Content-Type: multipart/mixed; boundary="-------------0508240153936" This is a multi-part message in MIME format. ---------------0508240153936 Content-Type: text/plain; name="05-286.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-286.comments" Subject classifications: 35Qxx, 35L30, 81U30. alain.joye@ujf-grenoble.fr ; magali.marx@ujf-grenoble.fr ---------------0508240153936 Content-Type: text/plain; name="05-286.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-286.keywords" Semi-classical analysis, exponential asymptotics, scattering theory, Landau-Zener mechanism ---------------0508240153936 Content-Type: application/postscript; name="avcrosstot.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="avcrosstot.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.94a Copyright 2003 Radical Eye Software %%Title: avcrosstot.dvi %%CreationDate: Wed Aug 24 05:53:58 2005 %%Pages: 33 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMBX10 CMR10 CMR9 CMCSC10 CMMI9 CMSY9 CMMI10 CMSY10 %%+ MSBM10 CMMI8 CMTI9 CMR8 CMSY8 CMEX10 CMTI10 CMMI6 CMR6 CMSY6 MSBM7 %%+ CMTT9 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: DVIPS.EXE -P pdf avcrosstot %DVIPSParameters: dpi=8000 %DVIPSSource: TeX output 2005.08.24:0553 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: alt-rule.pro 0 0 %! % Patch by TVZ % Makes dvips files draw rules with stroke rather than fill. % Makes narrow rules more predictable at low resolutions % after distilling to PDF. % May have unknown consequences for very thick rules. % Tested only with dvips 5.85(k). 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concatmatrix exch findfont exch makefont setfont } def /Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto x1 y1 lineto closepath } def /OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse /b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } ifelse } def /Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse } def /BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def /OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } ifelse } def /ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def /BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } def /Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def } def /Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if /dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i w add def } repeat grestore gsave n 0 gt % DG/SR modification begin - Nov. 7, 1997 - Patch 1 %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } % DG/SR modification end { 2 setlinecap } ifelse /i y1 def /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g exch t L stroke /i i h add def } repeat grestore } def /ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c mul neg d } def /Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def /Rot { CP CP translate 3 -1 roll neg rotate NET } def /RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle dup a add ] cvx def } def /RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def /PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def /PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def /PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def /Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { h1 abs h sub dup s mul abs } ifelse } def /UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q { x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add exch } def /BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible /IfVisible true def } if } { IfVisible { Invisible /IfVisible false def } if } ifelse } def /InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def /Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def /IfVisible true def } def end % END pstricks.pro %%EndProcSet %%BeginProcSet: pst-dots.pro 0 0 %!PS-Adobe-2.0 %%Title: Dot Font for PSTricks %%Creator: Timothy Van Zandt %%Creation Date: May 7, 1993 %% Version 97 patch 1, 99/12/16 %% Modified by Etienne Riga - Dec. 16, 1999 %% to add /Diamond, /SolidDiamond and /BoldDiamond 10 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put dup (P) 0 get /BoldPentagon put % DG/SR modification begin - Dec. 16, 1999 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450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def % DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath } def /SolidDiamond { DiamondPath fill } def /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def % DG/SR modification end /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind def end /PSTricksDotFont exch definefont pop %END pst-dots.pro %%EndProcSet %%BeginProcSet: pst-node.pro 0 0 %! % PostScript prologue for pst-node.tex. % Version 97 patch 1, 97/05/09. % For distribution, see pstricks.tex. % /tx@NodeDict 400 dict def tx@NodeDict begin tx@Dict begin /T /translate load def end /NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end grestore } def /InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def } def /InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch Sin mul } def } def /GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse } def /InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def /DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup Cos mul exch Sin mul } def /TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul } ifelse } def /InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan sin def /NodePos { TriNodePos } def } def /OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul } def /GetCenter { begin X Y NodeMtrx transform CM itransform end } def /XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } { 0 Dist Sin mul } ifelse } ifelse Do } def /GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse } def /AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def /GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA AddOffset yA add /yA1 ED xA add /xA1 ED } def /GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB AddOffset yB add /yB1 ED xB add /xB1 ED } def /GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED } ifelse } def /GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED } ifelse } def /InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED /NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def /LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def /LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop } repeat LPutLine cleartomark } def /BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def /HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def } def /HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def /HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def /VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def } def /VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def /VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark VPosEnd } def /HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx def grestore exec /LPutVar /SaveLPutVar load def } def /NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { LPutVar VPutLine } def LPutVar } def /NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop end } def /NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan /AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } ifelse } def /NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines } HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def /NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def % DG/SR modification begin - May 9, 1997 - Patch 1 %/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r %r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add %exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 %mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED /NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED % DG/SR modification end } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r Div def /y ED /x ED } def /NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB 180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def /LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos { xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar tx@Dict begin false Polygon end } def /NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def /x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } { x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def 0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos { LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } { t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def } def /Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos { LPutLines } def /VPutPos@ { LPutVar 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 46 /period put dup 64 /at put dup 97 /a put dup 98 /b put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{-6 -233 542 698}readonly def /UniqueID 5000831 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 21 /greaterequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 121 /dagger put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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C55547BD27F6679545C6D5503830 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /delta put dup 16 /zeta put dup 21 /lambda put dup 24 /xi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 59 /comma put dup 60 /less put dup 62 /greater put dup 64 /partialdiff put dup 69 /E put dup 77 /M put dup 78 /N put dup 82 /R put dup 89 /Y put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 114 /r put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 58 /colon put dup 65 /A put dup 66 /B put dup 68 /D put dup 70 /F put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 80 /P put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 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%!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 69 /E put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 121 /dagger put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 61 /equal put dup 82 /R put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 99 /c put dup 101 /e put dup 104 /h put dup 108 /l put dup 110 /n put dup 111 /o put dup 115 /s put dup 116 /t put dup 126 /tilde put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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12CAD454CAD565A113F705A4E986214057DA36C9EA2622 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueID 5000827 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB3DF7BFF10C9BDA4EFE5F68A8CB1526990D1357AE6D2F7C2D2EF8496 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 34 /epsilon put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 67 /C put dup 68 /D put dup 69 /E put dup 71 /G put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 86 /V put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 103 /g put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 73 /I put dup 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 39 /similarequal put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 57 /existential put dup 59 /emptyset put dup 69 /E put dup 70 /F put dup 77 /M put dup 82 /R put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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%%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 20 /kappa put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 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cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /grave put dup 19 /acute put dup 39 /quoteright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 55 /seven put dup 56 /eight put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 33 /arrowright put dup 49 /infinity put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 110 /n put dup 116 /t put dup 120 /x put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 18 /grave put dup 19 /acute put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 4 /Xi put dup 8 /Phi put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec 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%%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 88 /X put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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2432 y Fv(\()p Fp(E)70 b Fv(\)\))23265 1932 y Fk(2)24061 2432 y Fv(+)269 b(2)p Fp(c)p Fv(\()p Fp(E)70 b Fv(\)\()p Fp(z)323 b Fo(\000)269 b Fp(x)31574 2614 y Fk(0)32100 2432 y Fv(\()p Fp(E)70 b Fv(\)\))p Fp(\016)315 b Fv(+)270 b Fp(b)37065 1932 y Fk(2)37591 2432 y Fv(\()p Fp(E)70 b Fv(\))p Fp(\016)40083 1932 y Fk(2)40878 2432 y Fv(+)269 b Fp(R)43010 2614 y Fk(3)43536 2432 y Fv(\()p Fp(z)323 b Fo(\000)269 b Fp(x)46799 2614 y Fk(0)47324 2432 y Fv(\()p Fp(E)70 b Fv(\))p Fp(;)202 b(\016)46 b Fv(\))p Fp(;)3393 4375 y Fv(where)405 b Fp(R)7819 4557 y Fk(3)8749 4375 y Fv(is)f(a)g(remainder)f(of)i(order)f(3.)p 0 TeXcolorgray 1291 5814 a(\(2\))p 0 TeXcolorgray 554 w(W)-101 b(e)404 b(ha)-34 b(v)g(e:)11011 7299 y Fp(a)p Fv(\()p Fp(E)70 b Fv(\))337 b Fp(>)f Fv(0)p Fp(;)2626 b(b)p Fv(\()p Fp(E)70 b Fv(\))338 b Fp(>)e Fv(0)p Fp(;)2626 b(a)26998 6798 y Fk(2)27524 7299 y Fv(\()p Fp(E)70 b Fv(\))p Fp(b)29951 6798 y Fk(2)30477 7299 y Fv(\()p Fp(E)g Fv(\))270 b Fo(\000)f Fp(c)34391 6798 y Fk(2)34916 7299 y Fv(\()p Fp(E)70 b Fv(\))337 b Fp(>)g Fv(0)p Fp(:)-3150 8990 y Fv(According)329 b(to)h([26],)343 b(w)-34 b(e)330 b(kno)-34 b(w)330 b(a)f(priori)g(that) h(the)g(functions)g Fp(k)25821 9172 y Fm(j)26637 8990 y Fv(are)f(analytic)g(in)g(b)34 b(oth)330 b(v)-67 b(ariables)328 b(except)h(at)h(the)f(crossing)-3150 10429 y(p)34 b(oin)-34 b(ts.)502 b(The)290 b(assumptions)h(\()p Fw(H1)q Fv(\),)312 b(\()p Fw(H2)q Fv(\))290 b(and)g(\()p Fw(H3)p Fv(\))g(imply)g (analyticit)-34 b(y)289 b(in)h(b)34 b(oth)290 b(v)-67 b(ariables)289 b(at)h(the)g(real)f(crossing)h(p)34 b(oin)-34 b(ts:)p 0 TeXcolorgray -3150 12524 a Fw(Lemma)464 b(2.1.)p 0 TeXcolorgray 554 w Fh(Assume)432 b(that)g Fv(\()p Fw(H1)q Fv(\))p Fh(,)h Fv(\()p Fw(H2)q Fv(\))h Fh(and)f Fv(\()p Fw(H3)p Fv(\))h Fh(ar)-62 b(e)433 b(satis\014e)-62 b(d.)555 b(Then,)433 b(for)g Fv(\001)h Fh(smal)62 b(l)433 b(enough,)p 0 TeXcolorgray -1215 14215 a Fv(\(1\))p 0 TeXcolorgray 554 w Fh(the)g(numb)-62 b(er)433 b Fp(p)p Fv(\()p Fp(E)70 b Fv(\))434 b Fh(do)-62 b(es)432 b(not)h(dep)-62 b(end)432 b(on)i Fp(E)406 b Fo(2)337 b Fv(\001)p Fh(.)p 0 TeXcolorgray -1215 15654 a Fv(\(2\))p 0 TeXcolorgray 554 w Fh(ther)-62 b(e)432 b(exists)g Fp(Y)606 b(>)337 b Fv(0)433 b Fh(such)f(that)g Fv(\()p Fp(z)53 b(;)202 b(E)70 b Fv(\))337 b Fo(7!)g Fp(k)21670 15836 y Fm(j)22157 15654 y Fv(\()p Fp(z)53 b(;)202 b(E)70 b(;)202 b Fv(0\))434 b Fh(is)f(analytic)e(on)j Fp(\032)35046 15842 y Fm(Y)36125 15654 y Fo(\002)269 b Fv(\001)p Fh(,)433 b(for)g(any)g Fp(j)407 b Fo(2)336 b(f)p Fv(1)p Fp(;)202 b(:)g(:)g(:)f(;)h(md)p Fo(g)p Fh(.)p 0 TeXcolorgray -1215 17093 a Fv(\(3\))p 0 TeXcolorgray 554 w Fh(for)433 b Fp(l)360 b Fo(2)337 b(f)p Fv(1)p Fp(;)202 b Fo(\001)g(\001)g(\001)403 b Fp(;)202 b(p)p Fv(\()p Fp(E)70 b Fv(\))p Fo(g)p Fh(,)434 b(the)e(function)g Fp(E)407 b Fo(7!)336 b Fp(x)23053 17290 y Fm(l)23400 17093 y Fv(\()p Fp(E)70 b Fv(\))434 b Fh(is)f(analytic)f(on)h Fv(\001)p Fh(.)-315 19189 y Fv(W)-101 b(e)404 b(will)f(pro)-34 b(v)g(e)404 b(Lemma)g(2.1)g(in)g(Section)h(8.)-3150 21258 y(Similarly)-101 b(,)403 b(assumptions)j(\()p Fw(H1)p Fv(\))f(to)f(\()p Fw(H4)p Fv(\))h(imply)e(the)i(follo)-34 b(wing)405 b(result:)p 0 TeXcolorgray -3150 23353 a Fw(Lemma)422 b(2.2.)p 0 TeXcolorgray 523 w Fh(Under)399 b(assumptions)e Fv(\()p Fw(H1)p Fv(\))j Fh(to)f Fv(\()p Fw(H4)p Fv(\))q Fh(,)406 b(the)398 b(functions)g Fp(a)p Fh(,)406 b Fp(c)399 b Fh(and)g Fp(b)35410 22913 y Fk(2)36336 23353 y Fh(ar)-62 b(e)399 b(analytic)e(in)j(a)f(neighb)-62 b(orho)g(o)g(d)396 b(of)-3150 24792 y Fp(E)-2255 24974 y Fk(0)-1729 24792 y Fh(.)557 b(Besides,)431 b Fp(a)p Fv(\()p Fp(E)70 b Fv(\))337 b(=)g Fo(j)p Fp(@)9102 24974 y Fm(z)9631 24792 y Fv(\()p Fp(k)10733 24974 y Fm(i)11379 24792 y Fo(\000)269 b Fp(k)13222 24974 y Fm(j)13709 24792 y Fv(\)\()p Fp(x)15344 24974 y Fk(0)15870 24792 y Fv(\()p Fp(E)70 b Fv(\))p Fp(;)202 b(E)70 b Fv(\))p Fo(j)p Fh(.)-315 26888 y Fv(Lemma)404 b(2.2)f(is)h(pro)-34 b(v)g(en)405 b(in)f(Section)h(8.)-315 29766 y(Let)462 b(us)h(end)g(this)g(Section)g(b)-34 b(y)463 b(noting)h(here)e(that)i(our)e(h)-34 b(yp)34 b(otheses)464 b(imply)e(that)i(the)f(mo)34 b(des)462 b(are)g(real,)476 b(but)464 b(they)-3150 31205 y(do)486 b(not)g(guaran)-34 b(tee)486 b(that)g(the)g Fp(L)12192 30765 y Fk(2)13203 31205 y Fv(norm)f(is)g(conserv)-34 b(ed)485 b(under)h(the)g(time)f(ev) -34 b(olution.)782 b(This)486 b(question)f(is)g(addressed)h(in)-3150 32644 y(Section)405 b(5.)16193 35090 y(3.)606 b Fq(Generalized)459 b(Eigenvectors)-315 37249 y Fv(In)366 b(this)h(Section,)373 b(w)-34 b(e)367 b(assume)f(that)h Fp(R)376 b Fv(and)367 b(\001)f(satisfy)g(\()p Fw(H3)p Fv(\))q(,)373 b(and)367 b(w)-34 b(e)366 b(in)-34 b(v)g(estigate)367 b(the)f(prop)34 b(erties)366 b(of)g(the)h(mo)34 b(des,)-3150 38688 y(their)491 b(corresp)34 b(onding)492 b(p)34 b(olarization)490 b(v)-34 b(ectors)491 b(and)h(the)f(stationary)h(solutions.)800 b(F)-101 b(or)491 b(the)h(time)f(b)34 b(eing,)512 b(the)491 b(parameter)-3150 40127 y Fp(\016)504 b(>)457 b Fv(0)477 b(is)f(\014xed)h(and)h(w)-34 b(e)477 b(drop)g(it)g(in)f(the)h (notation.)758 b(The)477 b(generalized)f(eigen)-34 b(v)g(ectors)476 b Fp( )38872 40309 y Fm(")39362 40127 y Fv(\()p Fp(x;)202 b(E)70 b Fv(\))457 b Fo(2)h Fn(C)45099 39687 y Fm(d)46115 40127 y Fv(are)476 b(de\014ned)i(as)-3150 41566 y(solutions)405 b(of)g(the)f(time)g(indep)34 b(enden)-34 b(t)406 b(equation:)-3150 43564 y(\(3.1\))18598 43258 y(^)18336 43564 y Fp(R)9 b Fv(\()p Fp(x;)202 b(E)70 b(;)202 b(i\017@)24026 43746 y Fm(x)24610 43564 y Fv(\))p Fp( )25871 43746 y Fm(")26360 43564 y Fv(\()p Fp(x;)g(E)70 b Fv(\))337 b(=)f(0)p Fp(:)-3150 45507 y Fv(F)-101 b(or)404 b(an)-34 b(y)405 b Fp(E)h Fo(2)337 b Fv(\001,)404 b(the)h(set)f(of)g(suc)-34 b(h)405 b(solutions)g(is)f Fp(md)p Fv(-dimensional.)-315 47576 y(W)-101 b(e)404 b(de\014ne:)-3150 50208 y(\(3.2\))14640 b Fo(8)p Fp(l)360 b Fo(2)337 b(f)p Fv(1)p Fp(;)202 b(:)g(:)g(:)f(;)h(m) p Fo(g)1212 b Fp(N)24283 50405 y Fm(l)24630 50208 y Fv(\()p Fp(x;)202 b(E)70 b Fv(\))336 b(=)30046 48693 y Fm(r)29396 49057 y Fi(X)29385 51647 y Fm(n)p Fk(=0)31360 50208 y Fp(A)32269 50405 y Fm(l)11 b(n)33187 50208 y Fv(\()p Fp(x)p Fv(\))p Fp(E)35787 49708 y Fm(n)-3150 53225 y Fv(so)405 b(that)17868 55353 y Fp(R)9 b Fv(\()p Fp(x;)202 b(E)70 b(;)202 b(k)38 b Fv(\))337 b(=)25220 53838 y Fm(m)24761 54202 y Fi(X)24889 56837 y Fm(l)11 b Fk(=0)26714 55353 y Fp(N)27688 55550 y Fm(l)28034 55353 y Fv(\()p Fp(x;)202 b(E)70 b Fv(\))p Fp(k)31842 54853 y Fm(l)32189 55353 y Fp(:)-3150 58162 y Fv(W)-101 b(e)404 b(\014rst)h(pro)-34 b(v)g(e)404 b(the)h(follo)-34 b(wing)404 b(result:)p 0 TeXcolorgray -3150 60258 a Fw(Lemma)464 b(3.1.)p 0 TeXcolorgray 554 w Fh(We)433 b(assume)f(that)g Fp(R)443 b Fh(and)433 b Fv(\001)h Fh(satisfy)d Fv(\()p Fw(H1)p Fv(\))k Fh(and)e Fv(\()p Fw(H3)p Fv(\))p Fh(.)558 b(We)433 b(have)e(the)i(fol)62 b(lowing)432 b(pr)-62 b(op)g(erties.)p 0 TeXcolorgray -1215 61949 a Fv(\(1\))p 0 TeXcolorgray 554 w Fh(F)-93 b(or)434 b(any)f Fp(E)406 b Fo(2)337 b Fv(\001)434 b 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Fm(m)p Fj(\000)p Fk(1)47073 73247 y Fv(\)\()p Fp(x;)202 b(E)70 b Fv(\))51237 65793 y Fi(3)51237 67926 y(7)51237 68653 y(7)51237 69381 y(7)51237 70108 y(7)51237 70835 y(7)51237 71611 y(5)52247 70047 y Fp(;)p 0 TeXcolorgray 24962 74630 a Fk(7)p 0 TeXcolorgray eop end %%Page: 8 8 TeXDict begin 8 7 bop 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 887 940 a Fh(then)433 b Fp(\033)43 b Fv(\()p Fp(H)98 b Fv(\()p Fp(x;)202 b(E)70 b Fv(\)\))338 b(=)e Fo(f)p Fp(k)38 b Fv(;)636 b(det\()15855 -212 y Fm(m)15631 31 y Fi(P)15524 2060 y Fm(l)11 b Fk(=0)17220 940 y Fp(N)18194 1137 y Fm(l)18541 940 y Fv(\()p Fp(x;)202 b(E)70 b Fv(\))p Fp(k)22349 500 y Fm(l)22696 940 y Fv(\))337 b(=)f(0)p Fo(g)h Fv(=)f Fo(f)p Fp(k)38 b Fv(;)636 b(det)q(\()p Fp(R)9 b Fv(\()p Fp(x;)202 b(E)70 b(;)202 b(k)38 b Fv(\)\))337 b(=)g(0)p Fo(g)p Fp(:)p 0 TeXcolorgray -1215 3201 a Fv(\(4\))p 0 TeXcolorgray 554 w Fh(The)433 b(functions)f Fo(f)p Fv(\()p Fp(x;)202 b(E)70 b Fv(\))337 b Fo(7!)g Fp(k)14893 3383 y Fm(j)15380 3201 y Fv(\()p 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Fp(:)-3150 12418 y Fv(With)525 b(the)g(same)g(argumen)-34 b(ts)526 b(as)e(in)h([19],)554 b(w)-34 b(e)525 b(can)f(expand)i(the)f(in)-34 b(terv)-67 b(al)524 b(of)h(in)-34 b(tegration)525 b(to)g(the)g(whole)g(line)f(at)h (the)-3150 13857 y(exp)34 b(ense)404 b(of)g(an)h(error)e(that)i(is)f (uniform)h(in)f Fp(t)p Fv(,)g(and)g(in)h(the)f Fp(L)25076 13418 y Fk(2)26006 13857 y Fv(sense:)2806 15281 y Fi(Z)3480 18030 y Fm(k)3970 18141 y Ff(n)4536 18030 y Fk(\(+)p Fj(1)p Fm(;)p Fk(\001\))8244 16931 y Fp(e)8808 16431 y Fj(\000)p Fk(\003\()p Fm(k)24 b Fk(\))p Fm(=")12398 16931 y Fp(e)12962 16431 y Fj(\000)p Fm(itE)15094 16033 y Fe(+)15044 16571 y Ff(n)15770 16431 y Fk(\()p Fm(k)g Fk(\))p Fm(=")17976 16931 y Fp(e)18540 16431 y Fj(\000)p Fm(ik)g(x=")21596 16931 y Fp(dk)375 b Fv(=)24512 15281 y Fi(Z)25724 15632 y Fk(+)p Fj(1)25186 18030 y(\0001)27654 16931 y Fp(e)28218 16431 y Fj(\000)p Fk(\003\()p Fm(k)24 b Fk(\))p Fm(=")31809 16931 y Fp(e)32373 16431 y Fj(\000)p Fm(itE)34505 16033 y Fe(+)34455 16571 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b Fv(=)337 b Fp(\025)22850 28385 y Fk(2)23645 28203 y Fv(+)269 b Fp(i@)25986 27703 y Fk(2)25919 28512 y Fm(k)26511 28203 y Fp(E)27476 27703 y Fk(+)27406 28503 y Fm(n)28263 28203 y Fv(\()p Fp(k)29403 27703 y Fj(\003)29929 28203 y Fv(\))p Fp(t;)18453 30688 y(N)469 b Fv(=)336 b Fp(\025)21882 30870 y Fk(1)22678 30688 y Fv(+)269 b Fp(@)24534 30885 y Fm(k)25102 30688 y Fp(E)26067 30188 y Fk(+)25997 30988 y Fm(n)26854 30688 y Fv(\()p Fp(k)27994 30188 y Fj(\003)28520 30688 y Fv(\))p Fp(t)h Fv(+)f Fp(x:)-3150 33625 y Fv(8.9.)606 b Fw(Pro)39 b(of)464 b(of)h(Prop)39 b(osition)465 b(7.1.)606 b Fv(W)-101 b(e)404 b(will)f(mak)-34 b(e)404 b(use)h(of)f(the)h(follo) -34 b(wing)405 b(Lemma)e(whose)i(pro)34 b(of)404 b(w)-34 b(e)405 b(omit.)p 0 TeXcolorgray -3150 36006 a Fw(Lemma)464 b(8.2.)p 0 TeXcolorgray 554 w Fh(L)-62 b(et)433 b Fp(f)565 b Fh(and)433 b Fp(u)10813 36188 y Fm(")11736 36006 y Fh(b)-62 b(e)433 b Fp(C)14176 35567 y Fj(1)14089 36331 y Fk(0)15172 36006 y Fv(\()p Fn(R)p Fp(;)202 b Fn(R)p 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Fp(f)34879 40220 y Fj(0)35190 40570 y Fv(\()p Fp(k)g Fv(\))36935 38030 y Fi(\023)37828 38190 y Fj(0)38340 39739 y Fo(\001)202 b(\001)g(\001)39956 37666 y Fi(!)40916 37968 y Fj(0)42581 38919 y Fv(1)p 41561 39460 V 41561 40570 a Fp(f)42284 40220 y Fj(0)42596 40570 y Fv(\()p Fp(k)38 b Fv(\))44341 37666 y Fi(!)45300 37827 y Fj(0)46015 39739 y Fp(dk)472 b(;)-3150 43190 y Fh(wher)-62 b(e)383 b(ther)-62 b(e)382 b(ar)-62 b(e)383 b Fp(n)g Fh(factors)e Fv(1)p Fp(=f)12210 42750 y Fj(0)12521 43190 y Fv(\()p Fp(k)38 b Fv(\))p Fh(.)542 b(Mor)-62 b(e)g(over,)391 b(setting)382 b Fp(g)e Fv(=)336 b(1)p Fp(=f)28733 42750 y Fj(0)29045 43190 y Fh(,)393 b(ther)-62 b(e)382 b(exist)g(c)-62 b(onstants)382 b Fp(c)p Fv(\()p Fp(j)r(;)202 b(r)43414 43372 y Fk(1)43940 43190 y Fp(;)g Fo(\001)g(\001)g(\001)403 b Fp(;)202 b(r)47383 43372 y Fm(n)48008 43190 y Fv(\))337 b Fo(2)g Fn(R)384 b Fh(such)-3150 44629 y(that)4440 45437 y Fi(\022)5333 45801 y(\020)6056 47146 y Fo(\001)202 b(\001)g(\001)7673 46165 y Fi(\000)8228 47146 y Fv(\()q Fp(u)9394 47328 y Fm(")9883 47146 y Fp(g)43 b Fv(\))10976 46588 y Fj(0)11489 47146 y Fp(g)12110 46165 y Fi(\001)12666 46446 y Fj(0)13179 47146 y Fo(\001)202 b(\001)g(\001)14795 45801 y Fi(\021)15519 46103 y Fj(0)16031 47146 y Fp(g)16652 45437 y Fi(\023)17545 45739 y Fj(0)18192 47146 y Fv(=)20062 45631 y Fm(n)19472 45995 y Fi(X)19530 48601 y Fm(j)51 b Fk(=0)22709 45995 y Fi(X)21984 48332 y Ff(r)22369 48531 y Fe(1)22830 48332 y Ff(;)p Fd(\001\001\001)142 b Ff(;r)24617 48443 y(n)21558 48667 y Fc(P)22355 48937 y Ff(n)22355 49506 y(i)p Fe(=1)23875 49165 y Ff(r)24260 49377 y(i)24611 49165 y Fe(=)p Ff(j)25945 47146 y Fp(c)p Fv(\()p Fp(j)r(;)202 b(r)28528 47328 y Fk(1)29054 47146 y Fp(;)g Fo(\001)g(\001)g(\001)403 b Fp(;)202 b(r)32497 47328 y Fm(n)33123 47146 y Fv(\))p Fp(u)34288 46646 y Fk(\()p Fm(n)p Fj(\000)p Fm(j)51 b Fk(\))34288 47446 y Fm(")36809 47146 y Fp(g)37430 46646 y Fk(\()p Fm(r)38221 46769 y Fe(1)38683 46646 y Fk(\))39104 47146 y Fp(g)39725 46646 y Fk(\()p 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y Fv(,)404 b Fp(k)375 b Fo(7!)336 b Fp(c)20330 55807 y Fm(j)o(;n)21597 55625 y Fv(\()p Fp(k)38 b Fv(\))405 b(whic)-34 b(h)405 b(are)e(indep)34 b(enden)-34 b(t)406 b(of)f Fp(x)e Fv(and)i Fp(t)f Fv(and)h(suc)-34 b(h)405 b(that)-3150 59054 y(\(8.8\))13654 57345 y Fi(\022)15700 58234 y Fv(1)p 14679 58775 V 14679 59885 a Fp(f)15402 59535 y Fj(0)15714 59885 y Fv(\()p Fp(k)38 b Fv(\))17459 57345 y Fi(\023)18351 57647 y Fk(\()p Fm(n)p Fk(\))20046 59054 y Fv(=)21915 57539 y Fm(n)21325 57902 y Fi(X)21384 60508 y Fm(j)51 b Fk(=0)23278 59054 y Fp(c)23803 59236 y Fm(j)o(;n)25069 59054 y Fv(\()p Fp(k)38 b Fv(\))31181 58234 y Fp(t)31619 57794 y Fm(j)p 26813 58775 9658 49 v 26813 59885 a Fv(\()p Fp(x)271 b Fv(+)e Fp(@)30104 60082 y Fm(k)30672 59885 y Fp(E)31637 59468 y Fm(\033)31567 60277 y(l)32262 59885 y Fv(\()p Fp(k)38 b Fv(\))p Fp(t)p Fv(\))34782 59535 y Fm(j)51 b Fk(+1)36605 59054 y Fp(:)-3150 62647 y Fv(Then,)405 b(w)-34 b(e)405 b(get)f(from)g(the)h(ab)34 b(o)-34 b(v)g(e)p 0 TeXcolorgray -3150 65065 a Fw(Lemma)403 b(8.3.)p 0 TeXcolorgray 511 w Fh(Assume)383 b Fp(@)9531 65262 y Fm(k)10100 65065 y Fp(E)11065 64625 y Fm(\033)10995 65434 y(l)11689 65065 y Fv(\()12192 64745 y(~)12160 65065 y Fp(k)39 b Fv(\))337 b Fo(6)p Fv(=)f(0)385 b Fh(and)g(c)-62 b(onsider)383 b Fv(\()p Fp(x;)202 b(t)p Fv(\))385 b Fh(such)e(that)h Fv(inf)32560 65262 y Fm(k)24 b Fj(2)p Fm(S)34273 65373 y Ff(")34976 65065 y Fo(j)p Fp(x)164 b Fv(+)g Fp(@)37921 65262 y Fm(k)38488 65065 y Fp(E)39453 64625 y Fm(\033)39383 65434 y(l)40077 65065 y Fv(\()p Fp(k)38 b Fv(\))p Fp(t)p Fo(j)337 b Fp(>)g Fv(0)p Fh(.)541 b(F)-93 b(or)385 b(any)f Fp(n)336 b Fo(2)h Fn(N)p Fh(,)-3150 66504 y(ther)-62 b(e)433 b(exists)f(a)h(p)-62 b(ositive)431 b(c)-62 b(onstant)432 b Fp(C)87 b Fv(\()p Fp(n)p Fv(\))p Fh(,)434 b(uniform)f(in)g Fv(\()p Fp(x;)202 b(t)p Fv(\))434 b Fh(and)f Fp(")h Fh(such)e(that) -3150 69828 y Fv(\(8.9\))4306 68071 y Fi(\014)4306 68798 y(\014)4306 69525 y(\014)4306 70252 y(\014)4710 68178 y(Z)5383 70927 y Fb(R)6916 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Fp(;)-3150 73301 y Fh(for)433 b(al)62 b(l)433 b Fp(")337 b(<)f(")3267 73483 y Fk(0)3794 73301 y Fh(,)433 b(wher)-62 b(e)433 b Fp(")8587 73483 y Fk(0)9546 73301 y Fh(is)g(uniform)g(in)h Fp(n)f Fh(and)h Fv(\()p Fp(x;)202 b(t)p Fv(\))p Fh(.)p 0 TeXcolorgray 24726 74630 a Fk(31)p 0 TeXcolorgray eop end %%Page: 32 32 TeXDict begin 32 31 bop 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray -315 393 a Fw(Remark:)525 b Fv(The)378 b(Lemma)f(actually)g(holds)h(for)g(an)-34 b(y)377 b(v)-67 b(alue)377 b(of)h Fp(")g Fv(if)f(one)h(is)f(not)h(in)-34 b(terested)378 b(in)f(the)h(b)34 b(eha)-34 b(vior)378 b(in)f(that)-3150 1832 y(parameter.)-3150 3282 y Fh(Pr)-62 b(o)g(of.)1049 b Fv(One)430 b(\014rst)i(notes)f(that)h(b)-34 b(y)431 b(scaling)g(and)h(b)-34 b(y)431 b(our)g(c)-34 b(hoice)430 b(of)h Fp(\034)568 b Fv(the)431 b(successiv)-34 b(e)430 b(deriv)-67 b(ativ)-34 b(es)430 b(of)h Fp(u)46102 3464 y Fm(")46973 3282 y Fv(=)381 b Fp(e)48861 2842 y Fj(\000)p Fk(\003\()p Fm(k)24 b Fk(\))p Fm(=")52452 3282 y Fp(\021)53054 3464 y Fm(")-3150 4932 y Fv(satisfy)344 b(sup)2398 5223 y Fm(k)24 b Fj(2)p Fb(R)4436 4932 y Fp(u)5130 4293 y Fk(\()p Fm(j)51 b Fk(\))5130 5089 y Fm(")6349 4932 y Fv(\()p Fp(k)38 b Fv(\))337 b(=)g Fp(O)34 b Fv(\(1)p Fp(=")12784 4492 y Fm(j)13271 4932 y Fv(\),)355 b(if)343 b Fp(")g Fv(is)f(small)g(enough.)519 b(Then,)356 b(form)-34 b(ula)343 b(\(8.8\))h(and)f(the)g(restriction)46024 4023 y Fi(P)47303 4373 y Fm(n)47303 5290 y(i)p Fk(=1)49083 4932 y Fp(r)49630 5114 y Fm(i)50343 4932 y Fv(=)336 b Fp(j)412 b Fv(in)-3150 6631 y(the)349 b(second)g(p)34 b(oin)-34 b(t)350 b(of)e(Lemma)g(8.2)h(giv)-34 b(e)348 b(the)h(p)34 b(ossible)348 b(n)-34 b(um)g(b)34 b(ers)349 b(of)g(factors)35783 6153 y Fm(t)36123 5841 y Ff(j)p 32501 6351 7338 49 v 32501 7092 a Fk(\()p Fm(x)p Fk(+)p Fm(@)34625 7248 y Ff(k)35132 7092 y Fm(E)35872 6787 y Ff(\033)35822 7408 y(l)36427 7092 y Fk(\()p Fm(k)24 b Fk(\))p Fm(t)p Fk(\))38379 6840 y Ff(j)39 b Fe(+1)40320 6631 y Fv(in)348 b(the)h(in)-34 b(tegrand.)521 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0 TeXcolorgray 24726 74630 a Fk(33)p 0 TeXcolorgray eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0508240153936--