Content-Type: multipart/mixed; boundary="-------------0206251054651" This is a multi-part message in MIME format. ---------------0206251054651 Content-Type: text/plain; name="02-278.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-278.keywords" Atoms, magnetic field, ---------------0206251054651 Content-Type: application/postscript; name="BD1Formatpde2000.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="BD1Formatpde2000.ps" %!PS-Adobe-3.0 %%Title: (BD1Formatpde2000.tex) %%Creator: (Texture: LaserWriter 8 FU1-8.6.5) %%CreationDate: (17:50 mardi 25 juin 2002) %%For: (duclos) %%Routing: (mailto:\000duclos@univ-tln.fr) %%Pages: 11 %%DocumentFonts: CMBX12 CMCSC10 CMBX9 CMR9 CMMI9 CMR10 CMMI10 CMR7 CMMI7 CMEX10 CMSY10 MSBM10 CMMI5 CMBX7 CMBX10 CMSL10 CMSY7 CMR5 CMSY5 MSBM7 CMTI10 CMR6 CMSY9 CMSY6 CMTI9 %%DocumentNeededFonts: CMBX12 CMCSC10 CMBX9 CMR9 CMMI9 CMR10 CMMI10 CMR7 CMMI7 CMEX10 CMSY10 MSBM10 CMMI5 CMBX7 CMBX10 CMSL10 CMSY7 CMR5 CMSY5 MSBM7 CMTI10 CMR6 CMSY9 CMSY6 CMTI9 %%DocumentSuppliedFonts: %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: Default 595 842 0 () () %RBINumCopies: 1 %RBINupNess: 1 1 %RBIPCFileName: (HPLJ4000_1.PPD) %RBIPPDFileVersion: (1.0) %ADO_ImageableArea: 28 30 566 811 %%EndComments %%BeginDefaults %%ViewingOrientation: 1 0 0 1 %%EndDefaults userdict/dscInfo 5 dict dup begin /Title(BD1Formatpde2000.tex)def /Creator(Texture: LaserWriter 8 FU1-8.6.5)def /CreationDate(17:50 mardi 25 juin 2002)def /For(duclos)def /Pages 11 def end put %%BeginProlog /md 264 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: lw8_feature-1.01 %%Copyright: Copyright 1990-1998 Adobe Systems Incorporated and Apple Computer Incorporated. All Rights Reserved. /bd{bind def}bind def /ld{load def}bd /xs{exch store}bd /Z{0 def}bd /T true def /F false def /level2 /languagelevel where { pop languagelevel 2 ge }{ F }ifelse def /odictstk Z /oopstk Z /fcl { count oopstk sub dup 0 gt { {pop}repeat }{ pop }ifelse countdictstack odictstk sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /sfcl2 { /odictstk countdictstack store count/oopstk xs }bd /efcl2 { stopped{$error/newerror F put}if fcl }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd /setcopies{ level2 { 1 dict begin/NumCopies exch def currentdict end setpagedevice }{ userdict/#copies 3 -1 roll put }ifelse }def level2 startnoload /ststpgdev{}def /dopgdev{}def /stpgdev{}def /buf Z /didstop T def /sfcl { /didstop T store /odictstk countdictstack store count/oopstk xs currentfile cvx stopped { $error/newerror F put didstop { save/didstop xs /buf vmstatus exch sub exch pop dup 0 lt{pop 0}if dup 64000 gt{pop 64000}if string store { currentfile buf readline { (}efcl)eq{exit}if }{ /UnexpectedEOF errordict/rangecheck get exec }ifelse }loop didstop restore }if }if fcl }bd /efcl { /didstop F store exec stop }bd level2 endnoload level2 not startnoload /setpagedevice where{pop/realstpgdev/setpagedevice ld}if /SC_topddict Z /SC_spdict Z /$spusrdict F def /dopgdev { userdict/setpagedevice undef $spusrdict { userdict/setpagedevice/realstpgdev load put /$spusrdict F store }if SC_topddict realstpgdev }bd /stpgdev { SC_topddict dup 3 -1 roll { SC_spdict 2 index known { SC_spdict 2 index get dup 3 -1 roll { put dup }forall pop put dup }{ put dup }ifelse }forall pop pop }bd /ststpgdev { /setpagedevice where { userdict eq { /$spusrdict T store }if }if userdict/setpagedevice/stpgdev load put /SC_topddict 0 dict store /SC_spdict 3 dict begin /InputAttributes 0 dict def /Policies 0 dict def /OutputAttributes 0 dict def currentdict end store }def /sfcl/sfcl2 ld /efcl/efcl2 ld level2 not endnoload %%EndFile %%BeginFile: lw8_basic-3.0 /xdf{exch def}bd /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 12{ld}repeat /framewidth -1 def /QDframwid -1 def /numframes Z /mTS matrix def /$m matrix def /av 86 def /por T def /normland F def /psb-nosave{}def /pse-nosave{}def /us Z /psb{/us save store}bd /pse{us restore}bd /level3 /languagelevel where { pop languagelevel 3 ge }{ F }ifelse def level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /devg/DeviceGray def /devr/DeviceRGB def /devc/DeviceCMYK def level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /devg[/DeviceGray]def /devr[/DeviceRGB]def /devc[/DeviceCMYK]def level2 not endnoload /pm Z /mT Z /sD Z /initializepage { mT $m currentmatrix mTS concatmatrix pop /pm save store mT concat }bd /endp { pm restore }bd /adjRect { dup 2 mul 6 2 roll 4 index sub exch 5 -1 roll sub exch 4 2 roll 4 index add exch 5 -1 roll add exch 4 2 roll }bd /frame1up { gS mTS setmatrix QDframwid lw /setstrokeadjust where{pop T setstrokeadjust}if clippath pathbbox 2 index sub exch 3 index sub exch currentlinewidth framewidth mul adjRect numframes dup 0 lt{pop 0}if { 4 copy rS currentlinewidth framewidth mul 4 mul adjRect }repeat pop pop pop pop gR }bd /$c devr def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile level3 startnoload %%BeginFile: lw8_safeclipL12-1.0 /rectclip where { pop/rCa/rectclip ld }{ /rCa { np 0 1 index length 4 idiv { 2 copy 4 getinterval aload pop 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K 4 add }repeat clip np pop pop }bd }ifelse /savedstack Z /subsavedstack Z /execstring Z /saferCa { /execstring xs /odictstk countdictstack store /oopstk 0 store count 0 ne { savedstack 0 eq{ count 100 gt{count}{100}ifelse array/savedstack xs }{ count savedstack length gt { count array/savedstack xs }if }ifelse count savedstack 0 3 -1 roll getinterval astore/subsavedstack xs }{ /subsavedstack 0 store }ifelse execstring cvx stopped { $error/newerror F put newpath }if fcl subsavedstack 0 ne{ subsavedstack aload pop }if }bd %%EndFile level3 endnoload level3 not startnoload %%BeginFile: lw8_safeclipL3-1.0 /saferCa/pop ld %%EndFile level3 not endnoload %%BeginFile: lw8_level1_colorspace-2.0 /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /$cs Z /:rg{devr :ss}bd /:sc{$cs :ss}bd /:dc { dup type/arraytype eq{0 get}if dup/DeviceCMYK eq { pop devc }{ /DeviceGray eq { devg }{ devr }ifelse }ifelse /$cs xdf }bd /:sgl{}def /:dr{}bd /:fCRD{pop}bd /:ckcs{}bd /:ss{/$c xdf}bd %%EndFile %%BeginFile: lw8_bubn-2.1 /$t Z /$p Z /$s Z /$o 1. def /2state? F def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace T }{ currentcmykcolor F }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { 2state? $o $t $p $s $cs ps }bd /popstatic { /ps xs /$cs xs /$s xs /$p xs /$t xs /$o xs /2state? xs }bd /pushgstate { currentpoint pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { errordict/nocurrentpoint{pop 0 0}put 2state? { pushgstate gR }if pushgstate gR pushgstate pushstatic pm restore mTS setmatrix }bd /bn { /pm save store popstatic popgstate gS popgstate 2state? { gS popgstate }if }bd /cpat{pop 64 div setgray 8{pop}repeat}bd %%EndFile %%BeginFile: lw8_basic_text-2.1 /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg T def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg F store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding dup 9/space put dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/Euro/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd /$ckeyd md def /:skey { 1 index maxlength 2 index length sub ge { begin /$mkeys 20 dict def /$mkeys load end dup/$ckeyd xs }if 3 1 roll put }bd /fD1pass { 40 $ckeyd //md ne { pop 1 }if $ckeyd exch :skey }bd /:searchdict Z /:searchdict { exch 2 copy known { get }{ exch/$mkeys get :searchdict }ifelse }bd /lU { //md exch 2 copy known { get }{ exch /$mkeys get :searchdict }ifelse }bd /:xs{ exch 0 1 2 index length 1 sub{ 3 copy gsave 1 getinterval show grestore exch get 0.0 rmoveto }for pop pop }bd /:ys{ exch 0 1 2 index length 1 sub{ 3 copy gsave 1 getinterval show grestore exch get 0.0 exch rmoveto }for pop pop }bd /:xys{ exch 0 1 2 index length 1 sub{ 3 copy gsave 1 getinterval show grestore exch 2 mul 2 copy 1 add get 3 -2 roll get exch rmoveto }for pop pop }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd /fD1pass/def ld /lU/load ld level2{ /:xs/xshow ld /:ys/yshow ld /:xys/xyshow ld }if level2 not endnoload /fD Z /sf Z /scf Z /sf1pass { lU setfont }bd /scf1pass { exch lU exch scalefont fD }bd /scf2pass { scalefont fD }bd md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff fD }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff fD }bd /ps Z /fz{/ps xs}bd /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse fD }def %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin /fD/def ld/sf/setfont ld /scf/scf2pass ld 600/languagelevel where{pop languagelevel 2 ge}{false}ifelse{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse sfcl{ %%BeginFeature: *HPHalftone Enhanced << /Install { currentpagedevice /HWResolution get dup 0 get 600 eq exch 1 get 600 eq and {/EnhancedColorRendering600} {/EnhancedColorRendering} ifelse /ColorRendering findresource setcolorrendering /EnhancedHalftone /Halftone findresource sethalftone { } settransfer false setstrokeadjust } >> setpagedevice currentpagedevice /HWResolution get dup 0 get 600 eq exch 1 get 600 eq and { << /PostRenderingEnhance true /PostRenderingEnhanceDetails << /REValue 0 /Type 8 >> >> setpagedevice }if /setscreen { pop pop pop } def /setcolorscreen { pop pop pop pop pop pop pop pop pop pop pop pop } def /sethalftone { pop } def %%EndFeature }efcl sfcl{ %%BeginFeature: *ManualFeed False <> setpagedevice %%EndFeature }efcl sfcl{ %%BeginFeature: *PageSize A4Small <> setpagedevice %%EndFeature }efcl sfcl{ %%BeginFeature: *Duplex None <> setpagedevice %%EndFeature }efcl sfcl{ %%BeginFeature: *Smoothing None << /PostRenderingEnhance true /PostRenderingEnhanceDetails << /REValue 0 /Type 8 >> >> setpagedevice %%EndFeature }efcl (duclos)setjob sfcl{/currentdistillerparams where{pop 1 dict dup/Orientation 2 put setpagedevice}if }efcl /mT[1 0 0 -1 28 811]def /sD 16 dict def %%IncludeFont: CMBX12 /f43/CMBX12 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f55 f43 12 scf %%IncludeFont: CMCSC10 /f77/CMCSC10 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/less pd 61/equal pd 62/greater pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/arrowup pd 175/arrowdown pd 176/quotesingle pd 177/exclamdown pd 178/questiondown pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f90 f77 12 scf %%IncludeFont: CMBX9 /f111/CMBX9 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE pd 194/Oslash pd 195/suppress pd 196/dieresis pd :esr /f123 f111 12 scf %%IncludeFont: CMR9 /f144/CMR9 :bsr 0/.notdef pd 1/.notdef pd 2/.notdef pd 3/.notdef pd 4/.notdef pd 5/.notdef pd 6/.notdef pd 7/.notdef pd 8/.notdef pd 9/.notdef pd 10/.notdef pd 11/.notdef pd 12/.notdef pd 13/.notdef pd 14/.notdef pd 15/.notdef pd 16/.notdef pd 17/.notdef pd 18/.notdef pd 19/.notdef pd 20/.notdef pd 21/.notdef pd 22/.notdef pd 23/.notdef pd 24/.notdef pd 25/.notdef pd 26/.notdef pd 27/.notdef pd 28/.notdef pd 29/.notdef pd 30/.notdef pd 31/.notdef pd 32/space pd 33/exclam pd 34/quotedblright pd 35/numbersign pd 36/dollar pd 37/percent pd 38/ampersand pd 39/quoteright pd 40/parenleft pd 41/parenright pd 42/asterisk pd 43/plus pd 44/comma pd 45/hyphen pd 46/period pd 47/slash pd 48/zero pd 49/one pd 50/two pd 51/three pd 52/four pd 53/five pd 54/six pd 55/seven pd 56/eight pd 57/nine pd 58/colon pd 59/semicolon pd 60/exclamdown pd 61/equal pd 62/questiondown pd 63/question pd 64/at pd 65/A pd 66/B pd 67/C pd 68/D pd 69/E pd 70/F pd 71/G pd 72/H pd 73/I pd 74/J pd 75/K pd 76/L pd 77/M pd 78/N pd 79/O pd 80/P pd 81/Q pd 82/R pd 83/S pd 84/T pd 85/U pd 86/V pd 87/W pd 88/X pd 89/Y pd 90/Z pd 91/bracketleft pd 92/quotedblleft pd 93/bracketright pd 94/circumflex pd 95/dotaccent pd 96/quoteleft pd 97/a pd 98/b pd 99/c pd 100/d pd 101/e pd 102/f pd 103/g pd 104/h pd 105/i pd 106/j pd 107/k pd 108/l pd 109/m pd 110/n pd 111/o pd 112/p pd 113/q pd 114/r pd 115/s pd 116/t pd 117/u pd 118/v pd 119/w pd 120/x pd 121/y pd 122/z pd 123/endash pd 124/emdash pd 125/hungarumlaut pd 126/tilde pd 127/.notdef pd 128/.notdef pd 161/Gamma pd 162/Delta pd 163/Theta pd 164/Lambda pd 165/Xi pd 166/Pi pd 167/Sigma pd 168/Upsilon pd 169/Phi pd 170/Psi pd 173/Omega pd 174/ff pd 175/fi pd 176/fl pd 177/ffi pd 178/ffl pd 179/dotlessi pd 180/dotlessj pd 181/grave pd 182/acute pd 183/caron pd 184/breve pd 185/macron pd 186/ring pd 187/cedilla pd 188/germandbls pd 189/ae pd 190/oe pd 191/oslash pd 192/AE pd 193/OE 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y 63 (comm)s 88.833 (unication)s 132.442 (is)s 142.216 (also)s 161.991 (a)s 170.044 (call)s 188.097 (to)s 200.038 (exp)s 215.594 (erts)s 234.841 (in)s 246.227 (zero-range)s 294.335 (in)s 302.39 (teractions)s 348.304 (to)s 360.246 (dev)s 375.246 (ote)s 391.632 (e)s 396.076 (\256orts)s 66 y 63 (to)s 75.222 (study)s 102.778 (the)s 120 (ab)s 130.833 (o)s 135.556 (v)s 140.556 (e)s 148.333 (Hamiltonian)s 7 f 205.834 (h)s 6 f 211.595 (.)s 83.838 y 63 (W)s 72.444 (e)s 81.063 (are)s 98.598 (far)s 114.744 (from)s 139.224 (b)s 145.057 (eing)s 167.009 (the)s 185.072 (\257rst)s 206.552 (to)s 219.615 (tac)s 232.67 (kle)s 249.344 (this)s 269.685 (problem.)s 312.22 (W)s 321.665 (e)s 330.283 (recommand)s 385.041 (the)s 403.104 (t)s 406.715 (w)s 413.659 (o)s 95.838 y 63 (pap)s 79.389 (ers)s 94.894 ([LSoY)s 121.977 (],)s 130.732 ([BaSoY)s 163.649 (],)s 172.403 (whic)s 192.126 (h)s 200.88 (deal)s 221.857 (with)s 244.501 (fermionic)s 288.006 (atoms.)s 320.15 (Ho)s 332.372 (w)s 339.316 (ev)s 348.761 (er)s 360.321 (these)s 385.798 (authors)s 107.838 y 63 (use)s 79.613 (a)s 87.281 (v)s 92.003 (ariational)s 136.366 (approac)s 170.561 (h)s 178.785 (whic)s 198.507 (h)s 206.731 (do)s 217.564 (es)s 228.621 (not)s 245.734 (directly)s 281.486 (guaran)s 311.236 (tee)s 326.682 (that)s 347.684 (the)s 364.241 (ground)s 397.493 (state)s 119.838 y 63 (exists)s 91.367 (and)s 111.566 (whic)s 131.289 (h)s 140.933 (do)s 151.766 (es)s 164.244 (not)s 182.777 (seem)s 208.033 (to)s 221.01 (b)s 226.844 (e)s 235.377 (able)s 257.243 (to)s 270.221 (giv)s 282.999 (e)s 291.532 (information)s 346.482 (on)s 361.126 (the)s 379.104 (structure)s 131.838 y 63 (of)s 74.414 (this)s 93.94 (ground)s 127.882 (state.)s 155.185 (Tw)s 169.352 (o)s 177.711 (things)s 207.792 (w)s 214.736 (e)s 222.539 (can)s 240.898 (handle)s 273.146 (with)s 295.949 (our)s 313.78 (theorem)s 352.722 (b)s 358.555 (elo)s 370.5 (w)s 381.081 (\050)s 388.328 (but)s 406.687 (for)s 143.838 y 63 (b)s 68.833 (osonic)s 98.889 (atoms,)s 131.167 (though\051.)s 161.676 y 63 (The)s 83.839 (Hamiltonian)s 141.622 (of)s 153.295 (an)s 7 f 167.467 (N)s 6 f 176.592 (-electron)s 218.014 (atom)s 243.853 (in)s 255.803 (an)s 269.976 (homogeneous)s 331.426 (magnetic)s 374.487 (\257eld,)s 399.215 (with)s 173.676 y 63 (a)s 71.333 (\257xed)s 95.5 (cen)s 109.667 (tre)s 125.25 (of)s 136.639 (mass)s 161.195 (and)s 180.639 (without)s 217.861 (F)s 223.556 (ermi-statistics)s 288.195 (acts)s 308.806 (in)s 7 f 320.473 (L)s 8 f 170.047 y 327.278 (2)s 6 f 173.676 y 331.764 (\050)s 12 f 335.653 (R)s 8 f 170.047 y 342.875 (3)s 9 f 346.862 (N)s 6 f 173.676 y 354.446 (\051)s 361.669 (and)s 381.113 (reads)s 407.308 (as)s 7 f 204.018 y 83.87 (I)s 85.718 (H)s 6 f 97.62 (:=)s 9 f 191.518 y 114.633 (N)s 10 f 194.518 y 110.954 (X)s 9 f 215.817 y 111.257 (j)s 8 f 114.97 (=1)s 7 f 204.018 y 127.065 (H)s 9 f 205.518 y 135.377 (j)s 6 f 204.018 y 141.813 (+)s 10 f 194.518 y 151.813 (X)s 9 f 216.046 y 151.843 (j)s 155.557 (\074k)s 6 f 197.253 y 184.591 (1)s 35.935 .4 169.124 201.718 r 11 f 210.878 y 169.124 (j)s 7 f 171.902 (r)s 9 f 212.378 y 176.413 (j)s 11 f 210.878 y 182.849 (\241)s 7 f 192.849 (r)s 9 f 212.378 y 197.361 (k)s 11 f 210.878 y 202.281 (j)s 6 f 204.018 y 216.259 (where)s 7 f 251.842 (H)s 9 f 205.518 y 260.154 (j)s 6 f 204.018 y 267.146 (:=)s 280.479 (\050)s 11 f 284.368 (\241)s 7 f 292.146 (i)s 11 f 295.591 (r)s 9 f 205.518 y 303.924 (r)s 13 f 206.518 y 307.637 (j)s 11 f 204.018 y 314.095 (\241)s 7 f 324.095 (B)s 6 f 332.817 (\136)s 7 f 332.182 (x)s 11 f 340.119 (\136)s 7 f 349.008 (r)s 9 f 205.518 y 353.52 (j)s 6 f 204.018 y 357.733 (\051)s 8 f 199.889 y 361.622 (2)s 11 f 204.018 y 368.331 (\241)s 7 f 197.253 y 382.9 (Z)s 14.281 .4 379.531 201.718 r 11 f 210.878 y 379.531 (j)s 7 f 382.308 (r)s 9 f 212.378 y 386.82 (j)s 11 f 210.878 y 391.034 (j)s 7 f 204.018 y 395.011 (:)s 6 f 236.456 y 63 (Here)s 7 f 86.961 (r)s 9 f 237.956 y 91.472 (j)s 6 f 236.456 y 98.999 (=)s 110.091 (\050)s 7 f 113.98 (x)s 9 f 237.956 y 119.695 (j)s 7 f 236.456 y 123.909 (;)s 128.353 (y)s 9 f 237.956 y 133.256 (j)s 7 f 236.456 y 137.469 (;)s 141.914 (z)s 9 f 237.956 y 146.564 (j)s 6 f 236.456 y 150.778 (\051)s 158.322 (denotes)s 194.81 (the)s 212.354 (p)s 218.187 (osition)s 250.787 (of)s 262.497 (the)s 7 f 280.041 (j)s 8 f 232.827 y 284.732 (th)s 6 f 236.456 y 296.428 (electron)s 334.556 (with)s 357.655 (resp)s 375.794 (ect)s 392.227 (to)s 404.771 (the)s 248.456 y 63 (n)s 68.278 (ucleus,)s 7 f 102.534 (Z)s 6 f 114.832 (is)s 126.31 (the)s 144.955 (c)s 149.122 (harge)s 177.795 (of)s 190.606 (the)s 209.251 (n)s 214.529 (ucleus)s 246.008 (and)s 7 f 266.875 (B)s 6 f 279.718 (is)s 291.196 (prop)s 311.502 (ortional)s 350.175 (to)s 363.82 (the)s 382.465 (strength)s 260.456 y 63 (of)s 74.928 (the)s 92.689 (magnetic)s 136.006 (\257eld)s 158.211 (whic)s 177.934 (h)s 187.362 (p)s 193.195 (oin)s 206.251 (ts)s 217.956 (to)s 226.567 (w)s 233.512 (ards)s 255.801 (the)s 7 f 273.562 (x)s 6 f 279.277 (-axis;)s 306.896 (\136)s 7 f 306.261 (x)s 6 f 315.848 (denotes)s 352.554 (the)s 370.315 (unit)s 391.965 (v)s 396.965 (ector)s 272.456 y 63 (on)s 78.217 (the)s 7 f 96.767 (x)s 6 f 102.482 (-axis)s 127.477 (of)s 140.194 (the)s 158.744 (am)s 171.8 (bian)s 190.411 (t)s 198.961 (space)s 12 f 227.011 (R)s 8 f 268.827 y 234.234 (3)s 6 f 272.456 y 238.72 (.)s 246.159 (W)s 255.603 (e)s 264.709 (ha)s 274.987 (v)s 279.987 (e)s 289.093 (set)s 306.032 (the)s 324.582 (Planc)s 348.887 (k)s 358.827 (constan)s 391.938 (t)s 12 f 400.488 (\176)s 6 f 410.882 (=)s 284.456 y 63 (1)s 72.777 (and)s 93.666 (the)s 112.332 (mass)s 138.332 (of)s 151.164 (the)s 169.831 (electron)s 7 f 209.08 (m)s 9 f 285.956 y 217.86 (e)s 6 f 284.456 y 227.339 (=)s 240.301 (1)s 7 f 245.301 (=)s 6 f 250.301 (2)s 260.078 (since)s 286.022 (their)s 311.383 (v)s 316.105 (alues)s 342.605 (are)s 360.743 (irrelev)s 387.743 (an)s 398.021 (t)s 406.687 (for)s 296.456 y 63 (our)s 81.393 (discussion.)s 131.591 (If)s 142.178 (w)s 149.123 (e)s 157.488 (denote)s 190.297 (b)s 195.575 (y)s 7 f 204.773 (L)s 9 f 297.956 y 211.579 (x)s 13 f 298.956 y 216.113 (j)s 6 f 296.456 y 224.105 (:=)s 11 f 238.417 (\241)s 7 f 246.195 (i)s 249.64 (@)s 9 f 297.956 y 254.949 (z)s 13 f 298.956 y 258.77 (j)s 7 f 296.456 y 263.006 (y)s 9 f 297.956 y 267.908 (j)s 6 f 296.456 y 274.736 (+)s 7 f 285.127 (i)s 288.572 (@)s 9 f 297.956 y 293.881 (y)s 13 f 298.956 y 297.937 (j)s 7 f 296.456 y 302.173 (z)s 9 f 297.956 y 306.823 (j)s 6 f 296.456 y 314.957 (the)s 332.767 (angular)s 369.493 (momen)s 400.882 (tum)s 310.739 y 63 (op)s 73.833 (erator)s 103.169 (of)s 114.394 (the)s 7 f 131.452 (j)s 8 f 307.11 y 136.143 (th)s 6 f 310.739 y 147.354 (electron)s 184.995 (with)s 207.609 (resp)s 225.748 (ect)s 241.695 (to)s 253.753 (the)s 7 f 270.811 (x)s 6 f 276.526 (-axis)s 300.029 (and)s 7 f 319.309 (I)s 321.156 (L)s 6 f 330.74 (:=)s 10 f 303.239 y 344.073 (P)s 9 f 305.711 y 354.628 (N)s 313.739 y 354.628 (j)s 8 f 358.342 (=1)s 7 f 310.739 y 370.634 (L)s 9 f 312.239 y 377.439 (x)s 13 f 313.239 y 381.974 (j)s 6 f 310.739 y 389.379 (then)s 411.993 (it)s 322.739 y 63 (is)s 72.902 (straigh)s 102.708 (tforw)s 125.513 (ard)s 143.166 (to)s 155.234 (c)s 159.401 (hec)s 173.568 (k)s 182.026 (that)s 7 f 203.539 (I)s 205.386 (H)s 6 f 217.691 (comm)s 243.524 (utes)s 264.538 (with)s 7 f 287.162 (I)s 289.01 (L)s 6 f 295.815 (.)s 301.773 (Therefore)s 7 f 346.953 (I)s 348.8 (H)s 6 f 361.105 (is)s 371.007 (reduced)s 408.104 (b)s 413.382 (y)s 334.739 y 63 (the)s 80.25 (sp)s 90.027 (ectral)s 117.86 (pro)s 132.888 (jections)s 169.36 (of)s 7 f 180.776 (I)s 182.623 (L)s 6 f 189.429 (.)s 195.567 (W)s 205.012 (e)s 212.817 (shall)s 236.233 (b)s 242.066 (e)s 249.871 (concerned)s 296.593 (here)s 318.315 (b)s 323.592 (y)s 332.231 (the)s 349.48 (part)s 7 f 371.202 (I)s 373.049 (H)s 8 f 330.378 y 382.174 (\0500\051)s 6 f 334.739 y 396.271 (of)s 7 f 407.687 (I)s 409.534 (H)s 6 f 346.739 y 63 (whic)s 82.722 (h)s 91.831 (corresp)s 123.331 (onds)s 146.94 (to)s 159.382 (a)s 167.935 (zero)s 189.294 (total)s 213.403 (angular)s 249.761 (momen)s 281.15 (tum)s 302.481 (with)s 325.479 (resp)s 343.618 (ect)s 359.949 (to)s 372.391 (the)s 7 f 389.833 (x)s 6 f 395.548 (-axis.)s 358.739 y 63 (This)s 86.491 (c)s 90.658 (hoice)s 116.871 (is)s 127.584 (motiv)s 152.306 (ated)s 175.186 (partly)s 205.593 (to)s 218.473 (simplify)s 256.964 (the)s 274.844 (analysis)s 313.113 (and)s 333.215 (partly)s 363.622 (b)s 369.456 (ecause)s 401.28 (it)s 411.937 (is)s 370.739 y 63 (b)s 68.833 (eliev)s 88.278 (ed)s 101.521 (that)s 123.098 (the)s 140.231 (lo)s 147.731 (w)s 154.675 (est)s 170.196 (energy)s 202.079 (is)s 212.044 (reac)s 229.572 (hed)s 248.371 (in)s 259.948 (this)s 279.358 (sector,)s 311.019 (see)s 327.095 ([BaSe)s 351.957 (])s 357.978 (and)s 377.332 ([AHS)s 400.666 (])s 406.687 (for)s 382.739 y 63 (the)s 80.487 (sp)s 90.265 (ecial)s 113.307 (case)s 7 f 134.739 (N)s 6 f 147.083 (=)s 158.08 (1)s 163.08 (.)s 169.456 (T)s 175.844 (o)s 184.443 (state)s 209.207 (the)s 226.694 (main)s 251.959 (theorem)s 291.141 (of)s 302.795 (this)s 322.559 (note)s 345.046 (w)s 351.991 (e)s 360.033 (in)s 368.089 (tro)s 381.172 (duce)s 404.77 (the)s 394.739 y 63 (unitary)s 98.306 (transformation)s 7 f 166.472 (U)s 6 f 177.724 (asso)s 195.891 (ciated)s 225.335 (to)s 237.557 (the)s 254.78 (follo)s 273.113 (wing)s 297.002 (scaling)s 11 f 420.743 y 150.843 (8)s 7 f 156.399 (j)s 6 f 163.867 (=)s 174.423 (1)s 7 f 179.423 (;)s 183.867 (:)s 188.311 (:)s 192.756 (:)s 197.2 (N)s 205.77 (;)s 220.214 (r)s 9 f 422.243 y 224.726 (j)s 11 f 420.743 y 231.717 (!)s 10 f 406.643 y 244.495 (\265)s 7 f 413.978 y 259.426 (x)s 9 f 415.478 y 265.142 (j)s 22.67 .4 253.056 418.443 r 6 f 427.602 y 253.056 (log)s 7 f 267.639 (B)s 420.743 y 276.926 (;)s 413.978 y 286.222 (y)s 9 f 415.478 y 291.125 (j)s 16.42 .4 282.57 418.443 r 11 f 420.443 y 282.57 (p)s 8.087 .4 290.904 420.443 r 7 f 428.909 y 290.904 (B)s 420.743 y 300.19 (;)s 413.978 y 309.613 (z)s 9 f 415.478 y 314.263 (j)s 16.42 .4 305.835 418.443 r 11 f 420.443 y 305.835 (p)s 8.087 .4 314.168 420.443 r 7 f 428.909 y 314.168 (B)s 10 f 406.643 y 323.455 (\266)s 6 f 450.246 y 63 (and)s 82.314 (the)s 99.406 (pro)s 114.434 (jector)s 7 f 142.386 (I)s 144.234 (\246)s 8 f 445.052 y 153.359 (\0500\051)s 14 f 452.913 y 153.359 (0)s 6 f 450.246 y 167.298 (on)s 181.056 (states)s 209.37 (where)s 238.156 (all)s 251.915 (the)s 269.006 (electrons)s 310.626 (are)s 327.19 (in)s 338.726 (the)s 355.818 (lo)s 363.318 (w)s 370.262 (est)s 385.743 (Landau)s 462.246 y 63 (lev)s 75.222 (el)s 85.405 (and)s 104.477 (ha)s 114.755 (v)s 119.755 (e)s 127.16 (zero)s 147.926 (angular)s 183.692 (momen)s 215.081 (tum)s 235.819 (with)s 258.224 (resp)s 276.363 (ect)s 292.102 (to)s 303.951 (the)s 7 f 320.801 (x)s 6 f 326.516 (-axis.)s 352.588 (Although)s 396.382 (these)s 474.246 y 63 (ob)s 74.111 (jects)s 96.851 (are)s 113.174 (standard)s 154.552 (w)s 161.497 (e)s 168.903 (giv)s 181.681 (e)s 189.087 (a)s 197.048 (precise)s 229.538 (de)s 239.538 (\257nition)s 273.611 (of)s 284.628 (them)s 309.812 (in)s 321.107 (the)s 337.958 (next)s 360.087 (section.)s 395.882 (Then)s 486.246 y 63 (one)s 81.333 (has)s 99.167 (the)s 15 f 509.775 y 63 (Theorem)s 6 f 108 (.)s 16 f 114.701 (As)s 7 f 130.069 (B)s 16 f 142.08 (tends)s 169.393 (to)s 182.205 (in)s 190.539 (\257nit)s 208.039 (y)s 217.24 (one)s 236.164 (has,)s 257.365 (uniformly)s 303.539 (with)s 326.907 (resp)s 345.046 (ect)s 361.748 (to)s 7 f 374.56 (\273)s 16 f 383.319 (in)s 395.576 (ev)s 405.021 (ery)s 521.775 y 63 (compact)s 103 (of)s 114.389 (the)s 131.611 (resolv)s 156.695 (en)s 166.417 (t)s 173.639 (set)s 189.25 (of)s 7 f 200.639 (h)s 16 f 206.401 (,)s 212.512 (that:)s 10 f 535.717 y 70.602 (\265)s 6 f 543.052 y 94.13 (1)s 34.934 .4 79.163 547.517 r 556.677 y 79.163 (\050)s 83.052 (log)s 7 f 97.635 (B)s 6 f 105.722 (\051)s 8 f 553.788 y 109.611 (2)s 7 f 549.817 y 115.297 (U)s 10 f 538.717 y 124.882 (\263)s 7 f 549.817 y 130.854 (I)s 132.701 (H)s 8 f 545.456 y 141.826 (\0500\051)s 11 f 549.817 y 154.784 (\241)s 6 f 164.784 (2)s 7 f 169.784 (N)s 178.909 (B)s 10 f 538.717 y 186.996 (\264)s 7 f 549.817 y 194.635 (U)s 17 f 545.688 y 202.553 (\241)s 8 f 208.803 (1)s 11 f 549.817 y 215.511 (\241)s 7 f 225.511 (\273)s 10 f 535.717 y 230.346 (\266)s 17 f 537.789 y 237.708 (\241)s 8 f 243.958 (1)s 11 f 549.817 y 250.666 (\241)s 6 f 260.666 (\050)s 7 f 264.555 (h)s 11 f 272.539 (\241)s 7 f 282.539 (\273)s 6 f 287.374 (\051)s 17 f 545.688 y 291.262 (\241)s 8 f 297.513 (1)s 11 f 549.817 y 304.221 (\255)s 7 f 314.221 (I)s 316.068 (\246)s 8 f 544.623 y 325.193 (\0500\051)s 14 f 552.484 y 325.193 (0)s 6 f 549.817 y 338.707 (=)s 11 f 349.262 (O)s 6 f 357.501 (\050\050)s 365.279 (log)s 7 f 379.862 (B)s 6 f 387.949 (\051)s 17 f 545.688 y 391.838 (\241)s 18 f 543.001 y 399.288 (1)s 3.403 .34 399.288 544.108 r 548.098 y 399.288 (3)s 6 f 549.817 y 404.391 (\051)s 7 f 408.28 (:)s do-end end endp showpage %%Page: 3 3 %%BeginPageSetup initializepage (duclos ; page : 3 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f55 sf ( )S -990 -1000 :M f221 sf ( )S -984 -1000 :M f255 sf ( )S -978 -1000 :M f287 sf ( )S -972 -1000 :M f320 sf ( )S -966 -1000 :M f354 sf ( )S -960 -1000 :M f388 sf ( )S -954 -1000 :M f422 sf ( )S -951 -1000 :M f455 sf ( )S -945 -1000 :M f488 sf ( )S -939 -1000 :M f589 sf ( )S -933 -1000 :M f621 sf ( )S -927 -1000 :M f654 sf ( )S -921 -1000 :M f687 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 5 12 /CMBX12 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 12 10 /MSBM10 findfont fdef 13 5 /CMMI5 findfont fdef 14 7 /CMBX7 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 19 5 /CMSY5 findfont fdef 20 7 /MSBM7 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (1-d)s 78.93 (b)s 84.326 (eha)s 97.948 (viour)s 121.864 (of)s 132.399 (atoms)s 159.686 (in)s 170.478 (in)s 177.929 (tense)s 201.626 (magnetic)s 241.199 (\257elds)s 414.034 (3)s 6 f 54 y 63 (F)s 68.694 (rom)s 90.269 (this)s 110.761 (theorem)s 150.669 (w)s 157.613 (e)s 166.382 (can)s 185.707 (dra)s 199.901 (w)s 211.448 (t)s 215.059 (w)s 222.004 (o)s 231.328 (conclusions.)s 287.431 (Let)s 7 f 306.339 (Z)s 6 f 318.205 (and)s 7 f 338.641 (N)s 6 f 352.091 (b)s 357.924 (e)s 366.693 (suc)s 380.36 (h)s 390.24 (that)s 7 f 412.898 (h)s 6 f 66 y 63 (p)s 68.833 (ossesses)s 105.886 (a)s 114.327 (true)s 7 f 135.574 (L)s 8 f 62.371 y 142.38 (2)s 6 f 66 y 146.866 (-ground)s 184.224 (state)s 7 f 208.832 (\047)s 6 f 218.815 (with)s 241.701 (energy)s 7 f 273.782 (e)s 6 f 278.438 (.)s 284.657 (Then)s 310.876 (for)s 7 f 326.29 (B)s 6 f 337.818 (large)s 362.398 (enough)s 7 f 396.951 (I)s 398.798 (H)s 8 f 61.639 y 407.923 (\0500\051)s 6 f 78 y 63 (has)s 80.833 (also)s 100.889 (an)s 7 f 114.778 (L)s 8 f 74.371 y 121.583 (2)s 6 f 78 y 126.07 (-ground)s 163.32 (state)s 7 f 187.82 (\251)s 6 f 194.486 (\050)s 7 f 198.375 (B)s 6 f 206.462 (\051)s 213.684 (with)s 236.462 (energy)s 7 f 268.434 (E)s 6 f 276.393 (\050)s 7 f 280.282 (B)s 6 f 288.368 (\051)s 295.591 (suc)s 309.257 (h)s 318.146 (that)s 105.019 y 192.34 (lim)s 9 f 111.469 y 188.121 (B)s 17 f 194.504 (!)s 202.476 (1)s 7 f 98.254 y 213.315 (E)s 6 f 221.273 (\050)s 7 f 225.162 (B)s 6 f 233.249 (\051)s 11 f 239.36 (\241)s 6 f 249.36 (2)s 7 f 254.36 (N)s 263.485 (B)s 58.257 .4 213.315 102.719 r 6 f 111.878 y 224.976 (\050)s 228.865 (log)s 7 f 243.448 (B)s 6 f 251.535 (\051)s 8 f 108.989 y 255.424 (2)s 6 f 105.019 y 275.549 (=)s 7 f 286.105 (e;)s 6 f 131.576 y 63 (and)s 143.576 y 126.484 (lim)s 9 f 150.026 y 122.265 (B)s 17 f 128.648 (!)s 136.62 (1)s 11 f 143.576 y 146.259 (k)s 7 f 151.259 (\251)s 6 f 157.926 (\050)s 7 f 161.815 (B)s 6 f 169.902 (\051)s 11 f 176.013 (\241)s 10 f 134.538 y 186.013 (p)s 22.67 .4 196.013 134.538 r 6 f 143.576 y 196.013 (log)s 7 f 210.596 (B)s 220.349 (\047)s 6 f 226.891 (\050)s 230.78 (log)s 7 f 245.363 (B)s 11 f 255.117 (\242)s 6 f 257.894 (\051)s 11 f 264.006 (\255)s 134.622 y 274.006 (p)s 8.087 .4 282.339 134.622 r 7 f 143.576 y 282.339 (B)s 290.426 (\302)s 8 f 138.382 y 296.683 (\0500\051)s 14 f 146.243 y 296.683 (0)s 6 f 143.576 y 307.419 (\050)s 11 f 134.622 y 311.308 (p)s 8.087 .4 319.641 134.622 r 7 f 143.576 y 319.641 (B)s 11 f 329.394 (\242)s 6 f 332.172 (\051)s 11 f 336.061 (k)s 6 f 343.839 (=)s 354.394 (0)s 168.023 y 63 (where)s 7 f 93.49 (\302)s 8 f 162.829 y 99.746 (\0500\051)s 14 f 170.69 y 99.746 (0)s 6 f 168.023 y 115.389 (denotes)s 153.128 (the)s 171.923 (pro)s 186.674 (duct)s 211.024 (of)s 7 f 223.986 (N)s 6 f 238.017 (lo)s 245.517 (w)s 252.462 (est)s 269.646 (Landau)s 307.469 (lev)s 319.691 (el)s 331.819 (functions)s 376.503 (with)s 400.854 (zero)s 180.023 y 63 (angular)s 99.139 (momen)s 130.528 (tum)s 151.639 (with)s 174.417 (resp)s 192.556 (ect)s 208.667 (to)s 220.889 (the)s 7 f 238.111 (x)s 6 f 247.16 (axis.)s 5 f 217.563 y 63 (2)s 83.25 (Pro)s 105.111 (of)s 120.486 (of)s 135.861 (the)s 159.271 (theorem)s 6 f 247.103 y 63 (First,)s 89.321 (w)s 96.265 (e)s 103.198 (giv)s 115.975 (e)s 122.907 (the)s 139.284 (de)s 149.284 (\257nition)s 182.883 (of)s 7 f 193.426 (h)s 6 f 199.188 (.)s 204.453 (Let)s 7 f 221.524 (D)s 6 f 232.859 (:)s 12 f 238.414 (R)s 9 f 243.474 y 245.636 (N)s 17 f 252.721 (\241)s 8 f 258.971 (1)s 11 f 247.103 y 266.235 (!)s 12 f 279.013 (R)s 9 f 243.474 y 286.235 (N)s 6 f 247.103 y 296.307 (b)s 302.141 (e)s 309.073 (a)s 316.561 (regular)s 349.659 (parametrisation)s 259.103 y 63 (of)s 74.719 (a)s 83.382 (plane)s 110.378 (in)s 12 f 122.375 (R)s 9 f 255.474 y 129.597 (N)s 6 f 259.103 y 140.845 (of)s 152.564 (co)s 162.286 (dimension)s 209.894 (1)s 218.557 (and)s 7 f 238.331 (t)s 9 f 260.603 y 241.942 (D)s 6 f 259.103 y 252.523 (:)s 11 f 258.628 (H)s 8 f 255.474 y 267.17 (1)s 6 f 259.103 y 271.656 (\050)s 12 f 275.545 (R)s 9 f 255.474 y 282.767 (N)s 6 f 259.103 y 290.352 (\051)s 11 f 297.568 (!)s 12 f 310.896 (C)s 6 f 321.781 (b)s 327.614 (e)s 335.722 (the)s 353.274 (quadratic)s 398.354 (form)s 271.103 y 63 (de)s 73 (\257ned)s 97.445 (b)s 102.722 (y)s 111.333 (\050)s 11 f 118.556 (H)s 8 f 267.474 y 127.097 (1)s 6 f 271.103 y 131.583 (\050)s 12 f 135.472 (R)s 9 f 267.474 y 142.695 (N)s 6 f 271.103 y 150.279 (\051)s 157.502 (stands)s 188.724 (for)s 204.029 (the)s 221.252 (\257rst)s 7 f 241.891 (L)s 8 f 267.474 y 248.696 (2)s 6 f 271.103 y 256.516 (Sob)s 272.905 (olev)s 293.738 (space\051)s 7 f 297.468 y 160.844 (t)s 9 f 298.968 y 164.455 (D)s 6 f 297.468 y 171.709 ([)s 7 f 174.487 (\303)s 6 f 181.36 (])s 186.915 (:=)s 10 f 283.857 y 200.248 (Z)s 20 f 306.579 y 205.804 (R)s 13 f 304.579 y 210.86 (N)s 19 f 216.783 (\241)s 18 f 222.2 (1)s 11 f 297.468 y 228.269 (j)s 7 f 231.047 (\303)s 11 f 240.142 (\261)s 7 f 247.364 (D)s 6 f 255.921 (\050)s 7 f 259.81 (u)s 6 f 265.535 (\051)s 11 f 269.424 (j)s 8 f 293.339 y 272.201 (2)s 11 f 297.468 y 276.687 (j)s 7 f 279.465 (D)s 17 f 293.339 y 288.022 (0)s 6 f 297.468 y 290.828 (\050)s 7 f 294.717 (u)s 6 f 300.441 (\051)s 11 f 304.33 (j)s 7 f 307.108 (du:)s 6 f 323.777 y 63 (If)s 7 f 73.521 (D)s 9 f 325.277 y 81.801 (j)s 6 f 323.777 y 89.869 (and)s 7 f 109.835 (D)s 9 f 325.277 y 118.114 (j)s 121.397 (;k)s 6 f 323.777 y 132.547 (denote)s 165.29 (resp)s 183.429 (ectiv)s 203.985 (ely)s 220.34 (a)s 229.194 (parametrisation)s 302.049 (of)s 7 f 313.96 (x)s 9 f 325.277 y 319.675 (j)s 6 f 323.777 y 327.535 (=)s 338.96 (0)s 347.814 (and)s 7 f 367.78 (x)s 9 f 325.277 y 373.496 (j)s 6 f 323.777 y 381.356 (=)s 7 f 392.78 (x)s 9 f 325.277 y 398.496 (k)s 6 f 323.777 y 407.27 (w)s 414.215 (e)s 335.777 y 63 (let)s 7 f 78.171 (t)s 6 f 85.77 (:=)s 7 f 100.314 (t)s 8 f 337.277 y 103.925 (0)s 6 f 335.777 y 111.118 (+)s 7 f 121.602 (t)s 8 f 337.277 y 125.213 (1)s 6 f 335.777 y 133.759 (with)s 7 f 157.263 (t)s 8 f 337.277 y 160.874 (0)s 7 f 335.777 y 165.36 (;)s 169.805 (t)s 8 f 337.277 y 173.416 (1)s 6 f 335.777 y 181.89 (:)s 11 f 188.656 (H)s 8 f 332.148 y 197.198 (1)s 6 f 335.777 y 201.684 (\050)s 12 f 205.573 (R)s 9 f 332.148 y 212.795 (N)s 6 f 335.777 y 220.38 (\051)s 11 f 228.257 (!)s 12 f 242.245 (C)s 6 f 253.527 (b)s 259.361 (eing)s 281.198 (the)s 299.147 (quadratic)s 344.623 (forms)s 372.933 (de)s 382.933 (\257ned)s 408.104 (b)s 413.382 (y)s 7 f 349.089 y 63 (t)s 8 f 350.589 y 66.611 (0)s 6 f 349.089 y 71.097 ([)s 7 f 73.875 (\303)s 6 f 80.748 (])s 86.303 (:=)s 10 f 341.588 y 99.637 (P)s 9 f 344.061 y 110.192 (N)s 352.089 y 110.192 (j)s 8 f 113.906 (=1)s 11 f 349.089 y 126.197 (k)s 7 f 131.197 (@)s 9 f 350.589 y 136.506 (j)s 7 f 349.089 y 140.72 (\303)s 11 f 147.593 (k)s 8 f 345.46 y 152.593 (2)s 6 f 349.089 y 160.412 (and)s 7 f 381.987 y 180.717 (t)s 8 f 383.487 y 184.328 (1)s 6 f 381.987 y 191.592 (=)s 11 f 202.147 (\241)s 7 f 209.925 (Z)s 9 f 369.487 y 222.813 (N)s 10 f 372.487 y 219.133 (X)s 9 f 393.785 y 219.436 (j)s 8 f 223.15 (=1)s 7 f 381.987 y 235.245 (t)s 9 f 383.487 y 238.856 (D)s 13 f 384.487 y 245.394 (j)s 6 f 381.987 y 251.852 (+)s 9 f 369.487 y 265.532 (N)s 10 f 372.487 y 261.852 (X)s 9 f 394.015 y 261.883 (j)s 265.596 (\074k)s 7 f 381.987 y 277.963 (t)s 9 f 383.487 y 281.574 (D)s 13 f 384.548 y 288.113 (j)s 291.002 (;k)s 7 f 381.987 y 298.165 (:)s 6 f 413.574 y 63 (One)s 85.391 (can)s 105.003 (c)s 109.17 (hec)s 123.337 (k)s 133.227 (easily)s 162.062 (that)s 7 f 185.009 (t)s 6 f 193.232 (is)s 204.567 (closed)s 235.347 (symmetric,)s 288.099 (densely)s 324.712 (de)s 334.712 (\257ned)s 360.435 (and)s 381.159 (b)s 386.993 (ounded)s 425.574 y 63 (b)s 68.833 (elo)s 80.778 (w)s 91.333 (and)s 110.778 (therefore)s 7 f 152.778 (t)s 6 f 159.722 (de)s 169.722 (\257nes)s 192.556 (a)s 200.889 (selfadjoin)s 241.778 (t)s 249 (op)s 259.834 (erator)s 289.334 (that)s 311 (w)s 317.945 (e)s 325.723 (denote)s 357.945 (b)s 363.223 (y)s 7 f 371.834 (h)s 6 f 377.595 (.)s 445.1 y 63 (Next)s 87.444 (w)s 94.389 (e)s 102.167 (explain)s 136.889 (what)s 7 f 161.889 (I)s 163.736 (\246)s 8 f 439.905 y 172.861 (\0500\051)s 14 f 447.766 y 172.861 (0)s 6 f 445.1 y 186.931 (is.)s 199.764 (Eac)s 215.736 (h)s 7 f 224.625 (H)s 9 f 446.6 y 232.938 (j)s 6 f 445.1 y 240.485 (is)s 250.54 (unitarily)s 291.401 (equiv)s 314.179 (alen)s 331.679 (t)s 338.902 (to:)s 7 f 472.715 y 109.307 (H)s 9 f 474.215 y 117.62 (j)s 11 f 472.715 y 124.611 (\273)s 7 f 135.167 (B)s 10 f 463.215 y 147.808 (M)s 9 f 484.704 y 144.92 (m)s 13 f 485.704 y 152.016 (j)s 17 f 484.704 y 155.752 (2)s 20 f 161.141 (Z)s 10 f 458.614 y 167.474 (\265)s 11 f 472.715 y 174.835 (\241)s 7 f 182.613 (@)s 8 f 468.586 y 188.478 (2)s 9 f 475.187 y 187.922 (x)s 13 f 476.187 y 192.457 (j)s 6 f 472.715 y 198.915 (+)s 7 f 208.915 (H)s 8 f 467.298 y 218.04 (\050)s 9 f 221.165 (m)s 13 f 468.298 y 228.261 (j)s 8 f 467.298 y 231.997 (\051)s 475.502 y 217.227 (osc)s 9 f 227.937 (;j)s 11 f 472.715 y 237.844 (\241)s 6 f 247.844 (2)s 7 f 252.844 (m)s 9 f 474.215 y 261.624 (j)s 11 f 472.715 y 268.06 (\241)s 7 f 278.06 (\270)s 283.893 (Z)s 6 f 465.95 y 297.275 (1)s 14.281 .4 292.635 470.415 r 11 f 479.574 y 292.635 (j)s 7 f 295.413 (r)s 9 f 481.074 y 299.924 (j)s 11 f 479.574 y 304.138 (j)s 10 f 458.614 y 308.115 (\266)s 7 f 472.715 y 317.143 (;)s 331.588 (\270)s 6 f 340.199 (:=)s 465.95 y 360.442 (1)s 16.42 .4 354.732 470.415 r 11 f 472.414 y 354.732 (p)s 8.087 .4 363.065 472.414 r 7 f 480.881 y 363.065 (B)s 6 f 506.069 y 63 (where)s 7 f 91.505 (H)s 8 f 507.569 y 99.817 (osc)s 9 f 110.527 (;j)s 6 f 506.069 y 119.893 (:=)s 11 f 133.226 (\241)s 7 f 141.004 (@)s 8 f 502.441 y 146.869 (2)s 9 f 508.542 y 146.313 (y)s 13 f 509.542 y 150.369 (j)s 11 f 506.069 y 156.003 (\241)s 7 f 165.179 (@)s 8 f 502.441 y 171.043 (2)s 9 f 508.542 y 170.488 (z)s 13 f 509.542 y 174.308 (j)s 6 f 506.069 y 179.942 (+)s 7 f 189.118 (y)s 8 f 502.441 y 194.38 (2)s 9 f 508.672 y 194.021 (j)s 6 f 506.069 y 200.264 (+)s 7 f 209.44 (z)s 8 f 502.441 y 214.53 (2)s 9 f 508.672 y 214.09 (j)s 6 f 506.069 y 221.937 (is)s 231.581 (the)s 248.391 (harmonic)s 291.896 (oscillator)s 334.345 (whic)s 354.067 (h)s 362.544 (describ)s 393.46 (es)s 404.771 (the)s 521.958 y 63 (Landau)s 99.225 (lev)s 111.447 (els)s 125.923 (of)s 137.287 (the)s 7 f 154.484 (j)s 8 f 518.329 y 159.175 (th)s 6 f 521.958 y 170.525 (electron)s 208.305 (and)s 7 f 227.725 (H)s 8 f 516.764 y 236.85 (\050)s 9 f 239.975 (m)s 8 f 247.071 (\051)s 524.746 y 236.038 (osc)s 9 f 246.747 (;j)s 6 f 521.958 y 256.644 (its)s 270.564 (restriction)s 318.428 (to)s 330.626 (angular)s 366.74 (momen)s 398.129 (ta)s 410.326 (in)s 533.958 y 63 (the)s 7 f 80.222 (x)s 6 f 85.938 (-direction)s 130.965 (of)s 142.354 (v)s 147.077 (alue)s 7 f 168.188 (m)s 6 f 176.968 (.)s 183.079 (In)s 195.579 (other)s 221.718 (w)s 228.662 (ords)s 7 f 560.726 y 126.789 (H)s 8 f 555.309 y 135.914 (\050)s 9 f 139.039 (m)s 13 f 556.309 y 146.135 (j)s 8 f 555.309 y 149.871 (\051)s 563.513 y 135.102 (osc)s 9 f 145.811 (;j)s 11 f 560.726 y 155.718 (\241)s 6 f 165.718 (2)s 7 f 170.718 (m)s 9 f 562.226 y 179.498 (j)s 6 f 560.726 y 186.49 (=)s 17 f 548.226 y 202.461 (1)s 10 f 551.226 y 198.892 (M)s 9 f 572.404 y 197.045 (n)s 13 f 573.404 y 201.988 (j)s 8 f 572.404 y 205.724 (=0)s 6 f 560.726 y 217.516 (\050)s 221.405 (2\050)s 11 f 230.294 (j)s 7 f 233.072 (m)s 9 f 562.226 y 241.852 (j)s 11 f 560.726 y 246.065 (j)s 251.065 (\241)s 7 f 261.065 (m)s 9 f 562.226 y 269.845 (j)s 6 f 560.726 y 274.059 (\051)s 280.17 (+)s 290.17 (4)s 7 f 295.17 (n)s 9 f 562.226 y 301.172 (j)s 6 f 560.726 y 307.608 (+)s 317.608 (2)s 322.608 (\051)s 7 f 328.163 (\246)s 8 f 555.309 y 337.288 (\050)s 9 f 340.413 (m)s 13 f 556.309 y 347.51 (j)s 8 f 555.309 y 351.245 (\051)s 9 f 563.513 y 336.476 (j)s 339.759 (;n)s 13 f 564.513 y 347.077 (j)s do-end end endp showpage %%Page: 4 4 %%BeginPageSetup initializepage (duclos ; page : 4 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f221 sf ( )S -988 -1000 :M f255 sf ( )S -982 -1000 :M f287 sf ( )S -976 -1000 :M f320 sf ( )S -970 -1000 :M f354 sf ( )S -964 -1000 :M f388 sf ( )S -958 -1000 :M f455 sf ( )S -952 -1000 :M f488 sf ( )S -946 -1000 :M f589 sf ( )S -940 -1000 :M f621 sf ( )S -934 -1000 :M f687 sf ( )S -931 -1000 :M f721 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 13 5 /CMMI5 findfont fdef 14 7 /CMBX7 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 20 7 /MSBM7 findfont fdef 24 10 /CMTI10 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (4)s 308.564 (R.)s 321.025 (Brummelh)s 363.315 (uis,)s 380.325 (P)s 385.849 (.)s 391.501 (Duclos)s 6 f 54.667 y 63 (where)s 7 f 91.117 (\246)s 8 f 49.25 y 100.242 (\050)s 9 f 103.367 (m)s 13 f 50.25 y 110.463 (j)s 8 f 49.25 y 114.199 (\051)s 9 f 57.454 y 99.429 (j)s 102.712 (;n)s 13 f 58.454 y 110.031 (j)s 6 f 54.667 y 120.357 (is)s 129.613 (the)s 146.036 (eigenpro)s 183.286 (jector)s 210.569 (on)s 223.658 (the)s 7 f 240.081 (n)s 8 f 51.038 y 246.083 (th)s 9 f 57.27 y 246.083 (j)s 6 f 54.667 y 256.658 (lev)s 268.88 (el)s 278.636 (of)s 289.225 (this)s 307.925 (harmonic)s 351.042 (oscillator.)s 395.882 (Then)s 7 f 84.368 y 118.235 (I)s 120.083 (\246)s 8 f 79.174 y 129.208 (\0500\051)s 14 f 87.035 y 129.208 (0)s 6 f 84.368 y 142.721 (:=)s 7 f 156.055 (\246)s 8 f 79.174 y 165.18 (\0500\051)s 87.035 y 164.367 (1)s 9 f 168.353 (;)s 8 f 170.728 (0)s 11 f 84.368 y 178.138 (\255)s 7 f 188.138 (:)s 192.582 (:)s 197.027 (:)s 11 f 202.027 (\255)s 7 f 212.027 (\246)s 8 f 79.174 y 221.152 (\0500\051)s 9 f 87.307 y 220.339 (N)s 226.993 (;)s 8 f 229.368 (0)s 6 f 84.368 y 243.855 (and)s 81.841 y 272.952 (\136)s 7 f 84.368 y 269.966 (I)s 271.813 (\246)s 8 f 77.368 y 280.938 (\0500\051)s 14 f 86.84 y 280.938 (0)s 6 f 84.368 y 294.452 (:=)s 7 f 307.785 (I)s 309.632 (\246)s 8 f 80.007 y 318.757 (\0500\051)s 11 f 84.368 y 331.716 (\241)s 7 f 341.716 (I)s 343.563 (\246)s 8 f 79.174 y 352.688 (\0500\051)s 14 f 87.035 y 352.688 (0)s 6 f 108.06 y 63 (where)s 7 f 122.598 y 134.746 (I)s 136.593 (\246)s 8 f 118.237 y 145.718 (\0500\051)s 6 f 122.598 y 159.232 (:=)s 10 f 113.098 y 192.366 (X)s 9 f 134.276 y 172.565 (m)s 18 f 135.276 y 179.661 (1)s 8 f 134.276 y 183.564 (+)s 9 f 189.703 (:::)s 8 f 196.828 (+)s 9 f 202.967 (m)s 13 f 135.282 y 210.063 (N)s 8 f 134.276 y 216.487 (=0)s 10 f 113.098 y 231.962 (X)s 9 f 135.182 y 228.278 (n)s 17 f 233.222 (2)s 20 f 238.611 (N)s 13 f 133.182 y 243.666 (N)s 7 f 122.598 y 251.756 (\246)s 8 f 117.404 y 260.881 (\050)s 9 f 264.006 (m)s 18 f 118.404 y 271.102 (1)s 8 f 117.404 y 275.005 (\051)s 125.265 y 260.069 (1)s 9 f 264.055 (;n)s 18 f 126.265 y 271.373 (1)s 11 f 122.598 y 280.852 (\255)s 7 f 290.852 (:)s 295.297 (:)s 299.741 (:)s 11 f 304.741 (\255)s 7 f 314.741 (\246)s 8 f 117.404 y 323.866 (\050)s 9 f 326.991 (m)s 13 f 118.409 y 334.087 (N)s 8 f 117.404 y 340.511 (\051)s 9 f 125.537 y 323.054 (N)s 329.708 (;n)s 13 f 126.543 y 337.026 (N)s 7 f 122.598 y 344.136 (:)s 6 f 155.86 y 63 (With)s 88.833 (these)s 114.445 (notations)s 158.389 (one)s 176.722 (has:)s 7 f 197.334 (I)s 199.181 (H)s 8 f 151.499 y 208.306 (\0500\051)s 6 f 155.86 y 221.82 (:=)s 7 f 235.153 (I)s 237 (\246)s 8 f 151.499 y 246.125 (\0500\051)s 7 f 155.86 y 256.861 (I)s 258.709 (H)s 269.5 (I)s 271.348 (\246)s 8 f 151.499 y 280.473 (\0500\051)s 6 f 155.86 y 291.209 (.)s 176.14 y 63 (Then)s 89.111 (w)s 96.056 (e)s 103.833 (in)s 111.889 (tro)s 124.972 (duce)s 148.306 (new)s 168.861 (notations.)s 215.584 (Let)s 7 f 202.541 y 189.103 (a)s 6 f 197.167 (:=)s 210.5 (2)s 7 f 215.5 (\270)s 6 f 223 (log)s 7 f 237.583 (\270)s 17 f 198.413 y 243.417 (\241)s 8 f 249.667 (1)s 6 f 202.541 y 256.931 (=)s 195.776 y 268.686 (log)s 7 f 283.269 (B)s 22.67 .4 268.686 200.241 r 11 f 202.241 y 271.811 (p)s 8.087 .4 280.144 202.241 r 7 f 210.708 y 280.144 (B)s 6 f 231.478 y 63 (and)s 262.453 y 70.577 (\050)s 74.466 (log)s 7 f 89.05 (B)s 6 f 97.136 (\051)s 17 f 258.324 y 101.025 (\241)s 8 f 107.275 (2)s 7 f 262.453 y 111.761 (U)s 10 f 251.353 y 121.346 (\263)s 7 f 262.453 y 127.318 (I)s 129.166 (H)s 8 f 258.092 y 138.291 (\0500\051)s 11 f 262.453 y 151.249 (\241)s 6 f 161.249 (2)s 7 f 166.249 (N)s 175.374 (B)s 10 f 251.353 y 183.461 (\264)s 7 f 262.453 y 191.1 (U)s 17 f 258.324 y 199.018 (\241)s 8 f 205.268 (1)s 6 f 262.453 y 212.531 (=:)s 7 f 225.865 (T)s 9 f 258.324 y 233.097 (a)s 11 f 262.453 y 240.157 (\241)s 7 f 255.688 y 253.327 (\270)s 9.772 .4 251.357 260.153 r 269.313 y 251.357 (a)s 8 f 266.424 y 256.643 (2)s 11 f 262.453 y 262.329 (V)s 9 f 258.324 y 269.279 (a)s 7 f 262.453 y 274.117 (;)s 11 f 288.561 (V)s 6 f 298.289 (:=)s 9 f 249.953 y 315.302 (N)s 10 f 252.953 y 311.622 (X)s 9 f 274.252 y 311.925 (j)s 8 f 315.639 (=1)s 6 f 255.688 y 333.574 (1)s 14.281 .4 328.933 260.153 r 11 f 269.313 y 328.933 (j)s 7 f 331.711 (r)s 9 f 270.813 y 336.223 (j)s 11 f 269.313 y 340.436 (j)s 262.453 y 346.636 (\241)s 10 f 252.953 y 356.636 (X)s 9 f 274.481 y 356.667 (j)s 360.38 (\074k)s 6 f 255.688 y 389.415 (1)s 35.935 .4 373.947 260.153 r 11 f 269.313 y 373.947 (j)s 7 f 376.725 (r)s 9 f 270.813 y 381.237 (j)s 11 f 269.313 y 387.673 (\241)s 7 f 397.672 (r)s 9 f 270.813 y 402.184 (k)s 11 f 269.313 y 407.104 (j)s 6 f 299.345 y 63 (where)s 7 f 92.493 (T)s 9 f 295.716 y 99.726 (a)s 6 f 299.345 y 108.473 (is)s 119.105 (the)s 136.903 (kinetic)s 169.98 (part)s 192.25 (i.e.)s 7 f 208.938 (T)s 9 f 295.716 y 216.17 (a)s 6 f 299.345 y 224.746 (=)s 10 f 291.845 y 236.262 (P)s 9 f 294.317 y 246.818 (N)s 302.345 y 246.818 (j)s 8 f 250.531 (=1)s 11 f 299.345 y 262.823 (\241)s 7 f 270.601 (@)s 8 f 295.716 y 276.465 (2)s 9 f 301.817 y 275.91 (x)s 13 f 302.817 y 280.445 (j)s 6 f 299.345 y 287.287 (+)s 7 f 297.671 (a)s 17 f 295.716 y 302.957 (\241)s 8 f 309.207 (2)s 6 f 299.345 y 313.693 (\050)s 7 f 317.582 (H)s 8 f 300.845 y 325.894 (osc)s 9 f 336.604 (;j)s 11 f 299.345 y 345.799 (\241)s 6 f 356.183 (2)s 11 f 363.789 (\241)s 6 f 374.174 (2)s 7 f 379.174 (L)s 9 f 300.845 y 385.979 (x)s 13 f 301.845 y 390.514 (j)s 6 f 299.345 y 394.75 (\051)s 402.548 (and)s 11 f 314.401 y 63 (V)s 9 f 310.772 y 69.95 (a)s 6 f 314.401 y 74.788 (\050)s 7 f 78.677 (r)s 6 f 83.466 (\051)s 90.133 (:=)s 11 f 103.466 (V)s 6 f 110.416 (\050)s 7 f 114.305 (x=a;)s 134.75 (y)s 140.012 (;)s 144.456 (z)s 6 f 149.547 (\051)s 153.436 (,)s 159.547 (b)s 165.38 (oth)s 183.158 (sandwic)s 217.38 (hed)s 236.269 (b)s 242.102 (et)s 250.158 (w)s 257.102 (een)s 7 f 274.88 (I)s 276.728 (\246)s 8 f 310.04 y 285.852 (\0500\051)s 6 f 314.401 y 296.589 (.)s 334.68 y 63 (W)s 72.444 (e)s 80.728 (compute)s 121.789 (the)s 139.516 (resolv)s 164.6 (en)s 174.322 (t)s 182.049 (of)s 193.944 (this)s 213.949 (op)s 224.783 (erator)s 254.788 (at)s 267.516 (a)s 276.354 (p)s 282.188 (oin)s 295.243 (t)s 7 f 302.971 (\273)s 311.426 (\074)s 11 f 322.824 (\241)s 7 f 330.602 (N)s 339.727 (Z)s 8 f 331.051 y 347.268 (2)s 7 f 334.68 y 351.754 (=)s 6 f 356.754 (4)s 365.593 (since)s 390.599 (suc)s 404.265 (h)s 413.659 (a)s 346.68 y 63 (p)s 68.833 (oin)s 81.889 (t)s 89.84 (surely)s 119.819 (b)s 125.652 (elongs)s 156.437 (to)s 169.388 (the)s 187.339 (resolv)s 212.422 (en)s 222.144 (t)s 230.095 (set)s 246.435 (of)s 7 f 258.553 (h)s 6 f 264.314 (.)s 271.154 (W)s 280.599 (e)s 289.105 (do)s 303.723 (this)s 323.952 (with)s 347.458 (a)s 356.52 (F)s 362.215 (esh)s 375.882 (bac)s 390.604 (h-t)s 403.104 (yp)s 414.215 (e)s 358.68 y 63 (form)s 83.028 (ula)s 99.171 (using)s 124.813 (the)s 141.512 (decomp)s 175.123 (osition)s 206.877 (of)s 217.742 (Ran)s 7 f 237.325 (I)s 239.172 (\246)s 8 f 354.319 y 248.297 (\0500\051)s 6 f 358.68 y 261.843 (as)s 273.597 (Ran)s 7 f 293.18 (I)s 295.027 (\246)s 9 f 360.18 y 304.152 (s)s 11 f 358.68 y 309.601 (\251)s 6 f 318.553 (Ran)s 7 f 338.136 (I)s 339.984 (\246)s 9 f 360.18 y 349.109 (r)s 6 f 358.68 y 356.346 (where)s 384.739 (w)s 391.683 (e)s 398.937 (ha)s 409.215 (v)s 414.215 (e)s 373.875 y 63 (set)s 7 f 78.618 (I)s 80.465 (\246)s 9 f 375.375 y 89.59 (s)s 6 f 373.875 y 96.653 (:=)s 7 f 109.997 (I)s 111.845 (\246)s 8 f 368.68 y 120.97 (\0500\051)s 14 f 376.541 y 120.97 (0)s 6 f 373.875 y 135.046 (and)s 7 f 154.497 (I)s 156.344 (\246)s 9 f 375.375 y 165.469 (r)s 6 f 373.875 y 172.686 (:=)s 371.347 y 189.016 (\136)s 7 f 373.875 y 186.03 (I)s 187.878 (\246)s 8 f 366.875 y 197.003 (\0500\051)s 14 f 376.347 y 197.003 (0)s 6 f 373.875 y 207.739 (,)s 213.856 (to)s 226.085 (ease)s 247.258 (the)s 264.487 (notations.)s 311.216 (In)s 323.723 (the)s 340.952 (sequel)s 370.736 (a)s 379.076 (subscript)s 7 f 385.875 y 63 (s)s 6 f 71.84 (or)s 7 f 84.909 (r)s 6 f 93.851 (on)s 108.558 (an)s 123.266 (op)s 134.1 (erator)s 164.419 (indicate)s 203.016 (that)s 225.501 (the)s 243.543 (pro)s 258.57 (jection)s 7 f 291.889 (I)s 293.737 (\246)s 9 f 387.375 y 302.862 (s)s 6 f 385.875 y 311.288 (or)s 7 f 324.357 (I)s 326.205 (\246)s 9 f 387.375 y 335.33 (r)s 6 f 385.875 y 343.91 (has)s 362.563 (b)s 368.396 (een)s 386.993 (applied)s 397.875 y 63 (on)s 76.987 (the)s 94.306 (left)s 111.904 (or)s 124.252 (on)s 138.238 (the)s 155.558 (righ)s 172.53 (t)s 179.85 (according)s 224.976 (to)s 237.296 (the)s 254.615 (p)s 260.449 (osition)s 292.824 (of)s 304.311 (the)s 321.631 (subscript:)s 367.423 (for)s 382.826 (example)s 11 f 409.875 y 63 (V)s 9 f 406.246 y 69.95 (a)s 412.347 y 69.128 (s;r)s 6 f 409.875 y 82.483 (:=)s 7 f 95.816 (I)s 97.664 (\246)s 9 f 411.375 y 106.789 (s)s 11 f 409.875 y 111.063 (V)s 9 f 406.246 y 118.013 (a)s 7 f 409.875 y 122.851 (I)s 124.698 (\246)s 9 f 411.375 y 133.823 (r)s 6 f 409.875 y 138.251 (,)s 143.872 (or)s 155.632 (simply)s 7 f 187.141 (T)s 9 f 406.246 y 194.374 (a)s 412.347 y 192.985 (r)s 6 f 409.875 y 201.989 (:=)s 7 f 215.323 (I)s 217.17 (\246)s 9 f 411.375 y 226.295 (r)s 7 f 409.875 y 230.723 (T)s 9 f 406.246 y 237.956 (a)s 7 f 409.875 y 242.794 (I)s 244.641 (\246)s 9 f 411.375 y 253.766 (r)s 6 f 409.875 y 261.037 (when)s 286.658 (this)s 305.668 (pro)s 320.695 (jection)s 352.705 (comm)s 378.539 (utes)s 399.215 (with)s 421.875 y 63 (this)s 82.5 (op)s 93.333 (erator.)s 125.611 (So)s 451.516 y 100.08 (\050)s 7 f 103.969 (T)s 9 f 447.388 y 111.202 (a)s 11 f 451.516 y 118.262 (\241)s 7 f 444.751 y 131.431 (\270)s 9.772 .4 129.462 449.216 r 458.376 y 129.462 (a)s 8 f 455.487 y 134.748 (2)s 11 f 451.516 y 140.434 (V)s 9 f 447.388 y 147.384 (a)s 11 f 451.516 y 154.444 (\241)s 7 f 164.444 (\273)s 6 f 169.279 (\051)s 17 f 447.388 y 173.167 (\241)s 8 f 179.418 (1)s 6 f 451.516 y 186.681 (=)s 10 f 437.416 y 197.237 (\265)s 7 f 444.011 y 225.976 (S)s 9 f 440.382 y 232.685 (a)s 440.074 y 297.141 (\270)s 8.24 .4 295.393 441.711 r 447.46 y 295.393 (a)s 18 f 445.46 y 299.73 (2)s 7 f 444.011 y 304.833 (S)s 9 f 440.382 y 311.542 (a)s 11 f 444.011 y 316.379 (V)s 9 f 440.382 y 323.329 (a)s 446.483 y 322.507 (s;r)s 7 f 444.011 y 333.085 (R)s 9 f 440.382 y 340.755 (a)s 455.084 y 209.213 (\270)s 8.24 .4 207.465 456.722 r 462.47 y 207.465 (a)s 18 f 460.47 y 211.802 (2)s 7 f 459.022 y 216.905 (R)s 9 f 455.393 y 224.575 (a)s 11 f 459.022 y 229.413 (V)s 9 f 455.393 y 236.363 (a)s 461.494 y 235.541 (r)s 239.038 (;s)s 7 f 459.022 y 245.688 (S)s 9 f 455.393 y 252.396 (a)s 7 f 459.022 y 267.234 (R)s 9 f 455.393 y 274.904 (a)s 6 f 459.022 y 281.964 (+)s 9 f 455.084 y 293.164 (\270)s 18 f 452.067 y 297.907 (2)s 8.646 .4 293.164 456.722 r 9 f 462.47 y 293.366 (a)s 18 f 460.47 y 297.704 (4)s 7 f 459.022 y 303.01 (R)s 9 f 455.393 y 310.68 (a)s 11 f 459.022 y 315.517 (V)s 9 f 455.393 y 322.467 (a)s 461.494 y 321.645 (r)s 325.143 (;s)s 7 f 459.022 y 331.792 (S)s 9 f 455.393 y 338.501 (a)s 11 f 459.022 y 343.338 (V)s 9 f 455.393 y 350.288 (a)s 461.494 y 349.466 (s;r)s 7 f 459.022 y 360.044 (R)s 9 f 455.393 y 367.714 (a)s 10 f 437.416 y 374.218 (\266)s 6 f 481.158 y 63 (where)s 7 f 508.755 y 80.34 (R)s 9 f 504.626 y 88.01 (a)s 6 f 508.755 y 95.626 (:=)s 108.959 (\050)s 7 f 112.848 (T)s 9 f 504.626 y 120.081 (a)s 511.227 y 118.692 (r)s 11 f 508.755 y 127.14 (\241)s 7 f 501.99 y 140.31 (\270)s 9.772 .4 138.34 506.455 r 515.615 y 138.34 (a)s 8 f 512.726 y 143.626 (2)s 11 f 508.755 y 149.312 (V)s 9 f 504.626 y 156.262 (a)s 511.227 y 155.44 (r)s 158.938 (;r)s 11 f 508.755 y 167.963 (\241)s 7 f 177.963 (\273)s 6 f 182.798 (\051)s 17 f 504.626 y 186.687 (\241)s 8 f 192.937 (1)s 7 f 508.755 y 197.423 (;)s 211.868 (S)s 9 f 504.626 y 218.576 (a)s 6 f 508.755 y 226.191 (:=)s 239.525 (\050)s 7 f 243.414 (T)s 9 f 504.626 y 250.646 (a)s 511.227 y 249.257 (s)s 11 f 508.755 y 257.706 (\241)s 7 f 501.99 y 270.875 (\270)s 9.772 .4 268.906 506.455 r 515.615 y 268.906 (a)s 8 f 512.726 y 274.192 (2)s 11 f 508.755 y 279.878 (V)s 9 f 504.626 y 286.828 (a)s 511.227 y 286.006 (s;s)s 11 f 508.755 y 298.652 (\241)s 7 f 501.99 y 309.852 (\270)s 8 f 498.361 y 315.685 (2)s 10.319 .4 309.852 506.455 r 7 f 515.615 y 310.125 (a)s 8 f 512.726 y 315.411 (4)s 11 f 508.755 y 321.371 (V)s 9 f 504.626 y 328.321 (a)s 511.227 y 327.499 (s;r)s 7 f 508.755 y 338.077 (R)s 9 f 504.626 y 345.747 (a)s 11 f 508.755 y 350.584 (V)s 9 f 504.626 y 357.534 (a)s 511.227 y 356.712 (r)s 360.21 (;s)s 11 f 508.755 y 369.081 (\241)s 7 f 379.081 (\273)s 6 f 383.916 (\051)s 17 f 504.626 y 387.805 (\241)s 8 f 394.055 (1)s 7 f 508.755 y 398.541 (:)s 6 f 535.251 y 63 (W)s 72.444 (e)s 80.222 (insp)s 98.333 (ect)s 114.445 (all)s 128.333 (terms)s 156.195 (step)s 177.361 (b)s 182.639 (y)s 191.25 (step.)s 24 f 558.376 y 63 (Bound)s 94.246 (on)s 7 f 107.975 (R)s 9 f 554.747 y 115.645 (a)s 8 f 560.858 y 115.567 (0)s 6 f 558.376 y 123.26 (:=)s 136.593 (\050)s 7 f 140.482 (T)s 9 f 554.747 y 147.715 (a)s 560.848 y 146.326 (r)s 11 f 558.376 y 153.509 (\241)s 7 f 162.244 (\273)s 6 f 167.079 (\051)s 17 f 554.747 y 170.968 (\241)s 8 f 177.218 (1)s 6 f 558.376 y 181.704 (.)s 187.183 (Since)s 7 f 212.661 (T)s 9 f 554.747 y 219.894 (a)s 560.848 y 218.505 (r)s 11 f 558.376 y 227.509 (\270)s 6 f 238.065 (4)s 7 f 243.065 (a)s 17 f 554.747 y 248.351 (\241)s 8 f 254.601 (2)s 7 f 558.376 y 259.087 (I)s 260.934 (\246)s 9 f 559.876 y 270.059 (r)s 6 f 558.376 y 277.188 (one)s 294.889 (has)s 11 f 312.089 (k)s 7 f 317.089 (R)s 9 f 554.747 y 324.76 (a)s 8 f 560.858 y 324.682 (0)s 11 f 558.376 y 329.597 (k)s 337.375 (\267)s 7 f 347.93 (a)s 8 f 554.747 y 353.216 (2)s 7 f 558.376 y 357.702 (=)s 6 f 362.702 (4)s 367.702 (.)s 373.181 (W)s 382.625 (e)s 389.77 (denote)s 570.376 y 63 (b)s 68.278 (y)s 7 f 76.889 (R)s 8 f 571.876 y 84.482 (0)s 6 f 570.376 y 91.746 (:=)s 105.079 (\050)s 7 f 108.968 (T)s 9 f 571.876 y 114.812 (r)s 11 f 570.376 y 121.462 (\241)s 7 f 131.462 (a)s 8 f 566.747 y 136.748 (2)s 7 f 570.376 y 141.234 (\273)s 6 f 146.069 (\051)s 17 f 566.747 y 149.958 (\241)s 8 f 156.208 (1)s 6 f 570.376 y 164.027 (and)s 183.472 (therefore)s 11 f 225.472 (k)s 7 f 230.472 (R)s 8 f 571.876 y 238.065 (0)s 11 f 570.376 y 242.551 (k)s 250.329 (\267)s 6 f 260.884 (1)s 7 f 265.884 (=)s 6 f 270.884 (4)s 275.884 (.)s 281.995 (Here)s 7 f 305.634 (T)s 6 f 316.2 (means)s 7 f 346.811 (T)s 8 f 566.747 y 354.044 (1)s 6 f 570.376 y 358.53 (.)s do-end end endp showpage %%Page: 5 5 %%BeginPageSetup initializepage (duclos ; page : 5 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f221 sf ( )S -988 -1000 :M f255 sf ( )S -982 -1000 :M f287 sf ( )S -976 -1000 :M f320 sf ( )S -970 -1000 :M f354 sf ( )S -964 -1000 :M f388 sf ( )S -958 -1000 :M f455 sf ( )S -952 -1000 :M f589 sf ( )S -946 -1000 :M f621 sf ( )S -940 -1000 :M f721 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 13 5 /CMMI5 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 24 10 /CMTI10 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (1-d)s 78.93 (b)s 84.326 (eha)s 97.948 (viour)s 121.864 (of)s 132.399 (atoms)s 159.686 (in)s 170.478 (in)s 177.929 (tense)s 201.626 (magnetic)s 241.199 (\257elds)s 414.034 (5)s 24 f 54 y 63 (Bound)s 94.095 (on)s 11 f 107.674 (j)s 7 f 110.452 (r)s 9 f 55.5 y 114.963 (j)s 11 f 54 y 119.177 (j)s 17 f 50.371 y 121.955 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118.229 (\270)s 124.063 (a)s 17 f 236.002 y 129.348 (\241)s 8 f 135.598 (2)s 10 f 231.509 y 140.085 (p)s 12.508 .4 150.085 231.509 r 7 f 240.131 y 150.085 (R)s 9 f 236.687 y 157.755 (a)s 8 f 242.798 y 157.677 (0)s 7 f 240.131 y 164.259 (Z)s 11 f 171.801 (j)s 7 f 174.578 (r)s 9 f 236.002 y 179.368 (a)s 242.603 y 179.09 (j)s 11 f 240.131 y 184.205 (j)s 17 f 236.002 y 186.983 (\241)s 8 f 193.233 (1)s 10 f 231.509 y 197.719 (p)s 12.508 .4 207.719 231.509 r 7 f 240.131 y 207.719 (R)s 9 f 236.687 y 215.39 (a)s 8 f 242.798 y 215.312 (0)s 11 f 240.131 y 220.227 (k)s 6 f 228.227 (=)s 11 f 239.005 (k)s 7 f 244.005 (\270)s 249.838 (Z)s 10 f 230.926 y 257.38 (p)s 12.079 .4 267.38 230.926 r 7 f 240.131 y 267.38 (R)s 8 f 241.631 y 274.973 (0)s 11 f 240.131 y 281.126 (j)s 7 f 283.904 (r)s 9 f 241.631 y 288.415 (j)s 11 f 240.131 y 292.629 (j)s 17 f 236.002 y 295.406 (\241)s 8 f 301.656 (1)s 10 f 230.926 y 306.143 (p)s 12.079 .4 316.143 230.926 r 7 f 240.131 y 316.143 (R)s 8 f 241.631 y 323.736 (0)s 11 f 240.131 y 328.222 (k)s 258.003 y 228.227 (\267)s 239.005 (j)s 7 f 241.783 (\270)s 247.616 (Z)s 11 f 255.158 (j)s 257.936 (k)s 10 f 248.798 y 262.936 (p)s 12.079 .4 272.936 248.798 r 7 f 258.003 y 272.936 (R)s 8 f 259.503 y 280.529 (0)s 11 f 258.003 y 285.015 (k)s 290.015 (kj)s 7 f 297.792 (r)s 9 f 259.503 y 302.304 (j)s 11 f 258.003 y 306.518 (j)s 17 f 253.874 y 309.295 (\241)s 8 f 315.545 (1)s 7 f 258.003 y 320.032 (R)s 8 f 259.503 y 327.624 (0)s 11 f 258.003 y 332.111 (j)s 7 f 334.888 (r)s 9 f 259.503 y 339.4 (j)s 11 f 258.003 y 343.614 (j)s 17 f 253.874 y 346.391 (\241)s 8 f 352.641 (1)s 11 f 258.003 y 357.127 (k)s 18 f 251.186 y 363.327 (1)s 3.403 .34 363.327 252.294 r 256.283 y 363.327 (2)s 11 f 278.073 y 228.227 (\267)s 239.005 (j)s 7 f 241.783 (\270)s 247.616 (Z)s 11 f 255.158 (j)s 6 f 271.308 y 259.136 (1)s 5 .4 259.136 275.773 r 284.933 y 259.136 (2)s 11 f 269.313 y 265.336 (p)s 5 .4 273.669 269.313 r 6 f 278.073 y 273.669 (6)s 281.447 (=)s 11 f 292.002 (O)s 6 f 300.241 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174.462 (a)s 8 f 359.28 y 174.384 (0)s 10 f 336.514 y 180.966 (0)s 354.514 y 180.966 (@)s 6 f 356.614 y 189.716 (1)s 11 f 196.938 (\241)s 7 f 349.849 y 208.138 (\270)s 213.971 (Z)s 13.375 .4 208.138 354.314 r 363.473 y 209.94 (a)s 8 f 360.584 y 215.225 (2)s 9 f 344.114 y 228.06 (N)s 10 f 347.114 y 224.38 (X)s 9 f 368.412 y 224.683 (j)s 8 f 228.396 (=1)s 10 f 347.992 y 240.491 (p)s 12.508 .4 250.491 347.992 r 7 f 356.614 y 250.491 (R)s 9 f 353.169 y 258.161 (a)s 8 f 359.28 y 258.084 (0)s 11 f 356.614 y 262.999 (j)s 7 f 265.776 (r)s 9 f 352.485 y 270.566 (a)s 359.086 y 270.288 (j)s 11 f 356.614 y 275.403 (j)s 17 f 352.485 y 278.181 (\241)s 8 f 284.431 (1)s 10 f 347.992 y 288.917 (p)s 12.508 .4 298.917 347.992 r 7 f 356.614 y 298.917 (R)s 9 f 353.169 y 306.588 (a)s 8 f 359.28 y 306.51 (0)s 10 f 336.514 y 311.425 (1)s 354.514 y 311.425 (A)s 17 f 338.586 y 320.175 (\241)s 8 f 326.425 (1)s 10 f 347.992 y 332.578 (p)s 12.508 .4 342.578 347.992 r 7 f 356.614 y 342.578 (R)s 9 f 353.169 y 350.248 (a)s 8 f 359.28 y 350.171 (0)s 6 f 389.666 y 63 (whic)s 82.722 (h)s 91.611 (implies)s 11 f 125.556 (k)s 7 f 130.556 (R)s 9 f 386.037 y 138.226 (a)s 11 f 389.666 y 143.063 (k)s 6 f 150.841 (=)s 11 f 161.397 (O)s 6 f 169.636 (\050)s 7 f 173.525 (a)s 8 f 386.037 y 178.81 (2)s 6 f 389.666 y 183.297 (\051)s 187.185 (.)s 24 f 410.285 y 63 (Bound)s 94.701 (on)s 11 f 108.885 (j)s 7 f 111.663 (r)s 9 f 411.785 y 116.175 (j)s 11 f 410.285 y 122.335 (\241)s 7 f 132.06 (r)s 9 f 411.785 y 136.572 (k)s 11 f 410.285 y 141.492 (j)s 17 f 406.656 y 144.27 (\241)s 8 f 150.52 (1)s 7 f 410.285 y 155.006 (R)s 8 f 411.785 y 162.599 (0)s 11 f 410.285 y 167.085 (j)s 7 f 169.863 (r)s 9 f 411.785 y 174.374 (j)s 11 f 410.285 y 180.535 (\241)s 7 f 190.26 (r)s 9 f 411.785 y 194.771 (k)s 11 f 410.285 y 199.691 (j)s 17 f 406.656 y 202.469 (\241)s 8 f 208.719 (1)s 6 f 410.285 y 213.205 (.)s 219.179 (Using)s 247.153 (the)s 264.237 (unitary)s 299.405 (transform)s 345.212 (asso)s 363.379 (ciated)s 392.686 (to)s 404.771 (the)s 422.285 y 63 (c)s 67.167 (hange)s 96.056 (of)s 107.445 (v)s 112.167 (ariables)s 448.142 y 155.24 (\050)s 7 f 159.129 (r)s 9 f 449.642 y 163.64 (j)s 7 f 448.142 y 167.854 (;)s 172.298 (r)s 9 f 449.642 y 176.81 (k)s 6 f 448.142 y 181.73 (\051)s 11 f 188.397 (!)s 10 f 434.042 y 201.174 (\265)s 7 f 448.142 y 208.535 (t)s 6 f 214.924 (:=)s 7 f 441.377 y 229.458 (r)s 9 f 442.877 y 233.969 (j)s 11 f 441.377 y 240.405 (\241)s 7 f 250.405 (r)s 9 f 442.877 y 254.916 (k)s 30.379 .4 229.458 445.842 r 11 f 447.842 y 237.98 (p)s 5 .4 246.314 447.842 r 6 f 456.114 y 246.314 (2)s 7 f 448.142 y 261.037 (;)s 265.481 (s)s 6 f 272.946 (:=)s 7 f 441.377 y 287.48 (r)s 9 f 442.877 y 291.991 (j)s 6 f 441.377 y 298.427 (+)s 7 f 308.427 (r)s 9 f 442.877 y 312.938 (k)s 30.379 .4 287.48 445.842 r 11 f 447.842 y 296.002 (p)s 5 .4 304.336 447.842 r 6 f 456.114 y 304.336 (2)s 10 f 434.042 y 319.059 (\266)s 6 f 448.142 y 398.104 (\0502.1\051)s 11 f 475.194 y 63 (\241)s 7 f 70.778 (\242)s 9 f 476.694 y 79.111 (r)s 13 f 477.694 y 82.824 (j)s 11 f 475.194 y 89.321 (\241)s 7 f 99.36 (\242)s 9 f 476.694 y 107.693 (r)s 13 f 477.755 y 111.406 (k)s 6 f 475.194 y 118.539 (+)s 7 f 128.577 (y)s 8 f 471.565 y 133.839 (2)s 9 f 477.796 y 133.48 (j)s 6 f 475.194 y 140.586 (+)s 7 f 150.625 (z)s 8 f 471.565 y 155.715 (2)s 9 f 477.796 y 155.275 (j)s 6 f 475.194 y 162.462 (+)s 7 f 172.501 (y)s 8 f 471.565 y 177.762 (2)s 9 f 478.026 y 177.404 (k)s 6 f 475.194 y 184.585 (+)s 7 f 194.623 (z)s 8 f 471.565 y 199.714 (2)s 9 f 478.026 y 199.274 (k)s 6 f 475.194 y 207.591 (is)s 217.705 (c)s 221.872 (hanged)s 256.374 (in)s 11 f 268.099 (\241)s 7 f 275.877 (\242)s 9 f 476.694 y 284.21 (s)s 11 f 475.194 y 290.746 (\241)s 7 f 300.784 (\242)s 9 f 476.694 y 309.118 (t)s 6 f 475.194 y 314.9 (+)s 7 f 324.938 (s)s 8 f 471.565 y 329.626 (2)s 477.676 y 329.626 (2)s 6 f 475.194 y 336.373 (+)s 7 f 346.412 (s)s 8 f 471.565 y 351.099 (2)s 477.676 y 351.099 (3)s 6 f 475.194 y 357.846 (+)s 7 f 367.885 (t)s 8 f 471.565 y 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359.523 (j)s 17 f 484.669 y 362.301 (\241)s 8 f 368.551 (1)s 6 f 488.298 y 376.404 (to)s 388.659 (deduce)s 500.298 y 63 (that)s 11 f 512.298 y 152.181 (8)s 7 f 157.736 (j)s 11 f 165.204 (6)s 6 f 165.204 (=)s 7 f 175.76 (k)s 181.281 (;)s 11 f 195.725 (kj)s 7 f 203.503 (r)s 9 f 513.798 y 208.014 (j)s 11 f 512.298 y 214.45 (\241)s 7 f 224.45 (r)s 9 f 513.798 y 228.962 (k)s 11 f 512.298 y 233.882 (j)s 17 f 508.169 y 236.66 (\241)s 8 f 242.91 (1)s 7 f 512.298 y 247.396 (R)s 8 f 513.798 y 254.989 (0)s 11 f 512.298 y 259.475 (j)s 7 f 262.253 (r)s 9 f 513.798 y 266.764 (j)s 11 f 512.298 y 273.2 (\241)s 7 f 283.2 (r)s 9 f 513.798 y 287.712 (k)s 11 f 512.298 y 292.632 (j)s 17 f 508.169 y 295.41 (\241)s 8 f 301.66 (1)s 11 f 512.298 y 306.146 (k)s 313.923 (\267)s 6 f 324.479 (6)s 24 f 537.964 y 63 (Bound)s 94.635 (on)s 7 f 108.753 (\270)s 8 f 534.335 y 114.587 (2)s 7 f 537.964 y 119.073 (a)s 17 f 534.335 y 124.359 (\241)s 8 f 130.609 (4)s 11 f 537.964 y 135.095 (V)s 9 f 534.335 y 142.045 (a)s 540.436 y 141.223 (s;r)s 7 f 537.964 y 151.8 (R)s 9 f 534.335 y 159.47 (a)s 8 f 540.446 y 159.393 (0)s 11 f 537.964 y 164.308 (V)s 9 f 534.335 y 171.258 (a)s 540.436 y 170.436 (r)s 173.934 (;s)s 6 f 537.964 y 180.583 (.)s 186.485 (Doing)s 215.581 (the)s 232.594 (rev)s 245.955 (erse)s 265.829 (scaling)s 7 f 298.453 (x)s 9 f 539.464 y 304.168 (j)s 11 f 537.964 y 311.159 (!)s 7 f 323.937 (a)s 329.223 (x)s 9 f 539.464 y 334.938 (j)s 6 f 537.964 y 339.152 (,)s 7 f 345.054 (j)s 6 f 352.522 (=)s 363.077 (1)s 7 f 368.077 (;)s 372.522 (:)s 376.966 (:)s 381.411 (:)s 385.855 (;)s 390.299 (N)s 6 f 402.548 (and)s 549.964 y 63 (expanding)s 111.056 (giv)s 123.833 (es)s 135.556 (:)s 11 f 570.376 y 87.742 (k)s 7 f 92.742 (\270)s 8 f 566.247 y 98.576 (2)s 7 f 570.376 y 103.062 (a)s 17 f 566.247 y 108.348 (\241)s 8 f 114.598 (4)s 11 f 570.376 y 119.084 (V)s 9 f 566.247 y 126.034 (a)s 572.848 y 125.212 (s;r)s 7 f 570.376 y 135.789 (R)s 9 f 566.247 y 143.459 (a)s 8 f 572.848 y 143.382 (0)s 11 f 570.376 y 148.297 (V)s 9 f 566.247 y 155.247 (a)s 572.848 y 154.425 (r)s 157.923 (;s)s 11 f 570.376 y 164.572 (k)s 6 f 172.572 (=)s 11 f 183.35 (k)s 7 f 188.35 (\270)s 8 f 566.247 y 194.183 (2)s 7 f 570.376 y 198.669 (a)s 17 f 566.247 y 203.955 (\241)s 8 f 210.205 (2)s 11 f 570.376 y 214.691 (V)s 9 f 571.876 y 220.819 (s;r)s 7 f 570.376 y 231.397 (R)s 8 f 571.876 y 238.99 (0)s 11 f 570.376 y 243.476 (V)s 9 f 571.876 y 249.603 (r)s 253.101 (;s)s 11 f 570.376 y 259.75 (k)s do-end end endp showpage %%Page: 6 6 %%BeginPageSetup initializepage (duclos ; page : 6 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f221 sf ( )S -988 -1000 :M f255 sf ( )S -982 -1000 :M f287 sf ( )S -976 -1000 :M f320 sf ( )S -970 -1000 :M f354 sf ( )S -964 -1000 :M f388 sf ( )S -958 -1000 :M f455 sf ( )S -952 -1000 :M f522 sf ( )S -946 -1000 :M f556 sf ( )S -940 -1000 :M f589 sf ( )S -934 -1000 :M f621 sf ( )S -928 -1000 :M f654 sf ( )S -922 -1000 :M f721 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 13 5 /CMMI5 findfont fdef 15 10 /CMBX10 findfont fdef 16 10 /CMSL10 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 19 5 /CMSY5 findfont fdef 24 10 /CMTI10 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (6)s 308.564 (R.)s 321.025 (Brummelh)s 363.315 (uis,)s 380.325 (P)s 385.849 (.)s 391.501 (Duclos)s 11 f 54.5 y 172.572 (\267)s 6 f 183.35 (2)s 7 f 188.35 (N)s 10 f 45 y 199.141 (X)s 9 f 66.299 y 204.507 (j)s 11 f 54.5 y 215.252 (k)s 7 f 220.252 (\270)s 8 f 50.371 y 226.086 (2)s 7 f 54.5 y 230.572 (a)s 17 f 50.371 y 235.858 (\241)s 8 f 242.108 (2)s 11 f 54.5 y 246.594 (j)s 7 f 249.372 (r)s 9 f 56 y 253.883 (j)s 11 f 54.5 y 258.097 (j)s 17 f 50.371 y 260.875 (\241)s 8 f 267.125 (1)s 7 f 54.5 y 271.611 (R)s 8 f 56 y 279.204 (0)s 11 f 54.5 y 283.69 (j)s 7 f 286.468 (r)s 9 f 56 y 290.979 (j)s 11 f 54.5 y 295.193 (j)s 17 f 50.371 y 297.971 (\241)s 8 f 304.221 (1)s 11 f 54.5 y 308.707 (k)s 6 f 83.16 y 183.35 (+)s 7 f 191.127 (N)s 6 f 200.252 (\050)s 7 f 204.141 (N)s 11 f 215.488 (\241)s 6 f 225.488 (1\051)s 10 f 73.66 y 236.044 (X)s 9 f 95.188 y 236.13 (j)s 17 f 239.843 (6)s 8 f 239.843 (=)s 9 f 245.982 (k)s 11 f 83.16 y 252.155 (k)s 7 f 257.155 (\270)s 8 f 79.031 y 262.988 (2)s 7 f 83.16 y 267.475 (a)s 17 f 79.031 y 272.76 (\241)s 8 f 279.011 (2)s 11 f 83.16 y 283.497 (j)s 7 f 286.274 (r)s 9 f 84.66 y 290.786 (j)s 11 f 83.16 y 297.222 (\241)s 7 f 307.222 (r)s 9 f 84.66 y 311.733 (k)s 11 f 83.16 y 316.653 (j)s 17 f 79.031 y 319.431 (\241)s 8 f 325.681 (1)s 7 f 83.16 y 330.167 (R)s 8 f 84.66 y 337.76 (0)s 11 f 83.16 y 342.246 (j)s 7 f 345.024 (r)s 9 f 84.66 y 349.536 (j)s 11 f 83.16 y 355.972 (\241)s 7 f 365.971 (r)s 9 f 84.66 y 370.483 (k)s 11 f 83.16 y 375.403 (j)s 17 f 79.031 y 378.181 (\241)s 8 f 384.431 (1)s 11 f 83.16 y 388.917 (k)s 6 f 116.454 y 172.572 (=)s 11 f 183.35 (O)s 10 f 102.354 y 193.255 (\265)s 7 f 109.689 y 201.816 (\270)s 8 f 106.06 y 207.65 (2)s 10.319 .4 201.816 114.154 r 7 f 123.313 y 202.09 (a)s 8 f 120.425 y 207.376 (2)s 10 f 102.354 y 213.336 (\266)s 7 f 116.454 y 222.364 (:)s 24 f 150.866 y 63 (Bound)s 95.174 (on)s 7 f 109.831 (\270)s 8 f 147.237 y 115.665 (2)s 7 f 150.866 y 120.151 (a)s 17 f 147.237 y 125.437 (\241)s 8 f 131.687 (4)s 11 f 150.866 y 136.173 (V)s 9 f 147.237 y 143.123 (a)s 153.338 y 142.301 (s;r)s 7 f 150.866 y 152.878 (R)s 9 f 147.237 y 160.548 (a)s 11 f 150.866 y 165.386 (V)s 9 f 147.237 y 172.336 (a)s 153.338 y 171.514 (r)s 175.012 (;s)s 6 f 150.866 y 181.661 (.)s 188.148 (Using)s 7 f 216.636 (R)s 9 f 147.237 y 224.306 (a)s 11 f 150.866 y 232.549 (\267)s 7 f 243.732 (R)s 9 f 147.237 y 251.402 (a)s 8 f 153.62 y 251.325 (NI)s 6 f 150.866 y 260.616 (,)s 267.104 (the)s 284.703 (form)s 304.73 (ula)s 321.774 (for)s 7 f 337.456 (R)s 9 f 147.237 y 345.126 (a)s 8 f 153.62 y 345.048 (NI)s 6 f 150.866 y 358.05 (in)s 370.093 (term)s 394.386 (of)s 7 f 406.152 (R)s 9 f 147.237 y 413.822 (a)s 8 f 153.348 y 413.744 (0)s 6 f 162.866 y 63 (and)s 82.444 (the)s 99.667 (previous)s 139.472 (b)s 145.306 (ound)s 170.306 (giv)s 183.084 (es:)s 7 f 188.247 y 177.352 (\270)s 8 f 184.118 y 183.186 (2)s 7 f 188.247 y 187.672 (a)s 17 f 184.118 y 192.958 (\241)s 8 f 199.208 (4)s 11 f 188.247 y 203.694 (V)s 9 f 184.118 y 210.644 (a)s 190.719 y 209.822 (s;r)s 7 f 188.247 y 220.399 (R)s 9 f 184.118 y 228.07 (a)s 11 f 188.247 y 232.907 (V)s 9 f 184.118 y 239.857 (a)s 190.719 y 239.035 (r)s 242.533 (;s)s 6 f 188.247 y 251.96 (=)s 11 f 262.515 (O)s 10 f 174.147 y 272.421 (\265)s 7 f 181.482 y 280.982 (\270)s 8 f 177.853 y 286.815 (2)s 10.319 .4 280.982 185.947 r 7 f 195.106 y 281.256 (a)s 8 f 192.217 y 286.542 (2)s 10 f 174.147 y 292.501 (\266)s 7 f 188.247 y 301.529 (:)s 6 f 213.223 y 63 (No)s 75.222 (w)s 85.778 (w)s 92.722 (e)s 100.5 (need)s 123.833 (the)s 141.056 (follo)s 159.389 (wing)s 15 f 236.308 y 63 (Lemma)s 6 f 99.944 (.)s 16 f 106.055 (As)s 7 f 120.833 (B)s 16 f 132.253 (tends)s 158.976 (to)s 171.198 (in)s 179.531 (\257nit)s 197.031 (y)s 205.642 (one)s 223.976 (has)s 10 f 249.223 y 75.534 (\263)s 6 f 260.323 y 81.507 (\050)s 85.395 (log)s 7 f 99.979 (B)s 6 f 108.066 (\051)s 17 f 256.194 y 111.954 (\241)s 8 f 118.205 (2)s 7 f 260.323 y 122.691 (I)s 124.538 (\246)s 9 f 261.823 y 133.663 (s)s 7 f 260.323 y 137.937 (U)s 6 f 145.855 (\050)s 7 f 149.744 (I)s 151.591 (H)s 8 f 255.962 y 160.716 (\0500\051)s 11 f 260.323 y 173.675 (\241)s 6 f 183.675 (2)s 7 f 188.675 (N)s 197.8 (B)s 6 f 205.886 (\051)s 7 f 209.775 (U)s 17 f 256.194 y 217.693 (\241)s 8 f 223.943 (1)s 7 f 260.323 y 228.43 (I)s 230.277 (\246)s 9 f 261.823 y 239.402 (s)s 11 f 260.323 y 245.898 (\241)s 7 f 255.898 (\273)s 10 f 249.223 y 260.733 (\264)s 17 f 251.295 y 266.706 (\241)s 8 f 272.956 (1)s 11 f 260.323 y 279.664 (\241)s 6 f 289.664 (\050)s 7 f 293.553 (h)s 11 f 301.537 (\241)s 7 f 311.537 (\273)s 6 f 316.372 (\051)s 17 f 256.194 y 320.26 (\241)s 8 f 326.511 (1)s 6 f 260.323 y 333.774 (=)s 11 f 344.33 (O)s 6 f 352.569 (\050\050)s 360.347 (log)s 7 f 374.93 (B)s 6 f 383.017 (\051)s 17 f 256.194 y 386.906 (\241)s 18 f 253.507 y 394.356 (1)s 3.403 .34 394.356 254.614 r 258.604 y 394.356 (3)s 6 f 260.323 y 399.458 (\051)s 7 f 403.347 (:)s 6 f 302.94 y 63 (Pro)s 79 (of.)s 93.167 (Let)s 7 f 111.083 (W)s 6 f 125.25 (b)s 131.083 (e)s 138.861 (the)s 156.083 (follo)s 174.417 (wing)s 198.306 (one)s 216.639 (dimensional)s 271.695 (p)s 277.528 (oten)s 296.139 (tial)s 7 f 328.143 y 184.247 (W)s 6 f 195.081 (\050)s 7 f 198.969 (x)s 6 f 204.685 (\051)s 211.351 (:=)s 10 f 314.532 y 224.685 (Z)s 17 f 317.004 y 234.685 (1)s 8 f 337.255 y 230.24 (0)s 7 f 321.378 y 256.197 (e)s 17 f 317.749 y 260.853 (\241)s 9 f 267.103 (u)s 36.481 .4 246.024 325.843 r 11 f 327.843 y 246.024 (p)s 28.148 .4 254.357 327.843 r 7 f 336.177 y 254.357 (x)s 8 f 333.288 y 260.072 (2)s 6 f 336.177 y 266.78 (+)s 7 f 276.78 (u)s 328.143 y 283.705 (du:)s 6 f 357.475 y 63 (It)s 73.833 (is)s 83.889 (pro)s 98.083 (v)s 103.083 (en)s 116.417 (in)s 128.083 ([BRu)s 150.861 (])s 156.972 (that:)s 7 f 181.417 (B)s 17 f 353.846 y 189.504 (\241)s 8 f 195.754 (1)s 7 f 357.475 y 200.24 (I)s 202.087 (\246)s 9 f 358.975 y 211.212 (s)s 7 f 357.475 y 215.486 (U)s 9 f 362.603 y 222.314 (B)s 19 f 359.19 y 228.697 (\241)s 18 f 357.252 y 235.314 (1)s 3.403 .243 235.314 358.061 r 361.849 y 235.314 (2)s 10 f 346.374 y 242.583 (\263)s 7 f 357.475 y 248.556 (I)s 250.403 (H)s 8 f 353.113 y 259.528 (\0500\051)s 11 f 357.475 y 272.486 (\241)s 6 f 282.486 (2)s 7 f 287.486 (N)s 296.611 (B)s 10 f 346.374 y 304.698 (\264)s 7 f 357.475 y 312.337 (U)s 17 f 353.197 y 320.255 (\241)s 8 f 326.505 (1)s 9 f 364.203 y 319.165 (B)s 19 f 360.79 y 325.548 (\241)s 18 f 358.852 y 332.164 (1)s 3.403 .243 332.164 359.661 r 363.449 y 332.164 (2)s 7 f 357.475 y 337.767 (I)s 339.614 (\246)s 9 f 358.975 y 348.739 (s)s 6 f 357.475 y 356.347 (is)s 366.403 (equal)s 392.792 (to)s 9 f 378.517 y 147.302 (N)s 10 f 381.517 y 143.623 (X)s 9 f 402.816 y 143.926 (j)s 8 f 147.639 (=1)s 11 f 391.017 y 159.734 (\241)s 7 f 167.512 (@)s 8 f 386.888 y 173.376 (2)s 9 f 393.489 y 172.821 (x)s 13 f 394.489 y 177.355 (j)s 11 f 391.017 y 183.813 (\241)s 7 f 193.813 (\270)s 199.647 (Z)s 207.188 (W)s 6 f 218.022 (\050)s 7 f 221.911 (x)s 9 f 392.517 y 227.626 (j)s 6 f 391.017 y 231.839 (\051)s 237.95 (+)s 7 f 384.252 y 252.9 (\270)s 13.333 .4 249.15 388.717 r 11 f 390.717 y 249.15 (p)s 5 .4 257.484 390.717 r 6 f 398.989 y 257.484 (2)s 10 f 381.517 y 265.35 (X)s 9 f 403.045 y 265.381 (j)s 269.094 (\074k)s 7 f 391.017 y 281.462 (W)s 6 f 292.295 (\050)s 7 f 384.252 y 297.384 (x)s 9 f 385.752 y 303.099 (j)s 11 f 384.252 y 309.535 (\241)s 7 f 319.535 (x)s 9 f 385.752 y 325.25 (k)s 32.786 .4 297.384 388.717 r 11 f 390.717 y 307.11 (p)s 5 .4 315.444 390.717 r 6 f 398.989 y 315.444 (2)s 391.017 y 331.37 (\051;)s 423.476 y 63 (where)s 7 f 93.541 (U)s 9 f 428.604 y 100.368 (B)s 19 f 425.191 y 106.751 (\241)s 18 f 423.254 y 113.368 (1)s 3.403 .243 113.368 424.062 r 427.85 y 113.368 (2)s 6 f 423.476 y 123.928 (denotes)s 161.719 (the)s 180.565 (unitary)s 217.494 (implemen)s 259.439 (tation)s 290.507 (of)s 303.52 (the)s 322.366 (scaling)s 7 f 356.823 (r)s 9 f 424.976 y 361.335 (j)s 11 f 423.476 y 371.033 (!)s 7 f 386.517 (B)s 17 f 419.847 y 394.604 (\241)s 18 f 417.16 y 402.054 (1)s 3.403 .34 402.054 418.267 r 422.256 y 402.054 (2)s 7 f 423.476 y 407.156 (r)s 9 f 424.976 y 411.668 (j)s 6 f 423.476 y 415.882 (,)s 7 f 436.548 y 63 (j)s 6 f 70.468 (=)s 81.024 (1)s 7 f 86.024 (;)s 90.468 (:)s 94.913 (:)s 99.357 (:)s 103.801 (;)s 108.246 (N)s 6 f 117.371 (.)s 123.049 (This)s 145.449 (sho)s 159.672 (ws)s 173.739 (that)s 194.972 (w)s 201.917 (e)s 209.262 (ha)s 219.539 (v)s 224.539 (e)s 231.884 (to)s 243.674 (face)s 263.518 (a)s 271.419 (w)s 278.363 (eak)s 295.986 (coupling)s 335.553 (limit)s 359.009 (problem)s 397.493 (since)s 448.548 y 63 (w)s 69.944 (e)s 78.065 (are)s 95.102 (in)s 103.157 (terested)s 141.361 (in)s 153.37 (the)s 170.935 (limit)s 7 f 195.166 (\270)s 11 f 204.348 (!)s 6 f 217.697 (0)s 222.697 (.)s 229.15 (W)s 238.595 (e)s 246.715 (use)s 264.336 (the)s 281.9 (approac)s 316.095 (h)s 325.326 (describ)s 356.243 (ed)s 369.919 (in)s 381.928 (the)s 399.493 (next)s 460.548 y 63 (section.)s 99.117 (W)s 108.562 (e)s 116.29 (p)s 122.123 (erform)s 154.074 (an)s 167.914 (extra)s 193.725 (scaling)s 7 f 226.509 (x)s 9 f 462.048 y 232.225 (j)s 11 f 460.548 y 239.216 (!)s 7 f 251.994 (x)s 9 f 462.048 y 257.709 (j)s 7 f 460.548 y 261.922 (=a)s 6 f 272.208 (,)s 7 f 278.27 (j)s 6 f 285.738 (=)s 296.294 (1)s 7 f 301.294 (;)s 305.738 (:)s 310.183 (:)s 314.627 (:)s 319.071 (;)s 323.516 (N)s 6 f 335.925 (whic)s 355.647 (h)s 364.487 (\257nally)s 394.715 (giv)s 407.493 (es:)s 7 f 481.552 y 125.065 (h)s 6 f 130.827 (\050)s 7 f 134.716 (B)s 6 f 142.803 (\051)s 149.469 (:=)s 162.803 (\050)s 166.692 (log)s 7 f 181.275 (B)s 6 f 189.362 (\051)s 17 f 477.423 y 193.251 (\241)s 8 f 199.501 (2)s 7 f 481.552 y 203.987 (I)s 205.834 (\246)s 9 f 483.052 y 214.959 (s)s 7 f 481.552 y 219.233 (U)s 9 f 486.68 y 226.061 (B)s 19 f 483.267 y 232.444 (\241)s 18 f 481.33 y 239.061 (1)s 3.403 .243 239.061 482.138 r 485.926 y 239.061 (2)s 6 f 481.552 y 244.664 (\050)s 7 f 248.553 (I)s 250.4 (H)s 8 f 477.191 y 259.525 (\0500\051)s 11 f 481.552 y 272.483 (\241)s 6 f 282.483 (2)s 7 f 287.483 (N)s 296.608 (B)s 6 f 304.695 (\051)s 7 f 308.584 (U)s 17 f 477.274 y 316.502 (\241)s 8 f 322.752 (1)s 9 f 488.28 y 315.412 (B)s 19 f 484.867 y 321.795 (\241)s 18 f 482.93 y 328.411 (1)s 3.403 .243 328.411 483.738 r 487.526 y 328.411 (2)s 7 f 481.552 y 334.014 (I)s 335.861 (\246)s 9 f 483.052 y 344.986 (s)s 6 f 481.552 y 352.038 (=)s 9 f 498.063 y 128.745 (N)s 10 f 501.063 y 125.065 (X)s 9 f 522.362 y 125.368 (j)s 8 f 129.082 (=1)s 11 f 510.563 y 141.177 (\241)s 7 f 148.954 (@)s 8 f 506.434 y 154.819 (2)s 9 f 513.035 y 154.263 (x)s 13 f 514.035 y 158.798 (j)s 11 f 510.563 y 165.256 (\241)s 7 f 503.798 y 178.425 (\270)s 9.772 .4 176.456 508.263 r 517.423 y 176.456 (a)s 8 f 514.534 y 181.742 (2)s 7 f 510.563 y 187.428 (Z)s 194.97 (W)s 6 f 205.803 (\050)s 7 f 503.798 y 210.892 (x)s 9 f 505.298 y 216.607 (j)s 9.929 .4 210.892 508.263 r 7 f 517.423 y 213.214 (a)s 6 f 510.563 y 222.021 (\051)s 228.132 (+)s 7 f 503.798 y 247.968 (\270)s 23.105 .4 239.332 508.263 r 518.535 y 239.332 (a)s 8 f 515.646 y 244.618 (2)s 11 f 510.263 y 249.104 (p)s 5 .4 257.437 510.263 r 6 f 518.535 y 257.437 (2)s 10 f 501.063 y 265.304 (X)s 9 f 522.591 y 265.334 (j)s 269.048 (\074k)s 7 f 510.563 y 281.415 (W)s 6 f 292.248 (\050)s 7 f 503.798 y 297.337 (x)s 9 f 505.298 y 303.053 (j)s 11 f 503.798 y 309.488 (\241)s 7 f 319.488 (x)s 9 f 505.298 y 325.204 (k)s 32.786 .4 297.337 508.263 r 7 f 518.535 y 304.421 (a)s 11 f 510.263 y 309.707 (p)s 5 .4 318.04 510.263 r 6 f 518.535 y 318.04 (2)s 510.563 y 331.324 (\051)s 7 f 335.213 (:)s 6 f 540.428 y 63 (One)s 84.111 (can)s 102.445 (c)s 106.611 (hec)s 120.778 (k)s 129.389 (easily)s 156.945 (that)s 10 f 550.904 y 116.258 (Z)s 17 f 573.626 y 121.814 (j)s 9 f 124.189 (x)s 17 f 128.724 (j)s 9 f 131.099 (\074R)s 7 f 564.515 y 145.575 (W)s 6 f 156.409 (\050)s 7 f 160.298 (x)s 6 f 166.013 (\051)s 7 f 169.902 (dx)s 6 f 183.6 (=)s 194.155 (2)s 200.822 (log)s 213.738 (\0502)s 7 f 222.627 (R)s 6 f 230.298 (\051)s 236.409 (+)s 7 f 246.409 (\260)s 6 f 254.364 (+)s 11 f 264.364 (O)s 6 f 272.602 (\050)s 7 f 276.491 (R)s 17 f 560.386 y 284.162 (\241)s 8 f 290.412 (2)s 6 f 564.515 y 294.898 (\051)s 7 f 298.787 (;)s 6 f 313.231 (as)s 7 f 332.175 (R)s 11 f 342.623 (!)s 355.401 (1)s do-end end endp showpage %%Page: 7 7 %%BeginPageSetup initializepage (duclos ; page : 7 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f188 sf ( )S -988 -1000 :M f221 sf ( )S -982 -1000 :M f255 sf ( )S -976 -1000 :M f287 sf ( )S -970 -1000 :M f320 sf ( )S -964 -1000 :M f354 sf ( )S -958 -1000 :M f388 sf ( )S -952 -1000 :M f422 sf ( )S -949 -1000 :M f589 sf ( )S -943 -1000 :M f621 sf ( )S -937 -1000 :M f753 sf ( )S -931 -1000 :M f786 sf ( )S -925 -1000 :M f721 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 4 9 /CMMI9 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 12 10 /MSBM10 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 21 6 /CMR6 findfont fdef 22 9 /CMSY9 findfont fdef 24 10 /CMTI10 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (1-d)s 78.93 (b)s 84.326 (eha)s 97.948 (viour)s 121.864 (of)s 132.399 (atoms)s 159.686 (in)s 170.478 (in)s 177.929 (tense)s 201.626 (magnetic)s 241.199 (\257elds)s 414.034 (7)s 6 f 54 y 63 (where)s 7 f 91.429 (\260)s 6 f 100.008 (is)s 109.577 (the)s 126.312 (Euler)s 152.658 (constan)s 185.769 (t.)s 195.282 (It)s 205.628 (is)s 215.196 (sho)s 229.418 (wn)s 245.042 (in)s 256.222 (the)s 272.957 (next)s 294.969 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112.253 (and)s 131.698 (as)s 143.976 (an)s 157.865 (op)s 168.698 (erator)s 198.198 (from)s 11 f 221.837 (H)s 8 f 174.048 y 230.379 (1)s 6 f 177.677 y 234.865 (\050)s 12 f 238.754 (R)s 9 f 174.048 y 245.976 (n)s 6 f 177.677 y 251.419 (\051)s 258.641 (to)s 11 f 270.864 (H)s 17 f 174.048 y 279.405 (\241)s 8 f 285.655 (1)s 6 f 177.677 y 290.142 (\050)s 12 f 294.03 (R)s 9 f 174.048 y 301.253 (n)s 6 f 177.677 y 306.696 (\051)s 310.585 (,)s 316.696 (for)s 332.002 (all)s 7 f 345.891 (j)s 6 f 353.359 (=)s 363.914 (1)s 7 f 368.914 (;)s 373.359 (:)s 377.803 (:)s 382.247 (:)s 386.692 (N)s 6 f 395.817 (.)s 195.1 y 63 (The)s 83.556 (analogous)s 129.722 (statemen)s 168.945 (t,)s 178.945 (for)s 194.25 (all)s 7 f 208.139 (j)s 11 f 215.607 (6)s 6 f 215.607 (=)s 7 f 226.163 (k)s 6 f 231.684 (,)s 11 f 220.141 y 73.337 (k)s 6 f 78.337 (1)s 7 f 85.004 (:)s 89.448 (:)s 93.893 (:)s 6 f 98.337 (1)s 11 f 105.559 (\255)s 10 f 206.041 y 115.559 (\265)s 7 f 213.376 y 132.756 (\270)s 23.105 .4 124.12 217.841 r 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169.497 (\273)s 6 f 174.332 (\051)s 17 f 273.204 y 178.221 (\241)s 8 f 184.471 (1)s 6 f 277.333 y 191.735 (=)s 10 f 268.294 y 202.29 (p)s 41.333 .4 212.29 268.294 r 6 f 277.333 y 212.29 (\050)s 7 f 216.179 (h)s 11 f 224.163 (\241)s 7 f 234.163 (\273)s 6 f 238.998 (\051)s 17 f 274.444 y 242.887 (\241)s 8 f 249.137 (1)s 6 f 277.333 y 253.623 (\0501)s 264.734 (+)s 7 f 274.734 (K)s 6 f 283.942 (\051)s 17 f 273.204 y 287.831 (\241)s 8 f 294.081 (1)s 10 f 268.294 y 298.567 (p)s 41.333 .4 308.567 268.294 r 6 f 277.333 y 308.567 (\050)s 7 f 312.456 (h)s 11 f 320.44 (\241)s 7 f 330.44 (\273)s 6 f 335.275 (\051)s 17 f 274.444 y 339.164 (\241)s 8 f 345.414 (1)s 6 f 296.929 y 63 (with)s 7 f 326.025 y 128.482 (K)s 6 f 140.468 (:=)s 10 f 316.986 y 153.802 (p)s 41.333 .4 163.802 316.986 r 6 f 326.025 y 163.802 (\050)s 7 f 167.69 (h)s 11 f 175.674 (\241)s 7 f 185.674 (\273)s 6 f 190.509 (\051)s 17 f 323.136 y 194.398 (\241)s 8 f 200.648 (1)s 10 f 305.924 y 206.801 (0)s 323.925 y 206.801 (@)s 11 f 326.025 y 215.551 (\241)s 7 f 223.329 (Z)s 10 f 316.525 y 232.537 (X)s 9 f 337.823 y 237.903 (j)s 10 f 311.925 y 248.648 (\265)s 7 f 319.26 y 259.179 (\270)s 9.772 .4 257.209 323.725 r 332.884 y 257.209 (a)s 8 f 329.995 y 262.495 (2)s 7 f 326.025 y 268.181 (W)s 6 f 279.015 (\050)s 7 f 319.26 y 284.104 (x)s 9 f 320.76 y 289.819 (j)s 9.929 .4 284.104 323.725 r 7 f 332.884 y 286.425 (a)s 6 f 326.025 y 295.232 (\051)s 11 f 301.343 (\241)s 7 f 311.343 (\261)s 6 f 316.166 (\050)s 7 f 320.055 (x)s 9 f 327.525 y 325.771 (j)s 6 f 326.025 y 329.984 (\051)s 10 f 311.925 y 333.873 (\266)s 6 f 326.025 y 342.901 (+)s 10 f 356.525 y 129.682 (X)s 9 f 378.053 y 129.713 (j)s 133.426 (\074)s 139.676 (k)s 10 f 351.925 y 145.793 (\265)s 7 f 359.26 y 162.99 (\270)s 23.105 .4 154.354 363.725 r 373.997 y 154.354 (a)s 8 f 371.108 y 159.64 (2)s 11 f 365.725 y 164.126 (p)s 5 .4 172.46 365.725 r 6 f 373.997 y 172.46 (2)s 7 f 366.025 y 178.66 (W)s 6 f 189.493 (\050)s 7 f 359.26 y 194.582 (x)s 9 f 360.76 y 200.297 (j)s 11 f 359.26 y 206.733 (\241)s 7 f 216.733 (x)s 9 f 360.76 y 222.448 (k)s 32.786 .4 194.582 363.725 r 11 f 365.725 y 201.666 (p)s 5 .4 209.999 365.725 r 6 f 373.997 y 209.999 (2)s 7 f 214.999 (a)s 6 f 366.025 y 228.569 (\051)s 11 f 234.68 (\241)s 7 f 244.68 (\261)s 6 f 249.502 (\050)s 7 f 253.391 (x)s 9 f 367.525 y 259.107 (j)s 11 f 366.025 y 265.542 (\241)s 7 f 275.542 (x)s 9 f 367.525 y 281.258 (k)s 6 f 366.025 y 286.178 (\051)s 10 f 351.925 y 290.067 (\266)s 345.925 y 297.428 (1)s 363.925 y 297.428 (A)s 356.987 y 307.844 (p)s 41.333 .4 317.844 356.987 r 6 f 366.025 y 317.844 (\050)s 7 f 321.733 (h)s 11 f 329.717 (\241)s 7 f 339.717 (\273)s 6 f 344.552 (\051)s 17 f 363.136 y 348.441 (\241)s 8 f 354.691 (1)s 6 f 398.621 y 63 (and)s 7 f 82.444 (K)s 11 f 94.431 (!)s 6 f 107.208 (0)s 115.542 (as)s 7 f 127.819 (B)s 11 f 138.684 (!)s 151.462 (1)s 6 f 164.795 (thanks)s 197.351 (to)s 209.573 (them.)s 6 10 237.906 400.121 r 24 f 421.735 y 63 (Conver)s 93.794 (genc)s 112.705 (e)s 121.084 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141.707 (=)s 11 f 153.384 (O)s 10 f 426.968 y 163.289 (\263)s 6 f 438.068 y 169.262 (\050)s 173.151 (log)s 7 f 187.734 (B)s 6 f 195.821 (\051)s 17 f 434.439 y 199.71 (\241)s 18 f 431.752 y 207.16 (1)s 3.403 .34 207.16 432.859 r 436.849 y 207.16 (3)s 10 f 426.968 y 212.262 (\264)s 6 f 438.068 y 222.241 (whereas)s 260.774 (using)s 287.614 (the)s 305.508 (second)s 338.459 (resolv)s 363.542 (en)s 373.264 (t)s 381.159 (equation)s 454.367 y 63 (one)s 81.333 (gets)s 7 f 101.944 (S)s 9 f 450.738 y 108.653 (a)s 11 f 454.367 y 115.713 (\241)s 6 f 125.713 (\050)s 7 f 129.601 (T)s 9 f 450.738 y 136.834 (a)s 456.839 y 135.445 (s)s 11 f 454.367 y 143.894 (\241)s 9 f 450.429 y 156.843 (\270)s 8.24 .4 155.094 452.067 r 457.815 y 155.094 (a)s 18 f 455.815 y 159.432 (2)s 11 f 454.367 y 164.534 (V)s 9 f 450.738 y 171.484 (a)s 456.839 y 170.662 (s;s)s 11 f 454.367 y 183.308 (\241)s 7 f 193.308 (\273)s 6 f 198.143 (\051)s 17 f 450.738 y 202.032 (\241)s 8 f 208.282 (1)s 6 f 454.367 y 215.546 (=)s 11 f 226.101 (O)s 10 f 446.267 y 236.007 (\241)s 7 f 454.367 y 240.59 (\270)s 8 f 450.738 y 246.424 (2)s 7 f 454.367 y 250.91 (a)s 17 f 450.738 y 256.196 (\241)s 8 f 262.446 (2)s 10 f 446.267 y 266.932 (\242)s 6 f 454.367 y 274.293 (=)s 11 f 284.848 (O)s 6 f 293.087 (\050\050)s 300.865 (log)s 7 f 315.448 (B)s 6 f 323.535 (\051)s 17 f 450.738 y 327.424 (\241)s 8 f 333.674 (2)s 6 f 454.367 y 338.16 (\051)s 342.049 (.)s 24 f 474.635 y 63 (The)s 83.444 (last)s 102.1 (terms)s 6 f 126.505 (.)s 132.616 (It)s 143.45 (is)s 153.505 (no)s 163.783 (w)s 174.338 (easy)s 196.339 (to)s 208.561 (v)s 213.561 (erify)s 236.366 (that)s 11 f 258.033 (V)s 9 f 471.006 y 264.983 (a)s 477.107 y 264.161 (s;r)s 7 f 474.635 y 274.738 (R)s 9 f 471.006 y 282.409 (a)s 6 f 474.635 y 290.024 (=)s 11 f 300.58 (O)s 6 f 308.818 (\050)s 7 f 312.707 (a)s 8 f 471.006 y 317.993 (2)s 6 f 474.635 y 322.479 (\051)s 329.702 (and)s 349.146 (th)s 358.313 (us)s 7 f 495.204 y 106.279 (\270)s 9.772 .4 104.31 499.669 r 508.829 y 104.31 (a)s 8 f 505.94 y 109.595 (2)s 7 f 501.969 y 115.282 (S)s 9 f 497.84 y 121.99 (a)s 11 f 501.969 y 126.828 (V)s 9 f 497.84 y 133.778 (a)s 504.441 y 132.955 (s;r)s 7 f 501.969 y 143.533 (R)s 9 f 497.84 y 151.203 (a)s 6 f 501.969 y 158.818 (=)s 11 f 169.374 (O)s 6 f 177.613 (\050)s 7 f 181.502 (\270)s 6 f 187.335 (\051)s 7 f 191.224 (;)s 495.204 y 206.868 (\270)s 8 f 491.575 y 212.702 (2)s 10.319 .4 206.868 499.669 r 7 f 508.829 y 207.142 (a)s 8 f 505.94 y 212.428 (4)s 7 f 501.969 y 218.388 (R)s 9 f 497.84 y 226.058 (a)s 11 f 501.969 y 230.896 (V)s 9 f 497.84 y 237.846 (a)s 504.441 y 237.024 (r)s 240.521 (;s)s 7 f 501.969 y 247.171 (S)s 9 f 497.84 y 253.879 (a)s 11 f 501.969 y 258.717 (V)s 9 f 497.84 y 265.667 (a)s 504.441 y 264.844 (s;r)s 7 f 501.969 y 275.422 (R)s 9 f 497.84 y 283.092 (a)s 6 f 501.969 y 290.707 (=)s 11 f 301.263 (O)s 6 f 309.502 (\050)s 7 f 313.391 (\270)s 8 f 497.84 y 319.224 (2)s 6 f 501.969 y 323.71 (\051)s 330.377 (=)s 11 f 340.932 (O)s 6 f 349.171 (\050)s 7 f 353.06 (B)s 17 f 497.84 y 361.147 (\241)s 8 f 367.397 (1)s 6 f 501.969 y 371.883 (\051)s 7 f 375.772 (:)s 6 f 532.638 y 63 (The)s 83.556 (theorem)s 122.472 (is)s 132.528 (pro)s 146.722 (v)s 151.722 (en.)s 56.906 .4 63 538.076 r 21 f 544.553 y 65 (1)s 3 f 548.376 y 72.25 (w)s 78.674 (e)s 87.054 (w)s 93.478 (arn)s 111.125 (the)s 128.242 (reader)s 157.737 (that)s 178.961 (the)s 196.077 (parameters)s 4 f 245.151 (a)s 3 f 254.318 (and)s 4 f 273.486 (v)s 3 f 282.568 (of)s 294.285 (the)s 311.402 (next)s 333.4 (section)s 365.471 (are)s 382.094 (presen)s 407.611 (tly)s 559.376 y 72.25 (c)s 76.104 (hanged)s 107.838 (as)s 4 f 119.065 (a)s 22 f 126.534 (!)s 3 f 138.354 (2)s 4 f 142.979 (a)s 3 f 150.832 (and)s 4 f 168.688 (v)s 22 f 176.073 (!)s 4 f 187.893 (v)s 192.708 (=)s 3 f 197.333 (2;)s 207.481 (a)s 215.059 (c)s 218.913 (hange)s 245.508 (whic)s 263.751 (h)s 271.843 (do)s 281.864 (es)s 292.58 (not)s 308.894 (a\256ect)s 333.69 (the)s 349.494 (follo)s 366.452 (wing)s 388.419 (limit)s 410.386 (as)s 570.376 y 72.25 (one)s 89.212 (can)s 106.17 (see)s 121.131 (with)s 142.2 (a)s 149.908 (simple)s 178.741 (scaling)s 209.112 (argumen)s 243.823 (t.)s do-end end endp showpage %%Page: 8 8 %%BeginPageSetup initializepage (duclos ; page : 8 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f55 sf ( )S -990 -1000 :M f221 sf ( )S -984 -1000 :M f255 sf ( )S -978 -1000 :M f287 sf ( )S -972 -1000 :M f320 sf ( )S -966 -1000 :M f354 sf ( )S -960 -1000 :M f388 sf ( )S -954 -1000 :M f422 sf ( )S -951 -1000 :M f455 sf ( )S -945 -1000 :M f522 sf ( )S -939 -1000 :M f556 sf ( )S -933 -1000 :M f589 sf ( )S -927 -1000 :M f621 sf ( )S -921 -1000 :M f687 sf ( )S -918 -1000 :M f721 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 5 12 /CMBX12 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 12 10 /MSBM10 findfont fdef 13 5 /CMMI5 findfont fdef 15 10 /CMBX10 findfont fdef 16 10 /CMSL10 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 20 7 /MSBM7 findfont fdef 24 10 /CMTI10 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (8)s 308.564 (R.)s 321.025 (Brummelh)s 363.315 (uis,)s 380.325 (P)s 385.849 (.)s 391.501 (Duclos)s 5 f 54 y 63 (3)s 83.25 (The)s 110.799 (w)s 120.174 (eak)s 144.521 (coupling)s 198.521 (limit)s 230.771 (revisited)s 6 f 83.911 y 63 (In)s 74.879 (this)s 93.758 (section)s 126.526 (w)s 133.47 (e)s 140.627 (address)s 175.701 (the)s 192.302 (follo)s 210.635 (wing)s 233.903 (question.)s 275.838 (Let)s 7 f 293.134 (V)s 6 f 303.967 (:)s 12 f 309.522 (R)s 11 f 319.522 (!)s 12 f 332.3 (R)s 17 f 85.411 y 339.522 (\241)s 6 f 83.911 y 348.985 (b)s 354.818 (e)s 361.975 (a)s 369.687 (measurable)s 95.911 y 63 (function)s 102.167 (suc)s 115.833 (h)s 124.722 (that)s 146.389 (\050with)s 11 f 173.056 (h)s 7 f 176.945 (x)s 11 f 182.66 (i)s 6 f 189.327 (:=)s 11 f 87.578 y 202.66 (p)s 27.424 .4 210.993 87.578 r 6 f 95.911 y 210.993 (1)s 218.215 (+)s 7 f 228.215 (x)s 8 f 93.022 y 233.931 (2)s 6 f 95.911 y 238.417 (\051)s 11 f 117.466 y 208.805 (h)s 7 f 212.694 (x)s 11 f 218.41 (i)s 7 f 222.299 (V)s 11 f 233.132 (2)s 7 f 242.576 (L)s 17 f 113.337 y 249.382 (1)s 6 f 117.466 y 257.854 (\050)s 12 f 261.743 (R)s 6 f 268.965 (\051)s 395.604 (\050H1\051)s 7 f 415.882 (:)s 6 f 139.022 y 63 (Ho)s 75.222 (w)s 85.778 (m)s 93.833 (uc)s 103.556 (h)s 7 f 112.445 (V)s 6 f 123.833 (is)s 133.889 (attractiv)s 171.695 (e)s 179.472 (is)s 189.528 (made)s 216.195 (more)s 241.222 (precise)s 274.084 (b)s 279.361 (y)s 11 f 165.133 y 80.673 (9)s 7 f 86.229 (v)s 94.212 (\076)s 6 f 104.768 (0)s 7 f 109.768 (;)s 11 f 124.212 (V)s 6 f 131.162 (\050)s 7 f 135.051 (R)s 6 f 142.721 (\051)s 149.388 (:=)s 11 f 162.721 (\241)s 10 f 151.521 y 172.166 (Z)s 17 f 174.244 y 177.721 (j)s 9 f 180.096 (x)s 17 f 184.631 (j)s 9 f 187.006 (\074R)s 7 f 165.133 y 201.483 (V)s 6 f 209.538 (\050)s 7 f 213.427 (x)s 6 f 219.142 (\051)s 7 f 223.031 (dx)s 6 f 236.729 (=)s 7 f 247.285 (v)s 6 f 254.157 (log)s 267.074 (\050)s 7 f 270.963 (R)s 6 f 278.633 (\051)s 284.744 (+)s 11 f 294.744 (O)s 6 f 302.983 (\0501\051)s 325.761 (as)s 7 f 344.705 (R)s 11 f 355.153 (!)s 367.931 (1)s 6 f 395.604 (\050H2\051)s 7 f 415.882 (:)s 6 f 196.726 y 63 (Let)s 7 f 80.59 (H)s 9 f 198.226 y 88.902 (\270)s 6 f 196.726 y 96.923 (:=)s 11 f 110.256 (\241)s 9 f 192.789 y 121.502 (d)s 18 f 189.771 y 125.664 (2)s 12.6 .4 119.234 194.426 r 9 f 200.175 y 119.234 (dx)s 18 f 198.175 y 127.932 (2)s 6 f 196.726 y 134.603 (+)s 7 f 143.949 (\270)s 149.783 (V)s 6 f 157.838 (.)s 24 f 163.622 (Do)s 175.772 (es)s 7 f 187.738 (H)s 9 f 198.226 y 196.051 (\270)s 24 f 196.726 y 204.571 (p)s 209.171 (ossess)s 238.514 (ne)s 248.225 (gative)s 276.802 (eigenvalues)s 328.89 (as)s 7 f 341.367 (\270)s 24 f 350.477 (tends)s 376.498 (to)s 388.209 (0\077)s 6 f 401.437 (The)s 208.726 y 63 (answ)s 84.444 (er)s 95.722 (is)s 105.36 (y)s 110.36 (es)s 121.665 (as)s 133.526 (one)s 151.442 (can)s 169.358 (see)s 185.108 (with)s 207.468 (an)s 220.94 (easy)s 242.523 (v)s 247.245 (ariational)s 291.856 (argumen)s 329.384 (t.)s 338.966 (If)s 7 f 348.549 (V)s 6 f 359.521 (ob)s 370.354 (eys)s 386.937 (sligh)s 406.715 (tly)s 220.726 y 63 (stronger)s 101.705 (assumptions,)s 161.021 (a)s 169.059 (p)s 174.892 (erturbation)s 227.431 (expansion)s 273.58 (for)s 288.59 (the)s 305.517 (lo)s 313.017 (w)s 319.962 (est)s 335.278 (eigen)s 357.222 (v)s 361.944 (alue)s 382.76 (in)s 394.132 (terms)s 232.726 y 63 (of)s 7 f 73.807 (\270)s 6 f 82.392 (is)s 91.866 (deriv)s 113.56 (ed)s 126.312 (in)s 137.397 ([AHS)s 160.73 (])s 166.259 (whic)s 185.982 (h)s 194.289 (uses)s 214.929 (a)s 222.681 (mo)s 236.292 (di)s 244.625 (\257ed)s 262.932 (Birman-Sc)s 308.655 (h)s 313.932 (winger)s 345.601 (tec)s 358.101 (hnic.)s 381.963 (W)s 391.408 (e)s 398.604 (shall)s 244.726 y 63 (rederiv)s 93.056 (e)s 100.472 (part)s 121.805 (of)s 132.832 (this)s 151.97 (result)s 179.47 (with)s 201.886 (a)s 209.857 (di)s 218.191 (\256eren)s 242.108 (t)s 248.968 (metho)s 276.468 (d)s 284.995 (b)s 290.829 (etter)s 314.384 (suited)s 343.522 (to)s 355.383 (this)s 374.521 (note.)s 399.16 (This)s 256.726 y 63 (metho)s 90.5 (d)s 100.388 (is)s 111.443 (based)s 140.276 (on)s 155.164 (the)s 173.385 (follo)s 191.719 (wing)s 216.607 (prop)s 236.913 (ert)s 248.885 (y:)s 7 f 261.273 (H)s 9 f 258.226 y 269.586 (\270)s 6 f 256.726 y 274.829 (,)s 281.939 (when)s 309.05 (appropriately)s 372.049 (scaled)s 402.548 (and)s 269.848 y 63 (zo)s 72.722 (omed,)s 102.167 (con)s 116.889 (v)s 121.889 (erges)s 146.972 (in)s 158.639 (the)s 175.861 (norm)s 202 (resolv)s 227.084 (en)s 236.806 (t)s 244.028 (sense)s 269.695 (to)s 7 f 281.917 (h)s 8 f 271.348 y 287.679 (0)s 6 f 269.848 y 294.942 (:=)s 11 f 308.276 (\241)s 9 f 265.911 y 319.521 (d)s 18 f 262.893 y 323.684 (2)s 12.6 .4 317.253 267.548 r 9 f 273.297 y 317.253 (dx)s 18 f 271.297 y 325.951 (2)s 11 f 269.848 y 333.276 (\241)s 7 f 343.276 (v)s 348.482 (\261)s 6 f 353.305 (.)s 359.416 (Let)s 7 f 298.757 y 143.892 (h)s 6 f 149.653 (\050)s 7 f 153.542 (a;)s 163.272 (\270)s 6 f 169.106 (\051)s 175.772 (:=)s 11 f 189.106 (\241)s 7 f 291.992 y 200.941 (d)s 8 f 288.363 y 206.146 (2)s 15.406 .4 198.083 296.457 r 7 f 305.616 y 198.083 (dx)s 8 f 302.728 y 209.003 (2)s 6 f 298.757 y 216.912 (+)s 7 f 291.992 y 230.081 (\270)s 9.772 .4 228.112 296.457 r 305.616 y 228.112 (a)s 8 f 302.728 y 233.398 (2)s 7 f 298.757 y 239.084 (V)s 6 f 247.139 (\050)s 11 f 291.992 y 253.482 (\242)s 5.286 .4 252.228 296.457 r 7 f 305.616 y 252.228 (a)s 6 f 298.757 y 258.714 (\051)s 265.381 (=)s 7 f 275.936 (a)s 17 f 294.628 y 281.222 (\241)s 8 f 287.472 (2)s 7 f 298.757 y 291.958 (U)s 18 f 298.535 y 300.221 (1)s 3.872 .34 299.986 299.642 r 13 f 303.632 y 299.986 (a)s 7 f 298.757 y 305.558 (H)s 9 f 300.257 y 313.871 (\270)s 7 f 298.757 y 319.114 (U)s 17 f 294.479 y 327.032 (\241)s 8 f 333.282 (1)s 18 f 300.135 y 327.376 (1)s 3.872 .34 327.142 301.242 r 13 f 305.231 y 327.142 (a)s 6 f 323.672 y 63 (where)s 7 f 91.017 (U)s 18 f 323.45 y 99.279 (1)s 3.872 .34 99.045 324.557 r 13 f 328.546 y 99.045 (a)s 6 f 323.672 y 107.051 (denotes)s 142.318 (the)s 158.64 (unitary)s 193.046 (scaling)s 224.98 (asso)s 243.147 (ciated)s 271.691 (to)s 283.014 (the)s 299.336 (c)s 303.503 (hange)s 331.492 (of)s 341.982 (v)s 346.704 (ariable)s 7 f 378.61 (x)s 11 f 387.103 (!)s 7 f 399.88 (x=a)s 6 f 415.882 (,)s 7 f 335.672 y 63 (a)s 71.064 (\076)s 6 f 81.619 (0)s 86.619 (.)s 15 f 359.629 y 63 (Lemma)s 6 f 99.944 (.)s 16 f 107.232 (Let)s 7 f 126.325 (V)s 6 f 139.118 (:)s 12 f 146.634 (R)s 11 f 158.595 (!)s 12 f 173.333 (R)s 17 f 361.129 y 180.555 (\241)s 16 f 359.629 y 191.815 (satisfy)s 224.214 (\050H1,2\051)s 256.779 (and)s 7 f 277.4 (a)s 6 f 282.686 (\050)s 7 f 286.574 (\270)s 6 f 292.408 (\051)s 301.035 (:=)s 7 f 316.329 (\270)s 6 f 323.829 (log)s 7 f 338.412 (\270)s 17 f 356 y 344.245 (\241)s 8 f 350.495 (1)s 16 f 359.629 y 354.981 (.)s 362.269 (Then)s 7 f 389.556 (h)s 6 f 395.318 (\050)s 7 f 399.207 (a;)s 408.937 (\270)s 6 f 414.771 (\051)s 16 f 371.629 y 63 (con)s 77.722 (v)s 82.722 (erges)s 107.642 (in)s 119.145 (the)s 136.204 (norm)s 162.18 (resolv)s 187.263 (en)s 196.985 (t)s 204.044 (sense)s 229.547 (to)s 7 f 241.606 (h)s 8 f 373.129 y 247.368 (0)s 16 f 371.629 y 255.024 (as)s 7 f 267.138 (\270)s 11 f 275.749 (#)s 6 f 283.527 (0)s 16 f 288.527 (.)s 294.475 (More)s 320.172 (precisely)s 360.926 (for)s 376.068 (ev)s 385.512 (ery)s 7 f 402.321 (\273)s 16 f 410.326 (in)s 383.629 y 63 (the)s 80.222 (resolv)s 105.306 (en)s 115.028 (t)s 122.25 (set)s 137.861 (of)s 7 f 149.25 (h)s 8 f 385.129 y 155.012 (0)s 6 f 407.762 y 108.68 (\050)s 7 f 112.569 (h)s 6 f 118.331 (\050)s 7 f 122.22 (a;)s 131.95 (\270)s 6 f 137.784 (\051)s 11 f 143.895 (\241)s 7 f 153.895 (\273)s 6 f 158.73 (\051)s 17 f 403.633 y 162.619 (\241)s 8 f 168.869 (1)s 11 f 407.762 y 175.577 (\241)s 6 f 185.577 (\050)s 7 f 189.466 (h)s 8 f 409.262 y 195.227 (0)s 11 f 407.762 y 201.936 (\241)s 7 f 211.936 (\273)s 6 f 216.771 (\051)s 17 f 403.633 y 220.66 (\241)s 8 f 226.91 (1)s 6 f 407.762 y 234.173 (=)s 11 f 244.729 (O)s 10 f 396.662 y 254.634 (\263)s 399.662 y 260.607 (\241)s 6 f 407.762 y 265.19 (log)s 7 f 279.773 (\270)s 17 f 403.633 y 285.607 (\241)s 8 f 291.857 (1)s 10 f 399.662 y 296.343 (\242)s 18 f 398.907 y 302.126 (1)s 3.403 .34 302.126 400.014 r 404.003 y 302.126 (3)s 10 f 396.662 y 307.229 (\264)s 6 f 407.762 y 324.868 (as)s 7 f 343.812 (\270)s 11 f 352.423 (!)s 6 f 365.201 (0)s 7 f 370.201 (:)s 6 f 447.584 y 63 (Pro)s 79 (of.)s 93.167 (W)s 102.611 (e)s 110.389 (assume)s 144.945 (without)s 182.167 (loss)s 201.167 (of)s 212.556 (generalit)s 250.084 (y)s 258.695 (that)s 7 f 280.362 (v)s 6 f 288.345 (=)s 298.901 (1)s 303.901 (.)s 310.012 (W)s 319.456 (e)s 327.234 (split)s 7 f 349.512 (V)s 6 f 360.901 (in)s 372.567 (t)s 376.179 (w)s 383.123 (o)s 391.456 (parts:)s 11 f 472.334 y 102.48 (8)s 7 f 108.036 (R)s 118.484 (\076)s 6 f 129.039 (0)s 7 f 134.039 (;)s 148.483 (V)s 9 f 473.834 y 154.317 (R)s 6 f 472.334 y 160.877 (\050)s 7 f 164.766 (x)s 6 f 170.481 (\051)s 177.148 (:=)s 10 f 461.234 y 190.481 (n)s 7 f 467.584 y 198.814 (V)s 6 f 206.87 (\050)s 7 f 210.759 (x)s 6 f 216.474 (\051)s 230.363 (if)s 11 f 239.53 (j)s 7 f 242.307 (x)s 11 f 248.023 (j)s 7 f 253.578 (\074)s 264.134 (R)s 6 f 479.584 y 198.814 (0)s 230.363 (otherwise)s 7 f 472.334 y 274.67 (;)s 6 f 289.115 (and)s 469.806 y 316.754 (\176)s 7 f 472.334 y 315.226 (V)s 9 f 473.834 y 321.059 (R)s 6 f 472.334 y 330.397 (:=)s 7 f 343.73 (V)s 11 f 354.008 (\241)s 7 f 364.008 (V)s 9 f 473.834 y 369.841 (R)s 7 f 472.334 y 376.402 (:)s 6 f 497.083 y 63 (and)s 82.444 (w)s 89.389 (e)s 97.167 (imp)s 114.111 (ose)s 130.833 (the)s 148.056 (follo)s 166.389 (wing)s 190.278 (relation)s 226.973 (b)s 232.806 (et)s 240.861 (w)s 247.806 (een)s 265.584 (the)s 282.806 (three)s 308.389 (parameters)s 7 f 360.167 (a)s 6 f 365.453 (,)s 7 f 371.564 (R)s 6 f 382.568 (and)s 7 f 402.012 (\270)s 6 f 407.845 (:)s 7 f 523.194 y 154.841 (a)s 6 f 162.905 (=)s 11 f 173.46 (\241)s 7 f 181.238 (\270)s 10 f 509.583 y 188.738 (Z)s 17 f 532.306 y 194.293 (j)s 9 f 196.668 (x)s 17 f 201.203 (j)s 9 f 203.578 (\074R)s 7 f 523.194 y 218.055 (V)s 6 f 226.111 (\050)s 7 f 229.999 (x)s 6 f 235.715 (\051)s 7 f 239.604 (dx)s 11 f 256.079 (\050)s 264.413 (\051)s 7 f 279.968 (a)s 6 f 288.032 (=)s 7 f 298.587 (\270)s 11 f 304.42 (V)s 6 f 311.37 (\050)s 7 f 315.259 (R)s 6 f 322.93 (\051)s 398.104 (\0503.1\051)s 551.555 y 63 (so)s 75.278 (that)s 7 f 559.5 y 160.234 (\270)s 9.772 .4 158.265 563.965 r 573.124 y 158.265 (a)s 8 f 570.235 y 163.551 (2)s 10 f 552.654 y 170.904 (Z)s 20 f 575.376 y 176.459 (R)s 7 f 566.265 y 183.681 (V)s 9 f 567.765 y 189.515 (R)s 6 f 566.265 y 196.075 (\050)s 7 f 559.5 y 201.164 (x)s 5.715 .4 201.164 563.965 r 573.124 y 201.378 (a)s 6 f 566.265 y 208.079 (\051)s 7 f 211.968 (dx)s 6 f 225.666 (=)s 7 f 559.5 y 237.421 (\270)s 5.833 .4 237.421 563.965 r 573.124 y 237.695 (a)s 10 f 552.654 y 246.121 (Z)s 20 f 575.376 y 251.677 (R)s 7 f 566.265 y 258.899 (V)s 9 f 567.765 y 264.732 (R)s 6 f 566.265 y 271.292 (\050)s 7 f 275.181 (x)s 6 f 280.897 (\051)s 7 f 284.785 (dx)s 6 f 298.483 (=)s 11 f 309.039 (\241)s 6 f 316.817 (1)s 7 f 321.817 (:)s do-end end endp showpage %%Page: 9 9 %%BeginPageSetup initializepage (duclos ; page : 9 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f155 sf ( )S -994 -1000 :M f221 sf ( )S -988 -1000 :M f255 sf ( )S -982 -1000 :M f287 sf ( )S -976 -1000 :M f320 sf ( )S -970 -1000 :M f354 sf ( )S -964 -1000 :M f388 sf ( )S -958 -1000 :M f422 sf ( )S -955 -1000 :M f589 sf ( )S -949 -1000 :M f621 sf ( )S -943 -1000 :M f687 sf ( )S 0 0 :M initclip TeXdict begin do-bop 3 9 /CMR9 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 12 10 /MSBM10 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 20 7 /MSBM7 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (1-d)s 78.93 (b)s 84.326 (eha)s 97.948 (viour)s 121.864 (of)s 132.399 (atoms)s 159.686 (in)s 170.478 (in)s 177.929 (tense)s 201.626 (magnetic)s 241.199 (\257elds)s 414.034 (9)s 6 f 54 y 63 (Let)s 7 f 81.337 (r)s 8 f 55.5 y 85.849 (0)s 6 f 54 y 93.814 (:=)s 107.849 (\050)s 7 f 111.737 (h)s 8 f 55.5 y 117.499 (0)s 6 f 54 y 124.488 (+)s 134.768 (5)s 7 f 139.768 (=)s 6 f 144.768 (4\051)s 17 f 50.371 y 153.657 (\241)s 8 f 159.907 (1)s 6 f 54 y 168.147 (th)s 177.314 (us)s 11 f 190.568 (k)s 7 f 195.568 (r)s 8 f 55.5 y 200.08 (0)s 11 f 54 y 204.566 (k)s 213.045 (\267)s 6 f 224.301 (1)s 229.301 (;)s 235.833 (clearly)s 268.226 (the)s 285.869 (norm)s 312.429 (resolv)s 337.512 (en)s 347.235 (t)s 354.878 (con)s 369.6 (v)s 374.6 (ergence)s 410.604 (of)s 7 f 66 y 63 (h)s 6 f 68.762 (\050)s 7 f 72.65 (a;)s 82.381 (\270)s 6 f 88.214 (\051)s 95.436 (to)s 7 f 107.659 (h)s 8 f 67.5 y 113.42 (0)s 6 f 66 y 121.24 (follo)s 139.573 (ws)s 154.073 (from)s 177.712 (the)s 194.934 (con)s 209.656 (v)s 214.656 (ergence)s 250.24 (to)s 262.462 (0)s 270.795 (of)s 11 f 84.751 y 81.695 (p)s 8.998 .4 90.028 84.751 r 7 f 91.692 y 90.028 (r)s 8 f 93.192 y 94.54 (0)s 10 f 77.592 y 100.692 (\265)s 7 f 84.927 y 111.223 (\270)s 9.772 .4 109.253 89.392 r 98.551 y 109.253 (a)s 8 f 95.662 y 114.539 (2)s 7 f 91.692 y 120.225 (V)s 6 f 128.281 (\050)s 11 f 84.927 y 134.624 (\242)s 5.286 .4 133.37 89.392 r 7 f 98.551 y 133.37 (a)s 6 f 91.692 y 139.856 (\051)s 145.967 (+)s 7 f 155.967 (\261)s 10 f 77.592 y 160.79 (\266)s 11 f 84.751 y 169.818 (p)s 8.998 .4 178.151 84.751 r 7 f 91.692 y 178.151 (r)s 8 f 93.192 y 182.662 (0)s 6 f 91.692 y 189.926 (=)s 11 f 84.751 y 200.482 (p)s 8.998 .4 208.815 84.751 r 7 f 91.692 y 208.815 (r)s 8 f 93.192 y 213.327 (0)s 10 f 77.592 y 219.48 (\265)s 7 f 84.927 y 230.01 (\270)s 9.772 .4 228.041 89.392 r 98.551 y 228.041 (a)s 8 f 95.662 y 233.327 (2)s 7 f 91.692 y 239.013 (V)s 9 f 93.192 y 244.846 (R)s 6 f 91.692 y 251.406 (\050)s 11 f 84.927 y 257.749 (\242)s 5.286 .4 256.495 89.392 r 7 f 98.551 y 256.495 (a)s 6 f 91.692 y 262.981 (\051)s 269.092 (+)s 7 f 279.092 (\261)s 10 f 77.592 y 283.915 (\266)s 11 f 84.751 y 292.943 (p)s 8.998 .4 301.276 84.751 r 7 f 91.692 y 301.276 (r)s 8 f 93.192 y 305.788 (0)s 6 f 91.692 y 312.496 (+)s 11 f 84.751 y 322.496 (p)s 8.998 .4 330.829 84.751 r 7 f 91.692 y 330.829 (r)s 8 f 93.192 y 335.341 (0)s 7 f 84.927 y 342.996 (\270)s 9.772 .4 341.027 89.392 r 98.551 y 341.027 (a)s 8 f 95.662 y 346.313 (2)s 6 f 89.164 y 353.527 (\176)s 7 f 91.692 y 351.999 (V)s 9 f 93.192 y 357.832 (R)s 6 f 91.692 y 364.392 (\050)s 11 f 84.927 y 370.735 (\242)s 5.286 .4 369.481 89.392 r 7 f 98.551 y 369.481 (a)s 6 f 91.692 y 375.967 (\051)s 11 f 84.751 y 379.856 (p)s 8.998 .4 388.189 84.751 r 7 f 91.692 y 388.189 (r)s 8 f 93.192 y 392.701 (0)s 7 f 91.692 y 397.187 (:)s 6 f 117.383 y 63 (The)s 83.556 (second)s 115.833 (term)s 139.75 (is)s 149.806 (estimated)s 195.417 (as)s 207.695 (follo)s 226.028 (ws)s 240.528 (\050)s 247.75 (w)s 254.695 (e)s 262.472 (use)s 279.75 (\050)s 283.639 (3.1)s 296.417 (\051)s 303.639 (for)s 318.945 (the)s 336.167 (last)s 355.111 (inequalit)s 392.889 (y\051:)s 11 f 142.285 y 103.486 (k)s 135.344 y 108.486 (p)s 8.998 .4 116.819 135.344 r 7 f 142.285 y 116.819 (r)s 8 f 143.785 y 121.331 (0)s 7 f 135.519 y 128.986 (\270)s 9.772 .4 127.017 139.985 r 149.144 y 127.017 (a)s 8 f 146.255 y 132.303 (2)s 6 f 139.757 y 139.517 (\176)s 7 f 142.285 y 137.989 (V)s 9 f 143.785 y 143.822 (R)s 6 f 142.285 y 150.383 (\050)s 11 f 135.519 y 156.725 (\242)s 5.286 .4 155.471 139.985 r 7 f 149.144 y 155.471 (a)s 6 f 142.285 y 161.957 (\051)s 11 f 135.344 y 165.846 (p)s 8.998 .4 174.18 135.344 r 7 f 142.285 y 174.18 (r)s 8 f 143.785 y 178.691 (0)s 11 f 142.285 y 183.177 (k)s 191.177 (\267)s 7 f 135.519 y 205.124 (\270)s 9.772 .4 203.155 139.985 r 149.144 y 203.155 (a)s 8 f 146.255 y 208.441 (2)s 11 f 142.285 y 214.127 (k)s 6 f 139.757 y 220.655 (\176)s 7 f 142.285 y 219.127 (V)s 9 f 143.785 y 224.96 (R)s 6 f 142.285 y 231.521 (\050)s 11 f 135.519 y 237.864 (\242)s 5.286 .4 236.609 139.985 r 7 f 149.144 y 236.609 (a)s 6 f 142.285 y 243.095 (\051)s 11 f 246.984 (k)s 17 f 143.785 y 251.984 (1)s 11 f 142.285 y 263.234 (\267)s 7 f 135.519 y 276.959 (\270)s 9.772 .4 274.99 139.985 r 149.144 y 274.99 (a)s 8 f 146.255 y 280.276 (2)s 6 f 142.285 y 287.628 (sup)s 11 f 302.684 (fj)s 7 f 310.462 (V)s 6 f 318.517 (\050)s 7 f 322.406 (x)s 6 f 328.121 (\051)s 11 f 332.01 (j)s 7 f 334.788 (;)s 11 f 340.899 (j)s 7 f 343.677 (x)s 11 f 349.392 (j)s 354.948 (\270)s 7 f 365.503 (R)s 11 f 373.173 (g)s 167.409 y 191.177 (\267)s 7 f 160.644 y 205.124 (\270)s 9.772 .4 203.155 165.109 r 174.269 y 203.155 (a)s 8 f 171.38 y 208.441 (2)s 6 f 160.644 y 231.683 (1)s 37.712 .4 215.327 165.109 r 11 f 167.109 y 215.327 (p)s 29.378 .4 223.66 167.109 r 6 f 175.442 y 223.66 (1)s 230.883 (+)s 7 f 240.883 (R)s 8 f 172.553 y 248.553 (2)s 11 f 167.409 y 254.239 (k)s 259.239 (h)s 7 f 263.128 (x)s 11 f 268.843 (i)s 7 f 272.732 (V)s 11 f 280.788 (k)s 17 f 168.909 y 285.788 (1)s 11 f 167.409 y 297.038 (\267)s 160.644 y 308.976 (k)s 313.976 (h)s 7 f 317.865 (x)s 11 f 323.581 (i)s 7 f 327.469 (V)s 11 f 335.525 (k)s 17 f 162.144 y 340.525 (1)s 40.388 .4 308.793 165.109 r 7 f 174.269 y 308.793 (\270)s 314.626 (R)s 11 f 322.297 (V)s 6 f 329.247 (\050)s 7 f 333.135 (R)s 6 f 340.806 (\051)s 8 f 171.38 y 344.695 (2)s 7 f 167.409 y 350.381 (:)s 6 f 193.6 y 63 (F)s 68.694 (or)s 80.944 (the)s 98.167 (\257rst)s 118.806 (term)s 142.722 (w)s 149.667 (e)s 157.445 (ha)s 167.722 (v)s 172.722 (e,)s 183.278 (using)s 209.445 (also)s 229.5 (\050)s 233.389 (3.1)s 246.167 (\051)s 253.389 (and)s 272.834 (with)s 7 f 295.611 (u)s 6 f 301.336 (,)s 7 f 307.447 (v)s 6 f 315.987 (in)s 11 f 327.653 (H)s 8 f 189.971 y 336.195 (1)s 6 f 193.6 y 340.681 (\050)s 12 f 344.57 (R)s 6 f 351.792 (\051)s 359.014 (and)s 7 f 378.459 (\047)s 6 f 387.778 (:=)s 7 f 401.112 (u)s 5.206 .4 406.836 188.095 r 193.6 y 406.836 (v)s 6 f 412.042 (:)s 10 f 204.792 y 100.233 (\257)s 210.792 y 100.233 (\257)s 216.792 y 100.233 (\257)s 222.792 y 100.233 (\257)s 228.792 y 100.233 (\257)s 208.192 y 103.566 (\277)s 111.066 (\265)s 7 f 215.527 y 121.596 (\270)s 9.772 .4 119.627 219.992 r 229.151 y 119.627 (a)s 8 f 226.263 y 124.913 (2)s 7 f 222.292 y 130.599 (V)s 9 f 223.792 y 136.432 (R)s 6 f 222.292 y 142.992 (\050)s 11 f 215.527 y 149.335 (\242)s 5.286 .4 148.081 219.992 r 7 f 229.151 y 148.081 (a)s 6 f 222.292 y 154.567 (\051)s 160.678 (+)s 7 f 170.678 (\261)s 10 f 208.192 y 175.501 (\266)s 7 f 222.292 y 184.529 (u;)s 194.698 (v)s 10 f 208.192 y 199.904 (\300)s 17 f 232.292 y 207.404 (\241)s 8 f 213.654 (1)s 9 f 217.64 (;)s 8 f 220.015 (1)s 10 f 204.792 y 224.501 (\257)s 210.792 y 224.501 (\257)s 216.792 y 224.501 (\257)s 222.792 y 224.501 (\257)s 228.792 y 224.501 (\257)s 6 f 222.292 y 230.835 (=)s 10 f 207.792 y 241.612 (\257)s 213.792 y 241.612 (\257)s 219.792 y 241.612 (\257)s 225.792 y 241.612 (\257)s 208.681 y 244.946 (Z)s 20 f 231.403 y 250.501 (R)s 7 f 222.292 y 257.723 (dx)s 215.527 y 271.813 (\270)s 9.772 .4 269.844 219.992 r 229.151 y 269.844 (a)s 8 f 226.263 y 275.129 (2)s 7 f 222.292 y 280.816 (V)s 9 f 223.792 y 286.649 (R)s 6 f 222.292 y 293.209 (\050)s 7 f 215.527 y 298.298 (x)s 5.715 .4 298.298 219.992 r 229.151 y 298.513 (a)s 6 f 222.292 y 305.213 (\051\050)s 7 f 312.991 (\047)s 6 f 319.533 (\050)s 7 f 323.422 (x)s 6 f 329.137 (\051)s 11 f 335.248 (\241)s 7 f 345.248 (\047)s 6 f 351.79 (\0500\051\051)s 10 f 207.792 y 368.456 (\257)s 213.792 y 368.456 (\257)s 219.792 y 368.456 (\257)s 225.792 y 368.456 (\257)s 6 f 253.292 y 230.835 (=)s 10 f 238.792 y 241.612 (\257)s 244.792 y 241.612 (\257)s 250.792 y 241.612 (\257)s 256.792 y 241.612 (\257)s 239.681 y 244.946 (Z)s 20 f 262.403 y 250.501 (R)s 7 f 253.292 y 257.723 (dx)s 246.527 y 269.844 (\270)s 5.833 .4 269.844 250.992 r 260.152 y 270.117 (a)s 253.292 y 276.877 (V)s 9 f 254.792 y 282.71 (R)s 6 f 253.292 y 289.27 (\050)s 7 f 293.159 (x)s 6 f 298.875 (\051\050)s 7 f 306.652 (\047)s 6 f 313.194 (\050)s 7 f 317.083 (ax)s 6 f 328.084 (\051)s 11 f 334.195 (\241)s 7 f 344.195 (\047)s 6 f 350.737 (\0500\051\051)s 10 f 238.792 y 367.403 (\257)s 244.792 y 367.403 (\257)s 250.792 y 367.403 (\257)s 256.792 y 367.403 (\257)s 11 f 280.945 y 230.835 (\267)s 7 f 274.18 y 242.812 (\270)s 5.833 .4 242.812 278.645 r 287.805 y 243.086 (a)s 10 f 267.334 y 251.512 (Z)s 17 f 290.057 y 257.068 (j)s 9 f 259.443 (x)s 17 f 263.978 (j)s 9 f 266.353 (\074R)s 7 f 280.945 y 280.829 (dx)s 11 f 291.75 (j)s 7 f 294.527 (V)s 6 f 302.583 (\050)s 7 f 306.472 (x)s 6 f 312.187 (\051)s 10 f 267.334 y 317.743 (Z)s 9 f 269.806 y 327.743 (ax)s 8 f 290.057 y 323.298 (0)s 7 f 280.945 y 338.782 (dy)s 349.248 (\047)s 17 f 276.816 y 355.79 (0)s 6 f 280.945 y 358.595 (\050)s 7 f 362.484 (y)s 6 f 367.746 (\051)s 11 f 371.635 (j)s 309.516 y 230.835 (\267)s 7 f 302.751 y 242.812 (\270)s 5.833 .4 242.812 307.216 r 316.376 y 243.086 (a)s 11 f 300.561 y 249.846 (p)s 12.956 .4 258.179 300.561 r 7 f 309.516 y 258.179 (aR)s 10 f 295.905 y 272.802 (Z)s 17 f 318.627 y 278.357 (j)s 9 f 280.732 (x)s 17 f 285.267 (j)s 9 f 287.642 (\074R)s 7 f 309.516 y 302.119 (dx)s 11 f 313.039 (j)s 7 f 315.817 (V)s 6 f 323.872 (\050)s 7 f 327.761 (x)s 6 f 333.476 (\051)s 11 f 337.365 (j)s 340.143 (k)s 7 f 345.143 (\047)s 17 f 305.387 y 351.685 (0)s 11 f 309.516 y 354.49 (k)s 341.085 y 230.835 (\267)s 6 f 241.612 (2)s 7 f 246.612 (\270)s 10 f 325.177 y 252.446 (r)s 10.07 .4 262.446 325.177 r 7 f 334.32 y 263.646 (R)s 7.67 .4 263.646 338.785 r 347.944 y 264.838 (a)s 10 f 327.474 y 274.183 (Z)s 17 f 350.196 y 279.738 (j)s 9 f 282.113 (x)s 17 f 286.648 (j)s 9 f 289.023 (\074R)s 7 f 341.085 y 303.5 (dx)s 11 f 314.42 (j)s 7 f 317.198 (V)s 6 f 325.253 (\050)s 7 f 329.142 (x)s 6 f 334.857 (\051)s 11 f 338.746 (j)s 341.524 (k)s 7 f 346.524 (u)s 11 f 352.249 (k)s 8 f 342.585 y 357.249 (1)s 11 f 341.085 y 361.735 (k)s 7 f 366.735 (v)s 11 f 371.941 (k)s 8 f 342.585 y 376.941 (1)s 6 f 367.582 y 63 (and)s 82.444 (consequen)s 126.389 (tly)s 11 f 394.926 y 113.277 (k)s 387.985 y 118.277 (p)s 8.998 .4 126.61 387.985 r 7 f 394.926 y 126.61 (r)s 8 f 396.426 y 131.122 (0)s 10 f 380.826 y 137.275 (\265)s 7 f 388.161 y 147.805 (\270)s 9.772 .4 145.836 392.626 r 401.785 y 145.836 (a)s 8 f 398.897 y 151.122 (2)s 7 f 394.926 y 156.808 (V)s 9 f 396.426 y 162.641 (R)s 6 f 394.926 y 169.201 (\050)s 11 f 388.161 y 175.544 (\242)s 5.286 .4 174.29 392.626 r 7 f 401.785 y 174.29 (a)s 6 f 394.926 y 180.776 (\051)s 186.887 (+)s 7 f 196.887 (\261)s 10 f 380.826 y 201.71 (\266)s 11 f 387.985 y 210.738 (p)s 8.998 .4 219.071 387.985 r 7 f 394.926 y 219.071 (r)s 8 f 396.426 y 223.583 (0)s 11 f 394.926 y 228.069 (k)s 235.846 (\267)s 6 f 246.402 (2)s 7 f 251.402 (\270)s 10 f 379.018 y 257.235 (r)s 10.07 .4 267.235 379.018 r 7 f 388.161 y 268.435 (R)s 7.67 .4 268.435 392.626 r 401.785 y 269.627 (a)s 11 f 394.926 y 278.972 (V)s 6 f 285.922 (\050)s 7 f 289.811 (R)s 6 f 297.481 (\051)s 304.148 (=)s 314.703 (2)s 10 f 385.888 y 319.703 (p)s 35.902 .4 329.703 385.888 r 7 f 394.926 y 329.703 (\270)s 335.537 (R)s 11 f 343.207 (V)s 6 f 350.157 (\050)s 7 f 354.046 (R)s 6 f 361.716 (\051)s 365.605 (;)s 11 f 421.258 y 63 (h)s 66.889 (\242)s 7 f 69.667 (;)s 11 f 74.111 (\242)s 76.889 (i)s 17 f 422.758 y 80.778 (\241)s 8 f 87.028 (1)s 9 f 91.014 (;)s 8 f 93.389 (1)s 6 f 421.258 y 101.656 (denotes)s 138.27 (the)s 155.94 (dualit)s 181.218 (y)s 190.277 (brac)s 208.916 (k)s 213.916 (ets)s 229.974 (b)s 235.808 (et)s 243.863 (w)s 250.808 (een)s 11 f 269.033 (H)s 8 f 417.629 y 277.575 (1)s 6 f 421.258 y 282.061 (\050)s 12 f 285.95 (R)s 6 f 293.172 (\051)s 300.842 (and)s 11 f 320.734 (H)s 17 f 417.629 y 329.275 (\241)s 8 f 335.525 (1)s 6 f 421.258 y 340.012 (\050)s 12 f 343.901 (R)s 6 f 351.123 (\051)s 358.793 (and)s 11 f 378.685 (k)s 386.205 (\242)s 391.503 (k)s 8 f 422.758 y 396.503 (1)s 6 f 421.258 y 404.771 (the)s 433.258 y 63 (norm)s 89.139 (of)s 11 f 100.528 (H)s 8 f 429.629 y 109.07 (1)s 6 f 433.258 y 113.556 (\050)s 12 f 117.445 (R)s 6 f 124.667 (\051)s 128.556 (.)s 134.667 (Th)s 147.167 (us)s 160 (with)s 7 f 182.778 (C)s 9 f 434.758 y 189.925 (V)s 6 f 433.258 y 199.647 (:=)s 11 f 212.981 (k)s 217.981 (h)s 7 f 221.87 (x)s 11 f 227.585 (i)s 7 f 231.474 (V)s 17 f 434.758 y 237.307 (1)s 11 f 433.258 y 245.779 (k)s 458.949 y 119.923 (k)s 452.008 y 124.923 (p)s 8.998 .4 133.256 452.008 r 7 f 458.949 y 133.256 (r)s 8 f 460.449 y 137.768 (0)s 10 f 444.849 y 143.92 (\265)s 7 f 452.184 y 154.451 (\270)s 9.772 .4 152.481 456.649 r 465.809 y 152.481 (a)s 8 f 462.92 y 157.767 (2)s 7 f 458.949 y 163.454 (V)s 9 f 460.449 y 169.287 (R)s 6 f 458.949 y 175.847 (\050)s 11 f 452.184 y 182.19 (\242)s 5.286 .4 180.936 456.649 r 7 f 465.809 y 180.936 (a)s 6 f 458.949 y 187.422 (\051)s 193.533 (+)s 7 f 203.533 (\261)s 10 f 444.849 y 208.356 (\266)s 11 f 452.008 y 217.383 (p)s 8.998 .4 225.717 452.008 r 7 f 458.949 y 225.717 (r)s 8 f 460.449 y 230.228 (0)s 11 f 458.949 y 234.714 (k)s 242.492 (\267)s 6 f 253.048 (2)s 10 f 449.911 y 258.048 (p)s 35.902 .4 268.048 449.911 r 7 f 458.949 y 268.048 (\270)s 273.881 (R)s 11 f 281.551 (V)s 6 f 288.501 (\050)s 7 f 292.39 (R)s 6 f 300.06 (\051)s 306.171 (+)s 7 f 452.184 y 330.519 (C)s 9 f 453.684 y 337.667 (V)s 40.388 .4 317.371 456.649 r 7 f 465.809 y 317.371 (\270)s 323.205 (R)s 11 f 330.875 (V)s 6 f 337.825 (\050)s 7 f 341.714 (R)s 6 f 349.384 (\051)s 8 f 462.92 y 353.273 (2)s 7 f 458.949 y 358.959 (:)s 6 f 484.086 y 63 (W)s 72.444 (e)s 80.222 (c)s 84.389 (ho)s 95.222 (ose)s 7 f 111.944 (R)s 6 f 122.948 (as)s 135.226 (a)s 143.559 (function)s 182.726 (of)s 7 f 194.115 (\270)s 6 f 203.281 (so)s 215.559 (that)s 510.715 y 101.736 (2)s 10 f 501.676 y 106.736 (p)s 35.902 .4 116.736 501.676 r 7 f 510.715 y 116.736 (\270)s 122.57 (R)s 11 f 130.24 (V)s 6 f 137.19 (\050)s 7 f 141.079 (R)s 6 f 148.749 (\051)s 155.416 (=)s 7 f 503.949 y 180.319 (C)s 9 f 505.449 y 187.466 (V)s 40.388 .4 167.171 508.415 r 7 f 517.574 y 167.171 (\270)s 173.004 (R)s 11 f 180.675 (V)s 6 f 187.625 (\050)s 7 f 191.514 (R)s 6 f 199.184 (\051)s 8 f 514.685 y 203.073 (2)s 11 f 510.715 y 214.314 (\050)s 222.648 (\051)s 7 f 238.203 (\270)s 6 f 246.814 (=)s 10 f 496.614 y 257.37 (\265)s 7 f 503.949 y 265.931 (C)s 9 f 505.449 y 273.078 (V)s 14.092 .4 265.931 508.415 r 6 f 517.574 y 270.477 (2)s 10 f 496.614 y 281.222 (\266)s 18 f 495.999 y 289.783 (2)s 3.403 .34 289.783 497.107 r 501.096 y 289.783 (3)s 6 f 503.949 y 313.438 (1)s 36.371 .4 297.753 508.415 r 7 f 519.01 y 297.753 (R)s 11 f 305.423 (V)s 6 f 312.373 (\050)s 7 f 316.262 (R)s 6 f 323.932 (\051)s 18 f 512.837 y 329.021 (5)s 3.403 .34 329.021 513.944 r 517.933 y 329.021 (3)s 6 f 510.715 y 338.102 (=:)s 503.949 y 361.79 (1)s 23.31 .4 352.635 508.415 r 7 f 517.574 y 352.635 (G)s 6 f 360.497 (\050)s 7 f 364.386 (R)s 6 f 372.056 (\051)s 7 f 510.715 y 377.145 (:)s 6 f 537.146 y 63 (Let)s 7 f 81.747 (R)s 8 f 538.646 y 89.34 (0)s 11 f 537.146 y 97.987 (\270)s 6 f 109.926 (0)s 119.09 (b)s 124.923 (e)s 133.531 (the)s 151.583 (in)s 159.917 (\257m)s 173.528 (um)s 191.58 (of)s 203.799 (the)s 221.851 (essen)s 243.907 (tial)s 262.515 (supp)s 283.404 (ort)s 300.373 (of)s 7 f 312.592 (V)s 6 f 324.811 (in)s 12 f 337.308 (R)s 8 f 538.646 y 344.53 (+)s 6 f 537.146 y 351.169 (,)s 358.11 (then)s 381.718 (the)s 399.771 (map)s 7 f 549.146 y 63 (G)s 6 f 73.64 (:)s 79.196 ([)s 7 f 81.973 (R)s 8 f 550.646 y 89.566 (0)s 7 f 549.146 y 94.053 (;)s 11 f 98.497 (1)s 6 f 108.497 ([)s 11 f 111.275 (!)s 12 f 124.052 (R)s 6 f 134.608 (is)s 144.664 (strictly)s 178.914 (increasing)s 225.664 (since)s 570.376 y 110.798 (\050)s 7 f 114.687 (C)s 9 f 571.876 y 121.834 (V)s 7 f 570.376 y 128.778 (=)s 6 f 133.778 (2\051)s 18 f 563.56 y 143.867 (2)s 3.403 .34 143.867 564.667 r 568.657 y 143.867 (3)s 7 f 570.376 y 148.97 (G)s 17 f 566.247 y 156.833 (0)s 6 f 570.376 y 159.638 (\050)s 7 f 163.527 (R)s 6 f 171.197 (\051)s 177.864 (=)s 11 f 188.419 (V)s 6 f 195.369 (\050)s 7 f 199.258 (R)s 6 f 206.928 (\051)s 18 f 563.56 y 212.017 (2)s 3.403 .34 212.017 564.667 r 568.657 y 212.017 (3)s 6 f 570.376 y 218.787 (\050)s 222.676 (5)s 7 f 227.676 (=)s 6 f 232.676 (3\050)s 11 f 241.565 (\241)s 7 f 249.342 (V)s 6 f 257.398 (\050)s 7 f 261.287 (R)s 6 f 268.957 (\051)s 11 f 275.068 (\241)s 7 f 285.068 (V)s 6 f 293.124 (\050)s 11 f 297.012 (\241)s 7 f 304.79 (R)s 6 f 312.46 (\051\051)s 7 f 320.238 (R)s 6 f 330.131 (+)s 11 f 340.13 (V)s 6 f 347.081 (\050)s 7 f 350.969 (R)s 6 f 358.64 (\051)s 362.528 (\051)s 7 f 368.084 (:)s do-end end endp showpage %%Page: 10 10 %%BeginPageSetup initializepage (duclos ; page : 10 sur 11)setjob %%EndPageSetup gS 0 0 538 781 rC -1000 -1000 :M f123 sf ( )S -994 -1000 :M f155 sf ( )S -988 -1000 :M f55 sf ( )S -984 -1000 :M f221 sf ( )S -978 -1000 :M f255 sf ( )S -972 -1000 :M f287 sf ( )S -966 -1000 :M f320 sf ( )S -960 -1000 :M f354 sf ( )S -954 -1000 :M f388 sf ( )S -948 -1000 :M f589 sf ( )S -942 -1000 :M f621 sf ( )S -936 -1000 :M f819 sf ( )S -930 -1000 :M f852 sf ( )S 0 0 :M initclip TeXdict begin do-bop 2 9 /CMBX9 findfont fdef 3 9 /CMR9 findfont fdef 5 12 /CMBX12 findfont fdef 6 10 /CMR10 findfont fdef 7 10 /CMMI10 findfont fdef 8 7 /CMR7 findfont fdef 9 7 /CMMI7 findfont fdef 10 10 /CMEX10 findfont fdef 11 10 /CMSY10 findfont fdef 17 7 /CMSY7 findfont fdef 18 5 /CMR5 findfont fdef 23 6 /CMSY6 findfont fdef 25 9 /CMTI9 findfont fdef 44 41 translate 72 72.27 div dup scale 3 f 28 y 63 (10)s 308.564 (R.)s 321.025 (Brummelh)s 363.315 (uis,)s 380.325 (P)s 385.849 (.)s 391.501 (Duclos)s 6 f 54 y 63 (Therefore)s 108.147 (for)s 123.266 (ev)s 132.711 (ery)s 7 f 149.497 (\270)s 6 f 158.477 (in)s 169.958 (]0)s 7 f 177.735 (;)s 6 f 182.18 (1)s 7 f 187.18 (=G)s 6 f 200.042 (\050)s 7 f 203.931 (R)s 8 f 55.5 y 211.524 (0)s 6 f 54 y 216.01 (\051])s 225.824 (there)s 251.221 (exists)s 278.646 (a)s 286.793 (unique)s 7 f 319.107 (R)s 6 f 329.924 (solving)s 7 f 363.405 (\270)s 6 f 372.016 (=)s 382.571 (1)s 7 f 387.571 (=G)s 6 f 400.434 (\050)s 7 f 404.323 (R)s 6 f 411.993 (\051)s 415.882 (.)s 66 y 63 (With)s 88.833 (suc)s 102.5 (h)s 111.389 (a)s 119.722 (c)s 123.889 (hoice)s 149.445 (of)s 7 f 160.833 (R)s 6 f 171.837 (w)s 178.781 (e)s 186.559 (get)s 11 f 96.79 y 149.133 (k)s 89.849 y 154.133 (p)s 8.998 .4 162.467 89.849 r 7 f 96.79 y 162.467 (r)s 8 f 98.29 y 166.978 (0)s 10 f 82.69 y 173.131 (\265)s 7 f 90.025 y 183.662 (\270)s 9.772 .4 181.692 94.49 r 103.65 y 181.692 (a)s 8 f 100.761 y 186.978 (2)s 7 f 96.79 y 192.664 (V)s 9 f 98.29 y 198.498 (R)s 6 f 96.79 y 205.058 (\050)s 11 f 90.025 y 211.401 (\242)s 5.286 .4 210.147 94.49 r 7 f 103.65 y 210.147 (a)s 6 f 96.79 y 216.632 (\051)s 222.744 (+)s 7 f 232.744 (\261)s 10 f 82.69 y 237.566 (\266)s 11 f 89.849 y 246.594 (p)s 8.998 .4 254.928 89.849 r 7 f 96.79 y 254.928 (r)s 8 f 98.29 y 259.439 (0)s 11 f 96.79 y 263.925 (k)s 271.703 (\267)s 10 f 82.69 y 282.259 (\265)s 6 f 90.025 y 292.473 (4)s 7 f 297.473 (C)s 9 f 91.525 y 304.62 (V)s 22.398 .4 290.82 94.49 r 11 f 103.65 y 290.82 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324.286 (a)s 6 f 332.35 (=)s 7 f 342.905 (\270)s 6 f 350.405 (log)s 7 f 364.988 (\270)s 17 f 203.226 y 370.822 (\241)s 8 f 377.072 (1)s 6 f 206.855 y 381.558 (.)s 6 10 387.669 208.355 r 225.274 y 63 (Once)s 89.514 (the)s 107.695 (norm)s 134.793 (resolv)s 159.877 (en)s 169.599 (t)s 177.78 (con)s 192.502 (v)s 197.502 (ergence)s 234.044 (is)s 245.059 (pro)s 259.253 (v)s 264.253 (en)s 278.545 (it)s 289.504 (is)s 300.518 (standard)s 343.227 (to)s 356.408 (sho)s 370.631 (w)s 382.145 (that)s 404.77 (the)s 237.274 y 63 (in)s 71.333 (\257m)s 84.945 (um)s 101.932 (of)s 113.086 (the)s 130.074 (sp)s 139.852 (ectrum)s 173.534 (is)s 183.355 (a)s 191.453 (simple)s 222.385 (isolated)s 258.873 (eigen)s 280.817 (v)s 285.54 (alue)s 306.416 (for)s 7 f 321.487 (\270)s 6 f 330.419 (small)s 356.351 (enough)s 390.561 (and)s 409.77 (to)s 249.274 y 63 (deriv)s 84.694 (e)s 92.472 (the)s 109.695 (p)s 115.528 (erturbation)s 168.361 (expansion)s 214.806 (of)s 226.195 (this)s 245.695 (eigen)s 267.639 (v)s 272.362 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139.569 (ymond.brummelh)s 216.264 (uis@univ-reims.fr,)s 298.097 (duclos@univ-tln.fr)s 3 f 150.69 y 63 (1991)s 84.583 (Mathematics)s 139.879 (Sub)s 155.81 (ject)s 173.542 (Classi\257cation.)s 232.742 (81V55)s 261.261 (;)s 266.914 (81Q15)s do-end end endp showpage %%Trailer end %%EOF ---------------0206251054651--