm(s)p Fn(j\024)p Fm(s)1617 5418 y Fl(0)1667 5287 y Fo(g)1718 5246 y Fj(\()p Fm(i)p Fj(\))1714 5312 y Fm(s)1800 5287 y Fp(\()p Fo(x)p Fp(\))p Fo(D)2015 5246 y Fm(s)2052 5287 y Fo(;)87 b(i)27 b Fp(=)h(1)p Fo(;)17 b Fp(2)p Fo(;)1810 5634 y Fp(17)p eop %%Page: 18 18 18 17 bop -7 53 a Fe(satisfy)39 b(the)g(c)-5 b(ondition)38 b Fo(g)948 2 y Fj(\()p Fm(i)p Fj(\))944 63 y Fm(s)1066 53 y Fk(2)d Fo(C)1244 17 y Fn(1)1319 53 y Fp(\()p Fh(R)1423 17 y Fj(3)1468 53 y Fp(\))k Fe(and)g Fo(@)1795 17 y Fm(\013)1845 53 y Fo(g)1896 2 y Fj(\()p Fm(i)p Fj(\))1892 63 y Fm(s)1978 53 y Fp(\()p Fo(x)p Fp(\))d(=)f Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)2483 17 y Fm(n)p Fn(\000)p Fm(\013)2629 53 y Fp(\))k Fe(as)g Fk(j)p Fo(x)p Fk(j)c(!)g(1)j Fe(for)h(some)f Fo(n)-7 187 y Fe(and)c(al)5 b(l)35 b Fo(\013)q Fe(.)44 b(Set)35 b Fo(g)677 151 y Fj(\()p Fm(i)p Fj(\))759 187 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)1113 112 y Fi(P)1218 216 y Fn(j)p Fm(s)p Fn(j\024)p Fm(s)1379 225 y Fl(0)1433 187 y Fo(g)1484 136 y Fj(\()p Fm(i)p Fj(\))1480 197 y Fm(s)1566 187 y Fp(\()p Fo(x)p Fp(\))p Fo(\030)1745 151 y Fm(s)1782 187 y Fe(,)35 b(and)f(let)h Fo(T)48 b Fe(b)-5 b(e)35 b(the)g(PDO)f(with)h(symb)-5 b(ol)1152 433 y Fo(t)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))28 b(=)p 1541 343 368 4 v 27 w Fo(g)1592 405 y Fj(\(1\))1686 433 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))o Fo(g)1959 392 y Fj(\(2\))2053 433 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(b)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(:)-7 648 y Fe(Then)34 b(the)h(op)-5 b(er)g(ator)35 b Fk(h)p Fo(x)p Fk(i)926 611 y Fm(p)965 648 y Fp(\()p Fo(T)h Fk(\000)23 b Fo(G)1273 611 y Fn(\003)1273 672 y Fj(1)1312 648 y Fo(B)5 b(G)1468 663 y Fj(2)1508 648 y Fp(\))p Fk(h)p Fo(x)p Fk(i)1679 611 y Fm(p)1753 648 y Fe(is)35 b(b)-5 b(ounde)g(d)34 b(if)g Fp(2)p Fo(p)28 b Fp(=)f Fk(\000)p Fo(m)c Fk(\000)g Fp(2)p Fo(n)f Fp(+)g(1)g Fk(\000)h Fo(r)s Fe(.)134 808 y Ft(4.2.)127 b Fp(W)-8 b(e)38 b(assume)g(b)s(elo)m(w)f (that)h Fo(V)58 b Fp(=)36 b Fo(V)1732 823 y Fm(S)1808 808 y Fp(+)26 b Fo(V)1967 823 y Fm(L)2056 808 y Fp(where)39 b(the)f(short-range)g(part)f Fo(V)3310 823 y Fm(S)3399 808 y Fp(satis\014es)-7 928 y(estimate)f(\(2.6\))g(and)g(the)h (long-range)e(part)h Fo(V)1743 943 y Fm(L)1832 928 y Fp(satis\014es)h(condition)e(\(1.18\).)54 b(Let)37 b(\010)3207 943 y Fn(\006)3301 928 y Fp(=)d(\010)3481 943 y Fn(\006)3540 928 y Fp(\()p Fo(V)3635 943 y Fm(L)3687 928 y Fp(\))-7 1049 y(and)h Fo(p)234 1064 y Fn(\006)323 1049 y Fp(=)c Fo(p)479 1064 y Fn(\006)538 1049 y Fp(\()p Fo(V)633 1064 y Fm(L)685 1049 y Fp(\))j(b)s(e)h(the)g(functions)f(constructed)i(in)e (Theorem)h(3.5)f(with)g(resp)s(ect)h(to)f Fo(V)3438 1064 y Fm(L)3525 1049 y Fp(only)-8 b(.)-7 1169 y(The)34 b(op)s(erator)e Fo(J)641 1184 y Fn(\006)732 1169 y Fp(is)g(de\014ned)i(b)m(y)g(form)m (ula)c(\(1.15\))i(where)i(the)f(cut-o\013)f(function)821 1383 y Fo(\020)864 1398 y Fn(\006)923 1383 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(\021)t Fp(\()p Fo(x)p Fp(\))p Fo(\033)1514 1398 y Fn(\006)1574 1383 y Fp(\()p Fk(h)6 b Fp(^)-55 b Fo(x;)1760 1357 y Fp(^)1750 1383 y Fo(\030)t Fk(i)p Fp(\))p Fo(;)87 b Fp(^)-55 b Fo(x)29 b Fp(=)e Fo(x=)p Fk(j)p Fo(x)p Fk(j)p Fo(;)2503 1357 y Fp(^)2493 1383 y Fo(\030)32 b Fp(=)27 b Fo(\030)5 b(=)p Fk(j)p Fo(\030)g Fk(j)p Fo(;)-7 1598 y(\033)48 1613 y Fn(\006)135 1598 y Fk(2)59 b Fo(C)337 1561 y Fn(1)411 1598 y Fp(\()p Fk(\000)p Fp(1)p Fo(;)17 b Fp(1\),)31 b Fo(\033)819 1613 y Fn(\006)879 1598 y Fp(\()p Fo(\034)11 b Fp(\))28 b(=)f(1)j(near)h Fk(\006)p Fp(1,)g Fo(\033)1672 1613 y Fn(\006)1732 1598 y Fp(\()p Fo(\034)11 b Fp(\))28 b(=)g(0)i(near)h Fk(\007)p Fp(1,)g Fo(\021)g Fk(2)d Fo(C)2721 1561 y Fn(1)2796 1598 y Fp(\()p Fh(R)2900 1561 y Fj(3)2945 1598 y Fp(\),)j Fo(\021)t Fp(\()p Fo(x)p Fp(\))d(=)f(0)k(near)f(0,)-7 1718 y Fo(\021)t Fp(\()p Fo(x)p Fp(\))f(=)h(1)j(for)g(large)g Fo(x)h Fp(and)f Fo( )h Fk(2)29 b Fo(C)1331 1682 y Fn(1)1324 1743 y Fj(0)1406 1718 y Fp(\()p Fh(R)1510 1733 y Fj(+)1575 1718 y Fp(\).)46 b(Note)34 b(that)f Fo(\020)2178 1733 y Fn(\006)2271 1718 y Fp(is)g(supp)s(orted)h(in)f(a)g(cone)i Fk(C)3302 1733 y Fn(\006)3361 1718 y Fp(\()p Fo(\016)t Fp(\).)46 b(The)-7 1838 y(function)24 b Fo(\021)k Fp(is)c(in)m(tro)s (duced)g(only)g(to)g(a)m(v)m(oid)h(the)f(singularit)m(y)f(of)30 b(^)-55 b Fo(x)25 b Fp(at)f Fo(x)k Fp(=)f(0.)41 b(The)25 b(function)f Fo( )k Fp(allo)m(ws)-7 1959 y(us)41 b(to)f(lo)s(calize)e (our)j(considerations)f(on)g(a)h(compact)f(subin)m(terv)-5 b(al)40 b(of)g(\()p Fo(m;)17 b Fk(1)p Fp(\).)67 b(It)40 b(follo)m(ws)g(from)-7 2079 y(estimates)35 b(\(3.18\))g(that)g Fo(b)965 2094 y Fn(\006)1056 2079 y Fp(=)e Fo(p)1214 2094 y Fn(\006)1273 2079 y Fo(\020)1316 2094 y Fn(\006)1374 2079 y Fo( )j Fk(2)d Fo(S)1638 2043 y Fj(0)1632 2104 y(1)p Fm(;)p Fj(0)1727 2079 y Fp(.)51 b(Let)36 b(functions)k(~)-54 b Fo(\033)t Fp(,)43 b(~)-56 b Fo(\021)t(;)2643 2053 y Fp(~)2624 2079 y Fo( )38 b Fp(satisfy)e(the)f(assumptions)-7 2217 y(ab)s(o)m(v)m(e)g(on)e Fo(\033)462 2232 y Fn(\006)522 2217 y Fo(;)17 b(\021)t(;)g( )t Fp(,)33 b(resp)s(ectiv)m(ely)-8 b(,)35 b(and)k(~)-54 b Fo(\033)1587 2232 y Fn(\006)1653 2217 y Fp(~)f Fo(\021)1718 2191 y Fp(~)1698 2217 y Fo( )34 b Fp(=)c(1)j(on)h(supp)s(ort)g(of)f Fo(\033)2649 2232 y Fn(\006)2709 2217 y Fo(\021)t( )t Fp(.)47 b(Set)3082 2192 y(~)3071 2217 y(\010)3141 2232 y Fn(\006)3230 2217 y Fp(=)30 b(\010)3406 2232 y Fn(\006)3470 2217 y Fp(~)-54 b Fo(\033)3520 2232 y Fn(\006)3586 2217 y Fp(~)f Fo(\021)3651 2191 y Fp(~)3631 2217 y Fo( )t Fp(.)-7 2338 y(By)40 b(\(3.6\),)432 2313 y(~)422 2338 y(\010)492 2353 y Fn(\006)590 2338 y Fk(2)g Fo(S)762 2291 y Fj(1)p Fn(\000)p Fm(\032)756 2362 y Fj(1)p Fm(;)p Fj(0)932 2338 y Fp(and)f Fo(e)1173 2302 y Fm(i)p Fj(\010)1248 2311 y Ff(\006)1304 2338 y Fo(b)1345 2353 y Fn(\006)1444 2338 y Fp(=)g Fo(e)1604 2302 y Fm(i)1636 2285 y Fj(~)1628 2302 y(\010)1679 2311 y Ff(\006)1736 2338 y Fo(b)1777 2353 y Fn(\006)1836 2338 y Fp(.)64 b(Therefore)41 b(the)e(sym)m(b)s(ol)g Fo(a)2942 2353 y Fn(\006)3041 2338 y Fp(=)g Fo(e)3201 2302 y Fm(i)p Fj(\010)3276 2311 y Ff(\006)3332 2338 y Fo(b)3373 2353 y Fn(\006)3472 2338 y Fp(of)g(the)-7 2475 y(PDO)e Fo(J)301 2490 y Fn(\006)396 2475 y Fp(b)s(elongs)g(to)f(the)h(class)g Fo(C)1356 2439 y Fj(0)1396 2475 y Fp(\()1445 2450 y(~)1434 2475 y(\010)1504 2490 y Fn(\006)1563 2475 y Fp(\),)h(and)f(hence,)i(b)m (y)f(Prop)s(osition)d(4.1,)j Fo(J)3076 2490 y Fn(\006)3172 2475 y Fp(is)e(a)h(b)s(ounded)-7 2595 y(op)s(erator)32 b(in)g(the)h(space)g Fk(H)q Fp(.)134 2755 y(Our)42 b(\014rst)g(goal)f (is)g(to)g(sho)m(w)i(that)f(b)s(oth)g(triples)f Fo(H)2106 2770 y Fj(0)2145 2755 y Fo(;)17 b(H)r(;)g(J)2370 2770 y Fj(+)2470 2755 y Fp(and)42 b Fo(H)2750 2770 y Fj(0)2789 2755 y Fo(;)17 b(H)r(;)g(J)3014 2770 y Fn(\000)3114 2755 y Fp(satisfy)42 b(the)h(as-)-7 2876 y(sumptions)32 b(of)g(Prop)s (osition)f(2.4.)43 b(T)-8 b(o)33 b(that)f(end,)i(w)m(e)f(need)h(the)f (follo)m(wing)-7 3059 y Ft(Lemma)k(4.5)49 b Fe(L)-5 b(et)42 b(the)f(op)-5 b(er)g(ators)40 b Fk(r)1437 3023 y Fn(?)1437 3084 y Fm(j)1496 3059 y Fo(;)i(j)j Fp(=)39 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fe(,)41 b(b)-5 b(e)41 b(de\014ne)-5 b(d)40 b(by)h Fp(\(1)p Fo(:)p Fp(19\))p Fe(.)63 b(L)-5 b(et)41 b Fo(T)55 b Fe(b)-5 b(e)41 b(a)g(PDO)-7 3180 y(with)35 b(symb)-5 b(ol)1095 3300 y Fo(t)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(g)t Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(w)s Fp(\()p Fk(h)h Fp(^)-55 b Fo(x)n(;)2015 3274 y Fp(^)2005 3300 y Fo(\030)t Fk(i)p Fp(\))p Fo(\021)t Fp(\()p Fo(x)p Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)2521 3259 y Fj(2)2559 3300 y Fp(\))p Fo(;)-7 3472 y Fe(wher)-5 b(e)30 b Fo(g)h Fk(2)d Fo(C)513 3436 y Fn(\000)p Fj(1)608 3472 y Fp(\(\010\))p Fe(,)k Fp(\010)c Fk(2)g Fo(S)1074 3425 y Fj(1)p Fn(\000)p Fm(\032)1068 3496 y Fj(1)p Fm(;)p Fj(0)1204 3472 y Fe(,)k Fo(w)e Fk(2)e Fo(C)1537 3436 y Fn(1)1612 3472 y Fp(\()p Fk(\000)p Fp(1)13 b Fk(\000)g Fo(\017;)k Fp(1)c(+)g Fo(\017)p Fp(\))33 b Fe(for)e(some)f Fo(\017)e(>)f Fp(0)k Fe(et)g Fo(w)s Fp(\()p Fk(\006)p Fp(1\))c(=)h(0)p Fe(.)43 b(Then)-7 3592 y Fo(T)49 b Fe(admits)34 b(the)h(r)-5 b(epr)g(esentation)1091 3891 y Fo(T)41 b Fp(=)1347 3767 y Fj(3)1293 3797 y Fi(X)1303 4006 y Fm(j)t Fj(=1)1453 3891 y Fo(G)1530 3850 y Fn(\003)1530 3916 y Fm(j)1569 3891 y Fo(B)1648 3850 y Fj(\()p Fm(s)p Fj(\))1740 3891 y Fo(G)1817 3906 y Fm(j)1876 3891 y Fp(+)22 b Fk(h)p Fo(x)p Fk(i)2107 3850 y Fn(\000)p Fm(p)2201 3891 y Fo(B)2280 3850 y Fj(\()p Fm(r)r Fj(\))2373 3891 y Fk(h)p Fo(x)p Fk(i)2506 3850 y Fn(\000)p Fm(p)2601 3891 y Fo(;)897 b Fp(\(4.5\))-7 4218 y Fe(wher)-5 b(e)34 b Fo(G)345 4233 y Fm(j)409 4218 y Fp(=)28 b Fk(h)p Fo(x)p Fk(i)646 4181 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)811 4218 y Fk(r)894 4181 y Fn(?)894 4242 y Fm(j)953 4218 y Fe(,)35 b Fo(p)27 b Fp(=)h(\(1)22 b(+)g Fo(\032)p Fp(\))p Fo(=)p Fp(2)34 b Fe(and)h(the)g(op)-5 b(er)g(ators)34 b Fo(B)2479 4181 y Fj(\()p Fm(s)p Fj(\))2571 4218 y Fo(;)17 b(B)2694 4181 y Fj(\()p Fm(r)r Fj(\))2821 4218 y Fe(ar)-5 b(e)35 b(b)-5 b(ounde)g(d.)-7 4412 y(Pr)g(o)g(of)35 b({)67 b Fp(Let)33 b Fo(B)626 4376 y Fj(\()p Fm(s)p Fj(\))750 4412 y Fp(and)g Fo(T)997 4427 y Fm(j)1033 4412 y Fp(,)g Fo(j)h Fp(=)27 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)31 b Fp(b)s(e)i(PDO)g(with)f (sym)m(b)s(ols)1020 4638 y Fo(b)1061 4597 y Fj(\()p Fm(s)p Fj(\))1153 4638 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fk(h)p Fo(x)p Fk(ij)p Fo(\030)5 b Fk(j)1744 4597 y Fn(\000)p Fj(2)1837 4638 y Fp(\(1)22 b Fk(\000)g(h)2094 4612 y Fp(^)2084 4638 y Fo(\030)t(;)h Fp(^)-55 b Fo(x)p Fk(i)2269 4597 y Fj(2)2309 4638 y Fp(\))2347 4597 y Fn(\000)p Fj(1)2441 4638 y Fo(t)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))-7 4852 y(and)923 4973 y Fo(t)958 4988 y Fm(j)995 4973 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fk(h)p Fo(x)p Fk(i)1481 4932 y Fn(\000)p Fj(1)1576 4973 y Fp(\()p Fo(\030)1657 4988 y Fm(j)1715 4973 y Fk(\000)22 b(j)p Fo(x)p Fk(j)1925 4932 y Fn(\000)p Fj(2)2019 4973 y Fo(x)2074 4988 y Fm(j)2111 4973 y Fk(h)p Fo(\030)5 b(;)17 b(x)p Fk(i)p Fp(\))2374 4932 y Fj(2)2413 4973 y Fo(b)2454 4932 y Fj(\()p Fm(s)p Fj(\))2546 4973 y Fp(\()p Fo(x;)g(\030)5 b Fp(\))p Fo(:)-7 5145 y Fp(The)26 b(function)f(\(1)7 b Fk(\000)g Fo(\034)792 5108 y Fj(2)831 5145 y Fp(\))869 5108 y Fn(\000)p Fj(1)964 5145 y Fo(w)s Fp(\()p Fo(\034)k Fp(\))24 b(is)h Fo(C)1358 5108 y Fn(1)1433 5145 y Fp(,)h(so)g(that)e Fo(b)1843 5108 y Fj(\()p Fm(s)p Fj(\))1963 5145 y Fk(2)k Fo(C)2134 5108 y Fj(0)2174 5145 y Fp(\(\010\))d(and)g(the)h(op)s(erator)e Fo(B)3152 5108 y Fj(\()p Fm(s)p Fj(\))3269 5145 y Fp(is)h(b)s(ounded)-7 5265 y(b)m(y)g(Prop)s(osition)e(4.1.)41 b(Since)24 b(the)h(sym)m(b)s (ol)f(of)g(the)h(op)s(erator)f Fo(G)2287 5280 y Fm(j)2348 5265 y Fp(equals)h Fk(h)p Fo(x)p Fk(i)2769 5229 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2933 5265 y Fp(\()p Fo(\030)3014 5280 y Fm(j)3056 5265 y Fk(\000)6 b(j)p Fo(x)p Fk(j)3250 5229 y Fn(\000)p Fj(2)3344 5265 y Fo(x)3399 5280 y Fm(j)3436 5265 y Fk(h)p Fo(x;)17 b(\030)5 b Fk(i)p Fp(\),)-7 5385 y(it)29 b(follo)m(ws)g(from)g(Prop)s(osition)f(4.4)i(that)g(the)h(op)s (erators)f Fk(h)p Fo(x)p Fk(i)2248 5349 y Fm(p)2287 5385 y Fp(\()p Fo(G)2402 5349 y Fn(\003)2402 5410 y Fm(j)2442 5385 y Fo(B)2521 5349 y Fj(\()p Fm(s)p Fj(\))2613 5385 y Fo(G)2690 5400 y Fm(j)2743 5385 y Fk(\000)18 b Fo(T)2895 5400 y Fm(j)2932 5385 y Fp(\))p Fk(h)p Fo(x)p Fk(i)3103 5349 y Fm(p)3172 5385 y Fp(are)30 b(b)s(ounded.)1810 5634 y(18)p eop %%Page: 19 19 19 18 bop -7 52 a Fp(No)m(w)23 b(the)h(equalit)m(y)e Fo(t)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)1114 -23 y Fi(P)1219 3 y Fj(3)1219 81 y Fm(j)t Fj(=1)1362 52 y Fo(t)1397 67 y Fm(j)1434 52 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b(implies)f(the)i(b)s(oundedness)i(of)d(the)h(op)s(erator)f Fk(h)p Fo(x)p Fk(i)3497 16 y Fm(p)3537 52 y Fp(\()p Fo(T)16 b Fk(\000)-7 119 y Fi(P)98 145 y Fj(3)98 222 y Fm(j)t Fj(=1)242 193 y Fo(G)319 157 y Fn(\003)319 218 y Fm(j)358 193 y Fo(B)437 157 y Fj(\()p Fm(s)p Fj(\))529 193 y Fo(G)606 208 y Fm(j)642 193 y Fp(\))p Fk(h)p Fo(x)p Fk(i)813 157 y Fm(p)853 193 y Fp(.)43 b(This)33 b(is)f(equiv)-5 b(alen)m(t)32 b(to)h(\(4.5\).)43 b Fd(2)134 434 y Fp(Set)33 b Fo(H)383 449 y Fm(L)463 434 y Fp(=)27 b Fo(H)647 449 y Fj(0)709 434 y Fp(+)22 b Fo(V)864 449 y Fm(L)916 434 y Fp(.)43 b(Let)33 b(us)g(calculate)f(the)h(op)s(erator)f Fo(T)2325 383 y Fj(\()p Fm(L)p Fj(\))2311 455 y Fn(\006)2459 434 y Fp(=)c Fo(H)2644 449 y Fm(L)2696 434 y Fo(J)2750 449 y Fn(\006)2831 434 y Fk(\000)22 b Fo(J)2984 449 y Fn(\006)3043 434 y Fo(H)3124 449 y Fj(0)3163 434 y Fp(.)-7 612 y Ft(Lemma)37 b(4.6)49 b Fe(The)34 b(op)-5 b(er)g(ator)35 b Fo(T)1236 561 y Fj(\()p Fm(L)p Fj(\))1222 634 y Fn(\006)1378 612 y Fe(is)f(PDO)g(with)h(symb)-5 b(ol)1212 846 y Fo(t)1247 861 y Fn(\006)1306 846 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fo(t)1695 795 y Fj(\()p Fm(s)p Fj(\))1695 868 y Fn(\006)1787 846 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Fo(t)2164 795 y Fj(\()p Fm(r)r Fj(\))2164 868 y Fn(\006)2257 846 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)1018 b Fp(\(4.6\))-7 1062 y Fe(wher)-5 b(e)356 1279 y Fo(t)391 1228 y Fj(\()p Fm(s)p Fj(\))391 1301 y Fn(\006)483 1279 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(e)881 1238 y Fm(i)p Fj(\010)956 1247 y Ff(\006)1009 1238 y Fj(\()p Fm(x;\030)s Fj(\))1161 1279 y Fo(b)1202 1228 y Fj(\()p Fm(s)p Fj(\))1202 1301 y Fn(\006)1294 1279 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)1726 1238 y Fj(2)1763 1279 y Fp(\))p Fo(;)87 b(t)1950 1228 y Fj(\()p Fm(r)r Fj(\))1950 1301 y Fn(\006)2043 1279 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(e)2441 1238 y Fm(i)p Fj(\010)2516 1247 y Ff(\006)2569 1238 y Fj(\()p Fm(x;\030)s Fj(\))2721 1279 y Fo(b)2762 1228 y Fj(\()p Fm(r)r Fj(\))2762 1301 y Fn(\006)2855 1279 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)3287 1238 y Fj(2)3325 1279 y Fp(\))417 1589 y Fo(b)458 1538 y Fj(\()p Fm(s)p Fj(\))458 1611 y Fn(\006)550 1589 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)h Fk(\000)p Fo(i\021)t Fp(\()p Fo(x)p Fp(\))p Fk(j)p Fo(x)p Fk(j)1308 1548 y Fn(\000)p Fj(1)1474 1465 y(3)1419 1495 y Fi(X)1427 1707 y Fm(k)r Fj(=1)1563 1589 y Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)1705 1548 y Fn(\000)p Fj(1)1798 1589 y Fo(\030)1841 1604 y Fm(k)1906 1589 y Fk(\000)22 b(j)p Fo(x)p Fk(j)2116 1548 y Fn(\000)p Fj(1)2210 1589 y Fo(x)2265 1604 y Fm(k)2309 1589 y Fk(h)6 b Fp(^)-55 b Fo(x;)2457 1563 y Fp(^)2447 1589 y Fo(\030)t Fk(i)p Fp(\))p Fo(\033)2630 1548 y Fn(0)2626 1614 y(\006)2685 1589 y Fp(\()p Fk(h)6 b Fp(^)-55 b Fo(x;)2871 1563 y Fp(^)2861 1589 y Fo(\030)t Fk(i)p Fp(\))p Fo(\013)3047 1604 y Fm(k)3090 1589 y Fo(p)3139 1604 y Fj(0)3178 1589 y Fp(\()p Fo(\030)5 b Fp(\))-7 1878 y Fe(and)34 b(the)h(function)g Fo(b)769 1827 y Fj(\()p Fm(r)r Fj(\))769 1900 y Fn(\006)862 1878 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))34 b Fe(satis\014es)h(for)f (al)5 b(l)35 b Fo(\013)q(;)17 b(\014)40 b Fe(the)34 b(estimates)480 2112 y Fk(j)p Fo(@)564 2071 y Fm(\013)559 2137 y(x)614 2112 y Fo(@)670 2065 y Fm(\014)665 2140 y(\030)718 2112 y Fo(b)759 2061 y Fj(\()p Fm(r)r Fj(\))759 2134 y Fn(\006)852 2112 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fk(j)27 b(\024)h Fo(C)1305 2127 y Fm(\013;\014)1417 2112 y Fk(h)p Fo(x)p Fk(i)1550 2071 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)p Fn(\000j)p Fm(\013)p Fn(j)1867 2112 y Fo(;)87 b Fp(0)27 b Fo(<)h(c)f Fk(\024)h(j)p Fo(\030)5 b Fk(j)27 b(\024)h Fo(C)35 b(<)27 b Fk(1)p Fo(;)86 b(\017)28 b(>)g Fp(0)p Fo(:)286 b Fp(\(4.7\))-7 2369 y Fe(Pr)-5 b(o)g(of)35 b({)d Fp(Using)g(notation)f(\(3.1\))h(w)m(e)i(see)g(that)e Fo(H)1828 2384 y Fm(L)1880 2369 y Fo(J)1934 2384 y Fn(\006)2026 2369 y Fp(is)g(the)h(PDO)f(with)g(sym)m(b)s(ol)119 2676 y Fo(e)164 2635 y Fm(i)p Fj(\010)239 2644 y Ff(\006)291 2635 y Fj(\()p Fm(x;\030)s Fj(\))443 2676 y Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)652 2635 y Fj(2)690 2676 y Fp(\))745 2506 y Fi( )824 2676 y Fp(\()p Fo(\027)h Fp(\()p Fo(\030)f Fp(\))p Fo(p)1089 2691 y Fn(\006)1148 2676 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))21 b(+)h Ft(q)1549 2691 y Fn(\006)1608 2676 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\)\))p Fo(\020)1912 2691 y Fn(\006)1970 2676 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)h Fo(i)2419 2551 y Fj(3)2364 2581 y Fi(X)2372 2794 y Fm(k)r Fj(=1)2508 2676 y Fp(\()p Fo(@)2597 2691 y Fm(x)2637 2703 y Fc(k)2680 2676 y Fo(\020)2723 2691 y Fn(\006)2781 2676 y Fp(\)\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\013)3104 2691 y Fm(k)3146 2676 y Fo(p)3195 2691 y Fn(\006)3254 2676 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))3477 2506 y Fi(!)3572 2676 y Fo(:)3525 2887 y Fp(\(4.8\))-7 3007 y(The)34 b(op)s(erator)e Fo(J)641 3022 y Fn(\006)699 3007 y Fo(H)780 3022 y Fj(0)852 3007 y Fp(is)g(also)g(PDO)g(with)g(sym)m(b)s(ol)1266 3223 y Fo(e)1311 3182 y Fm(i)p Fj(\010)1386 3191 y Ff(\006)1439 3182 y Fj(\()p Fm(x;\030)s Fj(\))1591 3223 y Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)1800 3182 y Fj(2)1838 3223 y Fp(\))p Fo(p)1925 3238 y Fn(\006)1984 3223 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(h)2263 3238 y Fj(0)2302 3223 y Fp(\()p Fo(\030)g Fp(\))p Fo(;)1072 b Fp(\(4.9\))-7 3440 y(where)34 b(the)f(matrix-function)d Fo(h)1198 3455 y Fj(0)1238 3440 y Fp(\()p Fo(\030)5 b Fp(\))31 b(is)h(de\014ned)i(b)m (y)g(\(1.3\).)43 b(By)33 b(\(3.9\),)1251 3657 y Fo(p)1300 3672 y Fn(\006)1359 3657 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(h)1638 3672 y Fj(0)1677 3657 y Fp(\()p Fo(\030)g Fp(\))27 b(=)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(p)2159 3672 y Fn(\006)2218 3657 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(;)-7 3887 y Fp(so)28 b(that)f(\(4.9\))f(cancels)i (in)f Fo(T)1047 3836 y Fj(\()p Fm(L)p Fj(\))1033 3908 y Fn(\006)1181 3887 y Fp(with)g(the)g(\014rst)h(term)f(in)f(the)i(righ) m(t-hand)e(side)i(of)e(\(4.8\).)42 b(According)-7 4007 y(to)i(\(3.4\))h(the)g(second)h(term)e Ft(q)1181 4022 y Fn(\006)1240 4007 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\020)1506 4022 y Fn(\006)1564 4007 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))44 b(in)g(brac)m(k)m(ets)j(in)d(\(4.8\))g(satis\014es) i(estimate)e(\(4.7\).)-7 4141 y(Finally)-8 b(,)28 b Fo(b)383 4090 y Fj(\()p Fm(s)p Fj(\))383 4163 y Fn(\006)475 4141 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))29 b(is)h(the)g(part)g(of)f(order)h Fk(\000)p Fp(1)h(of)e(the)h(last)g(term)f(in)g(these)i(brac)m(k)m(ets.) 45 b(According)30 b(to)-7 4261 y(\(3.18\))i(the)h(remainder)f (satis\014es)h(again)e(estimate)h(\(4.7\).)43 b Fd(2)-7 4495 y Ft(Prop)s(osition)36 b(4.7)49 b Fe(The)33 b(op)-5 b(er)g(ator)33 b Fo(T)1428 4510 y Fn(\006)1515 4495 y Fp(=)28 b Fo(H)8 b(J)1762 4510 y Fn(\006)1840 4495 y Fk(\000)20 b Fo(J)1991 4510 y Fn(\006)2050 4495 y Fo(H)2131 4510 y Fj(0)2204 4495 y Fe(admits)33 b(the)h(r)-5 b(epr)g(esentation)33 b Fp(\(4)p Fo(:)p Fp(5\))h Fe(with)-7 4615 y Fo(p)28 b(>)f Fp(1)p Fo(=)p Fp(2)p Fe(.)-7 4800 y(Pr)-5 b(o)g(of)35 b({)67 b Fp(By)33 b(\(4.6\),)1329 4934 y Fo(T)1386 4949 y Fn(\006)1472 4934 y Fp(=)28 b Fo(T)1647 4883 y Fj(\()p Fm(s)p Fj(\))1633 4956 y Fn(\006)1760 4934 y Fp(+)22 b Fo(T)1929 4883 y Fj(\()p Fm(r)r Fj(\))1915 4956 y Fn(\006)2044 4934 y Fp(+)g Fo(V)2199 4949 y Fm(S)2250 4934 y Fo(J)2304 4949 y Fn(\006)2363 4934 y Fo(;)-7 5124 y Fp(where)i Fo(T)336 5073 y Fj(\()p Fm(s)p Fj(\))322 5146 y Fn(\006)451 5124 y Fp(and)f Fo(T)702 5073 y Fj(\()p Fm(r)r Fj(\))688 5146 y Fn(\006)818 5124 y Fp(are)g(PDO)g(with)f(sym)m(b)s(ols)h Fo(t)1821 5073 y Fj(\()p Fm(s)p Fj(\))1821 5146 y Fn(\006)1936 5124 y Fp(and)g Fo(t)2151 5073 y Fj(\()p Fm(r)r Fj(\))2151 5146 y Fn(\006)2244 5124 y Fp(,)j(resp)s(ectiv)m(ely)-8 b(.)41 b(Since)23 b Fo(t)3135 5073 y Fj(\()p Fm(s)p Fj(\))3135 5146 y Fn(\006)3255 5124 y Fk(2)28 b Fo(C)3426 5088 y Fn(\000)p Fj(1)3520 5124 y Fp(\()3569 5099 y(~)3558 5124 y(\010)3628 5139 y Fn(\006)3687 5124 y Fp(\))-7 5245 y(and)43 b Fo(\033)252 5209 y Fn(0)248 5269 y(\006)308 5245 y Fp(\()p Fo(s)p Fp(\))j(=)f(0)e(in)g(neigh)m(b)s(ourho)s(o)s(ds)f (of)h(the)h(p)s(oin)m(ts)f Fo(s)j Fp(=)f Fk(\000)p Fp(1)f(and)f Fo(s)j Fp(=)g(1,)f(Lemma)d(4.5)h(can)-7 5385 y(b)s(e)36 b(directly)f(applied)g(to)g Fo(T)1025 5334 y Fj(\()p Fm(s)p Fj(\))1011 5407 y Fn(\006)1116 5385 y Fp(.)53 b(It)36 b(follo)m(ws)f(from)f(\(4.7\))h(and)h(Prop)s(osition)e(4.1)h (that)h(the)g(op)s(erator)1810 5634 y(19)p eop %%Page: 20 20 20 19 bop -7 53 a Fk(h)p Fo(x)p Fk(i)126 17 y Fm(p)166 53 y Fo(T)237 2 y Fj(\()p Fm(r)r Fj(\))223 75 y Fn(\006)329 53 y Fk(h)p Fo(x)p Fk(i)462 17 y Fm(p)527 53 y Fp(is)24 b(b)s(ounded)i(if)e Fo(p)j Fp(=)h(\(1)7 b(+)g Fo(\017)p Fp(\))p Fo(=)p Fp(2.)39 b(Similarly)-8 b(,)23 b Fk(h)p Fo(x)p Fk(i)2249 17 y Fm(p)2288 53 y Fo(V)2345 68 y Fm(S)2396 53 y Fk(h)p Fo(x)p Fk(i)2529 17 y Fm(p)2594 53 y Fp(is)h(b)s(ounded)i (if)e Fo(p)j Fp(=)h(\(1)7 b(+)g Fo(\032)p Fp(\))p Fo(=)p Fp(2.)-7 173 y Fd(2)134 379 y Fp(By)25 b(virtue)f(of)g(Theorems)h(2.11) f(and)g(2.15,)i(the)f(op)s(erators)f Fk(h)p Fo(x)p Fk(i)2422 343 y Fn(\000)p Fm(p)2516 379 y Fo(;)17 b(p)28 b(>)f Fp(1)p Fo(=)p Fp(2,)e(and)g Fo(G)3198 394 y Fm(j)3234 379 y Fp(,)h Fo(j)34 b Fp(=)28 b(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)-7 500 y Fp(are)36 b Fo(H)240 515 y Fj(0)280 500 y Fp(-smo)s(oth)f(on)h(an)m(y)h(compact)f(in)m(terv)-5 b(al)35 b(\003)e Fk(\032)i Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))25 b Fk([)g Fp(\()p Fo(m;)17 b Fk(1)p Fp(\).)54 b(Moreo)m(v)m(er,)39 b(they)e(are)-7 620 y(also)i Fo(H)8 b Fp(-smo)s(oth)39 b(if)g(\003)27 b Fk(\\)h Fo(\033)1011 635 y Fm(p)1051 620 y Fp(\()p Fo(H)8 b Fp(\))40 b(=)h Fk(;)p Fp(.)66 b(Therefore)42 b(Prop)s(osition)c(4.7)i(implies)e(that)i(b)s(oth)g(triples)-7 741 y Fo(H)74 756 y Fj(0)113 741 y Fo(;)17 b(H)r(;)g(J)338 756 y Fj(+)434 741 y Fp(and)37 b Fo(H)709 756 y Fj(0)748 741 y Fo(;)17 b(H)r(;)g(J)973 756 y Fn(\000)1069 741 y Fp(satisfy)37 b(on)g(suc)m(h)i(\003)d(the)i(assumptions)f(of)g(Prop)s (osition)e(2.4.)57 b(T)-8 b(aking)-7 861 y(in)m(to)38 b(accoun)m(t)i(that)f(linear)e(com)m(binations)h(\(for)g(all)f (admissible)g(\003\))i(of)g(elemen)m(ts)g Fo(f)3190 876 y Fj(0)3268 861 y Fp(=)g Fo(E)3455 876 y Fj(0)3494 861 y Fp(\(\003\))p Fo(f)3686 876 y Fj(0)-7 981 y Fp(and)47 b Fo(f)64 b Fp(=)53 b Fo(E)6 b Fp(\(\003\))p Fo(f)57 b Fp(are)47 b(dense)i(in)e Fk(H)h Fp(and)g(the)f(absolutely)g(con)m (tin)m(uous)h(subspace)h Fo(P)14 b Fk(H)48 b Fp(of)f Fo(H)8 b Fp(,)-7 1102 y(resp)s(ectiv)m(ely)-8 b(,)34 b(w)m(e)f(obtain)f(the)h(follo)m(wing)d(result.)-7 1283 y Ft(Theorem)37 b(4.8)49 b Fe(Supp)-5 b(ose)28 b(that)i Fo(V)49 b Fp(=)28 b Fo(V)1486 1298 y Fm(S)1545 1283 y Fp(+)9 b Fo(V)1687 1298 y Fm(L)1768 1283 y Fe(wher)-5 b(e)29 b Fo(V)2095 1298 y Fm(S)2175 1283 y Fe(satis\014es)f Fp(\(2)p Fo(:)p Fp(6\))g Fe(and)h Fo(V)3005 1298 y Fm(L)3086 1283 y Fe(satis\014es)f Fp(\(1)p Fo(:)p Fp(18\))p Fe(.)-7 1403 y(L)-5 b(et)33 b Fo(J)213 1418 y Fn(\006)300 1403 y Fp(=)27 b Fo(J)457 1418 y Fn(\006)516 1403 y Fp(\()p Fo(V)611 1418 y Fm(L)663 1403 y Fp(\))33 b Fe(b)-5 b(e)32 b(PDO)h Fp(\(1)p Fo(:)p Fp(15\))f Fe(wher)-5 b(e)32 b(the)g(functions)h Fp(\010)2305 1418 y Fn(\006)2392 1403 y Fp(=)27 b(\010)2565 1418 y Fn(\006)2625 1403 y Fp(\()p Fo(V)2720 1418 y Fm(L)2772 1403 y Fp(\))33 b Fe(and)f Fo(p)3079 1418 y Fn(\006)3165 1403 y Fp(=)c Fo(p)3318 1418 y Fn(\006)3377 1403 y Fp(\()p Fo(V)3472 1418 y Fm(L)3524 1403 y Fp(\))33 b Fe(ar)-5 b(e)-7 1524 y(de\014ne)g(d)40 b(by)i(e)-5 b(qualities)41 b Fp(\(3)p Fo(:)p Fp(20\))p Fe(,)h Fp(\(3)p Fo(:)p Fp(21\))e Fe({)h Fp(\(3)p Fo(:)p Fp(23\))p Fe(,)h Fp(\(3)p Fo(:)p Fp(26\))f Fe(and)g Fp(\(3)p Fo(:)p Fp(8\))p Fe(,)h Fp(\(3)p Fo(:)p Fp(9\))f Fe(with)g Fo(V)63 b Fe(r)-5 b(eplac)g(e)g(d)40 b(by)-7 1644 y Fo(V)50 1659 y Fm(L)102 1644 y Fe(.)45 b(Then)34 b(the)h(wave)f(op)-5 b(er)g(ators)1117 1854 y Fo(W)1209 1869 y Fn(\006)1268 1854 y Fp(\()p Fo(H)r(;)17 b(H)1514 1869 y Fj(0)1553 1854 y Fp(;)g Fo(J)1651 1869 y Fn(\006)1710 1854 y Fp(\))174 b Fo(W)2014 1869 y Fn(\006)2073 1854 y Fp(\()p Fo(H)2192 1869 y Fj(0)2231 1854 y Fo(;)17 b(H)8 b Fp(;)17 b Fo(J)2471 1813 y Fn(\003)2462 1879 y(\006)2520 1854 y Fp(\))p Fo(;)891 b Fp(\(4.10\))-7 2064 y Fe(and)1125 2185 y Fo(W)1217 2200 y Fn(\006)1276 2185 y Fp(\()p Fo(H)r(;)17 b(H)1522 2200 y Fj(0)1561 2185 y Fp(;)g Fo(J)1659 2200 y Fn(\007)1718 2185 y Fp(\))174 b Fo(W)2022 2200 y Fn(\006)2081 2185 y Fp(\()p Fo(H)2200 2200 y Fj(0)2239 2185 y Fo(;)17 b(H)8 b Fp(;)17 b Fo(J)2479 2144 y Fn(\003)2470 2209 y(\007)2528 2185 y Fp(\))p Fo(;)883 b Fp(\(4.11\))-7 2355 y Fe(exist.)45 b(The)34 b(op)-5 b(er)g(ators)34 b Fp(\(4)p Fo(:)p Fp(10\))g Fe(as)h(wel)5 b(l)34 b(as)h Fp(\(4)p Fo(:)p Fp(11\))f Fe(ar)-5 b(e)35 b(adjoint)f(to)h(e)-5 b(ach)34 b(other.)-7 2605 y Ft(Corollary)i(4.9)49 b Fe(L)-5 b(et)35 b Ft(J)909 2620 y Fn(\006)1003 2605 y Fe(b)-5 b(e)34 b(PDO)h Fp(\(1)p Fo(:)p Fp(22\))p Fe(.)44 b(Then)34 b(al)5 b(l)34 b(wave)g(op)-5 b(er)g(ators)417 2815 y Fo(W)509 2830 y Fn(\006)568 2815 y Fp(\()p Fo(H)r(;)17 b(H)814 2830 y Fj(0)853 2815 y Fp(;)g Ft(J)955 2830 y Fn(\006)1014 2815 y Fp(\))p Fo(;)86 b(W)1257 2830 y Fn(\006)1316 2815 y Fp(\()p Fo(H)1435 2830 y Fj(0)1474 2815 y Fo(;)17 b(H)8 b Fp(;)17 b Ft(J)1709 2774 y Fn(\003)1709 2840 y(\006)1767 2815 y Fp(\))p Fo(;)87 b(W)2011 2830 y Fn(\006)2070 2815 y Fp(\()p Fo(H)r(;)17 b(H)2316 2830 y Fj(0)2355 2815 y Fo(;)g Ft(J)2457 2830 y Fn(\007)2515 2815 y Fp(\))p Fo(;)87 b(W)2759 2830 y Fn(\006)2818 2815 y Fp(\()p Fo(H)2937 2830 y Fj(0)2976 2815 y Fo(;)17 b(H)r(;)g Ft(J)3205 2774 y Fn(\003)3205 2840 y(\007)3264 2815 y Fp(\))-7 3026 y Fe(exist)35 b(and)f(c)-5 b(oincide)34 b(with)g(c)-5 b(orr)g(esp)g(onding)34 b(op)-5 b(er)g(ators)34 b Fp(\(4)p Fo(:)p Fp(10\))p Fe(,)g Fp(\(4)p Fo(:)p Fp(11\))p Fe(.)-7 3207 y(Pr)-5 b(o)g(of)35 b({)67 b Fp(The)33 b(op)s(erator)f Fo(J)1019 3222 y Fn(\006)1100 3207 y Fk(\000)23 b Ft(J)1258 3222 y Fn(\006)1349 3207 y Fp(is)33 b(PDO)f(with)g(sym)m(b)s(ol)685 3417 y Fo(e)730 3376 y Fm(i)p Fj(\010)805 3385 y Ff(\006)857 3376 y Fj(\()p Fm(x;\030)s Fj(\))1018 3417 y Fp(~)-58 b Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\020)1324 3432 y Fn(\006)1382 3417 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)1814 3376 y Fj(2)1852 3417 y Fp(\))p Fo(;)90 b Fp(~)-57 b Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))27 b(=)g Fo(p)p Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)g Fo(p)2843 3432 y Fj(0)2883 3417 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(:)-7 3627 y Fp(By)33 b(\(3.18\),)f(Prop)s(osition)f(4.1)h(implies)e(that)j (the)g(op)s(erator)e Fo(J)2294 3642 y Fn(\006)2376 3627 y Fk(\000)22 b Ft(J)2533 3642 y Fn(\006)2625 3627 y Fp(is)32 b(compact.)43 b Fd(2)134 3833 y Ft(4.3.)86 b Fp(Our)22 b(pro)s(of)f(of)g(the)h(isometricit)m(y)e(and)i(completeness)g(of)f (the)i(w)m(a)m(v)m(e)g(op)s(erators)f Fo(W)3358 3848 y Fn(\006)3417 3833 y Fp(\()p Fo(H)r(;)17 b(H)3663 3848 y Fj(0)3702 3833 y Fp(;)-7 3954 y Ft(J)51 3969 y Fn(\006)110 3954 y Fp(\))32 b(relies)g(on)-7 4113 y Ft(Lemma)37 b(4.10)49 b Fe(The)34 b(fol)5 b(lowing)34 b(r)-5 b(elations)34 b(hold)893 4323 y Fo(s)22 b Fk(\000)65 b Fp(lim)1060 4383 y Fm(t)p Fn(!\0061)1282 4323 y Fp(\()p Ft(J)1378 4282 y Fn(\003)1378 4347 y(\006)1437 4323 y Ft(J)1495 4338 y Fn(\006)1576 4323 y Fk(\000)22 b Fo( )1742 4282 y Fj(2)1782 4323 y Fp(\()p Fo(H)1909 4282 y Fj(2)1901 4347 y(0)1970 4323 y Fk(\000)g Fo(m)2154 4282 y Fj(2)2194 4323 y Fp(\))p Fo(P)2295 4338 y Fj(0)2334 4323 y Fp(\))p Fo(e)2417 4282 y Fn(\000)p Fm(iH)2554 4291 y Fl(0)2589 4282 y Fm(t)2646 4323 y Fp(=)28 b(0)p Fo(;)650 b Fp(\(4.12\))1313 4584 y Fo(s)22 b Fk(\000)65 b Fp(lim)1480 4644 y Fm(t)p Fn(!\0061)1719 4584 y Ft(J)1777 4543 y Fn(\003)1777 4609 y(\007)1835 4584 y Ft(J)1893 4599 y Fn(\007)1952 4584 y Fo(e)1997 4543 y Fn(\000)p Fm(iH)2134 4552 y Fl(0)2169 4543 y Fm(t)2226 4584 y Fp(=)28 b(0)p Fo(:)1070 b Fp(\(4.13\))-7 4827 y Fe(Pr)-5 b(o)g(of)45 b({)90 b Fp(Prop)s(osition)42 b(4.2)i(sho)m(ws)i(that,)h(up)d(to)g(a)g(compact)g(term,)j Ft(J)2766 4791 y Fn(\003)2766 4851 y(\007)2824 4827 y Ft(J)2882 4842 y Fn(\007)2986 4827 y Fp(is)c(the)i(PDO)f(with)-7 4947 y(sym)m(b)s(ol)32 b Fo(p)376 4962 y Fj(0)415 4947 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(\020)590 4911 y Fj(2)582 4972 y Fn(\007)640 4947 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )930 4911 y Fj(2)969 4947 y Fp(\()p Fk(j)p Fo(\030)g Fk(j)1111 4911 y Fj(2)1149 4947 y Fp(\).)44 b(It)32 b(follo)m(ws)g(that)134 5212 y(\()p Ft(J)230 5171 y Fn(\003)230 5237 y(\007)289 5212 y Ft(J)347 5227 y Fn(\007)406 5212 y Fo(e)451 5171 y Fn(\000)p Fm(iH)588 5180 y Fl(0)622 5171 y Fm(t)652 5212 y Fo(f)11 b Fp(\)\()p Fo(x)p Fp(\))28 b(=)f(\(2)p Fo(\031)t Fp(\))1195 5171 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1376 5077 y Fi(Z)1432 5302 y Fg(R)1480 5283 y Fl(3)1535 5212 y Fo(e)1580 5171 y Fm(i)p Fn(h)p Fm(\030)s(;x)p Fn(i\000)p Fm(i\027)t Fj(\()p Fm(\030)s Fj(\))p Fm(t)1988 5212 y Fo(p)2037 5227 y Fj(0)2077 5212 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(\020)2252 5171 y Fj(2)2244 5237 y Fn(\007)2301 5212 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )2591 5171 y Fj(2)2630 5212 y Fp(\()p Fk(j)p Fo(\030)g Fk(j)2772 5171 y Fj(2)2810 5212 y Fp(\))2870 5186 y(^)2848 5212 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)26 b Fp(+)c Fo(\017)3288 5227 y Fn(\007)3347 5212 y Fp(\()p Fo(x;)17 b(t)p Fp(\))p Fo(;)3476 5385 y Fp(\(4.14\))1810 5634 y(20)p eop %%Page: 21 21 21 20 bop -7 52 a Fp(where)38 b Fk(jj)p Fo(\017)374 67 y Fn(\007)432 52 y Fp(\()p Fk(\001)p Fo(;)17 b(t)p Fp(\))p Fk(jj)33 b Fp(=)h Fo(o)p Fp(\(1\))i(as)g Fk(j)p Fo(t)p Fk(j)e(!)g(1)p Fp(.)54 b(The)37 b(phase)g Fk(h)p Fo(\030)5 b(;)17 b(x)p Fk(i)24 b(\000)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(t)36 b Fp(do)s(es)h(not)f(ha)m(v)m(e)i(stationary)-7 172 y(p)s(oin)m(ts)31 b(if)g Fk(j)p Fo(x)p Fk(j)c Fo(>)h(t)p Fp(,)k(and)f(the)h(stationary)f(p)s(oin)m(t)g(equals)g(sgn)17 b(t)g Fo(mx)p Fp(\()p Fo(t)2502 136 y Fj(2)2562 172 y Fk(\000)k(j)p Fo(x)p Fk(j)2771 136 y Fj(2)2810 172 y Fp(\))2848 136 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)3044 172 y Fp(if)30 b Fk(j)p Fo(x)p Fk(j)e Fo(<)f Fk(j)p Fo(t)p Fk(j)p Fp(.)43 b(This)-7 293 y(p)s(oin)m(t)24 b(do)s(es)h(not)g(b)s (elong)e(to)i(the)g(supp)s(ort)g(of)f Fo(\020)1692 308 y Fn(\007)1751 293 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)g Fk(j)2183 256 y Fj(2)2220 293 y Fp(\))25 b(if)e Fo(t)28 b Fk(!)g(\0061)p Fp(.)41 b(Therefore,)27 b(in)m(tegrating)-7 413 y(b)m(y)i(parts,)g(w)m(e)f (estimate,)g(for)f(arbitrary)g Fo(N)10 b Fp(,)29 b(in)m(tegral)d (\(4.14\))h(as)g Fo(t)h Fk(!)g(\0061)f Fp(b)m(y)i Fo(C)2984 428 y Fm(N)3051 413 y Fp(\(1)12 b(+)g Fk(j)p Fo(x)p Fk(j)g Fp(+)g Fk(j)p Fo(t)p Fk(j)p Fp(\))3578 377 y Fn(\000)p Fm(N)3698 413 y Fp(.)-7 533 y(This)33 b(implies)e(\(4.13\).)44 b(Similarly)-8 b(,)29 b(w)m(e)34 b(\014nd)g(that,)f(up)g(to)g(a)g (compact)g(op)s(erator,)f Ft(J)3094 497 y Fn(\003)3094 558 y(\006)3153 533 y Ft(J)3211 548 y Fn(\006)3293 533 y Fk(\000)23 b Fo( )t Fp(\()p Fo(H)3587 497 y Fj(2)3579 558 y(0)3648 533 y Fk(\000)-7 654 y Fo(m)78 618 y Fj(2)118 654 y Fp(\))p Fo(P)219 669 y Fj(0)296 654 y Fp(is)37 b(the)h(PDO)f(with)h(sym)m(b)s(ol)f Fo(p)1442 669 y Fj(0)1481 654 y Fp(\()p Fo(\030)5 b Fp(\)\()p Fo(\020)1694 618 y Fj(2)1686 678 y Fn(\006)1744 654 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))25 b Fk(\000)h Fp(1\))p Fo( )2249 618 y Fj(2)2288 654 y Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)2430 618 y Fj(2)2468 654 y Fp(\).)59 b(Th)m(us)39 b(the)f(stationary)f (phase)-7 774 y(argumen)m(ts)c(can)g(b)s(e)f(again)g(applied.)42 b Fd(2)-7 1010 y Ft(Remark)37 b(4.11)49 b Fp(The)42 b(same)f(argumen)m (ts)h(sho)m(w)g(that)f(the)h(w)m(a)m(v)m(e)h(op)s(erators)e Fo(W)3038 1025 y Fn(\006)3098 1010 y Fp(\()p Fo(H)r(;)17 b(H)3344 1025 y Fj(0)3383 1010 y Fp(;)g Ft(J)3485 1025 y Fn(\006)3543 1010 y Fp(\))41 b(do)-7 1130 y(not)33 b(dep)s(end)i(on)f(the)g(c)m(hoice)g(of)f(the)h(functions)f Fo(\033)1861 1145 y Fn(\006)1921 1130 y Fp(\()p Fk(h)6 b Fp(^)-55 b Fo(x;)2107 1104 y Fp(^)2097 1130 y Fo(\030)t Fk(i)p Fp(\))33 b(\(and)h Fo(\021)t Fp(\()p Fo(x)p Fp(\)\))f(as)h(long) e(as)i Fo(\033)3246 1145 y Fn(\006)3305 1130 y Fp(\()p Fo(s)p Fp(\))c(=)f(1)k(in)-7 1250 y(a)38 b(neigh)m(b)s(ourho)s(o)s(d)f (of)h(the)h(p)s(oin)m(t)e Fo(s)h Fp(=)f Fk(\006)p Fp(1)h(and)h Fo(\033)1915 1265 y Fn(\006)1974 1250 y Fp(\()p Fo(s)p Fp(\))f(=)f(0)h(in)f(a)h(neigh)m(b)s(ourho)s(o)s(d)g(of)f(the)i(p)s (oin)m(t)-7 1371 y Fo(s)28 b Fp(=)f Fk(\007)p Fp(1.)-7 1557 y Ft(Prop)s(osition)36 b(4.12)49 b Fe(Under)34 b(the)h(asumptions) f(of)h(The)-5 b(or)g(em)34 b Fp(4)p Fo(:)p Fp(8)939 1776 y Fo(W)1031 1791 y Fn(\006)1091 1776 y Fp(\()p Fo(H)r(;)17 b(H)1337 1791 y Fj(0)1376 1776 y Fo(;)g Ft(J)1478 1791 y Fn(\007)1536 1776 y Fp(\))28 b(=)f(0)p Fo(;)156 b(W)2029 1791 y Fn(\006)2088 1776 y Fp(\()p Fo(H)2207 1791 y Fj(0)2247 1776 y Fo(;)17 b(H)r(;)g Ft(J)2476 1734 y Fn(\003)2476 1800 y(\007)2534 1776 y Fp(\))28 b(=)f(0)p Fo(:)697 b Fp(\(4.15\))-7 1994 y Fe(If)36 b Fp(\003)31 b Fk(\032)g Fp(\()p Fo(m;)17 b Fk(1)p Fp(\))36 b Fe(is)h(a)f(c)-5 b(omp)g(act)36 b(interval)g(and)g Fo( )t Fp(\()p Fo(\025)1928 1958 y Fj(2)1991 1994 y Fk(\000)24 b Fo(m)2177 1958 y Fj(2)2217 1994 y Fp(\))30 b(=)h(1)37 b Fe(for)f Fo(\025)31 b Fk(2)g Fp(\003)p Fe(,)37 b(then)f(the)h(op)-5 b(er)g(ators)-7 2115 y Fo(W)85 2130 y Fn(\006)144 2115 y Fp(\()p Fo(H)r(;)17 b(H)390 2130 y Fj(0)429 2115 y Fo(;)g Ft(J)531 2130 y Fn(\006)590 2115 y Fp(\))35 b Fe(ar)-5 b(e)34 b(isometric)g(on)h(the)g (subsp)-5 b(ac)g(e)34 b Fo(E)2020 2130 y Fj(0)2059 2115 y Fp(\(\003\))p Fk(H)q Fe(.)-7 2301 y(Pr)-5 b(o)g(of)35 b({)67 b Fp(Clearly)336 2519 y Fk(k)27 b Fo(W)505 2534 y Fn(\006)565 2519 y Fp(\()p Fo(H)r(;)17 b(H)811 2534 y Fj(0)850 2519 y Fo(;)g Ft(J)952 2534 y Fn(\006)1010 2519 y Fp(\))p Fo(f)38 b Fk(k)1184 2478 y Fj(2)1224 2519 y Fp(=)70 b(lim)1327 2579 y Fm(t)p Fn(!\0061)1576 2519 y Fk(k)28 b Ft(J)1712 2534 y Fn(\006)1771 2519 y Fo(e)1816 2478 y Fn(\000)p Fm(iH)1953 2487 y Fl(0)1988 2478 y Fm(t)2017 2519 y Fo(f)39 b Fk(k)2154 2478 y Fj(2)336 2716 y Fp(=)70 b(lim)439 2776 y Fm(t)p Fn(!\0061)661 2716 y Fp(\(\()p Ft(J)795 2675 y Fn(\003)795 2740 y(\006)854 2716 y Ft(J)912 2731 y Fn(\006)993 2716 y Fk(\000)22 b Fo( )1159 2675 y Fj(2)1199 2716 y Fp(\()p Fo(H)1326 2675 y Fj(2)1318 2740 y(0)1387 2716 y Fk(\000)h Fo(m)1572 2675 y Fj(2)1611 2716 y Fp(\)\))p Fo(e)1732 2675 y Fn(\000)p Fm(iH)1869 2684 y Fl(0)1904 2675 y Fm(t)1933 2716 y Fo(f)5 b(;)17 b(e)2075 2675 y Fn(\000)p Fm(iH)2212 2684 y Fl(0)2247 2675 y Fm(t)2277 2716 y Fo(f)11 b Fp(\)+)27 b Fk(k)g Fo( )t Fp(\()p Fo(H)2748 2675 y Fj(2)2740 2740 y(0)2810 2716 y Fk(\000)22 b Fo(m)2994 2675 y Fj(2)3034 2716 y Fp(\))p Fo(e)3117 2675 y Fn(\000)p Fm(iH)3254 2684 y Fl(0)3289 2675 y Fm(t)3318 2716 y Fo(f)39 b Fk(k)3455 2675 y Fj(2)3521 2716 y Fo(:)-7 2978 y Fp(If)c Fo(f)43 b Fk(2)33 b Fo(E)355 2993 y Fj(0)394 2978 y Fp(\(\003\))p Fk(H)q Fp(,)j(then,)g(b)m(y)g(\(4.12\),)g(the)f(righ)m(t-hand)f(side)i (here)g(equals)f Fk(jj)p Fo(f)11 b Fk(jj)2923 2942 y Fj(2)2961 2978 y Fp(.)51 b(Similarly)-8 b(,)32 b(\(4.13\))-7 3098 y(implies)37 b(the)j(\014rst)g(equalit)m(y)f(\(4.15\).)63 b(The)40 b(second)h(one)e(is)g(a)g(consequence)j(of)d(the)h(\014rst)g (b)s(ecause)-7 3219 y Fo(W)85 3234 y Fn(\006)144 3219 y Fp(\()p Fo(H)263 3234 y Fj(0)302 3219 y Fo(;)17 b(H)8 b Fp(;)17 b Ft(J)537 3183 y Fn(\003)537 3243 y(\007)595 3219 y Fp(\))28 b(=)f Fo(W)856 3234 y Fn(\006)916 3219 y Fp(\()p Fo(H)r(;)17 b(H)1162 3234 y Fj(0)1201 3219 y Fo(;)g Ft(J)1303 3234 y Fn(\007)1361 3219 y Fp(\))1399 3183 y Fn(\003)1439 3219 y Fp(.)43 b Fd(2)134 3430 y Fp(W)-8 b(e)33 b(are)g(no)m(w)g(able)f(to)g(c)m(hec)m(k)j(that)d(the)h (w)m(a)m(v)m(e)i(op)s(erators)d Fo(W)2397 3445 y Fn(\006)2456 3430 y Fp(\()p Fo(H)r(;)17 b(H)2702 3445 y Fj(0)2741 3430 y Fp(;)g Ft(J)2843 3445 y Fn(\006)2902 3430 y Fp(\))32 b(are)h(complete.)-7 3616 y Ft(Theorem)k(4.13)49 b Fe(Under)39 b(the)f(assumptions)g(of)g(The)-5 b(or)g(em)37 b Fp(4)p Fo(:)p Fp(8)h Fe(and)g(Pr)-5 b(op)g(osition)38 b Fp(4)p Fo(:)p Fp(12)g Fe(the)g(wave)-7 3736 y(op)-5 b(er)g(ators)32 b Fo(W)506 3751 y Fn(\006)565 3736 y Fp(\()p Fo(H)r(;)17 b(H)811 3751 y Fj(0)850 3736 y Fp(;)g Ft(J)952 3751 y Fn(\006)1011 3736 y Fp(\))32 b Fe(exist,)g(ar)-5 b(e)32 b(isometric)g(on)g(the)g(subsp)-5 b(ac)g(e)31 b Fo(E)2679 3751 y Fj(0)2719 3736 y Fp(\(\003\))p Fk(H)i Fe(and)e(ar)-5 b(e)32 b(c)-5 b(omplete,)-7 3857 y(i.e.,)34 b(e)-5 b(quality)36 b Fp(\(1)p Fo(:)p Fp(23\))e Fe(holds.)-7 4043 y(Pr)-5 b(o)g(of)43 b({)84 b Fp(By)42 b(Theorem)g(4.8,)h(Corollary)d(4.9)h(and) h(Prop)s(osition)d(4.12,)44 b(w)m(e)e(ha)m(v)m(e)h(only)e(to)g(pro)m(v) m(e)-7 4163 y(\(1.23\).)i(Since)33 b(the)g(op)s(erator)e Fo(W)1220 4178 y Fn(\006)1280 4163 y Fp(\()p Fo(H)1399 4178 y Fj(0)1438 4163 y Fo(;)17 b(H)8 b Fp(;)17 b Ft(J)1673 4127 y Fn(\003)1673 4188 y(\006)1731 4163 y Fp(\))32 b(exists,)i(for)e(an)m(y)h Fo(f)38 b Fk(2)28 b Fo(E)6 b Fp(\(\003\))p Fo(P)14 b Fk(H)q Fp(,)440 4382 y(lim)397 4442 y Fm(t)p Fn(!\0061)635 4382 y Fk(jj)p Ft(J)749 4341 y Fn(\003)749 4406 y(\006)807 4382 y Fo(e)852 4341 y Fn(\000)p Fm(iH)5 b(t)1024 4382 y Fo(f)33 b Fk(\000)22 b Fo(e)1249 4341 y Fn(\000)p Fm(iH)1386 4350 y Fl(0)1421 4341 y Fm(t)1451 4382 y Fo(f)1499 4397 y Fj(0)1538 4382 y Fk(jj)27 b Fp(=)h(0)p Fo(;)114 b(f)1963 4397 y Fj(0)2030 4382 y Fp(=)28 b Fo(W)2226 4397 y Fn(\006)2285 4382 y Fp(\()p Fo(H)2404 4397 y Fj(0)2443 4382 y Fo(;)17 b(H)8 b Fp(;)17 b Ft(J)2678 4341 y Fn(\003)2678 4406 y(\006)2736 4382 y Fp(\))p Fo(f)38 b Fk(2)28 b Fo(E)3026 4397 y Fj(0)3066 4382 y Fp(\(\003\))p Fk(H)q Fo(:)-7 4634 y Fp(This)33 b(implies)d(the)j(equalit)m(y)1083 4853 y(lim)1040 4913 y Fm(t)p Fn(!\0061)1278 4853 y Fk(jj)p Ft(J)1392 4868 y Fn(\006)1451 4853 y Ft(J)1509 4812 y Fn(\003)1509 4878 y(\006)1568 4853 y Fo(e)1613 4812 y Fn(\000)p Fm(iH)5 b(t)1784 4853 y Fo(f)33 b Fk(\000)23 b Ft(J)2023 4868 y Fn(\006)2082 4853 y Fo(e)2127 4812 y Fn(\000)p Fm(iH)2264 4821 y Fl(0)2299 4812 y Fm(t)2328 4853 y Fo(f)2376 4868 y Fj(0)2416 4853 y Fk(jj)k Fp(=)g(0)p Fo(:)798 b Fp(\(4.16\))-7 5118 y(On)28 b(the)g(other)f(hand,)i(according)e(to)g(the)h(second)h (relation)d(\(4.13\),)i Fk(jj)p Ft(J)2623 5082 y Fn(\003)2623 5142 y(\007)2681 5118 y Fo(e)2726 5082 y Fn(\000)p Fm(iH)5 b(t)2898 5118 y Fo(f)11 b Fk(jj)27 b(!)g Fp(0)g(as)h Fo(t)g Fk(!)f(\0061)-7 5238 y Fp(and)33 b(hence)1370 5358 y(lim)1327 5418 y Fm(t)p Fn(!\0061)1565 5358 y Fk(jj)p Ft(J)1679 5373 y Fn(\007)1737 5358 y Ft(J)1795 5317 y Fn(\003)1795 5383 y(\007)1854 5358 y Fo(e)1899 5317 y Fn(\000)p Fm(iH)5 b(t)2071 5358 y Fo(f)11 b Fk(jj)26 b Fp(=)i(0)p Fo(:)1084 b Fp(\(4.17\))1810 5634 y(21)p eop %%Page: 22 22 22 21 bop -7 52 a Fp(It)37 b(follo)m(ws)e(from)g(Prop)s(osition)f(4.3)i (that,)i(up)e(to)g(a)h(compact)f(term,)h Ft(J)2664 67 y Fn(\006)2722 52 y Ft(J)2780 16 y Fn(\003)2780 77 y(\006)2864 52 y Fp(+)25 b Ft(J)3023 67 y Fn(\007)3082 52 y Ft(J)3140 16 y Fn(\003)3140 77 y(\007)3235 52 y Fp(is)36 b(the)h(PDO)-7 172 y(with)28 b(sym)m(b)s(ol)g Fo(p)590 187 y Fj(0)629 172 y Fp(\()p Fo(\030)5 b Fp(\)\()p Fo(\020)842 136 y Fj(2)834 197 y Fn(\006)892 172 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))13 b(+)g Fo(\020)1268 136 y Fj(2)1260 197 y Fn(\007)1319 172 y Fp(\()p Fo(x;)k(\030)5 b Fp(\)\))p Fo( )1647 136 y Fj(2)1685 172 y Fp(\()p Fk(j)p Fo(\030)g Fk(j)1827 136 y Fj(2)1866 172 y Fp(\).)41 b(Cho)s(osing)28 b(\(see)i(Remark)d (4.11\))h Fo(\033)3243 187 y Fn(\006)3331 172 y Fp(suc)m(h)i(that)-7 293 y Fo(\033)52 256 y Fj(2)48 317 y Fn(\006)130 293 y Fp(+)22 b Fo(\033)287 256 y Fj(2)283 317 y Fn(\007)370 293 y Fp(=)27 b(1)33 b(and)f(taking)g(in)m(to)g(accoun)m(t)h(\(4.16\),) f(\(4.17\),)g(w)m(e)i(obtain)d(that)478 513 y(lim)435 572 y Fm(t)p Fn(!\0061)673 513 y Fk(jj)p Fo( )796 472 y Fj(2)835 513 y Fp(\()p Fo(H)962 472 y Fj(2)954 537 y(0)1023 513 y Fk(\000)23 b Fo(m)1208 472 y Fj(2)1247 513 y Fp(\))p Fo(E)1357 528 y Fj(0)1397 513 y Fp(\()p Fk(I)7 b Fp(\))p Fo(e)1579 472 y Fn(\000)p Fm(iH)e(t)1751 513 y Fo(f)33 b Fk(\000)23 b Ft(J)1990 528 y Fn(\006)2049 513 y Fo(e)2094 472 y Fn(\000)p Fm(iH)2231 481 y Fl(0)2265 472 y Fm(t)2295 513 y Fo(f)2343 528 y Fj(0)2382 513 y Fk(jj)k Fp(=)h(0)p Fo(;)114 b Fk(I)35 b Fp(=)28 b(\()p Fo(m;)17 b Fk(1)p Fp(\))p Fo(:)-7 766 y Fp(Since)33 b(the)g(op)s (erator)1009 887 y Fo( )1076 846 y Fj(2)1116 887 y Fp(\()p Fo(H)1243 846 y Fj(2)1304 887 y Fk(\000)22 b Fo(m)1488 846 y Fj(2)1528 887 y Fp(\))p Fo(E)6 b Fp(\()p Fk(I)h Fp(\))23 b Fk(\000)f Fo( )1970 846 y Fj(2)2010 887 y Fp(\()p Fo(H)2137 846 y Fj(2)2129 911 y(0)2198 887 y Fk(\000)g Fo(m)2382 846 y Fj(2)2422 887 y Fp(\))p Fo(E)2532 902 y Fj(0)2572 887 y Fp(\()p Fk(I)7 b Fp(\))-7 1061 y(is)32 b(compact)g(and)h Fo( )738 1025 y Fj(2)777 1061 y Fp(\()p Fo(H)904 1025 y Fj(2)966 1061 y Fk(\000)22 b Fo(m)1150 1025 y Fj(2)1190 1061 y Fp(\))p Fo(E)6 b Fp(\()p Fk(I)h Fp(\))p Fo(f)39 b Fp(=)27 b Fo(f)11 b Fp(,)33 b(this)f(leads)g(to)h(the)g(relation)1200 1281 y(lim)1157 1341 y Fm(t)p Fn(!\0061)1395 1281 y Fk(jj)p Fo(e)1496 1240 y Fn(\000)p Fm(iH)5 b(t)1668 1281 y Fo(f)32 b Fk(\000)23 b Ft(J)1906 1296 y Fn(\006)1965 1281 y Fo(e)2010 1240 y Fn(\000)p Fm(iH)2147 1249 y Fl(0)2182 1240 y Fm(t)2211 1281 y Fo(f)2259 1296 y Fj(0)2299 1281 y Fk(jj)k Fp(=)g(0)p Fo(:)915 b Fp(\(4.18\))-7 1540 y(Th)m(us)34 b Fo(f)39 b Fp(=)27 b Fo(W)522 1555 y Fn(\006)581 1540 y Fp(\()p Fo(H)r(;)17 b(H)827 1555 y Fj(0)866 1540 y Fp(;)g Ft(J)968 1555 y Fn(\006)1027 1540 y Fp(\))p Fo(f)1113 1555 y Fj(0)1152 1540 y Fp(.)44 b Fd(2)134 1752 y Ft(4.4.)144 b Fp(W)-8 b(a)m(v)m(e)41 b(op)s(erators)f(corresp)s(onding)h(to)f(the)g(negativ)m (e)h(part)f(of)g(the)h(sp)s(ectrum)g(can)f(b)s(e)-7 1873 y(considered)32 b(in)e(the)h(same)f(w)m(a)m(y)-8 b(.)45 b(In)31 b(this)f(case)i(the)f(functions)g(\010)2385 1831 y Fn(\000)2385 1894 y(\006)2475 1873 y Fp(are)g(again)e(de\014ned)j(b)m (y)g(form)m(ulas)-7 1993 y(\(3)p Fo(:)p Fp(20\),)e(\(3)p Fo(:)p Fp(21\))f({)h(\(3)p Fo(:)p Fp(23\),)g(\(3)p Fo(:)p Fp(26\),)g(if)f Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))30 b(in)f(de\014nition)g(\(1.12\))h(is)f(replaced)h(b)m(y)h Fk(\000)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\).)43 b(Similarly)-8 b(,)-7 2113 y(the)38 b(matrix-functions)d Fo(p)957 2072 y Fn(\000)957 2135 y(\006)1053 2113 y Fp(are)i(de\014ned)i(b)m(y)f (form)m(ulas)e(\(3.8\),)i(\(3.9\))e(if)g Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))37 b(in)g(\(3.8\))f(is)h(replaced)-7 2234 y(b)m(y)d Fk(\000)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\).)43 b(Then)34 b(the)f(op)s(erators)f Fo(J)1371 2192 y Fn(\000)1362 2255 y(\006)1463 2234 y Fp(are)h(giv)m(en)f(b)m(y)i (the)f(relations)301 2506 y(\()p Fo(J)402 2465 y Fn(\000)393 2531 y(\006)461 2506 y Fo(f)11 b Fp(\)\()p Fo(x)p Fp(\))28 b(=)g(\(2)p Fo(\031)t Fp(\))1005 2465 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1186 2370 y Fi(Z)1241 2596 y Fg(R)1289 2577 y Fc(d)1346 2506 y Fo(e)1391 2465 y Fm(i)p Fn(h)p Fm(x;\030)s Fn(i)p Fj(+)p Fm(i)p Fj(\010)1693 2435 y Ff(\000)1693 2486 y(\007)1745 2465 y Fj(\()p Fm(x;\030)s Fj(\))1897 2506 y Fo(p)1946 2465 y Fn(\000)1946 2531 y(\007)2005 2506 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))p Fo(\021)t Fp(\()p Fo(x)p Fp(\))p Fo(\033)2466 2521 y Fn(\007)2525 2506 y Fp(\()p Fk(h)h Fp(^)-55 b Fo(x;)2711 2480 y Fp(^)2701 2506 y Fo(\030)t Fk(i)p Fp(\))p Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)3034 2465 y Fj(2)3072 2506 y Fp(\))3131 2480 y(^)3110 2506 y Fo(f)11 b Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)g(:)-7 2785 y Fp(The)48 b(op)s(erators)f Ft(J)712 2744 y Fn(\000)712 2807 y(\006)818 2785 y Fp(are)g(obtained)g(if)f Fo(p)1564 2744 y Fn(\000)1564 2807 y(\007)1623 2785 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))46 b(is)h(replaced)g(here)h(b)m(y)g Fo(p)2829 2744 y Fn(\000)2829 2810 y Fj(0)2888 2785 y Fp(\()p Fo(\030)5 b Fp(\).)87 b(Theorem)47 b(4.13)-7 2906 y(remains)e(true)h(for)f(the)i(w)m(a)m(v)m(e)g(op)s(erators)f Fo(W)1721 2921 y Fn(\006)1780 2906 y Fp(\()p Fo(H)r(;)17 b(H)2026 2921 y Fj(0)2065 2906 y Fp(;)g Ft(J)2167 2864 y Fn(\000)2167 2927 y(\006)2226 2906 y Fp(\))45 b(if)g(\003)g(is)h(a)f (compact)g(subin)m(terv)-5 b(al)46 b(of)-7 3026 y(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\).)134 3188 y(Finally)31 b(w)m(e)j(note)f(that,)h(in)e(the)i(pro)s(of)e(of)h(the)h (existence)g(of)f(w)m(a)m(v)m(e)i(op)s(erators)e(\(Theorem)h(4.8\),)-7 3308 y(Theorem)48 b(2.15)e(can)i(b)s(e)g(substituted)g(b)m(y)g(the)g (tec)m(hnically)e(simpler)g(Theorem)i(2.14.)87 b(Indeed,)-7 3429 y(neglecting)31 b(\014rst)h(the)h(short-range)e(part)h Fo(V)1603 3444 y Fm(S)1685 3429 y Fp(and)g(setting)g Fo(H)2275 3444 y Fm(L)2354 3429 y Fp(=)c Fo(H)2539 3444 y Fj(0)2599 3429 y Fp(+)20 b Fo(V)2752 3444 y Fm(L)2804 3429 y Fp(,)32 b(w)m(e)h(obtain)e(that)g(w)m(a)m(v)m(e)-7 3549 y(op)s(erators)37 b(\(4.10\))e(\(4.11\))h(exist)h(for)f(the)h (triples)f Fo(H)1944 3564 y Fj(0)1983 3549 y Fo(;)17 b(H)2108 3564 y Fm(L)2160 3549 y Fo(;)g(J)2258 3564 y Fm(\034)2337 3549 y Fp(where)38 b Fo(\034)46 b Fp(=)34 b(\\)25 b(+)g(")36 b(and)h Fo(\034)46 b Fp(=)34 b(\\)25 b Fk(\000)g Fp(".)-7 3669 y(On)41 b(the)g(other)g(hand,)j(using)c(only) h(the)g(limiting)36 b(absorption)41 b(principle)e(for)h(the)i(op)s (erators)e Fo(H)3673 3684 y Fm(L)-7 3790 y Fp(and)g Fo(H)49 b Fp(=)40 b Fo(H)517 3805 y Fm(L)597 3790 y Fp(+)27 b Fo(V)757 3805 y Fm(S)808 3790 y Fp(,)42 b(w)m(e)f(see)h(that)e(the)g(w) m(a)m(v)m(e)j(op)s(erators)d Fo(W)2366 3805 y Fn(\006)2425 3790 y Fp(\()p Fo(H)r(;)17 b(H)2671 3805 y Fm(L)2723 3790 y Fp(\))40 b(and)g Fo(W)3090 3805 y Fn(\006)3149 3790 y Fp(\()p Fo(H)3268 3805 y Fm(L)3320 3790 y Fo(;)17 b(H)3445 3805 y Fj(0)3484 3790 y Fp(\))40 b(also)-7 3910 y(exist.)i(Therefore,)29 b(b)m(y)e(the)g(m)m(ultiplication)22 b(theorem)k(\(see)h(e.g.)42 b([20]\),)28 b(the)e(w)m(a)m(v)m(e)j(op)s (erators)d(\(4.10\),)-7 4030 y(\(4.11\))32 b(exist)h(and)897 4151 y Fo(W)989 4166 y Fn(\006)1048 4151 y Fp(\()p Fo(H)r(;)17 b(H)1294 4166 y Fj(0)1333 4151 y Fp(;)g Fo(J)1431 4166 y Fm(\034)1474 4151 y Fp(\))27 b(=)h Fo(W)1735 4166 y Fn(\006)1794 4151 y Fp(\()p Fo(H)r(;)17 b(H)2040 4166 y Fm(L)2092 4151 y Fp(\))p Fo(W)2222 4166 y Fn(\006)2281 4151 y Fp(\()p Fo(H)2400 4166 y Fm(L)2452 4151 y Fo(;)g(H)2577 4166 y Fj(0)2616 4151 y Fp(;)g Fo(J)2714 4166 y Fm(\034)2756 4151 y Fp(\))p Fo(;)886 4325 y(W)978 4340 y Fn(\006)1037 4325 y Fp(\()p Fo(H)1156 4340 y Fj(0)1195 4325 y Fo(;)g(H)8 b Fp(;)17 b Fo(J)1435 4284 y Fn(\003)1426 4350 y Fm(\034)1474 4325 y Fp(\))27 b(=)h Fo(W)1735 4340 y Fn(\006)1794 4325 y Fp(\()p Fo(H)1913 4340 y Fj(0)1952 4325 y Fo(;)17 b(H)2077 4340 y Fm(L)2129 4325 y Fp(\))p Fo(W)2259 4340 y Fn(\006)2318 4325 y Fp(\()p Fo(H)2437 4340 y Fm(L)2489 4325 y Fo(;)g(H)8 b Fp(;)17 b Fo(J)2729 4284 y Fn(\003)2720 4350 y Fm(\034)2767 4325 y Fp(\))p Fo(:)-7 4500 y Fp(Th)m(us)34 b(the)f(w)m(a)m(v)m(e)i(op) s(erators)d Fo(W)1170 4515 y Fn(\006)1229 4500 y Fp(\()p Fo(H)r(;)17 b(H)1475 4515 y Fj(0)1514 4500 y Fp(;)g Fo(J)1612 4515 y Fn(\006)1671 4500 y Fp(\))32 b(are)h(isometric)e(and)h (complete.)-7 4861 y Ft(5.)112 b(THE)37 b(ASYMPTOTICS)g(OF)h(SOLUTIONS) g(F)m(OR)f(LAR)m(GE)g(TIMES)-7 5122 y Fp(Here)31 b(w)m(e)g(\014nd)g (the)g(asymptotics)f(as)g Fo(t)e Fk(!)g(\0061)i Fp(of)g(a)g(solution)f Fo(u)p Fp(\()p Fo(x;)17 b(t)p Fp(\))27 b(=)h(\(exp\()p Fk(\000)p Fo(iH)8 b(t)p Fp(\))p Fo(f)j Fp(\)\()p Fo(x)p Fp(\))31 b(of)f(the)-7 5256 y(time-dep)s(enden)m(t)f(Dirac)f(equation)h (for)g(an)g(arbitrary)f Fo(f)38 b Fk(2)28 b(H)16 b(\011)f(H)2485 5205 y Fj(\()p Fm(p)p Fj(\))2484 5283 y Fm(H)2581 5256 y Fp(.)42 b(As)30 b(usual)f(w)m(e)h(supp)s(ose)h(that)-7 5376 y Fo(f)38 b Fk(2)29 b Fo(E)6 b Fp(\()p Fk(I)351 5340 y Fj(+)410 5376 y Fp(\))p Fk(H)34 b Fp(and)e(mak)m(e)h(commen)m (ts)g(on)f(the)h(case)h Fo(f)k Fk(2)28 b Fo(E)6 b Fp(\()p Fk(I)2336 5340 y Fn(\000)2396 5376 y Fp(\))p Fk(H)33 b Fp(at)f(the)h(end)h(of)e(the)h(section.)1810 5634 y(22)p eop %%Page: 23 23 23 22 bop 134 52 a Ft(5.1.)111 b Fp(Let)35 b(us)h(pro)s(ceed)g(from)e (Theorem)h(4.13.)51 b(According)35 b(to)g(\(4.18\))f(the)i(problem)d (reduces)-7 172 y(to)f(the)h(study)h(as)f Fo(t)28 b Fk(!)f(\0061)33 b Fp(of)f(the)h(in)m(tegral)259 428 y(\()p Ft(J)355 443 y Fn(\006)413 428 y Fo(e)458 387 y Fn(\000)p Fm(iH)595 396 y Fl(0)630 387 y Fm(t)660 428 y Fo(f)708 443 y Fj(0)747 428 y Fp(\)\()p Fo(x)p Fp(\))28 b(=)g(\(2)p Fo(\031)t Fp(\))1232 387 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)1396 428 y Fo(\021)t Fp(\()p Fo(x)p Fp(\))1596 293 y Fi(Z)1651 518 y Fg(R)1699 499 y Fl(3)1754 428 y Fo(e)1799 387 y Fm(i)p Fn(h)p Fm(x;\030)s Fn(i)p Fj(+)p Fm(i)p Fj(\010)2101 396 y Ff(\006)2154 387 y Fj(\()p Fm(x;\030)s Fj(\))p Fn(\000)p Fm(i\027)t Fj(\()p Fm(\030)s Fj(\))p Fm(t)2537 428 y Fo(\033)2592 443 y Fn(\006)2652 428 y Fp(\()p Fk(h)6 b Fp(^)-55 b Fo(x;)2838 402 y Fp(^)2828 428 y Fo(\030)t Fk(i)p Fp(\))p Fo(g)2999 443 y Fj(0)3038 428 y Fp(\()p Fo(\030)5 b Fp(\))p Fo(d\030)269 b Fp(\(5.1\))-7 689 y(where)970 809 y Fo(g)1017 824 y Fj(0)1056 809 y Fp(\()p Fo(\030)5 b Fp(\))27 b(=)h Fo( )t Fp(\()p Fk(j)p Fo(\030)5 b Fk(j)1520 768 y Fj(2)1558 809 y Fp(\))p Fo(p)1645 824 y Fj(0)1684 809 y Fp(\()p Fo(\030)g Fp(\))1829 783 y(^)1808 809 y Fo(f)1856 824 y Fj(0)1895 809 y Fp(\()p Fo(\030)g Fp(\))27 b Fk(2)h Fo(C)2217 768 y Fn(1)2210 834 y Fj(0)2292 809 y Fp(\()p Fh(R)2396 768 y Fj(3)2463 809 y Fk(n)22 b(f)p Fp(0)p Fk(g)p Fp(\))p Fo(:)-7 981 y Fp(The)34 b(asymptotics)e(of) g(this)g(in)m(tegral)f(can)i(b)s(e)g(found)g(b)m(y)g(the)g(stationary)f (phase)h(metho)s(d.)43 b(Set)875 1194 y(\002\()p Fo(x;)17 b(\030)5 b(;)17 b(t)p Fp(\))27 b(=)h Fk(h)p Fo(x;)17 b(\030)5 b Fk(i)21 b Fp(+)h(\010)1798 1209 y Fn(\006)1857 1194 y Fp(\()p Fo(x;)17 b(\030)5 b Fp(\))22 b Fk(\000)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))p Fo(t;)81 b Fk(\006)p Fo(t)29 b(>)e Fp(0)p Fo(:)682 b Fp(\(5.2\))-7 1407 y(The)34 b(stationary)e(p)s(oin)m(t)f Fo(\030)960 1371 y Fj(\()p Fm(st)p Fj(\))1104 1407 y Fp(=)d Fo(\030)1256 1371 y Fj(\()p Fm(st)p Fj(\))1373 1407 y Fp(\()p Fo(x;)17 b(t)p Fp(\))32 b(of)g(this)h(function)f(is)g(determined)g(b)m(y)i(the)f (equation)1018 1620 y Fo(x)22 b Fp(+)g Fk(r)1276 1635 y Fm(\030)1314 1620 y Fp(\010)1384 1635 y Fn(\006)1443 1620 y Fp(\()p Fo(x;)17 b(\030)1628 1579 y Fj(\()p Fm(st)p Fj(\))1745 1620 y Fp(\))22 b Fk(\000)h Fo(\027)6 b Fp(\()p Fo(\030)2045 1579 y Fj(\()p Fm(st)p Fj(\))2162 1620 y Fp(\))2200 1579 y Fn(\000)p Fj(1)2294 1620 y Fo(\030)2342 1579 y Fj(\()p Fm(st)p Fj(\))2459 1620 y Fo(t)27 b Fp(=)h(0)p Fo(;)824 b Fp(\(5.3\))-7 1834 y(whic)m(h)33 b(can)g(b)s(e)g(rewritten)g (as)442 2047 y Fo(\030)490 2006 y Fj(\()p Fm(st)p Fj(\))606 2047 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(=)g Fk(\006)p Fo(m)p Fp(\()p Fo(x)23 b Fp(+)f Fk(r)1407 2062 y Fm(\030)1445 2047 y Fp(\010)1515 2062 y Fn(\006)1575 2047 y Fp(\()p Fo(x;)17 b(\030)1760 2006 y Fj(\()p Fm(st)p Fj(\))1876 2047 y Fp(\)\)\()p Fo(t)2025 2006 y Fj(2)2087 2047 y Fk(\000)22 b(j)p Fo(x)h Fp(+)f Fk(r)2473 2062 y Fm(\030)2510 2047 y Fp(\010)2580 2062 y Fn(\006)2640 2047 y Fp(\()p Fo(x;)17 b(\030)2825 2006 y Fj(\()p Fm(st)p Fj(\))2942 2047 y Fp(\))p Fk(j)3008 2006 y Fj(2)3047 2047 y Fp(\))3085 2006 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)3249 2047 y Fo(:)249 b Fp(\(5.4\))-7 2260 y(Using)37 b(estimates)h(\(3.6\))f(it)g(is)g(easy) i(to)e(c)m(hec)m(k)j(that)d(for)h(su\016cien)m(tly)g(large)f Fk(j)p Fo(x)p Fk(j)p Fo(;)17 b Fk(j)p Fo(t)p Fk(j)36 b Fp(and)i Fk(j)p Fo(x)p Fk(j)e Fo(<)h Fk(j)p Fo(t)p Fk(j)p Fp(,)-7 2381 y(equation)32 b(\(5.4\))f(has)i(a)f(unique)g (solution)f(whic)m(h)h(can)h(b)s(e)f(obtained)g(b)m(y)h(iterations.)42 b(In)32 b(particular,)-7 2501 y(starting)42 b(from)g Fk(\006)p Fo(mx)p Fp(\()p Fo(t)898 2465 y Fj(2)968 2501 y Fk(\000)29 b(j)p Fo(x)p Fk(j)1185 2465 y Fj(2)1225 2501 y Fp(\))1263 2465 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)1470 2501 y Fp(\(the)43 b(exact)h(solution)e(for)g(the)h(free)g(case)h Fo(H)53 b Fp(=)45 b Fo(H)3421 2516 y Fj(0)3503 2501 y Fp(when)-7 2621 y(\010)63 2636 y Fn(\006)150 2621 y Fp(=)28 b(0\))k(w)m(e)i(see)f(that)960 2835 y Fo(\030)1008 2793 y Fj(\()p Fm(st)p Fj(\))1125 2835 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(=)f Fk(\006)p Fo(mx)p Fp(\()p Fo(t)1756 2793 y Fj(2)1819 2835 y Fk(\000)c(j)p Fo(x)p Fk(j)2030 2793 y Fj(2)2069 2835 y Fp(\))2107 2793 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2294 2835 y Fp(+)f Fo(O)s Fp(\()p Fk(j)p Fo(t)p Fk(j)2599 2793 y Fn(\000)p Fm(\032)2693 2835 y Fp(\))p Fo(:)767 b Fp(\(5.5\))-7 3048 y(In)31 b(the)g(ball)d Fk(j)p Fo(x)p Fk(j)g(\024)g Fo(c)752 3063 y Fj(1)791 3048 y Fk(j)p Fo(t)p Fk(j)i Fp(and)h(outside)g(of)f(the)h(ball)d Fk(j)p Fo(x)p Fk(j)g(\025)g Fo(c)2183 3063 y Fj(2)2222 3048 y Fk(j)p Fo(t)p Fk(j)i Fp(where)i Fo(c)2665 3063 y Fj(1)2732 3048 y Fp(=)c Fo(c)2878 3063 y Fj(1)2917 3048 y Fp(\()p Fo(f)11 b Fp(\))30 b(and)h Fo(c)3312 3063 y Fj(2)3379 3048 y Fp(=)c Fo(c)3524 3063 y Fj(2)3564 3048 y Fp(\()p Fo(f)11 b Fp(\),)-7 3168 y(w)m(e)34 b(ha)m(v)m(e,)g(for) e(an)g(arbitrary)g Fo(N)10 b Fp(,)33 b(the)g(estimate)1010 3381 y Fk(j)p Fp(\()p Ft(J)1134 3396 y Fn(\006)1192 3381 y Fo(e)1237 3340 y Fn(\000)p Fm(iH)1374 3349 y Fl(0)1409 3340 y Fm(t)1439 3381 y Fo(f)1487 3396 y Fj(0)1526 3381 y Fp(\)\()p Fo(x)p Fp(\))p Fk(j)28 b(\024)g Fo(C)1926 3396 y Fm(N)1993 3381 y Fp(\(1)22 b(+)g Fk(j)p Fo(x)p Fk(j)g Fp(+)g Fk(j)p Fo(t)p Fk(j)p Fp(\))2560 3340 y Fn(\000)p Fm(N)2681 3381 y Fo(:)-7 3595 y Fp(This)27 b(estimate)e(can)i(b)s(e)g(obtained)f(b)m(y)h(a)f(direct)g(in)m (tegration)f(b)m(y)i(parts.)42 b(Th)m(us)28 b(for)e(a)g(giv)m(en)h (function)14 3689 y(^)-7 3715 y Fo(f)41 3730 y Fj(0)108 3715 y Fk(2)h Fo(C)279 3679 y Fn(1)272 3740 y Fj(0)354 3715 y Fp(\()p Fh(R)458 3679 y Fj(3)525 3715 y Fk(n)22 b(f)p Fp(0)p Fk(g)p Fp(\))32 b(w)m(e)i(ma)m(y)e(supp)s(ose)i(that)1071 3928 y(0)28 b Fo(<)f(c)1293 3943 y Fj(1)1333 3928 y Fk(j)p Fo(t)p Fk(j)g Fo(<)g Fk(j)p Fo(x)p Fk(j)h Fo(<)f(c)1838 3943 y Fj(2)1878 3928 y Fk(j)p Fo(t)p Fk(j)p Fo(;)81 b Fp(where)34 b Fo(c)2401 3943 y Fj(2)2468 3928 y Fo(<)27 b Fp(1)p Fo(:)878 b Fp(\(5.6\))134 4181 y(Let)33 b(us)g(in)m(tro)s (duce)g(the)g(Hessian)g(matrix)e(of)h(function)g(\(5.2\))501 4454 y Fb(h)p Fp(\()p Fo(\030)5 b(;)17 b(x;)g(t)p Fp(\))27 b(=)h(Hess)18 b(\002\()p Fo(x;)f(\030)5 b(;)17 b(t)p Fp(\))27 b(=)1704 4313 y Fi(\032)1880 4386 y Fo(@)1936 4350 y Fj(2)p 1789 4431 279 4 v 1789 4522 a Fo(@)5 b(\030)1888 4537 y Fm(j)1925 4522 y Fo(@)g(\030)2024 4537 y Fm(k)2077 4454 y Fp(\002\()p Fo(x;)17 b(\030)5 b(;)17 b(t)p Fp(\))2455 4313 y Fi(\033)2546 4454 y Fo(;)114 b(j;)17 b(k)31 b Fp(=)c(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)307 b Fp(\(5.7\))-7 4720 y(and)33 b(set)1287 4841 y(\012\()p Fo(x;)17 b(t)p Fp(\))29 b(=)e(\002\()p Fo(x;)17 b(\030)1960 4799 y Fj(\()p Fm(st)p Fj(\))2077 4841 y Fp(\()p Fo(x;)g(t)p Fp(\))p Fo(;)g(t)p Fp(\))p Fo(:)1094 b Fp(\(5.8\))-7 5012 y(Applying)31 b(the)i(stationary)e(phase)i(metho)s(d)e(to)h(in)m (tegral)e(\(5.1\),)i(w)m(e)h(\014nd)f(that)g(in)f(the)i(region)e (\(5.6\))331 5240 y(\()p Ft(J)427 5255 y Fn(\006)485 5240 y Fo(e)530 5199 y Fn(\000)p Fm(iH)667 5208 y Fl(0)702 5199 y Fm(t)732 5240 y Fo(f)780 5255 y Fj(0)819 5240 y Fp(\)\()p Fo(x)p Fp(\))84 b(=)g Fk(j)p Fp(det)17 b Fb(h)p Fp(\()p Fo(\030)1550 5199 y Fj(\()p Fm(st)p Fj(\))1666 5240 y Fo(;)g(x;)g(t)p Fp(\))p Fk(j)1910 5199 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2075 5240 y Fo(e)2120 5199 y Fm(i)2154 5172 y Fc(\031)p 2154 5184 38 3 v 2158 5225 a Fl(4)2214 5199 y Fj(sgn)12 b Fa(h)p Fj(\()p Fm(\030)2425 5175 y Fl(\()p Fc(st)p Fl(\))2530 5199 y Fm(;x;t)p Fj(\))1071 5385 y Fk(\002)84 b Fo(e)1277 5344 y Fm(i)p Fj(\012\()p Fm(x;t)p Fj(\))1496 5385 y Fo(\020)1539 5400 y Fn(\006)1598 5385 y Fp(\()p Fo(x;)17 b(\030)1783 5344 y Fj(\()p Fm(st)p Fj(\))1899 5385 y Fp(\()p Fo(x;)g(t)p Fp(\)\))p Fo(g)2194 5400 y Fj(0)2234 5385 y Fp(\()p Fo(\030)2320 5344 y Fj(\()p Fm(st)p Fj(\))2436 5385 y Fp(\()p Fo(x;)g(t)p Fp(\)\)\(1)22 b(+)g Fo(o)p Fp(\(1\)\))p Fo(:)397 b Fp(\(5.9\))1810 5634 y(23)p eop %%Page: 24 24 24 23 bop -7 52 a Fp(Clearly)-8 b(,)414 385 y(Hess)18 b Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))27 b(=)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))1111 344 y Fn(\000)p Fj(3)1221 184 y Fi(0)1221 364 y(@)1350 263 y Fo(m)1435 227 y Fj(2)1497 263 y Fp(+)22 b Fo(\030)1643 227 y Fj(2)1638 288 y(2)1704 263 y Fp(+)g Fo(\030)1850 227 y Fj(2)1845 288 y(3)2120 263 y Fk(\000)p Fo(\030)2240 278 y Fj(1)2280 263 y Fo(\030)2323 278 y Fj(2)2742 263 y Fk(\000)p Fo(\030)2862 278 y Fj(1)2902 263 y Fo(\030)2945 278 y Fj(3)1499 384 y Fk(\000)p Fo(\030)1619 399 y Fj(1)1658 384 y Fo(\030)1701 399 y Fj(2)1972 384 y Fo(m)2057 348 y Fj(2)2119 384 y Fp(+)g Fo(\030)2265 348 y Fj(2)2260 408 y(1)2326 384 y Fp(+)g Fo(\030)2472 348 y Fj(2)2467 408 y(3)2742 384 y Fk(\000)p Fo(\030)2862 399 y Fj(2)2902 384 y Fo(\030)2945 399 y Fj(3)1499 504 y Fk(\000)p Fo(\030)1619 519 y Fj(1)1658 504 y Fo(\030)1701 519 y Fj(3)2120 504 y Fk(\000)p Fo(\030)2240 519 y Fj(2)2280 504 y Fo(\030)2323 519 y Fj(3)2594 504 y Fo(m)2679 468 y Fj(2)2741 504 y Fp(+)g Fo(\030)2887 468 y Fj(2)2882 529 y(1)2948 504 y Fp(+)g Fo(\030)3094 468 y Fj(2)3089 529 y(2)3174 184 y Fi(1)3174 364 y(A)3278 385 y Fo(;)-7 717 y Fp(and)33 b(hence)700 838 y(det)17 b(Hess)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))28 b(=)f Fo(m)1456 797 y Fj(2)1496 838 y Fp(\()p Fo(m)1619 797 y Fj(2)1681 838 y Fp(+)22 b Fk(j)p Fo(\030)5 b Fk(j)1883 797 y Fj(2)1921 838 y Fp(\))1959 797 y Fn(\000)p Fj(5)p Fm(=)p Fj(2)2124 838 y Fo(;)114 b Fp(sgn)17 b(Hess)h Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))28 b(=)f(3)p Fo(:)-7 1012 y Fp(Relation)k(\(5.2\))h(implies)e (that)195 1232 y Fk(j)p Fp(det)17 b Fb(h)p Fp(\()p Fo(\030)5 b(;)17 b(x;)g(t)p Fp(\))p Fk(j)26 b Fp(=)i Fo(m)972 1191 y Fj(2)1012 1232 y Fp(\()p Fo(m)1135 1191 y Fj(2)1196 1232 y Fp(+)22 b Fk(j)p Fo(\030)5 b Fk(j)1398 1191 y Fj(2)1437 1232 y Fp(\))1475 1191 y Fn(\000)p Fj(5)p Fm(=)p Fj(2)1639 1232 y Fk(j)p Fo(t)p Fk(j)1730 1191 y Fj(3)1769 1232 y Fp(\(1)22 b(+)g Fo(O)s Fp(\()p Fk(j)p Fo(t)p Fk(j)2183 1191 y Fn(\000)p Fm(\032)2277 1232 y Fp(\)\))p Fo(;)98 b Fp(sgn)17 b Fb(h)p Fp(\()p Fo(\030)5 b(;)17 b(x;)g(t)p Fp(\))27 b(=)h Fk(\007)p Fp(3)p Fo(:)202 b Fp(\(5.10\))-7 1452 y(In)33 b(particular,)e(it)g(follo)m(ws)h(from)f(\(5.5\))h(that) 623 1672 y Fk(j)p Fp(det)17 b Fb(h)p Fp(\()p Fo(\030)941 1631 y Fj(\()p Fm(st)p Fj(\))1058 1672 y Fp(\()p Fo(x;)g(t)p Fp(\))p Fo(;)g(x;)g(t)p Fp(\))p Fk(j)27 b Fp(=)h Fo(m)1728 1631 y Fn(\000)p Fj(3)1822 1672 y Fo(t)1857 1631 y Fn(\000)p Fj(2)1952 1672 y Fp(\()p Fo(t)2025 1631 y Fj(2)2087 1672 y Fk(\000)22 b(j)p Fo(x)p Fk(j)2297 1631 y Fj(2)2336 1672 y Fp(\))2374 1631 y Fj(5)p Fm(=)p Fj(2)2484 1672 y Fp(\(1)g(+)g Fo(O)s Fp(\()p Fk(j)p Fo(t)p Fk(j)2898 1631 y Fn(\000)p Fm(\032)2992 1672 y Fp(\)\))p Fo(:)-7 1892 y Fp(F)-8 b(urthermore,)30 b(according)g(to)g(\(5.5\),)g Fo(\020)1438 1907 y Fn(\006)1496 1892 y Fp(\()p Fo(x;)17 b(\030)1681 1856 y Fj(\()p Fm(st)p Fj(\))1798 1892 y Fp(\()p Fo(x;)g(t)p Fp(\)\))28 b(=)f(1)j(for)g(su\016cien)m(tly)h (large)e Fo(t)p Fp(,)i Fk(\006)p Fo(t)d(>)g Fp(0,)i(and)629 2161 y(lim)586 2220 y Fm(t)p Fn(!\0061)824 2025 y Fi(Z)879 2251 y Fn(j)p Fm(x)p Fn(j\024j)p Fm(t)p Fn(j)1098 2161 y Fk(j)p Fo(g)1173 2176 y Fj(0)1212 2161 y Fp(\()p Fo(\030)1298 2120 y Fj(\()p Fm(st)p Fj(\))1415 2161 y Fp(\()p Fo(x;)17 b(t)p Fp(\)\))22 b Fk(\000)h Fo(g)1832 2176 y Fj(0)1871 2161 y Fp(\()p Fk(\006)p Fo(mx)p Fp(\()p Fo(t)2199 2120 y Fj(2)2262 2161 y Fk(\000)f(j)p Fo(x)p Fk(j)2472 2120 y Fj(2)2512 2161 y Fp(\))2550 2120 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2714 2161 y Fp(\))p Fk(j)2780 2120 y Fj(2)2820 2161 y Fo(dx)27 b Fp(=)h(0)p Fo(:)134 2491 y Fp(Let)33 b(us)g(no)m(w)g(in)m(tro)s(duce)g(a)f(family)e(of)i(unitary)h(op)s (erators)f Fo(U)2403 2506 y Fj(0)2443 2491 y Fp(\()p Fo(t)p Fp(\))g(b)m(y)i(the)f(form)m(ula)43 2711 y(\()p Fo(U)147 2726 y Fj(0)187 2711 y Fp(\()p Fo(t)p Fp(\))p Fo(f)346 2726 y Fj(0)385 2711 y Fp(\)\()p Fo(x)p Fp(\))28 b(=)g Fo(m)771 2670 y Fj(3)p Fm(=)p Fj(2)881 2711 y Fk(j)p Fo(t)p Fk(j)p Fp(\()p Fo(t)1045 2670 y Fj(2)1092 2711 y Fk(\000)8 b(j)p Fo(x)p Fk(j)1288 2670 y Fj(2)1327 2711 y Fp(\))1365 2670 y Fn(\000)p Fj(5)p Fm(=)p Fj(4)1530 2711 y Fo(e)1575 2670 y Fn(\007)p Fj(3)p Fm(i\031)r(=)p Fj(4)1807 2711 y Fo(e)1852 2670 y Fm(i)p Fj(\012\()p Fm(x;t)p Fj(\))2093 2685 y Fp(^)2071 2711 y Fo(f)2119 2726 y Fj(0)2159 2711 y Fp(\()p Fk(\006)p Fo(mx)p Fp(\()p Fo(t)2487 2670 y Fj(2)2535 2711 y Fk(\000)g(j)p Fo(x)p Fk(j)2731 2670 y Fj(2)2771 2711 y Fp(\))2809 2670 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2974 2711 y Fp(\))p Fo(;)67 b Fk(\006)p Fo(t)29 b(>)e Fp(0)p Fo(;)50 b Fp(\(5.11\))-7 2931 y(for)40 b Fk(j)p Fo(x)p Fk(j)h Fo(<)g Fk(j)p Fo(t)p Fk(j)f Fp(and)g(\()p Fo(U)851 2946 y Fj(0)891 2931 y Fp(\()p Fo(t)p Fp(\))p Fo(f)1050 2946 y Fj(0)1089 2931 y Fp(\)\()p Fo(x)p Fp(\))i(=)f(0)f(for) g Fk(j)p Fo(x)p Fk(j)g(\025)i(j)p Fo(t)p Fk(j)p Fp(.)67 b(W)-8 b(e)40 b(recall)f(that)i(the)f(phases)i(\012\()p Fo(x;)17 b(t)p Fp(\))41 b(are)-7 3052 y(de\014ned)34 b(b)m(y)g(form)m(ulas)d(\(5.2\),)h(\(5.3\))g(and)h(\(5.8\).)134 3214 y(The)h(results)f(obtained)f(allo)m(w)f(us)i(to)f(form)m(ulate)f (the)i(follo)m(wing)d(result.)-7 3376 y Ft(Lemma)37 b(5.1)49 b Fe(F)-7 b(or)34 b(any)h Fo(f)999 3391 y Fj(0)1066 3376 y Fk(2)28 b Fo(E)1232 3391 y Fj(0)1272 3376 y Fp(\()p Fk(I)7 b Fp(\))p Fk(H)q Fe(,)927 3596 y Fp(lim)884 3655 y Fm(t)p Fn(!\0061)1122 3596 y Fk(jj)p Ft(J)1236 3611 y Fn(\006)1295 3596 y Fo(e)1340 3554 y Fn(\000)p Fm(iH)1477 3563 y Fl(0)1511 3554 y Fm(t)1541 3596 y Fo(f)1589 3611 y Fj(0)1651 3596 y Fk(\000)22 b Fo(U)1816 3611 y Fj(0)1856 3596 y Fp(\()p Fo(t)p Fp(\))p Fo( )t Fp(\()p Fo(H)2161 3554 y Fj(2)2153 3620 y(0)2222 3596 y Fk(\000)h Fo(m)2407 3554 y Fj(2)2446 3596 y Fp(\))p Fo(f)2532 3611 y Fj(0)2572 3596 y Fk(jj)k Fp(=)g(0)p Fo(:)134 3891 y Fp(No)m(w)33 b(w)m(e)h(can)f(reform)m(ulate)e(Theorem)i(4.13)f(in)g(the)h(follo)m (wing)d(form.)-7 4078 y Ft(Theorem)37 b(5.2)49 b Fe(Supp)-5 b(ose)28 b(that)i Fo(V)49 b Fp(=)28 b Fo(V)1486 4093 y Fm(S)1545 4078 y Fp(+)9 b Fo(V)1687 4093 y Fm(L)1768 4078 y Fe(wher)-5 b(e)29 b Fo(V)2095 4093 y Fm(S)2175 4078 y Fe(satis\014es)f Fp(\(2)p Fo(:)p Fp(6\))g Fe(and)h Fo(V)3005 4093 y Fm(L)3086 4078 y Fe(satis\014es)f Fp(\(1)p Fo(:)p Fp(18\))p Fe(.)-7 4198 y(L)-5 b(et)39 b(the)g(phase)f Fp(\012\()p Fo(x;)17 b(t)p Fp(\))39 b Fe(b)-5 b(e)38 b(de\014ne)-5 b(d)38 b(by)h(formulas)f Fp(\(5)p Fo(:)p Fp(2\))p Fe(,)h Fp(\(5)p Fo(:)p Fp(8\))f Fe(wher)-5 b(e)38 b Fo(\030)2752 4162 y Fj(\()p Fm(st)p Fj(\))2869 4198 y Fp(\()p Fo(x;)17 b(t)p Fp(\))38 b Fe(is)h(the)g(solution)-7 4318 y(of)c(e)-5 b(quation)34 b Fp(\(5)p Fo(:)p Fp(4\))p Fe(.)44 b(L)-5 b(et)36 b Fo(U)1006 4333 y Fj(0)1045 4318 y Fp(\()p Fo(t)p Fp(\))f Fe(b)-5 b(e)35 b(the)g(op)-5 b(er)g(ator)34 b Fp(\(5)p Fo(:)p Fp(11\))p Fe(.)44 b(Then)34 b(the)h(wave)f(op)-5 b(er)g(ators)1189 4538 y Ft(W)1305 4553 y Fn(\006)1392 4538 y Fp(=)27 b Fo(s)22 b Fk(\000)66 b Fp(lim)1663 4598 y Fm(t)p Fn(!\0061)1901 4538 y Fo(e)1946 4497 y Fm(iH)5 b(t)2063 4538 y Fo(U)2129 4553 y Fj(0)2169 4538 y Fp(\()p Fo(t)p Fp(\))p Fo(E)2352 4553 y Fj(0)2392 4538 y Fp(\()p Fk(I)i Fp(\))-7 4798 y Fe(exist,)33 b(ar)-5 b(e)33 b(isometric)f(and)g Fp(Ran)17 b Ft(W)1332 4813 y Fn(\006)1418 4798 y Fp(=)28 b Fo(E)6 b Fp(\()p Fk(I)h Fp(\))p Fo(P)14 b Fk(H)q Fe(.)44 b(F)-7 b(urthermor)i(e,)32 b Ft(W)2680 4813 y Fn(\006)2772 4798 y Fe(ar)-5 b(e)32 b(r)-5 b(elate)g(d)33 b(to)g(the)g(wave)-7 4918 y(op)-5 b(er)g(ators)34 b(of)h(The)-5 b(or)g(em)34 b Fp(4)p Fo(:)p Fp(13)g Fe(by)h(the)g(formula)f Ft(W)1911 4933 y Fn(\006)1970 4918 y Fo( )t Fp(\()p Fo(H)2164 4882 y Fj(2)2156 4943 y(0)2225 4918 y Fk(\000)23 b Fo(m)2410 4882 y Fj(2)2450 4918 y Fp(\))k(=)h Fo(W)2711 4933 y Fn(\006)2770 4918 y Fp(\()p Fo(H)r(;)17 b(H)3016 4933 y Fj(0)3055 4918 y Fp(;)g Ft(J)3157 4933 y Fn(\006)3216 4918 y Fp(\))p Fe(.)134 5105 y Fp(It)33 b(follo)m(ws)e(from)g(Theorem)i(5.2)g(that)f (for)g(an)m(y)h Fo(E)6 b Fp(\()p Fk(I)h Fp(\))p Fo(P)14 b Fk(H)979 5325 y Fp(lim)936 5385 y Fm(t)p Fn(!\0061)1175 5325 y Fk(jj)p Fo(e)1276 5284 y Fn(\000)p Fm(iH)5 b(t)1447 5325 y Fo(f)33 b Fk(\000)22 b Fo(U)1693 5340 y Fj(0)1733 5325 y Fp(\()p Fo(t)p Fp(\))p Fo(f)1892 5340 y Fj(0)1932 5325 y Fk(jj)27 b Fp(=)g(0)p Fo(;)114 b(f)2356 5340 y Fj(0)2423 5325 y Fp(=)28 b Ft(W)2645 5284 y Fn(\003)2643 5350 y(\006)2702 5325 y Fo(f)5 b(:)1810 5634 y Fp(24)p eop %%Page: 25 25 25 24 bop -7 52 a Fp(Th)m(us)34 b(similarly)29 b(to)k(the)g(Sc)m (hr\177)-49 b(odinger)33 b(case)g([20],)g(a)f(long-range)f(p)s (erturbation)h(c)m(hanges)i(for)e(large)-7 172 y(times)k(only)h(the)g (phase)h(\(see)g(\(5.11\)\))e(of)g(the)i(solution)d(of)i(the)g(Dirac)f (equation.)56 b(Of)37 b(course,)i(the)-7 293 y(leading)31 b(term)h(of)g(asymptotics)h(of)f(the)h(phase)g(\012\()p Fo(x;)17 b(t)p Fp(\))33 b(coincides)g(with)f(the)h(phase)1329 514 y(\012)1399 529 y Fj(0)1439 514 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(=)f Fk(\007)p Fo(m)1942 424 y Fi(p)p 2043 424 347 4 v 2043 514 a Fo(t)2078 485 y Fj(2)2140 514 y Fk(\000)22 b(j)p Fo(x)p Fk(j)2350 485 y Fj(2)3476 514 y Fp(\(5.12\))-7 724 y(for)32 b(the)h(free)g(problem)e Fo(H)36 b Fp(=)27 b Fo(H)1177 739 y Fj(0)1216 724 y Fp(.)134 883 y(The)38 b(case)h Fo(f)46 b Fk(2)36 b Fo(E)6 b Fp(\()p Fk(I)924 847 y Fn(\000)984 883 y Fp(\))p Fk(H)38 b Fp(can)g(b)s(e)g (considered)g(quite)f(similarly)-8 b(.)54 b(W)-8 b(e)38 b(ha)m(v)m(e)g(to)f(replace)h(in)e(all)-7 1004 y(form)m(ulas)d(\010)461 1019 y Fn(\006)551 1004 y Fp(=)e(\010)728 963 y Fj(+)728 1026 y Fn(\006)822 1004 y Fp(and)j Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\))35 b(b)m(y)g(\010)1433 963 y Fn(\000)1433 1026 y(\007)1527 1004 y Fp(and)f Fk(\000)p Fo(\027)6 b Fp(\()p Fo(\030)f Fp(\),)35 b(resp)s(ectiv)m(ely)-8 b(,)36 b(and)f(c)m(hange)g(\\)23 b Fk(\006)h Fp(")34 b(in)g(\(5.11\))-7 1124 y(to)28 b(\\)13 b Fk(\007)g Fp(".)42 b(This)28 b(giv)m(es)h(phase)g(function)f(\012)1546 1088 y Fn(\000)1605 1124 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(and)h(the)f(op)s(erator)g Fo(U)2657 1083 y Fn(\000)2647 1149 y Fj(0)2716 1124 y Fp(\()p Fo(t)p Fp(\).)42 b(The)29 b(w)m(a)m(v)m(e)h(op)s(erators)1144 1335 y Ft(W)1262 1294 y Fn(\000)1260 1359 y(\006)1348 1335 y Fp(=)e Fo(s)22 b Fk(\000)65 b Fp(lim)1619 1394 y Fm(t)p Fn(!\0061)1857 1335 y Fo(e)1902 1294 y Fm(iH)5 b(t)2019 1335 y Fo(U)2095 1294 y Fn(\000)2085 1359 y Fj(0)2155 1335 y Fp(\()p Fo(t)p Fp(\))p Fo(E)2338 1350 y Fj(0)2378 1335 y Fp(\()p Fk(I)2477 1294 y Fn(\000)2536 1335 y Fp(\))-7 1591 y(exist,)33 b(are)g(isometric,)e(Ran)17 b Ft(W)1169 1550 y Fn(\000)1167 1613 y(\006)1254 1591 y Fp(=)28 b Fo(E)6 b Fp(\()p Fk(I)1535 1555 y Fn(\000)1594 1591 y Fp(\))p Fo(P)14 b Fk(H)33 b Fp(and)g Ft(W)2134 1550 y Fn(\000)2132 1613 y(\006)2192 1591 y Fo( )t Fp(\()p Fo(H)2386 1555 y Fj(2)2378 1616 y(0)2447 1591 y Fk(\000)23 b Fo(m)2632 1555 y Fj(2)2672 1591 y Fp(\))k(=)h Fo(W)2933 1606 y Fn(\006)2992 1591 y Fp(\()p Fo(H)r(;)17 b(H)3238 1606 y Fj(0)3277 1591 y Fp(;)g Ft(J)3379 1550 y Fn(\000)3379 1613 y(\006)3437 1591 y Fp(\).)134 1750 y Ft(5.2)86 b Fp(The)41 b(expressions)h (\(5.3\),)g(\(5.8\))d(for)h(\012)g(ma)m(y)g(b)s(e)g(simpli\014ed.)64 b(Of)40 b(course,)j(w)m(e)e(need)g(the)-7 1871 y(function)j(\012\()p Fo(x;)17 b(t)p Fp(\))46 b(only)e(in)g(the)h(cone)h Fk(j)p Fo(x)p Fk(j)i Fo(<)g Fk(j)p Fo(t)p Fk(j)p Fp(.)80 b(Here)46 b(w)m(e)g(obtain)d(the)i(eik)m(onal)f(equation)h(for)-7 1991 y(\012\()p Fo(x;)17 b(t)p Fp(\))48 b(whic)m(h)f(then)h(can)f(b)s (e)h(solv)m(ed)f(b)m(y)h(iterations.)86 b(T)-8 b(o)47 b(that)g(end,)k(w)m(e)e(\014rst)e(\014nd)h(relations)-7 2111 y(b)s(et)m(w)m(een)c(deriv)-5 b(ativ)m(es)41 b(of)h(the)g(phase)g (functions)g(\010)1951 2126 y Fn(\006)2052 2111 y Fp(and)g(\012.)71 b(Let)42 b(us)g(di\013eren)m(tiate)f(expression)-7 2232 y(\(5.8\))32 b(in)g(the)h(v)-5 b(ariables)31 b Fo(x)i Fp(and)g Fo(t)p Fp(:)175 2533 y(\012)245 2548 y Fm(x)285 2558 y Fc(i)344 2533 y Fp(=)27 b Fo(\030)495 2482 y Fj(\()p Fm(st)p Fj(\))490 2558 y Fm(i)634 2533 y Fp(+)786 2408 y Fj(3)732 2438 y Fi(X)743 2648 y Fm(j)t Fj(=1)892 2533 y Fo(x)947 2548 y Fm(j)994 2456 y Fo(@)5 b(\030)1098 2405 y Fj(\()p Fm(st)p Fj(\))1093 2481 y Fm(j)p 994 2510 222 4 v 1031 2601 a Fo(@)g(x)1142 2616 y Fm(j)1248 2533 y Fk(\000)22 b Fo(t\027)6 b Fp(\()p Fo(\030)1522 2492 y Fj(\()p Fm(st)p Fj(\))1640 2533 y Fp(\))1678 2492 y Fn(\000)p Fj(1)1843 2408 y(3)1789 2438 y Fi(X)1799 2648 y Fm(j)t Fj(=1)1949 2533 y Fo(\030)1997 2482 y Fj(\()p Fm(st)p Fj(\))1992 2558 y Fm(j)2124 2456 y Fo(@)f(\030)2228 2405 y Fj(\()p Fm(st)p Fj(\))2223 2481 y Fm(j)p 2124 2510 V 2164 2601 a Fo(@)g(x)2275 2616 y Fm(i)2377 2533 y Fp(+)22 b(\010)2545 2548 y Fm(x)2585 2558 y Fc(i)2638 2533 y Fp(+)2790 2408 y Fj(3)2736 2438 y Fi(X)2747 2648 y Fm(j)t Fj(=1)2911 2466 y Fo(@)5 b Fp(\010)p 2907 2510 137 4 v 2907 2601 a Fo(@)g(\030)3006 2616 y Fm(j)3062 2456 y Fo(@)g(\030)3166 2405 y Fj(\()p Fm(st)p Fj(\))3161 2481 y Fm(j)p 3062 2510 222 4 v 3103 2601 a Fo(@)g(x)3214 2616 y Fm(i)3476 2533 y Fp(\(5.13\))-7 2839 y(and)525 2959 y(\012)595 2974 y Fm(t)652 2959 y Fp(=)28 b Fk(h)p Fo(x;)17 b(\030)942 2908 y Fj(\()p Fm(st)p Fj(\))937 2982 y Fm(t)1058 2959 y Fk(i)22 b(\000)h Fo(\027)6 b Fp(\()p Fo(\030)1359 2918 y Fj(\()p Fm(st)p Fj(\))1476 2959 y Fp(\))22 b Fk(\000)h Fo(t\027)6 b Fp(\()p Fo(\030)1811 2918 y Fj(\()p Fm(st)p Fj(\))1928 2959 y Fp(\))1966 2918 y Fn(\000)p Fj(1)2060 2959 y Fk(h)p Fo(\030)2147 2918 y Fj(\()p Fm(st)p Fj(\))2263 2959 y Fo(;)17 b(\030)2355 2908 y Fj(\()p Fm(st)p Fj(\))2350 2982 y Fm(t)2472 2959 y Fk(i)22 b Fp(+)g Fk(hr)2753 2974 y Fm(\030)2790 2959 y Fp(\010)2860 2974 y Fn(\006)2920 2959 y Fo(;)17 b(\030)3012 2908 y Fj(\()p Fm(st)p Fj(\))3007 2982 y Fm(t)3128 2959 y Fk(i)p Fo(:)282 b Fp(\(5.14\))-7 3129 y(Replacing)31 b Fk(r)527 3144 y Fm(\030)565 3129 y Fp(\010)635 3144 y Fn(\006)727 3129 y Fp(in)h(\(5.13\),)g(\(5.14\))g(b)m(y)h(its)f (expression)i(from)d(equation)i(\(5.3\),)f(w)m(e)h(\014nally)f(get)1161 3409 y Fk(r)1244 3424 y Fm(x)1288 3409 y Fp(\012)c(=)g Fo(\030)1538 3368 y Fj(\()p Fm(st)p Fj(\))1677 3409 y Fp(+)22 b Fk(r)1858 3424 y Fm(x)1901 3409 y Fp(\010)1971 3424 y Fn(\006)2031 3409 y Fo(;)114 b Fp(\012)2242 3424 y Fm(t)2300 3409 y Fp(=)28 b Fk(\000)p Fo(\027)q(:)919 b Fp(\(5.15\))134 3618 y(Our)37 b(goal)f(is)g(to)h(rewrite)g(equation)g (\(1.14\))g(where)h Fo(\030)i Fp(=)35 b Fo(\030)2329 3582 y Fj(\()p Fm(st)p Fj(\))2446 3618 y Fp(\()p Fo(x;)17 b(t)p Fp(\))37 b(in)f(terms)i(of)e(the)i(function)-7 3738 y(\012.)44 b(Using)32 b(expressions)j(\(5.15\),)c(w)m(e)j(\014nd)f (that)1161 3949 y Ft(v)r Fp(\()p Fo(x;)17 b(\030)1407 3907 y Fj(\()p Fm(st)p Fj(\))1523 3949 y Fp(\))28 b(=)f Fk(h)p Fo(\030)1779 3907 y Fj(\()p Fm(st)p Fj(\))1896 3949 y Fo(;)17 b(A)p Fk(i)k(\000)i Fo(v)t(@)2275 3964 y Fm(t)2305 3949 y Fp(\012)f(+)g Ft(b)-7 4159 y Fp(and)392 4369 y Fk(h)p Fo(\030)479 4328 y Fj(\()p Fm(st)p Fj(\))595 4369 y Fo(;)17 b Fk(r)p Fp(\010)792 4384 y Fn(\006)851 4369 y Fk(i)22 b Fp(+)g Ft(v)i Fp(+)e Fk(h)p Fo(A;)17 b Fk(r)p Fp(\010)1500 4384 y Fn(\006)1559 4369 y Fk(i)22 b Fp(+)g(2)1767 4328 y Fn(\000)p Fj(1)1861 4369 y Fk(jr)p Fp(\010)2042 4384 y Fn(\006)2101 4369 y Fk(j)2129 4328 y Fj(2)1009 4515 y Fp(=)28 b(2)1162 4474 y Fn(\000)p Fj(1)1256 4515 y Fk(jr)1367 4530 y Fm(x)1411 4515 y Fp(\012)p Fk(j)1509 4474 y Fj(2)1570 4515 y Fk(\000)23 b Fp(2)1719 4474 y Fn(\000)p Fj(1)1813 4515 y Fk(j)p Fo(@)1892 4530 y Fm(t)1922 4515 y Fp(\012)p Fk(j)2020 4474 y Fj(2)2082 4515 y Fp(+)f Fk(h)p Fo(A;)17 b Fk(r)2419 4530 y Fm(x)2462 4515 y Fp(\012)p Fk(i)22 b(\000)h Fo(v)t(@)2795 4530 y Fm(t)2825 4515 y Fp(\012)f(+)g Ft(b)h Fp(+)f(2)3247 4474 y Fn(\000)p Fj(1)3341 4515 y Fo(m)3426 4474 y Fj(2)3466 4515 y Fo(;)-7 4725 y Fp(where)33 b Ft(b)f Fp(is)f(giv)m(en)h(b)m(y)h (\(1.13\).)42 b(No)m(w)33 b(it)d(follo)m(ws)h(from)f(\(1.14\))h(that)h (\012)g(satis\014es)h(the)f(condition)e(\(cf.)-7 4846 y([6]\))534 4966 y Fk(jr)645 4981 y Fm(x)689 4966 y Fp(\012)p Fk(j)787 4925 y Fj(2)849 4966 y Fk(\000)22 b(j)p Fo(@)1027 4981 y Fm(t)1057 4966 y Fp(\012)p Fk(j)1155 4925 y Fj(2)1217 4966 y Fk(\000)g Fp(2)p Fo(v)t(@)1467 4981 y Fm(t)1497 4966 y Fp(\012)h(+)f(2)p Ft(b)g Fp(+)g(2)p Fk(h)p Fo(A;)17 b Fk(r)2207 4981 y Fm(x)2250 4966 y Fp(\012)p Fk(i)22 b Fp(+)g Fo(m)2564 4925 y Fj(2)2632 4966 y Fp(=)27 b Fo(O)s Fp(\()p Fk(j)p Fo(t)p Fk(j)2942 4925 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)3119 4966 y Fp(\))p Fo(:)134 5175 y Fp(This)33 b(equation)f(can)h(b)s(e)g(solv)m(ed)g(b)m(y)h (iterations)1339 5385 y(\012)28 b(=)f(\012)1610 5400 y Fj(0)1672 5385 y Fp(+)22 b(\012)1840 5400 y Fj(1)1902 5385 y Fp(+)h Fo(:)17 b(:)g(:)k Fp(+)h(\012)2305 5400 y Fm(n)2353 5385 y Fo(;)1810 5634 y Fp(25)p eop %%Page: 26 26 26 25 bop -7 52 a Fp(starting)27 b(from)g(the)h(phase)h(\(5.12\))e(for) g(the)h(free)g(problem)f Fo(H)35 b Fp(=)28 b Fo(H)2450 67 y Fj(0)2489 52 y Fp(.)42 b(Indeed,)30 b(setting)3225 27 y(~)3214 52 y(\012)e(=)g(\012)12 b Fk(\000)g Fp(\012)3657 67 y Fj(0)3698 52 y Fp(,)-7 172 y(w)m(e)34 b(obtain)d(for)600 147 y(~)589 172 y(\012)i(the)g(relation)162 344 y Fk(\007)p Fp(2)p Fo(m)p 44 389 447 4 v 44 409 a Fi(p)p 144 409 347 4 v 85 x Fo(t)179 465 y Fj(2)241 494 y Fk(\000)22 b(j)p Fo(x)p Fk(j)451 465 y Fj(2)517 301 y Fi(\020)577 412 y Fk(h)p Fo(x;)17 b Fk(r)798 427 y Fm(x)852 387 y Fp(~)841 412 y(\012)q Fk(i)22 b Fp(+)g Fo(t@)1157 427 y Fm(t)1198 387 y Fp(~)1187 412 y(\012)1258 301 y Fi(\021)1339 412 y Fp(+)g Fk(jr)1548 427 y Fm(x)1603 387 y Fp(~)1592 412 y(\012)p Fk(j)1690 371 y Fj(2)1751 412 y Fk(\000)h(j)p Fo(@)1930 427 y Fm(t)1971 387 y Fp(~)1960 412 y(\012)p Fk(j)2058 371 y Fj(2)2120 412 y Fk(\007)f Fp(2)p Fo(mv)t(t)p Fp(\()p Fo(t)2512 371 y Fj(2)2574 412 y Fk(\000)h(j)p Fo(x)p Fk(j)2785 371 y Fj(2)2824 412 y Fp(\))2862 371 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)3049 412 y Fp(+)f(2)p Ft(b)696 649 y Fk(\007)p Fp(2)p Fo(m)p Fp(\()p Fo(t)980 608 y Fj(2)1042 649 y Fk(\000)h(j)p Fo(x)p Fk(j)1253 608 y Fj(2)1292 649 y Fp(\))1330 608 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)1495 649 y Fk(h)p Fo(A;)17 b(x)p Fk(i)22 b(\000)g Fp(2)p Fo(v)t(@)2017 664 y Fm(t)2058 624 y Fp(~)2047 649 y(\012)h(+)f(2)p Fk(h)p Fo(A;)17 b Fk(r)2526 664 y Fm(x)2580 624 y Fp(~)2569 649 y(\012)p Fk(i)28 b Fp(=)f Fo(O)s Fp(\()p Fk(j)p Fo(t)p Fk(j)3016 608 y Fn(\000)p Fj(1)p Fn(\000)p Fm(\017)3193 649 y Fp(\))p Fo(:)218 b Fp(\(5.16\))134 910 y(No)m(w)33 b(w)m(e)h(use)g(the)f(follo)m(wing)c (ob)m(vious)-7 1072 y Ft(Lemma)37 b(5.3)49 b Fe(A)35 b(solution)g(of)g(the)g(e)-5 b(quation)871 1292 y Fk(h)p Fo(x;)17 b Fk(r)1092 1307 y Fm(x)1136 1292 y Fp(\012\()p Fo(x;)g(t)p Fp(\))p Fk(i)22 b Fp(+)g Fo(t@)1661 1307 y Fm(t)1692 1292 y Fp(\012\()p Fo(x;)17 b(t)p Fp(\))28 b(=)g Fo(f)11 b Fp(\()p Fo(x;)17 b(t)p Fp(\))p Fo(;)86 b Fk(j)p Fo(x)p Fk(j)28 b(\024)g(j)p Fo(t)p Fk(j)p Fo(;)-7 1512 y Fe(wher)-5 b(e)34 b Fo(f)46 b Fe(is)34 b Fo(C)543 1476 y Fj(1)618 1512 y Fe(and)g Fo(f)11 b Fp(\(0)p Fo(;)17 b Fp(0\))27 b(=)g(0)p Fe(,)35 b(c)-5 b(an)34 b(b)-5 b(e)35 b(c)-5 b(onstructe)g(d)34 b(by)h(the)g(formula)1244 1797 y Fp(\012\()p Fo(x;)17 b(t)p Fp(\))28 b(=)1656 1662 y Fi(Z)1755 1688 y Fj(1)1711 1887 y(0)1811 1797 y Fo(f)11 b Fp(\()p Fo(ux;)17 b(ut)p Fp(\))p Fo(u)2248 1756 y Fn(\000)p Fj(1)2341 1797 y Fo(du:)134 2111 y Fp(This)27 b(lemma)e(allo)m(ws)h(us) h(to)g(solv)m(e)g(\(5.16\))f(b)m(y)i(iterations.)40 b(F)-8 b(or)26 b(example,)i(for)f(the)g(\014rst)g(iteration)-7 2232 y(\012)63 2247 y Fj(1)103 2232 y Fp(,)33 b(equation)f(\(5.16\))g (giv)m(es)592 2452 y Fk(h)p Fo(x;)17 b Fk(r)813 2467 y Fm(x)857 2452 y Fp(\012)927 2467 y Fj(1)967 2452 y Fk(i)22 b Fp(+)g Fo(t@)1212 2467 y Fm(t)1242 2452 y Fp(\012)1312 2467 y Fj(1)1379 2452 y Fp(=)28 b Fo(v)t(t)22 b Fk(\007)h Fo(m)1776 2411 y Fn(\000)p Fj(1)1870 2452 y Ft(b)p Fp(\()p Fo(x)p Fp(\)\()p Fo(t)2136 2411 y Fj(2)2199 2452 y Fk(\000)f(j)p Fo(x)p Fk(j)2409 2411 y Fj(2)2449 2452 y Fp(\))2487 2411 y Fj(1)p Fm(=)p Fj(2)2619 2452 y Fk(\000)g(h)p Fo(A)p Fp(\()p Fo(x)p Fp(\))p Fo(;)17 b(x)p Fk(i)p Fo(:)-7 2672 y Fp(Applying)32 b(Lemma)f(5.3)h(w)m(e)i(obtain)137 2951 y(\012)207 2966 y Fj(1)247 2951 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(=)f Fo(t)640 2816 y Fi(Z)740 2842 y Fj(1)696 3041 y(0)796 2951 y Fo(v)t Fp(\()p Fo(ux)p Fp(\))p Fo(du)21 b Fk(\007)i Fo(m)1347 2910 y Fn(\000)p Fj(1)1441 2951 y Fp(\()p Fo(t)1514 2910 y Fj(2)1576 2951 y Fk(\000)g(j)p Fo(x)p Fk(j)1787 2910 y Fj(2)1826 2951 y Fp(\))1864 2910 y Fj(1)p Fm(=)p Fj(2)1990 2816 y Fi(Z)2090 2842 y Fj(1)2046 3041 y(0)2146 2951 y Ft(b)p Fp(\()p Fo(ux)p Fp(\))p Fo(du)e Fk(\000)2623 2816 y Fi(Z)2723 2842 y Fj(1)2678 3041 y(0)2762 2951 y Fk(h)p Fo(A)p Fp(\()p Fo(ux)p Fp(\))p Fo(;)c(x)p Fk(i)p Fo(du:)143 b Fp(\(5.17\))-7 3224 y(This)36 b(expression)h(is)f (su\016cien)m(t)h(for)e Fo(\032)f(>)f Fp(1)p Fo(=)p Fp(2.)53 b(Moreo)m(v)m(er,)38 b(in)d(this)h(case)g(the)h(quadratic)e(terms)h(in) -7 3344 y(\(1.13\))c(can)h(b)s(e)g(neglected)g(whic)m(h)g(giv)m(es)202 3629 y(\012)272 3644 y Fj(1)312 3629 y Fp(\()p Fo(x;)17 b(t)p Fp(\))28 b(=)f Fo(t)705 3493 y Fi(Z)805 3520 y Fj(1)760 3719 y(0)861 3629 y Fo(v)t Fp(\()p Fo(ux)p Fp(\))p Fo(du)21 b Fk(\007)h Fp(\()p Fo(t)1399 3588 y Fj(2)1461 3629 y Fk(\000)h(j)p Fo(x)p Fk(j)1672 3588 y Fj(2)1711 3629 y Fp(\))1749 3588 y Fj(1)p Fm(=)p Fj(2)1875 3493 y Fi(Z)1975 3520 y Fj(1)1931 3719 y(0)2031 3629 y Fo(A)2104 3644 y Fj(0)2144 3629 y Fp(\()p Fo(ux)p Fp(\))p Fo(du)e Fk(\000)2558 3493 y Fi(Z)2658 3520 y Fj(1)2614 3719 y(0)2697 3629 y Fk(h)p Fo(A)p Fp(\()p Fo(ux)p Fp(\))p Fo(;)c(x)p Fk(i)p Fo(du:)208 b Fp(\(5.18\))134 3960 y(Of)27 b(course,)j(the)e (phase)g(function)f(\012)1465 3924 y Fn(\000)1552 3960 y Fp(equals)g(\012)1912 3924 y Fn(\000)2000 3960 y Fp(=)g(\012)2173 3919 y Fn(\000)2173 3984 y Fj(0)2244 3960 y Fp(+)2343 3935 y(~)2332 3960 y(\012)2402 3924 y Fn(\000)2489 3960 y Fp(where)h(\012)2835 3919 y Fn(\000)2835 3984 y Fj(0)2922 3960 y Fp(is)f(de\014ned)i(b)m(y)f(\(5.12\))-7 4080 y(with)38 b(\\)26 b Fk(\007)g Fp(")38 b(replaced)g(b)m(y)h(\\)26 b Fk(\006)h Fp(")37 b(and)1488 4055 y(~)1478 4080 y(\012)1548 4044 y Fn(\000)1645 4080 y Fp(satis\014es)i(\(5.16\))f(with)f(\\)26 b Fk(\007)g Fp(")38 b(replaced)h(b)m(y)g(\\)26 b Fk(\006)g Fp(".)60 b(In)-7 4201 y(particular,)31 b(in)h(the)h(case)g Fo(\032)28 b(>)g Fp(1)p Fo(=)p Fp(2)k(\\)22 b Fk(\007)g Fp(")32 b(in)g(\(5.17\),)g(\(5.18\))g(should)g(b)s(e)h(replaced)g(b)m (y)h(\\)21 b Fk(\006)i Fp(".)134 4362 y(An)33 b(immediate)c (consequence)35 b(of)d(\(5.18\))f(and)h(Theorem)h(5.2)f(is)f(the)i(w)m (ell)e(kno)m(wn)j(result)e(of)f([8])-7 4483 y(ab)s(out)h(long-range)f (magnetic)g(scattering.)-7 4645 y Ft(Prop)s(osition)36 b(5.4)49 b Fe(L)-5 b(et)41 b(assumption)f Fp(\(1)p Fo(:)p Fp(18\))g Fe(b)-5 b(e)40 b(ful\014l)5 b(le)-5 b(d)40 b(for)h Fo(\032)d(>)h Fp(1)p Fo(=)p Fp(2)h Fe(and)g(supp)-5 b(ose)40 b(that)h Fo(v)h Fp(=)-7 4765 y Fo(A)66 4780 y Fj(0)142 4765 y Fp(=)37 b(0)p Fe(.)60 b(Supp)-5 b(ose)39 b(additional)5 b(ly)39 b(that)h Fo(A)g Fe(satis\014es)f(the)h(tr)-5 b(ansversal)39 b(gauge)g(c)-5 b(ondition,)40 b(i.e.,)h(for)-7 4885 y(any)35 b Fo(x)28 b Fk(2)g Fh(R)423 4849 y Fj(3)468 4885 y Fe(,)35 b Fk(h)p Fo(A)p Fp(\()p Fo(x)p Fp(\))p Fo(;)17 b(x)p Fk(i)28 b Fp(=)g(0)p Fe(.)44 b(Then)34 b(the)h(usual)g(wave)f(op)-5 b(er)g(ators)1311 5105 y Fo(W)1403 5120 y Fn(\006)1490 5105 y Fp(=)27 b Fo(s)22 b Fk(\000)66 b Fp(lim)1761 5165 y Fm(t)p Fn(!\0061)1999 5105 y Fo(e)2044 5064 y Fm(iH)5 b(t)2161 5105 y Fo(e)2206 5064 y Fn(\000)p Fm(iH)2343 5073 y Fl(0)2378 5064 y Fm(t)-7 5359 y Fe(exist)35 b(and)f(ar)-5 b(e)35 b(c)-5 b(omplete.)1810 5634 y Fp(26)p eop %%Page: 27 27 27 26 bop -7 52 a Ft(APPENDIX)35 b(A.)i(PR)m(OOF)g(OF)h(THEOREM)e(2.11) 15 334 y Fp(This)23 b(app)s(endix)g(is)f(dev)m(oted)h(to)g(the)f(pro)s (of)g(of)g(the)h(limiting)18 b(absorption)j(principle)g(for)h(the)h(op) s(erator)-7 455 y Fo(H)47 b Fp(=)40 b Fo(H)318 470 y Fj(0)384 455 y Fp(+)27 b Fo(V)61 b Fp(where)41 b Fo(V)61 b Fp(=)40 b Fo(V)1185 470 y Fm(L)1263 455 y Fp(+)27 b Fo(V)1423 470 y Fm(S)1513 455 y Fp(satis\014es)41 b(\(2.5\),)g (\(2.6\).)64 b(As)40 b(sho)m(wn)h(in)e(Section)g(2,)i(under)-7 575 y(these)47 b(assumptions)e(the)i(Mourre)f(estimate)f(\(2.7\))g(and) g(inclusion)g(\(2.13\))f(are)i(satis\014ed.)83 b(Our)-7 695 y(argumen)m(ts)34 b(here)g(follo)m(w)e(essen)m(tially)i(those)g(of) f([9],)h([12],)g([17])g(for)f(the)h(Sc)m(hr\177)-49 b(odinger)34 b(op)s(erator.)46 b(A)-7 816 y(di\013erence)28 b(b)s(et)m(w)m(een)g (the)g(Sc)m(hr\177)-49 b(odinger)27 b(and)g(Dirac)e(op)s(erators)i(is)f (that)h(their)f(domains)g(are)g Ft(H)3502 780 y Fj(2)3568 816 y Fp(and)-7 936 y Ft(H)81 900 y Fj(1)120 936 y Fp(,)38 b(resp)s(ectiv)m(ely)-8 b(.)57 b(Since)37 b(the)h(conjugate)f(op)s (erator)f Ft(A)g Fp(is)h(the)g(same,)h Fe(a)h(priori)d Fp(this)h(could)f(ha)m(v)m(e)-7 1056 y(created)e(new)f(di\016culties.) 43 b(As)33 b(w)m(e)g(shall)e(see,)j(there)g(are)e(not)h(essen)m(tial.) 134 1218 y(Let)46 b Fo(\025)j(>)h(m)p Fp(,)f Fo(\025)61 b(=)-61 b Fk(2)50 b Fo(\033)992 1233 y Fm(p)1033 1218 y Fp(\()p Fo(H)8 b Fp(\).)81 b(Then)47 b(for)e(su\016cien)m(tly)h (small)d Fo(\021)53 b(>)d Fp(0)45 b(estimate)g(\(2.7\))g(holds.)-7 1339 y(Let)h(us)g(c)m(ho)s(ose)h(a)e(function)g Fo(f)61 b Fk(2)50 b Fo(C)1433 1303 y Fn(1)1426 1363 y Fj(0)1508 1339 y Fp(\()p Fh(R)5 b Fp(\))52 b(suc)m(h)47 b(that)e(supp)17 b Fo(f)61 b Fk(\032)51 b Fo(X)2694 1354 y Fm(\021)2781 1339 y Fp(and)46 b Fo(f)11 b Fp(\()p Fo(\026)p Fp(\))50 b(=)f(1)d(if)e Fo(\026)50 b Fk(2)-7 1459 y Fp([)p Fo(\025)22 b Fk(\000)h Fo(\021)247 1474 y Fj(0)286 1459 y Fo(;)17 b(\025)22 b Fp(+)g Fo(\021)555 1474 y Fj(0)595 1459 y Fp(])p Fo(;)49 b(\021)746 1474 y Fj(0)813 1459 y Fo(<)28 b(\021)t Fp(.)43 b(Let)33 b Fo(Y)49 b Fp(=)27 b([)p Fo(\025)22 b Fk(\000)h Fo(\021)1677 1474 y Fj(0)1717 1459 y Fo(=)p Fp(2)p Fo(;)17 b(\025)k Fp(+)h Fo(\021)2083 1474 y Fj(0)2122 1459 y Fo(=)p Fp(2].)44 b(F)-8 b(ollo)m(wing)29 b([12],)k(w)m(e)g(set) 554 1679 y Fo(K)637 1694 y Fm(")702 1679 y Fp(=)27 b(\(1)22 b(+)g Fk(j)p Fo(x)p Fk(j)p Fp(\))1161 1638 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)p Fn(\000)p Fm(\033)1423 1679 y Fp(\(1)g(+)g Fk(j)p Fo("x)p Fk(j)p Fp(\))1825 1638 y Fn(\000)p Fj(1)p Fm(=)p Fj(2+)p Fm(\033)2087 1679 y Fo(;)82 b(\033)31 b Fp(=)d Fo(r)d Fk(\000)d Fp(1)p Fo(=)p Fp(2)27 b Fk(2)h Fp(\(0)p Fo(;)17 b Fp(1)p Fo(=)p Fp(2\))p Fo(;)232 1899 y(B)33 b Fp(=)27 b([)p Fo(H)r(;)17 b(i)p Ft(A)p Fp(])p Fo(;)82 b(M)39 b Fp(=)27 b Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(B)d(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)80 b(G)1797 1914 y Fm(")1862 1899 y Fp(=)27 b(\()p Fo(H)j Fk(\000)22 b Fo(i"M)33 b Fk(\000)23 b Fo(z)t Fp(\))2606 1858 y Fn(\000)p Fj(1)2701 1899 y Fo(;)49 b(")27 b Fk(\025)i Fp(0)p Fo(;)81 b Fp(Im)p Fo(z)32 b(>)27 b Fp(0)p Fo(;)-7 2073 y Fp(and)33 b Fo(F)246 2088 y Fm(")310 2073 y Fp(=)28 b Fo(K)497 2088 y Fm(")534 2073 y Fo(G)611 2088 y Fm(")647 2073 y Fo(K)730 2088 y Fm(")767 2073 y Fp(.)43 b(The)34 b(pro)s(of)e(of)g (Theorem)h(2.11)f(hinges)g(on)h(the)g(di\013eren)m(tial)d(inequalit)m (y)1120 2201 y Fi(\014)1120 2261 y(\014)1120 2320 y(\014)1120 2380 y(\014)1154 2201 y(\014)1154 2261 y(\014)1154 2320 y(\014)1154 2380 y(\014)1197 2278 y Fo(dF)1311 2293 y Fm(")p 1197 2322 151 4 v 1224 2414 a Fo(d")1357 2201 y Fi(\014)1357 2261 y(\014)1357 2320 y(\014)1357 2380 y(\014)1390 2201 y(\014)1390 2261 y(\014)1390 2320 y(\014)1390 2380 y(\014)1451 2345 y Fk(\024)f Fo(C)7 b(")1680 2304 y Fn(\000)p Fm(a)1776 2345 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2102 2360 y Fm(")2138 2345 y Fk(jj)p Fp(\))p Fo(;)81 b(a)28 b(<)f Fp(1)p Fo(:)902 b Fp(\(A.1\))-7 2617 y(W)-8 b(e)33 b(emphasize)g(that,)g(here)h(and)f(b)s(elo)m(w,)g(di\013eren)m (t)g(constan)m(ts)h(do)f(not)g(dep)s(end)h(neither)f(on)g Fo(")f Fp(nor)-7 2737 y(on)k Fo(z)t Fp(.)56 b(The)37 b(pro)s(of)e(of)h(\(A.1\))g(requires,)i(in)e(its)f(turn,)j(sev)m(eral)f (tec)m(hnical)f(assertions.)55 b(The)37 b(\014rst)g(of)-7 2858 y(them)d(is)g(b)s(orro)m(w)m(ed)h(from)d([12])i(\(see)h(Lemmas)f (7.3)f(and)i(7.4\).)47 b(Its)35 b(pro)s(of)e(relies)g(only)h(on)g (estimate)-7 2978 y(\(2.7\))e(and)h(the)g(b)s(oundedness)i(of)d Fo(M)43 b Fp(\(see)34 b(Remark)e(2.6\).)-7 3140 y Ft(Prop)s(osition)k (A.1)48 b Fe(F)-7 b(or)35 b Fo(")29 b(>)g Fp(0)35 b Fe(and)g Fp(Im)16 b Fo(z)34 b(>)29 b Fp(0)p Fe(,)35 b(the)h(op)-5 b(er)g(ator)35 b Fo(H)c Fk(\000)23 b Fo(i"M)33 b Fk(\000)23 b Fo(z)41 b Fe(is)35 b(invertible)g(and)-7 3260 y(the)k(op)-5 b(er)g(ator-function)37 b Fo(G)1006 3275 y Fm(")1043 3260 y Fp(\()p Fo(z)t Fp(\))i Fe(is)f(c)-5 b(ontinuously)39 b(di\013er)-5 b(entiable)37 b(in)h Fo(")c Fk(2)g Fp(\(0)p Fo(;)17 b Fk(1)p Fp(\))38 b Fe(and)g(c)-5 b(ontinuous)-7 3381 y(in)46 b Fo(")h Fk(2)i Fp([0)p Fo(;)17 b Fk(1)p Fp(\))p Fe(.)77 b(Mor)-5 b(e)g(over,)48 b(for)e Fp(Re)17 b Fo(z)69 b Fk(2)49 b Fo(Y)21 b Fe(,)49 b(some)c Fo(")2160 3396 y Fj(0)2247 3381 y Fo(>)j Fp(0)e Fe(and)f Fo(")j Fk(2)g Fp(\(0)p Fo(;)17 b(")3051 3396 y Fj(0)3090 3381 y Fp(\))46 b Fe(the)g(fol)5 b(lowing)-7 3501 y(estimates)34 b(ar)-5 b(e)35 b(valid)990 3622 y Fk(jj)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(G)1347 3637 y Fm(")1382 3622 y Fp(\()p Fo(z)t Fp(\))p Fo(')p Fk(jj)28 b(\024)g Fo(C)7 b(")1883 3580 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2048 3622 y Fk(jh)p Fo(';)17 b(G)2300 3637 y Fm(")2335 3622 y Fp(\()p Fo(z)t Fp(\))p Fo(')p Fk(ij)2591 3580 y Fj(1)p Fm(=)p Fj(2)2701 3622 y Fo(;)1321 3796 y Fk(jj)p Fp(\()p Fo(H)1496 3811 y Fj(0)1557 3796 y Fp(+)22 b Fo(i)p Fp(\))p Fo(G)1803 3811 y Fm(")1840 3796 y Fp(\()p Fo(z)t Fp(\))p Fk(jj)27 b(\024)h Fo(C)7 b(")2276 3755 y Fn(\000)p Fj(1)2370 3796 y Fo(;)1103 b Fp(\(A.2\))1158 3970 y Fk(jj)p Fp(\()p Fo(H)1333 3985 y Fj(0)1394 3970 y Fp(+)22 b Fo(i)p Fp(\)\()p Fo(I)30 b Fk(\000)22 b Fo(f)11 b Fp(\()p Fo(H)d Fp(\)\))p Fo(G)2112 3985 y Fm(")2148 3970 y Fp(\()p Fo(z)t Fp(\))p Fk(jj)28 b(\024)g Fo(C)r(;)939 b Fp(\(A.3\))-7 4145 y Fe(and)943 4265 y Fk(jj)p Fo(K)1082 4280 y Fm(")1118 4265 y Fo(G)1195 4280 y Fm(")1232 4265 y Fp(\()p Fo(z)t Fp(\)\()p Fo(H)1476 4280 y Fj(0)1538 4265 y Fp(+)22 b Fo(i)p Fp(\))p Fk(jj)27 b(\024)h Fo(C)7 b(")2018 4224 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2183 4265 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2509 4280 y Fm(")2545 4265 y Fk(jj)2601 4224 y Fj(1)p Fm(=)p Fj(2)2710 4265 y Fp(\))p Fo(:)725 b Fp(\(A.4\))-7 4481 y(Belo)m(w)36 b(w)m(e)h(alw)m(a)m(ys)g(supp)s(ose) g(that)f(Re)17 b Fo(z)37 b Fk(2)d Fo(Y)22 b Fp(,)36 b(Im)17 b Fo(z)38 b(>)33 b Fp(0,)k Fo(")c Fk(\025)h Fp(0)h(but)h(all)e(our)i (estimates)g(remain)-7 4601 y(true)d(for)f(Im)17 b Fo(z)32 b(<)27 b Fp(0,)33 b Fo(")27 b Fk(\024)h Fp(0.)43 b(W)-8 b(e)33 b(need)h(a)e(generalization)e(of)i(\(A.4\).)-7 4763 y Ft(Lemma)37 b(A.2)49 b Fe(F)-7 b(or)34 b(any)g Fo(s)28 b Fk(2)g Fp([0)p Fo(;)17 b Fp(1])p Fe(,)815 4983 y Fk(jj)p Fo(K)954 4998 y Fm(")990 4983 y Fo(G)1067 4998 y Fm(")1103 4983 y Fp(\()p Fo(z)t Fp(\)\()p Fo(H)1347 4998 y Fj(0)1409 4983 y Fp(+)22 b Fo(i)p Fp(\))p Fk(h)p Fo(x)p Fk(i)1711 4942 y Fm(s)1748 4983 y Fk(jj)27 b(\024)h Fo(C)7 b(")2059 4942 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)p Fn(\000)p Fm(s)2311 4983 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2637 4998 y Fm(")2673 4983 y Fk(jj)2729 4942 y Fj(1)p Fm(=)p Fj(2)2839 4983 y Fp(\))p Fo(:)596 b Fp(\(A.5\))1810 5634 y(27)p eop %%Page: 28 28 28 27 bop -7 52 a Fe(Pr)-5 b(o)g(of)34 b({)f Fp(If)e Fo(s)d Fp(=)g(0,)j(then)h(\(A.5\))f(reduces)i(to)e(\(A.4\).)43 b(So,)32 b(b)m(y)g(in)m(terp)s(olation)d(argumen)m(ts,)j(it)e (su\016ces)-7 172 y(to)i(c)m(hec)m(k)i(\(A.5\))e(for)g Fo(s)c Fp(=)f(1.)43 b(Since)33 b(the)f(comm)m(utator)f([)p Fo(H)2156 187 y Fj(0)2195 172 y Fo(;)17 b Fk(h)p Fo(x)p Fk(i)p Fp(])32 b(is)g(a)g(b)s(ounded)h(op)s(erator,)f(to)g(that)-7 293 y(end)h(w)m(e)h(need)g(to)e(v)m(erify)h(that)940 512 y Fk(jj)p Fo(K)1079 527 y Fm(")1115 512 y Fo(G)1192 527 y Fm(")1228 512 y Fk(h)p Fo(x)p Fk(i)p Fp(\()p Fo(H)1480 527 y Fj(0)1542 512 y Fp(+)22 b Fo(i)p Fp(\))p Fk(jj)27 b(\024)h Fo(C)7 b(")2022 471 y Fn(\000)p Fj(3)p Fm(=)p Fj(2)2186 512 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2512 527 y Fm(")2549 512 y Fk(jj)2605 471 y Fj(1)p Fm(=)p Fj(2)2714 512 y Fp(\))p Fo(:)721 b Fp(\(A.6\))-7 732 y(Comm)m(uting)31 b(the)i(op)s(erator)f Fo(G)1165 747 y Fm(")1234 732 y Fp(and)h Fk(h)p Fo(x)p Fk(i)p Fp(,)f(w)m(e)i(\014nd)f(that)1313 952 y Fo(G)1390 967 y Fm(")1426 952 y Fk(h)p Fo(x)p Fk(i)28 b Fp(=)g Fk(h)p Fo(x)p Fk(i)p Fo(G)1901 967 y Fm(")1959 952 y Fp(+)22 b Fo(G)2134 967 y Fm(")2171 952 y Fo(T)2228 967 y Fm(")2265 952 y Fo(G)2342 967 y Fm(")2379 952 y Fo(;)1094 b Fp(\(A.7\))-7 1171 y(where)1289 1292 y Fo(T)1346 1307 y Fm(")1411 1292 y Fp(=)28 b([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(H)1800 1307 y Fj(0)1839 1292 y Fp(])22 b Fk(\000)g Fo(i")p Fp([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(M)10 b Fp(])p Fo(:)1072 b Fp(\(A.8\))-7 1466 y(The)34 b(op)s(erator)e([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(H)872 1481 y Fj(0)910 1466 y Fp(])33 b(is)f(of)g(course)i(b)s(ounded.)44 b(Let)33 b(us)g(write)f(the)h(second)h(op)s(erator)e(as)245 1686 y([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(M)10 b Fp(])29 b(=)e([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(f)11 b Fp(\()p Fo(H)d Fp(\)])p Fo(B)d(f)11 b Fp(\()p Fo(H)d Fp(\))21 b(+)h Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(B)5 b Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))20 b(+)i Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(B)d Fp([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(f)11 b Fp(\()p Fo(H)d Fp(\)])p Fo(:)250 b Fp(\(A.9\))-7 1905 y(The)27 b(\014rst)f(and)g(the)h (third)e(terms)h(here)g(are)g(b)s(ounded)h(op)s(erators)f(b)s(ecause)h ([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(f)11 b Fp(\()p Fo(H)d Fp(\)]\()p Fo(H)3333 1920 y Fj(0)3380 1905 y Fp(+)h Fo(i)p Fp(\))27 b Fk(2)h(B)-7 2026 y Fp(b)m(y)h(Lemma)e(2.9)h(and)g(\()p Fo(H)925 2041 y Fj(0)978 2026 y Fp(+)13 b Fo(i)p Fp(\))1138 1990 y Fn(\000)p Fj(1)1233 2026 y Fo(B)5 b(f)11 b Fp(\()p Fo(H)d Fp(\))27 b Fk(2)h(B)j Fp(b)m(y)f(Remark)d(2.6.)42 b(Let)29 b(us)f(c)m(hec)m(k)j(that)d([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(B)5 b Fp(])28 b Fk(2)g(B)s Fp(.)-7 2146 y(Remark)36 b(that)g([)p Fo(V)663 2161 y Fm(L)716 2146 y Fo(;)17 b Ft(A)p Fp(])35 b(is)i(an)f(op)s(erator)g(of)g(m)m (ultiplication)c(and)k(hence)i([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b Fp([)p Fo(V)3047 2161 y Fm(L)3099 2146 y Fo(;)g Ft(A)p Fp(]])34 b(=)g(0.)55 b(The)-7 2267 y(equalit)m(y)30 b([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b Fp([)p Fo(V)650 2282 y Fm(S)701 2267 y Fo(;)g Ft(A)p Fp(]])27 b(=)g(0)k(follo)m(ws)e (from)g(represen)m(tation)i(\(2.10\).)42 b(Finally)-8 b(,)29 b(according)h(to)g(\(2.4\),)-7 2387 y([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b Fp([)p Fo(H)305 2402 y Fj(0)344 2387 y Fo(;)g(i)p Ft(A)p Fp(]])28 b(=)f([)p Fk(h)p Fo(x)p Fk(i)p Fo(;)17 b(H)976 2402 y Fj(0)1015 2387 y Fp(])32 b(is)g(a)f(b)s(ounded)i(op)s(erator.)43 b(Th)m(us)33 b(op)s(erator)e(\(A.9\))h(is)g(b)s(ounded)g(and)g(it)-7 2507 y(follo)m(ws)f(from)h(\(A.6\))g({)g(\(A.8\))h(that)589 2727 y Fk(jj)p Fo(K)728 2742 y Fm(")764 2727 y Fo(G)841 2742 y Fm(")878 2727 y Fk(h)p Fo(x)p Fk(i)p Fp(\()p Fo(H)1130 2742 y Fj(0)1191 2727 y Fp(+)22 b Fo(i)p Fp(\))p Fk(jj)27 b(\024)h Fp(\()p Fk(jj)p Fo(K)1725 2742 y Fm(")1761 2727 y Fk(h)p Fo(x)p Fk(ijj)22 b Fp(+)g Fo(C)7 b Fk(jj)p Fo(K)2286 2742 y Fm(")2322 2727 y Fo(G)2399 2742 y Fm(")2435 2727 y Fk(jj)p Fp(\))p Fk(jj)p Fo(G)2662 2742 y Fm(")2698 2727 y Fp(\()p Fo(H)2817 2742 y Fj(0)2878 2727 y Fp(+)22 b Fo(i)p Fp(\))p Fk(jj)p Fo(:)-7 2947 y Fp(By)33 b(de\014nition)f(of)g Fo(K)774 2962 y Fm(")811 2947 y Fp(,)1432 3067 y Fk(jj)p Fo(K)1571 3082 y Fm(")1608 3067 y Fk(h)p Fo(x)p Fk(ijj)27 b(\024)h Fo(C)7 b(")2052 3026 y Fm(\033)r Fn(\000)p Fj(1)p Fm(=)p Fj(2)2259 3067 y Fo(:)1166 b Fp(\(A.10\))-7 3241 y(T)-8 b(aking)32 b(in)m(to)g(accoun)m(t)h(\(A.2\))g(and)g(\(A.4\),)f (w)m(e)i(arriv)m(e)e(at)g(\(A.6\).)44 b Fd(2)134 3453 y Fp(The)34 b(condition)d(on)h(the)h(double)g(comm)m(utator)e(of)h Fo(V)54 b Fp(with)32 b Ft(A)g Fp(is)g(used)i(in)e(the)h(follo)m(wing)-7 3615 y Ft(Lemma)k(A.3)49 b Fe(L)-5 b(et)35 b(inclusion)f Fp(\(2)p Fo(:)p Fp(13\))g Fe(b)-5 b(e)35 b(ful\014l)5 b(le)-5 b(d.)44 b(Then)662 3834 y Fk(jj)p Fo(K)801 3849 y Fm(")837 3834 y Fo(G)914 3849 y Fm(")950 3834 y Fp([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(H)r(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])p Fo(G)1924 3849 y Fm(")1958 3834 y Fo(K)2041 3849 y Fm(")2078 3834 y Fk(jj)27 b(\024)h Fo(C)7 b(")2389 3793 y Fn(\000)p Fj(2+)p Fm(\032)2574 3834 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2900 3849 y Fm(")2936 3834 y Fk(jj)p Fp(\))p Fo(:)395 b Fp(\(A.11\))-7 4096 y Fe(Pr)-5 b(o)g(of)36 b({)e Fp(By)h(Remark)f(2.6,)g(the)h(op)s(erator)f([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])32 b(is)i(b)s(ounded)h(\(cf.)49 b(Lemma)33 b(2.9\).)48 b(Set)3524 4070 y(~)3499 4096 y Fo(H)3580 4111 y Fj(0)3649 4096 y Fp(=)-7 4216 y Fo(H)74 4231 y Fj(0)135 4216 y Fk(\000)23 b Fo(m\013)382 4231 y Fj(0)422 4216 y Fp(.)43 b(Therefore)34 b(the)f(op)s(erator)86 4436 y Fo(i)p Fp([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(H)478 4451 y Fj(0)517 4436 y Fo(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])81 b(=)i([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))1568 4410 y(~)1544 4436 y Fo(H)1625 4451 y Fj(0)1663 4436 y Fo(f)j Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])1134 4581 y(=)83 b Fo(f)11 b Fp(\()p Fo(H)d Fp(\))1541 4556 y(~)1517 4581 y Fo(H)1598 4596 y Fj(0)1636 4581 y Fp([)p Fo(f)j Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])k Fk(\000)i Fo(if)11 b Fp(\()p Fo(H)d Fp(\))2445 4556 y(~)2421 4581 y Fo(H)2502 4596 y Fj(0)2540 4581 y Fo(f)j Fp(\()p Fo(H)d Fp(\))21 b(+)h([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])3314 4556 y(~)3290 4581 y Fo(H)3371 4596 y Fj(0)3409 4581 y Fo(f)11 b Fp(\()p Fo(H)d Fp(\))-7 4801 y(is)32 b(also)g(b)s(ounded.)44 b(T)-8 b(aking)32 b(in)m(to)g(accoun)m(t)h(\(2.13\),)f(w)m(e)i(no)m(w)f (obtain)f(that)432 5020 y Fk(jj)p Fo(K)571 5035 y Fm(")607 5020 y Fo(G)684 5035 y Fm(")721 5020 y Fp([)p Fo(f)11 b Fp(\()p Fo(H)d Fp(\)[)p Fo(V)d(;)17 b Ft(A)p Fp(])p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(;)17 b Ft(A)p Fp(])p Fo(G)1674 5035 y Fm(")1708 5020 y Fo(K)1791 5035 y Fm(")1828 5020 y Fk(jj)82 b(\024)i Fo(C)7 b Fk(jj)p Fo(K)2343 5035 y Fm(")2379 5020 y Fo(G)2456 5035 y Fm(")2493 5020 y Fp(\()p Fo(H)2612 5035 y Fj(0)2673 5020 y Fp(+)22 b Fo(i)p Fp(\))p Fk(h)p Fo(x)p Fk(i)2975 4979 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)3231 5020 y Fk(jj)1966 5166 y(\002)84 b(jjh)p Fo(x)p Fk(i)2316 5124 y Fj(\(1)p Fn(\000)p Fm(\032)p Fj(\))p Fm(=)p Fj(2)2571 5166 y Fp(\()p Fo(H)2690 5181 y Fj(0)2751 5166 y Fk(\000)23 b Fo(i)p Fp(\))p Fo(G)2999 5181 y Fm(")3036 5166 y Fo(K)3119 5181 y Fm(")3156 5166 y Fk(jj)p Fo(:)-7 5385 y Fp(By)33 b(Lemma)e(A.2,)i (the)g(righ)m(t-hand)f(side)g(here)i(is)e(estimated)g(b)m(y)h Fo(C)7 b(")2559 5349 y Fn(\000)p Fj(2+)p Fm(\032)2744 5385 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)3070 5400 y Fm(")3106 5385 y Fk(jj)p Fp(\).)43 b Fd(2)1810 5634 y Fp(28)p eop %%Page: 29 29 29 28 bop 134 52 a Fp(W)-8 b(e)33 b(can)g(no)m(w)g(pro)m(v)m(e)h (\(A.1\))e(follo)m(wing)e(step)k(b)m(y)f(step)h([12)o(],)f([17].)43 b(Note)33 b(that)669 181 y Fi(\014)669 241 y(\014)669 301 y(\014)669 361 y(\014)702 181 y(\014)702 241 y(\014)702 301 y(\014)702 361 y(\014)745 258 y Fo(dF)859 273 y Fm(")p 745 303 151 4 v 772 394 a Fo(d")906 181 y Fi(\014)906 241 y(\014)906 301 y(\014)906 361 y(\014)939 181 y(\014)939 241 y(\014)939 301 y(\014)939 361 y(\014)1000 326 y Fk(\024)1105 181 y Fi(\014)1105 241 y(\014)1105 301 y(\014)1105 361 y(\014)1138 181 y(\014)1138 241 y(\014)1138 301 y(\014)1138 361 y(\014)1181 258 y Fo(dK)1315 273 y Fm(")p 1181 303 171 4 v 1218 394 a Fo(d")1362 181 y Fi(\014)1362 241 y(\014)1362 301 y(\014)1362 361 y(\014)1395 181 y(\014)1395 241 y(\014)1395 301 y(\014)1395 361 y(\014)1445 326 y Fp(\()p Fk(jj)p Fo(G)1616 341 y Fm(")1652 326 y Fo(K)1735 341 y Fm(")1772 326 y Fk(jj)21 b Fp(+)h Fk(jj)p Fo(K)2086 341 y Fm(")2122 326 y Fo(G)2199 341 y Fm(")2236 326 y Fk(jj)p Fp(\))f(+)2449 181 y Fi(\014)2449 241 y(\014)2449 301 y(\014)2449 361 y(\014)2482 181 y(\014)2482 241 y(\014)2482 301 y(\014)2482 361 y(\014)2516 326 y Fo(K)2599 341 y Fm(")2645 258 y Fo(dG)2773 273 y Fm(")p 2645 303 165 4 v 2679 394 a Fo(d")2820 326 y(K)2903 341 y Fm(")2939 181 y Fi(\014)2939 241 y(\014)2939 301 y(\014)2939 361 y(\014)2973 181 y(\014)2973 241 y(\014)2973 301 y(\014)2973 361 y(\014)3022 326 y Fo(:)403 b Fp(\(A.12\))-7 611 y(Since)37 b Fk(jj)p Fo(dK)442 626 y Fm(")478 611 y Fo(=d")p Fk(jj)32 b(\024)j Fo(C)7 b(")947 575 y Fm(\033)r Fn(\000)p Fj(1)p Fm(=)p Fj(2)1154 611 y Fp(,)38 b(estimate)e(\(A.4\))g(sho)m(ws)i(that)f (the)g(\014rst)g(term)f(in)f(the)i(righ)m(t-hand)-7 731 y(side)28 b(of)f(\(A.12\))g(do)s(es)h(not)f(exceed)j Fo(C)7 b(")1404 695 y Fm(\033)r Fn(\000)p Fj(1)1540 731 y Fp(\(1)12 b(+)g Fk(jj)p Fo(F)1846 746 y Fm(")1882 731 y Fk(jj)p Fp(\).)41 b(T)-8 b(o)27 b(consider)h(the)g(second)h(term,)f (w)m(e)h(remark)-7 852 y(that)425 1026 y Fo(dG)553 1041 y Fm(")p 425 1070 V 459 1161 a Fo(d")682 1093 y Fp(=)83 b Fo(iG)951 1108 y Fm(")988 1093 y Fo(M)10 b(G)1169 1108 y Fm(")1234 1093 y Fp(=)28 b Fo(iG)1448 1108 y Fm(")1485 1093 y Fp(\()p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b Fk(\000)h Fo(I)8 b Fp(\))p Fo(B)d(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(G)2336 1108 y Fm(")2394 1093 y Fp(+)22 b Fo(iG)2602 1108 y Fm(")2639 1093 y Fo(B)5 b Fp(\()p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))22 b Fk(\000)g Fo(I)8 b Fp(\))p Fo(G)3267 1108 y Fm(")841 1269 y Fk(\000)p Fo(G)995 1284 y Fm(")1032 1269 y Fp([)p Fo(H)30 b Fk(\000)23 b Fo(i"M)32 b Fk(\000)23 b Fo(z)t(;)17 b Ft(A)p Fp(])p Fo(G)1857 1284 y Fm(")1916 1269 y Fk(\000)23 b Fo(i"G)2172 1284 y Fm(")2208 1269 y Fp([)p Fo(M)5 b(;)17 b Ft(A)p Fp(])p Fo(G)2567 1284 y Fm(")2604 1269 y Fo(:)821 b Fp(\(A.13\))-7 1486 y(Let)36 b(us)h(m)m(ultiply)d(\(A.13\))h(b)m(y)i Fo(K)1225 1501 y Fm(")1298 1486 y Fp(from)e(the)h(left)f(and)h(from)f(the)h(righ)m(t)g (and)g(estimate)f(eac)m(h)i(term)-7 1606 y(separately)-8 b(.)134 1767 y(F)g(or)32 b(the)h(\014rst)g(term,)f(w)m(e)i(ha)m(v)m(e)g (that)e(according)g(to)g(\(A.3\),)h(\(A.4\))168 1984 y Fk(jj)p Fo(K)307 1999 y Fm(")343 1984 y Fo(G)420 1999 y Fm(")457 1984 y Fp(\()p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b Fk(\000)h Fo(I)8 b Fp(\))p Fo(B)d(f)11 b Fp(\()p Fo(H)d Fp(\))p Fo(G)1308 1999 y Fm(")1344 1984 y Fo(K)1427 1999 y Fm(")1464 1984 y Fk(jj)82 b(\024)i(jj)p Fo(K)1902 1999 y Fm(")1938 1984 y Fk(jj)17 b(jj)p Fo(G)2144 1999 y Fm(")2179 1984 y Fp(\()p Fo(f)11 b Fp(\()p Fo(H)d Fp(\))21 b Fk(\000)i Fo(I)8 b Fp(\)\()p Fo(H)2770 1999 y Fj(0)2831 1984 y Fp(+)22 b Fo(i)p Fp(\))p Fk(jj)1602 2129 y(\002)84 b(jj)p Fp(\()p Fo(H)1938 2144 y Fj(0)1998 2129 y Fp(+)22 b Fo(i)p Fp(\))2167 2088 y Fn(\000)p Fj(1)2262 2129 y Fo(B)5 b(f)11 b Fp(\()p Fo(H)d Fp(\))p Fk(jjjj)p Fo(G)2754 2144 y Fm(")2789 2129 y Fo(K)2872 2144 y Fm(")2908 2129 y Fk(jj)1602 2275 y(\024)84 b Fo(C)7 b(")1886 2233 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)2050 2275 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)2376 2290 y Fm(")2412 2275 y Fk(jj)2468 2233 y Fj(1)p Fm(=)p Fj(2)2578 2275 y Fp(\))27 b Fk(\024)h Fo(C)2818 2290 y Fj(1)2858 2275 y Fo(")2904 2233 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)3068 2275 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)3394 2290 y Fm(")3430 2275 y Fk(jj)p Fp(\))p Fo(:)-7 2491 y Fp(The)40 b(second)h(term)d(is)h (quite)g(similar.)60 b(Op)s(ening)38 b(the)i(comm)m(utator)e(in)g(the)i (third)e(term)h(w)m(e)h(\014nd)-7 2612 y(that)57 2828 y Fk(jj)p Fo(K)196 2843 y Fm(")232 2828 y Fo(G)309 2843 y Fm(")345 2828 y Fp([)p Fo(H)30 b Fk(\000)23 b Fo(i"M)33 b Fk(\000)22 b Fo(z)t(;)17 b Ft(A)p Fp(])p Fo(G)1170 2843 y Fm(")1207 2828 y Fo(K)1290 2843 y Fm(")1327 2828 y Fk(jj)544 2974 y(\024)28 b(jj)p Fo(K)788 2989 y Fm(")824 2974 y Fk(h)p Fo(x)p Fk(ijj)17 b(jjh)p Fo(x)p Fk(i)1219 2933 y Fn(\000)p Fj(1)1312 2974 y Ft(A)p Fp(\()p Fo(H)1516 2989 y Fj(0)1577 2974 y Fp(+)22 b Fo(i)p Fp(\))1746 2933 y Fn(\000)p Fj(1)1840 2974 y Fk(jj)17 b Fp(\()p Fk(jj)p Fp(\()p Fo(H)2126 2989 y Fj(0)2186 2974 y Fp(+)22 b Fo(i)p Fp(\))p Fo(G)2432 2989 y Fm(")2469 2974 y Fo(K)2552 2989 y Fm(")2589 2974 y Fk(jj)f Fp(+)h Fk(jj)p Fo(K)2903 2989 y Fm(")2939 2974 y Fo(G)3016 2989 y Fm(")3053 2974 y Fp(\()p Fo(H)3172 2989 y Fj(0)3233 2974 y Fp(+)g Fo(i)p Fp(\))p Fk(jj)p Fp(\))2649 3119 y Fk(\024)28 b Fo(C)7 b(")2877 3078 y Fm(\033)r Fn(\000)p Fj(1)3013 3119 y Fp(\(1)22 b(+)g Fk(jj)p Fo(F)3339 3134 y Fm(")3375 3119 y Fk(jj)p Fp(\))p Fo(;)-7 3336 y Fp(where)43 b(w)m(e)g(ha)m(v)m(e)g (used)h(\(A.4\))d(and)h(\(A.10\).)72 b(Finally)-8 b(,)41 b(the)h(last)g(term)f(is)g(estimated)h(b)m(y)h(\(A.11\).)-7 3456 y(Putting)37 b(the)g(results)h(obtained)f(together,)i(w)m(e)f(see) g(that)f(\(A.12\))g(en)m(tails)f(inequalit)m(y)h(\(A.1\))g(with)-7 3576 y Fo(a)28 b Fp(=)g(min)15 b Fk(f)p Fo(\033)n(;)i(\032)p Fk(g)p Fp(.)134 3737 y(Starting)24 b(from)h(the)h(b)s(ound)f Fk(jj)p Fo(F)1303 3752 y Fm(")1340 3737 y Fk(jj)i(\024)h Fo(C)7 b(")1651 3701 y Fn(\000)p Fj(1)1770 3737 y Fp(\(whic)m(h)26 b(follo)m(ws)e(from)g(\(A.2\)\))i(and)f(using)g(\(A.1\),)i(w)m(e)-7 3858 y(obtain)d(b)m(y)j(iterativ)m(e)d(argumen)m(ts)i(\(see)g([12])g (for)e(details\))h(that)g Fo(F)2378 3873 y Fm(")2440 3858 y Fp(is)g(actually)f(uniformly)f(b)s(ounded,)-7 3978 y(that)32 b(is)1480 4098 y(sup)1172 4180 y Fj(Re)12 b Fm(z)i Fn(2)p Fm(Y)t(;)e Fj(Im)f Fm(z)s(>)p Fj(0)p Fm(;)g Fj(0)p Fn(\024)p Fm("<")1902 4189 y Fl(0)1952 4098 y Fk(jj)p Fo(F)2071 4113 y Fm(")2108 4098 y Fp(\()p Fo(z)t Fp(\))p Fk(jj)27 b Fo(<)h Fk(1)p Fo(:)-7 4340 y Fp(In)h(particular,)e(for)h Fo(")g Fp(=)f(0)h(this)g(ensures)j(that)d (the)h(op)s(erator-function)e Fk(h)p Fo(x)p Fk(i)2783 4304 y Fn(\000)p Fm(r)2876 4340 y Fo(R)q Fp(\()p Fo(z)t Fp(\))p Fk(h)p Fo(x)p Fk(i)3209 4304 y Fn(\000)p Fm(r)3302 4340 y Fo(;)45 b(r)30 b(>)e Fp(1)p Fo(=)p Fp(2,)-7 4460 y(is)36 b(uniformly)f(b)s(ounded)j(for)e(Re)17 b Fo(z)39 b Fk(2)d Fp(\003,)h(Im)17 b Fo(z)39 b(>)c Fp(0,)j(where)g(\003)e(is)h (a)f(compact)h(in)m(terv)-5 b(al)35 b(suc)m(h)k(that)-7 4581 y(\003)22 b Fk(\\)h Fo(\033)227 4596 y Fm(p)268 4581 y Fp(\()p Fo(H)8 b Fp(\))28 b(=)g Fk(;)p Fp(.)46 b(Moreo)m(v)m(er,)35 b(the)e(same)g(inequalit)m(y)g(\(A.1\))g(ensures)i (con)m(tin)m(uit)m(y)e(of)g(this)g(function)-7 4701 y(with)f(resp)s (ect)i(to)e Fo(z)t Fp(.)-7 4984 y Ft(APPENDIX)j(B.)i(PR)m(OOF)g(OF)h (THEOREM)e(2.15)25 5265 y Fp(Let)c Fo(H)j Fp(=)28 b Fo(H)500 5280 y Fj(0)559 5265 y Fp(+)21 b Fo(V)53 b Fp(where)33 b Fo(V)49 b Fp(=)28 b Fo(V)1314 5280 y Fm(L)1386 5265 y Fp(+)21 b Fo(V)1540 5280 y Fm(S)1622 5265 y Fp(satis\014es)33 b(\(2.5\),)e(\(2.6\).)43 b(Our)32 b(goal)e(here)i(is)g(to)f(pro)m(v)m (e)i Fo(H)8 b Fp(-)-7 5385 y(smo)s(othness)31 b(of)f(the)g(op)s (erators)h Fo(G)1291 5400 y Fm(j)1355 5385 y Fp(=)c Fk(h)p Fo(x)p Fk(i)1591 5349 y Fn(\000)p Fj(1)p Fm(=)p Fj(2)1756 5385 y Fk(r)1839 5349 y Fn(?)1839 5410 y Fm(j)1928 5385 y Fp(on)k(an)m(y)g(compact)e(in)m(terv)-5 b(al)29 b(\003)f Fk(\032)g Fp(\()p Fk(\0001)p Fo(;)17 b Fk(\000)p Fo(m)p Fp(\))h Fk([)1810 5634 y Fp(29)p eop %%Page: 30 30 30 29 bop -7 52 a Fp(\()p Fo(m;)17 b Fk(1)p Fp(\))22 b(suc)m(h)j(that)e(\003)r Fk(\\)r Fo(\033)926 67 y Fm(p)967 52 y Fp(\()p Fo(H)8 b Fp(\))27 b(=)g Fk(;)p Fp(.)40 b(By)24 b(Prop)s(osition)d(2.2)i(it)e(su\016ces)k(to)e(v)m(erify)g(that)g(the)g (op)s(erators)-7 172 y Fo(G)70 187 y Fm(j)139 172 y Fp(are)33 b Fo(H)391 136 y Fj(2)430 172 y Fp(-smo)s(oth)e(on)h(\003)1010 136 y Fj(2)1049 172 y Fp(.)134 324 y(Our)k(pro)s(of)f(is)g(similar)d (to)k(that)f(of)g(subsection)i(2.3)e(and)h(relies)f(on)h(a)f(milder)f (mo)s(di\014cation)f(of)-7 444 y(inequalit)m(y)c(\(2.25\).)42 b(Actually)-8 b(,)30 b(w)m(e)h(shall)e(c)m(hec)m(k)j(that,)f(for)f(all) e Fo(k)j Fp(=)c(1)p Fo(;)17 b Fp(2)p Fo(;)g Fp(3)p Fo(;)29 b(r)i Fp(=)c(\(1)17 b(+)g Fo(\032)p Fp(\))p Fo(=)p Fp(2)30 b(and)h(an)m(y)-7 565 y Fo(u)c Fp(=)h Fo(E)6 b Fp(\(\003\))p Fo(u)p Fp(,)4 749 y(2)p Fk(jj)p Fo(G)186 764 y Fm(k)228 749 y Fo(u)p Fk(jj)340 708 y Fj(2)461 749 y Fk(\024)84 b(\000)p Fp(Im)16 b(\()p Ft(M)p Fo(u;)h(H)1165 708 y Fj(2)1204 749 y Fo(u)p Fp(\))462 984 y(+)84 b Fo(C)7 b Fp(\()p Fk(jjh)p Fo(x)p Fk(i)926 943 y Fn(\000)p Fm(r)1018 984 y Fo(u)p Fk(jj)1130 943 y Fj(2)1190 984 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)1477 943 y Fn(\000)p Fm(r)1569 984 y Fo(H)8 b(u)p Fk(jj)1770 943 y Fj(2)1830 984 y Fp(+)1982 860 y Fj(3)1928 890 y Fi(X)1939 1100 y Fm(j)t Fj(=1)2072 984 y Fp(\()p Fk(jjh)p Fo(x)p Fk(i)2299 943 y Fn(\000)p Fm(r)2391 984 y Fo(D)2472 999 y Fm(j)2509 984 y Fo(u)p Fk(jj)2621 943 y Fj(2)2681 984 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)2968 943 y Fn(\000)p Fm(r)3060 984 y Fo(D)3141 999 y Fm(j)3178 984 y Fo(H)8 b(u)p Fk(jj)3379 943 y Fj(2)3416 984 y Fp(\)\))p Fo(:)-14 b Fp(\(B.1\))-7 1274 y(Since,)37 b(b)m(y)f(Corollary)e(2.12,)i(the)g(op)s(erators)f Fk(h)p Fo(x)p Fk(i)1826 1238 y Fn(\000)p Fm(r)1919 1274 y Fp(,)i Fk(h)p Fo(x)p Fk(i)2116 1238 y Fn(\000)p Fm(r)2208 1274 y Fo(D)2289 1289 y Fm(j)2326 1274 y Fp(,)f Fk(h)p Fo(x)p Fk(i)2522 1238 y Fn(\000)p Fm(r)2615 1274 y Fo(H)43 b Fp(and)36 b Fk(h)p Fo(x)p Fk(i)3065 1238 y Fn(\000)p Fm(r)3158 1274 y Fo(D)3239 1289 y Fm(j)3275 1274 y Fo(H)43 b Fp(are)36 b Fo(H)3654 1238 y Fj(2)3693 1274 y Fp(-)-7 1394 y(smo)s(oth)43 b(on)g(\003)563 1358 y Fj(2)602 1394 y Fp(,)j(Prop)s(osition)c(2.3)h(implies)e(that)i(the)h(op)s(erators)f Fo(G)2641 1409 y Fm(k)2727 1394 y Fp(are)g(also)f Fo(H)3195 1358 y Fj(2)3234 1394 y Fp(-smo)s(oth)g(on)-7 1515 y(\003)61 1478 y Fj(2)100 1515 y Fp(.)134 1666 y(Belo)m(w)27 b(w)m(e)g(shall)e (pro)m(v)m(e)j(the)f(inequalit)m(y)e(\(B.1\).)41 b(T)-8 b(o)27 b(that)f(end,)i(w)m(e)g(ha)m(v)m(e)f(to)g(calculate)e(Im)16 b(\()p Ft(M)p Fo(u;)-7 1787 y(H)82 1751 y Fj(2)121 1787 y Fo(u)p Fp(\))35 b(for)g Fo(u)c Fp(=)i Fo(E)6 b Fp(\(\003\))p Fo(u)p Fp(.)50 b(Note)36 b(that)f(the)h(domain)d Fk(D)s Fp(\()p Fo(H)2133 1751 y Fj(2)2172 1787 y Fp(\))i(of)g(the)h(op)s (erator)e Fo(H)3014 1751 y Fj(2)3089 1787 y Fp(de\014ned)i(via)f(the)-7 1907 y(sp)s(ectral)25 b(theorem)g(remains)f(indetermined.)40 b(This)26 b(imp)s(edes)f(our)g(calculation)d(of)j(the)h(comm)m(utator) -7 2027 y(of)34 b Fo(H)195 1991 y Fj(2)268 2027 y Fp(and)g Ft(M)p Fp(.)49 b(In)35 b(particular,)e(the)i(terms)f(lik)m(e)g(\()p Ft(M)p Fo(u;)17 b(H)2201 1991 y Fj(2)2193 2052 y(0)2239 2027 y Fo(u)p Fp(\))34 b(or)g(\()p Ft(M)p Fo(u;)17 b(H)2813 2042 y Fj(0)2851 2027 y Fo(V)2908 2042 y Fm(S)2959 2027 y Fo(u)p Fp(\))34 b(mak)m(e)g(no)g(sense.)-7 2148 y(T)-8 b(o)33 b(a)m(v)m(oid)f(domain)f(problems,)h(w)m(e)i(\014rst)f(comm)m (ute)f Fo(H)2040 2112 y Fj(2)2111 2148 y Fp(with)g(a)h(b)s(ounded)g(op) s(erator)1020 2417 y Ft(M)1126 2432 y Fm(n)1201 2417 y Fp(=)1359 2292 y Fj(3)1305 2322 y Fi(X)1315 2532 y Fm(j)t Fj(=1)1465 2417 y Fp(\()p Ft(m)1597 2432 y Fm(j)1633 2417 y Fo(D)1714 2432 y Fm(j)1751 2417 y Fo(\020)1794 2432 y Fm(n)1840 2417 y Fp(\()p Fo(D)s Fp(\))22 b(+)g Fo(\020)2163 2432 y Fm(n)2210 2417 y Fp(\()p Fo(D)s Fp(\))p Fo(D)2451 2432 y Fm(j)2487 2417 y Ft(m)2581 2432 y Fm(j)2617 2417 y Fp(\))16 b Fo(;)-7 2706 y Fp(where)34 b Fo(\020)318 2721 y Fm(n)365 2706 y Fp(\()p Fo(\030)5 b Fp(\))28 b(=)g Fo(\020)8 b Fp(\()p Fo(\030)d(=n)p Fp(\))32 b(and)h Fo(\020)j Fk(2)29 b Fo(C)1376 2670 y Fn(1)1369 2731 y Fj(0)1450 2706 y Fp(\()p Fh(R)1554 2670 y Fj(3)1600 2706 y Fp(\),)k(suc)m(h)h (that)f Fo(\020)8 b Fp(\()p Fo(\030)d Fp(\))27 b(=)i(1)k(for)f Fk(j)p Fo(\030)5 b Fk(j)27 b(\024)i Fp(1.)45 b(Then)35 b(w)m(e)f(pass)g(to)-7 2827 y(the)f(limit)c Fo(n)f Fk(!)f(1)p Fp(.)43 b(Note)33 b(that)f Ft(M)1330 2842 y Fm(n)1378 2827 y Fo(u)27 b Fk(2)h Ft(H)1643 2790 y Fj(1)1682 2827 y Fp(\()p Fh(R)1786 2790 y Fj(3)1831 2827 y Fo(;)17 b Fh(C)1941 2790 y Fj(4)1987 2827 y Fp(\))32 b(and)1424 3011 y Fo(s)22 b Fk(\000)47 b Fp(lim)1592 3071 y Fm(n)p Fn(!1)1792 3011 y Ft(M)1898 3026 y Fm(n)1946 3011 y Fo(u)27 b Fp(=)g Ft(M)p Fo(u)-7 3232 y Fp(for)32 b(an)m(y)h Fo(u)28 b Fk(2)g Ft(H)592 3196 y Fj(1)631 3232 y Fp(\()p Fh(R)735 3196 y Fj(3)780 3232 y Fo(;)17 b Fh(C)890 3196 y Fj(4)935 3232 y Fp(\).)44 b(Therefore,)33 b(for)f(an)m(y)i Fo(u)27 b Fp(=)g Fo(E)6 b Fp(\(\003\))p Fo(u)27 b Fk(2)h Ft(H)2519 3196 y Fj(1)2558 3232 y Fp(\()p Fh(R)2662 3196 y Fj(3)2708 3232 y Fo(;)17 b Fh(C)2817 3196 y Fj(4)2863 3232 y Fp(\),)215 3416 y(\()p Ft(M)p Fo(u;)g(H)548 3375 y Fj(2)587 3416 y Fo(u)p Fp(\))82 b(=)107 b(lim)922 3476 y Fm(n)p Fn(!1)1106 3416 y Fp(\()p Ft(M)1250 3431 y Fm(n)1297 3416 y Fo(u;)17 b(H)1486 3375 y Fj(2)1524 3416 y Fo(u)p Fp(\))27 b(=)52 b(lim)1749 3476 y Fm(n)p Fn(!1)1933 3416 y Fp(\()p Fo(H)8 b Ft(M)2166 3431 y Fm(n)2213 3416 y Fo(u;)17 b(H)8 b(u)p Fp(\))763 3594 y(=)107 b(lim)922 3654 y Fm(n)p Fn(!1)1123 3594 y Fp([\()p Fo(H)1269 3609 y Fj(0)1308 3594 y Ft(M)1414 3609 y Fm(n)1461 3594 y Fo(u;)17 b(H)1642 3609 y Fj(0)1681 3594 y Fo(u)p Fp(\))k(+)h(\()p Fo(H)2013 3609 y Fj(0)2052 3594 y Ft(M)2158 3609 y Fm(n)2206 3594 y Fo(u;)17 b(V)2363 3609 y Fm(S)2413 3594 y Fo(u)p Fp(\)])k(+)h(\()p Fo(V)2748 3609 y Fm(S)2799 3594 y Ft(M)p Fo(u;)17 b(H)3086 3609 y Fj(0)3125 3594 y Fo(u)p Fp(\))763 3781 y(+)83 b(\()p Ft(M)p Fo(u;)17 b Fp(\()p Fo(H)1285 3796 y Fj(0)1324 3781 y Fo(V)1381 3796 y Fm(L)1455 3781 y Fp(+)22 b Fo(V)1610 3796 y Fm(L)1662 3781 y Fo(H)1743 3796 y Fj(0)1804 3781 y Fp(+)g Fo(V)1981 3740 y Fj(2)1959 3805 y Fm(L)2020 3781 y Fp(\))p Fo(u)p Fp(\))g(+)g(\()p Ft(M)p Fo(u;)17 b Fp(\()p Fo(V)2611 3796 y Fm(S)2661 3781 y Fo(V)2718 3796 y Fm(L)2792 3781 y Fp(+)22 b Fo(V)2947 3796 y Fm(L)2999 3781 y Fo(V)3056 3796 y Fm(S)3129 3781 y Fp(+)g Fo(V)3305 3740 y Fj(2)3284 3805 y Fm(S)3345 3781 y Fp(\))p Fo(u)p Fp(\))p Fo(:)q Fp(\(B.2\))-7 3965 y(In)37 b(the)g(righ)m(t-hand)f(side) h(w)m(e)h(ha)m(v)m(e)g(already)e(passed)i(to)e(the)i(limit)33 b Fo(n)i Fk(!)f(1)i Fp(in)g(the)h(terms)g(where)-7 4085 y(this)32 b(passage)i(is)e(ob)m(vious.)134 4237 y(Let)j(us)f(consider)h (ev)m(ery)h(term)e(in)f(the)i(righ)m(t-hand)e(side)h(separately)-8 b(.)49 b(First,)33 b(w)m(e)j(note)e(ob)m(vious)-7 4357 y(estimates)780 4542 y Fk(j)p Fp(\()p Fo(V)903 4557 y Fm(S)953 4542 y Ft(M)p Fo(u;)17 b(H)1240 4557 y Fj(0)1279 4542 y Fo(u)p Fp(\))p Fk(j)82 b(\024)i(jjh)p Fo(x)p Fk(i)1833 4501 y Fm(r)1870 4542 y Fo(V)1927 4557 y Fm(S)1978 4542 y Ft(M)p Fo(u)p Fk(jj)17 b(jjh)p Fo(x)p Fk(i)2402 4501 y Fn(\000)p Fm(r)2493 4542 y Fo(H)2574 4557 y Fj(0)2613 4542 y Fo(u)p Fk(jj)1483 4687 y(\024)84 b Fo(C)1737 4606 y Fi(\000)1783 4687 y Fk(jjh)p Fo(x)p Fk(i)1972 4646 y Fn(\000)p Fm(r)2064 4687 y Fo(u)p Fk(jj)2176 4646 y Fj(2)2237 4687 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)2524 4646 y Fn(\000)p Fm(r)2616 4687 y Fk(r)p Fo(u)p Fk(jj)2811 4646 y Fj(2)2849 4606 y Fi(\001)2911 4687 y Fo(;)248 4935 y Fk(j)p Fp(\()p Ft(M)p Fo(u;)17 b Fp(\()p Fo(V)615 4950 y Fm(S)665 4935 y Fo(V)722 4950 y Fm(L)796 4935 y Fp(+)22 b Fo(V)951 4950 y Fm(L)1003 4935 y Fo(V)1060 4950 y Fm(S)1133 4935 y Fp(+)g Fo(V)1309 4894 y Fj(2)1288 4960 y Fm(S)1349 4935 y Fp(\))p Fo(u)p Fp(\))p Fk(j)82 b(\024)h(jjh)p Fo(x)p Fk(i)1940 4894 y Fn(\000)p Fm(r)2032 4935 y Ft(M)p Fo(u)p Fk(jj)17 b(jjh)p Fo(x)p Fk(i)2456 4894 y Fm(r)2492 4935 y Fp(\()p Fo(V)2587 4950 y Fm(S)2638 4935 y Fo(V)2695 4950 y Fm(L)2769 4935 y Fp(+)22 b Fo(V)2924 4950 y Fm(L)2976 4935 y Fo(V)3033 4950 y Fm(S)3106 4935 y Fp(+)g Fo(V)3282 4894 y Fj(2)3261 4960 y Fm(S)3322 4935 y Fp(\))p Fo(u)p Fk(jj)1591 5081 y(\024)83 b Fo(C)1845 5000 y Fi(\000)1890 5081 y Fk(jjh)p Fo(x)p Fk(i)2079 5039 y Fn(\000)p Fm(r)2171 5081 y Fo(u)p Fk(jj)2283 5039 y Fj(2)2344 5081 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)2631 5039 y Fn(\000)p Fm(r)2723 5081 y Fk(r)p Fo(u)p Fk(jj)2918 5039 y Fj(2)2956 5000 y Fi(\001)3019 5081 y Fo(;)-7 5265 y Fp(follo)m(wing)32 b(from)h(the)h(assumption)g(\(2.6\))g(\(and)g(b)s (oundedness)i(of)e Fo(V)2534 5280 y Fm(L)2586 5265 y Fp(\).)48 b(T)-8 b(o)35 b(treat)f(other)g(terms)g(w)m(e)-7 5385 y(ha)m(v)m(e)g(to)e(tak)m(e)i(the)f(imaginary)d(part.)1810 5634 y(30)p eop %%Page: 31 31 31 30 bop -7 52 a Ft(Lemma)37 b(B.1)49 b Fe(F)-7 b(or)34 b(any)h Fo(u)27 b Fk(2)h Ft(H)1240 16 y Fj(1)1279 52 y Fp(\()p Fh(R)1383 16 y Fj(3)1428 52 y Fo(;)17 b Fh(C)1538 16 y Fj(4)1583 52 y Fp(\))p Fe(,)436 269 y Fk(j)p Fp(Im)f(\()p Ft(M)p Fo(u;)h Fp(\()p Fo(H)960 284 y Fj(0)999 269 y Fo(V)1056 284 y Fm(L)1130 269 y Fp(+)22 b Fo(V)1285 284 y Fm(L)1337 269 y Fo(H)1418 284 y Fj(0)1479 269 y Fp(+)g Fo(V)1656 228 y Fj(2)1634 294 y Fm(L)1695 269 y Fp(\))p Fo(u)p Fp(\))p Fk(j)27 b(\024)h Fo(C)2081 188 y Fi(\000)2127 269 y Fk(jjh)p Fo(x)p Fk(i)2316 228 y Fn(\000)p Fm(r)2408 269 y Fo(u)p Fk(jj)2520 228 y Fj(2)2580 269 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)2867 228 y Fn(\000)p Fm(r)2959 269 y Fk(r)p Fo(u)p Fk(jj)3154 228 y Fj(2)3193 188 y Fi(\001)3255 269 y Fo(:)-7 527 y Fe(Pr)-5 b(o)g(of)35 b({)f Fp(It)f(su\016ces)i(to)d(pro)m(v)m(e)i(this)e(inequalit)m(y)g (for)g Fo(u)27 b Fk(2)h Ft(H)2216 491 y Fj(2)2255 527 y Fp(\()p Fh(R)2359 491 y Fj(3)2404 527 y Fo(;)17 b Fh(C)2514 491 y Fj(4)2559 527 y Fp(\).)44 b(In)33 b(this)f(case)393 744 y(2)p Fk(j)p Fp(Im)16 b(\()p Ft(M)p Fo(u;)h Fp(\()p Fo(H)966 759 y Fj(0)1004 744 y Fo(V)1061 759 y Fm(L)1135 744 y Fp(+)23 b Fo(V)1291 759 y Fm(L)1343 744 y Fo(H)1424 759 y Fj(0)1485 744 y Fp(+)f Fo(V)1661 703 y Fj(2)1640 769 y Fm(L)1701 744 y Fp(\))p Fo(u)p Fp(\))p Fk(j)27 b Fp(=)g Fk(j)p Fp(\([)p Fo(H)2165 759 y Fj(0)2204 744 y Fo(V)2261 759 y Fm(L)2335 744 y Fp(+)22 b Fo(V)2490 759 y Fm(L)2542 744 y Fo(H)2623 759 y Fj(0)2685 744 y Fp(+)g Fo(V)2861 703 y Fj(2)2840 769 y Fm(L)2901 744 y Fo(;)17 b Ft(M)p Fp(])p Fo(u;)g(u)p Fp(\))p Fk(j)p Fo(:)-7 962 y Fp(Note)34 b(that,)g(b)m(y)g(assumption)f(\(2.5\),)h(the) g(comm)m(utators)e(of)i Ft(M)g Fp(with)f Fo(V)2676 977 y Fm(L)2761 962 y Fp(and)h Fo(V)3031 925 y Fj(2)3009 987 y Fm(L)3104 962 y Fp(are)f(m)m(ultiplica-)-7 1082 y(tions)f(b)m(y)h(short-range)g(functions.)43 b(Similarly)-8 b(,)29 b(the)k(comm)m(utators)e(of)h Ft(M)h Fp(and)f Fo(H)3051 1097 y Fj(0)3123 1082 y Fp(is)g(a)g(\014rst)h(order)-7 1202 y(di\013eren)m(tial)h(op)s(erators)h(whose)h(co)s(e\016cien)m(ts)h (are)e Fo(O)s Fp(\()p Fk(j)p Fo(x)p Fk(j)2097 1166 y Fn(\000)p Fj(1)2190 1202 y Fp(\).)52 b(Multiplied)33 b(b)m(y)j Fo(V)2979 1217 y Fm(L)3031 1202 y Fp(\()p Fo(x)p Fp(\))g(this)f(giv)m(es)h(us)-7 1323 y(again)31 b(a)i(short-range)f (function.)43 b Fd(2)134 1533 y Fp(Next)34 b(w)m(e)f(calculate)f(the)h (limit)c(in)j(the)h(righ)m(t-hand)e(side)i(of)f(\(B.2\).)-7 1694 y Ft(Lemma)37 b(B.2)49 b Fe(F)-7 b(or)34 b(any)h Fo(u)27 b Fk(2)h Ft(H)1240 1658 y Fj(1)1279 1694 y Fp(\()p Fh(R)1383 1658 y Fj(3)1428 1694 y Fo(;)17 b Fh(C)1538 1658 y Fj(4)1583 1694 y Fp(\))p Fe(,)35 b(ther)-5 b(e)35 b(exists)186 1929 y Fp(lim)161 1988 y Fm(n)p Fn(!1)362 1929 y Fp(Im)16 b(\()p Fo(H)614 1944 y Fj(0)653 1929 y Ft(M)759 1944 y Fm(n)806 1929 y Fo(u;)h(H)987 1944 y Fj(0)1026 1929 y Fo(u)p Fp(\))27 b(=)h Fk(\000)p Fp(2)1394 1834 y Fi(X)1422 2046 y Fm(j;k)1537 1929 y Fp(\()p Ft(m)1669 1944 y Fm(j)t(k)1744 1929 y Fo(u)1800 1944 y Fm(j)1836 1929 y Fo(;)17 b(u)1936 1944 y Fm(k)1978 1929 y Fp(\))22 b(+)g(2)2185 1887 y Fn(\000)p Fj(1)2279 1929 y Fp(\(\(\001)2436 1887 y Fj(2)2475 1929 y Ft(m)p Fp(\))p Fo(u;)17 b(u)p Fp(\))p Fo(;)85 b(u)2969 1944 y Fm(j)3033 1929 y Fp(=)27 b Fo(D)3217 1944 y Fm(j)3254 1929 y Fo(u:)168 b Fp(\(B.3\))-7 2284 y Fe(Pr)-5 b(o)g(of)35 b({)67 b Fp(Remark)32 b(that)617 2501 y(Im)16 b(\()p Fo(H)869 2516 y Fj(0)909 2501 y Ft(M)1015 2516 y Fm(n)1062 2501 y Fo(u;)h(H)1243 2516 y Fj(0)1281 2501 y Fo(u)p Fp(\))27 b(=)h(Im)16 b(\()p Fk(r)p Ft(M)1866 2516 y Fm(n)1913 2501 y Fo(u;)h Fk(r)p Fo(u)p Fp(\))27 b(=)g(Im)16 b(\([)p Fk(r)p Fo(;)h Ft(M)2751 2516 y Fm(n)2798 2501 y Fo(u;)g Fk(r)p Fo(u)p Fp(\))p Fo(:)403 b Fp(\(B.4\))-7 2719 y(Clearly)-8 b(,)219 2936 y(\([)p Fo(@)335 2951 y Fm(j)372 2936 y Fo(;)17 b Ft(m)510 2951 y Fm(k)552 2936 y Fo(@)603 2951 y Fm(k)646 2936 y Fo(\020)689 2951 y Fm(n)736 2936 y Fp(\()p Fo(D)s Fp(\))22 b(+)g Fo(@)1067 2951 y Fm(k)1110 2936 y Fo(\020)1153 2951 y Fm(n)1199 2936 y Fp(\()p Fo(D)s Fp(\))p Ft(m)1453 2951 y Fm(k)1495 2936 y Fp(])p Fo(u;)17 b(@)1673 2951 y Fm(j)1709 2936 y Fo(u)p Fp(\))27 b(=)h(\(\()p Ft(m)2104 2951 y Fm(k)r(j)2178 2936 y Fo(@)2229 2951 y Fm(k)2272 2936 y Fo(\020)2315 2951 y Fm(n)2362 2936 y Fp(\()p Fo(D)s Fp(\))22 b(+)g Fo(@)2693 2951 y Fm(k)2736 2936 y Fo(\020)2779 2951 y Fm(n)2825 2936 y Fp(\()p Fo(D)s Fp(\))p Ft(m)3079 2951 y Fm(k)r(j)3153 2936 y Fp(\))p Fo(u;)17 b(@)3342 2951 y Fm(j)3379 2936 y Fo(u)p Fp(\))p Fo(:)-7 3153 y Fp(W)-8 b(e)33 b(can)g(pass)g(here)h(to)e(the)h(limit)c Fo(n)f Fk(!)f(1)32 b Fp(whic)m(h)h(giv)m(es)1329 3370 y(\(\(2)p Ft(m)1548 3385 y Fm(k)r(j)1622 3370 y Fo(@)1673 3385 y Fm(k)1739 3370 y Fp(+)22 b Ft(m)1931 3385 y Fm(k)r(k)r(j)2044 3370 y Fp(\))p Fo(u;)17 b(@)2233 3385 y Fm(j)2269 3370 y Fo(u)p Fp(\))p Fo(:)-7 3587 y Fp(Summing)37 b(these)k(expressions)g (o)m(v)m(er)f Fo(k)i Fp(and)d Fo(j)45 b Fp(and)40 b(substituting)e (them)h(in)g(\(B.4\),)h(w)m(e)h(arriv)m(e)e(at)-7 3708 y(\(B.3\).)k Fd(2)134 3918 y Fp(Belo)m(w,)33 b(w)m(e)g(also)f(use)i (that,)e(for)g(an)m(y)h Fo(u)28 b Fk(2)g Ft(H)1795 3882 y Fj(1)1834 3918 y Fp(\()p Fh(R)1938 3882 y Fj(3)1983 3918 y Fo(;)17 b Fh(C)2093 3882 y Fj(4)2138 3918 y Fp(\),)774 4153 y(lim)749 4212 y Fm(n)p Fn(!1)933 4153 y Fp([)p Fo(H)1041 4168 y Fj(0)1081 4153 y Fo(;)g Ft(M)1231 4168 y Fm(n)1278 4153 y Fp(])p Fo(u)27 b Fp(=)h Fk(\000)1586 4058 y Fi(X)1614 4270 y Fm(j;k)1746 4153 y Fo(\013)1808 4168 y Fm(j)1845 4153 y Fp(\()p Ft(m)1977 4168 y Fm(j)t(k)2051 4153 y Fo(@)2102 4168 y Fm(k)2167 4153 y Fp(+)22 b Fo(@)2316 4168 y Fm(k)2360 4153 y Ft(m)2454 4168 y Fm(j)t(k)2528 4153 y Fp(\))p Fo(u)27 b Fp(=:)h Fk(W)8 b Fo(u:)536 b Fp(\(B.5\))-7 4473 y Ft(Lemma)37 b(B.3)49 b Fe(F)-7 b(or)34 b(any)h Fo(u)27 b Fp(=)g Fo(E)6 b Fp(\(\003\))p Fo(u)p Fe(,)34 b(ther)-5 b(e)35 b(exists)135 4690 y Fp(lim)111 4750 y Fm(n)p Fn(!1)311 4690 y Fp(Im)16 b(\()p Fo(H)563 4705 y Fj(0)602 4690 y Ft(M)708 4705 y Fm(n)756 4690 y Fo(u;)h(V)913 4705 y Fm(S)963 4690 y Fo(u)p Fp(\))27 b(=)g(Im)16 b(\()p Fk(W)8 b Fo(u;)17 b(V)1621 4705 y Fm(S)1672 4690 y Fo(u)p Fp(\))k(+)h(Im)16 b(\()p Ft(M)p Fo(H)8 b(u;)17 b(V)2408 4705 y Fm(S)2458 4690 y Fo(u)p Fp(\))22 b Fk(\000)g Fp(Im)16 b(\()p Ft(M)p Fo(V)3007 4705 y Fm(L)3060 4690 y Fo(u;)h(V)3217 4705 y Fm(S)3267 4690 y Fo(u)p Fp(\))p Fo(:)117 b Fp(\(B.6\))-7 4940 y Fe(Mor)-5 b(e)g(over,)35 b(the)f(right-hand)g(side)h(of)f Fp(\()p Fo(B)5 b(:)p Fp(6\))35 b Fe(is)g(b)-5 b(ounde)g(d)34 b(by)242 5247 y Fo(C)336 5077 y Fi( )415 5247 y Fk(jjh)p Fo(x)p Fk(i)604 5206 y Fn(\000)p Fm(r)696 5247 y Fo(u)p Fk(jj)808 5206 y Fj(2)868 5247 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)1155 5206 y Fn(\000)p Fm(r)1247 5247 y Fo(H)8 b(u)p Fk(jj)1448 5206 y Fj(2)1508 5247 y Fp(+)1661 5123 y Fj(3)1606 5152 y Fi(X)1617 5362 y Fm(j)t Fj(=1)1750 5247 y Fp(\()p Fk(jjh)p Fo(x)p Fk(i)1977 5206 y Fn(\000)p Fm(r)2069 5247 y Fo(D)2150 5262 y Fm(j)2187 5247 y Fo(u)p Fk(jj)2299 5206 y Fj(2)2359 5247 y Fp(+)22 b Fk(jjh)p Fo(x)p Fk(i)2646 5206 y Fn(\000)p Fm(r)2738 5247 y Fo(D)2819 5262 y Fm(j)2856 5247 y Fo(H)8 b(u)p Fk(jj)3057 5206 y Fj(2)3095 5247 y Fp(\))3133 5077 y Fi(!)3228 5247 y Fo(:)250 b Fp(\(B.7\))1810 5634 y(31)p eop %%Page: 32 32 32 31 bop -7 52 a Fe(Pr)-5 b(o)g(of)35 b({)67 b Fp(Clearly)-8 b(,)366 272 y(\()p Fo(H)485 287 y Fj(0)524 272 y Ft(M)630 287 y Fm(n)678 272 y Fo(u;)17 b(V)835 287 y Fm(S)884 272 y Fo(u)p Fp(\))84 b(=)f(\([)p Fo(H)1367 287 y Fj(0)1407 272 y Fo(;)17 b Ft(M)1557 287 y Fm(n)1604 272 y Fp(])p Fo(u;)g(V)1788 287 y Fm(S)1838 272 y Fo(u)p Fp(\))k(+)h(\()p Ft(M)2195 287 y Fm(n)2243 272 y Fo(H)8 b(u;)17 b(V)2489 287 y Fm(S)2538 272 y Fo(u)p Fp(\))22 b Fk(\000)g Fp(\()p Ft(M)2897 287 y Fm(n)2944 272 y Fo(V)3001 287 y Fm(S)3052 272 y Fo(u;)17 b(V)3209 287 y Fm(S)3259 272 y Fo(u)p Fp(\))1061 417 y Fk(\000)83 b Fp(\()p Ft(M)1365 432 y Fm(n)1413 417 y Fo(V)1470 432 y Fm(L)1522 417 y Fo(u;)17 b(V)1679 432 y Fm(S)1729 417 y Fo(u)p Fp(\))p Fo(:)1655 b Fp(\(B.8\))-7 637 y(It)29 b(is)f(imp)s(ortan)m(t)f(that)i(the)g (\\bad")f(term)g(\()p Ft(M)1674 652 y Fm(n)1722 637 y Fo(V)1779 652 y Fm(S)1829 637 y Fo(u;)17 b(V)1986 652 y Fm(S)2036 637 y Fo(u)p Fp(\))28 b(disapp)s(ears)h(here)h(if)d(the)i (imaginary)e(part)-7 758 y(is)22 b(tak)m(en.)42 b(In)23 b(all)d(other)j(terms)g(in)f(the)h(righ)m(t-hand)f(side)h(of)f(\(B.8\)) h(w)m(e)h(can)f(pass)h(to)e(the)h(limit)c Fo(n)28 b Fk(!)g(1)p Fp(.)-7 878 y(In)j(the)h(\014rst)f(term)g(w)m(e)h(use)f(\(B.5\),)h(in)e (the)h(next)h({)f(the)g(equalit)m(y)g Ft(M)2517 893 y Fm(n)2564 878 y Fo(H)8 b(u)27 b Fp(=)g(\()p Ft(M)2983 893 y Fm(n)3030 878 y Fo(E)6 b Fp(\(\003\)\)\()p Fo(H)i(u)p Fp(\),)30 b(and)-7 998 y(in)j(the)i(last)e({)h(the)g(inclusion)e Fo(V)1181 1013 y Fm(L)1233 998 y Fo(u)e Fk(2)h Ft(H)1504 962 y Fj(1)1543 998 y Fp(\()p Fh(R)1646 962 y Fj(3)1692 998 y Fo(;)17 b Fh(C)1802 962 y Fj(4)1847 998 y Fp(\))34 b(for)f Fo(u)d Fk(2)g Ft(H)2339 962 y Fj(1)2378 998 y Fp(\()p Fh(R)2482 962 y Fj(3)2528 998 y Fo(;)17 b Fh(C)2637 962 y Fj(4)2683 998 y Fp(\).)47 b(This)35 b(giv)m(es)f(us)h(equalit)m (y)-7 1119 y(\(B.6\).)43 b(It)33 b(follo)m(ws)e(from)h(\(B.5\))g(and)h (assumptions)f(\(2.5\),)g(\(2.6\))g(that)h(\()p Fk(W)8 b Fo(u;)17 b(V)2944 1134 y Fm(S)2994 1119 y Fo(u)p Fp(\))32 b(and)854 1339 y(\()p Ft(M)p Fo(V)1055 1354 y Fm(L)1107 1339 y Fo(u;)17 b(V)1264 1354 y Fm(S)1314 1339 y Fo(u)p Fp(\))27 b(=)h(\([)p Ft(M)p Fo(;)17 b(V)1811 1354 y Fm(L)1863 1339 y Fp(])p Fo(u;)g(V)2047 1354 y Fm(S)2097 1339 y Fo(u)p Fp(\))22 b(+)g(\()p Fo(V)2406 1354 y Fm(L)2458 1339 y Ft(M)p Fo(u;)17 b(V)2721 1354 y Fm(S)2771 1339 y Fo(u)p Fp(\))-7 1559 y(are)22 b(estimated)f(b)m(y)i Fo(C)7 b Fp(\()p Fk(jjh)p Fo(x)p Fk(i)1008 1523 y Fn(\000)p Fm(r)1100 1559 y Fo(u)p Fk(jj)p Fp(+)p Fk(jjh)p Fo(x)p Fk(i)1477 1523 y Fn(\000)p Fm(r)1568 1559 y Fk(r)p Fo(u)p Fk(jj)p Fp(\))p Fk(jjh)p Fo(x)p Fk(i)1990 1523 y Fn(\000)p Fm(r)2081 1559 y Fo(u)p Fk(jj)p Fp(.)39 b(The)22 b(term)g(\()p Ft(M)p Fo(H)8 b(u;)17 b(V)3061 1574 y Fm(S)3110 1559 y Fo(u)p Fp(\))22 b(is)f(estimated)-7 1679 y(b)m(y)34 b Fo(C)7 b Fp(\()p Fk(jjh)p Fo(x)p Fk(i)433 1643 y Fn(\000)p Fm(r)525 1679 y Fo(H)h(u)p Fk(jj)20 b Fp(+)i Fk(jjh)p Fo(x)p Fk(i)1033 1643 y Fn(\000)p Fm(r)1125 1679 y Fk(r)p Fo(H)8 b(u)p Fk(jj)p Fp(\))p Fk(jjh)p Fo(x)p Fk(i)1636 1643 y Fn(\000)p Fm(r)1727 1679 y Fo(u)p Fk(jj)p Fp(.)42 b Fd(2)134 1891 y Fp(Com)m(bining)25 b(the)h(results)g(obtained,)h(w)m (e)g(see)h(that)d(equalit)m(y)h(\(B.2\))g(implies)d(estimate)j (\(B.1\).)41 b(As)-7 2011 y(w)m(as)31 b(already)f(explained,)h(this)f (estimate,)g(in)f(its)h(turn,)h(ensures)h Fo(H)2502 1975 y Fj(2)2541 2011 y Fp(-smo)s(othness)e(of)g(the)h(op)s(erator)-7 2132 y Fo(G)70 2147 y Fm(k)145 2132 y Fp(on)i(\003)349 2095 y Fj(2)388 2132 y Fp(.)-7 2908 y Ft(REFERENCES)42 3177 y Fp([1])49 b(A.)d(Berthier,)j(V.)c(Georgescu,)50 b Fe(On)d(the)g(p)-5 b(oint)47 b(sp)-5 b(e)g(ctrum)46 b(for)h(Dir)-5 b(ac)46 b(op)-5 b(er)g(ators)p Fp(,)49 b(J.)d(F)-8 b(unc.)194 3298 y(Anal.,)32 b Ft(71)g Fp(\(1987\),)g (309-338.)42 3501 y([2])49 b(A.)32 b(Boutet)g(de)h(Mon)m(v)m (el-Berthier,)g(D.)e(Manda,)i(R.)f(Purice,)h Fe(Limiting)h(absorption)f (principle)194 3622 y(for)h(the)h(Dir)-5 b(ac)34 b(op)-5 b(er)g(ator)p Fp(,)33 b(Ann.)g(Inst.)g(Henri)f(P)m(oincar)m(\023)-46 b(e,)33 b(ph.)g(th.)g(,)f Ft(58-4)h Fp(\(1993\),)f(413-431.)42 3825 y([3])49 b(V.S.)27 b(Buslaev,)h(V.B.)f(Matv)m(eev,)j Fe(Wave)g(op)-5 b(er)g(ators)29 b(for)g(Schr\177)-50 b(odinger)28 b(e)-5 b(quation)29 b(with)h(a)f(slow)5 b(ly)194 3945 y(de)-5 b(cr)g(e)g(asing)33 b(p)-5 b(otential)p Fp(,)32 b(Theor.)i(Math.)f(Ph)m(ys.,)h Ft(2)f Fp(\(1971\),)e(266-274.) 42 4149 y([4])49 b(J.)c(Dollard,)h Fe(Asymptotic)h(c)-5 b(onver)g(genc)g(e)45 b(and)g(Coulomb)h(inter)-5 b(action)p Fp(,)48 b(J.)d(Math.)h(Ph)m(ys.,)k Ft(5)194 4269 y Fp(\(1964\),)31 b(729-738.)42 4473 y([5])49 b(J.)39 b(Dollard,)g(G.)f(V)-8 b(elo,)41 b Fe(Asymptotic)g(b)-5 b(ehaviour)40 b(of)h(a)g(Dir)-5 b(ac)40 b(p)-5 b(article)41 b(in)g(a)g(Coulomb)f(\014eld)p Fp(,)194 4593 y(Nuev)m(o)33 b(Cimen)m(to,)f Ft(45)h Fp(\(1966\),)f (801-812.)42 4796 y([6])49 b(M.V.)g(F)-8 b(edoro)m(yuk,)54 b(V.P)-8 b(.)49 b(Maslo)m(v,)k Fe(Semiclassic)-5 b(al)47 b(appr)-5 b(oximation)48 b(for)i(the)f(e)-5 b(quations)50 b(of)194 4917 y(quantum)35 b(me)-5 b(chanics)p Fp(,)31 b(Reidel,)g(Dordrec)m(h)m(t,)i(1981.)42 5120 y([7])49 b(H.)34 b(Isozaki,)g(H.)g(Kitada,)e Fe(Mo)-5 b(di\014e)g(d)36 b(wave)f(op)-5 b(er)g(ators)35 b(with)h(time-indep)-5 b(endent)34 b(mo)-5 b(di\014ers)p Fp(,)33 b(J.)194 5241 y(F)-8 b(ac.)32 b(Sci.)g(Univ.)h(T)-8 b(oky)m(o,)33 b Ft(32)g Fp(\(1985\),)f(77-104.)1810 5634 y(32)p eop %%Page: 33 33 33 32 bop 42 52 a Fp([8])49 b(M.)34 b(Loss,)h(B.)f(Thaller,)f Fe(Short-r)-5 b(ange)35 b(sc)-5 b(attering)36 b(in)g(long-r)-5 b(ange)34 b(magnetic)h(\014elds:)47 b(the)36 b(r)-5 b(ela-)194 172 y(tivistic)34 b(c)-5 b(ase)p Fp(,)32 b(J.)h(Di\013.)e(Eq.,)j Ft(73)e Fp(\(1988\),)g(225-236.)42 376 y([9])49 b(E.)34 b(Mourre,)i Fe(A)n(bsenc)-5 b(e)35 b(of)i(singular)f(sp)-5 b(e)g(ctrum)36 b(for)g(c)-5 b(ertain)37 b(self-adjoint)e(op)-5 b(er)g(ators)p Fp(,)34 b(Comm.)194 496 y(Math.)f(Ph)m(ys.,)h Ft(78)f Fp(\(1981\),)e(391-400.)-7 699 y([10])49 b(Pl.)36 b(Muth)m(uramalingam,)g Fe(Sc)-5 b(attering)39 b(the)-5 b(ory)39 b(by)g(Enss')g(metho)-5 b(d)39 b(for)f(op)-5 b(er)g(ator)39 b(value)-5 b(d)39 b(ma-)194 820 y(tric)-5 b(es:)42 b(Dir)-5 b(ac)31 b(op)-5 b(er)g(ator)31 b(in)g(a)g(ele)-5 b(ctric)31 b(\014eld)p Fp(,)e(J.)g(Math.)g(So)s(c.)g(Japan,)g Ft(37-3)h Fp(\(1985\),)e(415-432.)-7 1023 y([11])49 b(Pl.)38 b(Muth)m(uramalingam,)f(K.B.)h(Sinha,)i Fe(Existenc)-5 b(e)40 b(and)f(c)-5 b(ompleteness)39 b(of)h(wave)g(op)-5 b(er)g(ators)194 1144 y(for)46 b(the)g(Dir)-5 b(ac)46 b(op)-5 b(er)g(ator)46 b(in)g(an)g(ele)-5 b(ctr)g(o-magnetic)46 b(\014eld)f(with)i(long)e(r)-5 b(ange)46 b(p)-5 b(otentials)p Fp(,)48 b(J.)194 1264 y(Indian)32 b(Math.)h(So)s(c.)f(\(N.S.\),)h Ft(50)g Fp(\(1986\),)e(103-130.)-7 1467 y([12])49 b(P)-8 b(.)39 b(P)m(erry)-8 b(,)41 b(I.M.)e(Sigal,)g(B.)f(Simon,)h Fe(Sp)-5 b(e)g(ctr)g(al)40 b(analysis)g(of)g(N-b)-5 b(o)g(dy)41 b(Schr\177)-50 b(odinger)39 b(op)-5 b(er)g(ators)p Fp(,)194 1588 y(Annals)32 b(of)g(Math.,)h Ft(114)g Fp(\(1981\),)e(519-567.)-7 1791 y([13])49 b(M.)32 b(Reed,)h(B.)f(Simon,)f Fe(Metho)-5 b(ds)34 b(of)g(Mo)-5 b(dern)34 b(Mathematic)-5 b(al)34 b(Physics)g(IV)p Fp(,)d(New)i(Y)-8 b(ork,)33 b(Aca-)194 1912 y(demic)e(Press,)k(1979.)-7 2115 y([14])49 b(M.A.)d(Sh)m(ubin,)j Fe(Pseudo)-5 b(di\013er)g(ential)45 b(Op)-5 b(er)g(ators)46 b(and)h(Sp)-5 b(e)g(ctr)g(al)46 b(The)-5 b(ory)p Fp(,)48 b(Springer-V)-8 b(erlag,)194 2235 y(1987.)-7 2439 y([15])49 b(B.)36 b(Thaller,)f(V.)h(Enss,)i Fe(Asymptotic)h(observables)d(and)h (Coulomb)g(sc)-5 b(attering)38 b(for)f(the)h(Dir)-5 b(ac)194 2559 y(e)g(quation)p Fp(,)32 b(Ann.)h(Inst.)g(Henri)g(P)m(oincar)m (\023)-46 b(e,)32 b(ph.)h(th.)g Ft(45-2)g Fp(\(1986\),)f(147-171.)-7 2763 y([16])49 b(V.)f(V)-8 b(ogelsang,)51 b Fe(A)n(bsolutely)e(c)-5 b(ontinuous)49 b(sp)-5 b(e)g(ctrum)48 b(of)h(Dir)-5 b(ac)48 b(op)-5 b(er)g(ators)49 b(for)g(long)f(r)-5 b(ange)194 2883 y(p)g(otentials)p Fp(,)32 b(J.)g(F)-8 b(unct.)33 b(Anal.,)f Ft(76)h Fp(\(1988\),)e(67-86.)-7 3086 y([17])49 b(D.R.)33 b(Y)-8 b(afaev,)34 b Fe(R)-5 b(emarks)36 b(on)f(the)i(sp)-5 b(e)g(ctr)g(al)35 b(the)-5 b(ory)37 b(for)f(the)g(multip)-5 b(article-typ)g(e)36 b(Schr\177)-50 b(odinger)194 3207 y(op)-5 b(er)g(ator)p Fp(,)32 b(Journal)g(So)m(viet)g(Math.,)h Ft(31-6)g Fp(\(1985\),)f(3445-3459.)-7 3410 y([18])49 b(D.R.)29 b(Y)-8 b(afaev,)31 b Fe(Mathematic)-5 b(al)32 b(Sc)-5 b(attering)33 b(The)-5 b(ory,)32 b(Gener)-5 b(al)33 b(The)-5 b(ory)32 b Fp(,)f(Amer.)f(Math.)g(So)s(c.,)194 3531 y(1992.)-7 3734 y([19])49 b(D.R.)c(Y)-8 b(afaev,)50 b Fe(The)d(sc)-5 b(attering)47 b(amplitude)f(for)h(the)h(Schr\177)-50 b(odinger)46 b(e)-5 b(quation)47 b(with)g(a)g(long)194 3854 y(r)-5 b(ange)34 b(p)-5 b(otential)p Fp(,)32 b(Comm.)g(Math.)g(Ph) m(ys.,)j Ft(191)e Fp(\(1998\),)e(183-218.)-7 4058 y([20])49 b(D.R.)33 b(Y)-8 b(afaev,)35 b Fe(Sc)-5 b(attering)36 b(the)-5 b(ory:)48 b(some)35 b(old)h(and)g(new)g(pr)-5 b(oblems)p Fp(,)33 b(Lecture)i(Notes)g(Math.,)194 4178 y(v.)e(1735,)e(Springer-V)-8 b(erlag,)31 b(2000.)-7 4381 y([21])49 b(D.R.)43 b(Y)-8 b(afaev,)46 b Fe(A)f(class)g(of)f (pseudo-di\013er)-5 b(ential)44 b(op)-5 b(er)g(ators)44 b(with)h(oscil)5 b(lating)44 b(symb)-5 b(ols)p Fp(,)45 b(St)194 4502 y(P)m(etersb)s(ourg)33 b(Math.)g(J.,)g Ft(11)g Fp(\(2000\),)e(375-403.)-7 4705 y([22])49 b(O.)25 b(Y)-8 b(amada,)25 b Fe(The)i(nonr)-5 b(elativistic)27 b(limit)h(of)g(mo)-5 b(di\014e)g(d)26 b(wave)h(op)-5 b(er)g(ators)28 b(for)g(Dir)-5 b(ac)27 b(op)-5 b(er)g(ators)p Fp(,)194 4826 y(Pro)s(c.)32 b(Japan)h(Acad.,)g(Ser.)g(A,)g Ft(59)g Fp(\(1983\),)e(71-74.)1810 5634 y(33)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF