Content-Type: multipart/mixed; boundary="-------------0209250815915" This is a multi-part message in MIME format. ---------------0209250815915 Content-Type: text/plain; name="02-401.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-401.comments" http://www-fourier.ujf-grenoble.fr/~ycolver/ ---------------0209250815915 Content-Type: text/plain; name="02-401.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-401.keywords" Mode conversion, polarization, Born-Oppenheimer approximation, Maxwell equations, eigenvalues crossing, pseudo-differential systems, semi-classical analysis, Lagrangian manifold, propagation of singularities, coherent states, symplectic spinors ---------------0209250815915 Content-Type: application/postscript; name="cross.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="cross.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86d Copyright 1999 Radical Eye Software %%Title: cross.dvi %%Pages: 25 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR17 CMTI12 CMR12 CMR10 CMR7 CMTI10 CMBX9 CMR9 CMTI7 %%+ CMBX12 CMMI10 CMSY10 CMEX10 MSBM10 CMMI7 CMSY7 CMBX10 CMBX7 CMBX5 %%+ CMSY5 CMR5 MSAM10 CMR6 CMR8 MSBM7 CMMI12 CMMI8 CMSY8 CMMI5 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips cross.dvi -o cross.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.09.25:1437 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: color.pro %! TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet %%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 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 66 /parenleftex put dup 67 /parenrightex put dup 80 /summationtext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 98 /hatwide put dup 99 /hatwider put dup 100 /hatwidest put dup 113 /radicalBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83fe3482e8777114065d84bcd075b1ebbfdadfb36b587b08ceb3e1424f1954d8 8b957e8715d6c57d2ba7df5b04b84cb79dce46e039d730393018a356c467ca51 9522808a988909ca59a39bc3358ccf9859188579ba96fbb07545f81a2ce0a29d 28206e355304b48f23d07d9876869e991510b70fdf9fa283ad56fb50d02ad3cd d072928c6495955c200159ef0de3f2883a1bf14cc9faeb340d7acdd7c3370f5e fe7e24284a6574a070b895a1b75118540cb653c73ceb3616b0e56206d78d372d 6f8c65181441f1013209fbbb3e84f9b62ccd1d6075b74a95ca6a076b8ffe2095 b0a2f791aa4958c6f8fd79419eec819d6b63f9cf684812455356bf774ff7215c 211379ec1f09b13ad00c5983281a38624b9256e5c3253e8f8bb2739d6ca24534 73e582d411756f82ff8cbe4644740fc078e2d23b42f1d51add44d30aebbe2723 fc1de0bbfb6a6c25dc994f40e7cc95d02fb419e3e40665563336fd7529ecabc5 060140e9228f1e06b9af0b9ee4c8533e4f6b2eb7f2f4121adb85b002ed4b6b29 9654c151118d96065e7decac176e3126c3cac3fe7e1af0304f12a6de4faa5397 3c067321628816a3ccaf3e78515e58b0d390c75b75609cf14ef0929743c71a2d 5c8b7882294d04f79962801276b1177c3748e45184b36221497d7618a2b7adfe 808eb5aca05ad862cd6dd69b7f4e0ea511bd778f00c658bc947d4d3c49dc9a24 5d0009fa1f643a5647539359771c8213108d2063bbb36ed9c0127314624ae394 a2fa2922a9e25fa7655227460407fff7793b4d40694fb9d328770879191fff7a fe1f69eff1b7a81a5000ec7cb75a3b39ea12c9633772b0800f3c22b7b730b98f a3298b1d5f22121a479ccf595c2f466e09d27bcf9507b5c222040c9e2e025dcc 513cfa84cd9b0b65d418a2500a71555ec964ed640015288985e4e5ec06869f64 baea9978b61b9a004ffbbdda11ee8996efdecea2dccebb9d221e9e14d7ca8544 848da722c7e42639abd8b23f5e96663651f3019072290e476b7c2e9af866df99 1d7732b271bb2380ec9a985afcba32621b4ad14a609daad4dd394de679e0f576 bfff30205bc2730c4cc76321ea0fe8b500d2176e4867eb3fb9dfe8b2c9d3fb33 442979bf7cc1d93f855751f6666f209f04f788195ab51bf285ddd91a93c8a086 08159b8113cd285524a876f727ec8ea79215fee759760bbbd9bd50152d111c6d c5d5f268713c95cab40782b2ae714077ff1c4df9831987e78e5e7122f4f7e497 b8ae801a62a798790c269cfde16c1b53e29b39910d5e9566d38e9ec6a902bda6 cb69f4d39d481189750fc4315d434c1d85f223cfeeabf44b57c879aa83619f02 bc990af6c3e50302885e6c287c0368833a1c2fd04fb4951e813ad12d74b735e3 85a0871886bea5911c6eada46cbaaf720d3cc3aa43b707651788c29c175fc8b1 d500da552678cb1c0f005ec651f33f713b34774d3b8e04bbd8bd2882bef91e84 0391daeea71346e3c48cfa118a59b63dbc9df48281359160d405ff66ba8464cb 3643bdf0243de08488121e23647f430286dc2e643faa72b77ff26834990d0163 05116dfd122137dce8719cbb373345e6647b8bc3edb5001456ca27b19d282622 fa0727229fe359e7e53a641ad15624c4695efa63d7e454244d16990f64691968 397c8e84c690d1f5b9e7e836da8cfdf165b9f049666f8875153317ee0eb39261 fb344a85701a161a573ee8ca378675b1b31031c31cc8d4148aef11bb3ca4605a 2ab075be7b51aef484458d421c2939979eff758573bf0398c850ca5811d54694 39e54e1496ce33ddf6a5494c8ecd096f416aeca3eebe02c306e27f589a6e8d1a fb364b7346cf1b15a3d3f8fbc536ecd2790c1a6cefd96eb7d42895a7797c5e91 be384e429a4dbcfefb838bbc0958ebb50ed21b178f197713a92b993e7c163298 8ece31f7999d10034fa065626605b12f4c7e8ab6cdfb0c1712d279833a608ff3 79fad5cb60bc6db38c94ae12f02423d865fc4b0e01818596ebf80ff8ac2c54a9 3d088d8da28135fea37ec5b6e1175689bbbccf7f19c8166cc108325807b5d0dd 2af9d68c6206e6180fe2b9a9a07891434a51a22dca5e1106b0124e8146223652 235bb805772a2ccf52124ee6f6f396a309f83fdae0bac2dad9ed755e5ffad063 085ff50def0611539e844042cb5cc8356a5b674341b562d76b59d43b513ffa5e 2471daff3939d0150dea8b50823fa118c0260d7ee51c48ad60258a2405631c6b 9c5737bc2661e63fb2d4165ac3798243238c2eeddc72f0a661eb2be997bd0b86 43837179fe705aa145e985623df2770f083dbbd7d5f41d9e189e1ceed7d725df d2dda3145e2b1d09dc5fc2a543e0d6e40d18b25477bfdd62db5d5fd0a3f9efae 47148f1eca5a7ddf603639e4c363e665c1c0d7b9aa9c54209ec0789711f60755 aa8cdece2f9e61194b966f802af8b36a6aa4561530ed4197470af7dc34faa76e f442d52299b65bf77e89ba4fd33c513c002f1be3d4e43f4c6ae2db6ea8acdc22 e3636bd7d118f7789c30dbd06d88431f02cb76b6902a1d00c814dd2926f67e23 04d0a68eb7b3d35caa9cbf37e769b8d2330d221af200b9b77a1867ec9c9016c1 091c62aab66f1a4095807fdf21d93f7b1258cb19fb314068b3a058c8d6c4f0d8 61492ab17d6b8bcdef093a76ecef9428569517a446f7e47670d3212619b31c92 8d573aaf91ccbf2f4ced5ebea7bfd6b0f0776223397feab8d9ad05164ee658c8 9ea06d83b6352077e970ab02cb7a101e38e7ea047adaf30ca085f661eeecf18d d05b00ec7e6681a8c77f3bed1b258dac93ac392cd3fe228a0a1bc8a071d7254d ab75659412e9e5476f66ce6bede0701ac712f233a2d294682b8f8f761855a91f a2175307b7ec12ea7e8ca54a9993b0a17a7c99f4b06f92d85bc3799f34423454 e17783612e33f7f6987225dc58dd34d9333b6970df909bd0f37f319e7b59ce21 911da752bf060d18c5f4a70b4c73f6139c44adca0440403975ea74714af9dcc8 e5fd0e504f2dc1a8421727242d2a9934dcd61434092caa65b8fa4f231a615420 8c3546da7e17da9761a9cc2b164dcc4e8c59d9eabd8f9036c0c0d66f29620e7f ae389f098b285bd10b905d716f292d058e90797b6dcf84426cbd12257128a4ef 6d998b0f017f5ed95ca9a2090e5e2c60ba8f5f4089c49a672dcfccdbd132e4f9 a4a1172025f5f46799b80bcc9e9f9881d6ff40f5852ae7b5447ff68babce4cf0 612ef26897873bd39f1995425f0a895cffc866bd1da925ccfddff56743c50831 dbd1b0bde55ab6cc19b4f80cf06ad82455846245e30ab4408f6e9b44e078c53d ab41eed55f2873ca15ccd88bd737dd18910a1ba12a749efbeb8941264bd4ab0e a19ec254aab61c24c254f188b569d22dde1603589ff41f6f51083ee4c9b973fd e92616ca08bd8d935b8f6ca7e91513b0104f0fa80a1a8aabf236280f759612f6 cfde0dfd0a7ba6fa8c0e1e15d66c837ff7e35b56e5ab3f9833c05b668ec8e6df 03a58cf8b2fd5c094027674a4888f2442f06a63b8ae7599ffd3f2bdb01232e8c 0f461b9c101bc17190d7ec4031b2c954b507008324848d343478bea76c2b6ffd 98c7725eabc13f187947c4911bca6a08832304d1ad5291b5ddc5eaf567dd0507 396e812b8cc2cc04780a015f23969a91339d63a495b17db11b4cb33e6d8f7626 5a008b866874a6ebf9c0546fa117333aa20750f5e6bab60f8917dc2e15e92919 db83e383d29dec79266d80e9b15922004a0d8584c4642ad2d9ee9e41a8185a 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % 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 (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 25 /pi put dup 104 /h put dup 105 /i put dup 112 /p put dup 120 /x put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueXX 5087380 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311e252234d51741e18db3a68e8ad10242 29e5817a10e796a78d2c7f7c1f50961b9a57aa604c9f821dbf5a9295197bc666 31678d7d2c7e1f8f2151ce0c29efce46270570f4301c5dad1b38884732e53dad 05dfc36b020e726ca575f71f04abf2b49e1f1d6d2a08a477658ca9a48f1c8cce 14382f0a42201de56e2821ee2b0e91a818b1b753d810ec2428dae5153b66af66 9442192024becf743a8f6264a58a0b3aa823510a4957d1bab3e1b83135362888 3e392f49926471a8021fdb48637baf0abcf31204b1b214f48c99f44af7782323 69d772ae4f49be53a1bf584747bf29b94f530d59a5be5370b8dd0691e32a21ba 9d0d592cf3bb50a99a3ecd18d6c4114cb4cfecc49705da90d7edb10e3a28f9eb a49347a09d31eec896f2a28e9607d99d42914aea16545c16e136bdd0b75fe486 61e24c7a9e9b233a76754c760822d0a88c575e08ae3e3f081d7bfb80ec4c03ac a08b65fb6474f71fc95c7c2462f2eb3754e647c29498288f2ced0bd3a2bca5c3 2f80a61fa667802d376cacd34de1f9572d1b3ab09d6f352750db4a768f869638 a87457889aa502850427b40e1294c5ba33e6b17532b2d13b5f50e71582f93daa 231e86597872a2a968127afb0f36257a76ce1eb24e6c4f29fce2aaf6532fb5cf df84da03f03a45b915209f67d398c7c4f7a3b0623750259087a478dca684b29e a8b7f52060bae9394369ed1cecc645d113cca3772a8dc36c6d916b5c5e65454c 0a188a33395fd3da67ad0a31ddab6a8434dd80f0bd0ea1a2a62eecc331d88b3e 369552daa1c575a98fe84383548626b65be7c24ae7eb61159f149872cfd87cf7 6c1a7c155c7186c7600e58cb61b8cb0c5dea98268a39e928bf6fc53985eaa763 2b28c1eb3d82e4d3fe225223f4266d2b6147e344aad2d4884a9308aadc7801af a606838925e3e50ee7aaf73f090baefcfd4e34b795cd92d83c944d91a4940f2f c955d727ea5bd76f0c8057b12621eceb0947b0a5dd10dbcbc52957dd978d7db0 c794660afdd4e946b3d7fc1ba60907fb3f756aab0406c0e7bce5a2238fb3e12e 07e2c0a7f465e90057642d704434ae0b57bd46c8ea91ab2a386e24c6deaf9cb0 8cdaa8fc4ec3fadc06bf28659cb878453db16f4b03925b2127b83be8fc240f33 23ea950b51d70c8fe861e30c346efa0a0125137598caca5478991e35f5bbbc19 4c787488ba339830bca15f8333431902e82b66a514a41c0bff92719a6a0d9587 4cff62c622fc61a0308a69f9fb7ef51bb274ce9e059c04b64e817abdbfedc209 bb79b42ba58367eca2d70f126b3ec64b069ae8ebb3683fa5f7ebbd03dc8a8fcf 2b645eb0f19e56928197cd4ab0ac315dd8884e5bac52c89bc0d7e2771713c64a f8ff64b835960115034df8bb0b48d7fbb8f0e13176f0a482330cd647b187e9fe 64f0abb43527373a608add4d0e1f07599a9002131f0aae3fd8247fa2e7192c29 ba768dae1623efff2f2825620451cbd005014c3c6844c9cddfacf00dce9cfba2 1d90bef388597ce04ef99964b3ab1c283204293cd13d3b1552d6bb5478b0fedf 82c965d13903d43ceadaa0c974cab364a94270126ca0d3f75246eb1d496b897c abee6d22aebbea27408d3badd5ef9f0cb6478302481c9cf71ea3976efd2a5ee7 006d4bb73ba75175b4999f90d5da20106d5bcdb50d05480d4a44c365697263bc d3d14e9d3ee7a694a490364df866b73d7ee7ea990f76e5926db91d6c700092a2 716b503284d414d98970f0533de7f79f3867776acdf3c4c19c32dd7380ce1e95 fbe8a4f1b2940fdc6e05dbaf54a658179af5972ff42ab0a8200eb6577e8abba5 f8641ac7cd66385168f159368ebbc3d0d2b01630359508e0524e9061a73745c4 d311a43555f7bdcd8d5e725b1cf51bad643bc7783b42c8bb8ca712b6666ac447 d27105599dda45e9141acfeaf7916343a57edbe3fbc282e255c288bb9acc19e1 5e0e3e207f0c241df9b13163422dd238c00d4b256e5b33faf0ae6e7c27318e5e 4b0a79ef78576d0a99085f97433d65bc2f916671c4858d83b18aac46d0024586 8930438077d28f127bbede61700602ba68ed8776b25cfba1da6e091ad7fe26c3 8d6457c6066b0f6420d913a7f853bce13e35d5f0fbf199553c6078cbd12a4909 88b8a299c80bffc88a9ab5a6638f836259fe6c163c872514360aaafb5df65380 9f2666c0984c8c9149d541901a7b5bcb5014153acc44591876cc864005b5e9ef 217c2a37822f1c703f587024faed24ec68c303e473005d5a15b9940887a961d3 b124b219eb5eb714a7781e5cc231100951442a6c11d26a1daa9a7024f3b69e90 d263b372026b388ea8887773bb2f16a6d3f82d949e67e74bc13742f27797fd78 6fb2b312399e878e2eba4bd1ffdb9665941ec68591615ec03fcfb7ca440bb2ab d0b61bf63f8232b7ae87889913744bbe6a4889ec76f157ad74629c9e68166661 0fa93c08df115b60575bc23acd9faf4e8ceb4b075c81423c198d70c02a235406 14b72bb11b163ae139e0614ebb7339dde8fc5492e749b9018dbaf605b48aeaea 1462333ef72915bfd9798d9c6e4e1c7639bc5a5de5093a1bb4a85ec43a8800d1 6354c80ff42a1ae2b1e40573c30352fc9147975b549a9167d99e7b5b0983390e c1e0de795bb675ad9a7845e9356bce95a90eb4e5e426326e5a7806798b961bb2 199769fdf73bcbff4382b2e60486a6cf22ab95b3c96f146f6db3d7ff4261bc60 bf81b6c1839036998901c0506ade78e151a817ab56add476bcc83da1ef84c18c cc7dde9077eabe75033e2057273b669bee97d2b7db845360c9d847bf48cf4df8 5d019ef9880f28860e4e89de25f1f6a31a0fca3019acb2a71dc012d44cb3dec8 e296363ab8957b72370c955d4412b6ce1d682a1521c5f7ca840133876c76de30 031c14a1477dabc32c3e6cdcd0c23318a6884cd902567ba709eef9ad563016ef e53ee95af325bad6b1cfc6d321a4ce917f4e96ac0f8f49981985ae87f94227ae 6f2625b3ab8aee5d4a255b8b53398ce75fcea0a069c878 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY8 %!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 readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueXX 5000818 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a 5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8 7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345 191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc 430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474 5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5 08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d 98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b b910bf03a7a227d51386469ec9ef415f3bb849d30411890d9c6f5b9ee172e351 8cba2ea47be683900e1c23554cfb193067c35d0813c4bc68f817ef9f0206f08d 1d8be63236cb2d08f42c4a0b73a147cc7baf1a212637a7b9c3243332a162b8d4 955e17a50b678c6a322c4eccd28fd709ccef5f4a0c7f542c5ee8fec88895af93 48d3cc99e31f083e3f3d6be883803f7d3f4c4519360fc6d925a31d854e764f79 403b30ae39e581fb941615aa3c86287f7cf79b84e95db76ec8f15c8b43029a6c e93ae76e0320d0daece8c62f7f4d189fefdbb7bbdb43cb87 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 105 /i put dup 110 /n put dup 111 /o put dup 116 /t put dup 117 /u put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 52c190f50fc981dccb64bb2c1f7a62c216f211c162c2ed1c554ef49fbaf12b31 aa3b2a80fee259dc0a2a4242869ddec7c29e2941792b28bba7f2c6f77ef69638 12b07d6843f33b51e01c8626b26edc34e1e0fffadede5fb468e8cd5de7e5a64c 366967578f415484d122834de4a647541d66989f7d8b25d1712d8d16729bd9a6 4729b84ffb21a57faf172aa6716b257bd42d15dd11589dd3e9abb3ec41e1ad6b e580fa488678b33fcb6820d5ad08d0967fc6b91f5542bcc8e8809150d8a06a43 3a86036b8f8045456ec4d8f53a62b319a21a476f55dc8b266c33cbb06cb9faa5 9773f33021d16daf462dc876879457e97bb173af9c9ae1438fec91566ca2031f 0ccadb2df81832571c1b04edb63558326fbab51835f981e9d29c5af2d89aecb0 f4c389ec38d1cfa354f3e95ff692af63b3beddf16159a0592c2fa80670fae512 6b9f599eae87dc9be30558be46ca8afbeba241b911b75bfd824c4113a4b1213b 5fc6e215742ce1b5a1512b18307db3c945e0aa156368198b229e868a29a9ccad be52050f749688050c2789a97697a533d18e86e6168586bfc2b9806253e687af 0e4cab0acfe9e936bb1b12416e71fafc1f8bf0bf3fa83427a4922e8929053156 c37fec2acb89c5af6d99b842a82825d6896c5c884ede5f135ed88484630ea3e7 9680a277def29cc7fc93b78bf41b9a9c0b94f5cd581043409c0b86cf4546dc9e 9ebdf015dd5e619e09de838dca38cc16eda53ad0b9bf722f2c6ce0020afa8592 cc569c572e6a234128c496ee8f196d5a9a8b8b50c287e6ea5494cbb2d87b1e2b ed0c241e217bbb212a84643ff3a5158e40c996ce383cb6695c6bf4b2251cd92a ef552e3954a73189a72ea367f8e88622c59391a1393ae87b560dd42b6f399f04 5155085f449b3a1a529de092427dd70a396978b209494b878201e2ddbca390ec 94c0c76e06a250850f6186a5a5cf74c200bee6c135143186cb97d6092f83404e ca4f7e380ef77d1fc340541e25f594c1feb877544961953e7ace1398e1ca49f1 0dbd302b4a92a36cacfc0d35f9f3418336553b001c92da92ac2aef4914fc7186 81cd7d06f2a5f2eabc3837729f4c9d939fe0a63eba09440aa80bdf9402b466a2 34726156b5a4adbcb4173e035292c20b28e72a62d0e25c444afd446b95f321f5 ba313b9358f23bbd4f3a5ab2b023fe62cd8f1e80a360faa0e2a703b99a2e59f8 aaa0dd1240e4006e669d128e2fde6a1fbc1311df542de1393d21b06bc53a1cd5 cc8a48ab674b30b637a02ff1fc2ddbe437fcd100617f06b6e253e3f961ef170a 22d551c9f28409060111071f85d1836a9c915f5e8b01b8c86d924cd3e32fc7b4 c7f0895029eaa0b0eb59d7bf9067f5d7936e5bd22f6cfa9cfe53cdfc514f728c dc8c6ad0f8fc9755b8a2dc7b7a7a7a0473033917ca55770421f62c76d1b084a8 07db2308b294ea6d6ec91290cc781a7e30b9de73acd5afd8b15b2283041a4d85 56a38d0298220c7aec6a7fb34477b296c8a3a0cc7bcf88f03fafceb9e41e43c2 27bc14d18534ea829b28099f2555a7689ae72634e791d40d7e96bd623e0726a0 8d984a57c4cc73a23b937da6df0c215356a5f854e0260e5af0540658d4b16cd7 fcddbfa5dbd784024ecf3e0e4be442596b8878c4797546caad1f2bdb8ec1d538 201aa00b1d4df322275d2eb791541d8f596725f368ac26fc6072ced46d8109e9 24cec6 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % 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 (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /gamma put dup 67 /C put dup 85 /U put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueXX 5087386 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7bcb09b7064e91fa0ded228e42 09aae407a7aaca60b1076299ac4abd23ef02f108765f0e3d91f92f3afbfded37 2fcf6e4b1416901517da8f2fb3c9fe7a87bcbe6fd36cd5b5823fdb74229036a6 3c3346a1093e6b1036902c1bf42fc317c80abf04020a47b344c36de42f05c490 a0ff44ab6d5249e9f552a8707bb7661e242644814001c8430ebd5e5f0b944ceb 666ee64359d663e355b2f17093a964139d17287f6ca6a024767eba4fe4873855 babe2f07b91560f68300b06dfe27264c163195d446980c35bca0b48f7806626a e72636593a05ba403ce1c0f8b2cea3ecd586e90ac17d034ba4af708304f23131 3459fbbbfb97d4834d0395754ab3f22d6495d2144087d448616fa1ce27bc50d3 46543287e3860d99b433624119bb9920a2113604c0e260fd275ba55e0fd19c83 e19addc3baa1f32f6b7284038845ccee71a3311ddb17b84975f7a984bed7c6ec 2a06e5b335a763d081c6273f86a46632fd9141a27902074fc860df3a2eb59b89 774c767022dbb577e30da128bd7706a43af886d0c256b50fa968ef06776aac0b a5387e9011eb2334c1f42c090f06a1125c207ea6324e87f46414050d880b7d10 79d150cf64a1454568ce45d8a78fa387bc05670bd9f219310568aaf9a9a33b76 397a09633af7b2e1bf7614f39f1a12a9c65b414e874fa5657eaddf1497317560 44bbf56007d533d02e17959bf97e21dceb4ad655768ab4f5aa1106998814ca26 16af4aaed584527e7d439bc23545fb75df1f4d7f374cac010d9f88340986b327 02c8f4ea9ded9ca2889cbe0190aa78afbb6a83b1748d60e44e112f192fabd510 7caed62aea79a9f255a8ae49e4b5caecc521df4615171efa246fea1fd4e12426 a2f0a8610b1a60f5042da8ee830c390f1b21c1731fad6a798217ce7ef32b3fb9 2f3e77d0eb6be5e965a46c96e7a84bcd95181567eace950054f73d7fe8dae9b2 84ef1ba0cea57ad17edc97e753b35a59e48ee2e956fbabbe8a92fd5138a692ca 901534fa0b0adc24d9eb3033cf4259bb289b733d9553ac848d0fe6c2babf15d2 9566eee7fc690842b522d6213fc8db42e5ce9b3e50061600e9a846a429d27c2f d7d55c750b7537463df31f997554284a6d8a3be9a344be8788ae7a108e28db86 a7f0d3701d683ebc59e2b5188fa10dfa4b5028af3c4de4f4c2bbb99354da4d8c 6c7361967cb6e8bef2731fa24e2b1ce1b32f820f0e2cd64fdd49e9431347abcf a4e18f193b2b6cb02684bfa0e094409dc6eb47e5295b3b2fbd89066309d25695 35d78bbbef51477aab52a056ed0d091825e95ad9626b7274cac0568bb5ee4758 8b2d875fa73c9cd062f5217bd5c257c613be555b56351c491826413f2319042a 17daab13f521d39772a1678a12def100e9420c72240c12ca08824c5e6a295cd5 cad7589dddaabfdf11213f3e5cbc57068a5f4815570dd04860f0649c08ef40b6 0fd28506900112febbc82cbe774e36d3f6e2492444ce0020bdde05174cef2924 ef3135d3550a2105ff6c50bf7db0c171bcee49311adf676ef0924cdb892f5ea8 dd935f962ba7fd6f1642610d2009546a0cd3d7aedf5803e0cf25b5166972a0f9 47d8b0c6f53d63ef1e3552e7ee1c4dc4232c873b1bba645fb45b9da1a2c5d058 39dcf1d7e2af6a6f7a07e6e5c247df7195728ed2aafb1fa4d1f52d3e277f9975 5a796efbbae1550e3199104f5082182f33a5b9eca466d3c986087fa3c8951ec9 198b86e18d45013a51815a83cf0fdeebefd062240c5e8b427fbbf16b520b5c81 de8cf47c611409e318b831e494174f39703e8ab296d9f159deb9cf46e967c40c 326247af13f700aa9789439bdc0299b48b6843f80da7f3193acc5a6b394800a8 e694b046638c60cf4c0b52b68913b1b277c368d6 0000000000000000000000000000000000000000000000000000000000000000 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 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueXX 5032014 def currentdict end currentfile eexec b5e2457af4a6caaa4536453c498a618ecdce7b5f6f2d5944265309f833bd3d50 3df8bd14c071f404d2177500681a801856cb8c9c9cf0112c9bd17ccba9ab8944 1759a320b2078df0fafdd3e357994bd81740d1a7522ddfafb75d58f5def046f7 084d10fa2f702e570b09a7073d70efe37b48c355a7089772238b7b4538c4912f cf6703a14fa416057ea2e1b94455913dd271b42846ee10d78270a8118e7e4bcb 8deb048bb280c240d59409d47046c890e5f79e5dd4b0be65a28a77aeb53dd33e ac506a6da87bb55e329f433627e06c3c94b078838b908538d93f888e504e25e0 3a8ccf7d2c02122ab3d485525564295390d1154e15fee35edff4eb016fadd32c 26d1b4c09de87943780954cebc4965aa890fe1f80b03eb07103e13d468245c7b c26455f229e8859585c6eeafd9474acdb27290fd62950dc52f893c99a2a614d4 2a7e3618266f3fb0c68a01a30373e048385ffe7dd5844e208a55d1a9263ab2db cb9b19038724f95af00349840157be45cb337871b55a304b87ade64b10ff0eba 21aa0eaeef74aa01f049303a8b25de0acc26bb3a33fcf267f479a2a73f7dece3 2aa23083687322b417fe86e8f5afc2136d045ad6b392364811a17630a94ff097 038eedeedb8da4ebf8fa5a96ce27a2ebf771d14f4a11fb1f9f48cdd207209934 885ef9118463552984b0fd3cf15d55de967fbb051549dd65f60dfe07f299690e 58252f032bca78935b7d2df852ed688bd13dd171b91cf7bd46d5433aef9f50f1 41a2517c4912b837793f84ddcf1116f70f7e9b1e6ec752dbc9183d4791d92602 397bafe29ac6f879ceb72c673c8a1aa0135d6f92d0db7791f9a2f1a5b55347e0 3e63723efd258754f5f4a9ad35873a98d54b6c54b17a39892dc1d38660597448 fdba9258493a0db0d560c01d49f2d889a99eaa8a5b5919cbd33f6b3d97bf27b3 e0b94b48d5d21d6c29aee4faca71bd775bb9defa37ff627f1e4926f10d59313e 77d81a511027ef9a8ed5b7fa9b5bd67758cd13bab6ac18411c974a65d0c90085 67bf5860d0930d7f43e557ee45e76ecb2806d21f4732bb282ac8b591f2b8775d 4b3ce2a37ebb371cb74a3cc513bdd70a0115de4760c21f034f5080d769f7ff83 554af524184702a02e534d1eb98dd3f7c5d51900409354dea37de4ac74a12c3a 69320913de6a728bd887c57f4ee5dcb8772249587ce3190bb662ac853abcff77 d4bd77985a4a805f44f8cc8597416c488866ff8429f65cd0edeec1fe2f0015a3 2bb098b0b3d8c913007f5846ca593c491e1efabc8f420a5fa338c47fd2427813 3279d27f12022195e15827797fe71d898f17b8af955e5bd5ce1da5fae7b3ece8 87aa52db81daa819242c6acb7fbed098d59a27bbcb12dca67e16915a4709fa5e 16311a55ddda46359ab51be5964874f1d3612ec10d2444576c508ae6a285a57f b978458b6f5f93c00882f2227d43d42c648437715a27cefd8d4ffb490e3e9980 1d1b4f1cacbc8b9e59c04c677a04047cc4b655fd8985d8e619a99e71cad67c94 2744577e185ac8b225e5352ae93ef0d804b73b943353266c74677b899d45b286 869cbe8ce9ad231007381de74bd3c6c84958f07ffce0620e42902a01fd15c98a 421ff110e5de48cd65568060afaa1e11e9893e720f22b754c47c334a1f5d0933 9b1b1b91b036b981a6be8a3276634fd4e39af829e2f2ac2b2dde35379abd1bf5 3a1071f07537db5fff44d145fce9713d8a9e2660900c41b83f948e16731d3048 2c8fa2aef8de49e3cf649e8ff62a2748cd9e299c7b 0000000000000000000000000000000000000000000000000000000000000000 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 43 /plus put dup 46 /period put dup 55 /seven put dup 76 /L put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f 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 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e638fa27d38771d3b1 57eef72f7e1dd6d2b33fdce43fc0be3098a14e92e39274cd1ee5615b1c540365 b07e3217e463c6bd8214f6f6a71a78a0a9cff9cfd7edcaf9d287c158e2230863 80b953c7d1949422f191ec9f24b9c8166a5531c7457dd02e0116b02905d8a5bb a2433eb00f6d6ea2ebd9539497340eca840ae5cd3e2c2a6fc969033e84e364f9 1b3f23e15cf930853b69228205f9302a9671322a98959a0e3268caf592821f5c e8e0a55b409f6963ce52e4add48d40bd9b4a7df15f0965f9f8a96570f8f38585 b5f7c2a58172db4d3b78f892faaebc855bac71a69c48337af7e40a199cb1c550 ce4c453a71c9f931bdef473d3652f01e298fe7dd4e80d3ac4f71f7cb0ef3e0f6 93fc981646da044adc06efaef3b531b191e75da48ffce6a8a36d60b409ca0e93 f9cb549b23c120d29fa5d781f60edf82ed77702e6399c8c6e29f49fe7e0cd8f9 b63c2ba6cfe3fd00888c330355f8342972cbaacd1e23a8f1b8f299e250a40bb3 f19f043529c3e2e5ce53927f4933875d59a1fd2023a452ca5b1f495312d974c2 4db4f0995eed6813b66cdff2dd10c157b11e44d8e47b22803415fc504388d1d0 5e04ba7b1f3d37df1713738d7fc38bf1c2f9c396b7453f879c131982a142913c 4f7836d14d615ffdb0b182d173bef3760fd8447ff8930be29d3d7a2517b39bef e4963d3fde34ba3fe2e45c57d44753946489f0ef0ee515136b4fb594f65fc40a 05c883026382303d7f202475e64b440f9f45d87e30163a04930caa735fc8a20a d9909b3224b5cbed6ff2fd46848b2f3d1d89e516694620e9ccd7a0e399b907b3 ac82f19faeda26c71cff7f5261b5be65df1f1dd7e9ddfb8c38f2bc3aa12d1725 4552863530e13d845e014d4edd9a4b557ec519c56c2c7c65b32aec1a8310b3e6 7e8858eaa9265cbe53fef54f7533d7aabd425ce055c4a4b1ed2904fc374cb5ac 62709d7f3a9d495c1ffbf4a4df5a6deac453599ed8f9191b1aa9e13d0622c08f 72134345887bf60432210653c2ca57706c074fa65a61ec597629e68813619666 015966d10553580522b2551c57ecdfcdf79510eeaeeac86f173153a658534076 dd75cf9367eb182bac403454e0ccf6153f67fc342020c5ca5581bc646f29869f fc9f0a3bc2e9985384f7345373fcb7e7be02f1aa87d148cd87cc6980f55311cd 91cd6f4e20c085d8ce53a6691a1e7f7ffbb68f96dfd64536ab916637e19a3ba5 041f01edbc3606764fb66ff050dc68613c18e1a05eef145b1b72dbfc531962d5 febe9c29b2edc8688daa7ab261c555d1d767b4877f1ca7e17557d30afc48ca05 808c2f716dbbb08ef4815e4c8f5c73b281dd0f4d4d05488e09337f1389c1a6e3 58a602afdba03705794999a86ff675f1b3fe1aad790cf36c5024c8162a6eba7b 64c77f78e9b56a5df28e4b868ff3a9138431e9adb4cbe3fcb74d11f7336676fd f6ec309df84e1e5c2867efd8e474d06cba3e73e47daf782621eb0dcf256e0c1f 72c76dca497251b72362b9c5838958d21d53a5cc5dd912915f17a2168ab5bf93 71461f11d391f6671e289203a2bb8e9886d30914b43d76e37b3db56af843e294 35015697db00bfeb2ff28724a3ce00fb563056bb58211cea739cb21793edaa6d 380720cdcf514391f62883510a0a00b44a8e949d85eb3543f1d01b80c68f554d 282d7fed905ebac5ab660efddeb49bbfbfdec67827836c941aa0c9e0423ac4f8 17a1e14974fec056506ae70c50b7dba600f19954cafcbb00786e29885ac5652a 41dfddb3d7785eb27af8d8fc6324de8f5d980f4648c7a2c6c1dfeaed4c52d17c 13c7a21bd608eccf3106266bbd53cf385ea9cb9978bbe6ebf73c438502abe441 9195095952667250d28056e20d644dc2ef0d322778b26849f5008b8c1b827328 b0d84fd20eddb0611b322040e463228afcacbb28ae50db37eabe4eaef06ab459 558bb75f40f55f7f9517947960ae0dda4f53ada2b0bb0baa030dc41dd7ce7437 3e4caf3829b63bb88867b0920af009ddc8c5af092353928a36a3eaf1f646d25e 99141f1d7047e1eac65431f46a96ffa6bfd020c39174b0614d6bccac93972d91 2578ab3c6a952a88d0fb9a2bc227fc37dc10dc25a8082c2fb87452ff9e07a74b 4f1851c0c8b9289a4541a5517f013e993eb2749b0c5b7ccf87f8c75cd49b54d7 7e911058fada50b8a031b9698725d45fa1349fdfa583a65af7e993c663b63736 0aabaaef3bb650d4d458fb873081c54afcc73b9d63bb23ba2e141d49f60a9f0e 8ee41849fbd49e56eeaf5ab6d3e44a20dd1bc9481bb1eb43e084e7dbe29a30b4 70d93e5dd850ac0c43f0defe737a722accd751406a781ac798a73726702371a7 4d1ad3b46bc2266b1f723712886ff898ffa72cd9f702b3d7f48c539f32c45cbb 71f9183305b4062565e1e122a01565c8ff70b982779a3efe9edff294cfc167af a6dd6b7869b2f35e910b33e65df36a9daeda10e71bcc1c116e9cabfdb2ea9378 2a386c2724c85fa6658c7bcdfb46ac6946e53c204e1735495739ffddf7cb7211 a31f223f100e2dfef97a3ae58df409780b2be94d8acf50b353ea0d4a29bf749f cdf2e064b6a83ad0becbb8743309fc6ea77f436288cb4ba1d540a9b427521948 c23b4b170f478291e71c9238feaa4047faefcedcff53657980252c02388bc26c 475389613d5e891eb06ba2e0038faf59375e3e60db401f0cd844ae9361f0b8d4 329e460db56f4b9768361ced4adea57828c5bb61bc05bf54112ef8fd1e125c2a 6c4e99fdfb04422f8cbe9a6822d4c73e2e3dba606e051e3873027f27e5976651 7cb3552f421ed07a3736a145c5669cd7be3226f2837057300131993b535f8a95 6bff555377c76ec6cd6fb4c63d212d8a3ebd36c5e747938c8f43ac71f226220a 4839d901df209379790ba878e88f49d61b7ea78ea87d823d3f1a6957f04317d2 3cfac6048a94e7069a0afdbde192abf7909ec5f23d68cc9f946e8ef35e99c8d3 fe7d9695bb77ff7a2f6f8afea44748021ff0936f576b04d6b87e4b5bdf33a7cf e9075407bcd4a0cd8748a2c438601d3341cbb094d28eb2c08c3e90040cc28bb8 64c400d5a838308a29b0b519e44f2629ba41bf3478fbdce76d09d6472372e565 820083ab653e705d532b2b6aeb2e36f450c661d671c3b9756f544f0b75200055 1b062813a9e6eeadd65ab180e7f8c11bbd0c7ea5cd3e35ad81063906742d1142 6b23c6185fc7fcd94fc6cfcc0608fab4a52407463d1ed322ef11322f78d2694a 1bb1b3f251dea6997f742eb0d5dbae38e59508f89f034dd9502f75039692cc99 7c4cced0cbf539e50a15e00d3761f8613c7f4148ac0a2f784577cbf9c0176ecf 466587e015dd025b7df0a72398342512b0e4ace1f97de293a0bf062089be6ed0 9935a6545c3dc4e12e861edb552c5ba0086e9a6300724da6a4bb9fbd7fff8c36 3de3e0658192f3ef740d7e77d5e35903009f888a810c927e1f94d4612539c18d 4634adf80285cdb43c72273df8991208ab01ccb48e0b4ec2560db5fb8677df62 bdeb5b924d1d61e8144a6a27de4a9fe395f7d17a8c8d38665cbfcea2dae6d0d4 bb88d2c46e7b7d0a18509ec2f5f36f2fba26b73e3c9288fa9f466a956dedd2d6 6b16eab1162de4e585aa1d844a5b86e2937c685daeb237b4a8ba060003fdef39 374e57439abb60f3fa9dc31b14bd3511729f83e9e462c3298c3d6e7b80bc452a 4da5b5801cb2cb75976f0bb252622b3cb586c4969423feb434812d60d75b2e62 6f32af36e4489d33a3e2e9e09db97e19014e3a4fc029e449c520ae879cc0585c 6ffe32d1b273ecc0bc2c88780103304e68e9f018ea6738e2ba8ab36e06a61693 42f4ecba2979cff3a174728abd975dfff0b882443f1126681566feebfb3c8f09 9a3acff176730a44fe873f03e9ffd6d0907c8184bd2af984b88139321d0f54b4 7b466a5f72418f0b24419b5e8c63087d900c00e15c7391c3e98db81c42014836 443a937423e359629ff7e0183fa58074b7c5d5d6c6d74db97a98895af4b3fa1a 5ecc79fe79fb7ec559e6d6c69db73458eeec4be0ee13d5aecbdc33105df19fdd 1164f6ff413276d2a1a4f02f617c446e78047aa876c7efcdfae53cd3c5aa6bf3 5e23dfc8be1865b6bed28a8e9befb4ab2216a846761a5f304f76cc5bf33ecbc2 588ce17fa38caf6685e4e84a63050d7155b7cdbb79571314f441fb7e64eedeff 5fc285d208f1282589f5283de931e596675520fb63b1027b8ff35649cb828aaf ef14f9be68989189bf67eb579cccb286246e9e2989c29f83a15dd59d20d6d177 b218fe2005aa2fbe3d2a4c92302f98bad1cd388df52c6beb154e6bb37b86cc9d e9dc27d4981d4fd0239bd07d7fbbef8bc0204a60e7b448cea44d971dac140417 ffadfd3f7a5736578686ff20d642fe5e59ec8dd873417b75f8cabb87fe6e4648 7a361128393b4d720b68ad9fd57e9c1d54be945cd6c77daed6a05e02123e5a5a 224a5ba31e57b905716799a15aae85dbb58f77983e5278b2f74d6bd52a28179a d3ee61af29aeafe31a9cff68cf3009d54ffb4985c4106c51db191a17ae46347c a043ff12d84c8261fb3e77a7954693d9068122747f2981f068228d0ebd3f4fd3 f04f10051fcb73ae606ec0eea201fc79a29a7b448a93a5d6a3dc1b81a77989e7 4d0f233a0a35343af5830e9f629dc2d786c025319f83b25ede0c0a1eef898eb3 49cdd1d79e8408485060aa13be592c3a20add790fc2d6faba86a24e583ca3ab0 2b9807ecf3a07bf43a6948181b35ea03ad67bf2246ec74a10cb64488c6eec459 99334b04e3b799cbf387ea57800d991a20b121090ec9c588761203ed55c8820a ca26f336c9a205efb7d89f73a0d83d1ea02f4faf986613a7 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 49 /one put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523dfa618d367b001af bfc9543651fadf6389c92ef4bae29fb195b9804be0a74fa55212f722335cd860 e2a83c290596faf56fce1e1e636bc605010d102306ad03cb15f52144da46169c bdf5433936be1098db2db424a1fcf822feef43901ffc1a409e8584d22ff63547 041fc48403dce0ce04c14879b8da2f8ab14faf328290b38333445fc8268d346f 4c430b1a602977b77ca5eea5425fcf2c1dd579f0e4fa9834172cc5875e1501ff cbf67561c9161b39c7fa81f6858b6a3f63749cab3035165f77b3fa9908c3fd79 4646a9f4d5140c28de41ee565b8460076f6c75dd9e554fa4c83af2b7e47dbaed 246761a5801cad08bb166f5af47ad2c102389aad5032457556b2ee0d 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa581ff3172367ca325e6d23102c5c6a2 02cc99580287dbd76a05bb4cca591b12a9dd3d602d7957376ec30b16051a63c7 e26ddf009e21fdca5a31cc973f0b1f6967a66b30b973ddd9d9a3095b673ea8f8 5db8dbf3acb7bb2d85c04a0ea8853e4592e4f8e581adaadb78bc3ae58a2d4c80 3b09839eafc7bc3e7cdf784e852d6590ab1c4b7558e28505887c6858072f09dc 2caba91b6871920e5256b602a0de02b87e5eb456878d3634e8eb0e069fa2bb5c c10d5cd98401de1cf07ec9f7de62aaa20b583e2f7aad2fb7e727ebc43f712c74 e8eed1fa76133428ac71589b933cc37ad200c516045fc1a06d0086c541103b5d 4ec54dc77b 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % 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 (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueXX 5000788 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4a71813d2ffb26 445026f89b4787516ecd1afc78f8bd19e91e9ccc9402e8c36d2449c1ff850a8a f61165aac3fe931332dd28e261b91b05edd18f44ea7d58a8f35fe88493b64aad 6bfac3a0136215fc2f4ca8e91d70c5010e6f4013e6d63b44f6fb00afdbd7cdb4 5ec5b1d9736f45cefc8a0124b815987cebd81bbe0d44dedb2d5ef37923b3d551 abb6a1cefca7868fc7bf3814ef7d7b6b1ae6e869cb77aa29e3d90b12b0dc3ff6 ec945922b5899bbf2f12e92731486d2ef1230c528bf8d7e0ae09ad7632a38966 5963de49d1ef3d65bc483e4a577b927c940f5e121169ba52f6576c85793e5fd7 7f5863c488e55bdefd5d8b2514795533aabbc12e7f51816c7e1484f1c441aa9a 66a5dc77158e79cd6692d299b95e8058b35e771a6972d2b5eb1cd6d2bb8e835d 361a6eac0c90c906aea1cd75c4412a1339dc1439f93e59917311bf20af4f2bc8 bba5a4626f75f28a47d4595c37f4019df480d9385975159142618e22e964f019 d88125210e2ef21d65baf500adf802297b24eebbf4e93c617a613f856bd0d45f e17a9480980ef83950bdb8ebf208c895ebc4a7132f0765b7c19a332ebbf8a3c9 ab65063a42e19ca9d43dec3de7aba46b9a5d24fb93d615c0a1726ab7e31c378e ab77150858535b91362ab0e2b968dee1c539964126d937f9d4980ccefa92bc81 b054996a65a13995c9c9d819ff05511cfc89cbfe67447c940405001d61be633b b771eff383fc6977ec06af30f981504260de7b9ec97359974734f495ac073935 fb30e3700679092ef5d971b6b2da0e15960f2391fa6b63c33e7f56b4a9b86951 1d3686a5e8e613a69a0add8b8c73b127ddcd397a48d785079e786d24b755e4d7 27a8feff23826aabdb372dec537221d5970606b25d431cb0cf0e009ca00f59c6 c38fb65c47526d3474e19dc40df792ea6957e771dbb5a63d340a23ee230a0290 f77cfed663d8d97e066872202c9ab0c25092810e0dfaeea6b7e9a59c21ae3dd0 975d54e2efed43cb9e79f3a159c353476f5c173bc9d7b61950076a0cf39d3b70 728e1ae5759d43dd641368cadc778ed239410e9b11e489b020143b95a03f1a2e b3bb94d7665bd365a49843b4a66df8035c66cd09d4fb3224f192e1654ed96072 91ef68cfaaebdd41a72a37e9cc44628cb07f5766a982ea9b7fe0d46d49a4073a 508af260460b7b72632f064dbae5498bf06090ede2f9cfcd5e620dd310b8f1ca c63450aff1424c4e31874d317a195653a4fcea2f81384f5258bcc4ee3550e0a3 7b208a24c6c194e733be4a255f324d9b522b5b259cedbd348a9561a1011af73d 5f9970a1805488747e3ccfbf3c89d685e515114192f202cc434ffb3735900bff 026c7ce9bac2a8629d78823dc866c57737b67b7e98dae4e47a91e30a7d156ef6 e2f812da875f63dbaa04aeac27ae2af8b7d0071351791fd10920d00420ab3593 41106f901a0175b8e4a2af391ec6fff9c7b11af467b912392106fd122563ab6f 477eb47db7a487d113019a42c67bd477b8b420945485314d5eefa3eb33b0e904 981b2ffcf971f94cf2309beabc79da5b020d547b4f3830d007f1e284f1f64b0b e35f15d43c19ce3d19b80f422722887cf23e7a88c64675d4eb44442677308f21 85bac7f05317c84be510e5d0134f6c510225509849c0cb8a0ab6fbfd22826784 4cd56fdca3e024048a840c388b01f26d81d20f2d287c85f0e1c51c3387815516 a93204f5e15276950ae13b72e9c1b23a963270541a5ca37ce600cb23e41dba31 7c4adb5526d31a94dd540dd920ccce4c746d7ed2ba57d0466dd67a45ab936fcc 0ec14ccf95e8e997e28f920583321cf0f6638ebdb04f4856356a4760969e1c51 2e5c1bcfffb219f064c5e096dd30212224b1c72b9d5f8bc6f97b46662cdcd2d0 2e9a59d4318b71ce7f6ec0cb3ee1a729e0566bcb5b4590ad068eea3c29700754 c29521025e37a8105f4ffd9469924c9c9445080585521418c46dfb16cd40a82a c3f7525fbe6039902a0b27f2931a7e9ca3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % 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 (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 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 7 /minusplus put dup 48 /prime put dup 63 /perpendicular put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueXX 5000815 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6784decd2fb36dec8f 7478da853762e00bc9c52ba86ef50d222ff142abc18e4fb95b86b3e57d9390ca 86e8de6347bf7f48f93322a372c5d7830521b14e8fa0771961b027c81365426d d95d16b950e216a90f28ce806244ff28dd969cb512a23e05045e7b2bcaf7d6f0 ca8b51494f2ec0681bdfde60420628d9bce98a0ca1ecca9140f452a88db19a30 ed46ae881b098c843a51d06f9a153489357fd24de6a0c36cb5a9eb9b3b64dd75 18f83018ae7cefa1c12fd205df6880a705e28457af7b869a6dd28f6b37d82cc3 e51cba348dcdb34efb119b8ce5a996f15492b0f5d34538850a2c1b6a509fe5fa 015eceaf28b0223cb57ac422cc75ea5af6535ee85ace82cd3674b7407f29093e bdedc359e654b1b8f6fd7ec00f592fe46a806ef91ca0d902c83031b8043976f4 8f7fdc818c2b9dc1d11fb997865314bc2bc382270efd30a9ab4fb8f113142fb3 852ef36690347e4892469546ded1134201ba09fc80e74461ff2eba2246e36874 498307b67ead2ee81e7f266d3e37759215da326910ef2f24a88bd6891ab1bcb6 3093a3d152491ad57ee06562a1e5074973584c23b1fb03e8d29bce04e698c421 56ff6c96256b33e92fe84c6b6d9e400c022afcde1b654c981751ee16b9d5f106 f3d4d1b400031aef643f716ccea924d7e485b463fa2680e1844665bf809e6a5e db30f8a5d1be92cd724269ae3964d88ee526ea1f281f03b7368eb1988a8b1225 f7344b712c8978b83da3183ea5077be5f7954965dac3023427346212912702e1 bb28be3e2b65adf09ddd2194ca016b968e95d28691c4569a000a9e771eb11e0c 9a50f952a35b66f14d3a4ed5d077244275ed116edc238f87834b458397076935 dddbae62a27c36bfadfae9d12483d19142a7f07634ef12c253e321ccdf3beaea 67caea51175f64178decf6324fd1b71db2f4b96b0d995da9187fab81eb5596bb 24b6eb91d7e42cc171e3b5e6bf8ebbe11d0a8ba946245f766ed3121fb8f8b0b0 ad7a6825d94ac8e03beb7e82f82b5784151bd15234b8ec547d8fdd30fc8dafec 98de92644ae4c2cb26d02549144440b95660301f7086380a518d597194ac1d51 0961d9623715 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 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 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 90 /Z put dup 92 /quotedblleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueXX 5000769 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d555242a8ca08c49aef300945d 99b999a79ce74804ae6bfde623f4463371442f6523a5f6ce19c839a708c02513 2e22c696c8ccade45680e5197189d0f98e7f0d5f955e353970b392cf530a68cc 56b0035ddfbf206c3074beeb0739dcbca272a6e629fb7aea2c5ba7bae50c7b4c a595df78200c352997ec3ee564df229fbb5473f5e8ccb1cc0153e9a7e299a8ea a29b69d1b622b1f0cffc58291248759607d91150cb0651120970dc9f743bebef 44f6ae92facec57658999c8bf01f60611560043962c0695e1bb87d090e0fdaab 659d6557208a660be9aeef8ae55f71b8bc76394d792967e41bd8023b6e7f8c3d 9987d5e54c53bf2bbb32855b946473b44833bd78873df8e4c7e668ffff25aabb 8da4148f744b9d0524d6cb8281247b3052cc5d66f3f1bcf8a56a3fb446ea587b d8be30257652cee035628aeddfd8283b5ad21b8b1480ad24d898970ac8a1e33e 543ce4e3c48f9ee621c5ce3e8ae930f890011b630866c988606068d9e92396eb f51bb3db204505fc3d09d4701ac703a14d92bbfe27bd7411b363a88e33a8e9a8 025ac31f21e73dc52b333b918d0b1270c54873a490222d041a66e0192612be6d 2c88958a8f70c10390146ee5091df020ab97675e8e6acf98b28b539cd0a20d24 a42f535ae44b8f5e9290b38fc6b02e1bbbdf1aca96558c2dd5afbec53f03ab51 fbce958ed4a65b17fbc03f9defd4aea4a15229f3c320876235f2d8b69bda5f48 03a2798790d35b394c63295997dd487bc603cdd10d18f3e3fcc7f17d2a6afc77 f1d7f6cf69d2a86b104b9d3b260e4a78716927a485ad8a650d610e68378f4514 3610b087981f0a0655090163dd2dd4d0030faf6a953896a9cb2cd033ec9b2e01 f8b8c0af39a1b5fb7d35867da301f189f8d6f8f4af48aea63c6a4a04a4afd376 ea9854e7ad55749da43ddb2d673028e51a337d15f29b0d4fce04c3bb2f7f8d9a 1191ca4879769773381103c5b6ebdbeb91ff0c9e877c98eb7586600ae6f722df 8b452deb57e1972f97cc06d82101762ca1a3dd80bca94f7cbaf4bb01acc8568b 225fdd2f3d9ca2c0a8243caf997b7dd754a8b91db51feb6bcc5f37415999aee4 091282b4c6efc85d6629511113e73c06ff87e7b45d8baa6c905f5e9f99186e13 2edf3bdb3c705155ad887d2b3a32db14c5d50c6060925e19c7b0eb6a0483c454 8f17268ac35f470c683660d96ac8e4f8601e7a362bc1972069e331e2de776c79 8192a7787c4ae7c4cffd72ce19a2f87534d30df395d99e564da7beac5a59849a d4e2b2ea0fe2d16c160103043291abb54ce4064618cb094422151151097b974c 41ef19c13b73a483c91ca8e3a5b3d07ff09a5a230eeea867b0afca97335cd5c8 d307753fd3b158da31b207843d62c2a6fd528912296dcf61f1e6a7659ce84949 dc1a5ad66643f9b6f10bcdcc649a6b9a6a29c53ccd945ab6153b91a70c4990f5 768ce0fef532f5ae96c334b1d8d28ff875c10199901f1d48a994b1fdc57cfb99 85505ac9333fca56bf6bbb8db48f6785d7ca0e5dfb84c2156086eb1fa5b92317 0275745292e600b8a5c1eede9b191f3236ef4abc9f0c70b7d6230ed029014350 d52c640148c33b83e207ef28a735739fb768bdab0d41546a5a2c3e03031a856a 0e6668beb327ce90cc1b384b96bd63ee7a48daa94d441142533c0817d482a0f4 13aea93dc1cb2542a40f61ff4594ce5969fb40ef29d29fcb04372f837ae57c85 47fbb5a8a78f1ba3fbffad74da4705b58e5017b9325b4c3c123aef3740f0eef3 07b3804d998aabe04071e4b158ad1c532ded1a18c79eed68f279c222b719b9bb 2fe30d176532e0f3ac39acfa8e11fe5743a4c6743bc1ba9743d9f512a99835bb e03f3abf67cf0d8fe46433d72af3be35cbba1a31c3d2c0b97d041bea5ed214e3 1a58392252cfacb2eea0ff226e3f50cecaf115144cbfc73794b727781c492d65 68197f0a8e3054ea0fdb02ba2c323e6c4973a96edf483cb83b81be44a9ca05dd 3eeec2c7ae7fb1d0585a9d03bccd4856e1cb63835509a932b73cc399eb8815c4 45e5a78805de98f58a8c431a720aeaf8b4cb02cffe905be1e294bf63771bfeb7 e2e91252c4f37637453b541ca963b24dc5648a8c014101379008b8e2ef22f534 e72f0414587e9ee5481241a3d88e996f45a31b5f75120b218b06051b3f91c265 a4f50df90320a11a0262242b3e9c16ddad71e8bd70e9452871b151b32b2e57f8 598c619fc6919452b5fc66186780eaa7b9ed10c4ecb5e28a9519d4d7b128e7a0 02bdff040c39bc8168e231844d774384fc3b20a60c750966002b1e1e905f6f31 22212f2ead23fbe3e2d2312faa5c64d3265c6c10a2833a71dd7155fe95552e7a 8f68254c1ad861469f33db03294141369f19acbdf7d264b69a9d698183a91046 a197adc138b0297e420f60be5263fa9c4faad971f01fe9c441a2d70e9325c982 f8678f3e36efc54e8193e381b6adadef5bfbc4ef45b086b5d93e9df951ca6755 98660291f514987aacb7f83b2e30704c345a5c79773943f177e999345c1f159e b67914b4e821ed24296a9ed93a6c1f417c256b4490e7f19e3253e63cc52da9b9 abbba8a5387d3efda77062171fb026252b3339633ad6c8d6ec3683dec3071f98 d0438ab1e22fa117e76b55b1c952089de563154b64846f9e434a09d13a97a20c 1afa07ecbec3ea4ff9510dd66929eb65789e8ef1990e050afe13a5fdbc1b7338 5fceb6b8a02f87398d3a13c2044a3b554438d0c9ea807de4e09d879511dd652c 05ab102c19b2b5488bfdaee93703fee85e39647df42de2cdfd736d33dc118ddf 286d80bcc3dcc8387b9bbe3a28c900a20b3d652226415aa73b542688dfcda279 cf0366b37f51364dc9de94d4854f265ea6b777753a7d150028f69f5e23ccc10e 7dd73ad33bb13c4252864443a650f2d5ffea04dfedd33331e7dcb996d87683d3 9ca569813821d5db87f0a7dd17519dd4b5dd0ba17bd4c68def9dd85159c29582 de734ac0202686a3fbca047c5a7519787814665105f6f4eb0bf08078a9f88053 b3a7aab5aa708541aaf47fa35094b972e7c5a70b700d7aa5f20c47964c17a923 31f7c565e3e1d0f8aa0ac582ae2c91e60a6e20c704d08cf95d69e08ed24f82fa 546d9bd752366ee74837ff7e4d133129863f0449c35537a2fa28c73cad3a550d 3ba87920035d068f01f13f427b784455528ad1f7c28388c9d892a61d105ad895 415092859b054f08fbc7065cab6fa24301e829eeda243838d9866686df315b1d 917befb2ede6c9d46a8b2331a55851213900bdfc4cd438f6e21acc2233dbdbd5 d7c12d742b150350c26d5a45440113bb2c68ba954ba24286285587d471dd00f6 5454e13d3c094f7a70d71505426b79cd250a04048e841484061614f8add0f5b6 7105090d2b1124bb407d9d40b5e13462287a53bdc3fb1e3b01a2b05b40f150f1 b042b7648239d860f844c15e812d5adc3d0d6409247a0046e37d07b1802dd58e f91492b980cabd60aa55ac306102afb32818520713b350555368542ce93bdb92 9913c573ff3a62d6df3c0e8abe975423a52b4f48d87620466c86fc9831e52b74 381905c6ce34988bab11eea7cbf3b9b46ae1b29063c7adbebfb16d07db969f96 9046b35a973725c73a2f97ca2e4b2480ce7e777e3ef1208760ddaa2116a6f2c8 62a377bc23aada49c8bcfab353e8eadf2a489ea41a60f7e7608dff1a3dc4c449 2d1d0b8291bd7ee6d0924937b929cbd415320403f69a4b94ebf82fe5df8e07d0 9a960cb722b5b70202354408e88b7aabc6eda87165d48a47327c284f76bb86b1 08c8e9504b30cf7ad91e0404e9d0fb5d88a2db698a43da60744ea7e93b52e00f 28ec27da8d8cb6505e65b7b51a60b10fc44199fb37dfe00783ac0d4554d2cb20 d265f1dd4b444b6daa035b7340add466dbebcf9b983af776b51a2f78d835c89a 28453f08470a0252a6b5fce54b2eab180aefd8c76914ad821d67b8606869f3e7 e33c24af52b6f42e566c7a8d37b29f447889f500f7cb78b791b419246db8d616 8e5cedc16c1b160f9e7a3df943a438273fcfe7e56c0fc6fbff71c10867d270f5 031df39821a702ed105eab8099fcc360bf190967a1fc8788b1a85fc2e4c72dab 5638fc8280b8a19cff925afa6cd05c8373ab05f522bc4bf5f99dbeaa4f450d90 b88dcd349de7cb0277fe989da5f5c68d5117438d336ad198ad4fff83d3be5dd0 99f42b7e9a0c3c7f00674bea10ab96c72d2da63bbd168a850947e726dbc284ef 1212b1122d7d44e011a56e6e0b8439b7e419f2b99688eac1cd4c68bd58751598 f1d4bd0d970f8f973bbf421881661453d51652513447953ac2ea0d30104e9e48 47a6a962e7da049f4f17705e3de5a11371eee0da817df522beb164a3a0118e13 ad930ba50a94d4d7d174de4df549351308eafd680814d1a4d917f036c10aec52 31751be42785f88991a45be074e3bd462085cc3267988534ff2388c2d0afef0f 95b8c95727747dacf9ed0f977036dc80134b0da4f9042b5f2a1047800e626ba2 51e1fd120f7508e361362cb3100ee32545539cc5471543ff0719c6cc4cd265e0 9be13370f887f78dea8a1c33a83e228bcfc5c746670f632be30339e18c6984f9 0d4889199a74ad4585eb7dd839c9a794d71cb8594d2fc8ec8f78a84291cd3909 0d2d06be3cb478f565a9b3a5ee44014d334085422fe3369cde3bab2b7e19c1d1 170a9776e478f72274d3135ce8515f4c1e8195ed90c933d70dad17b2d416401b 085cc2a84104142065a6d12824d5e95b56f1f12ae20a0fd56d758f4155e0910c 98779db703f73f6c43481bf89e224d1377c95ec5a99a166a5efeb9849398d313 76625ad30e26f1ac9c7f2c78c281651f6bc587e51fa53047ff1124900d119027 b9491ef3c812fd3fee1a65964e5d30cdaf3cda10a7a03b3b373db10110338296 8229725811319abf264f80f076e4cd5d5833f497a3009bc9f0c3dd54a270e71a 1d48e0b564bed21182cc5ddbf1ea283cfac45c5ed33a9ece6d9044ed256e508f 0b50debec6af85b8520798e6747a1324b2376fb6ef82a7fdc3af9736426ab68f 64fc8cb1ac68712229a909d6f9ac2070baa099aa04e6345bb28857716cf33674 26630e61279a8b3af11ecbdea22067d30f5622c47dc4c94ad499f867c83594ce 525d5a7f2e48f92acdc2417a8244a538fb00dbaed2bb6f74fbd1864e66159bac 9661aab8e12c4b83b594a4a83b704c683e03155a137e0d1b5d300e025b2949f4 89f9bae49321546a18c9a21f0f3f66597262698c8e123b4c6a59ffa897efb840 b463969eb5c4f1be11ab5d9aeb554d5d0a6c8ba6481c1e21f3590e5a1b83c338 53a7d690e360839a5bf9809c68d5c86b6697e160f4f7cc5b32a488121ad9b19a 482d4da8bdb2d93028670d8228fa279ce6f4a9261348ffba00fec49ae6947895 462962ad84122ae4dc2d7c503d1fd9613b3cf21fb12d0ee6d8b8340b887bfc58 398e9cfa11687988464987f209ad7658b207a95151eb1e2ffef6ec221dc01faa af04574afe10efd9113e518d19cc7ebf52c88f7651d2ad1c9d417c673aa9f44a 23bdc155b2664f9f47f382082b4691fcc1866c38959372a7ce1802734d646e7d d46a992b8e4c4760f7b0169fe49b22f16dc5830f87b98d7daec87d212d6394be 9f25f1f5cfb31334b96861f56f19679745588099e5bfca34b6eddd57ba9ab450 b237b45a3877d56e85168a0efb9f7dad7413f7ba781f06e6da4b3977f5e4eb23 8108b58912fb314c77b140a3a7b21cecd6756f1408760d4e51deef9cb72f4960 88474c8a3bb0123dd481fffa949d9abfdc2d2fb68b22fcbb85c1915a85a76afe 4c7c3e45812c1a6e10db1353468ff55cab61797e86311ecf13b8438f1686ab10 66d0e4a502a802f3a1f648a350d080b77de32cce03a47d111c05dfee8be6bb25 7531a4f04cdcd61b560688a39f59521ae3dcd04b82fc4b6fd6141fb03f27261a 580cce4676f2bd41afe4234f042db3700c40e4d110030e826335b9980cae6da4 d7daac02f90d68b1c5ce6be996c83ca44d7505c0c71d334e3a820afafef17587 44f91ab302891d433638350218bfe6002fcc3067e0d71e5474aa5b76706511cc c54acd8807c33257fa66c232baf9d5f6ca559dacaf3d8775dcff6252ba30d5eb 981f5c6046b7bb4462f7e24c96266ce618c62b0b18e9623a9869eed7ab342f2c ea1de38412a1624ca1a142a946fe1134bd13e25090138683456c8e9b78ecf1fe abd1a460b6284904e5c6f194d1b992d8bfd039685772c83c3021962e49941c56 65a63ca525299feaf1808236e5a3f9ce2aac8abe24fa1055ae41290eef65ff8e d7b3cc4525329e4240dcd64695e25a8f39c7eb04286b5032dea234937c5fd915 4225280f4cef70f8abcaa1b31fa16560ae2e0d68a4373328a17ea87053aacf24 4cb5b793c48d854c2db7623aaf57dabf5a96faeb88568b5abf11c1f433a2ff4e 09b7d877c4c06aa7e1b861cce2a99becea5841192e911c0bec2b0c04648c2e0e 0b95e961a818ab4267d44e9d6d8b6526f5c61fb9b6073fa0255ac0dd046d30da 975898d08d301452cb30d9cdff0e52b6d55d91dc7385a7fc40e5760430029130 0034db876b96674231b47f7c9f90864e21ffe87050fe40bd6ae632158869a55f 4ea2c21e1b4286dec0b061ca14f49d193fae2b0d8c574afeb5bcbea2d8c8854c b64367e7caa5b098e0356b6a8cffe097d7283906ea663e6b33783c763aafbf3f d169e064e8241c679d15fbe3928896f28fbcf835a447d0557e5969be32baabe3 edee0f80b55460de34a84b0767b9c4661412c0633c90ae5e24c621bc9ed1bfe9 149d704cbd7068456e1b17f278650ad69860bcd136436651b12d93a5f1f2317c feac6ea2a630272e8755cf4b4d19ed23c2f9918836d4cf97296235db46f468b0 7915b553ad27635422b9e3f418c4c3d4cee27414506d3e633124a4995f6e40c5 7ea22e13cceece7c966ca710701456e3fb602117925b87f6e4e475943691da75 1bd8035eecd72893e27bbc80a3b1187df2f514b88ccab63af8feddbc76ea401a 25d8834bbcbf7ea03a26a9437b80ee0cc32a16e92dd15dbd416967bc19265517 7e4116b33d6dbc523b5eab7a73bafbb0c2ea63b176e8d9c90eb00e80c3643162 8b68764c2f4233c65a475f9c7f573a8e84e2f211f9fcfa246c9d0478ebf29656 8887157f28fb83edb4dedaff9bab09b3da4b0b6ce27f2d96fe299690c26abecc 097070130db0e99da88a208c7b5a2fefe76925950d1cfa053b5573b03b90621f 2650aa99807f7511d06c99fd11ad73119f9982c5aa5f0ead748dda7a4b0b97c2 4449ad3f3c863a256d4afe501466aa09177b6d4fb35df03644997a11c9cb1f4c ed1fde719cdb19f78c6d9cb79c1fe2beeaff1dfc6ca57c42d1a1ee0d18d6a135 68f5bd643fcd5e90b4e52128302c606c6aaf536d14e4db006a6e3c4553280f79 4d664d8db0e38ba957a7a219dfdaf9ca8c9dab47d296ac0c1c87d5a122dca984 b2b6ec938de2e76b6a3298ff8446a05c0b4f1e20184c77894ad7d7b903313a3e 62c43ff16efd2b3a6a7c0333f52ade95f162645c6cf3bf0a2466ae0e4d939d1d 52b39888a4579627b23e284dd1ad1b926cd731966626f393116c4b109ee8444e 687eae759341836fdc5ece6b3451b685c3b4d70435cfc223ee1c1c186e16a030 6345d87e5ea75af433f937c0b9c48c6a02c445938ddae177b830dbca7c43ec44 2f53d660eac5658f1fa35e57f8676a1e49c968b35d00c74e532e2b3a5698b971 88df0a7a46c3093869095223f331e1a538d6c2812d35179f0056db724fea1fcd bd5a54ace29dd446f590533b760c5716e5170304e0b450a5b90ab2b3e3055297 660a128d640988791dbc10568972245f195885cfef8fc8a9f50ae7e47641a3f1 f9b2fcdb589ba83debf4bb9b9eb04c1666f8ced7e72e64d666707f92328643d9 fdae81eaa28f866db18022bc827b83d0918253bbd7d9045491b2a4be8d7a1e21 13762712c5896bf6433ad7b982558d3a2e7d19618d9c1013736506279092fc4b eaf3b669ef61038b9bb046e466e1b3f22b9d91d7a330f4be9d9e252ab3ebd7ef 8ea22833e693f284f9db959ffd602fde24661cdb362176f04a8ea9da6204a7d2 c472484923cc706eec26b02b6eac7bd8f94314f54e619ac2a94e43ea2ebba5a8 56e1743812270f019ec1de34f5334c90f1ccdd976e6ec456a8ba01fc1069277e 9ff69248206777b176f22d45bb3f0091d8c0709bcdf187b5c8a0f4437ca5f5d5 8e73d2fe13d1eca26c3512b7d5d953c2766498d4faca31f84ebbd8505d17027b a695c42da02862ac5f27a9d712d3070170b66c32e5b4ed19b78dba8cf7a0f643 53b070f5a520321beafe9e809d15da05301746eb368f3e895562979ab95ac1c5 16f9db0c5cfa77aebccf750646e3a1776813d55d417cd507930ebe73be838bfb 6b753e4e2b59eec4422d4f14381e0f8826b29695a3d2d3a064d8a7e25a4edb2c 9387b0ba89268488b11fdf1516c2e87bdb68a8ec4e3ff9951ca1935a5373a2e4 0eea5b9f0e7492bb671cb53c361daa5bef22e34b0cdf4f93c504745dc450df9d 8ff82505b165ad943712504aa6fe58989705acbcc7747c3d4b139cf390aa8f13 5e75c6549244f92668def4d8440b47b92c148de50095fe3d7e20bb2ae577c4b0 bd5fd587d92313bc4d21ea7529b86b42c2a909af2d16427906494d19d48915cb f0852bb8b2959e9cca9472a5df2dd8b458e2816baa8d5b244b1ef5dfffa9ffc9 42c064c2ac415bb91fd8df711aef9a6bc599cfe6a095c912e976dfa1a3790f08 c53fced9473f7513e548478bee7ace4539fe2249b3d996aa4f12862a4bf426bb 0785b6b6b6a44bc0bcf4eff0843074adf8a59fca9ec60e834abcbf2b90860f62 9cf1854face57cb2176a7414938f9dbec44d14777117c585bcbbd3dfa4073f27 5a327c2c5dc82b59586c1edd890762c249c1fd736e3ef002fadbf3873fbc2247 6fe03e3685c127e61fad02e6a3b14e49dd5d123925fb15bc5e86d1b5d1e0b478 0e739b670247b688ceb5736e05cb57c4839c2178c81bf94158d5601350f518d6 31ad206700bd4005c8521331d475dfce3b4b2cfb496fb26ec2dd9a0ee7173684 7ac930b442e2a8d492969a34f0228bac3af7312628be5ae33b1b3de83c22d09c 04a17035a93f3e1c489969b997169a56681843b6af1da4ffb3f4ff39b27ebbff 981c4e168574b1daee25f5d082393ad73b7b22236ed9a5a3748eae8217aa3974 3ee3cacdf1a85bca2dffb62689fb0408ae5e86028a33c6238830ba9b38c70a34 60bf731661074ae4be71d64956a958acc7ca90caf79e494d796b01a88826c4ed be10298ce234900f0e85d8a99a7a731d4d840dd95ef3e8576886227fb5ac24a1 260fa651fe8d53f4215cfc3ea17ca03543b74c641028dd09780484d51660a8ab 79af5134808471876f6b9529448f91dc90305d01dc00e9b37cf0cd6d567233e8 fe6b14ece8c6dbf56699be1afeb58a868c149964ca9ce4b807aa801ea32804b6 572d5fcc435cee1dd2fac1516caa22f2161b4de706d43c50ae005530f24e351f c0d3d1dd6b48234406d08bfa775346352198f7582eb15529ff8a1a69a4819399 faf43fa39c0e581dab224296e4dbd7758ca9eedb33e9985b567de5968513cdf0 2d87873f520801a37ab3e142a90f26d559801672fcbc81f61dbd9d7f7378e6bc 6f34cb9846c721c84dbccb5873678dfd84f3ecca7598f0a6ffd230e798e59ca3 2f0dbe5b5b0c0e5575936804adacd9769f25683f93537ea66a1b8da7affa62d7 ad215a17bc98ea75eb8a149a4045e6576d587a308684860417506dbf24fada8c 69288a5f51c6fa42a5c63287c1143360ac0c5fcb531470c5d2526b6157f952b5 c8b3ca3b00c268ee8f427c18c492da17833444c031f0c381416d5a19cad10f8a bc6e350a94d56c693812176324cb051e3a46e78c1fc70c48bb892111b5e03ddb af35dac025b86e6b292c4bd82725a2155075d062f95569fa8744b534c7869ee2 19475eeb7e8e4bb288ed2b48ce00dd40da38783e772b574cdd71538d07ab2502 01a67b7d9a48ec8fd19668f174ffe86e6ce4c47859cf410da36e609388824555 2ceda735d9cfea352bc938e06050e8f6f33154d7dd44fbabb8fdac2f5e2912f1 688357f8f56ddb5bf6454bc207d0ed71052bc00f44ab679009a220708a86b9f9 754d864a721d7c325632e532a406e8b89afce2e82e8f56bc695849b4accbdcdc d1370662e26cfe5335d36de66701e63f1406e7332cf3d1a491f75a8f1924fdd5 7c4f1836f0189b92c63d791c2ea78189bb1b0cf217c0efec8c98db89b7dff073 5974afe4a52aa6a1b1701c5238caa28fad4f0214638453632923a1511980eb75 b78c3dc6fd692287a0d9e270796662013bbcd1559af0618a7f4c84b4d5d942c7 92c20e092040933ee3b7165996abbd48672a72fa5106fc39969e194f2e8b1703 d39790795c9e71a3413b4f3e3ef1d8ad02b592415a733238f23f72c81b1c8c7b 3366004109f703e68f688ae75aa618cf5b89a197907bafa27d957bdc1fcc1b94 da196d0d6bd24f8e7913f336cba7f6a137923d77e6ad68d6b7fa5bbe0330b259 a63ce92cbf51714336398d775f5d9af39da5a164b670e4e19ed687c7c90ad60d caf18fff0af864d344bd701c631e4b0efd3b7b299a7d38005534f73aabbfcc87 60e2e76135e9a61772c783fd69465eb4e4bccdca774ac59b718d1f04318330d6 68784789b8f6970209d83b0181790bef7717394ca79ef7c06e64435f92ee886d 8bcc3984abe01c5fc1d96080507668598c39b6b29a039caba1674bd75d9c8522 0edb88ccf440ecff7e2f170c7ea70d38044c178dccbed5f45e09265997e96afe b8a959653497e1a7374d0d7e3cdacff50ce1f232cb2ee5d71c37b024ef13dbed 9082d38dbade2c285c2017bec4df18ec3778021b10dd63f9a8bc355cd844b591 03954ef0904350766c6aa6aabc1b5a2b2cc066e508455258886a1fa69768c94b 89259621d4f27776f8972ae52db6a9a7a7497f8026e5cb759b4c66ea1b9d412b 310e14a44d85cb31152bda9719c57844d1feb54aa9e05396d6d679f2ae0ec3c1 674802a2d2b039469760268b3053c5f333e36f66851291b41be48105dbacd136 58e2d1c694c77b95ce9deeec15e7258b4e87a6bbf4329002ac962b022b4d2503 6dfcd2a3afc97b6e9ebb7d853c708f658c9c0d704af799f86fe3cacab6871e55 277711105ab41e84c6fdb17e84f4f6fa50a579b496a9d6af82e28a2876398e22 3da71a647d986e45f9f825aec96bb29ea9115f03c728deec30da10a9965c1e9e 3684c36db782bf8fe33008e5dc84b7e19480229dfe8aa5c7f226738b9b80da90 5f2e641ed1901b55df4c5cfa40e34a5045e3ec855f70396d0de03b38bad04023 12e1390e30d35a5da4008515cbf6a4471dcc9f4a867c856afdfc42f214988ed7 daca3cfaab2af5df037f7210e998b582bd268b90b217a38c991a14de7563a06f 15ce6d5055072b91b6bc48768699c80882850cac5b5b538e8ae0c91e30d0dfd7 197af6e484ee3ea2d5a643262b7abba56d92a57e32c993274a08dd28ca2f3700 819baf8b1f271649867ee7f3a186408e8a245c79e2101e24fa5dfca1938e3359 86dd64ea5316789124a4b7fb33d066117047be49d8e853c3f7928c9400c6bbff 342e73a1dfd7c1cdfae2ecc9d49ee42da7d8782ee804cec8299532ac1cbd64d0 2c391529a7f2b140d4b648f1e1595c0b6cf5b0d9088c6806a739b7ad424002cb 690876f2ab40a97bfca0e7942dcea01805e0f14c407d6f0dc0d1537dfa173cd1 779b494fd88d5b40f2e4d8c9328772cb4ccda41f153e36a249d05a69e62d4191 534c9673c20242cda2c09239ede688b433066859ea0c19f45b0e2a7348072c5b d26d37df6adc20ca355263cd8cc55e6404eb962e63dbdbd614041a99dd5358f5 70989e32d28b90ee81568df89c78b5809744e8bc95fefe3f1ddfadfbf5c64ee9 79eccac3313919dae4da1e66e8ba72a9aaaaf40964a4091d0ed82180ace9bfd9 cacd1732f945ccd18fbaf0786673b3531da307bab34d7cf51a7d840b7d7aebe6 7b0c7e42e40eb1c5bc371290665e205536b56cd4f64ba568e8aa00bbd8d11b74 4068f9f7b879a4362443f49959fd305cd2a47d33437995fc29789c2150a7a31f 063be749ade2359b9a855264006167e56ea56c7bff22eca12e850722d17d8156 9c8324a702d0ee5addcc7186fe0c4f25b45ec82469ad19be2485a2860022fa0d 547fb056efbd084b98eb7e889a8725671f512804d76646d729698c9a47660bdc 6472be1679e136d39c45fdc2e6d0c4a30404681180bea654189edb4dabc3d6b0 793dc14db43e3fef2cd799e0f8e3c84a27a0eab9030fddda38a70f89213cf6fb 66b95bea0420fd9d39de7a8319e6ae2aca5463c32d6dfd4b4a6c49153d8155ed 623c000244c1ee87ebe2448550d2e790d756da063190317295fb2cf44e8d78b7 f914181be99128d6163ddb2f8c73ed44f3ff24d74ae5e7196bbe950764b04e65 646df8a676487ea7f0f64f409e45b52351339d155f2b59cecd3ece8e341c986c 31a44fb6d2ac24c050f777c93467cff910731f8bb2f15e922206cc2e72e3a6a7 ad9db4cfe2693a96ea61502db3ee76017a715dc6c4c8dbdf7ab28fd8e33ae0ce 90262476b6bc34008817efde68c48a7344bb89905df344bf533ed3f734fac786 413be1cb1bd2dc548f25a8f3d1b1b804e385cbbf9ecce4fdd0196f53c698953a 478f16d2949c6fb7599f03d88894a97c53413e97d205957373d9ed322edeacae 17045641d6c9e1211603b35e701ade18c225daff099f4caa77985cc3e98c476a a6b24d9c7f70c4ddae9955cca14afedf5b0a0208d2b5f4031fe9581bd8664353 5a2cb5f46f2deb94fc9ea54cba72393a6a1f690fe3b795bd9821f716f46d3b1b 3bb41e4c2ef56ed365b7e7189a067c77ed2b5217263497aa938f648e6fcefbc6 233a509700941d14e712d4f8f603178678d60c42e7c14dd3dc6c47a33856e2ba 5bde7998de6e65ec057bb63bbcbb878a270f50d215095a04494bc9e9cf0cd882 c2ac45f2a2a90ec996924eb2b38b243e59bc683466166a907e94e68d75b904b3 39c535c7edeeef11de164beaf3ce5f7a5584700f1e87dc1d86dae5689d8c94f0 1586331ef39323831649c1d2d770d0dc288a2e8825d5d15dea42d6a6a3c03209 e0556e8fcb54133e2cc2cd36dde0502f1cf8ca2135c0bd5b6cf983d47e0d8c08 e100523898a7d3f81d18a292bdb5c9b86d2ce098ccf38c0816353624ed2c1cb5 0edb2b9833bc06d766b8b9dbc361cfc23093ff625889d039addd9d6e363e96dd e1c7d8c7bd12791936569cd537e685d75508a228195c618d18863805b9cfd48e 0d4a008dbe7abded4db4e7eecd9da8197c53254b71c91ac1318c061e6a9e7128 0df718c4a3b30dc02a34de64ff032d86583a3e6f88f8e192816e94efb872e33d eba04c26f0955da015f2aa28828b2757f54f6c6ef73db521e27f50f6089a219d f4e9da7bf4a8ecf806ec4c2bd6cb6497a8b9e860a5e239b06a556e6c3219b4fb f252024b37b5fc415d056f7674896b11bfc8b8c0cf5612be53ea1cde2210e470 c6718786e469a90e1fe82e4c1c759fa332380a0decb6339acab7d0e7d0f88edc eb68da19f2c8681b732baa9780323063f06c0dd46afb7bf8d7b60160fc5df677 741c19a4ec377c7faa14b9f659c7fbe59280143972f55cbcba6aa31607b7bffa a7ca27e36b7203616f36a0e1d2d0b095543a2a987db6fc11a99fe40831476f23 77b56f8e2026cd6fb29d1f068d54306d71c4dfeea2e12dd873c31277ddcfbbf2 5dae142544623c352867553cca8c4c1a7a8b3809d93a1f7897a2bd681c8b5488 3953380248907db996246b05775a497c7eebf709a0c3303a13c032cd665aceb4 9bb5b27774c41c9e25edad4351804289adb9fc42371e50590ab7914a2cbd1d2e 905155e467b3f36fc8cb2f58367f8159e87f69c337d0d873e1e772b6f0776eb9 1cae12087f4b62ffb19c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX5 %!PS-AdobeFont-1.1: CMBX5 1.0 %%CreationDate: 1991 Aug 20 16:35:12 % 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 (CMBX5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put readonly def /FontBBox{-40 -250 1483 756}readonly def /UniqueXX 5000763 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be28899b87700197ad7324570ad0fc53d9738 4a4e30a779b09ecbcd7b809dd648167d743332426b052cdfe33910579fd3bbab 2e760c399269571b5a80343c534ef49bd9740608f29379c5239eca7b4037cbb0 265c9efc841cb1a2ae57a601a16a789e5a588c3b39ca5e0db9cb4f7c193bba6a de9b9433619085040cd4068b0e0021b2b1f6518e2b6adbe1d48f33bebc15cb4f 8c70513fa15d916ea331a1c5576bf455e7ec5760567265bfdeafd91c6801be84 70032f036d9d61d27db018e2f35c85f5be645ad21502c177d36aa2b3851d4d66 2b5de0648c8c390ff33bf0d20cbb56a51969908fecce2ee79e9592862a6ff134 387379434a90905174ea81fd029b77146cc4a94ebefc2662eb7b19e7a5084d25 602fa58bd20b3c994f8f1e73704fc0812d92445e851ba513eab428e965b2b7c8 ea5b3f0db38245649ecff6daf3952ce3627e8ec8894ef187b86a8ef6aa3cb81c dac8b27b0dc31a2a064af93f6caa33e92d2b98e1df697a1c2fdb8d18fdf67f1f 8978bca712e32360481351d712d8ed45ecb97d23756b2d071ca1ebf2a665e121 5ce1848cd80c80600b9b7ee22ae0557a00ebcd6817a6a4e0a715a37850138a34 751bd5950b9cbef7c2043c4ee7e4c9dad028e9c175ddae33419f41e340a010b4 0c8eb0b52ba8530868095e3ba6a4e07608b36ef5297f51b545ea629b938046d4 ef48f1f2d594ddbd6bc10e711a5e6d58f871f6a199813f7f4e90c4f9e4341634 79ffcf4655ae7e1dc46198e3086347c5360f733c837de9060c14bf696a8e3e16 9e6051b88746cbfb6b11a522653121b3e5eff4711229e2cc5a3561351853992f fb82bc8c27dbb3dffd510200c2e03fa054f6f5b934877042f2a8b9e24fc0099d 6d1b717b2e37ac9642ce6f4f2de058ee70fe8b878dd769d7b99fb4a3034aecaa 28a9c0f18db4299115d70ebc128733281d70ad1083761ac21f3521a2ea6a7bce 2c7645b3178313e1afe70f17d86fa2b3e46673dd8396c7e4c47a42482ee5c462 8ad785137ff01cb153a8d79b5d735a739a0606ad80782692885b0d037eaf3082 7d229aec8487e33c1ca3ea53474a1064004688139395c51d054efa6505cb07b3 16946c0147b6e78414125fb82898627c1ef9ab945922eac8d059c0cadf05ff02 5745fc505b24843d14e4d5af3cca4a2867a7032c5d6ebf113cbe68021baf26b7 8d7f00683e4f613974f2e3cfa9e354cf3765013135d8b241c5e77cc331ac444e a594953b55eb8288c300b8c8dc1ce6e329fffe68a50cb2b1a43d2f3dc90a32b4 c9f73af809f743f9e66f676cfbc68c633a34954d78f8429c5559e7bb5b1def75 55b0186f85 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % 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 (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 69 /E put dup 97 /a put dup 99 /c put dup 100 /d put dup 108 /l put dup 110 /n put dup 112 /p put dup 115 /s put readonly def /FontBBox{-55 -250 1289 751}readonly def /UniqueXX 5000765 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b1ee2d9de5f5346241e154574f14a4532b35968596ef7a20 102dad629475cf5d654585d4caac68ba7b2ff21b103a98af3e9ec01fae180804 26b73d62e93f0328ce7775e81898de587dd0fbcfe98934a58afb1aa4dd8c6eec d19373ddd360a5e85cdd4b752b2f2baa13b48a282214a05632d28e915ec90824 21ff8f2166e940c7122c583f235bfd098f8aac0f1dbb9a625b02bd889869664e f1856608899ba509d6eb8ece665afc34a459dd5b54dc7711f6f04a288214efe4 53095e239bf19cd36b7028d46c07a2b8c17d452d8563ea88a3bc5e5ea29a9ea9 a7e38481679f893f9e6a983ccb5512bed4aca5888793526701796b3fcac0fb62 f69c66d0688eede0fefd590fbce954b2cdd2abc9017390077a2cf6f6fa7d0db2 dcb4b0963e3dfbf02be1dca9cad104f3d29495d19337fbffdd745e1729e7c0a6 41fdd3bf42c30d715670b3ade44f481d795071f1b24f4f03dff59d91bf9d678b 4560da27ad826c9fc8f8cd9a333248cb2007b4ac0a9e2d5c044774124f1ee23c 0e3e005a4a16e1d0cba15797fc42fa75cb45b24fcf8a8cf41de8e06388b5f995 04454646c3246074f495564cfc8ad75a949cc477ecf03f0511b90b6a7456b730 cf09773b5544f6ec17a9a179714e47e2eb1142d8005bd228affaa375eed7fb1b 075b3023be6386f3805aee05b47c7f370e8ad410110429d2ee8801d0d2da9e68 a453a323c147716ca588fbf563175e5f47d1086a21b04102cba338a3580225ce 00dfb1784fbcad0fcd11434afcc2ec13337ee24775c2952be02e20572aaab17f d21287775e4a4d9fbf877a487b252b5c880463541489f5578c7472d39fc27320 2e4ec86f9935ab2ded14ab9ea36770d79a1a72161102412bc57e27262c956031 edf5d048a6fb0142a0297699dd40f913392470529df3d5f4daf1a1ee65e2d322 dc520ddf449c6dd5bc755280c374f88387e87e074b331f8e1858771d00141ca2 094d57569396084849321f34b8f8b86f299610cd248222c66928ce290f05aaea dc5148bdd1d398e0dc9fb5c0c6477f145733f625d59a4befa0823cc480a178b8 291364503ce4ba8ab902c1995af355356eafab7684f04a28215509fa1ce54354 1f0902c35eddc42e463c6f1e07ce433f0b0d0ecf2660ce53841ce5eff95ee1dc 389efcc4926237e0d7d7510d2e0836902d9ba96ab43694e5130e628340ba8172 e61b448f9d17861dd8d8341bcc0408b6d0722645d5db494f17a43838534a9676 9d56e88633f972f9072f8d07306f4d110eaa5afa788ce12d6b237587c2a876dc 36f1e046f9cb8f8e3f785461d029c653da83170188cce5cb8b0b121d270ff9a9 7566d7678906ffc37bebd070e9de8989542d6840ced3782bb712ed1e26c7fda7 76e44735175e5e4e192cfc37b4564d29b1ff91786278865d12b7af5e016e46b7 d71c9352a3844b55d668268ba89300108029c729f869edda6a1b763011146ccf 4c882383e4293cb02f7bc148044dd1b4e103a1ec23f648d70ca6f0226c5db1fd 0c87874d2730c8a4176a6a122b5478633a156fc9c97fab2c248203d2f3ed4643 95d78889a38c42d4e17123be851dbff17f034264274db3ee4a322879959adc1f b243185f891754e80cf5f8998e48a6dd8c80bfa778ac00ea97ff93c45644a252 c52c865e18536e078b8e9c82417147f2a9bace8c9a9e4f241072a5d460e3a0ba f3420dc6bb7fb4d8f79ebf30edb07853093e8674aa35907de90182aa24ffe6ed 1a284234f4a2763210e73b133add5c72cc40a29d610bfdb3dd475ace5ca01244 8157793e47841ec988b9c74afa90fcd9481f23efff6485faac6badad31da189f 39a7567c2ad1a7bc034ac6302d1575be316c78a02845bdd9560213c158915ac1 4048ba275d45bb351434a68f6d54ac8e4fbb8307a5f546e903f0b34f30c22013 60cd18a9bbd4ccd2cc70c961a0f8589149bf1aa0f109a3d1f6a1d59afd0386c2 785827cd6b5a0e76fb58da17e67209b6b0139f3f8a911fc99c9ecb5e03a52431 b5e2c6f2add8b2a45dc725d82f39a5fa1cee8c9a16b446ef0b58fc5ce4b10afd 892ef48ae313485cef9cb66ac720e938e877e0f47eea10f94901a2f8df88f521 f2608d552bd4565cc9f6d4ea47a081fda2b515dc93e2cad1308e8e6cb55fae8a 8b835278e6917b58e4905ce1c2a55771819138121c4cb85eae33b8f5cb89ab76 9e90b558d06cc7fd0c4dea05f305c8bcfb2ea2502c9586313df16b2c6c95a4ee 65dee965c6b2959a675450936b15fa96fb79f26129ad549e340573157060bde9 eaa1fe901389829d5e53217fe3d958170aa93844d774a29ab97ca73a9032106b 1ec0e60ca1a4693df0526a3e93854932a24e139e9ce8760434aee56719ef853e 52f6eb1bfab4678a9a8dcd2986707dbc7c3394156c5cc4656f2f84fbabae7bc9 13ab2c1703b0e03ac16c1cb35b732204c50d6728d76a7df775265a0ca27b5e4b 3fab895d7dd075336085672e3383e2add3bd88f15a48a2748b8ba9459593b5ba 167c527851770713005e24ed3c0e83b89a72b8babfbe505ca20c86bbbddb2bd6 1e59a76f3b1368b627055143badd4548f740e4ae6a72125179f577b8a795da07 2ac4e0996856b6c40c7fd6b10529e2996f836e9ac6f83751591ebb28564294e6 b61eae2c9072b08ea794fd26eff1978ae323314648aff521f6adadc524b77408 9af3d209414e9e2063647501141e1d4c6ffee06a992a98589e9b2579d4119f8c 7e5faca3f61009ed651c480880f5b5db5184c7766aac7bc200d4dd354c5155f0 dca09a11a5086778ad0cada135d634f2837b5adebb166964f4e91dad22249791 b8b56f8d80aa6b328a956566d0a5832ba4762ee129302f45180adc4de2e93747 5fba1f7e6be94a4085d32a7ea322c60220cfe90ef7dc803e2b17802c7167cd90 2556f4f5eb8cac9c7ddda99964a62cfbf831e4e80203ff1eb0b58d4b1afe7827 af0b02ce3aa3c173469fb8f8570de36084ae08947809950bce022fb929058e95 d0706c41d3587c278bc7af7a324b8a5b801c9f4ea207a77aba49dce2e9001703 8ce03ef2c1bc87b8b5da6d3c6525cf944340e71eb5a03973f7b0652af52c0b2f e520278712921a4939a786465cfe243c88b1b603aa8d299eedd70f51f3e69a93 95699ee979e45d7f3d58e13cd2c1d2209fc7dce07d41941c022fa207d9a396bc 2e8cf3156ac7a4f1d9df3ac41dcab308fe32e198d612abaaacc981fd4e8f12f2 e68069a79ea86136a849ec45decbd77c8c3f5c7b3b09590dca156ffe83cc85d4 23656dbaa81f72289d2065d71240484fea7103c877b71fd8aada040e58fffa3b b2988fbd03c1828fbedbc4b824fb07a887605c2caff48668faa67c1c82620cbb 38db2b9c44c1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%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 6 /Sigma put dup 12 /fi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 68 /D put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T 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 121 /y put dup 122 /z put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueXX 5000768 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306462c563d51ece66fcc9c831843ecae 1fefc1a232e2724f7baee428ae03aadb95c3035345c15e9922fe49e1f2cfc980 237316572dbc57064edac9b0db8913a5e2d45e97e19a91435ccf8adfc835b585 48e74b291446d689c7f2f8c4325e8356e974ae30c3e2977477baeaa33d141fb7 80f59351e84bfc88c87b3a4a1d25e168b9d134554f6a581378c7d2d6eca8ac09 045cc3a5e0ed86f147133f094029e3483bebc81cfde69942cf645ea20d0a2b64 5140ccc2f9cb4a3d969f4b0a79cd3329b440dfcff5285494406f3dd08d804c86 df191e57232f6f1f83df6430f214e03fa5412b1e13d83c60c52a698bc9a38159 19a64162af7b83a9468fae9507c6cb55ea80df8c696dfbc3296c663902d77e89 a181502627281181ac8624f65be9de5fb32f056cc7dd7cbc7366a91717b5892a 34ef6b441871c6993da3a81afc9bf70ff3842a21a29c0e49da1ccba37dd6b920 2702db510b8b1109acf4c27ee8d676bdbd16abe189f34a9b61532eb777457698 cee0561838eaab2d3939c5093afbb215bac433d1918c739b62566906bb2187f3 378521fb52e70c18886e1aa15f53a1f8a169528cf2ddd54c203613ff88e619f2 6c9c50c2c3b8b8c868a88afab1dc8472e7b6f3f992a161723a3c0904865a7c42 3281601eee91f35222c4a71f343739f102eb43145a47e4fac3bd666e4c114a90 5950618ecb1bdc29f90f6ebed1d8325fe6b52e14a8870e9b4bb088e585c71b91 493c12845a101937e3473ac5e9ae24f7c358f06d590d7618e1a1d5834d87621f e3f5432b655eebd4ca61a7b00dde0aa740796ce88a43d1c6952f8d2ca63d30b6 dcbadbb0dadf13150a442714675dbe51ff838f2e47ebe8cd44f1eac6ae5b6ceb 0b07af03f5d3896ff935a198aa635e337e367e1e128d15e31afe3ffca8245e41 a3e17011340e49d52fa1e322b435b4f7f2f49ae01f6a319f68d3d786c24be810 1e1c975a8feb5dd7e4922e00e3a08cacae5a945e1e8f8a20f1fe9534153307aa 5ac7424759743e08af90b9bcca7447375222a66934e1e47f97f8985b0c694a87 1ee7eea9e0d7928e555a83f7456ba5f235a1b5ef8bad622dea313825a43446bf 0b300d86f38133965120d1dc43eb1118d1fbb2112412711a576c4cbbe90ca05a 8865da40d9bca6bf94a9dee1596b6ce5af218492f0f13797305d5ce027a15f62 e97b1a96f52bfdb35d7fb3291fc270beede6eefa93e4979c0133bf56ae6ba3f1 5780cd62e482645875d638a9a3452665b2f8c9428faf9fa1530a7f486ddeb242 d6b88dee354fe924ab2f20bf5c8b3c5405ce798825ed637bb0a2b7a6b12acdb3 f266b64fec31f52e316e8219fcec9692edb1e74f6427e841968238cadde66ea8 bee865f2adfe5ba165a73818213c41dd3654dde6a71ec0b02ac7646778963e34 73132880eb4a142df2c2f95f945c3d503c1612ebffef64f40bfa82faed82ae44 57e6d3ed84a42f8a8530552f6802005f4b13ec262287cfd767d135530c26dcef c0a8df654474afab1a0963eb932ff8778565a41bb77b2f49740ea45fea036977 332ccc69689d7754a2f1fbe51d063164f9d2152d7497ae7b085ae1f4e95aec17 c6575506a2fc117f27526e38e55c6756dd3c7c83663b824b00d1c48284d69414 6f14abc27ba60fa68145232cbb0aba6b94419f285b8d9cfa8b1f91db3dbaea33 569aded1d61230144fbfcb5eccf0f305631b2a0715116c951ae6529b2b2db60e 38d753fa2e8e95e663c6a1c668a45ca81f0b1c6139e5a1e37bd5ab83acc335ae 76e5e4f1a46f92701b8f73c66d2d277732934ace27c24444eccb69034b158846 a5f4ef78022d4d4ed9bb1a3278aa87e3e726e23a79063f718cb07aa71d910cf6 a5076911524b9653c926e7259a4228c363ad9db682de31ac298434e0492887d0 762b67a5b59df89c12b8aa45cd36fc3b8483b025bd2ea2791148eafe0fda45e4 f3a73f9adfc8bd1c6596bc5e858b736611d6f89b4dc652d372fef330b5fe2a40 b7ece121e2b4df0cfab25f470dcc6d1ed120aef461bdecc3bd08451f115d4271 4af1a266e32fdc5d6af48e2c94a272d2f131969d6e79b206848f65ea9cbff546 40d6538ba411cc1b393b5b64ec35c4a30c9f32fd835a11ed38607eb19a5c45c6 d2606a4b773ec2d6bf1502696a4c29b802b3f308ab0afc3a4d4869d26dbe9e1f e8973c266a7462db2441388245d8bf63b217e8d6e421e2a0ece3808a0b481d49 6f0f310c144402bfd028f09a62183fe918008e8990705b30daac427f4c91c868 b22e08ca441863e23e62bed21a6c10303e5e9743baeea9e192e45ce9354bd38d dc156a3bde46c02dd6d3b1eec5a73ef2bf1c6352177a38dbb9d851b79989cb2c dd369701072317a8a0f7d3aea578fbbd395090e74815a6d14413c54547ae5497 6075d26b2b8b5f104a7b7e569a4f5eecc5b6161bb96ca80f021bd7212d1c9656 56a7bae77f3c613d8d450ac1518b1dabdd138dbd38632f5a07286c8cb0470b5a 032275d335b7d69c255e1ccc5b966d0e6c7f459ba1de5e5a68fa4fd2de2fb821 96a6f36d6df1cedc6f091b146c16ee5d73fe0f32249d1c427d53c32cfda483fa 026cba5c189972870c4f8310b5fbd4bf2135d159d01b9ad76d7bf47ecd799783 a7d52042cb8ea056a8d29f6673043a7e9b48b48078c437a305a6e21e21d47f04 7599209efa42ff7da8c778932410f9dea6864c261a39a812d34c6a82d9973630 441458811e5643fd774d9609328082702913f400611b96d4693b4a22cff27f83 63ff4c30119f3737ca5a9aa6a92b99a94d0c0f4af2952b7e697ee11184ce2276 a136876f2fd6c92e17868e9673540a4efc955d259b563d795cebdfafd4aa8bb4 9c593e556a355e1f8aba9fd3e7d4beddd83a34fa61ff4000808a039e7138f05f 0ed2aedaf4b5246b7754b13eff227115e57af94c61b74dc60bb3db829c1ebc18 2eecd1d68764410457785fe35c1c47698a2567801bce0814d32bcfe027a4b563 c1847e5c11a4ce796375c5d69f822d74bc59e16536ecdd2829fbe02147ad334d 2e62cc357f5ed88ca1bd5373270cc27724f1cec437a53b85bd253f1461cf80be 4b6ec5c3b3febf459c6f41d6029d680bde10e2715a019eed00d6708352a216f7 49422cb22ef927c561a487015a0f00d1ffde62292b956a74db4f6b3f723d42b9 c4712b83376453a2bb7b0e252159ae7b4b3f1c802b4e9240ba87028042901280 91def4975d0c19dc852c8fede3bbb6c3d359bc5086efc3c95806c6bcfe3db379 207da66837a2ac4214d63b73a0162fd2e658ab91e1251d0aace1a070bf4aca3a 7ba1d4e1c37c1c052923d38567073e35ac059d786505e389cf7a4acb668f9fe6 1e6ce85566db797b4ea188e03115787b3c433050d61afed0d1d471269d0106c7 224741a5de97cede7df6b0762f65c44579c7efdc946102dee0a1bea4bc0594ad 4a2dde70b6d9d7b07898bf253908e539ac4f9f363e0dc7172166e37c2142e54a 96f3fa5dee8d9b9258c8876d0291530c1889e0b5132981deb2fd72aa3ff25b94 52b749ba6d78a8fb4a0ce8b1a0904718f5de9ea48c729485f6fd21b7df29a9d5 0fc889ea23d311952b7d44d90dfd615aaf05ebdd479078c9cbc4769387ca4e20 7d4f90b6f9918655b3a5ca42a8cc7dfe87278fc2a92efedfb8d017229d5be2ff cf852f7a5e3990bccb61b9da561a8bcc14a6bffa0dda7c1fd011a8c96525c320 19816be3952c098f6d3fcd74f4016c5ccc583a7ca1e6bd8dcb71f2fea3162443 510f76f8d1ae27a1a44a930b28eeef8fe04e88bd3e0477de64ca316601099512 c62a8cbe77be98898f83cddd06b62021f3f200b8544e6a8a6706a04eedffa3aa c53be24bc23b4c33d968a7520edf7d933fcb7d6640af67511598c9cc6043854a 2cad3b08ee267193654d01a1b108d6896053bf50f631b4c1b44f74dee4e5d074 0047437bccbafbf96132ddebb2a5ad873c8f3707498442a5c6ea506de11823bd 7b3068a7873f068cbe30d4a410cb7a6f342796cefa658ccd6bc9b2de4ea3ddf0 c313fa9de2216dda6a553fc1b3455fbf905765f1d7dcfdfd5c0d045548e75093 aaf31895fb34a8c779604ab8eebf27f657491fa2ca9b2e945f8f0e2a0edd7cb5 0e2125924d242167ade24e31c508423c79b05dacd8c529f62e26b267c9bfefa0 cea4a784f83e3b6fdfa2427016fd0c53efff04fed4c50986033eb34bad04fd64 4493ba66f7ce844464d67c78797223040c185ec5a4cd871bf9700596431c54e0 78cad5e96c9ce18516e906320af35e83b188b207bd9ac0de6bf63bbe76253109 71598cfb7f2fc6f3aa8df5d2968cc29252307f3f1d7e3fbcd744cdbba3c4fd7a 823d16c0f738fad0e2cb7653a3621f47c5f9c861273592252c7f9a762224a090 b36e3ccc75b54cb408810c7445e47343297c93b72db23729a5856338dfabc19b c6aced9eb312be7c84fcfe90c8bb4be44fdfa0b676973e64e331eb13ef983c0b 3fb9342c65d00e22741acd4a2a1708aaf905d8748201608164cead935e477c2c a92411ee384f8b7a03b17d90f3fb9e613fe1aecc12cfa36abff7cb95e412eb57 0f15f4145db93f586d206d6f94dcb95d05495c2cfb062d9ee6e1fe51bbaaac19 0e2b63f85dbe9642bf98813000a6494455e82ea0a09107c7e443f6278ce173b7 b376ebda479cfecb0404dc2bf10918652806269df51df49aeb4919ed331adae0 be44cc8bbc9426f81e124b832a30b0e24aca24808f11b5b4b52709adb6c93887 ad190c3402e1aa93fbe6ed8ef6553c79253d5fc78666ca160bdc92df68b83d83 b770e4067bb72790c0a552d52d20b46324ce15054715910886ffef6e22a2b46a a9edd329d4937108c7a74084a6d4c40ce41725017046175d4cf6458410dccfa7 d51fb498bd256d221494a846cab1ae7374ae3bab8e9a29f3f2fcaabab3c7efa9 c48e1fdf0c5036a3bd116cf2659456f2828833bae40731f26746b50e1237d6a0 f21734043c466d227d99d01d1c62194e19869965664fc114cc541e3c2eabe4b7 9adbdd217ee3d38b56fde6ab059f8805f15971fbb0a1c2f5731ab030082b4e9d 2e2ab396802e75bba13c6c0752df152b8817170b13c95388d965bacdba637986 ce79cfe8ce9c4a9412c36e28fdd8b6c0e6e8596994874e97f4641cf0638af1d8 bfbd4d95fe8a36626c67008a1e1a0fa36fb4038bda80bef048f61dd97109190c 064baa002df7fd400cd907256090cbbc9828d07812497e853853b54f2f233f1e 5fb7913bf253e5fde4c6d69b85c5bd1618ffc650d0d7ce923592b64e7f10abaa ba11c9dc52f65df6d05508e30b51dc9facae60082d9a6828155126cab93e4bb9 e292d243f66431c5182b5865a6662f532d1544a6c9bf39840489241a732e15bb 69f9610698d7b1f6b359834b8a18e2f430aeac73076dcbb42d2852cb29041b8b 296254928a1737167654a9fea9c1886f5fe453b0f5d99423d886ed80030d634f e8f8360ba76d0cbc52df057b63f95423091df5a3b0658ce0015842117a3cbcc4 7291deee1bb086621ee1f60d35ae59505525f6bba2e773a00da41653784e873d 54fbdaba0d83040348db744b0358b69c79d97234d34f26a2f11ed6c20604a615 6d1e84fa04f714e246f10be62d765be7343ebcc89b46aa0cd2fc42eec5577a8a 459ee1b39b22c901663e305f1464b54f6107e034a50539983363a24b51fe75cb 480c593ead5004d4da21ea29ab16e9813fa5f20618b8d55ecc769d4c5b8b4a88 32e14f98a7b1c7476ef9a235fc18eb0d233f4acdb8e60cea409f9a0edee31360 31b38b36a75e66ebfe9619ec86ba74f461bf5bbaa33341eeddffa558a161544e b506a18fb928e4960a603d056ba8a56074a1ee8c00f0a188cde9c1ee736284a6 b544933c047885cfc1e0cda15852545f2376ed21c9a00b5ab137e1914a5c00ac c4ad0968684b329a3490c094ad7adad0fe180227e1e58a4cc8624b354191db80 7f889d958ef00698ad640f1abf64b659eb7675348bba0abf4624029aa695f4b8 59c79817a3ad0dbfeacdaea07efeac14f12127eadf378a99a809dc5b525520e2 5b5fb1fe6baa81c41e67cc197c0a064c8693e9434e7371cae8d61c5395bf3160 83f081240b366e9c8f980b803060cf3d96bec7d9a2236a9fe30e1f65bacd2f8a 6da1213514ed1a237ac3dcf80178cf88222172a787fc43c8a2f44173183c9021 b2050b86ef362502310113392b6e69dddb8ac7dcf7d0e009258d8643c0bc0c85 e3ed228a39d07d6ad723f7d462ff9df9bb341c0da09adcf7015be644b284a584 b6f0631d55b2b6e33882f6bcb348dc409c1fce14db09d0e3fe6d08d22c7152aa af39723b87c435f6c2c9a941d7290361640de9e8f0e929cad86bc1d016c4a8e6 d7ab04f206fa6b7e10965cd0d904a003afa70ea5c7fce48ede93462373511ff8 d423fea02b1ba5f600fa669cf8341c9ca713271c7ed5c23655232d072c2fa85e c39ef3bf3bd159d01bdff24928471a1fb108416072b865a94172794f5fb77c87 f6d029cf63896dfe4ad143e0ea91bd466201e6b46c09decee9e5f11500772b64 f33f14f24a67f489ef946cb918a05cd95b8962452538cd810af43c56e5bd28e6 5d30a721d95c6ee344bfb3272fabd31dde53c32cfa71f5dba373f71e1792313e f419095f119fe5f7a883e2eb2757a5b7fa48b56fee804e76eb7e2f8acb8dbf3b 70aef8288df7c4b4d897ca86db9a0d1a0afb28606f8b2c39feac7efc33088aa4 92dbde91e32bcb0d318e89c6a0c6064962dd4dbe97d0fa9bc9deacecec12b8f2 6492bf2cb925338b5b0ea586530c178e55d4a77c2a89a745bb10f935c00ef3dc 22268916750dad6005be4f9f417087924ba3699fc7fd2b37d0b60fea3a3b29a1 de3cb1bb73ced29ce28c8cf654ed34c649822e4dbf7d337dbaf18b423a56a671 cdf25ca9e87f79eb491e22725bc2db6c56dbf638dcef8c0cccdb49dbb14d80ee 209ca95ff5f0709ef8c8febe9da0335c305ad2a0bba594ad3a5b75319b1adbf7 3a36256f7dc6a5665be7bca8bf9233f8bfebfed30ce4fdabbdf612b8972fd92c 9159f83815479eac423e105e0c19f3cb101f2c382569c7eaaee02da08c166886 181f33fe1823111ccf63dd45fbd031e14c49e5eb3a7dff87a92381f7f4a8da0f 5eb02be60fa27f12748f85ba6dcc985c0d0ff7b0f8397fdbe7ff63676a5e1727 7e5fe71d439586db667ee551c28ceb4951db7ed33b425c46c65ab443e18322cd a9cacffe78eb54419f045e1efab3dc09f5e30f7e28687bffd89b7ec2816018d2 30c0281203ec82bbbbe504b6a72a57ad2ef196da3ee9726b2f7f071c4de87ca7 13bf12b1148827e781e03ede8da395ba4e16f0ce8e1077b1d69c75efcb0fa469 51ab8dc1ab2feeb8c820c17c20f1f807177802812ed9c403c9fc5e9abc346d19 8379f94018d25ee3fe4ca936f4377704615ed1931b73f33f8562f6bab46df2fc 055eac457e505462acd8158fea7a2702c7da4faeb331f974f91154434f56c8c9 00ad5cda83c6cd8bf4c745a2ac87b644656c5a0c180a0083c8d080aa19e1aeb8 9a3b3e42cfa0d29a05f9a53ca542a3ba210d4e8cd1a208f69e31480a5e74e2d5 8ccfe28198a280ed4f0aa639cb62965e88e9fb73ca63bf95a56571242ffcff34 91d07882e37e4cd05f56cbbbcd63fc9945e152a8dbfd8c47f3772dc4ab0bebd7 c5beeadd595927081b9168ac1d1ee483efd7a14288ccd9f90a77c578df77b969 67a8a522e21dc4b6b955f5efd69b8ab89bc29955fa4563b3d969f15b1fddbbfb b50144032b282c66c517b7c3e04d25d480ad3c72569d9b213c4e57fcbd0bc3ec 2fd56ba4e591243aabfa9718d88678c1a8b81c8ca80e2a8962fa48a4637c63da 53388b6589d9d19f0b0c0e90bc5d3b31405adc0f6eeb0c825fce9af9f10a7f8a 7b8bbb38d1b5c31841437416c8a5907c5e89c43534c62c6ef7c473b0878a0b8a e80f08060d6238663b628a202b07bd1d815927482032c0bb28d955cffb5e075d 2b79ffff726d5e8fc8d572b40d730fd793188cbdfa72c53e5fcf8406d2e1eca3 d9148a9a4ea8911d3f3a621df70dab1a31fbbcda2e37e74a767b2d40eaeaa607 528be0c59bb998a19fc298953dc9197575f77251bda82d6f1afe7b1f943720f2 371e691336702011f49a257d1d429009e58687836a9ea92338658808b0ed992f e6d085f0cd7a995917360709818e20859009909f94aa0332b3d3ca2dbc93878c 8001564b343a6dcc801234c3cdc8e29dc6ca32c54521e6abb421e4a517b1f489 32f606b483cce29f513f0dcf22216b01536e6e6f2bd637de05c49ce82d65acd7 82403761e17234a56d8680778da2dcca570001b1c2884aabc877f17d214ac00a e2793da5f531c2ece8a1dcc113f6bb3051f3b8178f994191a63d927daf6aa81c dd6d4670fb4a2077e8b91d96a2452ea4d8b093b6038d0c38af53edf5d8971aa4 857ffd4cf7ffe0750a77d06b00c4c5c898976b00df1ab6f83ada9e5c7e0edd87 bb9331730f51cdacf3860f84ad3b8da64e43f23ad2e55e16fa16beb6e350bf6b adf11ad0af7a91e2cf2a249bfb13b8476d76d36129cb96942b11d698b5334fc8 cf9c07f2c2368311ac6128f3b4c044f7b5933f1d472cac5416adcad5ef1471e4 5a3b64622585e31deea6a73a9d904456ffe4e81e150fee8fb45bda52891d649f f0131ec138a6a3be051f20cce25e37398a34fce27c3cfbfb4d7432ad4f491d46 2923435731f73dadb2af6682c82586254680a568d1718271c249b0cff8451143 fdd9093a2a88067b4b6ee0b62f83b318080419289a813a68d6fe23a98f47ce91 e52cefd51eb139e2b3c7502c269d9afbbfedbea46bd16088d0f56660a4387ffe 283733949aa411cb4345c3ef958354d262161c9bcb2205d576565c00e6dc3d4d 73a3a2892318ad926a00883e01a7d2415481624452ce098d2b3d97cce490ba5e 14a5f86e4b74553b73001fd207c6de656af7bebbe42c8f2bb1161b40a7c55c1e f696e094ab8e7dc38ac7bc3716ba4ac9e4ea3539769871bac4fa0dcc3e4d21a4 a3a40841ff6b1e550babab2ec9086162669a5a73f5e336634ad7fc43317d0cf3 0cc8b7d44ff7593304d0ea3042534d565402a1cc520c2f28700f6aa7ef958606 e707b7515b642861942f02f2ec5a77691526d6dde2de1d5927ecfecb6ab01130 e1aa490266a2a03c883a99598b6f586cd0041ab9e1ca06cf8c66a7bebb5b697d 0fd6a444c567e036bd8f71c61f48bf78fe1e545bf60ff42fafc60cb3a497a49e dcf2e7b7d8b47eda97f70064b7f7119a4aae2535a38f455691233fd1bce6f0aa baaef447e3551e7e1826707b84af4be69e9e67b88359bd5643f1e72adb9dc50c bbae5d7f1787aa3ce2be1e5da97fee91deabe68d1acbe7fd72a5f5f236606158 232f327808c675b5023d484d07654b98a43055277b4144f6e183535f6261e541 ce3adaa06dd532633f899fa1768f6b5bcdc719b255ebc57d41f35fdf7c42f00e 15e5e4f37085a1c9316f1142bc4763a16e2ad7bfc8b440dc15a0f22ed70a3758 d10773fc2bd2ea0e279d00e85a564788113c42de15dfc26d50077c4349921817 a9c94d0fbe75354d92115344ba458258381e9659ebf6b3676874b44a4bbc52fd 97096926ef8bf29acdca41760cfcfc63f8bf5018ef1d821c3c0d2f563a8f55ac c70cc32a5f7576b3efd0d2f848e3e919be175836b1b6cea3ec2380b05ac22187 cca3ce7b0932bb722baab118e586cd85bb48b2c4b211cda5ab53f0d8622ef88d b81a4f382c294a25bbc040643d8fe416d28f588a5d73f1d2753fe875d906b12c 3172c8d8a28f5204b18992c36248baeb3abb6b3a129ebec26065a79eee83bf34 ff951a9ae45cf21860d7143c2f5dd76a4baa5f55331424a6dd5d01c2d662fd3c d8a04030c27d69c2b62019ba17da844c24e091bec4c8801acfca71eb2d6353cf 990b165792df9684dacea5728b4787ebb66bbe058fe50b847d2d7e8b8c3b0eb0 9ae07302b5df6811e3677c089962418821ce7a37f561750a6d57ff943a373b81 327f29feabcf0aad816dab93ffbcbc255c2c533742daddc57fe65311daf682c8 4cdb26f2960a81b74280c3a63b0977955e32477c758d7075a2dd76bca6e5e671 34410c0c413f8f3f876d3878c08a60a7a2d03d953bf9aeb3e69cfc6489e59993 c408e9007953c2991ad4b38239dd75f66dea7cfcbac876278286f74095bd43d4 dbdce1163b8937943400c6838b58337794d6e992cc4fc7c9eac5072ff9d19ce6 369a1d84ab0e9146216a6e8e90e97d9524c6b0cfe8455be58bc6195b80473eb6 1366255cb03d3220918b47b4223231a6ca108007c1782ba9a40f4bb3a6e7fae9 b3f9276268d4d80f4b83066d1b25c503df8d6ad8c11965e4b1888367a4d36564 c69da49dcb882b29ad2c32267a41be22488e47d16e07fbeb3139e95408685a96 a836e5d8a9adacd7b11f35325c87572877b5a0e9bad3d6c7457324b8cebc3b00 a9772503aca62060c657700df0a9bb7ac7a99fe23e1484e7ea06205e8f19a15c 3f5e05d247ecbf9919bdb87b74cc6e156b812e0ace6a1fbdc34e11004b9b46e0 7a1ec858fe2d7d588a5b2b5fe0fc895b75961fdd84b4cf69946d1baf1831c0ee 82a71f6fd5f9d54679d31331e8c08021949d778df20a04dfd7c76164b04c283f f90164b35cec84dc47a58c1ffa8a5db77d403ec1727fd65c21da6621312abf32 ae12ed5f62e4027160b5874a666420b3575c0a58ed33703c0885dc2a36756b31 d827c0276373fd3160d5c187eddb93ff1b235c250c278c3cf5988886e1c3a0d9 c5209f972632191e2646db93f0a38e6f17f4998083749847edadd9d1fa58d287 cc54588673a640bd193afdda27fc51d279c95bc755eea527e0660c35c4bb666d bebdd605c24783d73631aef1c1d8bd51e5731d1de2844e21bc7f9b53b8ae223b b659a3612651b2c798176b333fb2ccaef2cb769a8e479dda382316db396b2470 34f45644b3340f69c537df65c843ba8d95a0746c77931ea8dd471905599601f9 51728361646fe0a95dc9a00585be2cad3a82eae9766779b65c825193e15608e3 80c4a5d94273f0876d554f22192ab3d1d07372c4950559d5995319ba4506bf4e 8b5219c714d6f6971cd5e1625c76cc581ba10fd40fd95903e14119b6d16b5c2b a02f01cd802f95917419e833d97d04d9704284c8f594246c06484945964335b0 7b184c3e8b5575209974e193064b3e55f61b62d8747a403f75f58b8a9501113b 202072ee53ac31c89fa13292e4e19e98011e35932e3121f22734a3dde10851be b7e430635e206505304e5c12b2be916337c67806b5023d583fdb261ee2badca8 2463c240a3cb5c1ba0a5675eff7a31359f140736c254980cce08421d799ea96b 4dcf731b3260c085f6c02f2983dbfd752859ffea8ce264c0c419b17361750043 6f87183b9234c118012169ec4223de906c61142dc5748b7a56f2fe157bbd6cd3 66fef9a33ece3a8d04fb34ae86f43aa57e86f9371ddb6b270f2fc7f257752297 606502699a01de81d117f590cc26e15e51dd959e97d03130fd637b3d57094604 4d8050bf15db1c65232acbd3b3bc7781df12c6e153cd6ab3e0d805ee536c910b b51162d03663c9b2d15145979b66564cd1a7fc004fc3ac01e05d1025c87641b8 c8a29a734376bcb0b9843f8fe04d56a4c1d64020e57aa2132b120ea9026990ae b19128d9aa4b0c0810901a8eb6e74f8d134303308e9792db9a3239575aacabb5 e5806185cffdf23b61b53156e1f4af83fdf33162b9cb59bc862ec81a87ec3044 540efbd6a9d2adfd93a7f16731b8df0c6f542b44c7eef355596361c57ba99b83 1a940b9b987f077165736cf4bfb487795d68d7c5cb0b9ca82948fd38c361e1ba 3c647576012e5f5bdd43fe902c1d6384af95740ee3bbf7c4405c42c1ff1b5270 569f2b73dfda7fb0aa648163f22f8d63e4930dc0afe3c68c40b14801679950dc c3a3fc30fc291ec77c2c4b66f7d40cdb7632b328d75bfe6e00fd14ec4267dc39 e8a492c2b5423100d2d39a7234ffee11793d2d72f037a11ffb8a31c42a2ee6c8 b60e26e4c30a24c83c11098249f12de1f7aaa8bf19b665a9b192bb7705b90df5 2d8949af5f0b22408a8e1ab38f2b319a89e411645dac379dbe2c6ce2fd8354ea 784ea2702ba0cf72f5a30c49c26e083d351d295047d3b510f1fe0d495c3ce16c 1bc574b537d540a4395c7e5a1f9fe4517f264e521d1d5bf661ca95dab0e941ca 017a2f39002a3cc4d502628c38609bc93fa621605d098b3a8b5829cb6d94113d fe7c2e84dfb17ba78438d206e6553b58a6013792d852e6d5fffa481ebfe5ca4b 6b20ccffdf2a4d402f9ce314aa8327e82f279036f598da5f0bc6ad610af4486b 08a0340d5f5fa6e4adcb3ddeaa56ccef74e5becdc56ce4c58790ddf89d305ae4 7cba5faaec8dbd14a992f714aeae89853f80c1ddafad4796c7fa33e41e436913 c4327769343dab1f62a8204c3c28518fb25e5ec856f69d105520b7b319efec99 e20a07746c685d364b69dcbc907c480d5a2a06fb6d6e05d011ffd26f068d70c8 4ab4c34faf8956390034ba343fa273df26dff5fa71b053f652f137e3a1dad7bf 86032ec0f28fc593da379fea4342eb16a1f7b16e386f2aa3b1472ca2899ee4fc 64aaaeed13f1e4e09ca58b305fdc11b6362cb317cc3f78de8b564bdd3ae5509a d0ecdb46ac2508d6fa8ca4494c029063aa1b51142c350efddb70340e0d26c13f ff071f219d0a9a01054726a1e668a6577912e993d042bac46655e28c8a8fea58 ff0e10ae3de8ef454583c44af923e4ec2b9af6e50fecff8a957a601441cd9386 fbface6e7f8d13e8182922ee187d263ce71d59b20ac8ddeae136302b9bc9343d c4520fdfc80f88193deedcbadbfc332c34ecfe5a2e577a8e0625e1de392b63cb 4a4d52802186935bffec7edcfd685145167a9d5243669b489cbe905047b0bb15 276911186db0483f2bb4123db7559429d74f407d4457d730ca3d184379a9b40e 665ca32a18f01f11b1469f0080fbce312e476e889e978489d0c7ae54ab5d58ba 698e1016a666b6edd17e0425daf59f94fdaf93f0ab9744b62f01518dbcdd5da5 a43707d08540aa1a1a98cb602fcbdc6fcdd2c8d9461eba0bb04b5d68528ada8d d5d41c23171d2ed60b5db384329f95ab37331fa3c13ccf1ba7eed8c12d15bf2b 4405bd751990c2c1a53df0a82ee6879cf3a99cda0a5c0c3a5def85f84a0ad039 b65f5685a1eff416e02415d81e87a354807e6e5d46092fb61ecdce0f1ecd938a 9280692f75606d7278b1bc9a7aa194009b2fc6a8496065ef2e47f1b49c50ed7e 51f7df250b4a1d3df7fa163069551a52feb1d329424fbc466d5132e89f3537fd 36936c53cc94f8b74033b9d252f0dcfedecb6c37002995778af32745835b3acf b34ffa738af00a452712444df3bc08cec5ad45716bf836ae63b2dc32e13aded0 45c286aadd102a984549e3c05a7d8aec736885c714bfb1ce8cc1acf7f1dae331 dbcaf6a989ceea09329abee9ed6aa28c1d230e4e1f7148f3d9950070db648b0c 5dfddc9303130cd5eccc2fc8ec601011bc7171c23c91edb88ccf430ac7c90306 7af8a61f21ba0166325ffc24bdcfe896369dca8fa1d53b04f2c0fb428753617c 923e2e8a66894636060b18bd0858750d7403aa494b8715107eb5886008f19d7f d5c525308d03aa132a0a8413398ffd1905a5cf2a3003a4f21c82aead2f895f3c 4d8a4160b9d95a3ead1fc1cfaa158d33f27bf09ff122c6c7532e2a56d710e6f0 17e2c3c688ec75bcc69047ac7926517ed9d2123fe6765a2d6be44c42c159d3ed 185e6e6511c32d20d3a94d0cf10617bcb9536a03f0019f4010aefc6b94745edb bb05be83c7a9f1fa5de1c97755e4f226a84b29ca1cfdbefaa92e0d8a2d78de95 1b4fe5a70a747c54c6d78421ee898136581a9210e77c34a8570c8d6dd186940e 998362cd8d2163f101868bb5fe63d1db91722d6831e0758b0c710bb20f5c51ad 186df334a00f708edf01ef7e2ccf8c0809f723ad90405ebca876f08d78c0070f 6f9f19569dbd63e2598cdb1250fb598e2f2d3f0cf502dd2d56ab7fec325f63ef dc23ea86bfdfccd0c40b2c9ffc361e95a94c9877b4d214a28b78d79ea080b28c eb717de8ae7bb60e1c459e23c4210a32ad4f538cb62e4ed1011c3f8abc2a5146 059e4a7d0091474fb853dfff537464300df3ea7502ca2943bf5afec24047fa0a 928e344f41d6cb68abf0e12271faaccf8a203624c2c72c9abc517e4121f54fe2 a28942f3226f153e19398ae230e59d5d5dd304bccb0520665277a0faeaa3111b c5958e222daf1995e2440463ebd8ceeca1ea2d323736fa1922b474a68348f845 681d61b4bf644f952410d67ae39132e392a7189df17bce351ad7d79a13b7e5b9 81aca839e1c33cac128c4749046b94321f59fd9fa1bf92dab8d4ef697e3c6d52 6c5301e1fa2821ed10cd10045ce84a2e826f483c34558a90711f513ab497ed33 4284ed34d775c27b254a8911c5bb0a269a801f9fb59eb838aa657c35a0573ab3 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 6 /plusminus put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 88 /X put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueXX 5000817 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2 75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6 17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c 7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2 72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b 98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2 24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014 ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a 4a93d9b87124d146d8836482f73a24389afb8a74364f22077cc3fd6015cd4469 c34470c86925433a77fb3c838a1a7158139e96980de23ff461382df32c6cb4c8 59d292d187a7c919a1c3e51647cecd04d7e091b936aaf37b758d1de4f684782f fa7a4aaf6595c788c228079975eeb7f7abd394b23dcbceb355eeb5d49d2d64de f98a42cceee945385f451ec3a2b703e3f52ca1096e7f980e6465450bb9e6e31e 60635efe5d6c6f1ed8aaba6f72fe2b2b7ea10b1a30cf5f20f3ee1910d8385537 e59b6d848638ddce2b0346e0c04ee91c634caf9788ae366f918192b22a3880b8 543389fa75d9ea905b2087c500f7a86f63dad25384f63b5be8835e90723d1380 e94e745464b7fe84681815023ccc85d01bfa99249a6091acd114689cf29c1889 b5036d12459c8537530592f488cc28191d5190f5eeaac8c55d00d64c8b548f66 e3e0299cfce1a742f3e42c0412d8f47dc55902efce4f21945a420c15b45ee9e9 b5bd58f65767db80f5105b7976825d7de4cfd7186450cede8d876417b6a70a9d bf39be588c3f5259e5ce68fcb688792ec3787df836717df7576d38678981649e 4baae627d97c8bd0cf845d756127f3f17d0146a46e5984cd67314f83779fc11c 92b105613b792e27abd49b714dd4e36499b961ef8faa01ac84fff8ac62dad0a1 2ff934aed9861f3e809644c3adcb5636cc2c3db159603580d8a5fcd2f159d2e1 a9a6470889dc21c24bbc844d6be5bca3433a15f9eeb51cec3a1bdb901ad9f667 d347d4eb713888297b49d7d2160ab6f34329cd94678ddd485c6f671b229875cf a80557f17a1d70e54b1967c530dcd6b7657bcbcfe77d2199675bbc0c8be3d001 2f32299747f2f33a9656d761f1e61a4170853b6b6db90f94087bce5627cbc638 9fb09895fb120162fefbdf379a72dfcc734dcaecdf361c7340ac86a9a5193101 37e2cec5eff50e3614d185d6c8397ac3bceab3df454aa9d9afeb5fe8f9be8ebf 2a64d5412c118ad152285627760738ce1da8285a7a126aafa5469f607d70d8b2 baf8744cd2a2f48c8805eacf6dceeabfc030b84b5a63cd4f7044cf490e41e081 4a02d6f113222a430fb5374a31ba49f314562fcaef313fd5de4c9675af57ce16 8ad18c9ea6651ba0f17d8886cc3f494fb310a7887b9136105455e993cf6af343 0004c6b1a344079dbf60fe74dbe37323517b50185b98c48689c9a6148e573b4e 30b8740c28c975390046a76cce08bd4bb1b4a1e66af16c06f40343fb46eb278d 984f198573ddb0755cf82936ba05e7022e76f07c74b8a9bc4c6a806b9185b0ed 816f2e7f7ec8b08d2f99a35c978571a0b70811ad000088396aa9b57017cc161e dc0196ae5b9ed4baee0662f03997eb206908ee566e828abffbb1211ab6cf00d8 88e33ef6d659231ccd3535f10dbe04c48f69af36baf8cf43585b267596fcb9e6 7b8f85910c9989768495d594718377003a15677cc93867925a56965696596a44 5cdfafb701119a6d59b7cae48a0c7f97e4ff731b1d03132997ddcb49e7d8b1d2 db03f093a0696b54e483d3159130f5e2944d64b178ae76396f8c98dd5f795b2f b2ee2cf720181563f93384239b5d13275543363c98e02ecbc568490a6724124d 05650dbb3ad758b14e468d326bfffbac89a81ae3625a46706178bea993fff72f 583b3088fd3ea8944ea696ddbe497e948e3235b8936bd8b83247c239d584f3c5 56f60a2cb9b181e19974537376ab5a90f29ab83d61032c3fd901c8a8a0acc016 c440ee6379f05dd0366d480d9250e312d5cc8b5df61eb772dcf4095df84cf409 461b8b20e12d2aea3f12927b8823f6ee9c082abe7ed252fd8eb754765c5c78f9 901508300c4ac133e12cb6763a1fe3b849ba761b815b965f2eeb265880eb9b82 d2486db5546337ff208700a88e56a7647d362baa64d382be1ec441ca24a7bf4f c922bfa22f32859e7273d43c1594efad46d0c1dbdd57c90938c6b93e28364d0b 89644a131eef128b9afc13c412f1999515be3e594ed1d18baa828f3cbba242e7 ec347a8f7f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 24 /xi put dup 25 /pi put dup 27 /sigma put dup 34 /epsilon put dup 39 /phi1 put dup 59 /comma put dup 61 /slash put dup 63 /star put dup 64 /partialdiff put dup 66 /B put dup 69 /E put dup 75 /K put dup 78 /N put dup 80 /P put dup 81 /Q put dup 83 /S put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 99 /c put dup 100 /d 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 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueXX 5087382 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489 e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e 3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781 25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead 4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7 546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749 a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82 ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96 0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0 24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772 0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2 364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba 0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279 617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a387b3 80db88cca083b06f5af70d768d1699826fb12ce12efc2b4c70923e052dbb964f 5fa957c3ce225c0fda64d9b5321ee1ade207c1cc93105096cc73118f4082594c 8ecddeb0d7bfde6f70bc62f10407c26a476ed88be7999d64a15912493829a9de 62c71f5a34fbf5a843e311873cd98817dc9f8a4aeb7e0738b5de10043f5cfea7 147908151b1bea3ac8852a244a3ddfa721781b8b57f77ad9db0fd935bc57771f 19b5fdcfa433f1e2f581708dcde2b659bdef5f81b0a80518270c2e78ea32ea5c 1af2d99a9fdacf3a34eb2d608e9164c51e769cc7db5637577798c53480a11a94 f6823082e886262f64bd327abc33178d16fb473dc97554a22246f1a1ba0d9c44 bed8d95a2a2224e8007fe074253ccad7428c67f816797745072787cba9e54a86 dccbc2e4ac13335f24c599dce1f6130abf0b4b0f4fa7d27c2743627e74d51127 d959c3f621f2153f99d58d467d7413fa665e9e76020d31a1c0c8013054275743 eddb0d70943d8ea3831b7e4d39af92b98ebb10db98bf7561c73ff67b5c219006 931cb3e934eeae7091d6162ae302ec2f1d5ecb3835eca29dabf83f54909165e9 724d8a91ac5c101cc72a35b6d97cbd4355296a27415041bc13947914aef428aa f7167121867e9fe4d7a5c4b4a0a081dd10cb854241cc309da13a7e5e1a5fd4fa 5fd09409ce8612e4a83465e7a0f9e8582bd036a0f97ca0c97ff4ebecfb109fbd a2092cead1dbf5222dc4ceb65fb9edc2253ae4165caf4360dd0bd1d7fcdc210f 1291f9902c9de8bb77f0976745d7a4fc8a5a17bcd56103e257bbe7cf5f6340d7 043bec0fdaa00bf79ff54c52ffe594c2479caac7ce7808f5c8b9b51543b491a7 267b20493d92207a1966ab6d5af53f26476dbd52b55935b57d679615e43a9068 011fe6364bd7aa634e34d7a10b0b53527fa291f1ab2632ec66ffab654c516e37 477d420f0ab8a4c7e59c03a3718020df627600d4e9df11b959d6f05cbb8037d8 87fdbb86da6bb72dfd63d62c3c8d0688bd88f4d4f6beac7aaf8523e702748c97 6e7db5a7abc322ff78bda7dcee3cca321fe494e0f51d873e79390778bb082837 5f433f54db5286e32a4ef18499a9684c3d01e72a5736331c1be94c405aa5901b 86ec7636f11c07709ea0d80211c4ff5451eb6dce424ae48cab1b13ccb13e6f89 58505ee75be031a3dca0f8477843bf24bebc74ca2eb89a557f53179ee2115f26 fadcdb8628e86d1a605a6c1f6f07bbffb8a03249543b69644409da38aaf8350c 49c4fc33dd7738b43a6b9f99b33eb6bdc7fc1c641d0b52530aa6e8b8fb6a2e18 57de41b7045983deb04f5cfbe0d11d59fc0f61092056fbd48ffcdbfbf0f8d738 aef8e50269460f962c298fb58bf985fd75f07e61f9498dd8fb7d27a601683d0e b19033cb15f8ea59163c8e94b6460d9245ce1c967ad120dac24b4ec418ba1994 f0137c14e01592f852021a9c029e29bd2eb53946b4991ce9b4b8b8bc9502602f 465bcf4b59bcfc354f87adfd38d449fea389a7fdc819324930fd31c1158a597e eaeafc719dbf782306fb24d4f09da9dd36793c3b750d78af189985274aa24c57 514b5448bb68dd47920de99787d946a547850619a2c8199c80552a04951eddc4 7e761a7787e5f80da3c363a272d60c0e0f185b1099ad6dd3f61fd8ddeb3e07b1 9a2b6cfcc421b03f2b2466db6f6c01fd20d55875125a5011819e15343c621407 6546e819969791c65b49ccdb9ca034b0824a91e89226d5b03f10183d9d404a05 9b96b908c795c2a37baaf2fe397ef708ab242fd6a025099f722f494345502ed6 edfea285261901df514f15966b5f647f6b45ba752b93df4b6faa413fdee3be87 b3ae036ba3239b8b7d3b953c06f6fa44342b0cb55de8133e01ab6c453a05df53 776606159c9db4581aad95ff825dc7fd4aa8365b7909333f66b11de5182900aa bf30a8a3154e1c012b70a0de3cadd688f661221188a60d2812d519a68d76e056 a76daf1f4bca118edd454a1e7f5b3e7b81576964a6fd3e3aae628715ca4e391b cf405932f6640b6a7348095345adf07b683722f328f1e845672faeb3c5bb5210 98b3d84ed73c825910f02edb5e55a8abf4236fbee3a325066f0be17c5ba03d53 9204102b879028e3a96307fde0ce020e45feb9691691b4c8695db89016d0a6eb 361e7f47ca1ea066177ecd99b5aa64532f8c9609e58a0ac3a2a2825d0ed5e51c 301d931fff9fd86b35b4ba6f7f10b7c0f89f9b71624fb1415c7f76f1ba62c650 886755a28abd948cc727bb231ff3ac14611aa54076507620f4f70ce7ac7bc756 55bb64c23d0e5da609f34894956b89d26b49bfa53e14b82a1988b17b28797b5a db116031fa0e098187483b50e6ffc96d23590de3ec6c3cd257cb9f9d769f73f4 a960d4bb1d41ee2de905e4d0369461cfb05ae23e744f013b6caebeb22335723c ab2ebe6ad8feb10c31a0d4ad9c26d0666075c203971d395206d55a1424685bb3 109f5c59e7b5ba647ede39c41c418a974e56f17cc83af34556a32f8a045ec5e8 37168732b0aa711d335ad5fe811f8bd759366191d34f3569db336d861cbe3c9e d2c8ddf595fb661f73f20f524bfc7dd652d73d8660df4fa790b047f38a24e9e1 3632121a54b98409186f1fdc1ded43db4a0e386c66d32654f2ccbe04b96ca13e d13678aca9a517c6748da9469eabb46fb798a3211d72abf33afdfee19e8e8813 9ae545743ada0d2ba3e1ac510caf77de291e6fa807e4ebea900bb016aaabc01a 175916bb299bd663d36eeb88c8d2a0c8c823da35b1f57bb27cbf5c5f9a6b9bad 8c213a3ebd41b3d954a2d9033cbb124baab066e4fcf5ffe9d48e5a461518efcb 8b441905909b5ef9812f1f2804183244f72f1095e641037cda75e300fef8992c ce2e6e0f3ea90ceffcfe75223ce28c563118918719ac7afa7509326afa8fa3a1 d12cd3a12e3d93344a324b6cc7d753f593f7397b1377b1ef7578f6006ffd2005 f845af1e451731416de396d4b7b489e25b9882bdb31a19ab2b10e0882d8ef1fa 4e93cb8ce150df8fce0627510471aafdad46a1e6263e87dfcbffe1ba7cc2de2c d4c8014f225242471b0e1902be5aa86d26a276684c8bf3098cfcd533a64b734f c8c15404712be99d754841645cd9d461b67dd71d7e87a5457a05a9f19a4b4336 3da96df121eefdc61046333aa08106f93cfc926236d2945def9d80e5abf35cff b075b067f7ae864dd6d4db25a52bd54c51d7925b53e0f75059d5e6c98e2effa3 7d84194aa46fed75ce8378ed075febf43ca31f5c185d3c4589420aac65d2ef29 fb35591a5fab6ced43bd1078ef35f24b58a9caff7a94bb43ebde226563697ca1 491f5054d3b06b3659fde1a27206ff99bb03e9974373d76ff5818765a30a7783 743ef630b97904013ea918cb6a559c96f91bbeab2e3fd7f8caf9ad7ed8f68d06 3d7b97a034bd1ed1838cd598f07977e9acd99a7500612aa939f5057c95d93d23 f1e5094a1f33eb72092bdb3ed8dd4e0ab6e1c19fccc829603a3e93e1a76b1481 e9653772d4a069319e000f9f4f8aa2a22cde21ce5a36853aeb87de53e33d2b22 ee6c2e40bd1d06a416d1cbb9c81078fe822069c08116b45e21f6f2e732b58bf0 44ded32eba00c3c80fe7024051d52768929b2a3a7e66254d5332cd1f0d28803f d69365f1179b9dde85cda583988cebc0dd2f5f694d6d7d9556079738774138d8 fb4d7848d81f078f09a9b9782d5c26acb76c7a39f0f91511e7b966655b5b890b 8ca2ba8ab0a29a88b9535f3d9e2ab3763562b0ab5b8576c94345142a49726264 f7956d6d339c5e5f4be528966fca5dfd84ebe06be883f8d8bc54510bccf53219 f9a45a4cc5415afa7ce6775c24ed850579b36ac4d31fa97f63cb834508e31a65 aa2cbc975dd7d98e3319f3802e1ffe3eae0f20528a0e2a61c9506a4f41b12e48 c71eac687e1b91a28f7c2235f92b9949edf008ca3be5736c2015adbbccad625d 6a7c41a9184d8253a1850a8de8da8b3b3a6cad37a63717b968aba9a0344108de 0d2dd035db840a8f2f71f36391b43b0faa72c318014d5dcf7948abaa4c1ecbf7 630e81bcb509252f5c773ac24e6ed5e724c7d166a361bf2ddfcf350aba110089 d3ffed55e219936196699bba7e1f7dec634d0f1a77deee959ae974d74a74c956 611288d6dd037d4acfa93fa240560ca04d5a3302df369d13bdb476f2e73c08f8 1bb89456e474e16b87826c694055ba7b74f499b60b6d26f9700db1421184ca4a eb7aa66989b7f88a10992406aac97134d9af589e1104ee47da61711d16bd3d9b 84d3cf1d032a448c93b2eb49c2a463a82539df142eff56ddb4dc07e71b291d27 2f1c1d8cb9968d872fab9a6e24b0fef43b8422fb275ff2a4ba14b735d3ba2486 e76997c4b793a58dc8897c35245e93bdd24032864ccc84c420fb0f40de04c6fa c33fdb7eea06cb780dc1298181d49abf8667320aaa77be0290f7a315ee27eb41 4c3f6c0fdb82d315d61c7d165bce5708a45cc5afc5372c6b834b457a0ec7cc8a b19db6244103f893a334d7629e1f2bfc230f737a028323bf68cada6d5a468063 c500070c499c340b3ffac2380c17402129f3e3ab5609b98afa71df202105ee7e 5258e0e7a88090f4cbcd03df73d3e74553849a0bd49562b6234d3b8e43c7b9fd 01e7e8236c5b52a3d36c6e49f90d6f87a440068c2e635e917b551eccc37f1f6e 6479faacaaa0c58d9d317b1d532682612a35e469b70690ce32db8420f8b239a1 dd0eaf66ace05930e11872f8d1b269465bad2542e0e5087afd9c0edef521514e 172442bc8771a0b02e0fdb8dfced4cc8ba80c019e11dafb0b738d90c24d3a1ee 7cb8905169c5a3320229e4bc46b13e3f5ca13b253db515609aea2ad5e22d75e9 c64aae0895e53b761bbf5c768130020ef765619add50295c0a8d79b4f5468f75 15f912681e3414a9245c94a18a868556d9180ae5dbc1e8089951b7087d5e4188 e6a3f99311f8f7f376dfb00ddaffd90b9887d7b8fb673da48804260d1a5bdc39 cf1a8df465c277eda959805a28808d50b546be4fa70857150cd7ab5993dfb9ab 599da58c8e6dd3b693747b41575c669567c09f4a54b48e265a45d02902037f7a 5aabf0383a52d3eb0d2af76931c0c1b0468a65bba66dbb6c60ccbbe44bf7da6e a7b6a62f7dc45c19a2127043fc22fe8233a4db311df3f5f366bddf1651ee73b9 e7a581067ba3fb18201a5b1d6821194ee1fbe71f5c9a5a0482341c0f8991b20f 8c9d68edcf2b621b27b34ee510a7d73ed89b08defe60b304eeb385da0243ebee 7140cd7e7b4eb88cbfcb596b0e481db3c74cb82b252c7ca16c907410b9a7d785 9c8f707b7e353f164d29681cec614570968de57cdf776391dc2249697aa30e33 aee32b64557fa8a2f2f1e50df89be51d798d4ed706f539bf12954ed7c2f3ec15 782776768ed8f12cdcdab8b41849507abb88e71f87ecc7dddd56a88a73f84d4d 807ad9085c120b3fb36b29ed698915cfb972805857983bc543a03d6297350e53 857bde7cc13bedea5edfbdfe75c6c10fe791c6f9d256ee40072efef37ba40e3d 419e77bda0763f5e3baa8011dff6effa120611d5f21a581401dc4b2d934fda6a 96a91d8ca003dc197031575d06eaeef5f29ed59e9692033cdc0f6490b1ccb1e4 ddb5791baa87e1111a640abf82a924e7c7e048c121cba66be4f9bc355b09d12e 4eb478245261869fae8159217e4c7381fb6c0fa36989a55b0b1e9e8d42eb252b fc3ea69b973ddd6d714e5687b4b5109b74e9849266c7259e66d86ded9c583d34 6ed7489451820fdcab9c5e31e01a98f85cbd90e97660ad50033134ce55d4d644 03be1efd767daff1781a54000bbcd12e910e7a255448af3f42154c0120abacf9 9b4e4acd38e58a4af8743ebbc2b7c60c29f54b8a1608d86ecc078776473f3881 757425be04cc4e01764f98b4bbee5844902a5a03376898f91723bc4934ee69cd 8e07cf2913e6ea41fc69ccc4d01f90a4937c59dc1b2739977cf40d49f32c21b7 41b52ccbdb1e208818dada484c4c2d1fe2ff974c2eb045d0c505ae762b9d8b7a 02de026876979159e26aa63dc2c9a155f452a214f05809b429b4fb5f7b15d39e 5be199ae2f68fc047cb0dea2c393640866241719b0d26994e552a9be441d6809 b5c0e3a81c93924dfab8057dc933ee8d690d3f38c10e8afcb64a6926e6cfa6de dcbef8cb230f4ce4bc9e39f8cb7fcf0c1c9797c3da6a5ee0d56a7a5b90afb95b b12c6dd56cdfe114aea2773b24a031c84f1e47727f21bf6c4504c3ebfc7173df ede4e265e8d91a9007964b8a590393ac5a0de5df194989d3651198130f1e34c1 672ea9541f9094cf858203cf2750af405ffa7e954345bccf19f1af29c7ed3daa 18015e9da12499ad48837fa6a4308cf0b0e89a8bf9bfb7897f7374483a1ef54c e5355837567e956ae20ebaf84300c1a246caa9b7b1dda0ab57c939b6d1b6164d 3132ffa7eccfcb625f690ee8f91a0a76e505fb2ad653fa452e8597cfd080b46e b2eeb23fdb637492ace63589afe92a2b07f310d3751e74a85d8fc5227886f948 9d159c08940683a8834c3f64e7777fec1e497741d680fc56f242019eea354b02 ce07dfbe9539643774c1e8054af1ad0031188dfa62f85b06bfcd0f924d693097 88fa45df1ea2c89a999da33cd71083e9c719e27abc8f49e9dce1a648c4d07f23 655101dfc0d649ae71e8e8ccf69343258a3b7ecfb55001f74910952e2c8dfc4a f0ec5255d07de29dae5f12e79a25cb2011a41687ebecf790808bc038bfc3e713 1bef316580ad312b468273c5950f298784f67bc4334c8187a805fd977b023d31 cbeb1f1b7ff7f727c284860d118f495ea7d782d3855eaee311073e83609bc7f1 3f534da3eab44908ff3089ed2efd3a98b548f56795078b8935e4887a9d23b8d5 a83a1fbf41a70154fd81caa45a6e67a68b2eb0e88b2e42a6a8798cace014f997 6c6a089e01307072854a35394709078c1e6e0b010d7e9d18879fe76f2b15ae1e bd4a7c5be8c8e8315a829acab66d15fe5763295cd8eca8f24206e7f2cb64d51c c96ea6a307b02b0f2e8f574549f02441647b9181bf0fca90f3556ec9f9f232a7 25f0a3b3f941841299c174e76d80a3839fa7b965b68eb462f4ace448a71fd67f 61ab04683af7af690816fd89c29ee4ae7554bac07e16f547d5be81a38a12b82e 344480c81b52cb1e9803a78fd9697ec5cdf40d582680ca6f8262e3cec6cc60d4 f740d1a555e1164fae8236fe83a4553f63aca19946d643e711fe1658286e9f5f 9e965691527c5e06caf3d03c86aa7c2ecd8e65012bec1de4c80f68592af0795d fbb8bb7518a2419b94117aea8d956305375aaa58b56b9db3d3af89f06616e458 adfeea53d61a9a601eeb3eeac1e70d8683bcf2026abbc1d97b0bd92add54e7dd 6653c29671fccb9b55de8d2886ca9ee29fc7fa9b21dd53a25f3436af31a2a2e2 0f4c547b322f51d73d64b460be6e656a8e05053ed6ba41ea0aab4829ef58be83 7bb3b3cd8ab486978e699b0be4d9e0a94c321a4cfab332deaab7a6404a476228 55bfd1418a491611b96f5768f7a84d843d1ba4e9bbcdbb98f3a008d094a8c0c5 7d7bef577d2af444e807317e09dcb330f1adc519d5125be7d393065ad4011c92 2435c17a36e30aae5734a4a95a512d858d8a4ae988b02bccbeb640773109d531 1678affc4efb04d7e6c6d5ca059eff521b0ff33853644165d847d07ad0109a09 aeca8828a113f0e489678be6778be6198d000126cebd59d37c9af313eff9033b f0670b99ce785c3fc03d0cc49e10097a6288a3e031d200a9737d9a57b1b37cb9 9bc45673ec00067886883a3d07ae4a8abb9debdb28088f8de66915dac479fdd5 829e9846f219ee966c0ffd4c5dd544a33916fa81049fa2695dc63d603bb064a3 f08d0260862b86570c776c591c3a2fff049bcb33414a033f0ebf267b1565fd86 f4e880dc72257d2b62015d8fa507383f4c4aab75d2581ca7e6b45717dfe80d6b 93dabe7b46ab8a257201eefe174eae68425175238f420854ee02fdebb0f03433 a7b2a56807404505bf94731be0bf8f6563ed6ae3cd3f6d82090e513f51d2c705 5b6954d4a36511f24ff17d23bfb284a5a296f4e2b6c441a00b755a7b3c77f0cb 775da0e8e4777931d725469f971c1a83e5ec890f537d4240fbf2e9484754bfc6 e48881ef5352b29237db5eddbd71d7c98a7c6d7e051be459f9303550d7580a8d 65b6feb79116ac537e3cd855b69ab1172946ac76383188f371b9e98fb869f1de 2887fef30398545f0a32a470e5ba7c931f1a7d7b6aa6ff2843ea0be48ce6dc87 ade1e6e1768f1c877e54d7db4a23196ea825d7a7cef1a1d07ffc1228ff47c15f e95556a488533810cad618c441f2084e14d14853c8a29be36d23cde17c825e4a e65084e09b60e9f153f16844bfe141e287b726bccd7bc367f44d93c8c141cc99 cbd705e34cd0e59cd43af3773f112dee7ad371bd7d887866b0ffb872ac1c5082 c135986f4ae7aed66bf3923d301592da54a48feeebad56a73bca1eb3fcf01526 79911b0b4ec503574643d34bc45e4cab56c2627fbc5cf93bf535083e30cb2b64 25ae160a3eb776bba2ff46e2d86b118dfcadc405585b7ab2d783ab82af08996d 4818519ccfa2fa477acf222cbca17c064e6aa7b0de6bc3b37e402daa2ba4f5bb 4c0c54855bcaa9dfce56ab4f544b6548d3f4685b4ac9be85fa493390bb2537ae 9d7add8f026ab52e5e8c115323b2d560f231d433081f07ed492be92af3b20f6e 7fe4b17de43fe25b6d6e04270059fac735efd89f187dd4d5735a4330741dc59c b5bc41ccfcb42b8f7aa2fb35deda5f709760ecd03689e423d084f15f3a74cade 582e4bdd5f4078fb957b3d8512f994e7ec8caf20e482f5760fb792fc9262e756 681c724e7d0e779bea21d2ee879c0380464f9058c360254143e17f502ff939da af68488b6b378d4bed0243b4d3404e9719d42045791884a31809241ea6ab5dd0 c0a0396e7d51e572ecd115e9f4629baa9e18a90e5f44f158b98a49a978496db8 a9dc3d02102f9f890ebfd99d691a02cea75c22f83fc019cbe20995d94e481b36 37d9c813464033cd00ee00ebf3fab7d9a2ed797d97f922106ca6bffe367aec3f 6555a7b772cddd9f5344fc05c4bcc5979b780a0f9c720912ec3bb53ede6d5186 b7dd18a5df909f8f1d3d7545e57ee4bf90fb4202d9c1be4bf0bc0781f9e2ac4c ad997416d69bf730e3a1d7dc2a9f9701de02fa273274a037d440f4d7bddafe3d 5f7b2f75ef1ab0a1ff83281a6fde1f6f49dbf9c21707998bd3a0db3ba0ae3346 34b890d6b22fad94c4b838ba1016eb3a130a3ce66c02a3a410aebc0e9c4c6eab bf744b2bc63dbcf5ff9a1a3766a0fe9708040e8d0e54a5751964f549c1f1fd5f 291254ff34284cb91b9d9492b68b0e236ceaa0fb9c134b86ba55bb636b9cadaf 7235ac83ae2ac968cbe02162c2be9afc793398d0759274d7ba18aaa205cce379 464818b30c91f06c34f0d0d18a0b164ac2151cc80bbaf89e2f0e52ccd28bfe83 043ef561d2bdb165ea4314aaedd3b0c11a4348435ff8e910c992058a73ba4849 3aa180c56fbef98e5774021ba5ea66a8e1388e019705d7677a57d5625178b644 e5e15e4d6efd719ba530d67debdc102f41c2c1329c0f4b92c08e640c7857e68d 63577a9c9024617d2b9d66cb7565ffc593e4914db34d908f46020e7d0de7bfd5 5d423202198f83fef641f7d986e02a35e6a77fdef404395a51de957cfc3e1606 6cba6dc0df65dd97bc50142c318885fe84273959741cb7594e4c2bab84d5d418 a12fd5d839bbe8d38c553b594e1a0fd9ad773a050d281595dbb484e091c675aa 1327d141233ae67998799b99c7c956ccdecb456113646ae08e3a63bb181980e7 345f5d40c783c78e29142c28de1d45cac4f8b32171807cd06878de4475bf866a 72e2b759e88b1312c6fcb692abc630d4895933d1cef90d685a957ac26ca85d98 6218427c7f5ad0b3ae7c81e08690e7cbdf8ec4a14171d135043a1c65b1cf8924 d81c31cea64f9e68c31832bc19cfd3b55266a3ea9e0fddd0b8968cc8db5c8eb5 de73f11a7c22c23b2d782859470250f6f37fc287c333a9cd4596df9d4b44a44f d472b379437352220dae4df92ee5531848f1bfddfd1c1b05e2f1fb1bd80994f7 9e191cd7017e787e3fb4a19e3f4947499d1920daa8a3414511290866611060b3 27ec96a572633ede1c02091b778722d67c7b8ad0d83139570e54572a03446da8 bab48976c145634035d3b6ed08d6e42181fdd957474769d97fa87de3f232684c fb7d48e4c98482c8d6b237068697fb1dad81ab84fcdf431ffe10c9babfcd74a6 78152e87cfb3028ec04ce6e13c354e6e5c3830c3f589e1f720ccf7c1bfc95f4c 625413d5cfb8a522b9f327842b5c33c893551c0d44614a49167341d800d514a0 49f520547e0e717c85dfda0b9ca83167aec6d0ba88b16a8a84b94d219fc5e2d4 219c689d9b99ce0f355f46733d3a058a28cf7317d231cff1e1ace779a079a8ff 146ec781cd12f2af234a18067e9abc2f4da020708118676217d565fb475a3dab be767c396ec80b61504360184c471159257089ba8570a9ca7f069e40b64eef82 41a2be62f896480476c46986f795812f70fbd7dca1933427dc9d2de50dc5a07c 59abf01c3d971f59ac03218314caed68f1134bfff896b95e3fd059bae1fb88ce ad9ea146eec964bafc3c04704f4dbddcb22e614c6e0b57f189aa32c3c027ce81 2a9b6852df9ba8add1f89ea3319291bb683c3b9c8754cec949237d3f9a3eae34 1d2357536beeedd50ea8d5d1fe8eea3006607a1baa53328f933cddb92d5e04a2 0354c67f2a8d7f13a4638fed8586590e90464540b679e4a7c70a8f6b69ca4031 171e1a6e3190f6761780ce9ac2969a272c7fdce269452f1ede0100b839ee9c48 0435f8a4e203c4d646afa1b68c4960a6da68be1588adc1fa4e3fc14d5b17f2c0 70190a273eb901f88181b5b748b53975f53bed027eb778d69f918170aeef2fa4 23db1c496fb772789b9e0c8bb14de277a79c7d907038532cb3e7ca338bd72124 3357f6477a3e89f78c9651b677ec0ce42d82628a4123418c507a605207ec9f6a 01b472b6bab9e0c8a3187d2a2d8220b2844d97575ac322d8acd19300487cc0bf e36ddc3639e8054a90cfea5cc384a7958ded6c44c175dc5c9a7de60d4629b816 14322b4ed974fdf5b757554a16774b1a86ad912e916cf365b49cf1f3b4b46d05 8c75d3c3c3d91d2ab960531b1a578e63ea3ac69d53d766c6586de4b5ef3c4278 84fc7ff0d50a809180dfe2291a1a60ca0ea7873ec6ff0f2005e4b8845eb20e15 aacf0fa5e36ff581a2cec3117f1953d4420dc0f06a63e2c24fa806ad1bfcd351 00117ce79402ae06c750c7730aa9a2ba6798b36d6ffcd0539805ebaadd3276d8 2efe79758c9dbaf89bdef7e8f630403302465986615f77a881664f1da409a7aa 5199375a274e803004fbb34a21167443136120c76b5cce19645c2963315b3f36 fcede46376daafb91abefb572ae2db5998f2f177ffba9105d614bf7921dc4c24 1a02217d45393a12e0e7523b77ae148f6666262c6e72a7143385fe5224228965 2458c838092a455efe6b9c44fd5a811a79c180a7423ca05ca955f3473846cf65 83c9d25448837215ba0e3ca6ef7212c8b39f955e0a244176132bcb57203066c5 19aa992ac5fd4c68ce83d1cac37ae510ea93fcce9961a78d5c978e534b284b39 06bcde2cabc85b228805cc1c8241bdfcda7d8bba70f3ba44ab78cda39a5a6e60 20e45a499879816cf2157cd5466ec05a4b0d9310beefad955f64a773a93f494f 801e27ae7b2657719959bfd3ac83f9efaac1fa61570bf6549ec90ac491f46e3d 3f23b1b316496cd9f89f8c9f18acc04bf2e29ec3319004045aa4013eba36c94b 0b200fcbf2d5bd40462dfcf695e07cc2148c27d926e76b1e4d8421b78210e269 bf5fd72713274bbd90a120a93683ac84ba122f66399afb930e035c19b03d725d 42a4d6c693d117ff4e44f04ef56541c64f9ae01f42771908b9be50e9a612e560 cab569aca85fef70bd25ec0a1c7f6c93a5f9587d6eb64e92d43e59fa2c2785cc f019315b851c13e8ecf65830a90ccec753be657364646701a57b2a46db779dd7 d2dd41a4bbd21c2f2d89572454d072a2090befb5bb42697403f511afe1d5fb1f c677057f16b2cd67c7b2bae0b15526356d52a16c2933187fcc9ad84aad4c7f14 9389ca5e7e6c54e98bdfc4ff9df9e7c76d36fbfcfd495fc256db9a8da31e7673 59e1f7d9eadc7eee894ce0505139ea33d2a804a95ae1f31ead1919c5810adbef 43f8487c664f828aa23535115220ea30a591be3a5b2f153102c36dfcd8b711ae 58ac8c47e3b9603e333edf271193c70f447368d0dfc7d9250c1db7627d92cc43 e092774cb921a45f2a9d8f10ee55fdac9835c35e901e9419d3f0eac197411603 3864bb517edcd257912325c50767c9986b6814cf34429383e088abf6a9ef9d6d c1846d32d13f252c07349e14848b8b429acd7079b1dc6f20ec84380da9d703b3 e7e4ca74db510cf870f8ea55491ab660f8c1ee4b96345a03ce4b31e9a9ec6216 6e22bab1230ae1f83ffdc2105a4b2bef64a74873d0ba589aaffa7b30e1694faf b8b5b2cf4cf8274e25e478946c230121dc039744dee55ce15859317d4294478b 0f034c4506d622d76cce370600b7685b0e315c6732b2a57c9e0134f763e06c20 39c4fa74b3f9443db16d883f229044cb6a9dc5e5f26879a1c5cf44c8debb1c04 1151a3a3d6d44d3a3222349169e5b827946d43b5151f43770d0014e2946267c6 406ea6d4dd45dde7aa2144e1fb2e5b9ad3bf056c0e214e9448a771c595698605 53a8a10924e3808396dc06afc629a5e1bf5f13ad386369adc91fad2a976f52bf 5d225a6f3e084c2d4d56fa9dc872c99ad62f3d8d5809f2fcfdd9e7d148bea93a 9b76be373ab9a92b4cea2cbf1ad485e5567470f7715a5918908f16e5ba85ba8c 6234278e70765a2f1fae3897cf0045351721ec17ad1962ce278285626fe83d0e 8c0f789c1b12d3a8b4e2f655b048ac0ba9604428b5650f41ce7b9b8ba5f1a6f0 edd6179cf10b6270e7db8b6d42b0e2b966eec5ec87a2d381ba3e0901b2cc7b4b e8e7b491d0b031747e2304a1df8bce6be8edd60c4c15078deafb6fcdb5223c 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 78 /N put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueXX 5031982 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d56491bdecdcafdc988206c5a457a19270b 37d0ab776e03eaa7eb568eeab6b5e79dec03b0dcbf923a2aa8e4f4deda2cb043 858d8b430efef0ed914a80ffc9818aba0fb30dae3694e5b31df3855892d59b89 7f82ff79fce8444c7926ffc4ea008e63bc518936c9098afc2d1c14030a2c15bc c9285c1b57e80570d2f6301009e63d9ddeba44e3251c75ca9616a2c5de9ade66 1a15db37b40b67c1bd71f77343912c62f47dd24be0e03dd833ea60d2eb020407 eaf042fed30f0c2f01956c83d46d982b50dd979c2026ed5f71979dd98c9c1eee 25054000a5eed5ce9498b2cb59a7ee55e0538ab47d86e69b2ac79229c8c6bfc9 3a24e822a2f1c9964fe630344579a25f66646113f73d1315c447f070c575de76 266c6773b01137e4a039df5e4c2f199e8e3396ef9fd001eebe090e04384c4089 ec9f13a07ad8733c6af775f432f154ef50ec4477e08760c03c006e4d1eb1c7cd acb8955ca4b0d62c7de046ff58d431bb9883d28586552c51809e3ced4dfc2198 b97ad9e52ea33c91b9e335a80d9b77d3430e0487930f992459664abca5dd9177 150b0fb502fbb04ccaa94ffe2697ed07906f95fd98e7b325bfbf10ea6b39fd76 c1e5295022cb39e9cd471b7b0b3f9d72da99deb0615d35cc22f42dbf5cfb70dc 6279fd520d99f32201abf25e621cfe1d37961d9c0ad36ef3d9264c547638152a be30812b1188a10f6327c9e8714449de2ae636420f56a44cebd774f0b131c629 818455cc8dd8d40939f3ba8aa5abc54590c7286b172193c23adb1b4f9931a9f7 73b960b1f5b760438028478e4442dc93a567b07e20017c18fca2a1daa2649dee 5a6ec51fd6c3f4b27367c31e95a56ba4bbeda0493bc02306037e2ba69add9b94 373364db316691e73d6811cd76fbc92b0c67ca18dcdf05807f17d1b309456ea9 d113ea0fccd6eb73bd8dfdbd5905a5e38bbf61cfe58fb01ec95a4bdd9565433d 4a7abb8dca6f76c459484ad29c3480b588fae3d782340da9ccf5a3d15ebc4b0e 37e0e981f80deda1e9edc94ebc4269488bc7d09c3feaf61f454abe05a5c41289 f919b23cbd7cc570de9de9854d6be3f91530fd17c83115c02f6b34beeff7942c fae26f720a6defb2716a35ceb107fb9fdb87b6bcc3481ae05e08ca8eadc508b0 4b7ff96b6d32f54dec7e8b464057722370f5903fbc264c89eb31ed7e18c1a047 a7c173d8e80fe2fe10bfd4ef52781a5ac7d618463633c73d8e414e9129e2f05e abf6f3f2e9ff1a5e48863c810ba563fc8c1a1f1945422414ba0eb4086eaf68bf f0eabc6258f2d9015cef22a54c9417a293521eaa35917ff95937ae1b1a0dd3f9 98835ce49a704000529dd9cb93afebbebb69155c0b158bc0aadb786f1cde5f35 26cb4dc0baefde30ea5e277dc17e6037df3fe03283cc889a55498040985817ef 6af3b4d335e85314aa81a6fab86184ecb0f9cd53ab6b52673c6e0ce1afed5e83 50f55d705184b3f2e1f1ef51bb8b217e9f5c34314b677b375e7099d51e0b79eb ad84d113b155df64e6aaa5e1a80427862cc1c4c7ae5b6bd3dffa0f5312c6fc5a 66c6015faf233d08e090f7bd1907844c8a55b0d078afe863ab50469b5101ee45 6132a08a5901e40e3834f9c0bdafd9c29884f077783a3c1a1e9a6742f73f0d1b 599f84733fda79fbcc7a2ab64f3e722b6ab3a5d085d19b53bd3663ed7f80b2ae 650101063e7033b1c5c29ffa251605d6f4f7bb4a086068823a7bf37b091002e9 6ffb935b164d92835ebe08648d7312a5b26b82b9fcef182eb69fbdc7bcfbc509 a441d6e9f815949503bad5deee7a641293d740e6c942a4f4477f16fb6cd73296 e755c5db4b7246db87cfef1cbcfc76da11e1ffc136eec32a4bbae4e17e88aa30 b5b14695fc99a342d3bac179ff423edeea8dd6ae38c20120922daa7fc9ef1a4a 372067795107cf12b8ae6297a37fa4ac7056a97fb38b6f8ffe8212fb8399dca1 f7b6c29e821a92905579eae68c8c9343a7f5c1c9233f26d15ea56b3be0e9c6ee 717053a5eb4508632e8f93eba56eb5548999b000e17c300f1e7b589bd69398bd 6e0a084ca920a9b4e22a97d976c93edc285eb39638af274b5334ac1ac52a27e7 888b666b2ca668d7a54016260725afc68b239a54a918500667a57e96feac5d05 a293f9fb751d306a36f2e409f028fd267a7229f4188213e80449643c264741e0 194732d842ad35cfd947de0a43ef9fb9d9577ffffdbae496c1078aec6f050067 4a0123525ce76ba027b9e1c62b0690c7e2eba30ba3454f6492 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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 7 /minusplus put dup 8 /circleplus put dup 10 /circlemultiply put dup 14 /openbullet put dup 15 /bullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 33 /arrowright put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 59 /emptyset put dup 61 /Ifractur put dup 76 /L put dup 83 /S put dup 88 /X put dup 91 /union put dup 92 /intersection put dup 94 /logicaland 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 /UniqueXX 5000820 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0 aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a 9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4 9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa 4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79 c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074 b64c4300265fd2347a3a851a9cb00aa30bbb57598cca6485e51c30bb78bf8307 1bcb3fea6ce14383cb382f324afa02d18cff3ac22b494d3d02302ee13ec9ffff 860b0bdac4c968e9168d001095bafd61afec9a5a23e727abaf5b193f527df2af 10123a3aad31cf3d8b4bb2e32a699afcfdd2612aa694bbd53a6ea0bf3ec61b47 ff905e5e898717c40328643d610218c2fee0b1ab6bea10870a7acf2b59d179b5 d0d0643d73bd771d34e998f2a43766fb826480f5c00a787818e8ed460612c5d2 86c799428a405262e066668b2c1070989d5c6828e0ebd20259d1535c76dbf996 7bee994ca9546d3a52fed6cad0ddeaeafc4b4ddaaf8b0c8298f72ff9ff37111b 5c7f64e20651fab5c678d2dc91977aef35de0e5b949f9361320a425125932193 d6281f91ce97ac30c72c4bb921c6e820e4a68a18121577d7c5179c01872582a7 5244018a589b04c718e7b38044a65dce2ff02fe4df83a28e2fc037b5ff3d71f7 370cfdf22df912f630fd0566cc650833b394d00aa9da7673e96642c5e1b2d6c2 7d170c423e0c0015c888e25c87fe41ec32b63b5ce2a13fa67f007350bfa3b19d 51b33245e70a74983f0134bb6ed753ad650cd3d6f7e3a8fdda6d8124294ac0be e08a1716553cd9f1fb38e050b0f1ad475ca762f49f3ccdd1804174ef727bd993 f34f692ab2b140d7da9b266315500b79b1061f099f2718fdbe0d356273722817 93cbd1111cb87a7d708d3416eb2ce2496fae41d34ea824fe471d17c6b4972d51 c923b10e7da015a234d242f0fee1bc694710de2fa48a5b4f61afc7c498cd7a13 1ee17ddccb17cfb55af3f8420fdd9beae173dc28e8faadccbadd2f4cc45d7266 1d0172de38c474041c76eff1bd9173b2b32e64f6def1ec39bb092a4dedb7f6a4 f700062dac0c8a724e2205fe77934051b20e230cc286c4f004850c42f0986c6c 5dc777c5458b95e47966897064c18a1577e128843c6f8ff1a939ece9c781c541 06fbdec3c60d18022e2c2e27aa1a634b401e40be7aa5083a139bca3189c07d1b 663c711c847afe89e597d05b98fdef4ece6a54457d389ab57270e8f6f59d7e2b c0eaa27285e094554b00b35d46e8616faf77d17d0d7bdfb30a60eab8cece5f18 a05072344cea7308d075a2f7e533b5e65efb3e699062486e3b197942e7f41be1 d990ed1eee603f78af93ddb8b24413f37e4e6f0acf8ae2f397ceb57a2a33a0ea 87cee6b49e42c6ed7f49911c99c98abbb475de0d5db6e1956136d8027d5fc4f4 31544fd45b33f91330b8bf6e9c21ccd612146f305f4faef447c20881ba423c3c f65437454401c65f2cbdd8f1dbde00453fa765ff5ee0c948b17bc0f6c47f930e 4a0aae14258147e589831773e3aad6ecbe1a81d3087367f4d09360b72ad80522 deaf4903832bb59de2d925075f0736d61639288dc5518c72b687c70ec516871a 10809fa15ae74018ff0ddd22597920a27df2a57178d5f4379eee9db003727ad6 249261d51c6fef7a541ff32c77f064a9e3093e823abf4f4742786d1b03fc6fed a67d566e81cbc6417b5e1e5df4ffba8c04222ffda9a01d87da0c5ed92caf8678 18c2534ca08e0dd8c6ffcc2f976ad7b71860124ce0801c035ccf9d108b43087c db244911baaf385466acfb5c963b7a6895e80431ac6e2a7a4060568043aca7d8 50c20a63cdbd8d65ce6c8b698ae3fd2b53bbe6d3742a8742d11063e4382c808f 7a37bc4538abaaceed54b4e9e5ab5d2977f83920b6a6f0619256c678dc8d48d3 85fa28820c6902b9d638540f4fbf9d6283ed7b81fdadc2723caf7eec7d81d10d 7bdfe5cf450619798e7e88b05754bcda3b183853f6ed231a3f75138deb2228d5 d4a74bafcfd1aa40d6babd940ec4036426f9dbf4f30fd3b74dcda00ef40dbb2e 0552f1080101b1df511e9238235859b225428f3c3ebe6a83f8b7457c2754a288 480e98c9c26a7492786e0c015ea5d3eda59af84746f6948e72a6a7c04047f5bd 3ae8bd42be1552c18f3793f14f2024f8f0e89d4f669558cc828e66116ac127d4 8380ff58e9c673e7eb8ac71f6c6699b1dc66b421d92b8b987d808c960cc0326f 1c1a611549005df29e4fae2609aeba6f950b6af2dba07b19f563e30b90dfa665 76e75f671b62051799cf74806b599bd94b27ec70fd5fbe75a82f2676ac5260dc bd0996ad52bb5acb7dc2fc5144c42d6a3e8ac845b41024dff19dddd3d93fee57 c82f8bc3a8004413b00cb4baaf3f9e460f44b70d189af8038e17e9565badb789 1f923694b1a67db3cdbf3a034182ae825308cd2bb8f16eb93ed613c2a902f67e 7ee562cec93362f05bdc4d0932b6ebc6a10be881ffef010afdb23e10ac6d1143 1c67bcf8dd4d9ca387737910bc672af0f20ce1ed076297597a2fbc2183812a5d c84e25af31415ee2943d74c0eeba27fce3054c15c5a53f35f17be1966e3c4582 cd01bfe06342263ccd1dca0a6c25fc22eb26f5c0ab0e89914b704ef70b255cf0 5963c72add3d7842ad1d6684dd79eca0ebebc1edef1dd8b7244616b5f11ca0cb c4b86f0af098429ea4176d33f1e61affbe3ba318f44f9f2619329efd44068d7e 53052ce452ae99064faeb26ddb96c2be2bfdff754ad895ff5fef8bfc80b32842 77107cfb3637fcd51133afbdd455620fed6b0acf48d52bcc856b8b2af931a54d 2667dab83d5d343ee7756e7c2b6ec837a6e95a0c75bd5f84d6417454ef55436d 718a5ac9c0e283caed36a240990c9e842d4aa1f542fd11c737dcf5ef9efb39f5 f1d03d836dd2d5947640b68ec266058c0d25c65ebe829b16f864e87663ca286f 9d6bf9a114f5e19e2aa1b8cbbe3962d3d395bb8c8036f6bc2790d32abab11680 963d9ac639d769836bdeee84a34215f520452dfc1ecb90b35798301f6736041b e377be9b71b4cdc879b3dab72e3d8854c56589ae84f0b744441ca20b315d1db7 7a193a14ceb6cbfbea384acac88c89428f9c148c4ea4e0e470261ae1955a25be c156204ba7f12c7e2ef89928af6c90aed98f9a73a8bb44e7accea55ea20ce217 d1ab3481f2d35612e8010934c460bbaae7c55d84a8c5cd7092107abd224f19fa 1ff8d40dbfc0efc5f65a6f9a9efb2ec90b086f1c6b3d80570dcead57cd1eb7cb 4f67c7f7ed7ceefd9f1176a9ea97797989ae3bc4883efcf2fe74cc6855897c4c 28715464d13f3b3d182d0c7dfd20baef4e2415983cec29cb8117322cb847cc9c deacb7ce6ffdbc6a66539ae15d292ae1ffc8a4ec6fbfdef10df3320b1395d1dc 8a76e4f21487b823d9ea26e1e19380ae76ba9b6468f5011c3e7413404fe53a6f 1d696dfffbd3b940b1435527e925737a2267a57c030cf10cac755b85ced545dc 2d721d750541d0da679d2a9d62655fdc51bc0ce8bf07c1b4697473c4e3e6af33 be1ef31c22439128980132547f3d88153ed72bbfe425877bf1976c8817b6f555 55ba57de78eae72a081925ffad5fc66543facd21033e99daa441aa69094d4c80 8346df49ae0f628f9ffaec85e5516c9b9d0a6a78fc1f2082e3c59cbd2ee12342 3d7ada7d04ebd5d3830d6d0103150b5a3f097211f2a37338509ebffdbbc2baea 15ec64babb32a8c08d12a3353cbd62810603fb6c155cc887991242b1cd0b2192 bf268d3ac66e8310b6b1bfa6acb47604df19e8831d7ef535ac9f264b850233e7 16321eea84f3082436b3b55f886cb0d838b3db1860a0c68ca08ffe38a03d05d6 350dc3b3db4b46e233319f7f827768e2b1caf4474b55af77180e9252e45a2963 3dedf60574772664641c653616bb7ec8f2c1500033d4b345e8efd466b44f9b49 4e5d9c59eeaa0092f9d34039982eb42a8164508da63426ac2851fffc070ff587 5ea825f43dafb0038bb1a55a7fce24b2f9fbc4d68fa2f58ed6f10bba7bddd975 3892039d2bae3db2f45f2e58b905a231bf2ec4662637daf190fe0a081e6a1554 4f89010592c83376b5657046f5b49d98854cc45dda25ee18a63d17d6fcd2345d d1b1379e668c38ea6697e70966267c734d8b1f9e887c2b963332f0f46a3f3014 6c69b91317a2e60a5aac21144819eeebbbf8db6c6c752c3310075c3e35fde7ff bce28147db1c996f76914f8b827bc17ba0a0833ff662a064cc125af9851dd4b8 69c3d0b62cc6d98a9d05e75e996c9d927c68b116eb1f0a9e56d0bfbb7eff8b23 b38eb0c05cce87d7ad4c5db8229afc4dde58d2d6d114588fd680446adcf678b4 948b79064f9a80e488c0df33a74e38b6ca26f44cc63a58738e877f793a550d75 79232febe6e82cbdf8a5af9d540c23b47ae8832fc3d42ff924d8f4b78d8b3bfa fc9173ff68c0338908da64289b006060476db032b4a4d802682d595210ec2fef ec9ac9eba15e6bb43ec9983c38d17300a4022aa71d8c6f361ba65756fa1a926a ad1a1adefd612f81d8b0c265577635350a20a1713b478691559d2bf9dad39c82 3037227d6dbbb89e819c7023237b288edaacb55b40ca85e8b6628b6d3c15347a b8ef09ee54f032b831b8ec1cebd6087b869c31db4d2f699eaa1ae02a5450fee0 7395f93b73e9c5fb9b746ca86933f8d4eb28704f18d88deb5f42b0686209d7d0 f7124d6aeb9be650ed33579fb9d50c391259c2c18a4b8a6768ddf10a8a3b2660 99d3ef7f4fcd2c33816c41cc6969d20977e65924df677757a0cd7e5d891e5d41 e0a6b9952094bd569113cbcb529e2d5aff9766cf39e2c98f475bcf27614ce897 97ac9ceb3a3cfc99ab960626b98d1f229103407286c62bfd935f31aea72d52dc f225e42114d5b5b4d00c746e5f9e3225eea61dd2a77401b36dded0f75f8a6a57 a631638210ea90025ef1a3ce4941448492510c8fe19fe1f03011769952c5b4e0 28b665537f8e05774fc0b9de2197f69fc25d0c01b666e9420aa04bc54fdfbff2 3ba7f6b18db9cf6e35646fb01fb813427b51d772ba54439131ab95280f75e35c e20d56d362d0a4c21dda8e1a61ccd266e5c5fc7d5f1ba9a492b20a55ea39c58f eb339023109b74e43eadb906b2cc07869821718d4effc92e31889fce814ae456 d5e0119bf597eb5a89ebfd1fee94f84906f8f86c6511efbff9be56591f06619e 7b668e1ac1ec17df75b10dae48b0649bc978a0784d9d92ae62d0f7c3f6872ef3 34ce48ffce636f21a13541947ded2336bce011be83233ca2bfd75e28fd925e11 da3f70aaa0cbe5b58fbd2cc179e54ea82fcdf55f7e1798e7fefc081ca165c28d a4ed283a8be07429e5582b4c98d8016c35c85d85d5f12392d0c72158b56fc240 8c44481c74476548a3e3c8f0a8ca87d60e38ba060ff58793150fa998ba25fe74 bd6e695fc8b7092d02c3ee14c608f17cba33424d0dd79132ecee9705a42d50c2 287b57edbb3533be2c2bb81be6d13ff68d91ad9c826310c0ab3a7cc8388ade9a 75ed5b1f5a72d1ee966d41ca8391867f9a2d63dcb48d89754b47a3ea8a8b44bf 3ef4ae85bbb983005928e77052bdb979de510622181d3b705e4f12e16dfa55ae 1d6cbf7ce64a6b407079c69403abf3694e3ed1f602d6f7cd4e5b512f21f5c29f 3a8b22f27910b03b57c27599cacf9ab0188208438467c4501b58bbf28ddf52ee 169fe25a6ac3723ee163344cb90e4d90e3a8d573417df4329e5fc735d01ebb02 dff7d9639c318591f669d0c14309e12628eec6da453cad91cc7b2cda9ee74600 0550ff7c1b1d167bedc3ee3425613cef6623cb421995c98357748077a66e286e a9649c0872b3c6d75f446b5de92112ccb7e5f9c411593990e41ffa09cf551852 57b180c692e5eae7d4129df1cb9e5aed7778bc3794061da8417a2e63089f538f 8cd9416f6fbcc9e1648f3465357d96a4217e0b5d8ed3d43da7b20162d738f7aa b4a1c26ca6ec8ccc6b1d58ea1fb32058cfc61dd6f5028bdbbe7a2ab7902057f9 adf0a4944552d6dd7f0be7edd13eba00c4e09b9f1c8b7a4a469d80d4c47d4eb1 4e7bbb9b9b0489f6eff29ec63b41cae425187f451a7b87a49b81323665f18501 9b3922c463ec6d287024321eef1bb76fdfa9f8879e02405187ac3cafe54b4956 42f2d63ab409766feab7e8143669b903ba634d64fe70be5852fe50372fa4a0f9 d21a8d176164e42859baf2c1658d4c377e822f2f3bd96dd8ce67280f36b6a1bb 39ac46b106bf78a4ab7506e9cb66ec90345ad9ff820b5cf324c32cd363925dd1 dcf1a2ee1ae63689572f6e92cd12e102da5bba520dca014612abfbd3c53fba32 df964ca5daa630efb43e2b376387076ed93e8d143c1919d850b41f408900be6b 0d63ece4dde15881c7da9978dea12a4840593e5c511ce591cae78e92d1805477 d8ccb1923f5797010a473ad08b195b4272c93c1917cb32e9b3db7a9f22fd6a0e 69ac36d2c7f027571b4373668e0e69eccadeadf22ba64fd7b9cfbf9955161d8b 852349a17b4aff4a49e356832a9ab28dbf196c8f2ddee4896a510294b5f6903e 23b50234ea7bcc5c8f3baa5d89018441219f5cbf283d7aaf07e29e2981cd5af8 9a78ac7ba96a888301e3b8525c0f8470f196dd2c3848be2b92e393abcae96df6 a8d7237ef643884d11b4cf677cbea1d2c2d7f080ee54d1f68bfde9377a3adc3b f20b41f3ee724061b08fe7eaae10206b7eb6dd7443b9ca4513d295732bfed0c2 ea924c0dde8c091988b7e0d3c0aa090efb3d87314cae0b5f62e93ffcee1d7dc8 62b892818d26cb90d947329fb8a90e903b4c01572f22c1c9f7da19f940e785e6 8d08fc8528d67d8d3ba49b6083888cd4403549bad435c026fdbec9ad9315a97c c6b2042c26baac20d19addaf1cda020505ef5592ada5a4fe8f7bf4b7c6209faf 06d727c032741a95dcce8da6632c9c229dfc1fe3e10b38f659f8f487b3eb20cd e2f3f0efe80337fd60dad6e8c10fd96f1ce97feab88132fa7ea406f189e8ec43 dbd8dfc2c99c9f357f7f5adb557dcd13ed0db2aa8d622d38f853dfb9a5075cc8 e85acea7f0b546457dddaec76f2de7eb698a97f606a41ae9b47a5c22dad8a2aa 32cd7d54396627 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 18 /theta put dup 21 /lambda put dup 22 /mu 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 63 /star 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 88 /X put dup 89 /Y put dup 90 /Z 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 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 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /vector put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueXX 5087385 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792 3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6 4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876 d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18 6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22 168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0 26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6 84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2 b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc 55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7 8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316 ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325 e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1 24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd47deb8 5405d720de0bb4dcae731a8e27bdbb6e6be38d168b7daff815acfc32ce367374 bf9fd98c0ae5ba1bccdb84d94b5c173abc92f7d18e19a68f64a2241a0a163910 8dc46b8a04ead17662b7bbff3d3d9a95d5937698573bfac64973dc8d8b8d9f68 c52d0c133119eca4fae72f7553d276c817003234a98337d7c037c0f1bce8a804 57113bcd97515c002d20f836fa086a3277727873ec2b64a92bedb01193491134 b6692a08de4a201a3f11dbe070d797f7629ad487d2b8dbf89a0631956c93864a 42812131afb9f784fa2b0eadd3eda3492dcb4d0ed7f950df370ba339bd691a98 7a6d5071d7446aada34156a5b0cddea1044f2a8aa476a9c0403793d1cbce94db 5b9e447d76e72842092c89fb88fb4a5c2199e88ab4c0a3592f4be883d6d13ed3 153abb55e897f17ba394609457d3550669b54d9c6b9d4b850435eae42b9a6fe0 7ffe251add10321dc227fdb8254052305c8bf99015d24c020a3e6976345f9718 3b403096c58fa4f2153ac7e7f5e0f5929924d42000e8e4cae702f57e6e84eeee bb7fcf06340253064b7f8f60ccf1bf8d53a52ab61917e25797d7f21ae6ead6ac 997867cb1e71711b95bda71a15e474c863fac0a1ec9ea00484da7ec000075644 670cf956809ef4ae88119385c4284cd008acdff42e293377a0bd8cdf89535947 c98a287460c146c2f70698ca5faa4998a5d1d7118c27031240d7eda5a7ae8a59 dbe8949b3c0e90ff1d8aeed9cabdea1188768691e446cf2118b4f9e2d3fb2beb efdb479901f92eef41a19433d9b86edd893fb61c0e4ac771bc1d98d21d60b770 296cb90f2c5935db9fd382eba3382f2bf61e79c6351025f1bd437572f5245e25 205967460fa829a031e3b4721304aa6c4f7cecc3f23bdfd1d47bba7d997f1ee3 df125e931ac57e74c94e146880b28b624cce87d5247000b8ecc645595139658c 46c2c9806a5d2a2c45ac83ca6d4a9893bc5eb8627908609cb2725412196298dc 6b57ec16a17d1c65db7c39c83810910a41d01f575450b15435d4b2ac37326554 f47c6e1124ba3baa801f9aca6d8f9af336471e253ee439a6407475b9c27b953c 8211edbaed25f5dc148ee0ad6dfbba6d1e3671be73bb84421546d5dd1b8dd634 ec84275d8e9be527046eb71963ecd914c096a544488c6db5defd8eb504d4de2e 51d37e0b523f01a09ccd41c075c4b39a207e03768c2b926ec1db883a03b2e62f 12520ee5a61002e743e46bcff4f49de05e97a1bde9fe3c5e0afdf99b12054a59 f18f8443b03fb3cdae09500819ba2f7cc28ba0fbafe3e264c622f99ac64e55f4 ed128afa0861681b2a430eeaa043eaf164c00495a3a2b196f6caa262481134bb ab787c74e145bc838318829acbd8b0036b1923ffa9a56315c34298254fb8eb5d 56a293bd6703f996777a192cd8d2fdfa952908495c5d2e9ad161c67d2dab00d4 275e3a443c8ad1602e0fb118aed5dbc499fa082c447d93af284a48e2f46d5b0c 3653cdd5f5f96abf269919ee332423bf9db0a1df1cbce15c3566bbad942277fd 6c3173333b0c5beb3e2df79bb0349b7519d6df6d16533836c37d28b96c34214b 12ece7f60e0ce074e0ec5d9666db6fc3e1101f98ff64d4dc599c9e88abd57062 573d35122ec3664e1d7329c4e967cb6ce66357a1a345d0b8bb501d14fe898560 bd10210f36654b66b6b6d42ea5ee7bf7df932d275512e8ca91c32c8ffb0be8df 84c3db478c134db7253499a67e3fae87ddbed543dd45021ab0f65f6fc9f86edb 696fc61346964d47ab57be147ffeff6177364bbd8636f11d47988d5ef0e1a615 86c29542d296561ee0e0ad0070e79c3bbc738bf8780f248031de07267dfb46e3 a26cc105bca1c7e402cbf94ffa60b66ea44c6ba07285902db533ec242cc5e15f d263daff134d863cc30f68cd6412f2f004be4e37b2c4b2a2bc30c0580f1eb3e3 c53741eab07cf3f599ca30c9211e4c6e96be827bea7494b0f3f33c140c8a1fc7 723eb470aece7516fc7afeb723ddf7a5ca219fa20f509b9d30edfb4077069edd e419966154528ad13ceb9e71f32d35fcc2ace9cfba044f2146ff7644f1378407 e0e90faa3ae707ceae8daa6e4a529d3c97e5cd59be7d223d321f793d68a216a5 613c19f0e7ce7ee279d7dcd3d009d14050cd15b500fccc48080bf008a7101937 7104ad6bb8cf16c4831af4a2bcbbcfe2ed03018aecf3b646fb4a86cbb514630c 212a0b1ed5f74d483eab43f09594a0a4029577d8b5b6d30ddbdee654400abda1 7f70a1c36dc67f178d46377cf139e68a4f91f913183476ddfceffa4519464cf9 5d56b9912f12c28ed804013693ed5b2ef9ce4cd4ca88f88f2b94de4843adade7 0fb74fa78bf05058d8e409f545855ac53fcac93e176b38b5b6ef430b62469f19 08de61c9a36849e12667a4a8cb8a2c2679a9a67757662eca45b2b0db78e97f9b e9ca5751ad63ca0ace410f49d065522d396cf6323e7fd2ceef16bfdfb30d5d7d db90ce81b21e64294b92f1ffbcfc19991cfae1906ace277ec0b04aeba22d2714 d498bf2060fc01d00e2e8f5a3633ca9248739bf1248a2ba4c5ceedfc4e77739d 6e1fdac2554d9ed26c3233199d251618a7012cb38c1f341453092c8e0326d853 5003dc2770a53fa0bba3f92a09f25ebd26a76ea08137f5de84367039c8afca77 b5f9d1a665c703a3510c5ef85033dc98e13bdc96d032a502d12f3766197074d9 44e7f4353ea68ee3eb3cc1321bb99bd8851a06139ef5a956f185687ca81c9564 b694cb5be12bd49168c3efedafeb6f9375e0795e6a2e0f18392383640be4e07d cab8f91585c6fb0315683399b40fa3ac32ab32e48ee031434c7a545578c06b4b b31819b0ac80d9bcdea89230cd2b7bf904ccab3d97d50c0767ed672e44df74cc 4326287fb43e82ceefba46fefe5daff6bc4e9bef30b8f113142fac2fc1a6fb75 4380eceb0a98e286d9329fc427e990c196804e8ae5293890f9847713b5c37fae cbbe2e0ec05a1e10c748b8d705b222bd2a8cb0dfe7aed23494c91022381f2bda d248e5c5dd2aca0043fdbc2561fa17353abb6abdfb4697ddc81c3ac2e8a7aeba 9baf6c62c6741dcf2a151686280c6394e432b3a4f446939b48e07a20a117b0f7 16895800e407b0bb457676ea6fae6fc485c494586215935558f554308c5bf09e bf4658621cd1304cd93a9276cab725791a92a97dacedf98462954d6bc618ab10 7541f7c8942a21daa131fdf1fb1dd27d78f25c54117af2864a1638b9e1163d58 23ded1c4ac34e3d1ec3fd9f4997f804084b595214260f204e932b8a67bfa514a 8d7943dc99b008432dedaad1d7d577322aa7acae25e4c12fc2748b251301572a 14ba27e7cad52cc1dc78f1cb7efb56a20f68e052d5556b48ed20dae94cb2f80c df4ac19326280fae6ed5fab2e0c5b7b59bffe94c3f7642c92a0d7a4adb2fc5dd 41af475aa7198a4d084a62622e1583450177063f4a8fc61a27189eb2e7a46fa2 531a39cb07573e1b00b672ed691b890a24e8596d15ab8693d25e4c1c8017598a 906961ca278dcc4af5309d56d3eb71716c93585939640a86d552bb4846fc3353 60746ed7379b384253840d61247514da26a85f3f2b4d4b19323191a08f56499e 432009ec8a776a04b0525b552f4692de864b00097c16efaaba355b95158f3637 b1e84f3d5fea2b3317253df25ebc4875886098461bd9c4848f6fbb345124cc18 bb9204d7f43c9ababd8a0d1477b4f6306ea4e31a5c975705365ac47a5996816e 2521af6f31c381acf512cb5044879d378f3be18827a4fad5f8e23ba0dee5c9ba 3f767ca1a7be3927ad4eb5f8d171ffce05dc358a43df2ac7d62e50ca75768a88 96769ed3059dd3f6727bfe6ebf2a07e0fb98c7f07d4f9b424525eafa91f04c60 7875215fa32d39679b5a96087ec9eb0e2d961d84b1b70671dbad9078a0aa4abd 1c3764805a5e80026e829a9cd3254fcfef8c7b729d617036a3174579517f1104 8f43f69f14b5a55b91de0d16b84d71ae4cc29c69a03c824710add10360399163 424f28ad5d2484e9d0d6ddc589c1fed237b8e512486958fc82bf079f6541b6cb fafe11211ac705c7631f15b4f7d0029f783baab63415969a00090bd422db05c7 c1e4175043298382d37d5bea24342fc018ff321b5b51ebbc530fddf4eb83f4f9 b437d1c4cf2da9903777e2524ef1b3a980edc85bd2d59073592fbb80b509b3d6 44103b040bc55f71f1293b072ea50f1b426115f478b2ca235893273c756628b6 08f69cdbd9a75eec337f7ef9bd6014b9f1149510d7d4bfc391f79c44666ef4b8 357d80d159bf3410031e02e8bb8f412760c4edbfe7e669297dfcd3f7701e6375 5fe96f6eff9fe9e7d654582653b4f3f94d255a1625889fb3af6dde9af20ed81c 8ac922a7b7eb6ade0dc4c9cea78d87ab7bcd3aae153ef76ca716b77daba41176 50cc1bd550ad66f5b2864d50019bdcbaf7f5d962c3ef2c357be2d7283d142bdc e2ebac651efa7042b80b6af352ff0de2191cf14013b0703dfdae9515b5d1abf7 3b3d0cfe34ced283941afcfcb15dab45a366a50ef2429ced00a03583351aa481 cb0eb205baeed427872b7462490573f96fef8ad421d0afc6cf1856abbbcf912b c3419159b0082733fa9b9b4548a1a7be430af7c13578bae7109a5e5478871bbf 3c5d2c6f0f047c338c1478b67b02d9f9104a15226d0b8e554580160882265844 2486c1c19490ac2f2c5a3b18db2e90ae6e47ddef400ff8daa44d397d707e83f6 6b86e971b316579e0db0f93bfa76e7bdfadbb975470e56e838ce674980cb59e7 ea6b724530028204e2d61a6ec3edbe2e1316f573c7318a96104abbc460bdfbdb 98d85bec3a69711111af776dba426ba6a006b8cfff125efe2fd26978688a8d90 6caa3aabd9df98ca0edee18b0cda6ba1e31cc255be1bed0dc55208f83359067e 57b9bdb82fdbd21734bd4a31ba171419873481fbfa62c0857fd51e60a113b1b6 cbab2d5441307657691133a7db37bce2792d2b578c26343fb57fa779e6ee8d99 c3accb3c82de90c5a4d7211a8390ba6f9d032affe0babce619ac4037ebeae093 fc9508b08058ee4689341b27c75182015f8c9d43f47ad114afe884cec0ed4788 cfa6078fcf0509b27b582d6b2c9b0dfff7bc8e98f0eeaed795624a3cb4a72220 3b6be983dbffae264b2fba22ddd458d47d4df9cebacef9f0964d6089ef0fc2a7 5791c1ff51de9835b87adfb01eeef6af5b4470615258528b54af29012d2aad49 9acf06f5500064ba855428baf05f640b6df6f63702d210ca5935aeba5369ee0a 4010ba9f056e22777b034fb3c9c87c79b33a24006fcc93176e26ad6b5e666876 fd183a9a609fe66d0459cab250368209c9fa7f2cc17e31b08a195a27f1e63afc 715dd8203a17405c7d40e1276773b98ed02ce06e5ec7bdc365a83acfab7233d9 279a5b511e63b05d1fa3988a6490a6517a3866b0cff7c32fa190ae33cf32c350 6e2945475238b7180cacbbcf67f3ef6fbf0366347a48d70fa863cbe74ecc578b 00b7e6025bf9947d36336079b99176210dac7c7f2e8ea9de3de54aefce0ab4e9 99e18f55a462e639c202adf1ce503badc42bd2c5fb212eb6125576f290d0dc73 d8c9677162c5792a53fb1c381e4d4771001c49d1bf9071b279c31de0bff68ac2 c9b80a315b5abc10f8a0ab980be0cb00951c50ab871ef5e448a4e961d800eb2b 03c31af949f2e0426b394fd4a14f8407cca41e05f3fe704abc40f6cce3c21256 fdd40387184a46aa53a6e7183435ee99a9069be2ab3614067f2713c287b923ba a5a17ccc88fc98090ff5fc392a7eb4a510f6c84823a3a9e4ac42667f863b4006 4e00a24539ad060f6dfaea5cb3a87bad67cb1ba6ff6e0ddda98f472b5ec1fa24 d53fdaf1ba47f6c5a85cdd8b046642938eb48fc3c528baf8af8007c00bcbeed6 6b6ede76e9bc540dfc9bb313ad0e123c01667dab5050bb873206cf09f18a6eea b18606c09ee3baaaf1cb6676b9bcf4d6ca1bfe07f7afdaea91ffcadae91d416f 7ad7fdf556ec05cce66a19327b86cd367242098a3a593466aa41816b15061e97 b39ebe2536d12abb2b4548970e7c137a1574eb03b867bd72361a17a5e150e223 f7db5924471f946e1707f21e77bd0d8b9fc7176c76d45222b6752f22b5362040 f2c7cd5c512de7b4fc80e4c1c913d51f26526b915db1406e0a6cdaa59cb3e127 3901a0b900a0d248168071e74d310ba07d52eb28957195796a79a46c03858e0d 28fb884aa5e8b51739d4fce9a7e151b811cc090d15460ef721e89078c1660fdb 8a09e88b1efee74ece0a5963d734218b7d60e6d8ab92bf01ea8196f9fa4024dd 1d1faa84f2b0f3d761b2428d9338c330e7b84e57bf24689fedba51446a5c4b79 4f0bb625b92111f79b7449b847e708fe0aa2a9354583b2d1a85d960297a1f2be b483585575b9e765f9111ad2b4a48a879d244470848f0ea49a79613ea1d3e376 463401d1a02f89e1bed4bae0e4960a8ec05fac84a57032325d6343ccd13a7dc3 fdaed6251a3017834fe7af10b969c0e825047f298af58c555df5d5a9c9c0f326 9e476f87e3ce3dd19ee64380d9bf173e3180e0b37bb6f8581b2f51aedf3fcd97 fc5a06a20f252274b5171a1bf68439e0a350a9acade738c7ce49512257e58cd6 931015abafab3c876345a08d50f955490ea0d4c00d3478fd1ce9e632a0fb5daa 091f04e64c598446f8b6df59d0f37e7052a205f4d670211974d6edf88e27eaab a52f3b651fbd485b4682e83d60bafdb4c79dd4b49498616a9a0a6ac68b1192c8 e9607e3afff4df58091e458dcf1e9e7950cfd9d351c7f64ca413fecaca6bb371 7edf766ec7cc85b0bd97e1c9b5f9cd94e34aa39ae26789188652df27a9e430ce 18a571abb4cd15cee8bb76cabbbf665da2dfb6e4b7381b8661c07ab0b160fea7 b14a845d04f46be0534083370b9b770a89e4fe976c4dcf3bd8223e10faad3a77 ab97b072071390b31d574ddc819c3a3ae9c635e7d087b159fb840bdaff68b6b7 e244cba4d4147934d691cda63e197ab2624b62a7ca25d1d53e03ee0cf4df87d8 c0aac7c3ffd3dccb03b435f59c0b35a0e89d5771ffc62a3b63c4f8db0736031a 474c738ec5f08d31c11a2210ea41cc41ec05c88609f122d0f02761a5b541c412 34d805e1666dbd142e4efc8d8b696f51943c57880f4d77460a88979a614aa3cb 6e7a106f880111f76818324e929caf24c4b75c6f5a5b629a6cfdc265a8fd0d33 cf419ec9d7ffbe01f8e45c2d7145bd21c29ac167811d83e9bcf57e0f0963743a 4090f0f3882068091f5c0481c9658d3b7cb09aadb75efa484e0d54ad3e6debfd 93fcddf58b7285494d5d2454aafa65957aebd0261ef276d67af467026dee1cb3 5807515d0c51a12f00f3f79863c1a879cf2db79ab81a80f7ae14980aeab62b8e a46b7237373cc174e8374b7042414a7b2c1cf6dcf5fb6ac67a8da0b8bef82cb9 5387f8779614192dafa4c054cd3d8e9cf5f6ad006bc84ea8e37a3725ee6b5587 66064750f65a2a46798f9fc07dc6574ab136e8e5ef3bea0de5041546e8167b5c 60f1bc3bec04f637025af2010c5873d0dd70ce9d7b203378064ee8fec0a38173 175f7e178434675b155989f07f7c9f562d0d201179d3ef0dd25340d398eab9fe 3e7e8643adeed49aa54eb75633bb924eaefa605bb42e1d04364760e094aa3e10 b73d727a38d094aacd5b836c91dbe3f398e44fca1e193360907cf46469dfc4e4 ae48f949fc258a6df41eb0dce3b200894cd47f34f5e4618cf61f3c087b5d8fac f7c6d7162e9b51368aeb1a8b1bad0ebf8ff43b2fa6f80c4af54df20e3fef2ae6 2505d898031465fbfdbc9f46cd6ca5631243bb64323454fb5b4b198b0315c398 9c4a38bb0cf49afdc784529e075be72183cb1aa8be740b902653ccb204825a0e f4c339010c06df883e529b785b46cca2076d52d05b2f75971802850658a23fd3 7bceed086c8b27e93f4f2924759e959852adf5d5ba0262f14c7bbd9adea05559 d60896f2bd831859324a2c6bac620cfa82db0dfcd5ebcf4227575851f1e96712 d9e05c98301d29d59d8cd7231f0dd4bfcfcd29c02a91b22337e8b0cf8f873e23 1bd9a71815ef89dbed93401529e47843aedea7e215160f3264c2f6f66e1907f7 96bef308047cd9539571f64a343b73b855961fb6dc2a40c04231840a5d3eb96b 0475538b677e4dd30f443c119720150899602d8b7664d63708102f5e40463ce1 32893722f2dbaf4157c3f0fd0010d275ee045be10fcd44ac546da874b6c964f9 d7be2723926742bd3c849db5b8b017af4e65289ec445d4aec33a1f7ccde91029 69cd42c5011cc701e181f34c95557ee8b01457c12fad1c97dcb06da82aa3fba8 8edc65968c469516d8253ba0a58392ae8acab4c4458b6a0d4adb1885421f56c8 a0f5625ec392a619bcfb0cb974e2adec9a887715d7e788187b0d28734b8cde56 81c22b093eef3a3b6f4d7eef73d3f12acda141df149157b4ab2452e1527b0ccc b485adbc309fc5ad333580ecdfc47fd1da6970e707bb0127865ead4896f984a1 ab3ad0ccea686b3ccc0d2a6e27820c141e04e9cb93b2685550c6fbfd68954154 6355dda041c061d7e0d71d6add0f13e5b48da5839493a7f30ced3aa81cc699eb f593147440c29d0a027c0572b7f29ad16389445ed60b7b8e461212c13e0ad499 54396ba8a0c303b87d75e8ceb9801e997f61991157dba9bd5ea62b99ff626d2f ba37eade27035325b65baa3e60f605ecaabf8992fd614fbf70d76217dec8001d e7c1a5a5e6019e0265fdd9aab2c58d774357452302449992a6fed0c52cdbd017 0dbefe94a67a1a00baa43e41ad1a3e30d9c6a436d492ac03ba642b24ba888c1f 18feaadc2a83ba74c8ddb45b991f11b3714ec2d44d0ef1f9e78f4344fc0dc1aa eea80180ce2a1e185aa66040376ab31d323be7c4079e30eb30c1271ec5e685fa c71c6e8dd7c805707af8038d0dee5ff97874510bc0da7ca615be6c21c23e5939 0a84d83da35ca42ea248a7664e56a34c9bc56bd87e0919da20945ad47ea6ba60 c28d1b7f730b4bc1e80801733249abe6e626a530882c90b4ad22e0a395538fe0 7e819540bf3b2c3f805d3dc7e8cfc230ab25d326c351e780c68c872772e2e1d9 62610916f4bb021d863ec13bc1f1beef3f1f0d8b93dc97781395775362ba85d1 3c55bca807b01567a58b20bacb2731908a83e39ee928324ea1c77287439cf1bb 40b5f46372895bef9de4eadb3612f2590a877293d39655fe7113866fbef6fd94 b3f31f427b46cb42c4b81d29a19e7975ed45c8fa38a31fe058ec96fc363900c4 c167b6d8513c1d3c09a0426c14662b4309c099ee169d12435681bd8831a1819a 9aaa53322962c88f3947d3b9e6f9d388b6507efb651cbc09ebb63f1cbc44efac 2f6d635e8a0974ce222eb2956921f08c0ed03647be2c67bad9271b8cf641e6b5 f4abf1384690a0542d9257a91e5de103627eb2df361b5e273407a8b052deb5e3 653cddf72ad9eeb0bf5aab41da47259ed098b8ec364f5e72166aec93daf8b30c c7f0a87ba658be13a0018355f6038c9c2ef5da6f1ed414e7b8016f28f45fbd85 b617cd2d4a7751118db5311da9d3079a7f57baaf3dd1de018f78ab7dbd8223cf fb92f909748d77774ccef7732f852ffda58dae75e2e971a85aaf7ab84473afa2 a4d444ab3b27229d0b71ceaef1fefc3998d9c9c95e110ce1b55b2f7b64effa63 014c84e0a711d58c413816470e04f2744bb896ba9314cb95e2d4f2c20a1fe76e c602463e447df70a4d4133823f0cb8fab324bee4a2b939612774c5a446235483 f1555c1028cf7f8de0f7f4b003e798715eecc9445e43ae675ea4c9891d1425bf 36c176b66b5c3a3cbb2a3a6df2ef4f633dbf1e62167196ce1e1240bb9d013fc3 0813792594810a536ea4327bae4fab010a01e53bcd89d71c2d3fb5baf6171e27 ecc5a42a927f7e2ce62744d5b9866402192f731b8e69ad022cdaaaf42a42c252 0287aaaebadd60f30b4a964676bbbb8e4522a9064e6042369000454144c75f75 39934bc1a9a9d2c501a7d8e40a50e7ef0ce3c31acd9511fb0f480c487232dd6e 68cdfc68464a585d51934b32e67f5aba8c45bac6e10130dc0acc09e08d68ef44 255cb452bee5b846c9b8f35da4deef7baa64d281fcd7f06f8499537455c949d5 946bc91faee172a1cc1b49cef362ac2079b973183bb7617b9af621a5d0844295 6d83d9cd719a14617d7e209426182d4f704e6899f48634bbfd0f528c8148d773 551c715129675cbcd4e7c1dd4db9cdc16e145784f56cdded5e32fba2542a7714 39a0a44a6d8ed2a7e6494a3cadf8d311e48de60cc35acc5a28e28dc64ae44175 29552da866e41c7bcf470f2cfab7202debe87620ae99728811a5b178cde799e5 b50a92fe03f3efb12ae72aa46303ddb0a1ef6ee83d012dfa344dba9f9b0b7d24 b704da79a9c05c6d0963ef82006c2305d3086727baea53d6fd8ff9693d5982bd 0e7b26c3c6df8d43bee4c4b4cdd657825873beee01ba3fdc06bc65375e14c3fa 8155c7d21ba3c831bcc3633f2ace48ab6e8955ac8a3f206471cbb1479e181f7f 9c929baf942eb0d6037f352e43697527ede02aea75aa3b722fb60a2f0d5aa6ca f2da0af8e23c36a7cbfdacd9479c3ebab0077b918acd99bbcf22efdedc4d712a 8593928be82f1d1d2e1588a9e4697eca578172d137e1547b6efaebeb7bbbebcd a7f27f350109e9e75b6bf574231a867a54b542c48421109980562516d620d29f b381ddce5754a7289e233627c1cb7239796fbe19425886e85eb37cd7d9e45e49 ef5a3a21ad8af77f30f337afa930e8381defc863f969dcb00c6d0bcf1a890b64 8821af48411181806182ff810decfb1440c7e0272a79b26e8d4f18c8b5cf359c fc07ef2337e9d3dc625cb504689309bfabc4adffea4e8daed057782e76547cd5 56180065b5f9d6a77bacfed38581a3fff603c1dcd0f00e197239e34eeb2e3a40 757937799f0b45b2ff567dd651d70cbcf6f4f8809b2caf18ed8046eaf1209ae8 1ef1f942aa9e91a8a853e0b1ef2adaa9b8013e9e808d7d884beec3d528631873 3c37b15592036376531786c61772a0d01a475bb527b2ce9cdfb70aa0b9b1a699 141312dfd8330e44ab75b890097100bac912d0f1fd4032245c373ba7ad0b6990 6d6cfa2a90c1bf416e6b9f2fa851f4f7628738400eca903abf92752f7266de4d 5ae189f8b8eb4937a046ea78c0d233457f1340cd13f1387e35172ee41c2ca07a 299a15011c65165de7d47a24d670edea23161cf0931929f96056bae25d1c96de eb90652d3b185a43bc380f7c1d64c56e77cd65723a3fcb6cf2116ab466ef34b6 845df290bdb87b15f4c3050553ce8c32759d59321a0a284fa597182591a4cc77 6dfd44a971409011db847ee8d8d88b1f15dc3333f5dfb5181aa6bbd2c44c1c1e 00ae1a3b81854acf7bc522da9311276da668ca080805d78832dc7c68a7de9ebb 596a52ce6b5e4a51975e0e83100e0227a67d8d4690541f95e0906fda69a4a1c8 8a863b91126d429fb189e15a4a2a9379f4e3ff9998065a829347c157cd2d5147 d61c1a8bd9056fc5e2460ecb4c8fadaa58306f4db09177f630c8d8f57e12a635 4e9fb7e6467179ad496484014f3e3466cac76b093f71de759857e4febdd08861 69737042c8aa7fb32400da8698b632cb589a60c0cdaca58116cd14414e43ab31 1c807aae9b4e667ba65cf54e968eebc2f49374c888622b66500d20b613d258ca 1f17d064673334a2bdf7704001d2600850bc63db06ba957d4ba133a64e4a12f5 3837f684380663ce41bae1f1a900785a5b7eb94ebfe11fb233ee78b106c45686 4c19171eff4b354d018aa9a3434b746f176aa40da7c6c1e953ea6c16dbd4841a 080c7aba3db34aa1cb34e22de524a4cb422ec844fb0c147985f7538105460004 12832ba4631656d0ae50a44dc85ba18406576a110078f09c9360ef3905188003 3be1bb99c89c16f8de732ee771ae78e423ff4fea3a0cc4d842b051bf7c7e433c b05ef343b9cf1d3c4ceea5c3d614f56c2315c73d36e25ae45abc53384b596e55 ca4934fbd2c4a215916fa68c9757be909188ce9f90d37afed28ef69d1b263e86 af8f98fc720e5bf7f39be7a4260422781ff5c5b9480b5b53d76979384a599551 b94d73be0741e057f3740c0e11d5becd419a81a8cad659f639323ce72a3114b3 09c036ffe5b877d8687e00c3b5a245045c000cf82129a7b7ed6112fd366b11af 60032a60ecf594f517b7a8f0ac973165a860eef2ebd20a3c9b9ea80e0258a1b3 956b398f051db50675e187714f2d4af576ce425125edf58bb31778b4544b44d4 177a97f989824457bae92454203401923e30846ee712599cdb416113b899709b 8bd557a33836760abf186269c56cd6ad2e9e2fd88b09caee1dcf9db06e8ba216 387e829fe3bada3514112703584102c5d3866a727d260a4d316b99a5e366e928 a62912db38f9760ccc00ef024f66f31bf5cd7dae63609a2220fe71fe6282499b e79112fdf6a361ccffddbcc390452d9adf83273fd80333e54882e20569c0b2bf 3d26ccfb7ae39eb8308166bf7e3c8cc4ba222f5b2f90574d34e3c9f6759cf8b6 220a57487deb0004702691c5be6e763e352e7bb9e50c05af2fcbfbaa17901d57 2b0e37bca3e64ec00bfa8c019c6fc4441216c8028e5748ea22986786b1aecf83 e83109baa0dfd52bbc54af39b185ec08c09b13e19c951163c244bce8af1b5889 bddeb6c3b0d33041c45989633315d6a60cfefb9d4eefdf445e9c856eb193aa60 e5a5ec2821161dc7841245ba735b214913f5d5c16ae0833debe446dad03132ac b4a11ad0561228c20b66d4f1537f8d841faeb6bc91595cf76355e03f44628d1f 4021549a6a548025efad211ea6152e957322e8684cbe7410dcd6332553cd54bf 98b5a5d08f71685e977e853cf144ffca516d9b9cdb150bacb61e2d106012a66c 253da5aa77582adad5ba48696ca14d41c51ff23b803213727a238371b4345515 7401691c044ac96635946f3699288a742008cbd3fad39a6d470e3ed9ae4f6c5c 635f31dc6880573c9dbf94bc864439cfa41eb3b7a26cd47e7ed42d2b562ad879 285361962526aa8117ccb5725895d138211e00da2c2f147cb854a3d9a3a62d5e 9ee1a1ffc8947cf0c304db73688b4c2947dec1746d5320c2580bdf20047c66d2 640ff9933d044c52447310021d379a9f243f0e18e011ae1c08c3d44c65905e45 c32fb86969f9397ce08a2b3a6a55cf2168607605964217bfaab1dbf5e7f2e53d 57183107cc17ed02144d04cca5e3de701866a296d77afa1a4bf3e4853fc2d7cb c333b39cd92796e07fd9d4e93c0454fc8d06e4b8c0268c529e1733a54fcaa482 5ecf1376f42b59cd32908d4816755fa4b8dba99c71871e6676cef129d95a7d9b 1939d39aa726279881c31159776a563bb66aa87ce800244d3fc3e890bab4b0f5 6c218f8e2a54ef04a732f7b0ddf06143157215ec6de3dad6c5401ce5a92b4552 c8df5bf48c735419a37282a56c2fd981a94f0f9c397cfaa6ffc9602b9cbce6b7 70e2405f62e02473b946f8b82712c3be8b8af0c83fca6dd243aa984dc7ab073c 80f40c2ceceb60c96b1023749d46ec28baf4cf0aea9f397720ae8a7a8b36aa0b ab6de33d3978e75c0a4cb82da350f985e3b6fae15e771a78ebeebcfb363b224a b96f4e3935dab1b58c1fb06b6b3e2b1b1fdd8fac4da302165f0145bd60bf914b 129bdf7d88bc0d601b7f745d7a4cefe6d828e819c1e56d547383612bd011531e 811dc4f3c87293a3a552588aad68d2844b6199757a05b7dfd35cbf65e84ace64 175ab2a69c63b1eabd7475766ec043a265bdce6608f2b97be61abe2e2fa0de52 bc310f960861a5d2bc66daa10009e0a0a46c00a666b2babcfde159f810a5b45f 6a5c3a3331471393e88cf2ccaf2d42ddfe37e7b850dd24560212fee586be8bda 483c5e59440b9d3ce942a7fa6222c94b699a4713eb9f0c6de6339734d4ea9c49 22c9e9ee0b25d4ff025ff33268c557af3ec20a812064eccdba8eacfeabb5c7c3 4ad0428f7aa3e4267358c7b3888f08b2738ed23f05a16bd863294c2b1c53de64 41a98e8cacd79cdb2df2199ce3be884f3cc95534ef5f5b81aa164aff1589077f 31d2bc3798cfbb58081ae3d61acd550b8c56c3e768e4a18fc46c9083b37b12ee d1dc1a06107eb16ad5c1a031e1046ac098078ba9647e89c676fcb75aca895ef1 0657eb5546058e08475ddde9277dcb062608d70ab25247de5e3fd5b8d58ed28b b36c6f1112c9f55d0fada01b511930a12be076f84cfd133f6073b9bc60d0a238 52f3bac880dfebf4a5476af31177b90c9ddcf317ed76778774628202332eff8f a0b94496a5a5b04e99d09b409677927c55619ebeeedadeec25fefc6d39d8ba8a 977f82bcc8a8cb1d0d6fcb84f3be2f3e56cf3368c1d4dd8d9d8caafd48544cd1 8ae0f339bcda820203f6f243a766b16182a87cc4dae72fa18a61eef7c4c6728a 3d7f8f1c56e9a4dc506174ffa394479d4f5bdb075c62031be3028896b8908f04 d9bfe83b16f1f67b60133ec0eeffcd6018e33e2007c1130d77e7cc73ed368235 a0d246e019209c46c865d4c55ef4076c5e9ba39741aa0496432a38e56b9edd88 03128dd6065e15b454f8b5e1e278fa539ba8f271a77847d41320723e4d1b5e2a 1fedbf60e7e231e3f09334a04e21f09683580054decb4611ff05b6402163f806 ee9b182da2b4aacf2103c3e46cce420600d2940bcf46e9a03f88af71be14a9ca b9aa2e58757d1c12c58820aa0dad213c056120ae9a79e8250fe75c250d63d676 10c3b0b986529d4d8b92711da71c836985534dc0d93fc7fab75f25a3b6356926 7fb72de9c25f49d43c7184f8dcf29410383fc75a3285198114d333036799824f 25cfc5f49478c416491a55dfa9107a4e89d4145ca8f547634e93d8f47551418b e93211110fab5ce3de2858242d1fa9cea4690ddf5f4975a92f0a71bf9f85d83e cefe922f4d6dd02ccbd5315817250399ac1e7837db61d88fdf206f070ae24c42 e265438fd565eeca09c1cd58217140ae17cf9cd8832b7b88bed975ff1659156f 3b7990bf5335e335cd78bc3c69d6333b12c31e387f143537d40379e07f7fbf1a 7019aff7f4d8fb7eb8c072e777a899846b1de140772c1ff9eec4758f74a526aa 57fc755b7b5ceab446e0b01cd66edaf32c405170f9196577f66dab6c63781619 fbd610cf1f9493b4ece9057fe7c700a5ea1a8d5e5b25a42f23e13b71d64f7a75 9b35939509dbe96c79586a69751c929ff73d70ecdef4cc7b8d9059ad7ea4770b 3b62b562533a2cc33df7ee462e003e94b3e844df93c0784119d2313bf145e432 e5608e44867834779ddd0481f8c20f99776dd67a0c55b691b5eac706f9c11ffa b653a55aa15c81bc623a1fef4dde0deac947788514a248161f59a37b0c447ce6 183d76822726157c90afba1ebc8e1b25dab1b6bad00f1c5169e678002289f368 0271a0f296dd06888b6094aee0b3e218886b5a5cd4157d151900df7039c30ab5 cb86e2acd81969bb1ec4d6bcbd92f3a01c1b2f5369297d98e66f39b01fd3e846 23cf96b37cb50d25c3f8b3caae4ec92c8cb6da0447a392ea8a9b11661eca8aac fc382ca970d3867661ca7ec58dc78ef9befb70fd51092b8140cebcb3b362bc86 746be42ddc17ecb04165c6f43dd78664cf1b134866c622d6ac5d0d4c52d39d27 e000fc6eee5d98f6352d0fb5d6489507e1be86c7b35f47675379b9bb3016798a b060bead4fa4d758cf8f5c5c920ed54422dbb486129adf2dd6d1f5682d8c1b57 44f3fdd797992501269e6801e5c8bc13bc36c7a17362279ca5e725a1959a7b84 d62e132a38a3fd10bd571e8431d4b3b9369040596cc44a49e65cd75ff4292a2c 317058750e00f9a3e58e7afe888a8ddff214836c40a6a7a9111e3cc3c696008e ddca6a5d32d182f4395c60fa2a8209e88842b4cfc7e2afb3ad107412ca775cd2 92c908c237748eb98ba255486d56b4cb578c0336cb37caf5a1201e9de96624bd 26f92994c79e5b84e22b7cda99220cc79f6593e80605962aecd405eb89940934 895f0045f9bebdd54d5a68de959643869eba6e14358a9fc6cda226de4c2fa8cd db9b56d61b317a200512369f204c157fb4a88ff8f5b2c63d836568dd25ecf1f0 1a9831895fc404408637f54af409e83e49041ce86993771e4666f352a3275422 ebe2a77ef5f36fba8bd9f00abe0eaa172400bb1c96924a522201381739d2ab40 9b77e7ab492df2b02c8a5af699586a4f599b24693eb1d7b20a3636fb3a271ce2 80206fba7c8d1e28db88427f97339fd5d4848af3f31f162872cf1ceb9d9b148f 174c2db55746f22a6f9c535167662a7f1ae74c6ef80b2662f91790aaff3d0ffe 51f96ed8a73dffd7b4f2b9785364f9027d3e7b0f21989746d790065726bc928e 8068c4d06323ed0108a8649cf572a86564c4b38dab65bb681521c42c1635e4c5 c995e6d03d2f1008060eae50d7dbf4b11bda50656dd91011e0c088b9092ddea2 28bdecfe598692c8149743f0c1cebf58169decf54d5a4662db7024b886a1a87c 92032059887314b09bf7bd32d03f7cf6e8ee056f568cf653e7ce050ae69c6e3e 5786208053174d14d91b8637ff8cc966c2d206a7804024fdfb9826cc054cfc2d 833ec422f35b676527afcf9e6864b2660289c07f6c57633799db787bd302d54c 3f18e28e12a00b906a26493cdaa53bf31a4197a2b1da4231b59c2312df5d6c52 0ac33b749cb0758b8cc85536fcff5818c1136671a1c8a7eb9c4735620b0de07b beef28ddfdb0dae7c78d166917f18bf9554f97b433e03e2ce0ab355b7c26a48d 141775ed14696af30453a4c6357e220a734de688052093e4fb2dcd9114247863 6cdc9057b0cddddda070b1782ee0bb43a4618e322ea5fde2d3c549c4e2e85cdd eacb0a79e5a4e45b34d72937c4096578ec0531f2816127e757e7026d5a8d3688 30ee63b3c64667803a0ef1b47b789da4f97d71a7968461b587c002be962f7ae8 408b078a2c36085db4e1b45951c97568ce4350d51032aef4fbc1b0195ce837a7 ec1d7de66ea64ba5d31e6a564bfc3ad3e4813b3208d4fde8d3eeb1739d7de13f 4f32b63c8a05f1180a1a1b14967d19a0a8510be7c9aa8cb83560c647576799b4 d98d98c51a144d7b4054b84f7eb6950f256e464e572a72d93db027a473b8795d 00c077dbda473b2b9a5ea7b1233173bfaff9ca29874cdda325091d061e6e3228 9a94bb3bb41bdfb864941373a40bdac3fbeaf9954afdf8b0a7c45b075c7262fd da230d24a0d031ff8fd8ba28ef6706d1ed68b8df06f5daa378d45d4a6bb012b5 5e02fbf75b60e133a91c0517722567cdf121a75d649dc7a5de510e0f08257706 e11ac8d47a205dee880f1d5a322740f1b4bcdc4610bfd8022494e2cc39a262a3 0a4c4a734dded4ee9ac2a8de646b3ba00dfdcd6263d05e10aea6d10970abe432 efe8e882dddd37178085ffec610881dec2aff9f2307be6caf5c65978e1309bae b1a01e04d42615fcbf9a7d30ebdcfac26fd0352ab58510c7b6418f6352240cef cb23d6c0edc1249dfb319808ae559f45ad968332c14cc99efd29c4ffe53c2363 845ded84ec71f7925cb9a40594d622038ca204044c9d49e5670918fd43896ed6 b88821e488ecf7fe5acfb4b70ea77d0e29275aada21773eafe083f9f440d82b2 eeff4542306c8aef14789304ca464307e52a0a8cc6f350ff648ec1d8e0f275b9 58bbe9fe3047ec7b514b9c71bb09a340b3675910c77b80cee92b4278730de17f 54bd80e906cad3b4aae6d64b3b5ac3cd360881e4f074fea8d62864a5201be15b da2a9b96f53ebd904c799590cac003a916d3066511041ee99beb93d28e94a79b 6fe38185256850b4bc5b66058b1f1323f4afe14cb46981d0a3907bc09b7cff88 12a22a568d921f803dabf86283ae2cc6ced0a71baba5592ccd9f44f9c508aa95 54588a4865f5ef25c7e1d130f83fe0165dcdc10de3ad0bbebec8d3781fe65cee d732323f454d83aa888190baa4e8ec230a327a8dd76b36a11ef257a4bda52d22 3a453db3c1d7bb604910a79df23f10372015a8b9a81fcc7d9705a37ca7a55a73 5cdc2ed9f293b600925229179489280111eaf67790eb19abe00924927a12ba68 c340b96d7ccf1cef2cced2a28b486b735de08501fb2ac0253f5ffa8147a1ff79 b0daafa2a037025567cf35a1e9bf66abfbfa9d582d5f038e71584f5665ac28dd 8ae92306a272760bdf134fa0d378e5c700e6c90151c1b32b1e44c506644c72a0 7e8bca4053d836781f0654501fe8ff954516bc5c3b84db6b3defdf839f6625a6 024460624c06231673cbe9cd65960b33d1f7958d6268d8df60bc36ca370c62ea efcf39ca1e6371fa37a0d1f6bedeccbf7de3deda62fb83cc8f685a86364b2280 c4d21a851a2c04373ddee0c384060bd06696ff44f1763a41a0d39a79d11ce72c 4d0a9ee7c0c80d9e608b8a8caea6fdf1212075a405591fd67573ca4a2bf93951 341d6aea3725225caa514b8940086937a4eeed2a6bef22aa84b83d84fc9fa609 77c39aed75ec9426bcae8c9f731448d0836e71832089ccd5f036b2c8ff743a3f ac319b34d00bed3eba0369b48bd16130dfc5dcf196882d2fedfd674b9012426f 8d6fd6cce66e35394dfec69e183ef535c8268cd61deddbe4dc0e7371135cae2d b5e4c3047bb79a6d10db63a780c23a1b2033e44525e1e46a1bbf786384f4e08c 49be17703a7a243c54639e0103a5da57c4fddd90c6e5e1afab829177e382ceaa 752c386bad601bfae3874526a08be13c3d92beddbdbd96008fcca5b4538a7239 71de3b80c5691e66cc7a72b2d2c2c8228ceac2ffd5c6aca2871c445d25ec73a2 114b63560dd2cb56a8883d993d8be4fe9e507a7daf22d0ab4f01beea2ae3d3a9 67344dca123a887fa803f59fee59d7a0c548986e24180b4d148db09eb52a5466 e853343fa4d4a5067c88f36bcafa34eff335e119ad6c867b33b81fce26a5acdf e8e848e568309815e1030bc38cca7e5c243bfe25361f77c2afdd76049591a04a 265518cf66462835041ccecd1a5ef93353868064df42bfc5c4a155d79cff3d33 b185932a0598aa3da6bc4e97c3706438e747cc2f6f3b4aae6cd6bd33c503b4df 2332a27b05d6a77beab6ddb693f5c95337012da95d70fcdbec5482825fb8228d 543b31ea6fc609366f9ed3a563d718023b1f5690f0f213698c04194138d5a0f2 7500473aa762aba886e88491198350c273d099fc87eb5c44f03d27aa3e0c2535 df1130ce016cfb0168d6acd0d6962ba6bf350c5ba0690a662af5de08479f35dc b0f76333a3028c1215d19227c5094d203c7798984d4d7f49f0a6f22b6f04a11a 01731f899a9d65b5cc8bb3cce3b8d038ea3382164c6acc228b8397c7892f797f 9741dba17eb7bbefb5b7f82a7792f338f9bb90bb6b2cb885dcaaa99c5d13ceae 3c048f3419f8418ce6a5c72499f2b634d7f2d22804774a790064e1ac7b790811 5edfb8fa03eb4a347332a69792aaa8869bbe4e7701559eb2f4838adfe463916c 438ac78b95841028855f66b9c2757755ed0045a76719233f1aa3e962d3803a9e 4b75510dab26cb928aaee76f0b86934be180b7ac4b39d0277d0d40c533085c62 6e8d4fc572ac26767c847b1f30b12bb1bf3b0767009b764c95aea13da24ddd77 593b6611dac7b011f88362116318fa574a1f09cef2fb234356d1c73dff370b03 1445d420cae21a85ed109f838008411ad4082276bd0e52ffabf9de25c9979248 52f2fbd82b44f775a23c2bddb5061b0625b22b60346f5c0a3fe09842de9d9a06 34f5e39c3ad0248e434c69b7e8934d9ad37f00d4d1c0e0ce15fb30496c94bf67 382b8b70ccdc65e618a61a733267618c3faef70b7dc2bd6c74ef423d5d2588b7 7ddf51f083cc9dd905babc1b82c7305d335b1a0231a10573e7da0aa77e7c8836 e6c9a31ecdcee10e1e00de98a2faa911d028178904df8b8b546d8dbe9b486bdd a9d9faece2adc048d49f1a989782daaeb7480912be5f74686f2e1e3aa4559a0f 9b2833ede4e2c733d305c690e9eafc3db23094cf966cb0b300a277d5cf3e775f 06326e0e8ff8d3e02b341975d2302d93ca570fa0f57442cf971d81ed8f7098b2 ab145ca5c5e332baa76dd8430439053854582331beaf117ef9ad4318866baada 98032c0f76652801020f514aa3abbaa88b106ea056ad0047e5270852d5f7e1bc d4842de88f00361d0b1bfd1d6140d9b1d082d9ddba75883eccb675ad8a9ca98f 77a957c89861c02b9920be72f8539904e007731aacfbf127cedf477d752f2156 b7e1d5fa9764d8062c9bba90a67174108c4af8e29a8d9285dde707900ec4087e 573d9f93053766b85d4d30cdb51edb43d11ab1585e54737b2c19463b9283bf86 6e6b9b97e80ce6d6f9c4a401da9ac429994e759fc023ddb7d2bb45bc39ac448e c2946fc0129743b7ae029cb5e96e9fe74c5395108621b309cf10a58411736d10 2646a2e8f2c3e4da77f5d600c63327ff82f45365ab2a45c064f3e0cdf14f474c 04fdf742423cfc46c584cab9b9e0da9c3f111e4dfd8b4d9d6a8b084bba7c3a2b 9774781063d2989303a933c90703583a7f9aa2f4eb4cef3a0e8e4dd9042cc27c 258174735d030236868d24203ea7ff52e9c6b9976308d0172a041dd57b1c2e68 ef9a6d1b543def416f7d1d2c28ff1ba7da60351fd244d47380b3d38382b934f5 2631139a88d984a25eb60babb8371e0ee1d18f0a6b142723fde5cfae12769390 db82f6eb0d2e11e8f8eafa483ae9642d34809c969debd341c573a9556cfb1eec af30932de1829b99cae9feef1dc1551d7964efa2bd924a4c8904ae28a89fb909 b2119c56c0080734e37789466a81c206e2ed45680a02955cb9cde10cb9e8e24c 2c3f846fcc0e3dbf2705e02c13e611cfd89425c29c2c27d837ebc9282aa9bb12 abef5b95a65127fa756748ec00bea9130315595416306c22b57f596a11318b03 32d0176e06465470b1660e77f2593c0f235b7fa7352cab5318dcd2a1a5326000 11d34166967898fcdcf9b6f22d2c727fd6ef21abb44aaae0e3b176619bddd527 b699888ca9d987681dd874a4d8ab919f1bdfe1072a393868859ee6e462fba608 b79389d5b5bc6541e7225347ee715d258f086f553709278dd2d7fcc20510c492 7d05738cb07aa758f46fb396116613a5a5d2f7f64f38861df995d4e320a0d192 541ee6d2888e7b8724ab2b201591752ddfc73395c18e504beaadcfe10eafc3fd e1f6b59fa37b9e66458dc37b5643eb08dcea83b14dd0def0a16a4af75a697230 53672ea303dc5b201ccd1324d3cdbaf53ce4ef3c95507ba04ab9ba43022e01c6 a27461673cc054ce727f72f28ce3195d82ec9e4d61aefc3c31b3758aafb56a4e 409aa731efa061ad44debbea71d6724d50ebda93913be945b512f04f3841a8af 36b5abbc9ed41ddcf34da8afd0962513d64c780a58aa90b8c58ec1e6f5b1dd1a f23379b6a350397435c1444133c0fc4b9b16128ccebfcacc95fe5021a3417400 d9dd45c5ac1f684c2ab581c8784e80536cc788ed4bbcce15d387ec263bd6f760 7e68731e74c1e7e9c6c110cbf658d571ca842fbc17ce0553bfe5f80393d29045 590c2455c63e6fcf8d04ec5c13b3fa683383b56bbd0d5a5cb280cc558e3fab24 99770c29a85cb6a62bcee6d348637a2198a288de53bfe5c5c70a5a5a1443051b d25034b291263b1a72f097ec714f4970c34c596d2b33d3168384bdf287dfb7fd a1d03895d01ad1de3303a9001cc4b7af4d1a032f7037c9931d0c3a521124561b 24cfa421f930256786dcc4ba251b3369c04028d9d61a23c3c7183f3492430dac c4826701c5c4ede3e9698a8ef7311a4a751ebbb9931772878c258bf6cb80c727 ee4c9060a7f8f9d8d5dad41e14241c01c216462308253d329df29de03372cede 7bc384d6490f19c108a468ea93cdf717b115ac813e5e6739e4878d8f69a1eaeb 3090c169de47663b4d29028459f111b3d7b523460468cc8aa7e641cf0e89c336 abbc80fad23b55d03ee1822eff8cff91542b516bd758e9638c58a35e3b26f717 ffa0162db4f19289922e4bbfc185f51684e73daa23838b617133482274ed66e8 748c94dc5405be7ca7cc0d8e866d2fe04cf372f2d244dde71653f4bf12a8c76b f49277530e04941dfa1dcde7aae3c69c2033a8b3dd8277341ce7 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI7 %!PS-AdobeFont-1.1: CMTI7 1.0 %%CreationDate: 1991 Aug 18 21:07:18 % 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 (CMTI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI7 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 49 /one put dup 57 /nine put dup 58 /colon put dup 67 /C put dup 75 /K put dup 77 /M put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 119 /w put dup 121 /y put readonly def /FontBBox{-27 -250 1268 750}readonly def /UniqueXX 5000825 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd80219794832af151fe9d5386d1ed91db54d1f 56dbec55d7c48ed295977e18f23fda49f00cbf6b37dbcbd34dd98770e780450f ab0bb54cb467b1038527da84f47b0cdff9561b343383c7cd96f818e10597fb39 4e91fc05dacdb7b418c8e6362ca4e803b563f227624bc4d8e0e1f76925affaeb 710c3b8220db48814ac08cc6a4d735d85316555bd4ab77a1098370dcb2bd272e fce72e2125b0a783a9b1fe202217eae8eb51e4ee2b9735b997af5b43174c58b4 07c1c7a4b7528d6ddbc7091f1fb8d4a731d78ec08e4c996301846cbeb5673597 69578272b49423899ffa88ed9e3fb5511c3e471150a3e257ba5656d21b8ed57c 4d1f6433eb9e04012c52e0fad62312eb2a88dbff69cde9d39d372dd7934fde7f 906a9c4828c1762dd4e1ae410026c58b56db7df324dad8fc3696323900480ff9 09c9f4b9acbf7d983b9429b25d317613beae8ea83b7626fa7b010aeda862d9d0 9b45c73d841e6d5e36bc8db0151d6dd635442552fa4d942210b738d3b6258846 28e541a7abb75c347ec149ecc27a148cea9cdf7f1e6842ec26e2b9fdac2bd6ae a7bb0a594e0298b7003b2b858a51d0da0ecdb9172942c16eec62c8b4352d64ac ee149e55cd6a72b0e80c67782b42c244b955a3885f87c6b7fa8d83a611e2e10d 5a6fce63f0a6cbeac3684f01f7cb60166a924849aa33626d97a1f7c7d323388b 666e15a2b4a21ee5542aef982c7c88902127b872f9405c9f3ddee6f09361efbb 93e28d89714b02c9263ff96cd423a693ae2834a8f26e926aaab01f70ad759640 dc6d18b0867d828a3c9a3a8758c2b3408100b416b920aee2155e70bcf5c76920 2d54ad46f5af53045e6040862d2cd51f0571f3d440aeb71635a5d3d55570cc88 adfa48addabb0d679e225a1c234de34623cff1285aec530f11ed435d89350f1a fcec3fec85d1d450bdd634ab819fac2536005f7a5c19245fefc55bb6a1aaa1aa 187eca998cea2c5c19ac026747be1925c4fc7ce91243eb3c5f4a2d7c290294c1 ad397629019b85aa6cb197aad3b5eb206379e9be288cf0b23059bc58d938d44b 05c1e82a658f5e1df036873bbd74d9df20796c696e6848e55c46c1d85c3e83a8 2052da09fa881c9742843f274818144f164b0cccf7dac807a5e89217d0f9caa7 fed7f8145896ec2f7f521be0b39cd8b1e68d295e16b4ef76dbb9ca5751a5ccf2 4cd929031f64e5ea29bee1235258bb6a03088781f0e5e866bed3cddc9b8619c0 f5b758883436e44e4fad929a1dace47ac388e32aecbfbe84e051a295f175e323 8bf6c3423d014c5ce7426d44f7f16ac2249f6312f4a758f707a272dc1531b3c4 f5f892eab7904a27d7c98d5d593f4d823caf43e83d5851f3c1f811b90b9f251f 58b6d223a170f861055c3757e2eeadc9f00967a779ce97f79b724921101cdc9c c3e3c424028910479ef68be0c57ebc5db22c4b3a61631cde33dea5c723478015 2097467bd7090efc8ebc622b78eae4a2450672e2e809dd7ee9fd26b88c3a936b 176cbf96760969cf41654e068f0b83335a22d75993b448205c8caf50d97df171 825e198f213915ee0236c0f703a5eee92e09d7c297aabb4032066e098a2659b9 4eb29af3822a0574ec353ba50f4d02fefd491c6e9749f1bc97b6334de89dda26 402c25d84f698ad868621c6c13b7c429e573fa05cde8c590a78e2d52061302d5 2117d9c6fd9a9d5f1e8b9920c413fe379af0e22d0748eba1f106ce97095f537d 8cee4f7a425dc05d10e45d6991c7263008c7a336f3ee8a979efe528ee964801c 7e5ce0a285cd83ab34cd8d5b90ee033d95174149609bd09d6e57945fbebb06e0 e27b075d6e0f5c176a58981106aa08519ef46616376e101adaf0a32c4d385e52 0acc9798b17d7d03a8281304281a23c6496a2c45a8cff53f5cfa59c13f5ddaa1 aa60d3c61d1aa61fbb384b84030fcadf615e6567e52f88c7c2e3438a2aed9645 14a7f58081ae38d5c9eac9ce240737eab09d8f52b5461cad5fd366799a16d1f3 8537e7fd1da2a107f3965fa857f517aca4530fa140798cd8a3d40d8e98462674 63cf2a7df5a3fcbac23a81e466b3e63cc724c44bc3eb48409fc884bc84a439b5 1ddb91edbe6f2635f9f837e74d335a3759c8d17c9d39d1f0b2550091d4862d44 c039353e3165e29ccae04c00b6f6bc497780da48ae62d345822864e584bbd1f0 92a44cbe01d1c7b809502b44ba14c66e9901475ea4aa6ecd6e5ffdbdd608d429 270b88887c23075aeeba097054b0ba28ad44b2b05e40f8eba04c5e242bab0cba 62ac201de35c7ea4e79efc7c16691c969203eefbee00a65e6bde2d617b9b0b4e 9bbce007854fcf665e5ee8c3b643f38afd08fba403129ab6ea4117b7429a60fc e59afb49a93d0c1712ba6c3b68ccdc526d0383fbf01319c2169c8dd2a5681448 6ca337c017ecfb1653c79d6d486a0f8f5b348d0d3af19bba462a51e45d4ef243 a536fb107a1272ac5dc677c8ef4586cd6da0b959b9162b75e6ba919f11a232f5 9b238360aa0874c5b21021128a83f4116164afb53a517435bcd39cbecb9bb0db cab74b9aa0150bf73a80531e3d206bb7432a48cd64ad2ddd1ecd147a09bc773b 06c9b55a2c1fbb9678ad26f8f5dadb876eb1a34cbf2cc4975e2b1571bf7f5986 de34a157cf531cad48bc072f58c0d4e4774cbd54a06a783894c3651b58317aa0 50e91aec85ee0760a4b8c7d5ad695514a2cd659c6f8880f8b9cfdce01589c616 a598840307f14989dc22c108466ff21bb417add95cf886aee7f30c1f8aa17da0 9bdad2dca087987fdd78318e98832831239110719e154e24b56c88ebb1f66263 0954f81bcaa58faff172b6c6913541dbd789363a0b51cb4b2f4b14855fea69d3 7aaffe799fff4bc6e5e57f5a33d9593ea64259a7c2d1108d918fc45ba05a3bf0 aa747569a12f51f13753d802a2b47a55f15acfc40797a4b925d8234929a96924 681bf9e475af8965f922a00ef9c419a7fa1e41626d55036e801022c83eece213 02582eb85c36417ef88e49e8b3ed67c59c64a5170982b0b342267688e7a31b6a 7510e5ab9a108b8509a7972ed942dc1cc2ea1bb2241ea83d1e89bd9ef234d665 11280445602dcc90d86d791299e4ad0303fdb4d3c0e90290c11391c2314517d0 b31c5bca13c9ac0824c787380d1f81a890f609fc55f363eec5995f89cc53e7f6 e8b058eeede5e056c1afc080eb99e9d6b1f666df65abf1084f4e61dc3ffb1035 0fadcfab1bb540681b9b94b868367726194e67f149bf6e8d4057fd159fc4b708 38ecea96b307733a34abcfe2f847ee8b75d3ae0a60befc9acf72d14d3e6559f3 7ba0b3c59f9ebff5564354a9e7dd59103b9a1b89599eb823506389b9b946060b 1e88e6f7ea8fc21c5ee299e6064dc5062fdcd4882f6496439e8a903522d0ff22 44a5502ac955ac6920cc323d57f617c27031923cbd25d331f46188a4f1ac8c79 3d32f5a9eb7f0bc1ddd4599705b5a0d98da4c3f828fd85d16e85e5f49397ae89 fc827d1cf8b7e300175db05eb7c97e71f0c88c96089dc18f09e3a63fff50b346 986cf9d1af83becd167f017d8c7e2de3df1a58c80e299525a9e609cf04ed89d5 7e45326f146c6995e158829d3cd4a3b22a6271407c38fc71a959ce0547ada158 b8da2a8820461050b58c55e7ef99e27d336d38f9e4b265a734f845b9b85b0684 7ee79c652738678cfa46896aa10fc932b4d243408f80be84cb341f4cf4f14170 00bdf8f1366cdfc6e7a9d1d118defea0dfb6e8cd6edd8cd68e69b14701268f60 4e0bb9dbeb771d52c8fc4b7c432d5aed705cdbdf26b75e6df3b8e50ff99841dd 8e2618b85bf2a61ab8bc6d25c3d2d802e80e179e1cab4eabc4d3570a9ceeae3f 9fbe1b5a10fd5458e66359b0062d7d9e5d33ac0544caafd49a2bc0412a070229 406853b52bd11c9926dabe505c6c8cd56c52fca5f85dbb4a7f6607dee42906ec 9e61b1fafc298288d041b2aed97a249289218d4f9cac04cd59aaee05f89a678b fa97f056e05c7e35ff38ef3ad476f63a37e88f112bfe44dd7d30b172e7ce2db7 4bbd4bafb6b66542681cc2ed9bde0f4d4d1649c03f126eb399decf4d8014db5e e35a89a8133f0026f153d7e8e139b048a3ad9c16c32bb5863683b2364ba20456 433e6a4c0606a94deaa03d46831ac60d36d6627cd366c5a0f5ef70554071d7f5 13873f68ca7ec0737b1267a53751c48d6732443183f1f776be50b0e7e1f1c3ee 2d59087a2b13fbee9828cfe5ae5b00dec43b12ab78478c2dad9d019ae0e3c658 a878c23c9dd89dd9fad86a3bbb5afa53e232521403965fab9b1a4e84e3cf5e13 7b2e2e1e7d4b8c71e9791307cdcdca6f36590a4b2114538a94f819fc65f0d50c 9f89335ff59bbc50b05dd6461e1b3d1283c38fd164a55085959f2ba327006dbf 6691bc4eaef80d577f0c762b0342ec0cd6844746951e6ef8758ef746ac932bd9 06d4b1ea0f968bc82b514084f01429450d03d9830959e0188d0acf0fc5d190c5 df02fcef1f8edab45b7ca3d24421be8ce6e95cae2a6eeee3608be314819e66b2 e8815324b49ae28ffdfa4634bdbf9fce631ae112288a46506343685471aab719 23cb2dc12221916e62133c1cd9731bd2807c82b91914806e69437c2619c3af99 7e0ce320bd2834fe47d68832ac3c7375d21991581c85cea7691dfd4e05fe58bd 851f79a983eef9a61cea2a8b5292664d45b4577e1d1e62ce7049d21b3d76b120 7c5b8571a5237ec07ec4bd6e4f6b5c1a000900b0b9fc879a1cdff946195a66d0 e18ab593f51b76ae60bdb1f1b18cdea5fa16ce20280e70cc598a35722e94b556 75619c2960d343a3b2431de4d39f61b913f22e54cd918a857300cb10390d86fe 984185f166fc03fe3664b4be82aad061a3992ef2a4ba66ecde429e86b517f5c9 ddd6e720ac53bce2349b318eb94afae7385602b57e28e2df7b743d35004a12f4 d39b05bf736bb06f08e8c4c97426e47e1c1c89b9fdc124c6666f0fc8f85534c3 1c846c24c1bae6a2cf2ffa6c1c96b6fc252fd9de3b635d0491d4295f5e46776c 2eca0a606db48ab2721aef8ad941aefccaec4f7702351f52ea19099259a610e7 a2ca89ab6b65d236035e6e643a558c915747fba69ce081ad15d25eb1c4490532 b13f0bd57b94080c19626bd9c26290b8528f77f04270a0da66b8001ac2f9a900 a9270a23b3a430c7c7cdc30f05026d5351d6d8d31975679ed5deb832e59a9c3d 65a8ce6b59c821d4e41ab88a25715768812528e7ea4d3fb9151cde6704143545 537de1da16f5b0e8e01238532828422621123574338d6c4b0b52ff5a694b41c4 f02722ddedf0e00918260ad260a53eb16d00c456f3c00afa69e7606309da0774 581d39534c3668fdb9658c6b13cf1a78d5e01906479abbcafa93da822c556d02 141f2aa2b23d4aaa3a8fef14efe1594cd7144d72c488994bb27f6f41e7385955 9187d5931295709e1c02789a66476b7efa9708230d1cfc9f87a7d40f6364eb23 3f26114d5b2a064bdb78e36ec114df4c142f7302a33b81652b1b98402f11b676 78d5a5a2aef194cfec7ac05e7c300807f72553ec50f6656cfeed7b76e3d6170c 6279da0c29dbce3512e18dd5e50228e05308af0df2223a0d3f9d9184ae01e5af 84f06590df287f8df81bb6d10bcf218a60287b4e392b55782b344469e9c7e64b 3363ce25d073eb16bcd20e7b7e3f5c3c00145698a008cb9b4c69bf6aa28e1296 7b7de8b4839df9c8d851f66d9df25e18f247e8c5d1244f10f29b167e92b916a2 86313cfa08360ce8b2a939b2739602262f3a54220c3ac85bd03feec2dfab731a 0adc9b1916118bd9fb278241559fcce76bc944930e5d7da0f92dfa1042d964fb 5a8ededb0fda00f81f971f25b6a1a5911f8d2a8850f76b449c153e1c3dcbb5af 0f76d4e84a96654e0ddf1653a1109c4327527ba5acf127eccab0c446511fee06 325e0c2e08abeb03a726c264f078b9f2e1e2eaaab3c89fce3dcd48348ee53944 5783e4f12bb2fb5d656c198a792f5fca9917869cde34b4a2f3726bcd6fc5fd47 c1e296cde7c68b7b64b6ec573e5ef326f5b93fbae307707c1a23a31ecbd35493 ca96879805da180a354c346341c2d01ee64b39037840077061dfe2ea6d3b233f 25cc893a8b1dcfb31acb7a13443d99349fa24eb5beac0308c014161fda178eb1 e64695afec0a5494e24832664ac5ccea9ce6502f4239f3eabbb431ebdef157c3 6ea2f2ec350a860c027395706d32642e40d5904ee0197ac90a84df08c551e1b8 32707e5ce4b98f94fd48da12c785a6b01e165e7243d2721d234d10a5931611ab aa7b4a3cd7f4dcb843d41c419d211b7179ef48e4217f30f8f3be6e9a5e5ce399 e87f637b8c04e743abcba909c5840f138d97ed16d6ac82996656f3f024f01460 25920408843165da1ed374a8e81a48d7bd76b550d286f6c24f9f85440c7dffe3 94581e70ebd1c36bd1fa727fb0a567d0383ff0a0b6a3a639bd9323d6791ea1f2 35559c4662ceb33e588879ba883724eb4f2c244b2e3842771e9719c19a46a0a4 7b619d1c357c67e1b0d3b9bfd3261b068364a554a329a7984ab3e117cb2fd701 e8cbb5c4632dd935d743af2be930ec2cf102988afb844cb2d8a7e72b18a1b9d3 7843e1033f24b3e81cf81d4d69dd9d297c84f9b10953470bca379e06daaf2c59 ffbe66302c20cac8790eea114c359ef52b76bc59015446d6ad931066c0146f3f 77792cbf6b9f1d120aa8889be6fd8474ce02c953928424c3382255339cd87356 db7216f34467cf0c30b5b4d3205fe28eaeaa49baf7a4ed2f7e8c1a9a7d814d29 995f6fabefd7c38b6592a191efb457b39b29ecf00b0d21175bb2175bf2bcd71d 8b31458797b85a1e25d784445f81efd200bfbf0f1852161273279256e282eb58 2735ed68b5b5cc65eedd3a8f6513fd438d799f2d0309883d4d6fe4e693688798 fda7d4dd9ad8a9f7e864672983c248ac1fcf687f3837dbf800066f53938c43f9 40d23f1c20a1d021b500e3fad398e61087ff18e8a7f189db9c8df93620994bbe 7c2745b8a3eb16e49865ee9c63af8a61598b63f30a316951af62c9f1038d9e8a 381fc1b8a278c5a84f77a2d81a10b9e7f3d73274f4109b032169d552aba77610 2db87e80ed515601c743899ced4a65ca770b695b7efda03df34afe753dc4c854 8c2b9027b65bf9f2184f927b52c525f4a809952f75b4aef9a5b38c936e8dca85 7715cffd42fdc57d27a19b2f8c6a37e1b04a8eba5c331a9b9e883c3dddfe059e d1514e2273797d27454c0680a68026629ca68a43742079d6915047a239e28378 81d23120dcca2bc588d008cf044bf0155cc9672b65ea507642905e38a8e381fd 30fb35481aefbd8ae011eed6738157ee7a51b3d50410289a7444927d5d9ccb48 e05b04d1955f8f0973b472d9cc4a92b0a965db1713dcae8800f4d5e975c74ea8 f81c5b0031fdf0c794122850cb1979649e63c96eea07dadc00f1d5ff0e3236b1 5e5fcee65b89ca271e8a4a91942ce2dc5e8d569079139604fd8d369f314d0b8c f11b299f128ee4a5b891a35e51693288f2a758525a075d89f89dc69b53618f5d 9daf122a6528c4e7bca9277aed3c3239e92b8001a191a34137d25746ccd85017 4a4b92c87415fed98c3e93a9c11e73baed842ec43221e7c3f794aae2a6026d58 1801fc7fd5e1eecac6bf3c33dfe60c93939065da10585b28b9d64a823ca1501a 04487fa7bd7f5c169de7ec60244e67527e114d63c56b14192e7a7b2837e2354c a580fed6e893119bc1eac66a770efd1c8a7f25a1c55ce74c23ac11dc69e16b24 3bc6533d91b26a8cede97a7531784d1f6798143a69a94cd39ccc39efed532f24 6b9185c1b86be7db9b74ffbf87a2cf50c0e8a940c99b45099946bcb02c28890e 163afdd5b48495429042b6ff51127107a7e769fb9f0d2a1c973495fbc427b526 5544ab8a0696641eedea8745a07b56946bd9fbb5273f12442187d0af0f317d9c a541a5dc0a1637f5ffa7a6f9e8c60c5f085832851a736f13e1ef8f604fc89099 bd9010ccfb12ff213b393316c30763052b2d3c5a5285b1c8f6eba5fdf9d2796a b2d87b1ba3e8a203a7ea6189a1e5a86a24ef0a0faf46d85056c87dbd1932f8bc d915ad0c20b4be2bb3886d50c5424a4eea8cddcf295df123c26e2ebff3370094 0b3e95805e4c30b3172ed56484e46c22ffe46e1e87213e67c5626addc3ec43a3 c609e1078e13631c6e17e8471ab3a3511de0fbaa0ae33f4fd54f7c5616ca8ff6 968a587901eaa928ee04f687a032dca18d991b8fbc4c10291a4c63e2c148040c d03a1162bceec39fcae4a6d6bad5d1c993f60b2a82eaf9028d4e305544c3e877 94bcdbd3a62e65e1af59a7126caff80bba67b803cd9680e52759da17bdba7846 c17e782697a4104a9372476f775f4a733d4051359279f30d7a365d6ca5a89839 7f2e0d428764d712534bf1e3e1ffc52d70314f142a419040c413808245c08f94 d508561b8a21c90a260c922cdd8f3224116fb0376319a598e56a24b2eeff293d 4381229de8264a169b956db7543e8bcf1250 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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 33 /exclam put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 55 /seven put dup 57 /nine put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 84 /T put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 dcf4871a5d023c9ef57d3362d9f2d7a440bb69bf653364105f16f4d0f03582f9 aced3d05cc76489b16e3fa8a446094d30038b06ecceda269f2eab9d19a99c7f9 39f9548f206c5a457a19270b2b82c43b091dfc5573468eaa3e7a4a32f8042891 d85e4b180fcbcb3091d2800e54c87d84ce9cad6869b5aabbbe47f40c68799893 d22b765295e1e69e33aa048b7ed98ba480ceca91f3ebf8ef85fe9a3976909626 b95ac5940d53f9b02215d84a44837ba25ed15cce0d504f1d335065594f3bc824 5405407591cccb11cfd4645da60d960c0b93f187b0cf7b105543c0b70f89af5d 264b6c026e3ae646acf145950202ec73282111e3e601cf2bcde22ce3edf6db23 516481420f26552ff4472d749811f27768150450d0d0ebe3c79f999e99b5c0f2 2eaebb12d97782b1bd91b2a1f62a76412548ad53c0dd411d4a08c0f071c2c218 63d9adb75a4621803ecb84c2bb235b620b658984b2d8e0c4637e2811bc8f0d04 6c8935afc70141e1b2d9c23bdb251d304b3378faf8928bd09686aa0340fb0cb1 dc48c996ef91530ff078666fad227a3589f50b605267212d3a65ebc1019a8eec 9a0739a00279471a01e1505c17658c10030fae32f274fdc8c8774b0d5406c384 a1d17068dcb0c2575c562fdc5a2176609bad9a2c255e426a4325a4fc3053c7b3 2f35f7bbc9aa50135f30223360fa2fbf019294b2e1d1405e078341097090ddba 1561f22f8738fe105c0e3b84532bed145d51428c9cb1807e655408807dc69161 1109a98af82680d6dccc987cb312835dec4ea0645f47a15b6707d654ae54846b 3d3301d61150fdea8ae2da33e79976812c7764050a3e86a2a819ffd3c64c38ec 16b2d0bec3922847fde375ffdd82f8f8bcdfa39c53068da393b35277ba7af682 9e48b1607f22eeefd7d0eea93ba1e2fb9b5ecc6c6fe1075db980999f0be7a3e0 e8021f1657fb5c18e996009eb94ced22846c21e3afc8acf7d8f9f4402a00df48 d9c0eb196f6272b4fd1df76563ff2e3b22bbe0179354d8b721265cd299c99b33 706b9a040fad5a36f7e09d255799da13276bf08e803a43fd16734c0d547a20b8 7f9ac43c2bcc227108f7cc47745fabd1ccb3a347ec13b854626c54bb3e8417fc 62eb327ed7891cfa42d117179cf1768cc4549ec36601adcc6f55d095808ceb0c 3a44dfd8728cd53d7a3d1406f1dc3eb2ef10fd99da850405be87a0ff1edeb7c4 f6abd7a0e02003945ecce903d79c34f8232c48d7d78e534c8ad3d402fc30a32e 14a9fa6ac2a07666c4768108b68676ca4223d762f6f57c1752eefabee59cfc9c 32693bd5756129c633f46af45905802f7fdf9f06ab9b382f646e4cf0ddfd31c9 dd7f95082b5e028125e502198faae514771e3069d7b419f3e78c58dbccb65a75 6be1e32306abc8be436c44e67049fd775a309a110c1344864f9dce8bc5db9361 d38004150fcb8fabb81e6ff8d8bc617b43a164f7ca9a5fe4ae35c6284fc7d512 947f1b3486226a9998c75d0cdbff68c099c80385cb4f3515a76b6448ac4b90e4 e3f496278f5709db3935f2f1040ae889b63d53414336845596991ae9fc9c4795 846ad63132669e2ab3e1d9400b9cf685ad35e9eb0e7db8fb552f8e863ff25203 8409f4bc960f6516b91902438e0b65fce7ae56bd33e76dc9e5a4f435ce26d0a9 c64e95645e978c8a3bcd70e8ee782094606439374c657b8710fdac0496ef16e9 d16a4b017a1482fb7bd5f8bebb106ed5ffcea71174614c381124366c88ad86f5 4e804e76c58bfc2122d5c1e2ed595ccf7458ede4f8e752fb0e3fc6828d08531a f92603bdbee52853033349dbe8b8c9a35312b850bc62e27acecee482ec38d202 d6600563b386153327e7fb4df096de1373c75ddebf72252752d1816c189327f0 92c349808c32272d58d1ab9aabcda4844e1e4aa725f44131375281d156ad1c30 39f1fbe113d2eca763558deb6d0619366d27ba477f0a9efe2734d40b5530b456 4aa644a6b321aaeab90217706c31e82bf5a471f6baa35d016f8d37848f59ad99 8c9403ce13156b023942f8eec8837470776a3e6626354cb30a0ce3f50afac8fc c44c9ee858b07950416a0e355c053720ccba135979ec2cfc492275bdd9e902b7 d138166c064a33cf47e4bbaddb66afbce17e841d977d0c848564298af9940074 3ffb82e38da174bc8ab1770d6cbcb0969b71b1fe84e46bec9641c53ab4fc3461 2d4d8e917016e390e4a9e40e1575dc0d56ab3aa888f096cc27eef14c1f496242 11f29b031af0bf0293fb40bc90d19c59622cb1052e7f581880cc5eef58ea5811 033b0c231e857506a7c49f9a250fe10464281ee6a34e3709ac5b5f664fbbc5da d8c4d16b2ef06a34f9bdbd61a042493140c7e34bfe0e6794c32274f1b50456bf b4ae80bbce48544c3dfdcde141d0b4ced807572075d6f6b0af90c7e1a936f6b7 49bafa8310e983f95b46080704f0efd565fde22dd8a49ba50723829d6e48289b 54486e63838c00bbc38dd163851b0ed9e5932175a37104305bce366630e116e3 9542a575461913964a782f22ff9a8647214aec4031e925ea737c45cf9ddb6469 4b1c5969958c3bcf9f7314d958dcaa8d61c231ead3c57de74649770fb9ec2d36 fb2fc5d851d114ee87a03aac30b6862fefb05e36a3d89dc5d6ccfbd7d6192a7f 5f7a9d4124805b664d0cacbd4d8d409bdc2cb255388374c1d2a5822f43cde5c9 f316d0fae26dc452d5236632a4c68b5d0df561a081a7d3680ac64cf770bedf4e 00e18a0051adc8af030887440e8856f9ee76e0ca002ad06639a69e44baeb94f4 4a4abe684f0804cdddf60651b3ad06e811de6394c50f65b8bc33778cf64e1f38 92d02d3cc64360a5bd1dabe0746dfd96b0b628a120d98cd49729f2de63f4daad b8145a64dfef11afbb3a70b2e47e10ee654205025393300e27c04469608e7a69 34a379e14528524e6cf633616a74337abd4fa1b47f297a0df247366ea6853084 0e9e0fbdca2d0cbd428f91ab11c52bf1c6033b372a5f665bd30473725670e920 344b1a76d68b3f76bab361ffde6ebd5210626af7577f053f9f0199cf38975454 27f0574a043c30eb79b97942333668905fee76866b22d7bc636001627d950705 9f4945763b671919a77df1cecc6d239e6724bb14df11802190407166849040f3 b51d9456fd273a18d4bafd5c192ff121665d0499e6de007af1642f9704f0db63 dfd8ed6652ee1d678433748bf684746888850b623e89ca241886673638f10012 50fd12173d2bfe1fffc5c48021e1c14869804c9df555fd16d28415be0718b49f d7a1d9e3abacfd44fe5268df60bbe1b3d6c5de5232458e20cfbaf98746729720 43a1d8986815140f3c173109009b5dfa1abe0ba3a9b82e5e9ae00b6269d2b925 e21088c30bd0acfc66d2160ce4b276fa39f5da78b8788f0e3afec475822644a6 6677242d35a55e94bd2b410cac90b3b34bb0ed78a4633dd2a150c0b934c280fe 63b86fda99404335db839dd7ffc3a2b765b48f18668ed19f799adeeb061b539e 6893ded52215aa60fae068bf2ad0dfce27c33374a766e29af80028c745f793eb 967faf072c6f8541df28eabd8614fabd86a361ebc0ee135229f97a08e0d87b05 6382c648ddadd9d3b533f0165d2569331dcbdc9aca5a4bb92e08d70bc52e9710 dc0ce3c40a17a78f92935c4ad2be86e751fef2a89ef06b827f224959f27dd707 96ff329047af7666d3631f88af4c3a777fa97195dfc14ca293b210f9682cba37 c6ef5b3a4a6249da7977cd38bad0dd4d5e96af05e4cb957aa60d3bc341af343c 55360f7c9cdb1df0d0cf46382ce83377fa49785fab7041eb97c837230e01adb4 48b4cc24fcac4245212a5be33c4e17f9989ecd72be01e778945af4522d81279c 94149871740953c35efcca55a2d678d663277a28bcb7a09073bf02a81cdfec80 db24e5d89148c61faec10f2eaa2ca0c824949a9a3820389264e2561ce30482a3 aa997c2f4a82747c0bba45ca4d95e5fafef7b6510f0df23d499b1da757a21e77 f6a8752704e2274ef0e8ed9e6837264a3f05f95593e4938a2fdd5d7eb00214eb 61ccf2e1ea88bf1b14e760044061eeee27d8199e601cdaad20e043e8ae772733 7ab5f37c301e3a1eefd60e20e83f1e9cfc2feba796cae3b7823caeb6ab812cf6 5b76be2c2face79cda7121b52fb09d653a849d55f1b973f84db389412b46e033 1ff075d3f76dc30474701f4493883633ef944d3fce1cffd6dc7c5eb4598152b3 388a12b6d6592b62d499b3469321071527d2cbdcc62ad11a95e5c1f1f8f0804c 4f846d442134b676a7883a036d987218d2829a736aa93013612aaf5bfc9c42b1 b2437ae06103ef76cc334ac313b5fa3d54fc91a4083e879cb5c2aec6e14ec2e4 0444eeed8a848d3073da9ed84094d199e93937c9dd94fdd7f9d18362e3d76566 1dbd90ee66025787450efbd36b3b81aad7786ff61c244ba9dea5cc546b508250 80c21e1520e7567d5d6d1d13723b19720d17b2fb248c0617d98a108aec2b2052 a4d3d5631f6580d0d04f2514b76fe2189326528876bba0fe98bf4024a407d46b 7d9942d65d7cba9cbaf0e71761793d9173841e3ade41363b23c4ab537786562c 2bfb2a7fc20d54a643d0b130729cce62e2d126a362311ba5a7445720134cb2b9 da1f05be3bc4cea314a576b53ae95350026c7be31134b9298069c56367a885a0 8332c89bf933b78b9ac138395ac05356a2aa5079e20db4a1d7129999c79a7ae4 6e56e51505849004776523e2c9a9b99e2ca7f873aae6b995199556e8d654c61b 055388e28271d57fe8bf38eeeaa719002d6e095910b63537abb823227f430e9f f257e33cc59417f5e12b8b96477e674dfd8a044799d63ed4b4720e6aaf093773 5bfec519847a8b354d7aba0908f807a1fde5a1e01c8d923bf84d4bd780dc11bf 5ccc07ea42842ca19ef00ca489731ada64f95c5c0ff26a6c049d051087c2d1d2 4197ac1b1a09ec8b9f154e8ed3dc29dc08b94e2708abef845eac45be4c05197b c70a344c26e3e91357ddd834d6ace80aced37b8c7ac4a7b36b9a6de90d57fc88 859d9adf4eb8474ae4de7d228d1ee0e809fbdaf5bfd3dd3c1ebdc9839105ee92 4905479e1b55d661d528fd73feec495a9311f05580a23f206bd1c8dba6f0a575 8aa39ce9c1e5232b8b5b560ace18ef5613e973a4173a288d317b8a0440b6e77e 58048b6d4e46b4a956c638227948c7c6f56e4e5ed2cc569400e6c1080bb9b200 d387b33af8e2445d4f68631a2040e95cb0d8f006d12e08187db80fa5451df1a1 224e5ec7c46361a4437c61249f0751e90edd2de46bf04ce033e1476b85ecad5f 0b0cc9e95d920d4918109b100850c6fc086b70ae831029908990b82beba853a0 e7e9f640f9981ac7cc6b7c3a74736013560c73473f12265e82e3369eb9e3c3cb 793a16b4f4c17de886526642239fa6c0ff7d44ba18c019c196a41d700aa7c399 9b0fdfd2ac5c19ce1226b6623bec76f2cdb9e9dd429c73965876b7c96be3bf5b 967b0d720592e839471580b9074dc7fa86ffd5c0ec5cc453e370357861525107 64814d9985f276ec7404ead45e60ce3bacccc9753dc57f84804e8dd4f79523fa bdca123fe1b6025ec51d0ef7475fb517156d89063ab919861cac67837a282773 c6d318fec6d41ad8038b73d58d98968cc872e053e89a5adf64a2cb38012bc5b5 541ead7464c060a24a192d35d8f04b83dfc03b7a33cb3fa99550e55415c14843 54b5531d07fe50565198efc90491c42b3feb9627f34a27707b807ecc29634169 bbae7ad8d6c5928553277b14eb07c57916c9bf022eb5313061fd5e79cb042af2 569d727ff2e2925eb15c740f9a2db53e0b25b8ffb80225b7f97ced8ae4ab9651 0f6c1b38bd832c586b19f57cc51d45ca973ce3f191533c81ec6ca9338ecb3b6a 7f7e410879ec9d47e345386d83c967463de5001a7c81b316923e8031fc73b361 bd6549c1e56451acd84e6e49bc0ea77181e539d43c4bdc1bed6f033c674bdaf5 6ebc4ff35bcef84c7c168c211a2ea1abbfa8a84b19df13c9f75f252c3d89187f 846069df1431325e2ee6b044b2a87222c1b3ba83cc369a0af52a3cb98da7358f dc81352850b4d8b9c79b897a94f7ceb8beec803ecdd7e930de792576f46606f9 1150c146dd852751660ffa03f26b3b12b88fd62287a31dc10a25294fabefe634 2a0d9f9d62b05993fd0306ba0809de37e946cd84eb570ca2bca70db1b5cc96fb d90495051ca860f7c66c746599c5ff661bb57f999fa4139c4c5ae1efd5d6450b 59fda10413a361532373469122359516b521ae3405283401c968173eea5599ea e581e2200b9e0172afc4645c7c6f2fc98897cb201e3ddb9ccd4ea84f99ee27d0 a86de54d096082a72e92fb22333b99b2ffc4c5506d6cd97502eed5ec5e66dee9 c289e2307575fae9fdcbab3f1e3292656f7a74d9a52b85fc467415c2c94de2f5 e78a6c76d0ea9b54cee63ec5d9c28ce3b6ce59ef405c6e8236c0981c1e967316 ef139184f7fc9d7d5c95616bb4f934e6a6c5c0a5b190779cd6a7dd58c8650c27 8910b156a21925f326b39514d401db800eb02bf4f39b81a30b0dc1a6a433072a a52f65cbb25c1b0b1ad5db174ffca7655d2d0f895e55fbe4c2eea220148e9263 4cf04e08db665ed53ea9973ef69306dafe02dd5d94b0baaea8df73ebdf0a5fb3 3669a7f78a077b774ad9d803c0aff5a43cc5183ff0ca071b999ffcdd037d99a4 b2cbed3d14706a019c98a60b30241d418a256dc4b3dc2343cf567a2fd328b1df 1b47a9c9b77776b16e4b533fa805c7b23316a03ab4568b95c04b01ec001164f9 e6edf8325d8ed11d49909f6e626c566d474f808d7272dbf9a77ed365bfc2fca4 c2caa835fb86824c07c78043e57f402bd4800d7d11fa5dbd6ce6eeaea6e7ce6f b39a3b3b0982aff5c276f79fe8447a075391aeb8ec67f716f9ab0c92c041912a a55875376cc683e4d17f688722f3e0fc66695c60ae8150fb75bcd5d826218800 2ade725a81046a54732e37677896bdac53a6630f8359eeb50ef184e67873542c d94fc2097581ef2f7e4d45caa0de6befd99fa44beb82b9860021a9449c426dca 50a3263a51636af3f475a7aa24be64fbbb785dcf286ca03db47f28ba396a6cae 41c95a07e3106abdd8612be0259f4a24b5731a3c637cda76283ae1496e72b708 88b89ec66292cb86d632209ee5ec773884b99e1fc8ee0bcecd78be6d05d37d76 054ead6c10f5325b75e79f62a5fe9a5fc43830b75a296a7031c1706a7eae7d08 baf56bb2848422f604d7ba0e39b5c267f138dfd089031899f40df91109c9bd88 5674badbcc56745e5d7d217485e95b68c2bc256c5e29bffb893ebab25fc8440a 0a74889a73ed7945538187190757262b0ff579abd195fa2ede2fda734d34b9dd 9417c26ba999ff58e6545950c2da6024fc09902bc9985b47e25b76669fc66ff2 33f35d3b5e1c4ee22609d26e919cc1e8de1ee8a051ecc1ddf1986e3ea1450517 c0e4a7a4fa740496dec1c62c72733c9bf51c090596d756beb7f3976c669c7cf9 601087b2fc75cabec329d7fb4b8e9e7beb2f3f54266aa39902be4ff45a2e824f 4c9b6bdafca53664e648b095d2ec568f393dfec35dd8dd6540987f94ed83283a e9b65b6220480fd1cb16281080dceee3300ba1477c6db222e4d2f9a4716fd57e 3694d2d9e0b3698dbba567776925d7ceccccec8f6ccaaed802af1ebf87f77959 bbdfaea8f7bf4b0dcb19ea65fd2ac995f4f8e5adedc5a811244735c3f541e616 3487b5678996476a822e624f5b7e0d5ec54e2867d701c6ffe1539569721f2644 13010925ae14246612e210969e707455aead59e6276b1b0355f2eca34997754d 612e163a91bcb13e20ab84632d9524b1ab14dd5aea28d00861ac9b24783093fb 28f39c8653d8aebce55f5c4187aae45e60b75ae9fb2dd3bfe7a59e41c3a0cfee a0f40fe5926c21c2bae4ddaeea4b16bd56c489a724c4e7662d76b57bff64764d 540efa4fd6cc2da7da8954f807443098402d206e8bd7db66974626b997fe0884 ec409e88ff6c1ad451a89da759da739cd65877ad7a6a660a1fb79afee0ca274e bda749f570de54e8568d3e6007433ca3195f12bb931c174abfa6e8cac610640f 4b0678adc4f35b73f83cb74d1652a9f121e51493a2d9e1fcecb817043f0f24fb c5f7d214ca4d2345399d94cfd1c5983520d81c2f55381d329351c0225119b7db aa4b8d00af9310e017dd859c41f3761e87aaf7a28a5a08c64814265f73a573cc 43afe2262deb38a54d8000034ffb0615b19abd70cf29d422814c63fad6ba2668 290429dab1f9dd1df220398c43976bc1647952e3ce954ea799ef1c722d8ed2b3 8ace7cf7de643731c239a4bf9f27385bdfe60b279389f829fe7bf9550a6222a4 7eb509c196c4aa557ca0aa721e51994a124c384eeb7946000ee1c4116f45cf9a 8de9848879d68124efedc1cfa08cfb0aa1b3617a7c403509c8227c8e3690a11e 0beaf11fec0c3dac79e9adb46d64bcf1c3d73958334a36eea83c8831c12a992b f5bb69e9ebe9b8997b5099c7950ac09122bc2e5e0bae4d130601e5f3b464ffce d0be2eff5380b11560629ac3678facbd84504429d9afc86b7ad21b8562956a02 80a2a44b5c5437f8534a301cdb46444d553e79d31c51fdf306379bf6e5b07f3b 730cdcc0644a572fcdb78951e0b93cf3d870d3901f956db4010f9c23d2d4c38b 0ba140876fe9136b2fde0228d7610475fc24edb954a6c48102ad3e448c5e2b9a fa4dd7b5978a2d9d7401c02cbfa3a49cc49756bd215369a17829488f850c4a09 cbc2cf579f04e40abca50915a55e153e86ce02be6107a2bf681f2cd1fff40d3a 7c7c1c747bec1102c496ab215e9b320d8561cbb134764a7925e8b013ce0d362b fe9cb67df2b43af628a7163dde3bd0e4cd7e9d4390a7d32bf2615a7e31b08a19 48cde231afe371da22a948630ac56f05121292aac33b1618b2b45c35d8ec6463 7c5cb32dd65c6d395e56c73fedc058f166878270ca0b6bf1baed28616e2d8228 1e310971024979d884d7156b5a02951f65b2ae9468947431a5e6624287a0d4ed 78ec03cece27b2ca137b91a8a18d6990d6de0f4a17ff7a27813735a44fff3ec4 9c1ab206235ffd94007368885724a2b938e13d9cec5b3a5ca76d81a268144275 99f13ec260b40bc774502415c31d94d782f19d704ecdc1cf468e8fc0e4b35a6f 6006221a5e6897db327297122ec94cb58f0508046e0b6e79bbf1676b8fc4a275 b76ff02f84c9edaf3bf0f24319327ae983799c12baf7d053177407dc98b5f4e1 1ac94de42fcd56016b38bec14571ff76c3952e79e9b01c754ee00736c013fe20 4f00edcb355e120ff8e04b453a0b6df6576572483f45e8a57954ad7ee39717fc ad06ae2e2440c7b49f34f6decce3a7b5d39cd4b56b91d255f85862861e9f586f 94c02413313d1cd7ca51c30a6e49e5dff700b1885066bfa72c1da3688508c722 5f49da7b3713fdc9a35144767ce1713ca9a7d67274f9a3579369fa35eacb7a6e 03487b3ae7b1e7a42f1d469513bd2b1919cae525adbc2476e223e574cb591c90 a7e8e03270797a90d006e2e5ff50d2c439ea2915ac8b56b805f91e70c8127094 5a631e34a0ef20eb352600ef7b4674352694d7a6ec21a65e8f4c8a0a97320732 ce694370311336b9a9fa31f00fed1c68ae093802a1173d0700a508fb5200755c cf0ff25a577efb7565cbe8be7af7f40aa3254bd5828c977784abc63acd8f6104 04a310b8dd7264fcfb5b357ee543f2696afa68cb390a841206e7b26229b7e664 2193e1cdcd131d0ef85c489d95ddd4435ffdbaaea41ff07e005a3ab263d36989 de47ed2f99e63e9f88badd6f5b769f269f501aab07c725748a33bc7baffd6a72 4684fa6f292882da99cb5e1d9ac0b7c3c89f40db5a0cb9dc7923cfb2c73ae79f 97dd2926583d3e19fd97476374d6fa36fded42ee43e624f957efd1cc82a3c554 4a897f1c2be52018c553789f108b252e8498e1cea24aff845e4ab4a1cc16bbb9 864d2b12766cd65134d62e3caa1f16d27e2a4af808715445323fa6babc10a826 106264989cc32b0a3bd51245b323b6aae687352211f2f965892eafbd7c83d295 d5277961e2bedefe4a37a0b938e0ddb96c244f71905227ae3c52cf60922c38cf 6922c6360f76691b4e1f8a962d56304612f5d26117f9f73657476efcba97d433 84a8ff0bfcaeb823ceec2113693d73dcd1478a12087e26b10af4944b73f2c115 0d3806400c5651ae0cc720f4fd4eddd8a5742d9376ee396d26ac2d10ac7d92e6 272df7745325414f248450a616a7c0493ab32e8539f49a54cb69492be91d1ece e2bce12b43cc49c33f0b2098b28d7997e1489b3c30682ad39058450cd9ae831d 835ca08f4fba9bda7632e5029674fe6accd587402b27d51b5460234f87947cdd b6656e8bfbf09a9fce7ce678a9bc007e90d4bfaafae6d31146b9fa6544a6eccb 6466e9f04c413d83dcd499d7f5e02ddd952dc51c13bc2b1a79a14b27eb320fd9 6520f2f109aeb1610b86ae3a8b359eaf82d68e11c12bcd43356531d70b0a4947 932a8e4c29562c1b2647842509daa9a3cba687f18ddb878899ccfaa040cf63ea 00360c0542bb741f2743e3875c85cd18c747041d7eb6f0a12fa2427cf00dfa23 6720a81bb5fac86cc10fe29c5601cf99ee9eee42f43c25055bc00137ed50de86 3039d5c2efa68898cdf9176b9ff7ab66771f784648355f80ef848d40b0cccfde 19588ef79b678f204b721dc5e7f7f50639e73169793b86a03737bde66cc28479 9be44bc6a3bbd2769cc286226ca8c05f0717d0517900a34ea53ca349236b2c17 82784287bcba1897f564c9da83df83123e1a3960c55f459ecab72eea5d4a60a6 902004162080776258dcbc7b47d79c7008c6b8dcf0778565c8202b4f33b05092 5b0b33aab832807a423b52b29b7480086cff2842bfa537ddccac2e1e35bf5238 75cf90578a4882babc4c594a81b127ccd64fd76d47777704e5927111e24c3276 be32ab442e86d2e10ae2d5afa248e51b55b024dd2949d8961f3400452a05fbe7 da760875f4373ebbfde751dd15c10b14e26bf967469180146f1fbe1d0a501b56 e166bbbc19ed5c13f06e535a1feec6ef4ff738ecbc179b5ecf239360255fdad6 2c4ef02b027066da4eaf3de496204877d3bbf1d379defcdc64092e82cdeca81e 5373ddbc1c693aabb3b6ba958dc7e806afcb93c2f08a2848d54dc6adb5bcadf7 2b42faa98663007c7ea7ca6e536c35816607253accb5c58ce8fe8d24e088c7bc e49bab032c2f4c01f57c11738cdb60e9ef61fa4bfec85b115891affe95bbda2e fcb5623dcee115bf5e68671d8120274bca7517498530869c0147ab6e890a92f2 9622413dcae5a87b3d6d3f8a39b1989e9dea837af3e1653f4cdb27fd60ab75bf 44634309f4337b8f1ab53b26bdd3936ca6cb60b60863fd7b79c9f6997c4e60b6 1f9efa4b4ff222684176d5e41e0763351e6ceea6088f2ae84f4ca875c949baf1 bd3c5f7ca6a6534e3b061d835eb8d18a7b058105df0123bc37c66aa84da6c1b8 52c88f6f109ec6b191fe17d98a7818a45cec6396a3d29198615e584cd9c3b750 2fbae5cd5ba61d9ef9bb70cc635f1252f380dd73ef1b6d2877d1fae41701db70 b4eca6c8825ec79b62c08869a82b50c21dba61555540229631584702791980f1 92068cb76b52bae785530e5e2257344dbcca5ca04fd75e2f3b6abae19a5073e5 e58e65e2cc3ad4af52008d31cd7bfe9f37291937e0a6f6f38d1d9f2862242253 ec6612ef07de7afee1456c8e812baad186aae8f611e8f63bb43819ed40b1ecff 7f117befeb6261479a5ec1fe5f48a9b103e73b245bc2fce9de170a095dd2edc3 7693ac6e3561c3b4d30e1e74719aed6210fcf9bff39d60df622eca2b4c83aa53 76ab20634a1ceada31f813aee0e465bd03c3166532f9fcf785d6dbfd3f3e7df0 5f60dc0ef04b436261a0cf7d0d7b8e52b7b1e0754202fc19c88bd21a6c1e526d 8a4c7837d3f9fdd8ede58020f21ab2789899bc81f24bbca03f291bdba35f09d4 e39c2bac0c9bfe62d5f79c1d7c999beeb70d04c1e84a654b5432e4cb52087822 5bf1f3a9aebf9fd3d7dc5ad91e64c74885462c31c77792cea8460a74f8d773a1 ff00b1b380d62b937a185273e89e77bfd625f64b34c44a2ec9ed97a6f1d134a2 a2795256bfa9efa852f86547fec307f22810dd115ddb437d6029dfbb972a59da 79f636b10a1e84c39c16afbe0e871d5ecad26a492db71d62918c884ae1a262a5 284dc735f3a60c76a1f32a4d1f394f6d3dcd718833e5431adf1f73cbf2e9c8ce 9f107b29915fc15e7cc1da1439f16f413a819aa88d8831c6125389477e3cff07 8fc099dac1317f9a90e6b90ed6f7effadbed72660a514d34deb15db431c8fb6f 173ca6d0c783e3fdac5a2f82693580bb1e9d8c86bb67d38f7cb7be12cbd5eaf2 917799b1762f88b14cbd068264cc77b5d206a6cbd5d745321b2bb156232513fb 2105d622091e6b3cf1534439abe195be35bef153021aaeb0bec82aca232519c5 8124a65990e838c72607c62fe7a98315de6cccad746ccea92ebc092c0595a7c4 3c16a4551035dd586f60a48706cb39164b65cefff3ade609d96ef9cd6350871c 5bb999c95397ebe8c8133f1e7bfbdc50714bd8ae2dbe18ef21baa28e6778afb0 24ebdea9367b1e0986b58beea24481b1563a8cfb5035607bf7fbd12ae1352a63 0d382762f2e2dcc54891700bbd3bc3c7f24bcf0b486b31d6e83335ad5adc62bc 6db8425566182ae5a2c33379fb7689e2e7c14c2d305a4ced41b7356973aba6d6 36c78ce5f13990e999f8dea3915ec02e80b55afe216f2980f3d365225de366e7 dac7d09617d38fec1ea2ac4d96cb448541779668f4e5ef7be710a616732f6521 b89415e6330b3f10ce16d662af651ea7efab3decf9009f946106fbe8dc70f5d8 06baf3567d899f5aa4a5242046436c2ed085f92b560bf900912aca3287c2b4a1 730d9881cc27f27981cdfe61ad8fe54529e4536847dc30f6655740e905808d49 ba7b736c3c2ab9048724f8e35b008d1f1353fac166be2b38612adfebe8066fb5 dd8be972113978f6fa943910f3fed3dcc958be4acd0e9ca5dba7dafe321a15b6 e2b547aa00561d93232658d094ea0cfd48799b22fd0b263d6e63daaf92ed87ca 2533226f17d31f6c72a0c2a333e235cf80e99189294606a5b00c325a50c8aa8b 7d3ca3af7677e88f78cf6b5187dbc29422a1a7f0afcd7086336bf5dfb435b33b 33f0953825925ab3003e0e88d166539caf9fe46e2f9a0c6cae034a328fad83c4 145ae35595fcf6b25c7d476cbc855efbb6cb35284b3bb668bc2bdedc264d867a ef006fad50cd508c9ba1830fbcd269e616fe7ce731ba378cde4521e96512c1c8 dabe15c50efebd1fbc14998e13565c8772f97aa834d39edd4278414ba2717489 404935ff73dfcdcf79bc3d439ce07bffda010eb467b87ad77aa38da3662c5aea 891b726305f38af8b9bd6dc6198ba3af54ec927553225ef2eaa04c0bef62ef66 53bdd4dc15c20071e1f5b561e71f96021408bdd778a2d577a6b7e135cfd7feaf 550f2acb8d60b96b8286acf33ab12450cd1895c22b4d915d6836aba507437504 e23b0ee308ce142e989c1afa1695417f6db17499aeca0092d6aea98d53886522 1e8a2453748a5a97bc4efcb7c28f782ef828fa2440096ad077fa35afa314453a 427aaf610b6157a47d3f36b48df81bfdcead07ca72efb09fa4c7ffbec70aee7a 7d2db9fff970fc5e17d363276f8c8d9708e8bbf0b6a2a4362db36e243ad81eb1 2e89cb597f4ce7c1ad50561b0f655e5d15bcbe7433a27771c674aae7ba93afb5 f73086a45f630c8f0d39d282f5f27b264225523a704bdd8bf17917d25ef2c924 4ba43e1bdc5a440cf9cf23d639100395e4e72f6c73c32f27a8e31534921f874e c6e244fb76f1ff64ea3d845655d5a9360cd21e1ff27ceeee1081ad6ea7700232 4631eb2f243557563439b5b0c89c0ccec877911fe3ac1555c46d0610fe8c96cc aea2ab741ac7a2a89637e1a91b2f83e29df92763df7cf86ed784ab734edc9d8b 54673d89cb922c3698e31f1ee79662a276ddd531eae4b7bc52097a69a1dfe228 8bc0c184720d3c3104d280c64a28ed750d0e477d97a232454704d945b76888d7 229b7c9cb0614c77301d8821cd6961243d9fcd341ff5e735b81bd58efea2724f 30f90525d67969386b354c48f45a1758d9e603077ae0f9f55eb84780c206e3a0 ddc455807043cab6c1a7e946fae887176c927ef2c63ecd20ee08852d603ee78d a1a167012b171405266f7ef5e96e5419f40f0bdcc1ae703f39f442dcf05218e9 73d6981079fff0e34d8db4c182a253a56fafab0966627c34a304291114ea9b0b c150baaa38c57f1e98161c5ad1951679508c0a648b1e13600f6069dab6aa6212 0f1709adca8138a81ac0af5c4159b073d083c40de240acf0348cbeb0b1d1c4fe 6f829b8c83f273d8ce46eeb6d677910379be8ae826125ed6bb76d2662f14b280 305e3d1e35986ff772b85811297eee2272881fe6af824b3310110b5bb5590540 d3fdb56b3f9320853c697dc1d8a7acdfa6b399583cf28b1e3274bb74805088bf daf6a839f3b753c0cf18e7537467a985c3fd87e64dd8fa3c8bc4892151808fbc 1d0a62e6a5a27dbc6779ebf783a1106fd5906193a102eabdfb1eef99ef8a6fca ad9b387ecaa09d825ccb63e7da89ebd84b81ee898a173e39c63c5bc19c7fc14d 25ca62e029dfa4c82930874dce38ed65a273e05fa31fd64f2fff633aeed10195 852137bea7c27c6ab0b7333f28b8beb72498e81fdc92e794bf72038c8775dcba 10971ebc4939f75c6841db393c87579adf18a8a7734216010065f94c98b7c4c5 a4c9f92f5321a48eedd1482bc393bb33b1fdb38ba078d5de4cd1677b961a1941 b4f4e73b438b4655a9a40de95617137a1eb720794be9b83d335b23e4a1daa7fd 3ce752e8ecdf11d352fd493a4f99cfc10c4b2e7bfba08397215134f787a5575f a117b1773d85a4698b12170e991db58967666a9ce9a06f3432c52f9a12e1efb0 41cbc4567a61faa74af3b60c0d9388d951fdf28e4574dc71d86d2ab099d3be6c d5d94ca6bcc8cd75d254aab225e3fabe87a3f64e921c8004985198eb8de567c8 367d75cf77ad904e2e11ece6438230653a7b300445de21ada1bb60b8143c5ec4 2d185a09e07adf3345d915d64241d23beda4b4878fcc0855e7bf9a8910b5428f 24a05f5fe6e173deb8306081fb7a24b8637d79af9901af9155f72435b0c96288 d6bbadb927984e7613776398a8c39f91f9a1da4e7a96923491eb7d314094fbeb 92e5f4b9806ee1a88fe0084b3ea376734ddf 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % 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 (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 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 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d55fd4dda249cff0b56b9f3aff e9d0de215c02a52a6bc77155ff6b8cba5cd6646ba331254ac58ace650a967d3b 272331b87b6df06d5ab9d80fabe9f9ceac10139b61244814dd9fc295ed42d1b5 cd11c2e4beab318b20f51ca2c2930657e5343ab7bcf0e8870a0d12de4ffacb6c b3fdbdda481c2fcb84408d3d902e9a32070b2af6cd9317a33a42a43857c114b3 f4c3005cef9401f1c2bad3e69150d7145b79f95c9cfaf7a335b277e6435ab374 f6a3e78e124ac1e4615511f743ad65c5d778403a840310ac4902985f107fd33c 0049623e4c496cd353d2ae2a4804110c6a420a38ece5d5b235c5e35886a0987d 284e6110527b653b1b2c68c636ef423536180acadb954843eff4d9a82568a713 b682c574e30f793f093aef755c650e0e7175c2e3138695212d9fea7bd4b5805c a90985b134c6bc15a19afae0bfb3066363ca3e2568c2ac4559a69fc32feb443b 61243b4508b7524d974636855c83c8149d489b68fe18bd497116a953431251df bd09fa1d2ef66c85b997ab2f6b7c6d9d096cb43931379ff9782fa00c5f3cbd06 04265d16891ffc4f66e4a0307765d384c32aa83a4e4f89ac79ef8e76eed08450 e3466fbaf54f85324f0a4f04bd00ccc22d32e4132c51749bea28f112c2051857 423ea203df902ae80224d75efeb59094bdc5f4b6784ebeb01c38c34b695e681e 57a93ae18b657d13770300bde28833c732010ded4c8e79078d17acc3d4b521b1 6f2cac338c4f72e2e07c667227ef142d0273e5b501f24b02e9cad75fe9d18741 b36bbb29c9cd3d46964e00d8ba318912e69a6aa7ccf823c12a9f899264b172dc 4ba703f409dee59ff373e9e7ff2f5f56f29671216ef109b85314e1da17c9679c 2d7ffa3eada3f8b67f92d6dedf04502734e41017bed6852784631ee0b5ec8cff 984214283e540703e33b9c25a43b725e30fc70bd285571a564662d699adc5b3a a741da6ae9e90a0922bf02f690053fe14145e7bdb56a89c7be0563d321d2bb2c 9b50a920873013ba1a0e574d539a7b1d2e1b67492d71319bb807c341bb31c5e0 4d3a319385cc787860ce34c911e3a9ded3a059b8906c17cea75f0e4f2a094e41 35690d97ea76e79765eb9940bdda1791c9e99fb640269b0c2f380c63aeee568c 2e539e180af7d301c5aa085330bda242420a5fe528a9e6985789cd49d807f966 9b72145c59809c2a4495c470b7007d1751a45651033edddb55b484cad6254f1c 62a6c7e4ff123d6bc5683446d1d22cb4d95e94e8d51c90f8b03245c4471f2796 738ef5bc71c155a02d8f22fb937ad5e0859fba27465ba0bd41e06844010f6520 dfcbbe65acebf937f7099d1f5e62e666ed88886f674cf7d3bdd829db734e1351 c5d0dbae95c05d882faa8c6a290bef91d4defebccf65591e5bc4d79edfbd8f25 2261ce5f5b80a3d5b05dd71dd25011d2641c32e793dd1384483a3e297531e05a 5b7d7909b40b8a7b0a10fd9066c696df7cfdc39556da7fe10ca91652f048c399 945acee3e3453bf7ead5b3af2042175b239496f80d501f1b74a0a14cdbee6a87 4399b170911ed99b0a0b37d5c8e6688e78486976affcc8e74bfe52782f3fe838 0de0be783e217274095a39cd23999ff209da182ee2a846ba6843ef561135237f 34205db4e4bfc08f357f206aaa37175bd03c30c3dbb7f955109d225a93b4ae47 88ceede6a57e38371db28e19a163556d4afa3a0d5cdc029984dec1e4be531aec bcb6ffc0985a0e3491b438b1603c0e63b49ffd9e0c1bb1a7a6a5e1640baa2297 9fd7c136b1cba76e92be354c4df0682496c15bbdfa0296c99a18ba60a3aa3ad9 701071fe4990e15a230a23d456724d59966096c9b96c0e90e660157789c04675 314f2f098963e8f78aa888db00167a021af4a4b7243c1104b3a2480df077ecc5 7d41a49fa79d927709c777008adb58f5ed959f25ab6e125a2fb15af35eff32ad 42cc36ea6428cbcb074eb0d6c09de44f5dcd4baf74a680c3d1f26231bd956b20 385d23b2c68a1619fe2441af6eabbf203c339af755063771d42b4c9fcfdf1859 84b013ce91b074112a866b5a42a31a50a163940470d04cdd3239c3145e6953c4 a023ff958542a63cb6494edf4e8827113fd1835608aeda65faf500450eebd22f 19ec5c3032dd2161b6d92551d07fc4f104ad2a85e455da9032b156adf5bf74ee cb875b4d2e9e93400a24c4908539d8fccc0c2488a6f1fd9f38293d24d9c5d0bc 64f0d077fc97496444436cc5a53e7e396c16aeee0ed40a0652fbd7f3759904e0 6e80612d8cb804f9a72a3a76641173415dc07fc79bf8ced1eea521e0a1adeacc 939906f1a234e36c526e75261273c5b3ccac65480f8dfa9c35b8a6232f7ccdfb 073a8e6b113ad610c0419e9a57b5528ad42e2b578377fa4effbf855d553b7b2f f7cff7ebcb05925f8150930c42355e5124b8a8e20ebd0bdd2815e9966f03d143 5117c5a138e8287e1e2e5c07af239d2ed22d9913bc5d8e69af710d5612cec7fd 9c 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 12 /fi put dup 13 /fl put dup 19 /acute put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 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 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 89 /Y put dup 90 /Z 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 readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueXX 5000828 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3ffd20326947b1065649b533eb5e9e3 a88a87fe987918a687950b26f647d6e08bf14d983ed1d4a8ca1e2da8d985f944 2eb916f5b6ed0697ac7c33e1e36a3bf460d34ce45f1631871097cb04f18e3889 4cf4ac1538eb19481311d24fe3be7beaa4a3730e8b4831fe59d6d9ce2e46116b 629c7ba2f9ce3ecba2f43bc162a5a077ca1b2882a42afdcec3f4b75b5d63e0bc 8e5dc95257766d8ea467ad9cbaf47be60f797580cced6884b3a68f70c91f4fdf 80fd00ed9139e7f480dc3a76af72ad9b434187730bdfaefe4cbfe5c7edcaaf24 9204fd703011932e5a3c27be468b7dab69daa18dbbb6335ab8ddfdc607961c7c 02582763fa069d43563ba17704029945cf42fcb19cf78c51df0ec4d851086d43 c1ab38e865ef36865fff3a08b01cbcb070ba4893f7482dc7819ad03d337e520e 7d8cd83bb8ac7aff4df36751f4f12aaaea2b6d7260c09a26e987c904003e0723 7dbcc4a8e4e85cd3259f40d3caf55c742cbb40ad0db1044c20a4f122a63f7b81 1d945bfa69662189ce4d089464d2ead9f6ed60b581b04114d5d45e97be27a576 35154e9b8464f2a0df18da855eb51b8f64d3054b0b2e84621f025a0776d16fed b988a43d2d64c32768dd106b9f541ae8e68ac0bb7399e16f4d4ba074b2152d0a 4e9b5bfc21bfa0d531e28165e518ffc054dd4ed0d74eca079d20e79670419f92 e03bcbfeecf3554d661596f6f29e12170804d15a250d917ffe7a8b6e8fa53047 1ed97ba56481589a65ca13619129f1e26affe6c22f0c38540f8ce37efb6e9e9b 60b51a5a9cb4454fd7c7f92f2f9437159687ab590f35b946a54491a7739c9269 e0f1fb48b129811c82edb3171cbd5105fe65906974db8a7da92f4f43dc7f6b36 6981146d86d23613a0b38d9d6191db9fea0172e982cb1cc50e382f69da1b377c 1be9407f88a2a761b56f398467a057f35d18c01cc377e006182c891ec80272e2 2e3a5c7123cd27eccdc87392a9fdf63bb40f02b7649cfc53ef933c6518744cb8 9cbbd437830ef5b1d58b00b67bbcf4426dc1e6ef583b0b4ad3aebd741e3ff0f7 29ae271f032019b1e7268043fd215be590f9cf24da14a90f1683afcba8006cef 5d5632c2481fbc1bd8224e8952debb7c4596a237e5505ac143180956ca1f603e ec70cdb4a33e1c4ca174436a38b06fd9d2b9196f02114b77a9a5f66595727faa ba323668573ae328f1f84e5299e9eebaedb380024f83e0ba39519bdaffd36eba d88c26ffd8ad02b0f3b11cece842d5a02973232999932846d95b6eb507bb39c3 d2bfe42904065c637c3f27e8bfd224a50d1d6adb4fe4addc41cba8253c3ae97e fa1dc8abb62ba4ab86b7a4ff9a810fb0ecbc71c06e9089fc42a864d6f5aad7e2 276183beedef909cd4a4fa2c7268cd8725bda0bf1895a671dff05e8a76de8004 cce04fd871006ccfebd0e08e0541af85c96a5db4018c92b440a66ea0c4d8d0fc a5271ff144c6a43d2f334f7c0f9ea0fda591438ba271a63dad588cd801bf73ad 97b87815345f3b60dc4701dd38eeae3c214117eb03b82f1d51fb326f67ca490c fcc6dec7699beb08e736ad121a5e2aec58aee88968ac9b2152ab5bc590f791f9 dd4f1f52c0b76f95bb02e771073108f8481ef48e196b0e2e20a37ea939881d33 30352bd9dca1858535a848d78b357fa881a10a46b8a9ec9f9b48bcfae4d1c5ce cd764834dbac0c1f4ee61c299da8193972171a7d9e37cb21aab582877ebacf67 20732993b6dd17fe1b39d644416f63665500c25a9ab5a3cd08dc8368e8a7f099 e7bc7ec51dc11fbbfdae9a4ab37662c5c3b9b1ea8228deed9cb0df93c8672e55 6cef7d466677b505139825d6a3fea516e3bf8c38b153ede9de111dd09ba236bf 4479fd03811cf82307c313cabc22d0da20e71ba60b81ac7756a4fa2d4931b1a7 cabfa5c64800c190b4fe749188c2949470eef91fd11b765cd6d60944c8a6fa1a 49c1b23aceec85c40facfecec78b388b915ed0df13f37d62a15ceafd19093639 b360c58ca11aa9ce128cb0bb0e75db778e6051ae6dc4855b1345960060c2251f 38a99d2e73025974f77dc8b994b5e5895d576d5c3218ae8770f7959b021e6702 d476343e8388a15522f38ccb50c3deb96973b6469b71e9a4d3624b75db7d10d1 d58a3a14b2ae48d93a49dd63dd8e4900c1856b9d224a15c451575ee453bf7d97 65646be5034574d550c68f1b032726ef06f17447d0877486bdd0da5e596b76fe 4baeb6337282f1bf4ac813f61ee992b7baed491ad1621cbf7c42d3b71293bd16 26da9294d262ed15735115c35c79c32e8cf426da4df727eab5d3eb4015b7b7a2 8753dfacb7d7d25166789940d5ad6b52648b3dc3348e892de7d4cb9d020bae30 c3543e12028d1b5bf6633c58cdc899c083c6fcc41af256c407c4f3861337e6b4 f16476447761ca6e34480e85932946a6463c7e0fe67ff2bb389a13d0a5690d2f 52160e76fbcc020e22e255f484da09cd50d225d7a0e21c696122796e19f0418a b9206efea124f184eda17c5ab781b939d9fecdc59ddb609a8f6cb337c37d69ba 80a58422265a5c70ddc4e6ec803622e043bd96842334400b1920df8ef35b6611 c320527a0b7715b7daa4461e4a7f070f3037363dfa5b3946afd353be5abd5143 9bdb364ce5afb06043fde812d55338cc9f6df699892331d5b144f5fd1b4fa702 666b54750e1d08bf61a71f3e37e91fabfd331bf04ea989ae1b06bdd36f5deb3e e02ebc8abb0bd8e57f4bd9cd688df839b7bd782532fd56dd9685a3a73589efe0 ab019e0af3ee6482a0a42d18dc9d063c6d78f50eb80b085aa6a58c5d404e1084 512994eed272c60d8868d937d22bea51c91c51ac464459b27640a76f9baec256 48b0c1fb11479073d4d96a85245f31cabba60cb9a0510125c5254939c9b8e8f8 2eec6167ebb21e2f036db0a0b1cac50d885ee5da525a96d6310994cf3835b6fb eeafb3532882265c3bc372ddcf0d3f8b35c824b1d4bf10c8677f0b0cb520ea73 dd71f5ec9d6c5ab1f55c9f600f4c29ebeacfbcdf45522c737b52be8025d5a092 7dbbc378082e40526334c79c8ed1d72fd936b96aa48a3e3abcecb26511d91ee9 a57a2980fac3613d597db8d029bb7d95210e59b30e4d9228c4f62e7dc8b7b82b cc0d57f6f9becfd47d304d3c731bfb95af5caf5f007633bb934ca925ad854af9 e3951a2c454ff7b2fbe617026ff2d2e3005109123fad752d2d0aebe380f73d9a 1486044c1c4a346f7ca6a387bf3daff94d5fa6fc7da3340fd25c4147ce41b568 1dd68a939c73c04160304fc8d3ce299d0268e45086f4afbbaf53df21b1a3e1a6 d8d4f13b6ed59dac615f87f67e89dcd90c44da4be42207d49dcace1a003290df 188a3675074b6a02a4483bc82622d183919edfc8ca76d4bc7b2286592f77ee87 254a355fb6df16c485d424689484539a4491fd26827da18269864404a0ab3a6d 35f55b25f4b5f0c8ee3a7a8474f588048eef70f1d9b4457102596cbd6194b815 5f0639d27b5a6afa4211654bdea51f57fb7c03e0af14c4c12022cb9fdcd51d3c 94dd90dc45d6d7f2d84c5e607d9b68c43bfe9358be0c7c655631e0141fb9f60a b7160565811290727af1b612e016a0444ae146a708b62bb104c097e9ccf206e3 15531d0e478a554a9b90e4585a459351b8ac413acb78008cff5166b18a5317d1 60d3ba3a19991df61e022fc7f1e3d1fe10958a8476fed9f4f35be304142c71da 336777bb1d634205830cdbcfe1625898f96c594b355e9914f1a2240eafb3be6a b6dd79fdea415b8171aae73c8c4e29b882433b1c11a5bb65831919a6be3e75e4 66684a884d01d8242c9ca924722f9c83c4592b04979d36437707ed4147bd30cf 0bcf849089a5d507b241d2d784fb98a365819eb153234e0a395300b183fb571d c78f2b785c95b635a212cd30c0a160493976f5d870393029e3ef698b5a4b5496 4359c6051a8cd8d91d3035e3970ad1c7931ad04b455f4b2b6d4b92f5dd5764ab fbf1448bceb36fd152aa5334d12ed3d5ad7d2ecb0f15bdfadae3e2ad5d1237ad 164f4a626dd4aadc0507db0fd408dd3d89df0b78906126ca8c83ed898f89efe1 df4571a6d4cebe44aa374df450edf3bc42d8e6f1c752eb8873ddf334fcca78be 3d4c17f2bac6dd36d6522d754440358ea59e6e704d0cceb6aaedf68077ae3ae2 d54a35f1e940a2fc4752a4a3dee51febb91d390ce89499d1b659e0412f4a81a6 c9dbab4e16e957a7888ed351ca13ab2fe4ade802d40a590438d5eda0a238adaa d45868f3cc87d8fbdc4a275146e2485882e12d8c2e99499a180f1505f3497f82 08b5954941a187fdad82fc3431e8f4de56430062a52131d3b70e8775242ff5ad 8c91bc3dad6be615ba9e3462c3540ecca4398d799b2fe1ccd1b930d0a544d621 f19342f8b8f6848140a9ddd38e9467da9fb37ad08c58651d4a93165ab9bb57fb e66da7c14dfca2fe2cdfb52a9bd704b59b428ff409f43a9b594c042b23541c0b f834ea71678d3e3e0cbf83602a509c7d5073520e159b73b00b97c7481752c344 17a950f4bdc2f29eeb1dab987ea1f4aa6477acf501efa98ca8695e27dc4a1168 558ac508a2db8d7b8a9cbef7136ff0530ee596d8bd1f95cdf7a62107449e176d 84bfac932c61ec260e8d6dcff9525b3477695abe6e24c78273ae6eb43984430a 703e8f11a34cc1cedc294e2cdd2da9ff1b3cb1b1d4dd4c7869b3fa6eff9759d0 ba75fa1ae598b4fa3593a47af99b2d0fe389b9a693680eb939eb8a8bff702c2e bcacdc1458551811ebc0573e7f678cec872a09fe1339685391965ce19fe4a3fa e36b0fb663d920e6f9e105363cc07d4d3385f83be33dcca7fd2b963adcd81a49 1474e64d6bdaa8833a99810274f02a8a26c66a1cc6742f280d9843e80aaf17d2 769fa4b2d81c3915e2fda67da3bd6edb7fc308aef803d1d20920d139e4b80375 d912dd4d4e994593b493b6e259d8b28d1a41ab7f2fb52cf1c7b4e25cc21f0733 d959f0529ed3d36a04d36af0b7928c7932ab011bbf93b8bc59d53ebdede6adeb c74935cf6e200da84fb74a5ea069bd98660f929fd321d2629ded7632da8a64d0 3642aa1428fb140411bcba16b227775b16c1210de7b9ab12effb9a1d9ad747ff c72198b8c9b26a216954eacf8a849190e2d96d4af4d63eae34bbac6e4e2ad9f9 74403189f11d0413479311500d4daa9c93ccee30c8e4a2d70c0510b67aec6ace 287fd242121c63a89f37b3801a468d8da5f185a4f155772265849e51c53175fa b970ef502a7d584f09c731190c0a53e996c6f8938d0287a74f9f4825b6098bd7 373520fc6271a9266e310fd56ac80d75c693dba4ef839d9b2b12cc433b1f9e9d 1d2684288ec8d3b23fbe1ac711ad7e035506e6f2e501c9305cca80ab4ee01e77 0090e48b26dcbfe25f248ba42271b7c67a5d426a2296377b12bc719591949bd8 a0620b2bedcad97c3c190e5d688021f627d101526bfae553ad3a3cfc94c9c404 0a29fb1baefe6983b848cd7f7cd7f2c6c38da22ec557cadcf6af6a793c4ff0a2 e2fbfff71c1ee660e0d111ccb91c371f24930a210ac5a12a0c3fb7cefab1dd7c 5775410b1ac97290af90fe55c017e3ece4ef3c44c129a9b5f1146b1a118b52aa a009b7f4efd1717878eb5859f460ad5d15edc7ddc571fcd62f6cfb69c9b632de 72ea66806aac6038e424d2b836c86552caf5e171ce833979a4c6da3650d5d85b 3106c10387c493369c548b2e80caa7d3f37211ed6395e5f9a30a924b99fa598c 523228d28d0df5a1aa8323c5ca75c084f68dde318b8805ef3666a0c8dcb335ed ae0c5982c39638660dba8aa24e3fd8eab50dd6c5f3ed5f0ab172003259a2098f dc35a015473b9d60aa7ddf72a56d8b629458f1d106fa69af8737d57fb5020fae 5348a07e45226d8cf9b6f2f6d1d72f34378a99a420d7443797a474f5a1056a8e 41ba3a2388b8fca0dad04695b2514bb50926b47826bf64f37602bbb9174fffff 92a56af34f33a5dda2476cac0367e00fd9f0e7799ca8a5702fdb8bb4920e4368 35bdf1c2646befac94c54dbf85b80459888b8e212afdcebbfb04aac545a0624d 0f56e83a2d690566c174fb466abfbd51d94d5f47878e4b6685cd2abc726d7522 7c7bf66d7c36475300f6500ef6fb4e800965222a845b2edd9db991824e35f754 6b0a4f6b623255d688f152eee26abacf45bf8f39a0cdcd972c450af55f6b7fd2 e7857a9a9da24eeb7540e542ce78ca1394d56ac8cddb93282442cf1eacd52a16 7618853c66a7b7668bab73a2eb8b02aec4ee1311a95f793e38b12a50670ea941 465b3c34a0e5311c9128a6bb85556bc485c91b21e39de628d6b46b660f0caaa1 1a8631f01f78250cb4e0554d485b7c16c9e77edbc71c708b528fe0ab4ab278e9 e3913ffbe5718d86f85f68b409e29bdc71bab849377429f056c597af2afa32f6 da2a0064717d462bdf5d1604e37c8c6f96e52f5cd53ed944aa2112ebda0848b7 a353e340975a52e08e89fb0be1d8514d6dde8d11f18f5b08c00eeaf588704798 d1c7b69fd4cf0d9fe564eeb70a0ffd908b8dfa43383f96d1e54d7af467ab0ef8 100d6557145eef14ff9addda1c2c10b4adc3721546588faca0d67f742f38ce40 32b0144a83e3bf800515bdce6af4d72f2cd07cef297f7746adc897b88cca3e32 bc58e1c6fd5b6b13367f576e7e1fde489f9dac96104524c085cb541fce02dc69 d0211ee995892f21643081cf138e8f44f035924a0e78af7c81fc53cbf005739c 8eea1c5846a22a771c72bf1e4ead6aa22b0d92672be2a38de94b1eb6b0a216ab 29e3923fa1666b3e8ae1deca0285c9a9996f319a8d172f75308bfe91732b5238 70094342030e9ebe9f45958495b67cafd3d08f70230aaeeb09f9bc4b8d8a7de0 f673ee52d44f838ca5f1e7c1cd8b7a77a138b5ae41d427837ba7bce3aa2befcc ac89910323d852a159fb7eff061b99818d8ba202aac2125c64bc518e1da60c27 ddff024f887240b67b7e857d69f48e5732c7b1c846adf4f8adebd9e5936e119a 6da570f63d62951b364f78874e31a228311ac577e86b8239ef5cefbbdab59e7e 309bd75fbd6ec6fb94d3a0f07754909d4487a133fec66bfa32e38c49f48ee52a 2c2e3b8dd9136a348ef239352fcc6cd0c6f80d3c37561c491d1a9a0f27710c43 cd4f7392eae9a1f5eb08684a60e99c1716aa5661c5e4d3d035b64f6c15ae6981 6cc4a58e1bc68d76ef63433015d00c0def6a367fe39afc1fbc650487fb3002f6 21b3038ff3e806f5904f58235ee805a272bc781377044ea30627453591883e39 9815c69a9293cbf0839937e30f42129b54923e69c8049fc52064bb388aec881c bba564e9e3e8c6f70735446974cf8fa45471e8d701e21e5fe5da8a708e8f6732 ee4b9005256f87427f3043d3caa44ac9440f8c61ef5779df012e005fef5fbf0a dfbb2dbdfbdb8ac9dd6ea738d9e59b8f29c6f57646c0722588a93dee46ca65c0 bff65704d46d8a9488b2af983f3854c5c4a320b15f06067c9d3b59eb760f929d a440f501aa2309e5f66ee3a58863e7a7d6ee3a5e8073bef780c3602736b7b9ba 85a397fde704d817b625afd80a0daf09a46e84dc3159c112b691529411b63261 8eca55a4cd18fc952dc58be154fc47a9a2c75a6afc377745d7d7d9d4615363f1 1c4d02d828247f878e428a20813e9798f98fa2a011fa4994b9101951752e5d52 4151c56e38077c0e41fe83bef11d9fc1efb40a7e5801e86e6937512053a38a5a efc41182f9edb289b80900f47e9e7222fb93273920c04052d9dc373c13e02958 834e16aa51564a235e3e8cec6f61daa4ba0c83e2b48df2bb2463d4544af2c67b f864c46f0b3436af1da4bd8dc6128a07c1a409cfd913e2814cf77a98d5836c66 9f691d35fdf7ddec0c09e82b0b2c763cb5313bb7f050f55d7204eda164790e9e b7c7ef20e60a52af7807bdd370bf41e823fd2c7b3225aaf55f932fc08c8a9aaf 9e93d1096f060a092eeec8496e0ca3b0049d58923c2e9bb4b42f09980397ece7 ebde984a6053cbaf20b08dace017a13e11d85cc354bd5ccd84c5d71b208a852e 4c656b1437d26da65acbaabfb96b7c3c5a75cec280edacc94721ec7921edd6bc e852a722a0c6516be41fda3dde8d8f57300b7882933fdd6a1de75ee978f7db39 7c09c8c8744a362d00feacf156af3bccb2c1b23bf601bab1d35dc8eb432bfc42 1e3778cbd3b9d25dd55e9daf9ed95cdf1fa64778afb62785b7fbe218c939fd1e 8acdb2cad67bac261bbbd0969855b9315aa7cc1a196f5f4aebf1cdf8b130db59 34f6b9bd85bc31f7f2c4e44fbdb9b4683f32112393302e7be7be9214e78e6f71 6a9933ebfe1e935049c269e711727f5991606580681745c2789fe25fa1ffa364 f6aa8764043d17671db1df97cb05b6b1c8b45056aa16a84da2edb56f1094a6c6 9b1430842d7da362c4a9e1b6eb4563a910e121d11ed782cfa469c69edf429a98 de41b3cb4f4ab07c74a19c5f7aa3564612eba6daa929454bff649df82eb61379 585800835f4f9cf8f34c42fdb8ce48b28203a576a1735f5a4f0fbb2684562c37 38ac449d3cac64764c989bb0f54621d2f1b36064e2969b9dc70ade64fe889462 3863f1a264e0feae5a32bbabc9f3beae1b2880d0e8efe07e84a9837f324c7aae 42e8963bd3c941126c1a35b7b4c76697d66c4552f20940b14a13ab3814cc21d7 7d833f3f11c5a2e36fd606d4a6fcfec979309824562d8ebc2ec5e8e1fff79746 547760cae36e504a8e8472ca30f737152b50c8208d0913abb23ecedae0a9cf98 515318b7e08670527f5de3d61e845dd6dfaabc6ee69c02932ddf9b548122b12d 1e804276d8adc3cf3328048804653931927d48462c527592c19640ddb31099d3 7a2c5be92cc0955ae57120a1baccb3fabe468c026f9068631e02fd21c20d5e4d 64f106f614c2b3085e77ae12bdd3edb5aeb59416ed9af1b9211e707a1b68022c 921d09856f71b82f9e4d6d9fc7cf3ac6f76c7132dfe9d24e6d4e17bfe434df21 a7574636696e237a6af3f7b1b59e931b9909ff8755178325e2f221a212a5b306 83f2f8d76f414c64fdb6804f810ca0340c27193f001acfc65b96eb123ea86889 ef526b2060449c07b48b91fbf10c1e5bdabc64f1e8ac29abbd650d86e05551fa b8b55583baab8d1545ca2e611390c980caf40cc1cc69b8f24eaeea3d717ef7ce 4144dad4e5f5f5dc62804750f3f30108ff95f31e7554c11427eff0da46197494 6cb66328413b0e67aef08e5eb92468c8deef6109779b702f51e8648a8efad5fb c3867b32716aabe3b068eccd69db77be2df5f11044767049378973a31c51075b 87c93f4b96e09ba9626347c86f007f1e02f4f310abf7d67d26c9c4baa1405289 9b3074629b436a195950afe9e13f1f72c6299d1bbd655b61ab665abc645adad6 72b4d7b09fdc18e3154fbcb58a9ceb8227d306eb12ac9ac3b8f7c092c8ac5ab8 5849b533005d797ebba4704f63c76ed3b5ed622c6690d5600a59cd1ccced1a77 fd584db2b5a48741b07a5b14f704f108b0eba5f885ffca89e1e7c3a617a100ff eee7844bdf5a3d57b03bdab033b6a6a720afdf9175b80b64f78c96ba1db277d0 b4c57cabc81287da37e5edca71d95e90fd471868471c832946a4c9e4532ab2a2 2c13390ba5990611d82deadb9ebe5e795d1378c2a5911706def337acbbc49e0c 6ce1d12f52b74faed404f42a7865d45c726d942ac0d1e3f44cf2cad987626faf 6e3cc912e5daefe264a5fbdbec55df1324f02cf18929b467ea5c6d8d6f4833a0 947f77b94740fd2b6c695b597161ee04a824a8ea3b2033781e12a81a541d4a01 8b5b53b558d5f8fc4981c059356567090db003c3ecd36713bc117d3cfea5357f 326205e56c4d1d1e71cd381155d78d3eeee9f5a7b2c11992ed4ffe1910520445 1f82318bcf030d7a1b3814ddd3b60e4f7b8ab851dc0afe32199468ae3fbafb3a a7f36898194d346613f1363225547ae45eb573a606756a009d9e8a083fd06e81 5caf063ecf81d5c02a8141febdbabbccfff3ce08c5728ba5639b7fd984973b4f e573f09396233e6b0af1da5d14df31e335768fff584c3b7d39f81de568d8db05 0e809e3e90b005ed1e04b14bbf10c82ac1e0303daaf08161c316cfbc5e6b15ee 9c1ce04f3430a9f1115100d2a6b3c045a196420a2e694a74e06f2f48ffa62127 735d87ae3144553a157fcf98da156d63df4c00fa38b8e4883bc9b8fbac73c50b 82bb567c5c46c1ef0a40ad9ca222a7e037b25ab86aca21d683fe5a7d9066858b e4b9ebe92bd4d6a062e19d5c09193f871f61f4468e8d43c75aa2cbd0f75295e2 39f7ec6b838d94c2ce0770ed0f34b379fd9ec16192cf90ed3cb40490a2fcdaa6 5738b5247864677c8dd66a924d602cc9a36002c9f1e610290a4218b732f3e0a0 ec8c0cf56e3b623f97aebbc49ec0ce0f2528206c5cad2133a1e806b1b066315a 79aff059c300eb0fd2a75197fb342e88dd141633556d41b6ecb4b3f9af0b5365 5fcea481159b52d4f711c59e8d8e6ad0cabb80f538da519cad57fc077fed68f3 2353fed45a804630883b85f7f2590271046db0114ac687958da65f11a90d41f3 7f7f958cff8d41484ec70de018f2e9b7680e54ea9f1d045d8ff777b51a8a983f 749d885a31e3961afb5fa59023c25160e855f1c06ef165cd424b0ba941b1cbd4 c81681dbbee3ab6b596c4e9776a8a4d7bdabde1fef8dd6e86f7effd37db437f6 29ce61826f73efd8d890781f2db0b17b09b35f0a18934b16dae73fa796947223 8939229562cdcf8ed702ac04ded732c9e8ff2723081aa5e0a0b55759e3dd293f f65c770761fb4fd7e1808eacb94f5fc8803478e0e1c6f4b5d6a9e4506e2cd37e feeeef7ab75b249a8597fec4adec85ccd1c5dd76b609b47598695c8c111c6761 4142ce20dd78967378897a9ace00408e29e0728629c01c21316c8d9506560447 2e045f03fc9854496bcb123858abb2c4028bbab5d3c1f0ceb2d30929ed91c3fe 6b1b0a6cff8aab2d425cecddb0d7e689554d558c00f8f95cd9a8e29e38b1d361 2a937df99e3d1582873d985f98e33190f11217188544244eef24fb83432b2356 cdc4132f8249964a4dab1f37f3c5a2fc66c67aa9a57b68f2396cb45d2ed46df3 93762b4f73edca158141e90dc43b233bcf3c0782f40f70191b197a06038a1f5b e76491ba1d5d55f35e86e6af3e7fe63fad7420d85f500a5cb5ea217099a72be1 3517524b445a51d8cbba118dc1a42acce680447cfcd76d914590e8f2d3aac89f 992577e09bf93f3d6c34a6bc2729deaa1172a044664450960a13b0b389158903 2f524c98232e59fee5d8253618639fb0bee270f3da5db3edd65cd53a5b381a9a 688487c2ab83ed6d70a926ed7e2118b4f8f0c369e5fe62598d9cf297d8c82a88 4b617aae705a04dd458b73c36e11b2e345c40e4c5c82df4b61222193065df566 99ce510460c010c1316fe74d86b54d0268fe99e9b7191450231e373c9df75bf5 1ae8a2611bbc475b6252601f4605f0893af5b17849cbd1fa76dc9ba2df551cd2 1e167f708a1018e45993e560fb47d2ac97ffc0809030ddd79abeafa5d0956111 f901698b46169550b7d7bc964a42279b80f5294d62c70a6e206e70b9d0435632 d59c3e8fe576ef30ba7a5e1a67b205652b323dd9f82f885e2186181948c22ff1 b3b13b3ec5378d5f73bc2a780e04cd8f3d95fb23f06dbbf0a246603a0b2456ab e5962dd5edcaef43cbfa262d3baea72df826a226308c6d294adb1093a0ee589e ff93ce16160e01d934aed1ee5089bb13d84b3bf122e4706f6ac84990a7ee19c2 2a4f89c73016018c0a265007b56d02248fee1080447b3039caea3263f515087f ac2c04b2ac4c14b9124b2f8c615335749a138aec52f7ba7f3e3b50cf81bc37c2 0be7355c627b2d2dd9101143af12c7bae12744b38e49047367f777ba40b7c20c d6f160c76ad266f63093bdfd594dd5b101cfeb14c5b61ddcf91476a7409cdf12 fdbb0ed0f8cd63a72c273b2e2eb25f23c967156ba422c1f61e276dae82210cb6 54201af91bead721ac78c8bb2242f7d4a80cf067be73e22b240ca65b015e5855 d7f2f1ef2a9b87d0f0415490c172d2ff7d0aa65c476ef5bb6b45a77ef9b081ce b01949740cde31122ef95378b934fb95cb9c884bb4066cd7ade5f1dc61b0a49e 0739c9c3b11257e30332c88126393c1a1831b7c30b4ffbe6e91989024525302c 31c884f9e886d031eaefdb3831b1b1cf6c3cc5720fef10fab081308c40592b94 5005dde8f85eb6745c555d084f42e138f7094b49886667c666beae5b5f9c8119 2c23933d638fd113424be968fb4a6274b82bc8b770006977b31cc3190f7b5ed0 17190cea399c8190dad2397d5223e468b9ae9bfc12709e62829378a33f407786 1df5935059500bce57e481438ccb4b927718f6d586f17cc0527fb3b2b1a7f8ee 5abcd9b5c7497449bc652bf19a532222e83e1dfa177a57f99da553157c0d719e 32cd6f81e824f05a8c75cdc82b7ce1e1de091c5bd9d7fb1d60baf2b847043f17 f0b1d7b263731084ed474180ccf15c77854843bda0785b0c0340b1a875da23ca 99be5cfb869979e3a8bfb3bd52e01ac7d03e1397e4cc38e1ea5f9c6f29c3cd4a 1147be398df902016f299c4b67a2c94eb141a294f3b977bef4292aba7c44a5eb 2d7ed3b549852625e6592f7111f23673459e594c0c34b2dc4879c9ed32168898 2f325bb1e1c822761950e717d44d3b056b5538424ea4274f35aba24d2c580c62 dc647684022301848da653a57f75a2c6906a789306b184a312b1308ba0dd3d0c 7d5d9066013dc817121153ff60ec73065a7a4c1856c49a046677a058aa0f7a9b cfb69f7ad65720433ec038579bcfb9a2799958c1894a4ef9b811f4e10ad07c5d f2c046467635fce519977e5a412d8e83bc9eca398b1ae73661231dddbd7fc94f 9ab306c491d67dec3da9530353d27abf167f92596bc670d021a42bfed4108225 e4b37450292d21bdde8f88cb213285ecd6c4184a51d1616b3f1c9fc5a229084b f071f70475d382b4cea87caaf085c5e645d03ef7662ce79023403f8ba6b10f6c 6e3a0544a4f5333a3f7a96b8d54200cb148f9d263382da8409079138888627d2 2160484997a4d58854f568a826dfa1bd6519005f4b5a64b93ce9fd11c9f00c3a a0a80b054f1c13a5ecdadfa00ebb582653c92a92da9fcd521f3ef859ce48ebe2 95d368bdc261b84dc466bb5d497a54b6d80db90743b58a0eb21d45467b700326 9e3a84bc393c1824586974eceec194d9a989a2fdfafc679e3102883d8a88ea81 c350f5e3365f123f687dafc3a4df09e9e448a067e000985f1d452fe10803e9ea 4f6b62fec8267639783ba655fb25b43e02dc5831fd5ea17fb97ba8c05c3805a0 8aacc22909d6887b1ced46f5b256a647980b145d9a3ded0949bf04d5c7a9e6e0 3e519e2a1f7ba8af2959db77110a9748b514b4b1823ab56b5170865b2126abcb 409dc4dd596059f99d0025488d5323ab28a5cead2adeb933a3ad28d5a28b8aa0 1303e4840a70d063c525d57267bd13449daa4e2dd886bbe250a160d74d612d8c 07434c4304c474716880be2bdd858025d95dd30b55229d284d177829b6beac4f b01df23800d5c0a7d91265acb8b607f0f818cbaa3eb4573689578731b2458e89 8b6524588f015ff0984183d616a68b1ab12a6320a0bd9ffd9d4e9b5b4b6acca7 969390775a4762e0e4527eb035b18734e1a22831db01d510036375c728efc534 86318ddfccda0ee624fbbcaa38d60f5f8868cad0a9f45200244b0c119dd8bfbf 7c12bac5f55910fb7207af81dceb39026fda905696613ac0f022137c85b531e6 3d39b72b2d58f01bfb69dedb10cc1604a93ee804ec07a90b697af9dd30ee0f3c 1b17740868c6127e3954278155a2d943f2d7b157f0bcafca316204a4cd56a5a1 b3050d1f22348b6008100efd14188718b9e47bd00998a735c4437a38f17393ad 9804ac7c1f717fd6d50d8f1e59fbb1bc6cd5dd0d1ed5e8fc58b964432072e844 f21ef51bcb93e5c537923a31ce854e3dc08f3c091c3a3a29a2abe2719b05be0e cd2a48d191aea503e2484a7d2060ff245705d0e5366f477f58e74320a75ada40 1fa55578ddbe885804d757fe24e6ea918b40e13197c2fa3f99a39c6ea0bccd2e cba75922c6b862986cdc6680b2c11ba30fe50be16a49640e5ef79d9bb678b775 6504958643d392b1539f5ff3d90d66524f6a1ffc042ed4bdb2a141884cb4b46c 0f753c7e4686d3e5bf3e1f10919a66a562d36d3ed25f2f24ee8c0210f8981fea cea54b70fb4b2668e714e39c6bc15769b166cc5842790e7275ceb5c2c61afe1c 75d7e97864838962a32d35122ef2519935f4b1789df1b5a5b3eaf418748aeec1 cc907c1dfae336e8e58b1c8b6cb452b30bd4554ecf88031efba3039571858505 48251e83bc3714a03a3f2ea639bdf32f66eafdf2628e26b6ff3e161662dfb5b8 2328659d88b47bcd92d1856096b7b5917cf1643b87bf30a163f19dfe9fc99653 e3b87ef9bfc0d07715b5d8df0fbc9bf5fe91da1a9b9c341c10a9fab83f605864 985dedfeda19573cee4ca9a3faad0326f5a1f6757a105cf755f7c26a62630d87 fe288629ce1d1cf1c8f6c4fe443d9a8e347ef391faee77aedf2aa4afac3ca3ed 94c83ecc44f1768bc353b0206e06e134676f1463cc3212fa5882591ad168eb6e 8159f6179a8daa265da8fcaab6282d2539b445cc59e47a7002ad3fdfc5296537 428dbf4e806609ac482b98fcdfc2699f9960a04f50fb640726b9e78595d3c298 9528776664244cc6273cea1ed9e6be15ba505d533370fcf5b2b2eb02245c5f10 dbcab91c4e778bfbce4e6834be7eaded9d85f7d570afa35444225a18b6e547de a33e33994c040ea742d3b1575572ce7c06040bb6652c3042a435f8731b70a012 3d46f858c707041bf3f0449b2f11e67a36e89d94153f784ee6d15cc16f8f7973 15036b577213bf78dfe7868b543361c9bf343892eed137c808e0b62572d54df3 b1431d5727bc2c595fe2c22f54aefcb08408f7d2f145012b50a308e82dcc7e6a d0e6926f34a18f8596e9a32ddf065306a6f053abad7372be25fcf59002601798 903a82bf02c3a33c216d47e10d692cc7e17368079f65d389d91615ed911f4c03 8f7d17b66165e723f837420b640cb5209304a718c9ec3296e293283ec3f36d61 f30505f07dfe936eea6888b58669295063f6639ad3c083c542b13a5cafd75a66 2b2d68b5b3baed7afd73a483b5f5dbf4c6b1277dc7cd31f5f6ba301a4afaa25a 84632faf7cfe278015f18197de9c53cb686bb94c7e36a689ac7c158f8396cd2f 2060e4e881616050a5210d1443a767c8c6496518b0cb676b92b8060a976a26e7 528f8faaef6c489070c19f44782698e6485cdd5ffc1ed8929e203d287ee03895 42aade251391844f1f17a36d24216192b994c57a6d204177480a4ed801ab8d7d 9f4eae5311d91c7054bde3533af0465cdbeb4b5781e2e7b4ba5a1fc3cd969a74 bf676cf6342aa476a2c7c054b7f90eef4e65a5388f9582800354104f0dfc600f 11027888fec55c954e2c63d41955f03159598e8fbec7f0bc473164c7bd568b7e bcef0c341eef7e6db82cbf3f2b198e42775846e5c1745037b8a84b84fdf902e4 f67f22963a125c920b5c73e2348893a4a686ae7b74b9a398eeac34b4853e3ccb 94fc6a8882ff19257724fa8233f16de18f3e38fd22e2c1fa883b7cae990a57d4 e1312b602e5c98e9dca7d86f5530169a878a28e1b3b23a9bf3e639430290e8fb 6dd4a9cde726efecbc2281565432016023227a3f8e063a369aa2eda8c0fa159f 6e4c0820fff659bc8d153ab7a234fb67e678743da585d6ca07cf72b76fe48435 4b4ada3e7eecfae98e4d26cf86d71647fee9070599036c5016a7035a1f7f32db 32ad2a5597cb2cce7805282bb6e4806feb41a8a83c4f5df4735d99a55b4593fc 355a441bad03977c49d7a321bd0cebf6989d6344ff99946356bf926b9117e597 4ba732d52fd0f29949e849acf2dc9dca10005480603c6848ab023f0381efdbc3 72b26a2ed367c4247e899dffac26020e87e8a96f9d7952b930ad496bd58fbc0b 0da1a0f82df14124cffe392a077c5221381c683c3cb13a3f5700ac363219b6e4 694c38f2dcfdfb7ed95387efd2dde895293ec651033aa2a2dfa91fbb6897a661 a9af62bdf1e4ca4cad54b9aa54e775d12e4cf876e741c6071d0a6f1c3bfb1ef7 1d111799defd05837723c74052e241040df22b487543ab3d53941b563b8066a2 711411ba684dcb00fe9a0fed248b6917f619ed26b86d996b898af9b273892a83 dde15f2c45ba37c170e34e2ebe867cf0c2737329f9bd2d759ab3da23e1c0445d d76561cedfcc0fc87624ff9cfef9b2917fbfe03f3cc64b6ed25756cbd4f30c0b 8efd71739e180454e127872d094a5ed6e43018ff2b86d188104175697137f8a3 4f9cbd10ab1ec5160c552915d441c3a3b6c4a5c75d60167dac58c278321ee506 13eaf8c9f64f7db47a8eab43d5e7bf65a95cd2d22142a6c8aac9aefca5541f83 83daf3b383d33d091aa3b1c274ffd9ecfb50c133595cb029328f80ec969a13fe 4faf57fb7e731d67c40780b2f31f113202aaea8332222100e49e3a6bff20e5ff 15fe9b935fa979fa6a95dbd0d27edad0b88f1946d22003a0b381c2d5b32c6a11 e56e40956a016c4613018886491257cf39d9dc355597a59b9edd378328a44e08 30caaf86add6bdb297f950f19ee559efb168e625c5366e514b3f81945c762072 1091bd7352ada0ab952d740306e884f7cf89d85b99503e8e721137f80b9c2e7f 92d2cbd94dd140983e8a066a2994d67d54b960da248ed1f8616bfe4f4ec6a8da ee7bae78e13ecb1c4873aa05925dceafbde936dc2063a95e516139acadb869df 9ab4efced86b5001aba5086a19122d176e7457de58a9c67dadd25dadef3eb601 e9dc41a508fae22dfb003d53308e48d46c8468c06d4de777dcd3d0164806e74a 0790fdf219315327e751887c061fa5930793469b2176bc91123206b40b8ad578 c3b4272ad8e3b2d50df08b79a0329bfc535325b3f157a263a9800a1d1a91ca7c ebee906d7d8d21cc74d55681e5adf29174ebb6646dbd97d1518f898ac7b896a1 445fddaed19555fb751efeb19742c990975e644e9bd6b30506f28e138293d17b 77b7246153cc606e7575649d62e010ce654a0f3236dc7ce964e911f224104664 f2a947fe9a5fd4c29de697e388a7abc47c9d95b4ae7cbd92828fa5ae414e74fc a3d8077349062d9ee59f7d5f1c6c355cc3ec8eaf5c3fc21c7bb734bc7ff4908a b94f1ad52a2c437912711a55e499fa133afab83d8058a3498b6869477aecf766 4fd84d798aa4a34403410a8557e8e3d5f34122d70309b436de4cadaae556c417 b0943976d361e2e1dcb8d2e77123edc67ea205021df35674edd2fc12cb279038 15a7d1854e3685f114731813eb2ed111af921e8e3374987eee59cbd7e7c979b6 6d20740af24ee9e6833cfd7db4746f2a29c462c894ad414e64f13cd068b3349e bc9504e15de2c0dde9e6a6df5638bf55a73d878cb9ee1d8248fe141402dabbba 2f3cea7aa137a2a6662268404f5ca1209361e5a1426bc181338f5b9d0631967f 459bce0d3d38e8bd4823bf725d6ec3c998afa90b879a288e49bd5177276c8ea8 f397c0738ea2511e1361180b1c1d5782cf739dd33a561580db9a0e5e670a6251 1d23494a6b7a6f4e983c69a33611205c588f8ed4f30d61113f2485d9e0c619e3 6579cfbffe7c80898bacca73905e8e961d133aa728c8dea1e133a34684316084 86567fcb85499eb743afee4d5cee93eadc50c5afe9d42498ae79d106ca3359cb ce99b06d3fd793afa13e38eb21487b8600df42a385a131ca72e17d650a091733 c4f9be4118c66d19ab15777a238d814f4f111a233fd18724913b325845b54bcc 716e50334d444a701b26047a8a5d93a31dd414842d599987eee05b25f8094dce 435df11637da451f1f20f05619879a8c92df6032427138f62c9fac59fe047dcb 96c9bca44e263682220587414f2e2326a99548e7ca7a2870b222723e7e19d1a2 61db7cbf04fda4c818b0cd4e90dc4c74defd439ed7525ac8ccaeb2b743313fb9 c5c0622f5ac3db6bd3af17c33e8ff6b3193cba479b00dff205f2c37d18593212 32bf9824c9257a765d7831179242efb1a79697818dc6ae880fa86b7efb929e0c 34075316673595dc2722f33e2ba7839135322f43150c34131173da278e7d2144 0314676241aeab2f7642e845d57eb451bc410c1d75ef89df97061ddc97a79e44 39f27a628b4245b528614f298039fee66789b12eb3f5c13a7f592905ac07045a dfb83087f99b63d609f2ab2d02f71f85a7e3b7192447d97ffc88bb34c2b93516 b1ea6c25e24bdcbd9be12c32dfaecf0b430547519b3a8d0c58a5885fbee4d35c bf361dffac5a48e11f498c977f357d7991b4a00f922017c417e5b24f6967af67 8da9eb72b76a133b73d7f2f45179dd92a91d15336a1bc2b4e4d089af20ea5a86 b7a46c4adf09f2c51557c2b42d7d476ef70cff9fc96abb9e7f70bbc368fb11ae 70e6a1cb9512d01c21d59254f495d51f2db3ccd968471548b2a817f38c8a5b23 796eab325dfdbeac91646e403c710056b1efa223d5ea8bb41b7004df839086d7 e6c782d10f8ded2485b80d140425052f96cdfe3d39dbbda9f0d5bd6c2a471129 9bd0273d6db7384616b0e14909aea4890f93dbb76913d3036690e92915476dd2 bdfcf7386c3561a1999ec7b373045aeb4e89a60409fb3385d5a5747e88e58080 44b4c2edba49197b7a7efbe26416ca8ecc79c713dc5d44ad68f86fb96c3c3bf4 efcd2f6ec8b686f59d8f46b880ec9cdcb1efdec7f299ee8f7986f79f4018a2ab dfb44d199824f27dd90e831f516fe17fa514ad34bb666fe0ce1e6f90c0351d66 c13f6d1865e7491d1e028f37dd34ad5945f19c9134818d55fa36b11c30d7dd92 3e707cd558abb2fbc1be41a33d90c952af702e1ee276cfe0910ed331bb357a7c 98cc133917f3a719d32e609cc8d738cbd939ed8919c23ed4446b2c3dd314d771 07c1817716ead9a2926375b884e005208003a93401e456e15f7e486a5ec0fd5f c073291d7a79368f0f7dd7fa6bba6196322add6dfb6c99dffced305bc9ef6771 77f2eb32c1a7b37b2038db015da9297a8067db51e66585cb5ed6494f610cc52e 026bf3323f10f5546a63895f763a2abf623f54dfc4cdcd8ede2feda892b1c212 5ea88e7ef33e6cf880a6614910e370aa90f9203ede108258d78d24b4bc88d783 51e2fe69ff2f9ecaad302aeabce2f3bc91f6f8f624c650ff17b97cbd31a81beb 21a6d1ccb293af1bbc85b39cf99f8c3d3b8855290d68a549e7622d93f2f5cc6b 6db96c6727ed40c8ede053bc8254fcd3cf9ed6f579e86b7cd698df9c396eaae8 ca85d5288cc15c380419c271918c72ec4304cb07896b19ff9aea978da2841d86 5896a5f830af9f190a9d7b2217b765462ef4af58e70e3be7c535730f569a5041 ab91ec3b9079ee4810323a0d141b8a77f4e13a67485ee3eaceb7e64bbc8312cb c2713be1792da2103eae46cd3b815b9e262d105bce24cfc1fa752bed8f2b9fb3 888205d96a90c4b6c875de2f89499d44db994215426f1c30cf795d3789a3542c bd59ac6bdb00aef79c390f8070207c66d09697251f0269111fbe98bc157e2552 3fd8fd14a883c0623a38441a4458b846af3ce0fb3041415df2b2db6eb354d713 a35b35d8492b4ef3929d791b1c533579d516996671c9b4c88d37005f12a3809c 0a4fb20385a3f520bf9da76fa30765d292c3c8ea9e2a565d6d1a58f36be23f8d e925193824712d25218962ded656b3a40e2289a7411d0ee243a225969034f758 95eccafde4782686cb16e72ba58f590e199d7c5a2311419282600f6cf0ddc4ad 0e884312c51e615af59cb889280489b218e863c09c93c1ac82bbee42cf29632c f7f936e4ef5c4743d449be61e7f96afd125a5a60a25401fdfc8fd3a19cd9603f 306bde70ab16fab0ab3239ed6135f29f097f2b8aeb35284793bc13776f18916e c0840235e07f343d60a93d7c10eb6cad02a1e21f21ae0fc38dabf0586ca9c06d 456c89bb45595afd46378447dbe5134181e7a6e11cc0aa7ed36c83e3c6de28d9 ec1ebf04927b3683f9e70ffd9288755bdc76faf9b6332a07a965b26b54348a7b 190f6d504d53699c79162ad4136f608393d60c7abead78a08e11039539c1ebf9 adf6c530cb5efb3f242877f133e37f9e469c30ea063b592f984b8eb63e0f5c76 ffe6eb0b4553fb31fd420a222d0cb8d207e30c5a5dd7faa73ce3df41859288d7 c67cf4bd5b289c29d0efee123985f4bdaa60b5513fe3cb0dad6a39afc594c29a 67d34993ea4cb59e59793f6a1e4ddccacc0a7a0d4e54c1484b98ab2fc771a96e 70f4f546a64c552ddf75d9c2a6253828f82f8c47acb154e64dd280b111c43f7c 535d149443c7ce9043841337d0ae6c1566eab09e9d357702f1f69830650a8786 0dfc8992b763c8ed22ea20e1133659438826a4e22ad23153efd00825621eb8f0 3c036898546ffad37e3e12b954beed85a0a4d4913371569524afe8d602211ea0 ef880053e6d5e0fe71b62fee399aeecbd857326ff2af95d6d69a86b3b368466f 07c77b031aeb519b3eac139c824d56d3ca1938d8291f38c11ec33f1a354249b7 526ff066a93621f3f3a9c48e87d49076dfd941384c2ced556822894a6f0244d4 05d251c75a9dadaa46ccdb415f2690ef288ac76b5f2c3654a92e0e27702b8b61 a6b5a3e21c618bfa4ec62a51af828649e87ae65436ddf09e2948f554562f5fb2 a962cb50504cb39f73ca1afb9b35adf99972d02771707f33445f36cc8c15da0d a2c260157ba61a817538f0a39f3cfe9362296d402151c1acffa63e781dfa4136 858291279a2aaf385a03ad8053740bb2a64efe4f9806edab1c0e86 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 6 /Sigma put dup 11 /ff put dup 18 /grave put dup 19 /acute 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 55 /seven put dup 56 /eight put dup 58 /colon put dup 61 /equal put dup 64 /at put dup 66 /B put dup 67 /C put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J 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 85 /U put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 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 readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueXX 5000790 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950 93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21 c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644 7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e 13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03 22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56 25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1 c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2 b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e 2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd 6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4 07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331 51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6 0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3 d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1 34e48d740607ff2e7804164a16d47735864db8463a486ce4314ce68a4abbfd0c 1d8090a1146e51c1147146f1189098b0ac1b31819e481ca297840873961ddd87 af46c4d818cc252607802320dde80926c63221841035992073004f7dc1ec8b82 581e2e62ed4d0cc3ef0599b2dee151270a188a7649e96e60b4578236e03bb332 6e18e077fa8af24e434ae05a3139f24b6da32f4ae82a86570b3f933c7c8ab503 7809a99ab190d89e32c8f9a62383c0b3ef7ec5822b4938ad704a29a00d16231e f68f84c483f69471530811765847c68246062e48838d8e92cf0d52c6764247b5 0c8cf326f0f32fb46c81662d46c137ba905bbfda842751caa8409f92029465d8 f55643c85cc5ede777da832975c097314e4ed8c0b86bea59d981cd118cafdad2 0f7626101f2a511e48ed33b6ed1414d3ef32e6de489de2e7a5c5b891edc3ae2f b98aae92762b23e92dc2f92f1262e099eb36d01e7f9f1de9d293a5913fe411c4 d97bc3d196b60ef310ebe39c20ff4c9b9ff3760bd0881feeca6909a0b82639fe 369fb13a600707d9b31fcdb17d142d3affc2124f1e37d2384e052c3289365ac2 93141036dd5a3db8e9d5d05f20f9893c057fc7ca0aff98ad820a152ef34d7da7 e6b995be64c9d2ae86b4f8d29dc91e7e7b419daa3af8d9ea0b123d4ad389192d 85fb3578d29f034745e58ed153ed480fc2c3df1a55f6679a0cd7515078a04e7c 1fe7a17eb824bc6e3befa95220fa2e4233a39f00d1687be414dc31820e4fbb4c 72fe23fb5ff39e06b3964fa7388dca58cc12fb5a16807ac5b4a88cd56203f5f8 607b3bdc0c950a6152179d87cc8a25c756c88865a58bf688a6b3a4181cccc6ad 2c136d16aca1a6a8f01cfbfa8117198ae9023b31b9f698657a6870de851f642a 71ab8ca4a2844b55efac1df5a7ff7ba7181c4a673f7156e06f923f7328de16a2 e613dcc327753a8cd95d5af7069ffed72fc5e0e55d0dd817f59f9247dd63393b d4f61babb905176495254afd83cfb568aa73a3662a9482130d0c96bfd357c402 9b9680b531913b811171d0a70a27e2e8e65c6677e70d2d57ae29604618d67206 cf70204b85611fef46552d70d2d747aa8c2a4673838d2fb42f36c2ba3be104fe fafc74a6d284885d7eb533d787e3adc0e9ccd8f9d8c06826ff6f21e63cd88a01 8174e7cdd30938c4e20113fcad1d837d3e577672b6b3d7e39097916ebc761812 2e2890cc8614a7841201f37af861b7cf6f710ed0a8177f710ef372c85e53e79a e2f5ab668a486b09555a91aa636d82919d2d6d4727d173170d0ff0e949bb4894 08119c03d1a8908f99da8592d2bbc339b42548b741d5f5e2807806eeebea8006 397fb2a36ea7da5a4ec4862e43f9fc89f0318052096677dbf4e8abbf6ca68d49 1f2e777a66ea88f5fa7e13b7af73877bd6565e5bf8fc4ef85a1e960ec302107c 6712b744c96a9fd00311762bd562833291a3d2aaac09f83e942e350704ee3059 7405130408fde7ab3b8dcdc6f3b1bcb12ff328626a6a530cf6334328bdc8c577 a444c0e879242dd4f4bacc7bf4390edaab36090bc0492ea54f13c1f2400a1311 c11427da195bffb2b6c1953ef5de55f28862991cffacabdfbafa40e361146380 100ebb8626af77675587b68f24f9a6b0981b4ec7d7490b2d88c6809bbfab28bb 699b3a880786e2071c94a3627439c673fe9afb75291452fd0c0dcaf86c70035d b0122f159f54cd683b5d5c288eb95ee17e8c58288c09bd43133162e4c397057b 8ecee4fa5c2e21fe1464b99d6f80908629e831ee811e690004b00da5f01e49d4 3068d4fae87d8f1e866c76ce893a8609a20576dd8ec322b25f11d676ce19f01e 50225fb249c7f0e5693004028a2abed57a4c4b0bd23aa1f801091e0afcce7e10 d0a1b6a9343586c6afcc3a29ebaacab917082048f17944a18cbf40302213b967 8ebb2e0748c8633092fc785a4c0c560b90085a31d25a466350c15648ee6dc263 70aa1240be682911ec9b951df676fc00617d83b0960fe715ba0185df6106aa20 bcad8783564c7c7bd95bc9fe3f9251d0e5ba4848093fe9e27663694e54fdc52b a94c4f4e328468ef292c05664913f053b710a0ad6ee68124dcae1ca71f94a842 ba789ff9c86830011fef16c62590328b3b74c9e801e8d9a8aabef1ec544860d6 e3c843080f0326a9d7ab368000db3970a6165939087f17d449949165d737fcf1 d00811c0ebae2de711af99c95704b8d8231d2ab4c14a625f31757238350df4b0 dfd9609fe374182768c9cdac2eb2fea9ca301a28fb2ca9dbc2400e2cf76c4717 c0711d7c3d5dfa0c5dd5c6fbb8a817417c070e473f885046bf25d95aa82a052d f89ad84ee5950d1b67f302fd3c948afcfbebc586d92a04c65f94da8a60a2ed6b 79ec6cf0d93fb55eb2c851397c966e81c8e01b89a0a1d91bd5ad3e0103d87d0f bd797ec31397e07835ab7dd2573fc8f7cc2f12151365d2f6c207960a80bbbb39 38434ad482b684cfa1e5f6fcee2c4740ce3a111a08263b217a694c19dc1b4033 9e234b6cfb901769d4fc9abe47a9cf329a3962e4e01402ba0b66cda1a86c2a90 2b07866802928ab4e542dd80e7be5ffda7e727458129237dac8114030ec6e7ac 77f2d0e3694209bec5621445ec083f4d04f1654b4884bc920e0de4b5dd9753cd 649b4527bfe29d2f82495488bd23df9cd297c26e9db2ac0337294030c3bb533c 3ed0a414a6f8c9a71d8dc28dadfbeea02456754311e236a28378d59f49910513 06f263b44a606e94716a4b80a516e8f1c19388e8e68a78a586e6662f27bdcfda d98222eee234a3428d46f03fa3e1e8dd97fd0a88754a6ef1386e90da2b8f32fc d7f31ab59b69599adf39b10c4e9eb807adc1d5290fa874e6cdccf76c127bc231 172d9ca2e17c2658b186199a53163dbcdf0f25bb172f16192a942edf811d574f 2cedbe6f4675bcb5c058cb5c1081b36c07f1c29aa4928a3b5f81ecb4eb07a659 dbffb7ea81603c6d1dd35b4d0ca362832412cda66bad2c1d29c8dc51fd9397ac 080c9e3cfa1132a173c1d2b966e3f146c70becbe38be6a4e2bc272b4c1bab59c 82fe74945bf89f2fb1d40fed2905a5a02ef3c62ef86e1c1125c6ca4c2bed6c22 05ec60feb251381983a8dfd09adf0d8b9af61d1efc838ed7af99dd340fff2ffb 45fb3e97b978ba1bedf8a05745f7553e89c444b3c62697ebb821a754501bb3e2 4b1c4f16ca6900e28eba1fbdcff87ebc4188bdff5e6e1e21fcaa5d732f25caa2 e8c3e33c1392f589bbe73ba37018f914aa6103ba4f5f38f6a92dd895605d1915 464303d42251866ad57ea42ad305d5ec03bfa0654e1e274087de7b9d66a6dc1f 3bc0f79ff56b7665842571de66484fa851b37ca63afeeac14c19b452430a2f20 03513a05766c9cf7094094678d5395b2ec4949d8fa218cec2d3f4958f9db6fd8 a123f7b5a1e4aeba35d7bf679a842844c19a56a46c9387e5c2a6972200c6bdc7 2dab06f5cc7472ac0796150ad46b288ee8b1a6ea2e95e26406a8119f7024e4ea 43b70a9c9e6985d54d0baeec8218daca50c1c733071a2560e8d3b70f1a22b0af afc1b558e980db30d317185fcae63f03d5be09ae90fe1abac4926bb91adea871 563e6245ad54ee3fc590ceb91a0fb284a7e1877638bcad1607b96f1a74818314 b94d3ee6f842584b3d71e78bbe163d7e37711eb8663b8eecaecc3f3459254855 d215865d8a059b22717f0e806a842e78d4385f33d84957a5dc61881cc1e5cb43 ef6d25b00ad495662b37b00607cb416200e7fb3975acdcb86d890fec6fb602c2 2e73c75417e044ecdf21524062c9a096e8328fc56924a745f6e402936db89aed 657d12e7322906d8bf4a86a8ffdb2922abd6fd9251415ddf861087ac01b467a7 e39f2e487414b5c1fd6db765d883347333dd1f21644c616d678d8455f44e8541 19c6cfa9e33a0f2135eb7162241014101bb35b1379e6cc8a01d02b5aa3ebe5f1 4f843f71d9d4530934a5c912a91e8a6dd5670bf37964bcf3b9e1ed9154d592b4 7c7773dc6845b0abadb1f0d0795dad9f00c1098872df9dbf35ab25342ff73e5c e382870f4a7de2bbe8fa0e3aa4132b01f909c84b72ce30bfdab573d95cbd6a63 9c7f4b9d49d0e22f649c73d1ffa8e1b61067956adafb4776b412514b2ccd4985 543319058cdddefadfd6fa8f1d388f1f83a21837cb7c4bf09a1c4b7ad5feb9ad c2c30c0b8522728c09f624ddd1d3f3f5a57055ea4a1bae785b16835ff2a78e82 cc4f6e2eec000240c7a7e4b4f7dacfc3b7af6afcb09141abf36a6cc83c075c6b 91eecb8ccd985c273eeb3a3dc03c6f448ae0de42f0c217ea4056c437f9aecc5c 32e664e405e22064ef41b7ff296cc57904b273d7c2fd92608a2f6ac2c1602a26 606177332b1f09d8792a6ffaffc2cb8aa81c82ca513d5d313aaa43ecb083935e 3565eb50e2788d7b8230341fb0e2584a1bd8e91d2132e1e9bffb49dff00a5242 39f785791bceacfdd177af0d6e8104055bbe505e0de806a4bda9e4fe6f0d1900 c08b24f63700521659f66f9bd7c5c2497b7fb9cbe77165ab9d79c043c91f31db 0accb68a620cf34c6198fa11e5390ed4f9a605968c34a33fe4a0d9ea9dac8f80 67ec974e956864a1c08efe221308bd5b1bb4b9ba89553f0d605272e8dbf19418 95b7b5e62038ebb6cd832d0a78b6ac4ed256bb2d879348e902f257a4ee6a0392 b6447c901b5f5bf7fe102db575dc45a085f58e79b446dc8190ac0c5e5aba37c4 747559cf34cbf7ab03832ed30baefc16987e32a5efa0675003157501bef6ecf1 d2aeeb12bad664417229e2bbc9bdac2d338ae904fce542a70741c15c6ee7ca2e ce2b26e160e65d422d07d6db8956de3e9c29d6650439e6f879b96e7f5fb64bc4 2959937dad51c863ca76c667f83697ae69572f93ccf56222fd6166eb83c73ce5 2a2f1260e6eb9607f56d58184392ed9dc113b10a752b173accc980f61e5175d7 f8daa22e62ffcdebc327ce85d1f1d471a2d1a38434810e9df5b42d52b4f2d0fa 51eff494001aec5124a55ca9fe6b9e84d051933ce2626a9942b52430017a8ee7 0386cbcf8c8ca3c9beddc483f1e8a833a5345b5e642fc1b9ed756a72e036293c 1dfcce27247e3d2e605782e82999598e907143e7a613c6146f61dc23d978946d 1f42272c07b31c4c82022377eb8df7a48cdedc5e74aa0f63317fa844ea4249ae 32b74e886eb7fbeaced70ffd7957ecaf68a62eeb2c71af60044b59df0d392971 1a5a27c2d402d8a28c87c9820025314b7902f51c846738da90f52eb13c1c91bf 3f6bed8489df418e688fc8b800029c2b3ec45f4ccc803823a3a90182a042248c c3d4c7eea8f0edd548ed6f0f0e25c553cfe38719460bf6b6ea5511ee77dadfb2 933f61b012dc4ae16a27dc068929ab45685b9c8c9328fb11571250c4af617a9d f2a4cdac9aa30245b9b9fcc105e54ae6a0ff8ebbeaa15a86f86742ffa458b316 56e6821dc38bc153ba8e3a061722c58b5a6fd86e5b883f268f972aba5ef26d18 4297c10c14d1de98baf933e662ddd76ed260c78b7cc7912f010623625d53dcd0 ddb07c9710aab0520d4aeeab5c04d844ebec8a739935dbb576c20a7e3cd4d0bd 8f34c4a72eb48fe0f680b67851756c0e11fc2bde704ccd814e6b643fef0cd029 38d6a62b52c027a889034e4da40b5c0c3039660e1033b606b912f72cc6b3080d 752f06517edf4c8d917f488041b14549ceca6aec36214c47ca67692fdee36857 31a7254ffdab681a49788acc5e33fa69658a1c6eb19ba13829d99ca4f693b85b c9e1f4aaa0ca1bc478023fac43bb5fa120fe2c80928c9744138baf175a21b980 84b1f366194548469469b8b2163cee54bb1148943559c93708ad8df50252b0d2 e322a32718b32751ef354eef77727f5a374547caacad085849f77eb92b3d2c7f 93b65dcb428c0757a9b5522d8d5d219679351bf5ff97195649ef5aba0a8f4db4 08b66ef0fca4c2b9162f4e0fb2cbfb1c2d408b89668a9725ad4cc97132996258 18249b78053ea85b8945e28cd3cedf8727a236bc6b983986acbcfef6f1e9346a 8a15936b82297f7700b6d08de830b63e8661aa29b01a004344b566c6bb874f44 ddaa1df585423e31737eafd859d2b619e35e105afb29229056bdd1233d1f353b 75ceffcc7fe59c8f25ba48abb970ff55636e93cb3b366649c3b56208901b0187 1cc9b2c6c1a54247a6eae342825dc5ecebd883b410fa334fb83334164bd42f86 be650211c3df3882e87a09542d752f49653aa5ed21ab68da42f0cb0071795fa6 97acf59d0175aceb5720bf3aa42de8e4f03e2c28ac228209bc676145cd9909eb 5515436e33da3b94090dee729130dabe82a2b25d750bd5d40ea40c78ef151a1a 82e7d014db6b91a2a50208b2ef102ae69f37b959fd7f901816b9175b692e3950 3fe3d612130e05adbb9fb8ec6dc9cc0a6e3053cb53fd64a3cec6d8a47355803d 7215c1d0b80e66cf9dca606b550ca47af89e8863ce186dec89258ebac1be6221 fcebbc4d69920550291161c34e41e66f7ae9013cd16c6e5f490bd081865dbe35 23356b5221b46db27db6aefe9ce815580efd586425e3c4e5fe8686940ea6e4ce 93c25b43c86072f0af69ec0fe8cc4885f714ae4eb5abc2eec430bdde1914bf5a ed6d8231c3af0b4859d60911f2b9ff024e604ec2eb896a68ca7e2f4bd4fd0378 57d930428548757f1e7fc8794cadc05604c50b769f609a95677f9998d1044c41 4140f6051c394f1d4dba7db6d46464470159b26cdab41f4f3ed5a5608d9a3e91 0711a7643bb71b028a51de0ed33320ef26b9966659718c13f9c95de29153645c c36f476717a61a9286c0cdd50be35f083c020cec955466a9e84607d14c092a24 46a880b7791a28c14355f5036ed3136f9f8c9a39d2d769a8340155df9039f6c6 d643a5c9c96baffb9969d372f755474bb65477f80009760991be55a1587544f1 c42e9eedd7450cc1018b0516cb4755d8bc4bb58a54382bf2650d0e8e5cc64449 cae31ce5c8d82e308f1fe6c74672c4edc4fb0da6f444469e1381139fa94961a6 1dfe30cf59ee71d914643f73f888670d8220e9a8009a4481bb66b227004ba448 cb012bc40c7e19ac65c1ed4676c110c7758666f1393649074f4213c3bc1088aa 1dac182ebe48006ffe7d5041f133fa934a80c0412c22f5bfac1a29c2b742209b a43d953102097774d25abe86eb0f9992aafbee24157885af3b2c41386f299cc7 63e6ab10865c9fdc765665c25ee2fff90b67c312d08f2e0f438b15764aad3c11 bc56d27d37602f8e1113f5bf37bfe3362271fab75ab641cb502d8eb300527c97 40c3595311f349fb8dcc8822b4c8a9a61c82ac23380e92a6de4c88e409070a90 b54e1fa9c2e7a00ab2a094e60d59dc132c3820b12cacd81622bf82937c9698e1 d3c8bf2d34a963d81e3654ad3d9c8882108b700550332b37ae61e6eb3889da65 7731f249732f686ff8d368506f01fbaf5d45567f72482fb9c302469aeca2e4d5 8a2791acd9de9f888d4b711ec1eae5c684ed37d4d10e9c4a6dea5f5062ed0b02 9294bff9d40f508bc5f4e64fc8fdf815ed67ea4d3567bcd709d8b607f9919ede 4e34926814ba275359bedd75a97722c8f788f29a7bbb728bd133f6b934144eb4 7d740227a98186933371879cb2b508bc6afacfc7fdac7107ce52e3b09ea0ab0b bbc8d0ab02935388edce5fb33d505816cd9c377f1c5ce4a89fd21345a60706da 5c5872f2550dd2fd7daaae96ab4a99df5b112ac5c27a1d49c68eead42759cb14 fe23fe58971475c67f4add87eec8a8dc3221b9e0c638796b683ec7af30022b1a a61a4e4a25897f9af5b869b82b854a02a54d03a9b4c03aed3e35617099383592 788175836670be7616b6c4b608ae5b332404e922a648e6e0d8c9ff0c684768ac 715a13fd30352b29836dc9184087296fb4dd4c0163422af2d08319f2355ecb34 e01f764350d3712a4293ad8517a74ead9c0e590686d1745978b941487b5616a9 c5c3f8c63e4ad46c013dd19fa24588b9b803de35700174d23bb145e70ee7f8c8 9b2e4ef69c97a2fd4dc997a0d3ed4ad344791d7e087f0ca3a046c0d3f35a6c89 d1417b8d82584c3f26da0cee1d7c6e98fcfa832be5c93875f00633de5d07f599 d1122c53adbb46527a11569d0501094eca0402c691bc00f9f7ee7f8c63d3fd9c d8102d852f465b54f04f602d929f1bbf12a104d901a1b4cd2fcc67c4fc86d6c9 dbf3f9f52691d74c94e5a5510b975f7b75cddc16cc8fc749b9e54cf4abe31f29 12749429b7782eea6c9b143068733922cf31bdc941e207faecdd627c9818a181 c018bb7eae8889caad2966092dcaeb69ea2d41f51c74d610bd8eac92a8e3db95 2860c8a3412a6fe5bd7fe44d0be21d2ab24557b8e3e7db559e42091d99d4222b b9869aff2b3d79c4bbb4362a2de431d5d7f7889a73dd462d3502c8a50c83307f 36fc5965a6855b7b3e6cff3dfcfb98c2a0d5a2a164d27f1998594799cbc5d7de cbda8e65001c9dfb206f904fa3abb2dc2cd621aa306994b6afdcc83e8ae22303 1ac7006a3c7f10559c155ee9d5296ba25ac786a434d76701a296386248931d4b be71b73c79ced729636040157faddf73cf9dcddb160f0c99a422accfbd240316 7a4b73fe809a94b0a5eb11394c6bbb6acba89e919a9995a225fc588c212dfe45 a0c2c633eca9e92680a715ba4135ada28420e753952f4c82b71c17b17d288680 f26e8ecfdedb021d80f0baaf61798e446e3fcbc3be1ab730a26866f231e2c5e1 13963ddeb6f6a5218db1638b97010addbdef54a09433a3704605ecc2ad1d7d9b dd2a3135f60913816c46eaeba8c8a28918c0c1b4f15e8ae253e75134a065da3a 36620cf53402dde8f775a3e893ed0269900737fb0f66e4d339313f44da90078b 2449d6687e25c308e2a8867e3d91b6b95cd3f5cc59515f420cfb0579252313f4 cb6776d98f048f687b20b7614dc163674cb49cda5a2869363519d5e4eb890ac6 c6bd4339d8163df3807ae12130c654efe60888131742e82945188c4c9a9200c3 47fc52afdedff8fd9865cdd51a41d972bd0784696dc7ac94b9e646ed59dbf87c adc6a3a8523d2480e4ea994fca964ae5bfc22e75c28e4b0761acd382cfb69076 616356c02365b1bba7a41664fe570211263ffbfffc21aaa2661ae85f89da4ca8 68b63b1a88e4df5cb4ae5db23dc2d4669a00e24550a6e609e6fdd98b2f796e97 c481fffb91addbc079844c2ac992d3f91e2e736d6b2de099793d2b8d95f4ab24 e5b521e5d5553f5e054f4ab2be9ee1928c25bcc4a8e4a7fe1b86bec5d9fabce3 7d678ce9e7bba9e5cb74959a440ebfbb16ffdf56867357df66339c426d5f4252 d241586c063c9c0e31ada1ab8e695cee8a7667709c115ed0dbf875ce71d2c39f a9fa2f07337353e295c82f9af9e2656f5e952ffa088abc72f0d064662cb64ec2 d9949aa7fdbcf97475687f445aa1cdf14b3732574bf489eb3eec6fc9066ed339 18ab7504057dcab1a3e92202689fe02edd6b8626d096ad43a0124c20428df7f3 1df7488e083c26fd09d3906551e5a64207a368aa1c7f304557fbd4a3f9b250c7 a7004a5345e57dd0441b208c07f5eb8ffd6450e7964deb3836782a2a75f966e2 42292f2c9f30efcc4a5c7690f6000f6a32e16b9252663601df0c7df381273c71 66a10eb7a7d07ccd72677dbb7221a58857c47393883db96ae3c824c992cc7bb9 100689add0e733dd5ceedd9ce845aeda2363c9711bfcf570d95bb3ed75721261 8ed894367fae81479db2bbbe6ce0b4f5950c0b3ff7984816dff2d4091d64b483 5bc47204a3495780538fdee71c96c02ef70cfd2ab1e3df7c7218af36daa36169 742a9f10f44afd0d93a7aee938edeb18e525ec8cfca6629a40c981edc22a9b3f 22dadcaa4834314368926963fec6bae7dec15ca84d2f07845643a47102c09cbd f88a41950ad6e3f68cdc7a67c512d158cb366cabe041f254aa76e280bed5f098 249d76af4d3e62836582a9a1a75ab727e4d168e4e3332204ba055bdd43154652 fa0b8231e616e79d3b358e58d7b34ee1328314f3a8f9d6a8491b6b9d7ea2b1d8 ca4c94e548a89c62c01bbf27f5d07d76a638684b8aea1d20db00ce236811a6b2 f76044cf7aeba2e948f92d14fe0fba03e4d044c328131fd4579fbe4a2148edeb a92a08e926bf117abb74a68467031dc40b4fa1aaea1f066a6e51eebeee0772d4 affb16310bf8ce5ce4b451098c34a920d707c79bd24b98189c8cc45abd84a9fb c7a660769299289ced85f1bfdef5ac364e580ecfbed21a40a77151d249759a0a 4817281f6bcbecd20ecc7faaa922790ec5283fa80df267a2101af4f85df7ae59 479615c90d05d35baa3d0a1413f21dd3f3246d7cd26cdc5a87c954c1f0b05739 3fa6e03d42d0f43f1557119035235770383e9c702baa6f2518aa3d1d122406e5 25f4a4acf2f0907dadb180d4dc500117977d0958529d1200ab127ac3ff66a869 08ce2a99711ac268d1ebb28de7f77fad95e70f89a0e6ac34eb313645d382ecc1 266f8ffaffe0a5dada89eece79365c39e33691ddcb84340e751a1f6dcf750f96 94ab0fe9a2eed4e13dea01cf029f2ed4db623ca34d0f2fafca60b0a295b5b5a1 e213bbeacc9caa3167165cdfced27cbd303e23e6f9afdfd3a21ba4a10bfd3c00 f70cbdda15173eeec3b05fa0199c8c92ce09908512383c3955ca4f50f322a6bb 2a38065d85f4f9813e438efbcaa739e52810c4bcfaf827dae552f39088c01d92 d99fd2aab0b23056bc745b98c3e2ca7af6e4b41bf6a00f17a4e0dd9d8b9dccfc 601fea11ba1eac4c235bc68861a6f4a2eaca4886ebe6480438103f31d98ce974 69e985b756efb4d313b652758045468c8c4f7e692f16cc877445dec1d035dacf ed70fd60bdfb485786737a9bac224756b5d46d0d4903ffea5dddbc0ba7099b1b 25923fd3d9a1708106e8ec4a173b792e5e29cc13fa709bc2b75023e0623073d9 9797d20131a8a1c2aac0912b7c8f38d84a9e2d85b148e5302c5822f9f249cc58 a7e90730047fd699290b7e8ed649859ec6754d3c10b1fc0f4ae71d75af128e5e 333160e9889904ee025d7d6ced88a0be487324dab93e21be0ff0d448db5b4975 5f2d8f96afdcc021b20399bdd1b40885c5c99105e1980dcb0cadf930a1d43662 2ea4dd0613909e23914283e9d7277522292af17871ce432e004928fc9a6087d2 e7bf724c7ad17409ae59e218b4e5974660b43b78319f34b3d9e770c495cd2891 3273e35628a5de06b8d00f42694b1b192c7979b382743586918c9e95434f80e0 a289430fd9d8a3eb7a0322b0bd328e7e3b04058131204291831c9ace3dd12d02 86133dbff88a0afdcd6d6f00912db86ca06dafc8b41c82afa6939b4df4ab2381 ff44704e8ad5b31470cb93206223932069a75b46a0f15ab79c4522b7b4398126 d52ee33b44b84193c947c7f59511e3d104073118046bebdc712f26099b5b53bb 712b14db4119da58504be84f865900ed903d4f8712931a7cfe84d156cc059551 0172e25a540943ebbb49cc3ba3b929f7433c0c6fbf046579ef485cdfc72a8d74 4ab0b58252bcffd7b35ea12cedb42a9c21b6086b63e3e77fdc981b8284baa4f3 a09f8a4c895fceb0ab14abd90d43e9d562e66ab006ddc0543703f789ebfa216b e3a4b5afb7bf8c7e52793743ba43692955e4943d67b06e177c3e5df65ebef801 cb87f7d111d40c02b911160a795a617a6bfb58ea0a8671820d55cc2d8181d04f e888594f7831965d1e5a4f24c9b6d965a8a67da67916f8a1a881fcbe8853a271 fd907c258d32da8cbaa637ba7b65ebf4adfe7abe734ffede6b5c2bdaa9ebdb55 7c4edc35251a7cf249a46d97d8b9f9e1ce74e03a9651a59b26127a1dd385bad5 4748ee77b49ac161c92ae9058bdfef95170e021cc16434cc6df96c987c935b86 5bd1d51e6d12bc076c539b6d99ab3721d8685beb9fca129136e6b891c1a527c2 a90222c11f312bb41b5a8a4f4bff0791e8280547437ea2d3bee76377207ed4c5 45911910599ddadb49f7a680c7cdd01ef6c0eb0ad950427b02f362f2dff77995 92f7027c819b1b9ab75e5ba6cfbe5d9b1b0064d719c63cace6e805d6056988bf 0667821d44a5f0e50d945e262868218f73a524ccc49d21f51d7aff6bba87413f 33db37c560d9777ac71c6cb1534e7b99872ad5032bdebd52df9caf4f90083fd4 272d3bc344485dfcafb0e2b5391f6c0e376020a5baf1054114f34c11a171bf84 d6b2fc71be1ddcb6453ca570c5e7ff247b12faa99bd3a0b306c0a201b2db086c 47a3ca7a3f0a3b269dddf1dff7d4505bb35ec955207d74a2cd29b63c844837f9 03cfa16cd65bd1070db78982ae4b38dfba047c9246672ca5b6fcc20836f843d2 3a22184a0da3531220633cdabf1265de4bce955300b8a5d50c204cf9e229ff08 43677c812f711369cee4694adea57e296601bbd0515d4f5733393f5d3386ec7b c1bdbcb2f1083a657740c953cfeb28c53678f4aac31c5b95836558bff0f1c162 caedf2f8ed18f9c7dce80ad685d83a7ddcdb30fd29bdc99e2ef606a40b335f70 903d382a100c1cd70591f6f65e70e4280b5e0bc3ac3aa5247e045433afbaa48f 0c9ddc81e34417ee35fdf97456e51b0c88b6b165c5062192097015e0b1d990d8 2c602a09adbcec5ecf07dec65a834722fabb71b036a3b038097419e342e5f655 a644c887ee2e86d272a54c08547c7bfa13b93a5eb42ef335d172ef215c6730de 917de05dc86abe984074c6b63f0c34937b51c3b272dfb284f80f75c06f008672 322fda11624de47eefdb78e5edefc9a95cbbe276020270d6ec049a14af3dfed6 b91cb5343ab06cf110548e5adb137f68a3326f43b2279fe35f2db7c568170114 12247f00da1c8fc6c7b4f42b654e8e67285a563a03d0d666a9758ebad25f91ff 8a5de0d47fc6403c37d03f4b9275302d7cebeacf1dfae9a1f07a93c6cbf898af 58a163299297bc0d2941d0e67c30e5383a026d8338fad46c61dcf59dd070a262 9412ba6c438e65d2b193ddc9ac8a1016d95c6dae04f77bf181cf65f79cc1420f 679c67a0870cae0a845059c9e6d16b9f63fde4fff08c7e324725df2949c23687 e856237fabf0b406be4a6cd02f13ceff1b1d114241f0b5b9e1b1c00b2264c6e9 19694abbca3726efe752c676291e1b4ab60c74bba2a1c85c457f97dac493eebc a9e86cb26cc76291d3ff856aedb52e4d964c15c0af87750753429c692f71263f 995f3b4c2449cea76d4b2b6222b67faf878ad11eb5e18ee1c61345560c1e7b48 35f595bd7fe9dfada11055ba5b411161ce60f1b922c6709fc90da8abbf0fd1ba beec4793a4c239e22c363c0fc6c3161e20ef1e60a499295726ed8110c76f499a e74ec53a4ab07a86bcee549310ebc984be757d174ad487a88678a849c1a42f43 9147ec4dcd7611a24422d35be4621dd243af9cdee4ca1c0777d56755adf24296 3f1cad7f8655a5c8e0aeebe0733af30bd114ea8c51c2f5137edef0332a3087b8 529407e505cda5ed10262f6918fa1557842d306e6c4a5d7e47c460314c625348 370d4986605d57fd4d0cc69c32ed5cc53ed1df9984d3c5860094ac191c7884e8 e6950de8299316809615768c1965237852d1abced13dcc2f8fae95d7ccc741ed 0b633b6dd9de08e132dffeaaed4d80243d66d3d023e61f4c5e7a788adea9f494 23f6c39c50f34c1ab6aa1f8cb05a16d6a169e602592a5105db2b2884cfaa211e 1c827cec417e02c1daaf4353a53972b25e4becdf3668131d85d614545c0fbeac 4295ced1680eb34b32ffc473b984b576647f1e99c9a62de754685e94de088466 23a5a8a9d9d71db7638a8551b1cfa1e9ee37aa119e8d332cda2ee961004ff6c3 ae39315409fac8c494a72d3ecc9a5eead8e02475c671c812aa55a879362a418b 1b068e9c5095846d31091aa5bb30a9efde534ef7892e089ec8366b169883cdbb 52a2fab033e47cb43518950f806fad8599451608229bd1faf933e363f2a4455e f308274904a5ebb02c6bcdf1dc2d9cd4b90652050d43f9c915807d3cd559cd6e 01b94c3adab1179634 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 4 /Xi put dup 6 /Sigma put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 18 /grave 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 63 /question 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 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 123 /endash put dup 126 /tilde put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueXX 5000793 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5 2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12 cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e 4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618 99b8ea06b092c3c1e503e6e436e0a9fa22576c8930ab3dc8c20f5d82b69cddf8 ff4dacfa9c54bed5a3aa3ea5b129fe96be632843b9b6bc91b615581a985db56b 1e01ca60ee69ca92cf5c0882ece62edad3e106d835348822400f0b66af658f2a e56ed08f8b0010571807009b73ab12a8cf14ca6c71f03c2a48c500f9d62266af 154a6375ff600d9bac3f05ce34142d6867a79581c533176bb2f3117336671e2e 44638a97167e2ea9644e31ea16c2ad2990ea33c54001e0c8156e6de8ab6a4d40 a7137ba275f39589fea2e2db8256adc103d6f9cc038037a47e8fd469c5f98a5e 3c15bd4ace40d340018b1cff7d1ed8abb0ac57b5b5a2c20a51957b96c453edb7 dae5affd91a46d938fe0a13363001d844ded4323f1ee6d30012aea19b024a552 315505535c85dc26bad31e09c50e6512802976d298c4e90d0044c362e6bf3ab3 62a454ee93de25ce54411090c29e9d75c80ce26a84404bd9de3aee0e3f921ac5 87f907572b8354a5c3165eea7e8b2ba4e333802132f760b41a900c698eb3d273 8bea0aaf7aae96a558f08b61aec7c7d65b2889bb7b99800cffee5ba19ac90fce 11437be1ddfcf0bca5670b543b9644a71c8726d0c1005abdb96f6e0cf7caaa31 95017ca81519151c2c0b04f81e717c0691b63a76e9b25329ce2625b711cb7bf9 9d23ec2bb5ec8aefb8c1a3b422ad617b3da4d49685fd44cc21a1fe5e1541163a b3e1594601d63c7e98801d7746474377ce93f81404f3570afbd5dbfe77578605 917ab96963987e6efc2d3f99fa56ecae6422579852567f90cc90e4ef6d6f71d1 858270205477e221018a375ca83c572b3f972c5181d18643cecb04909d84cf76 7174b3c0c8ec69bf1e9fdfbc0fc7ed97ec67d878ea4ddac8caa522fdc6932df7 21b81af837a200e1d96e90a7ad7589fa917658d7a173a511db53af1848892270 44c4603be1a5ac1893c15a21fe5979a09aed3473a98e06c98356dc01ed3f5e14 1c3c057c3f97e2f9e8718b12bea7715a3432abe07df50291d1a395e7ba2f06ba 7cf20988904310104fa43c7a1f6d32f5fd290d4d572cdb5ab4b433bb849dd1a3 58b292cbd5c762262751c26d8756c7a3c4e6bef14ad9a628fa2ef5c0010ee4a8 d530f3786bd4e0af07d5587e90e19687d1a31921f975bff26ec2cf07f3efd4fc 54fd4f92f08a60ce2b3beb2dc8d81a303c8103283e6e5341eaf61191f0122624 2a4a88caca606438a767277972e2ad7ddc9a36f43d5b2d010b30cac07a383c1f 9c18c89749e610d026f72e5ee2477286eb57b77567af9c4f20f7454a5719b0f1 9581ebf64277e8f2ddf1ce08ee33f2a532228509a9ec0d95bec2b7beb23319d4 236fb1446ff7df90952101435fdb0a0fe7622a6a3972afa4b2cd99b5822b1bbd c28f623efa3532adbe2bb8f50ee214454f95d282af029d174edec357747b4d50 b02e2f47b1e9d736f85d789b598b19994b4bd1216a964efa28c5125a6ff6d16a 9e89fd1b4fdada3be2a18b5a305b22290c90980dba0562ab6d2ac1435683e40d 0d978602ba184a88e40ec0c33d17bdc368ffc918a3bfe4e2c8615950b45a6153 79e242cce3f5586ff100efe5e4e91c83678ec855bb8ef048f4d3e4af0cb56503 11178f8928bbac72e594effd9b0b6f1fa8bb0753a6e677f0cb709f9df41d3961 598f9e7e873eac311efb9b55706d89e0d82ef720a47ba58eae5bdfaa880a1b05 162ca0489a3730572a59b7731b8959d167e775fb07fd908b63f9529efa6607a0 d7dc30ccd04f643758b7c0539ee3dad62979168a0177c3a3eae5d1bc600eb740 03425bc2b16f3464562837b09edb51f5cda22660b503c147cbed3f5f14e6d4bc 08ed7d088744cadddb0daa6ad59d1bf41acd72d83e7560afcfeafa21c3043170 aabcabaf2e351988f8f87b8ef50e4474552dfdd8cde761440aaa7af123f4b364 4231b2f347bfcc39eadc63ed4aac86f421026140028e8354a9dd676ae1418376 8451c4ea7185936fc36921d48b579610388be4cd119595f8c8604d9ecee70f41 80357538110d001831e8fe2c0b3f53486a3ae64904b1a69a37126369f754c145 d0df01a4cecbcb6a2a7bd6daaf2aba5f41002bcce37694dedbfcb5a3b9076094 d0dd4280e79cc4b1576d4dd0894c8fbb4c23811e4f49aef049253fe45e699a22 085c3566e9edaeb91bdd6b563069ca3560069b8f8147c5805dc5cd7a8db50136 40da1df5e91a087199b1b5b9834ea0c512663ecc934d69d990001cddc316151c 6d7d87efc69ffdac29eb7f9f34c69a32903b05cbcbd562dcd5c3f7e9f3ff7e8e dbcb262684e7a45d55ab53d7823384d4e2550fc82e2a40c3547eda037d199418 11e7ca5209fd4cb70ecba6d16338ef1ca44aef339f3e2c9edbc3cf533e112de5 84761a7c076a43f76ce1421ffac62eb86d1a00010bcd21178398643a704f9032 a4d5d94a4e9a3e6805211d626097724cc18da1a87e61678ac0684de2004d2d33 9e6388617a7a52b7544e8aa76ca20d6e4e6f47a21c01ca7754b26a91efae3b08 5eb89be881c4e18f0bab78e77668dfbc93bc2f1902cf51da9b22849b005cc2ce 3081cef3183f5ef4edcc54176a382bbf5dacfe36cc726a4980848dd5dd284ecc 131d2ad26d3edc62e78363f10aad858e01b8b8cb4790f847aba067723ba719e9 76260cb975cbc3046d0a4557700dc0856c3cd6267aaa7f5493de2610fbc09eac d6e41787877ae16bb75f4d7e0041e9a26cff26da2dab8270f6ec7e2b1f57f1e0 b97061c7323d901e4d6b9e41dd8222c34c9d45a19de055723288a844ce5a959c 659c6ba60190b88e73866915ad4a605602b1625039bead841fe09fa9c63c28c2 36fee6a3edbfa33f779798877240f0f22ef6295ec5666030b73c7df64387ee28 e483e93b5df2b6becc107bcdc050ea2a9dfbf97547bd60dc22d4492dbe8d3458 69ad4e5421beb90af770c32964bada76999a8a386ef0a6d1ed2ada0a9945101c 176ee8eff9bc0c38355d0c9bd0419962368f77dc9ccdd621b782be43d1b84d51 abe2f9e48ac31d207dbf03c402008eedf04c1da20050aa3f664a9235ff7664e6 81a3d8aa7ca36455eef0b6442d9ee2ce16940c1533a594d29bc412fa50278f4e e20b18d78cf4d1d662e90cf4455957c09cabdb934c2c997619f7188b6e4f53ff e9f0c196036ff4bf9a663417fc38fc6224ecdea0bb7f54f1a920084dfcda77a7 8c82069d92d34c8902ece39f16fd6eea2f45ca3b34ea96f84f52f0d83595c1e3 2d51815178fea9cbad677ebedbc1eb883942a013e0f3056c2789f94f2c580cb5 302caf329ae4a0eecd5da7879f8a9086b3e7dca61aaa0a346110f017ec6f6cc0 1c574ada14994a8fbd1bb0a0d2e55dc08d24180b9ff3e78bada735eb1f5a5211 94d37c74ea10c8f08fb24e4569a272d605a7757b0cfbd195695d4e35cf1af855 5c38e588bb960d8835015cf141c7cfb065be79e3c5fb9a8f65d61276f7cdd4dd a656cdf7f58edd620af7f72516e7a81fc6291ccbe447f455a92e8cac46207177 e11db9f470be0e76916a6b374fffb654568361aa2d0dc2eaf5d9a9c0568e8da1 3d4327ca79ce6070b83cccafbcbdee0119b2b65298327b96f77aa392beb7e926 9086a006a3a14aaf0455b7f6dc0bcabfe092b8bdd8be8cefd7b07fc62178f02e 3a11b8edbaa56e3e3e3ec57c2be002f2da24c59c9932351f88b628cee9f2844d 73373012c8191e9139795cbd6db32931fd9ba8f5113843d57750740f113bb67e 24af8b2a0067f24071fcd4ed049fb8d59f8ebbc2cb5095c22d6cb5e2319d45f3 2a1934306188bb343205562eed64d1f02bc2e8002dd126c17869c2b6979eb2fd d81a07af01f496177a3acc33fcf4d7314fc6deb45b478b797ed19369f1dd3478 d32dd249f1ad0e3272f2e4b6dc09e63c1055427bf334f9f4eaa35eb673c8b363 fb2e3725f78cc3c1e911f8dd7e732d0ede3c2c8684402e3dfdf9e70674b5fbbe 4decfee3eee3c2bb4985b50f4ae93c5f9dfa4739db1ff607ceed96c314f97653 5c523b36b0ffa36982d72bf5b552e475488f7a7fec071597964ceddf32d4adc0 3f683af1b65de74384ea68346ff07811bf9b6523987b839cc4a2dea0a1241453 9a6d1c02ee9516f0c049b94f335a344b1a3dcb080e9378bc1ff7d9c58456b43c 92516170b3fffb561b846fbc728c220704e763e8a4e5517ef1aad188ead91b25 1abb650b18d41cb09727a64ae8753cb85ddf22cb614695411a4dba3652411046 5bf8d785d89245ca2af503a02b0301f00bec8e1d72fe3713fd49086a80424bfe 4f3f9294420d71978cb68a7688cf53301bca3c1dfb2de8249e8a39e147ae2b73 1ca1d36124a091a72f37359b23e3558eafc565124470b1a36a36c0c94cd2f136 ec9e92774c1563a061fd5b3154368149d60ff26b891bfa2bff8fe616f8cca597 6d75d6fb6b89f003b5c192f5f237a0df8e8631882e5cf6d111cefdfde6776fec 388098deaf571d88d63594fb928b676b05a81f17882fdac43ad5406a90e72249 a7f534b06be5db817ab09d370bcfb5e5d4c2fa06a9c42aa8088e991529f3612f 0f16234e42fd7ac2fe29c979f35e6311d94ac93e4c5b2eb8a23df65e57d80221 c8e986a98fc86db4803b0fc8f773e4387a9105591ae4fed3e97af23a8239c3f3 d139c31b7f25a62596503e762116495d1824ca3768b03ace0d6938fe05ea9e61 2c603538e682493732d45248c075a529d47a823c1bf48b98e2931ae9583b1278 ecffe2a3d9f9bc21b75af4e4ee94c610a289ead0123dc7051d28c8cd247e7a27 81c6536a47ca7528725b7db49c0580214e4ee45af92dc6b87a8e6576d4c022bd 2affb7125929711ad6fd0e84bd39c4d4e25a109eb88608b45fd6bf2ae0ae44b4 e1d40bc3512bb9f33e23eaee4eef27c424263b3ecba34d12aae48eebaacec302 a302a0f5405fd5ab0595c22a67f87649da6844c60f9b86859f6feb4cf13e865e 46f8366f055134ad7276de7d49120ddf76590b0be415232e09fffbfcd7949938 5d152c8a631b714f4d56caec53cd4e9c9cdd70dc97da099056644134929b6268 e100232c5da858c6ac7779f0e5e75735e88efbae84af2ba23114a22145956e5f 728eb053cf4e351f751fc9cf4d8824f9d19ce124ba6bacac1c33493486d471a1 b61ec8c04ccc25a281afb05f753457fd2535c668cd2df506e478a55d20b764b5 74a4f4cf2bdcb31ca4e38a9557b9523ccfff6bc0c3323b50683ff0b68100a7cf 7b7af34e56e71a1017dbf4e75f48e1a400b34213c5ab698bb42df19cc8573ee2 74d9ea2b4203ee1e0e06624a895c618530d510bb47a2efe418891781d16cefb8 839886f8562188dd806406c446f5d84dd2490deeab5dba76d292d7288bdf3697 931c6559f8b06cd830bba9485595b5b22a0ab091a7c25688ef7810ba7d9aa945 13efe3ed20d53c6a72a6de580bad65dc62597ff95248632f6dc03dba83067233 6590aa36198463b92e92b7bd472d175ecc1d93de08eb0e28932e02c8805d5c37 16fc5270bef29a6c750bf91e0f36994832e76e56b6e605d60ed9ffd5d959e1d2 b4e7ffc90612ebdef4328bc17c4f839d60e11c9afa67f4aa090b98a13a3bbc91 4bedb090d0118c76d6bb38e5801a78ff8850e759f6e7d4dc57454fc5c2a3ed24 10e97c89af4ac531720feee5aa11f2a1ec039330d50fac8d7451fee4a2f9ea6c ad79635874abc4a797cf39a51375e663c8f6baafbb4cc917bce5471fea680e7c 88423302158608d1cec53f2a4a7f92955233aa635d3d4f7097f107a07a1f3a77 2464f5235eacd472c2ef52c2980df1c0bbf7320cedfe76dfb81cf95ece446bf6 53cef2b4e6a75e5c64d20d53b836cd4f41fa5ccc3f6c2e6cb5ced753253f5656 6ffe532f78f9eb65c16b200156818a1805c6ed229b2bcd61af46722932d1a455 7446106a5beab292e4fab24055697521917b3714434908072c041f30d4973a1c c8122a4ee232935ed09b734ae2ed9da2d7600436b139f226203ba3b10322f142 a308fc266e6d2ce4e434da4ab7d31b0015ad003630fef7310550ddb69c703401 e180ee5f7ac57014f1816e849222723f736f76da059707ddb0737dd0d246249e f9d8feb20cbc8aab7e303b4777cd7a4774bac5da26d2d9d9685973cd54425393 4f2db782e73d69fea8526b6075f501ee2735387913d51beffea921e2cbca0dd3 63ed73b8a5974e833eed627115c6d3ff5e03caef4986cc28d1e5455c95b46799 b6a0f41062382a27251dc92ad8b9d4ea16d6f471768c44db0e475c3397c2cab7 6a782ce53c30a3206270bd5fcee1b7ca2e5335409060c3e0be7dc47f512ea51a 9a4c2b64b7d403917252630f8fd3db912501b247e1f16f6c03ccc0901b77f757 82ed45e03e33048a16108fd427ab7fbf00551e6d2f658cc388e54df8e30bf2c2 1e532caa9d22e58a2daf24a0120a5fdf0df16fce42c42562e1fe288c09ae4586 5b94c9e401fd81db2a3fd314c399f6616e629a3fb08865d47044467753df2bcd b2e6b8a656bd10492403c342345f2ef7b25f478ca9cd9b509de189d058ff65ef 6ea7d421de1a011559eed2a7fecbaab4de0acf6719e185c8d801930b541a2b9f 0d50f6be4a402bf90bb2e5de164ead6512861962f59b294d2ff049fdf6b609e7 fff5f72ba2c45bc0b711351288c57c1c936ac31b7bea46fd1d09354a6e34a227 fe4dfdf6ca5930f6effb18f306132e1855757ae47eb5d6ee3c32bb2f15f92f4d 4ef00b961f8e83bb1a2003cdec20b023910537a808c235c659e6ddd476e285af 2bfd43e4a1724bacc030c157280c790e29d0ffa351d53d9cf64267e1e77dcc74 d5aad13db86a0a0edb455e1aa1f92edf0a4e095acc234616eb459b6e9acd4251 871d69e838bda9a4013e465401938cf5eb9df38c239e87c0cbbf2f7df9e7f005 042631450cd44e489c19aadd2ed00e62de6ea1284142fc2ef798c97a490a446b cbe894e7b0eeae347772d53caa2467cb86757e6ce6181cc9235859b347f3b6f2 d9ce0974d15f49dbb1652a501291ad65aa56e3ef711d134df5945e98046becc0 6b7b18bbf1af436d6c6201535c48d7d2aef49981f1932378a140f8f0d4127ebb b009540d3d717c862fb172f3aa73255b36950710e1c514eb520ce9c061a35a7f 170722690e8cb649e97c9e778a5535f5e9bda8ece7c7f0e72053b2fc6b22e071 fd065790041978aea27f02a3bb614bfe2a373c3c19449866ed91c91e317feb84 2120210b3f02194d9844d3bc64fc9e9381802a4b07bd7c821c4364b45c2f4d86 65fa864fb67c1d7d6931b89652f14824cd858c90c6836f972724e077c57f66c1 6455853242edce7dfab640f2608cf9819f74ff1de824319e935d9bc9b68d750a c946b85d0a47ae867ec3238d25e01027be617d3e3e1fd01d5df1e20683d35aa3 8e04ff0be010db4702e95b2419d985efceaacc084c45ebed14bf123017e43da4 a8b5325133dc36574dfba605fb1b918c148de227b1dcb843668c0d714110a770 d22ecbe42d47231db42ba462960a21abdd7e16215d98286b421334fee8779c6c bbbbc27adf4e53dc92a90434143d379d80b1f16c2cd6d3d08d800d38c5495c04 1e0173542d57349814bfb3a4c381a865d167fde73e7fabfb3b92fea0677866b5 bad5e36686f3c0c6998a4caa3ddadfc1eb010da2a6cf6dc563cefa9f47f839f2 59bb6a3ceaf3c22c272ef87f8f90453d1eb3fcc7549e4e7e23f6dad118bb3014 49a485fbc891891033595d0954cd3ce55c23d329a0bf6b417b97ffc5543bbdbf 825d8655f467a41810dbc80a1921e1aede2cb56ec3781f97b23c7e1b19c018a4 6f55174c115e4851fbd5cdf2dec1a771ba591618aae0d073d8dc54f22c155613 9b2e07ec38cbb87b8356d485e9c6ae646ae57cda8d1941fb26a6ab23830f892a a9d94ac23e75c28dd86583cbe3bb72a069c298dbfb68851796da69091fa63230 778a2724397abdfe7889561828488385d6fb3934cfecfb4bfc82cfa23161a0dc 8e6a2a7b50873ae99d1a70ae2502401fbca2e98c03e2f3df84a2fc4434921e91 ca4bc47fc02826ab30cb54928d401a2af6964f997199755b692e2d6d14f3d8e0 575592ae1c24b1ff49d74d674eb5a1ab228cfe9e77a3c5fce6fb9f69b54352c0 daa6dd5d2721c695a4175f4e667c52619e51aaf420f52a75d2eec11d2c3da042 3710017a484b6035e0369c9a953155f252b9d725078ef381f1ca175878bf5d0a 9b2978160286f3b313cf24c9787586a1fa1eec411253eaedc5727e0d2903d223 7b95e2f39fd954e16f4a8e888871d7e91d0f909df06b57591ea9113cfccf71db a8db1ea460da2c24e5c0129dd314bf90b2880997d3e2ae27815519a7fe38914f 19c6c515c936f627cc5bc5ced435ab1e0051bbaa6e1b4fff180f3e81523c5403 accedbdbd9a68d40f24ae8fa985d7de9988c1896d3b8adeac477b8777c62d2d1 619842041ee661a20dd417fddfd39b02579643a9d9605ca367c3b6ac18366fc6 82585fa72b03497c84c1b0694b74bb02686b4e0b53fb1c7dbbeef2647bf61e40 cfe97ea0431d7d5b6c68836477fb44cb9dcc0d616b15de3639627ef8e3832803 ad9e5cfdecf11b9ac2c6d42b347ae3c8504a1d429d07b76d36c5c4aeea857c2f ffe556035ac8ad9b78d33bbc189120d57569f574f870b292bceed172790ae1a8 a2e701f9c413da109d177bec4b4c449a02bef8396988280b6d2c93dd41105e77 cfe32ab8f11749a2d02feebb09da22d2e9ba0f759079634c990057841632362b be603ac3c2d1326b2aaaf701f5385bfd721cf0442ddb4487db42b5c955182fbd 4b0bba8ff08eb13dad5b1a25f1455309ea380566c22a87fc1a81edabd3aa3192 a776f583fd9f97a3dac3d8c383fddf28a9e40e8e1a700d4c92fabb1c3fff60f4 d419df6620900d9de2a8e81c05c08cb453bd738da30d4699e1dd3c077f64e53e b8b7782f1359380dfa44466933b2b8955873ad303a1dbe53b2f7455b8a235d2e 9143d0450aa8fe6bebb2e796c20f20cabe0fb07753670cebab076d64542ba5db d8e8afd7d8a5700d1e82d8a473d70982cd1ca31d9de8a4e3a81010650c7ef3d8 91ac77652bc8e05a7532ec56f150ad3a9aaaf41c17959abcd0225887bc841b1c 72843f1548b557e2b1391dfd049dc83186747972b5b78a8b4393ababb75ab6c1 79cb453fc7e887e491b9bf2aeb5bae03ef312ffffb68f714594c0fbf998dc740 e3bc8a2ec354d66bcfb40255ad5e8dee8902860876b9f8ae7b198ab230982a3c 3350b1a59f5ca2ffbbcde21e8fd5179ef6cbdcfc9e40a77df591d240f9a7f363 3629f830a5359d969a339892b8d50cbb1ff6e0c90f37e43c2cc73a82f2206da4 24dbd2ca9ee4f872ed4c627444f98da53915e900b301999cff81abdf69de47b1 246ec65433a25fd281a3c7b70f1c1939f7243d4006428c9f30159ec9ecb83f2e af898e7655d58b5e54ce65d47448ea12762d373adc9b8eb0c5ba3e50f23df6ea 33bdc75c66609251b9080e774fd77e7e9ff63cddfa756d4f2809c3a61b2f5500 8f56bacf7bf0e797d7a1557543654fd929e4890ee2151d5a2429f470c83be4b4 0abea40a9b0db65d7bb0b366e516783f1bc6408cd963a2180d733cae6ad916a1 b916442edcc69f78431e6d682a88a0c71ebd5d2be609562279d72c3ede4cff22 ccd3361fd95912f80e376953e5bfc2b141eb25d8577cfd39b7664f45df0cb219 eff17efe89f6bfe42688d7c6024eeee76f697f2740b9c4de12dffc4b214fd5d0 3ee0b3c4ecd3793fea1b8b6f80ff0f8114e6e8639fe83171c1677725183ceb22 3b4e3637d31be5c587b568d9a07e3db473868dc27bb9248c1efd58a71dd7ff5d ea528ad75ae9bf2df90a0da470eaebe79d5818c59eb5deeee16ae0d8368ab8b5 6eb56b5851ed730f6b8a8c1055542ceeb9ac4eddb6cb896451d69b263c709b7f 7b6e490c331b609102110265ce0a2c76e11dbfd4a393679fcfedbc5b092cd865 1c44c9e52b273b3fde2294905f04b6b51fa19bc2af9be31235f44009cda89058 fe260dd4a7d05c4b14ad31f9fdd31930958927d7b9abde7f1d78830c233c8be5 ae6b777c5e2bd0389157d4234ea3ef4673317577682a2996781c75f7999c1449 062d759e560d64e41d01d3c7e43ff5ca76527668e3907ebdb31427d54c7d204e f7e7ca53a753bf4be41b5a55a37c07937d502cb2123013f1c67532e5fa7fde5e 667dc7150702de5f44ad72360f330cae1aa9ffcc2e5baa5d004807f578ba3077 adf1739f63a38a4939eb246c14423d347f50c5e0b7b8cfe9d83ff4debf1c146f 4d696bd6c4bfb0755fb77ea3104c3d2dcc349399738140bd1789de6f6ca7cbd6 2027557a24e8a34bbcc93726439429dcdef2491eb85af770adce7a6ed3221b40 d80dbf4cbba468805609de760cf4619a13cb067d73a7a6f29cb01fc908987f6b b7a398a5a0a21aaf0307c08ccaafeca15106dec1e4b7e8f2047fb93ef01e5b1d 6121593f0f997fc1cf788c8c23e5860ed345339f9615bc90e3f59cbe073835d9 2564f580e4f0eab56d3fdfcff49bafb6a34bf2901cdd9376b071ced33256fa0d 37f9ec1d847e20b98f59e92d6222c4048ea70819c961aced911483f8db6335f1 ae9e47fa4c7d6654b19b8328ce5a7666c9bc4f2cb5fbd67b5194fe1702a98c83 fd70b7aebb6d1591a3cd98a05d430738540f88140269316cd9fec8a16971b1a2 ab16336d0b24386d13dec17a6f7a6431855d46ecb4c68479e63893e5bcae7a32 97343a72572ed013c830afc58f064eb722afdd908d816deb623cfce9ab9e81df 1a6cb62de22f7fbd51e7d2cef9ff19c720b56db124d89238cb80bb399d887c9c ba51b73e9b3e799ebff8c7cacb6e2c9b958c376c1c12edf6d6dfe71171400ef1 265435479f7b6f55075d4184cd690d7121e54c009ef6390e3bade75aa26ff3aa 4cfbf4a96e31017f67244588ea8f42c899d043a82ef6f5a074c6c45eac431146 da014511aad404d58a70b49a4b7ee0d8506d84678f01823c372a64f22d118258 a6de326fb737f93cf9d582a843ebca5636e492c2ffbd9e76641fcd677f87a507 9408c96c2bdebddb1d04a2124faf390c686c7e9bb59b63538aceb66328837d90 712a20005eb85b561c6a8d9f9d9e14ca370df52b426f63305371073330cb7cc2 fcdd85581ec5319b5aa96dd00a416e2efe85702e04b12e574dde477b6cd74df4 1c28d8bf68bc2c8c2fed6920d4435fe7573349a0864c2f9ed58d860a2ebeaec9 d79f4c7a344fe1fc271fce12fa96d468d02f508de6c754a9856ed8ff7b493e78 6ba66c5e0ba25d76bfcd1f6d6fe6673eb3b49006b8e4a07da15eb372fe22965d c7fe22a69c0c06aabe0a9ea00992cd4b5b8a50fd58dc1ce5cefc1847d5505238 18133fc9c425bedf73e1c4295907d5884ac1b386fc3398af2ddd7b3108043005 e7734384f0821561c202bbbfde7748be4a2bd2a8236817171e72f30354c34a5b 0737654fc4c1189dd70251628a87ffca9583853b1fb1391119f0ff47757306dd e6f48dc12158460afdf808811e7352127fdd9ea08522f25aa2c089952b88881c a8e853e67713fef3e4eeb897a11ed315424841d4ed677774976b54ed7bd187e2 36ca9762880b48355afdbbd5a3ccbd84fb0a769f83b88570afd7720f71bcfdad 517925460cf9c2480f9ea9ba8512335f85ac7cbb3976c89fb36cbacff323b2c0 0f75f6712c7a4e68785d7a6d3f75271ad1d6715a43db26dc02f8c0d612e0388d 23dbb5f98fb87775ff2817223fc42f8e6e6b2e7981bd24c95e94a0fc54be3dc8 54c49ec354346cb9f9082c3476b7cf32c0f76f58ff44a12bb1ced19c0ddff0fa 7e0b5f0c15c40aa6e60b70bd1ef397f77bae03d7fdb575698b6cddd57bd8f505 9aee453e285aa2c3a42ccfa549db1fffd4e5320545df860a6988fb2d7ec150b1 e2884464465108a889b99452c8d271b76462dfea838382ad7f49bbe4f06e0491 05ddc1312bfb9796e9a7e0fd1c276c626f2cc9a91682be3dc3068034e353c30f 064c34f4d74d3cce6487a472de009d920b2c70123ccffc07cce0f4522cc34d93 b119450082aaf03647a5223b95027478eef26aaa8fccc168c2163bee31d1b748 ef99dccd3a2cd8d1de969123f45fe63ced7cabb51d2ab998923ea504f74d4698 c927122084e15e50f3705f9a6f57e5a6f0546766f9c56532558bb9d7a3a52904 64d7f9f68fb5f2517a86f300f0abecf40b1ebbeef74659cff3084400c5a0f6f2 18ed59e9a3fa093d0590bcee50a5f2686224bae984a1414ee2ad92f597d2c53f 8a122a9deedfa92b03b24276842ced4f6320123460989cdbce308852fc78189d c8df22a49d4a86f0d488e01f73a0a89ac041a9b58265357b3793c7d864f9f19c 4774ae6955bd5461a2ab48eeea924ffcbbf26fc4f70fa33b276974782e8cb02b 61cb14654d0851585a5d52380b058b1b41f2444745d165d8bf5342e20c127d39 d35435479f7b6f5e4920033e4bb921caefff68e5f46caee197dbd054f7550342 9db43d2097e7c29363009630c366fa807b6989d6a9c6c858322d5f2a992018b9 f32d819348f82663b3e23ef857b7da1658be37ac644ccb689d46691312ae516d 04fe1c40a88d989551ae4cbbc603520432f1b7252f15e6594bbd00d586b95fc2 f25cba2f27aec6df34b475dbc5969f1553fddf3919ec305acf01a8f35c46162d 36f5265fc7793af99711f3b4f80817c3e169ca5326560deb94d07c14a13962d3 06bca8820ae5f9f0f152ee7e70a186d413b9061eebe81a8e40bf67acd8b7847d f308f3df2d757e65103fbb11753486e5fc890ce15f028682db24bf49f088edd2 a8197940af4ddf08ae89cc219348bb4efe321162d0ac0eb457d0e86e096b276b 46a3aa3260619ba4d28e5b7e21f714d253adee82ba6e0c16008efa22b12c347c f67f6fc7eb1d6398bcadf39fafef306a555cb8140c79dcc137e42ea7a397007b bcf3664dd606162b577a08547640004c47b6af1da4b66c2b79c5f442f58214e3 0e1c9b7dec7fb978a5ffa4e48b1bfad0a56f2bdbef07a42c05035ba496b3d229 c70a93bd017199c88b1da90c81ca2401c4c543db7c2c694c99dfcf8e3597c37a c9541ba938988f61b4e75eb4becb47b09375234ea19d48778724a312e391a269 b4cf9dc60a54752fe225d41d2b0a6b79513fa74f6504bc34272c5afeb7b94ae5 8250f410a42a0c158c0bcd0aed893bd512b8817bcc231108b1ce00f9678b249d b060db7e1af877d2dba50d72f912033c1f8d294863aee1093a8f4b7eb33147d1 426088dbb1066bb18cf71c2c283190ef4a3f96001c971499c7c9b471a1d09451 c81770ae46cc86fc533018877b6fa096dccd61c7a9bdd22f3a99270be9f4be3f 04f4bc6ebb920aae481f6f9b319ae560aaa8217016e611e38d4beb6a753b93f4 c0850f320881859624c2a32dfae1faf0d925a31f94b1f6a58c9fdfb072e690af 9ae57f6b2388e9b27cc483060ec1c6c6ddffc0c05d29b37eb082ff8d0a7c7865 dcc710e1d240691a08c75b4ebfccde515e415a825d869d425128a21a7ecfa723 862bee817884970ab6c3f87b879d0a63d3dc7e0dfac30f75a5f45dbeebfcaff9 925cdf24bfb89ad79ef4cdf5b62924a871f26145f1c3893e0db64a9f29cdf9d1 026b3c001f4479967b458f32e8e91a2467c3a06e260d69147215b2d2889851eb f661da8492c578f7ce10fe8771dd5a4af8c024365c21365c5b1237cbd49d6e12 73d2ad02cd518dc1db99e1ea5b596b91daaaff21198c707142f10b44693b288b 143b3bf718f9f2c52779bb03a678a038fea140145d34b1ee6154ba26030157a3 1139ef97a2a869f572c4f563fae800e61b00931bfb753ca703c435247af71661 1a22980206950c26552f15c79b4e858b3a3b0105fa179cc32ffd9a9c050ec6ba f96318ab57b9c78a1bb4321cb25361503b588969ab755c4a554c2b5f081fcefb f14cd74501da751b3e5c4629d48f533ef78343ab22afaef200d25c4a9a9f7bea e51ddfe9b5d6441b88e49591b47a900542539633c14466584f8dcfdd24dd8720 9c6195358e56ba6051a708f78a813add026b8f738e23efbf77b2ddeecfccdd9d 017b97e8a211aeb6160d4c03b0c27e9b555ccdfed1872bf14af3cf78465d6bed f14feb5030f2ac5ea7d88e2aa9e1a048db065aba2303613d029a8f0feacc743d b97aecb50678e3a1861421ba04476feb3b582d220580a22b325410ce970be791 330a9a9182f700293bc6d838a87df065373e8a7dbb6effd242dbb64823aaa81e 685df12b25cdc3d2f60ac7574515cd5defffefb2fd6ca9bc728628246817f5f3 ac9181a6ce6240e838a06c814804d81c66de680e2ae520c637c386cb8b8342b4 991180bf686d5a0abb9e73263fcac44a21d2cd2c4d27868e48fe5bb935eaaa00 17859e6adc7b29e92f2b3671674550d8fd7690a6692591d59ffb9aa75749bb69 713ef062ae9728db2489e0627d747aa6dfad789f09c0f24cf1f96bbee17d5d67 ac52b5abf14ca5fed37d10a6c3f655c04339efe8b63bf3339395b531fc7f3409 ce3136bd0bf7f6f0705a518f2b880828dd600f705b97adddcca1f6a11b215c0c 7041aaa3bc8a01c9bb92420fb7c044c8e955b5c5d4e23b92b82e4e1a323d7d00 2d977ea21f4e9de648b60944787938470281e241074bbc0b2f8b7f22b7f38c46 02882468ceb1ae737cdfe161f5313df36565927bd97d82a64ee83024f8955ccc a30fa26323c3997d75a6185cee152410624faa4b9ebb2a3fb93afb23168bec5d a1780fdf8d8b6c008ba801ac829990eae699c71e7f94341fb7ea665151c81efe bfc816e16ec451b3db1cba9ddad9e6b2e53300a04d26dd85332f56ce53ca1ae4 3bf70495ea26e4bc07047300771f78c42d11579dc96c0348c0361f9410c13c1a 6b4451ec60050834c491ea2c31a61d1cf38bdfd89437d025c950d9f7fa8ac07c 1fdc5d58f4f22db8f23ba8e8e3f8531553666a97b5269c3c91f9e98910884c8b b5a7bbe81fa3914d1b7eced1f46c6477d236f586f8e0bf7282a9608137541ced daa7a677fe86fbbd4c8678422b92756249e524b24589d0a457be48ab68500700 aa77fc2439b96184074243e0f86b9ec45692a9b1263b88989af6d6d46f240335 323bb20a2b268ea114b2da8480dc36f1155bd7fd78e15741c3ed35aa47d52312 db7cc3e1e4e488d8ee7b94f1cd7e32de9c85ca4ef7ca59480fb7f386ec98ac7c 046c8e24ea0684442100fa9b7d531ff08b5c922a62ad40a19035919e75839669 bcb68f6f26741dc8cef19cd84e09ae8a1b0fb2854a9de70690c61de26e3e3348 808b1338fa4731b4e4a489cabbb698832d39b621f89f8a744332edb7365d5606 1aecc39e07bebd5e232023fed2e07fa66db25468089fae614e8a9af9f8157d59 332131db69a992f0c1d8bb9f03ce1196e99812a81c1b4dfe781f658765acb3f3 073477e195d7b73e6b9601ef015eb793a8e6aee7374d6f98ab3936e024ebadb0 a3f51ca27a32d037fd80098247dc90b390610a2b17fe4b6fc7f439e84101f2f9 d0e3476fd4ad0d2e57a1d93a6f8ce1f586dfbe4a6fd448b0e2c2dfd54b642e26 c6325a63e39b2018224518bc855516fc87b00544bd87697c32e3a010ec11df21 d5f61b150371105bc26368f3dd049aa19cb1478a091d99cef35f053e015c4fa6 56f4efd9fd13c6128ff1d3b06a95c7a3e7ccbca8ffb3b87804c7ee6f91f0fa88 bcc45441942b42ecea637568e4341011f1521e75f5a77375badc4b2fa4076e54 2f5cccf0b7271f39714f0c8fdf70c9e34f813407f590bfcc21e5e44646152375 51bcc44f4586edbf4afa66223b57f54ff1b0e173bc17794d945324bf40244a5f 47126ce9fe716f57b95f7a4d0b03d2592e8cff76272eebf78ea2d67c5ab94e9e f87fd4dfed14b1d9d17978c305b9913a87a80224b65b414649dde70922abb6df e81a0405be57c474522e9092c323adb7b1488b74a42f6ca118984980f25f637a b72fdf031fd01b4c08ee6379e3d5bff18468358681933b47f1ac44fa5335d789 742d0727b3c0c3f75021be12724131fdced88985bd23d3ea4051df8f53fb7511 cdbf804bebe2c051a8d56630e56a239b38fe43d82aff7cab0b0a4bda28037fa8 796835af3ed3bccf433f11a0ff8f8a2b2241ca0224872743612674360acd7e45 5c888a5b150dfbfafc036f8b05f39085ed3bdbb0b9da7c7d5ac850a5650897b1 bfc3e6626018e106def28bb1d77e314a63528217549feafd3fdb3191807616ba 0a4427ff108e38e2e389a9356c60d9d4a07233ce678b3690f23c69b47a86d23b 60ee88f95b09d02f26dc52a24f91031c47b65e4c7c83322e181625704be4e25b 0e5a2eb14da49396eed3c1ef0318aaf4a860cd019cd0388f345ea502fcc43d3d 17591f711865e0d1e9074e7578869f6c887d4915fda876a88158274f7d6ed06a 5c6c5cf7f32757d03238940d9648162ec39fb8c3a108567e5402c0b31cfeae13 268ca43021ec2a377b843a5d62e21f6958a92d5b8efd366a352e9d0cc7d1349c 191268ddfd3d20ac3e66a5775f3f871df35be5ea95781844930a676b2668e166 333530356ffb80bf92620982a944cdf54ae1f3bfbde9d37badeba38d0248aa15 78f4a686c53899dada3a977b1df69bb221fd47e0fc6b8e530a3e0178faa8ed28 648b7c63504b32020fdaedf7816b737a3811b221d8eabb8a5d0112be19fb2950 6fce66d642f4cf974ee9c3b5b749bf6e06e8ac18e122dcd1137346b43f0993ef 76886ecb4308ecad6e2aec0d81e14a6f24c2cd612a3489abf813596b76db3459 23e009dbc62f689fed981b50c31234c9ca706175ab2999a090d86951f6431d89 11b26d056878a216e60b04b9a8d9827e35cb9a744659e9c65360e1db45beae85 1c45d5a78ef096da66326e62ed3aa30348aa94fe2fa89fe805e5fd34585fad34 98da79ed7c7fd0346a3ef62f2a8707641876ee4a89c80ba8563b5ea31119e292 9b8fdc92bc49ff2dc80737592bec3a16f5970d6fc166d377f5d9afe2627da36f 5c5b627956557c3960fd065ec75870c537bbbabdb22ff5315f2a5f7c552c5b11 483907a7a955a8e76ff046f974f07907b8aeda4877b421f847b2b85ecb56bb91 1b6d0b4a8cd01c758187b611b42a52da11b60dcdb8c41fb9f54e025bc6d1e2b9 f380d3d42e5ecc89010c6e12b877e06ce7f3943ca78e3c65fbf09f49e08ebe92 eeafba14a25f86bfa258fafaee707e4eaa477322bbe990fedbaacf78607e87f1 c4c30f66447ac8093b1c98729b6bfef3724889cddef47b05bb58acf91022ceba b81409d651cad0a5e93c0c27bdd176808c1697cbf58bf5b4aace23696fe5af34 73439ba1175e7f2c4918179190c29c12bfeda5228de6c4dda9df668abcc9dcff 39ee5b75844bdb3b9f9b9349168015df44e8afdfb08b2f98483e446246392d6f e1b83cfd5d72478eab5590c06c4163c435af3947a8d81fbcecb031a4ec3a882b c48b977673b7e1a9191e4941eb15afe41d0066050a66fc34f8cd2f8d11eccc51 8ba5823c9c1bd10ff4599a72cece548e8a6ca8059284358f003573109c712b59 818dfb83f6777839974be456dea184200d154c2f2ca3ab7797ab145b6deb90c5 2cb53c7d85e37aaa09e8ca673273bef93fd6de1069a6d4afd5aad87d8979c648 99a7b1f3f93a3230b605f82dd6a73aad953c9c9d42ee48ff65e6b9d5b730907f 80b192d8ac312543a6754589b16dd619ec8e15daade2c546c88a7a7600819a1e 4dd4d012cba17285374f28811cf1f1c19d6857acd7d4536d1015b1a6c12daf20 fd5d89ef778a524accf523664c0e4b3907e7922dc9be44bf8dc49c4471e95b78 035b0b608dcc4c0b0e83a7965f9825f4925f3fc0667441145b81996e3d4235d7 80e83c58fdb8ee88d78befcb205fb35814813ab0410cb11254226b07a4099e88 74fd68c4a0c72625b2992d5bb99dae564ba9fa28f55500cb12f7010000c5be19 a1b91bf416e44609dd31daa7f6d7ab325d9b04e8f5c5f5588b656e6ba88a78ea 7e5ca710d20e00163415de3805203060da621bc29354c8088e473135b84395a5 8c7f39be2e930599d9fb4f34587d71aafef22c2254798e33989590e4dad7f9d7 0d93ae3baf122a5085aeed3b72981346a3fa435fef90d435c8c99764a34477ad d01059a7fbd20a2d22565b1a2fb3a9a744c82483192d79291d3dccedc21b1c25 f3b809eafc657d84b0cb42acd0d00e1b150d158ed0e238ad67dc9a8e63ed2440 c549617d0c56ae76ee362dacd23b80eab7aa84b72ad60983b4caaf08bbe217fc a85b52e410e7f1ccd3c04cbad4e86a246536cc46c31a3f7942ed05284a2bf62d 469622400645bf9eca0a2edd0221b09f2b72610a076c356e79dfc3c99ee8372e d26860599f624c14d4ab08211d80307d65b90261df563a127784c5ebcdcdfbe6 e0375c88a3c8a9bee9e6b63a62e15119f3437dcdf604b046d17b13ebceccf8e4 2f3c22484af73376dd7027af768d9bfe235107047d8eec07b9734fe83c0537b9 bb1ccc73bb38d97a121817a35e0cfabe567c3801ae0dbe7aa617e06a838ab4d0 9b1b629b3e15dd717979f4bb85ccde16229b136aafdb4e6486e6ed2a4a0b8ba6 63624479d929975e040ddedc015bbce4bf43df536c8c591d01596757b17ec32b 2f51f3ec30de8f990285491e3a5aa3f934fc6f5513c23db26e34efd742416fde 563a1ccd7e4478c936d32813f896f839c755c141f8e901d6a10203b6072579c0 8d4f7b31dc1e0468b99d002abe703b1515653acf1b743fed77df59ee1f440035 ae841a489d112eb9101c7a1d27fbbc40064d0b7f9e7dc42575c1d2d7dc70ac5f f17cdf4a7f03196179b2b098cdff8e32e2bbc1faa80185046f709ef93b6aa11f 6e645154bae4fdd71b7c599ac385bbf49ae65cc4cd2e8e77c241bcf0ba1ba981 c9b4c5e2de5b306bc311fc377ee65ce4cadb0c3ca01a724e428955e894846622 f8b1ef41cbf81d970eca85f21540a585896ca6472314424278fa5c237a71ddde 865d2a36928817cf78a038d04b9b2d644940f06fd28a8e11d71adb9e44c9c667 8296d2abc57b3386466f1b9855da61bc0f23d358b6746492258e8d3601ef4a0b 8ea72e54bd9cbc5baedbb78a67101c1950f6d5c417ecdf6e164a238506937f5c d606dd99cdb73fe78795af3941ef36f2c696da6f34cceba2ed60cc3fe40cc0f2 32acc14941eb1350e92f8eecb7f273075dd6a123f42a5bb9e84b213f91d7381f b5cfa0c481103031ae5656ea896c1ba151895ce1bf9de06cf913b51a9c2443e1 719593cc23626e234bbbda2b3b28ab40f553bb0a418ad69f7a436b0116a417c3 118d01a2a93ac9a63c63a8db4ac8966eb0f8e50f86764ac269a7fcbd8a6b4df4 f87c4eaf9e49839d71976bcf42e80e4fdaf53e1d5d03aeb97c7a2586a71e6320 858df85a72abe8756917538188f3428be34bdb2e30a75e57ffbd925b5131f379 76f380ee53d4b00cb2e16de24e86f48e626853e1fdc0fd8890e9be783f39d077 f459c7ac8c92d5b88be98be1b94f20daa2d19cb5f6a592fbe1cf6c0c26d298ec dafd46c2b74941a0cca3a991c650c88d7b396f97db73cb2239249b002d56a3af a15abe79b468f85e57c138a04da015d171aa09176a6faf31655c1b839e3816f5 6a9d3fa0fa6265b136dd2612135939a53141ef0b5c1130c642fab5e2e3bd8bca 7b8d0fac1803769ef8fba6fdf236466edf0d65d817d2a480c319c26ff2b65ec5 4ea07d67d9d8692a8c70566aeef7706c246ccce385b89b3228755b0b20c44e94 ca70910cdf9a8af0bed4e102f1609cfe6be80fc8fed3844a22b35da6df75181c 016629fab4e57afaa9413b1451ff96e95afdcad26e58057025a3e7fe335ef79f f2a32c136cf48f72404c7172084ec2ebc56a84f65b9820df9f5dd149ae3c766a 06a10bffdd1f85c714e093542eb1f26610722f66f1dbd30a048dfa4c1cd5f8b6 3946351c161e60ecbd35d2dd64612c404a4b80767c1f5e4143c55da5f614410f cab8ba8ee0695ccf72ad57b7bced810f5388afb138c82c0d6126ebbc7521565e f0781528c9dbb2ed4fe6e186c0b83331178f14bb89ed7c43089924a7fc6efb4d d4a4830ddbb589672dda3021dbebf905e2c0b29bb1649c4d2305522975c77292 1c30622b0e4d982e72cf1979d83f3ca55c8347b6f1290ed2cf57b175d64fb734 76462cb45464fc95daa2959e84b5ad6accb7278979d8c5a093119beae6e40046 efc4ab6c026b3e5c9d2956c054218ca5221b1b728633c6ecb17e8c1a8e1f9996 55ca42c82e1ea682c299b3be03dab4d0636e6ea61ec3dfb3b9c70fb157586de6 beaba6d1c942f40032443157d1a6f0eef20f7033dffd9acc147d92b1a33acec4 27eece77cff3c97eeb776c3f964c0283cdec620f6b26133e30a7f8d257ede90e 597fe824c7113b0ac5aa88f27001aa3942328ad1853ff6546a5172bee6982495 2563a6fa985c960d27b207f9ffabe2933f2347dba1874f2dc89d54f99c28aaab e75225d8fe5146a02b6ec9f27ac99d7ba0a500904cef9ff7af32e55ee2808fab 6800276e0b889288fdf8ccebf48bf74860a2a3a462bc4c4b4ea08ad64618bb33 b842151aa93c416d94bedbc25635e8e21bd48317fd43a6b60f68d9dee597a170 265c97b7950883c54ea8c5e5fdc8b9661584d86366ddaaffaf783278b64f9363 356d3ec5f80d1e0d4886fd9be564a9ba60798f014d4ff3ab0564b52f7827db92 e09f0aa59d85aad4c7ec9c7bcaf720409de7a2473bcfaa2e11bda74047dc471b e30fd376f03865ae9c94c678325ab823bd2218e8482b7862b62bb2b4b1c929db a7806844116ed674ae984d106039f76e3c1686c672a0be76e9ccc1af92ea7311 05070d67e9e63c7302d8408fc61a8a4c360106e4e76a0197e00cab3831d477a1 85a243e377804bc3f71bb65f3ae478b536df3ea140a4a106382ac3ee5c813bcc ababf40ca8459e83bafb79948b956cc652d45ad844f8451c2be1cf21d5cdcde9 dedaa0d6b8cd1ca7bcb842ee2f0391318d2657bd855537fb418aef68db7db90d 9724e53ad51ccd206ecbcec14d32be0e4a588e1447f81385a4aa760f5897045a 50ab01212146eca1840d6e9b7c47a5cefb0485c534da80990f51076d3f473ed6 45217d5e5f371b53bdf06c3b630d293a69d5e49a839c88bf4ef4128c726551a0 97cbd0ee4a4abe3c69d8dfd5c609048c0aa4f1c1a202c4fef76db66472359ad9 11a997033b5e605ec6ceac766ebbb12702b7c0fe8a5b1db2140d9bbc32ab276f 703cf09bc0be982a7aed7ed9aed22a36d6e1bc89c39263abecd636b6c3cbbb30 07dc69501efe0eb53c4077bff3efbbfd262b58c3bad93ca4b40f1a5efe7e7c83 d176300e4fa7e6252ab93e5a15fd6a8c60dfb95e19dcff8bf0303daaa969c442 fbad48f1b231334360f3b2739f9c220f557119f684481d2b094f6287081386ff e113a8a252a9f61c8ba0cba2be9cf1f8973bc6c9b86ad526ffc52a43d8c335f5 fe3f2bb80dbd57590d872b57779a87a8836d6902a61ee5d43fab59024fbfbefa c6e62768d5831a3cc68f37d5cc19a409c93f126eecb51f8ce7812b238084ec4a f35f878b2dc3c00711e6425d1662dcd479f7b2c62a689fd58a1690921d523036 9ccf0585a9614a2b2935c1314ddeedcdbaca9f9f241bac53d3dea5302bc90fe7 45f1c4ed10128677a62a1d2c021e38aba2466418f1f636ecb41d296fc5f490d8 fa2b901c6db1fe0a9e69ea5382775f0d05ce31f4ab2981ce83a226d1efdd72cf 12ab15e236abed281f9ff1e52fb164ed1a2b5b7a31c06d1b10f32fdb555bce89 ac0a7f5902eb33ed552cf65085e791f4231c273906b64e92ac78b6b31bb6da7b c4dc4614edf540281c49f9a6f2f99625d6a10c3e105accaf0896eaa6c3c35503 7081ddd2e18c682df0437bacf8afe90bc6aa3428bff12ea594c18e7af19adc60 60b6a5fa441e082ee0dc30bb3adf87e4722981749dd51fc752cc485fa513cdc0 1083d7ecc93f8a8d6b7707bca616281433ff81360a8d8216722f0b2d0217abed 9e11cb8906e87300eddc929cfe10a6282cf5b6125b9abe55cfd28d8e6e3b0ead cb6a6f3246938dcaf828ee06b3d765712d68d87e2d0abfb0a5ed2241f5c25be4 96f0ec4a7ed58aaf1bda42ff4278ba6953aa99bde847ba0f1988a5754162f8c1 568bf3bdcc439d1d1d0db3c3be5659c5e49e1d09fc95ce6b4e0dc93cc1b52bcc 91b4f203a9a0ef84f5f3f0e6f3744c1abf29800e8c909586b57120a9068bbbc5 0753aa9c752441ba7d6ee2b177ff4cce5d9a542d5381f0df985e28047ce5cc4e c654585658dff11e6c473508e721e0404c438d6ea68922eb0aaf4eb6b3649551 9b1ac194c7b1d23d7a666df87381816b233c06d57e6d3f80f957d7ee4de217c1 bb9d69e82e02ab56f6f3e983f69501c633ef9f307a9494ef688f63d6bcc74284 b4b7476b3f627e80f00c99998f8275d94f9c6ade443f75406f3e1d0cba4f0fca 1da5a0529eceb35be6e67921c133fb526e8caec3445740a0434e7135e94ac090 7b297f9d8c3e71e38db1cd9365b5d3480dda22c218c5ded0099a5aaa298c710d 8dd8329c2fd4b967739929b2598ec1e4d15fccb8289589d35cf6bfda8b79355f 7ccb939b75b24c024fd22342c88cad64ac18e2ef8f365ca6e6eec9eae7e4d8ce 3242e73d8fc65bc5ba5efd8eaaf3747f547c5d407d6e2c95b86c12c5fbabc09e 9d0c83a2e17fdd5acd4a695299b731fd0ed06f4620f866afab7b215b890d71c2 9112c2b9b48402a883fdefeede879a453c7595aa2080b9523278419ef43bfa7e a8bbc755c501c6850fa525e030942610d9504f39e5660239c39f2f3e416ac7ce e935b3e3f2bb6f72e9729769b3d1981387a78c6c0d04b65c41ec679d39d7c62c 394a5f04e819def62ddcdf01d6b5d1a83afb5443f3237441d2bc9271fa481300 dbfa2b2928ba2b5adc7f92e05e3aad0dba681a3a7294ba4fe389a4a208a854af 6d718435b34352cd35da36ab47f9ca1b664809056bc79eab88df0f46808a174a 4c220e844c4e28493445b11000b8302ccac90e8621d073840515b126427c630c 35c185a1504e893de20153f4c96244d1bc87ec383b1a0f3469caa6440473c134 fd7bb0e95b877269ca9893c050ba5afff02ff49934dc0ed7526d8605b5878d01 267b010ee929 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % 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 (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 6 /Sigma put dup 18 /grave put dup 44 /comma put dup 48 /zero put dup 50 /two put dup 53 /five put dup 67 /C put dup 83 /S put dup 86 /V put dup 89 /Y put dup 98 /b put dup 100 /d put dup 101 /e 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 114 /r put dup 115 /s put dup 116 /t put dup 118 /v put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueXX 5000794 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204a520640fd7c4d05e35ea5486f a43d0e970787203855daccb1ed0b16325828b13b7c767a1a58c87902f0546ea5 404440fa6526975783c2d7a9572b8e5d5176bac598b8960609f49016aebf3763 89c1adfe6a1ffc0c53b3acd9d168ec3a278fd4f1d9b085dc2df701346c9d0887 3d230a161692b42a45bb5da343b4edd839dd60685a59aaa49fc65cd8e2ad2a9c 5cab953495172a1a9f40d5f38e922443a519dd96f667201a408bd1d89e35f4ab 98e2f68c3366efc14b5afe1018d9c845d808d4f8e07ea8168518a171ab4d6e21 70eeac099eb7ef46eb9781384da1fac3b3133bb718bc80082eaea88759745188 f266b31d0c7e791d633f16ed94e05517a32163e74cbd96dc5db066f2a5313d6d 7f09465608cb404613e0f058073af000e5bdfafbbf9da0c0d5c02a3447f2cdc1 f56481901e34265c26d331ac3f85bdcbc7c51ef9eddf2b9c189c5253f8e74282 d6f053d7d183ae17ea175e5ebc401e67d21a9fea139cbbf3bb1358c713a75843 b39a69aa2b1a7b975f53ff22d1dc3bdf7acd17afa1da21568310c68241b31d3d 03bf404bd30baf9cc19c75b958bce7155f03cb0cfe2cae0327aad4b603284a51 7c26de75b8c6f6aaa9debe4aec08ca4b646d787a9dfac85b2c01760e9c6c6162 fbbc67dbd0796831e00c477d8e23c375ffab46d289be9d2328aec2b7534ae4cd d782ec2453e7787f6e6b4537b46c01545cba6f90b8e9a1bccac1937bceeaa5e7 8e9f368ce067a0a31da98bfbb545be555a7270f0031fadd4f9b186629e5d2c5f d264f8f24cd5a1c0f68399ff4b29fd77c4a54d8296523413c84c88bd031f936c 3fea43f7789c3b850653f1339d10e8c8eac9706083a90194dcabf30a07151476 29270656a4bc54ed37fc584db183319ed5151b825c302f1fc76e2abf40219e12 6a62e12530b262a231051cf17b7c694d464ee8613be9cc7d51ea93d29f807f00 adbd5a924fd6cbef02751ce876a0a47d9b668c9bef15c8deab1143947c6aaed2 3b25186b8294fdf252485865bfee0427fa2cc3680cdd9fb1a05212dc75c488fc caf2cc7ee50274dfc4d2806993bdf077c99b655bc759b135be8727d8af16fb5e 8a9484d678df9fd0546b45b2c32f8c88b70195b990dc63b947d16ecbd209f507 3d3e64c7ebd29c4a1bb95c725e3c9f5c610cbbb07308bd5885f7b1fadb6eb5b3 ba3916e492dc2c3ef8876c12fcd0da3c2f2273be75c5c21755ea19732cee5d0a 9e6bd5f263e3f1c5b7c38dcfe87bed91cb9f6ba7c7a6a979043136583f267080 cef9bc86a073affb9597b0a15eb0e459ef90833645189bd8c89b97f59ea50703 6c5c86a9dd18e5101d9556a863e7baea8719f065fa9e28c775724d33af0b72d4 e982412c8585791d9bafc9bf36882f4c23f8c21190c3eb42cf9cd7794218e3b5 1734fde0aa90e2bf009bc61e27351525dc8604f119537624cbf772bf8d03a6ed 8d1a032d352bd58d60bf4c410e709d495f7d9ce4ec5d61b21bf8e21506a60927 46a7286811e01cb16f1dc6956339f7d6744450c824e4964a3df4c3928e7ce372 601b0e366b5ebc340255adc877bae8bffd12af8f6e9d00fd52f2d3636bd68a7c f4f9ca6352ad2e7e24fec2e196f9a1f20e70922334fb7e6b1866e5dc833f58ce 559b997d48f72d632744b437b58a4e58d090c2a702af93df5b5d9cf793abc7cd 28c3404807dda3653b7a4cf451773c22ef8d7c2fd06d9a63e275a07cae38ad44 b7acd61de70dec6acde0d043a35afcc1b0d112d60a718fecdb3a7f8f635d7c75 6c290d50a6c18824ed2efcbc564fa94eb439a744776cdeb21f647d80695351fd 666596b848aacea2dae59f7dee45c4a3827c88c50ea3972a40847d941b56f95f 2d5e3840f5ebaef64d059cb8fd63f029c908c288bfaa328b7327566aeff467df 0219d292da6d433a68456e88b77503308ff729fe19fffe74b1af224c498f72ee d984d70d44910da05d2f497bc5d5006db3371febcfff1ea6eec594c1bc527e6f 692d524ff20fbcc69a75ba0ca372acd37efb25e8ca93dd0dfea3b439075ee7cc 731e8941fcf0ab5c90908a650ff1d9a6433b630029d5faa2244d9c5270bb53c3 bd86a630bff2d279bd4308af06b1238d09fd6f06b7d00364f6a256b5de7c518f 23c5713bcf340f9e4b8eeb8860062ee8684b1cd8e2947a63fca6d2c98cbc6a4c 36eb96403a93b245cdd70aedb935d5a4656e567b437a6389970165ef1b90c50e c7430770f0ec96aca0c8934bc311145830dabccbff241957cf9a6d2781f55876 b0fe28ec05a5debfc7bf4133e2102fc735824b162406b20355a6d759fc8ca16f 8842bdb77a5ee0bfbf910ff03e24c079f3191f7a942497bbe293f10a3f2f701f e43b67aa105b55a32414806ceb8eb83f660f20ce4f8ea902c481043d676299a0 efe31a3689a05919d01147751b8585133c91f789b50e61acff04b76ec56c3636 84b485fcf8743dc9dcd49fa55b62cbe1126e5ec21b99c429db96e978a415ee9e dc281a7ef69bbb28b8efe80520d1272d9fcce1471d42e63099f940bcfde887d6 40b0dff4a3ee3db2b43ea3ef411ee00f9c8a96971d88e838a638d425f3f9ad77 e92667e71c6c838d99b6f3855d0a54303087f46fbe665d54afc353d507ede54d 26a0a7cdf0613987ec9a4fc035caa5a1b76e1dc7b0bb7b3c8ed7434696e52976 010cadc2f3187489d0ab2a61272374fa33c1b969c61c3ffe4299622c5944d4d3 2e7377caeb0401c470088539769837eb9bfb702d1c6e992f530ffbc73136b54a a3e92f1db47ea68ead542598726a9c52ef6d43afa49e2246f1ececebb6e7442b f4703e5d1402925a4202fe57e5bea994b8cda99f2f22d270da059926dc70c2c0 88409483399f9c349100888f659f392ac6fd95f71b3b07ff96e5b6604de1329e b33f2a332fb7c80aa7d786ec56837677984227a7dc2e2b20e5fa7ae609997352 bfd02fd62fd99ee8e857d29da30f255f45060625c5b4fe0c49b468291388d427 508b9e47714440ab5647ad9f7dd09dd6ae3a6bfa5084b8636299c0beca368287 663a47c818ee9c48da371b39f4cb632f70a10b8db1af7a4dfc299165e81772e7 881e43e7efb5cbea80bdc5daaa5d88eb83953b0d6ba17b6029ee889ff564bc55 993e79575464b023729d9d8560e5ca2bdd26d85b622e39629713ebc42f073a47 2f62f1b9894b921b7697bb1172359f811ca9ef7bc9acc9b1212b8e204ad86a02 68915a44178abce8a854aa427c9bb9ba927bae55148f15619de1168c8930304b 5a92df97442809079cf9d0d4d672f8039fc5f06ae066989178a1bb726b4312e8 c50501460a9f40fc3b638c608b6d1fa25c3ffcfca333818413818d12078aeae6 a10b91f637c169a03c42e247b6998f1a73c247c1a63e762bbec4d3f3916dbf1e 7eba2dbd7d88f969bfecac283431b2d2bb40fb998d7d4fad99364aeff8eaea9e 1e949d6a11c14805f5e9a753cdf8a5ec0c1c3eb5db7f6968ec1ecb3302c3a617 7059a6e9a74f0b89c9d2dd213b60c077f7b314fd58109c63d824a1d07db69e3d 51a301d18c2fc082c15004d6f59f1aeaaa61d5e8589333360e33d43ccafb9168 0b56c0ed9b333a15fbc999cae77960790e5067a60d8cfcf0baf6daab7955ba28 ed2a89983f4adedebfa3b905a55153fe1e96b3b304b80e441b798a09c11d19eb db87ddd470b496564abe3c6c43654c20101e2dde38c731aab8ac98f17a381cfd ae0162ca31a311b3565d45baff05206b29f7c1fd6abc689ac30c16fcf055b0a2 ab6d0bb4d8014e23112ebf9b2c0ca093cc39f21e19de9454ba89243dcd95dc27 94f6184ecad79edb6b09389616ac7be7bcbe7a95ea4d88eb71320c34093adc8e a2578f06c6d2639a295b5c3f422df922ac8271112c4d537d710a6e2f77a9ec2b 2e700d18fdb849f0b78d25cdd3731eb9e23550e9247381ed0d705ae9c77817d6 8a3fde64d0ed42823bc6da9a553929edac4619a9a3e0b93c7fff493148ec5578 b7e83a7e1cf8d92cb41c9ee3558d301bc7b41d195b1603432708f36d183fe727 728caef4a5797f713a202288c00b6d06826cf42a2b75185a68d9e739785ffb76 bd26f2f5f73288f11898c60bcb4b39ab49163dcb725585fcae8c18d65c54c414 9ab64005b98dd3c0478eac407055ac58947faf3b1b0f32d67108f4ab58f640a2 bce378496d6a0fc311715179ca17a368d70b5bdddbacb2f0fbc338d4ee21bee2 ccca336c4a9ef36d21c085b0039662127550ad51a0eeb90189b93af603fd812d c4fecf71335678b50a545c859dc6c3fcbe69803754ead812621596a4c9c41438 0d8840db3f0b74dcab74a4d01f10c96a147add68b180bd7ccf0c6d4b8b30002a 2ff04a5440432686afac9da1d107f4be109d0574f6fc8f3dd076fdb48b35c932 e9b22ef8e50f32d04411cf4ef1136231f539cb05dc5d4334d62d41fed75c8b4b cec2d5619260ea217969a33c2db85f660e498332b4c35d8db1173bae368a336c 846a7bb718c05e7b2f331ce28ce2a610e88cd1bae1f6d853093da75b1d5b6b31 be03a3ab202cab4b763fdfe7fd04ba3f5bbb5766b3ded2657eca65f7e5bc816a c50d73d20804406bd2c288a916db434ba051f1699276ca27dcd544ce62300533 6c97fe6ac872244df2ffa7d402fc66cc30be5f00831f6ab5ca15352898812664 c3067bc59695d2c4379988e1a01590400acbde9da2526524fbb60f175b5d717f 22d10b9407c3b98a19055b83acf1375ba3a1533edaaf1b949cf7e6a6ef771d63 eebc4ff363d56d408c407966435ec6405cd7818e447a6c60c8785a066e247fe6 484dc34e0f05f3df75fcecb3b356f981e679b3d0d5958db5519365306b5753ca 0a7bdcb865f2a98705496ae7e792ad462ef0665fe32f3edddf626f49604914b4 402531dd0220e311212cd19ab0ec011850308ae9f552f9744a6af58bb119f68b 46f8a2283ac3b77fbed0d3a1905c86a50989a3c4de8c88973bc12be2acb86e96 1f6bc6ad6e00bf5e40f52633d7f01e963d2e0f00b566e505b86a8e777a48c4cf a97643b64a90607c46564744a8327aaeaff48d3fa90d5e381f5d64b52d0aa3ab 839c046d557652d0e32de4d0e82f2a18c40d55e61963ac89af93d79dcc634f1f 10f607509112dcea1962b57a342d887c6998cebe515c6e8043f8279a12eaac2c e50c43aedf7e9006000a4377582040ec9fc55fb43a0d1b4573f360ae028bd988 f4f8e14819637d815eb9b3bdc629bb0408a3e4a8e99d95051da4a4f7e64995ff e6c25df782ef0ec7a87eeb53f5984bdeb17446fcf98b1f8ec6fb40300a336b67 075a1cb30d1205fc4bc9b4e015f6412c06cd5aa15229555ea27294316fea5a1a 22fc38cf3badb976cba3179274168f2ed4d3e98fe9627558bb441168a17880bf 152a5a8433681674cfe3e97e1d793ae499307bf1c391ef2877b2995b04569e26 1a9ffce4f443429ef58d826cc95599770dbd01fe6c8945a937ae5e87930750ea aadf3e5814d2038fa5d6de26f19fe6ddab81a4f372b4e611b3189c5b099accbb e5fb015ca22db1efda0f135e9fc2c1e730f97eb38700774494dfcbba90391a24 6c494e69f25b68e41a4509543e54baa12dd2b056a7d1b48186d7f3a82882d204 56433f0db51254af4231e5c788b4cb3e6246a3c8b808e0422bfd3f8982d88824 5a206a66ae95da89956bf6365401665573d343649841c418ef979dee0de56ab3 0c6fc50b7c3142bee40c4d7832c3b7bb1854e7772f1ec48d49ac3aee8379249f 6035c1fca8a53af61a49165f813eb6c216d32d2e6ec6852e2b5559a166813bbf ad77763fa16c7c7292a594ce142c396d92230c138c546e592a0af599e4e84358 0236f59a080aadbe5e2ac257a6ab7acb85423e00df127bb70e2e527fe1d597a9 935ab9d341a9b2b0a374c301851d4924b4ccda49ea2b86ea8c2e0fdcb66ebacc b3d05a73e99abe65351c4ff50b842f723f347c3275c1b5f437baec17815e59e3 410521dd3da2b82e4713d78f 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 19 /acute put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 70 /F put dup 80 /P put dup 97 /a 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 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueXX 5000829 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacee583a5c939393e012707b47e0c1f a47d284a1edc9d01a497d772bca8c543388e6dc0d1e2c4944740470e0914f65e fb0737b0851b2ba713a9a00b36d07da6bcb52920b9b59efe587734027a3c5e65 66aad332fe6fbcced1417802822a3b81d6187875263d6bbda04bbcf6e4870fee ad60f104bb3c5a766610dd11aea64a6b107b0b04439fa2888b8cc39232bb83f7 695aba81f0260cd5248b9e649cd803271dc8bb1656323089e9e2bb50f2b95088 87d31dc36e555668d9578b338402f8c259f6813b0b71e6cbd95e19c20ced8495 2559e47577e612a4d94de3c1b4c6c41a6a3fa9e2313457242de74c7e4c0d722b 3e224d18baa726369542682e9459b951b2ac638494880c42be4e2175a3c067e5 945bfc1a05d3de8c3e8ab97f80ab6000e1f78fc258b85d3c84b038d7d0f5be85 0d43fe03e26cdfbb41c36d14cb552e8447ca678efea1d275e85503123a2263b1 4077587683de69a8f5a88d666172668411d0d0fed3e037ee468627207505dbb3 59cfdc5d7f526fca5416d741073284f5dd2471e09f5916f4bff1a90eea4d1283 7731f6a36e5ea695f4efc3bf5669b7f60ab606df5819149c0c8a4817f06dc172 0543467645daeffe4457293e0c0407c4ec7857558d0452de2ac773f141783edf 81b30215ae8d2d062aeb3cb69eb0d62bf04780997c9c027a22896f456b784378 7f2ccdd4804375321e7946d3d254521249a4d28a360f4d3163912a688c16e807 15d0440bd27bb78fcbc89bc28028aab2f594f8b641e45b9c599180b69663eef0 03465a2425aa4f8b29dade493002fb335b23eb145108ef3ab828755d3753ea8d f0683265497b1cb5cb484c13f7a4e003fa6ab3ed5e24fcc6125cee4e33936122 3cc907af3c64e5aaad882c356e673e6ca2509a71920e99549d8797e9aea189f7 fe18bbf718017cd2e32b4652acf12f16e785462980f5895afc917ea83e9c3eab 6297f1de23785f79172538b39984ab261f14ee296a42cca3159e63fb30583af1 911646257a99b4162635fb79e25404242cccc3bf224d4c279e731333107ab2cb 2598dc582dd185669c1fad35d2be0428389a4b175db159508c08a77e842fd400 bd17b48ffd886a733287387a2963a7d6efc89ee584cce5411ca68be74ca73b14 edd3ecd77dba31c7f2c6a49669dc785bbf16603bfef0f3099d6eed78c28e40f1 5c5e0945c6ed65a57ca3cdd83b56c8eb1e4b00c6464eff0605503a9c8bd5d160 ec63f8ccdb5b7b87530c3ac4f7a267d6e775b37e5c0c72f8addc5659b0308f5f b9d81e1131a2ed56dbdb423fc41ca7240491ce9a6bd3e34ae71b2e21caa7039d 0df5eca055db019a215ee6614fa03e74c1ae2a2d7a79dc7b230315dea34e9525 eb2a5da81b39e23ebbf5379eadce5538dcc39eb2a61c22a05287fdaf47ca8706 859ef10d8e6b418e44510b2e8c0614b14531de5d2af2db8973ba9bbabcb276bd 723615d1e0a78f09a6a8737c1ba4842e661bd74b1d15223a40b2eedc43ceadc1 6ee8f64355b4fa9530c3cc1c5aa9e4ed093ea1b270cdb33e4ed513000c0fa5bc f5cb1fcd3aec0845dfa2340be3549cb03f86a075acaee0bfdecae007a48bcae0 98e1fc2f1ae115b02dd8ca584d93c6ebe37058dd5a6f492cc84bd6ed19cc34e7 9ab44eb1edc74d160ade7919cdcfc404ba44083cfeb0ba2371c7d5c92451fcd2 929e0a6e74f5e7c882b11c49c934c20cfa05c4e83188dcfca3471857c0a4db31 c851c16e049d2445a21d6c0f39b6b501ed80010535a7f343af3820d34a6865db ef97920cb8c23a6c57266959309fd91ad70ed4148cbdd783a92af75bf80109a6 76bbdb3337e649644fb92aabcfe937bbb9ff4db3c59cce677eb6d4846ebd6ecd dc887a9455bef7ed3d48b9328e93a96f93bc6a70ed1c1b978eb344119e6dc476 882790473b46d5a14f02181a66c1105681a8f1f6587c080850029d7f0205bee3 5f950c12225487479586c7e824d278808eb42f481f1abbc0b411f9465fd8ba73 3c634de2c39c515950d1ee0a2206534607226d1a21442e65a1f50c0c79ef955c ac9b8ec6658a20faa0e2135bf5ec6e229d92c91878c62475a9d44e4cf64f647f 2415b0d2257c9c0be8d678709b6356c2418a41561fb31b7c4e85cfe7cee7dab8 b040c838276b970d465cda5febaaceb9d1e021667a1e14c481943c8e77a4f449 546de1fb7bc93143476615c9b627f3582c8bce3df66cff86e22938b59d7c7400 2f8669a8189ef0a07198af80dbf5a0e04ec3fdbad59b81aaa11c671ecfabe5d3 6531754c36f6da1a01e9f6d02fd827123c84dac145f27998af859add6ba49d29 768ac8c24ea4b1e4c790ef92b4836c9aed8ec92e9d1c6e0e1db04040cd01f8cc 41e74001c8c29a3f35503b25f27b0e7aac4d8f0293c5b45001895f06b26814f8 cc689a49c31ce1da29a6fbe195f0cea2d8f56f6eee6e6b746b6730e50c2f2862 83d6820a05207800b3b6ed905ba8b51ac0dfd47f0d90ca4698dbfd0b0deef1db 88f09adc7e26ada23f86735c113a83b5d5740adbc18d8c1a8c9ed1721840a3f0 12927b01d8af41431ae3b195425a8e83c72efe57373700fe24421210e00632ff 3fb2517063190923730a4da7e6873f63f80534db19918f2ad09201316524af68 696a1e9e2ea6db63247298f699ccdd35a2608935d623a0926c41f5715c8936f3 736986ac8e7f45e1150614c80500c7cc4ea8a2ef9ff659b2ef6852d6533c42ca 3405f0697150b929f5fafc4f2b0af7a32c78d641d90318e480be94670e070a88 d2db9bd3015f472ed3b2b184f87d7db39226dfa9ed32fffff733cabdd1236ce4 b892f9f2b42f4b5545af7d6e0c9acfb7e110340f2b263d94dde025c10d009a4e 3c229fdc6573bba01499beeaee8f43032c7d2cb241c2a1083dbb67c424ae84bb 8c7359dc9a303312e5cb6d46d4f3432c3e67677af1ac06625b7f397f0f01c571 9898adbda1875147fd964c57e9401508dac9dbeff48db620920faefc1f407040 e3f1937fab194cd087cbc0fd320b763f8251d465102d1d610a38f5b8bf015726 1ef949f2242d63c6cbc2cc7119912d4d38bfeb897d58359bb9f7c1cd32f2981d 113fc87971a4c1ed17428895bfd0c103b08d20534e505f0379855cae6c91deff 561f0a383a70fa9e56049b4d425622221c4173fbb775d4157e7b64def967fa25 56478da2e80ec5c84ae95f6b1d74e6ff4c9fa8f9bc789806c9bddfb96c02c336 880993109fef4c7edec60fa509c37b7f9399fdd05ad0c89628373a4322d8dfda 089fe7257302f478b3acd35b1e3a4eadf2f5b107932a4014ff4c5f9d542ce051 fda15a5cb0bcf15b0e530f37c0b3815195ae09db7590120604cd1f8bf5791e41 dab32f4adf02287819b3d8ee47df4b653cc440e9aeac090bbec7282b0eb4950a 430716fe5fe2d5e6f340f395fc12ac328bc86bf05db93b7e4101cd583a4a8d45 f9146728fea893669f3c550b3330bacdd444339ee9f004efa2fd258903809c23 f425037ce8c925e872b7566b9890cbb2a6b1f6e056c22e471360525b9feb650b 9aea0415eb6584e26d3f05ca2dd0c90f04ef14b0ebe39ac37151c413f22ae091 ddd037cbd05e67ab3dd7c08b43c7471eedd3f402c07f2b9634e4d7f81235d9b5 e093516c078a2f25daa8601ed76958c0177e26fbcc984aaeb61df024a2df16ae 4826eff5fd00910df183a07babe18823d2619e6ce212284a696935c35a11299b 01bfa965275d6f281e43bc6519e9fcdc3325ed5a20917e88f91df2d048d4a798 e51f1bd317338e2095f0036d0d42f71caddf00d6743efb960cb0e1e2d26322c0 6f220a5ce240c4b0b885dbcb5419f652674a77893d40aa6c6e425f49bef33829 8233e7323ea3713cd7aea0ae55ca2bcbaebef139376eb985234d30c42472bb8b 99d5cb80554bf2d2729eb2d2b0f17ad1166f1caaea08d407b2a0bf5cc85aa7ae e18bd366cc29ee9a66bcd3f6ac8f0e251abdc2bc15908db11a5fa4618a0dff2e 75ace064a7da39bb1e29c1cb717eb37006d7a37a62b23cf719f789a15f931e06 8c38e6a0425510b311405e1b207ab62022c17a16586db1c9b928e22fc71dda91 4cfc89c1891290cb16f6cd0ef3116e085bc988109c356f51a8d9e949fac1b308 efa89f80dd58d4d7baa178e5970d13fe1ae635d2d3796d51522d1fa2a9197074 0833ebf8724ba7bf77a776f15ef40f3831b5d3969cd1ea5f81ff2d4420a2c660 143a27221a8277a1710257f9c7dfc329d7444f99c22a21fe356963cbd470d44f 41fc8809c035209c6f11fc0aed82c44c9e91d08f83d2b13439f83c4e012dfd08 99a777b895bffbcc287ad2292ea95df64868f8ef82e5642bea29cbdd671803e0 21d8f442967fe7b4e1b5b22222f36382fac6f8ca83b0cb81855eb2645d92f4bf 5d91f135bb372827c6196015253796d9093e96440b55c64b5d8720a7ada6b119 0e7b511c7c5e7873b115975dacc8cffc6850590ef9c0f5d5aebfb413dfeaf57f f6f4e50a04b2acbdf0817c32b307a9d879328fd2e9385a143f56f5bfc70edef4 bb63e613b1b2da7b50d20735bd4d8358fbeb994ff32341fee6b8948a9d55e622 9c3345fdc3867a458f4a608b949f39c6ae21898e7244b160213d11ffb31ed56c e5a9471c85825acdf5fdaa3f6d73824f9e5977ca4541209ae80287d43c4a1f62 7212abd7695540f9d177b3c7499bd8791dc9b56ced62b70dbdbbfc90811a52d1 fe00e5f1978ff8cf8f798208a2ce536a39ee0bfab7e01c6d900bb5803cb7635e 6098d96cdd23caa83774447bac3dda7d80130ae66f54fa9b2dc5fcc4569b4a58 16a4f25bb8a1efd917e4e63b876d1e563a5df035fb6ce6b36aac972839688158 3ecdcecafe427130f3113b503115f217fdce714ed1655bc743f2f4974c092488 c44422a6c8be174dbb8c5451719a92cd709bc06a2afe0a323cf1ad5275965890 d4d97087235efff8f38789ed14da0a0889f50b10082e783f54ea2ace9e2d56a2 bf1ffd5236c7ffbad72d80d187a3bfacb52bd9199a11e44a66ef6ce819a80ee1 f59366236c1ae3ea656957b10f32737382098689bde9825053971d3538f6af04 764dd2b73d488317a10c39b91b7149ad857ed16221e84693d18af596919b685d d27546e17009e1561a864d6012ee3e11917a6dc005c129ebc4e9248c2d4519ff 0cda9c1434d6726167125e45375a66aa2b19394b3b198b938d79bf8957005a14 4139efbc4a58f06f340e7d24760cef9eacb7745e52d8dc013a129261516cda58 960af34db67a31d3d3ea422d8aa0299bbc7f1f55f1d82c4cb84c4bf28ef5a815 3d2eb23f640fce63ba4868efd20a4cef2dd7c8fb5fac0610317b7d00a9047bfb 6a559a760d5afad96c4bcceee2ad99eca57785f4a86e5c7d5e4795bc0eded7df aadac45905b704670fe24f9c29350bc8f57a2d26fc206188155f409c8dca35ef 6c7c6a15e35c9d426d2651bd9bb6d882f6aedeedc7a67593ccc424210532574e 43a5b454dae6c6e997a2cc55d360dd894e8ecd61cf7943f5ce7441f4cb5f6b3a a35deadf785206670a9c22b3f5fadf95c64b45273d4beb23bcefee6d129346c1 4b53411b4f27d68af825a934ef42ef57692a2682224305364a729d10284071fd c2d0e2865554b6be99a322795d7bd1facb1dd2ae7ce846550b140d880d76eb1f cc03e148fa167f0b62a4db438c29d2ef4fd686f352af6ac6320e0ca593e9cd9c e21c386a8c80c1e5f4a6a63043721d64320f8c8ed5a1f632abaa46ab25c2f64d 7b54caae08206ea1ff8d114644773c8086e5f6c87e66ad10c07249a68da79ec0 8a436836a4b9d997d1676d3d852121d88e3b308fff9140d01355e19aa04d9334 769b47dd2f13be086e502533679f7c7d0e0595540f9c7b9d282860e723cf2000 1b1dcb9382dac6b82cae85ff62ae614dfb210243d177e5e0b80a8bf9ef13ff64 3a5da5777b17ed71c16aadafb8d1acf4db68769c7468aca0d49f06a52add5b87 57e40a8be9301fd21bff070173d7ff29ac99fa5ee167bb73705aef773aa5a6ba 3155f2407c7876453cb6c968b0877bfe3d09a32d77f2156b69af0055458c95af 90a4de8d5562da88821f6b51c66cf23f45cc915bd0ecfb2b50bf796f8c35a20d 49b7845647b5756f8c7804caccd0615b4414c184914d3ebe4ca800e7e80e7369 7e68006942777b65d46279921d9646b8075cab6f09e58d4df7eb27ad3b5846f3 c2d9176e214501e1409dd2675dc0559b9cfecf02cbda79238b1aa880aa99a478 be235041f316b5317a398479937e852f4ee2d2a70f05bcf0e9ab73caba42b011 8bad84dabbd8d4bb3c57ef121d5a33055d564a9bdd9742dd95f9fa0573b9150f 4e9c0989de33ce1674d431f11d156c82054312d96f351eb5ec 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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 (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 65 /A put dup 66 /B put dup 67 /C put dup 69 /E 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 89 /Y put dup 97 /a put dup 99 /c put dup 101 /e put dup 104 /h put dup 105 /i put dup 109 /m put dup 114 /r put dup 115 /s put dup 116 /t put dup 121 /y put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueXX 5000795 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be356c29c3aec91ef17f5d31183b1e489f1fa 559a6693fbdd04d4f7e99886d8cb7cca13d4aa9ceb34a708af22e69ccef0e504 c3997075243585edf60b6447c8d01cffb04b6e3ddbaa7da5891286861322a795 e9d990fd56af2f5c2b35801a0b07874e4ac3170481d232e150443253c92a8b05 513d4a4154a99d91f629ccd30376500f5d16aaa9b203bad6350e4b19424c0e33 75f2949bc1927a6f6221252f8a96618e646aa1b0810753c98becc26b37837775 24bca72b818d314074c1c91f4e1f4148d3d703d12d179ee6970bd55d04aa9a9d 97f63f2c7dbd129ec2ed3ba5f8080270ea5854ea165dbcc061e2f47f1aaf0997 2ac9a689a2a9620b91b53f6b5092884372f5f7afca495f331138d85a97c5bb83 d8072dc88010fc89108b60bc06d4f93c722e8908d7ce3c1ea3c70e9e65edd769 7db17ce0e012ad37d4030f33d30a73fd655b7a2e572f3378ac933dd75082f2f1 68702be19bc60cef6bd5f0ada180d21408c04b7f7db9b6dbaefe09e809a80ddf a5366d10930d3e68ca53e4721ff525853f4c784f2c2c3aa0129a34d9df00debc ae4037e4c0fbdce3989f35964b4c07e7817b805bfe8c15f0c0ebf226cff606b6 2954f0f42dff8c214a6537ab666d25389c44db7b5866440bbfc137712bcdcc89 c68cd1adfd85648b1ed29bfb45a564b02172137feef782d604e0d7e1f1737c96 719cca9e4b9dfdc87e5999b886a15ac572183dfb8bfa2dc13fdc0e284bce7cd6 6ed1b5f7b1ff17c54fc6a268ae7043a6923e81a7e1bdb92395e80a77ed627764 3e33ac20fafb8039cefdd1abd6c0aa5bafc7dccaeaa408d45216e77d305ed0c7 ad5af3da933dc33436a35995b50c494f1655f2bf24ec70a02e7d477b8b3d24fb fd85dbe2db98f0b858008d6c1fca52b8dccd20dd02d9c271a4a5c414e4f51d41 3c8053c9b5ffa383679e380b37f82f53d6696d19093fd67bc013d75874819886 ea83428f2d02416d3edb65ede951944d5b1e395ae245c8b80a7cd7d15a6a6b25 75cdf93f0889be91b91384aa8d9be21ef779ad3772bc4e90142d1a1c9037378a 496d230a174b97bb0ff2244bb3de720e8eaf5a4816208dd55f0cee07ea1e1115 78ad49654a758490892d502b4db22746c9fec926eae1031aa2b5cb637c14295d 748dfcf18535e6e36273e0300d03ac8da9a08fc7d9d051772bdcdfde58df8e57 e8df6b49e226c8dddb6e4224bee18bd2bb7b3ffb0b5468f8edb48ac245d7a9a0 f712e8d32e9f1b4957337d1c7befbec53b210c28e46c8836ca075c3466d5d6db 7057ac42faa7a3d9507aad6b2eaffdb84ae34f17e345da366a1816b0379950be ebe264bd0870d5cd5247146af2f3fded0f14d56bd09edda21150a10c241e121c 8632d319051b0470e8d1934fc9888e0f025cb9123da0bff96f9270895d2143bb 57366d2932984fda1a609fca7dd6aae5ec4de3e054b858d0739031708a9c78c2 4ffd3ba828a82942a19f80f8f8a1791d6fea4cb300590cb2f44a2581bb5131af 303b7fa0adc2d6c951b929ba7984c5939d6fcd2b51e790dddd013e34aecbafda 6c3d7ce220c3620feeda07851c90ff9aed2b5a0da08017887475a6376719cf80 5a00560c38c976a69830a2d05633d644e045912d1241cc2764fd2fdfb11d2588 47f7296f0591a67c3145597f2e807745336f90a04b24e8221ff5c981ffc7cd3d bce69fbc1f704f61809c5d3d82e953342eae364003fb612d8bfe9dd97c20df9c 15314969df25b41d97a17c2106804c0bd0da56300483ea2b25a14bdfdd86f203 8668290ea04130e57a7e6a03dd55b295428321640b8c05939c46a3d78472570f d5b592029b671a13d9348123bdebfa5c31740203a8c027b56cce738fd14ef23f 6798308205b62a00e9f35aef0eaa7e0ba2fb4efaa501f0febcc2e92e936cc1fe cc217310831ec59b01251b65daef79608eae03d4e8ab6eabffc3f162c85cfed1 ba7831f3d25609e0f5cd41c8db6f068ae063a1149d455e20b1f0c1f3c6cf641b a967c3915ae18d5e74a3dff24bb429468f28f0504aa1542d1edc85bbc73bfa58 796e54ebf9140070a3b684ac98c467710d412c1645164ed4ed31db1646abfc5e 72ad05c4dae95f866038371560835e6c9b0277eabf8cf1562b1782d3be0b42ea ca60ca906adb76324cd7766bbffe5ea8e8f3315cf5c7a7b6645db0cf937e93a8 7175f311e4a1823d5cfdc4a28f04e49dafe112476a108d966d16b0ee0a66df65 971ee43156f221036ee7dbce2270efd9bd50a31f2e782568ebfae0a32944fecd 27f2a1f9205962f78fe242a06e764605e97359f27070614fb21fc4cbe798dd9f 718d2eb1ee99fe97bde304b9cae72e7a2fcecd92ff76f642a515c6047fed0296 3bf3682f90f8b0ec26e53ec3fa4f76fdd5c61f887d45e4d3f689a4cb66590c90 145c2960e7f7ef625e299042dc23707dd8a3d6ebd4e320b94d321ddb5e2a487a ead7497bc22382171ab32282e83a52d6d3bc35c723aef455661da4f28d73925c d386df0c6575df6a8cae6356d20ad9c14c87d10d5a8678cde89cfe11641822e7 20e086813fc47f18120286c536c7eb3376a890aef4097075b89dd5398c690894 fa77884e1dbc9b5eda54511d2877d4d02de11ecdbd76a5b539b7030561aa03d8 795f6adc5733f4c0cd903d5f27b29137658fa46a53b0d8dff02a28a7bd20ec3c 72632530839a9dcfd9e02a0519e18c39474c71933cd2333bfb8eb33c0aac57d9 89f42ae3a5bd5e3f1087a23ed233a8aeaa224643b02c40a7d54dae0897cf71f6 ea1298de70ad2530e72d314dab23acb77e8604fb77f0acadd220ccbcb529a0ab 914c8e89b3b860b3620ccc1525401de2868ff706faab6b0a3942d1584259483e 6923012ee800765a2d2693d0afef2431c4b5942a542625d4315a33e10c57f108 a5d681b1b88783004d45e02363482a200220b88c8cdb324a98c1432e0d0c4ee7 08d25d26957c9c4c79e763d20c99dc320fd69086764ce82908170822b3e6b7f6 17938745f3725c815e5a57b7e8ea625587b64776bbd3cb126361850ffa150397 6a9c816fa97303d2962a686032f397a51b54a3a2339ec83ba91020638f7bc7ac 41e6b8dca080224fc74bd5d0c54a5e6ee9c2a3f27bcc22c8c1caf8c188c7c4d3 26b5a8b40eeee4748c388d949505c4270a4e3d8921d757dba1ba24e44f231bb2 223ccc63bdb63c632a65a8f13ae2de5583224ace5dcf8f58987f1c01e9c58848 a290a6a4dec5a9fe9329186140b944902d65a99cbcd2544e37df49f9a7185dd6 28853e51a61d0cee63e3e9be03b5074e9984a5b2a329058658a275b9f46695df 2abe0ab05ac39de641cf53fda0259231fdea58c7612e0a4b44f93adfe0960fe6 49348a962a4420e4293a44564b5dc7fb22e5040b2f0ed26f50470433cbd92c79 8395e4274f2cc2d69adca9168e6c2bba250f85fbe4183b11dacecad247deeb38 3c1cf593bf80cf0ea4868c30ac058bcff70e1d85f3d5f9762a50c172e5ae16f8 05fe4040d365cfd3db77bc6a4afd2e9788755f40a00ceea450db62f4d20b6afa 4b8b6d28a9abd806b4176a7f44c50cab63b07ab1e4b62d77a448b02772a8f195 ed834e14d8b9774ff80a9a3d3c25327bbb2f5093acc59c7ac0d8b555b834fc46 59aca86ee387219815034145bbcb556d47ec5fce4fd47d7f8894215c3e554b95 492f9051930ecb5b364507f3bb47e910b7e2a72be2dfe18df96a40a8c0a60556 e7cfbc380af6a5518558237099d12644c03c0066675c2bdcff0aa79433ff4eaf cb1f521f4a2df5a68d49b9939544feb7da83b1b751d30a1708c4b2851bab4922 2b5409d45a66efb29f50eb46072879f7cde7e1bb998cb0139d5825c3d791bc8d fc1a3bdf9d2dab77767d1f8d7de66459251e316ba215c6a87bea1214921ff98f d3dc894b33f53729ea9da8a56c2127b0f187c0590ac2657dff2f5df0750cb21d b7e75e6bb5482ff1f7531bb1f4b562ba5dc9698e4b0d256470aa85d3f7491bbf 2cb83c905c02e8c25cbe563bd591c0812ad68a6ff091720e94c4cd0bb9f62735 37ead6be301b9a6c835e6bbdfde267019e55237a79dbf728501b8ca0c18cb25c 4f802151f896d660cfc4c5d80a0e24fe0c05c49660dada5156b7e55037878df8 977330d60dd74faef83124e50872a11af939f4de0bfb3cacfe737254749ae8db a7a7bc2f2443439b9c136b59972b3fc4e1a7fcc3e17629ce27c252f7e37886c5 36fbfdb682a3d6295e4ac85999f0e8650d2c8733443b2cc41b9a90d601d99e37 d33b15011982fedcf5dda86038a63067f7abf808c0db389bb8c21b4a6b4daba4 a3f2835d3900729ae1a846b49a1f8f0882a54b589f61a1e0e28df8c0d359bc50 86efcee166c8f264b90bb35afc62d1dc5e614ec9c18b8c341b38d154a02fe9f8 275d56ae69b7a35a8b0b6d6e92ef1eb3392f4072fae851095f607e22649dc653 cab986a7f6ecfa9b5752cc7f6ddf53cb39a13f0daf156e33f3543c32e4cd3113 419c23ce7bbe8b4f8e0bfbf63a89fd6a37df18bc3f0e970f58ef2236a7f7f374 ca6512dbfe6572541a282e622ac7a96ac522d486f813e7f39e108ceddaee2418 3a92d2228c70341d5af17023caa09b36970b25dc776c340cec423234b890b8bc 7cd1f1d83a96b3be8d10324fa97c44388704b029a8c73f9331c51364bf328f6a 4da06c26b81ff8595e13f441d7df280a12c0386b0b870de9bc170cad0c2d1589 8bc2ceb94b2b8fba4b72516602cd33a02a916f66ea30813b42fd1cbe76eb0608 2487ae0f3bfa8453ff1dba07b3b19a5ad2bcce3ce06b66fbf314bc36c40812a4 aa8d202cea2820a611035687f183ed239eb58b49626914b4bef55452b32f42bb 42948bb63ef306c7a611a889eedf7b5df824f2712ed61ba2b62982f4556b98ec 840e8196b8f8619a82b41f5082ef4f7d1ffe0f2396b1aef2bc6bb9d6368dfca2 93b5bc300bff985cbb42d949a4862ad3795a2679231a655d205e35278d070984 bac45fe8f75b4a78109c629924e5308ff771f9a4849e406544f119e7e2d07205 21c8ce4d3252a6452357793ab2e963b873c0d8bd8b23c86d0d55badf68935da2 94d9d8f7241a61f05a58d0d602f8a4c87a1ad67dbfe69bf91c57314aba218a1c 138024b98f03a1f8e37520a2e62aff55c7a1e9447c1191efae3dd3a937457b47 aa7731b5f5dc042bc1bc811c539009321d8dfd68524f2069c5b794b69d5b3f97 3aac2b8c7d0034d402ae2cd196129ed3a31e318686145ed103bc0956b8b36bda afa55e2abda77269738aebd0971ae009a968db7f06b840bf366af584039277f1 9a9f30be187ef86a9309125c6e681a046e99313e29906f173dd8d86e4ab74f9c 2d8899fb5672b907de505e850cacad3cf81ee8fd1c4729bd5f3718bd8d6cb28d 9faee9333d30869e47a2e481a76d3cc3c7eab7aa6c996d976c8c8fbdd9c75d14 15b913017d72647578005907ac0ad47282134dff4cc4dccf8742617d1aa52bd9 d45dd080726823384a5638f9244f1feb94fd6a3033278df9857d929fb68ba254 1d3c17c665cc3d7e5a0091a7cd89ae72c3aeecdf37fa34877f160a749dafbd38 b1b8a932941812b9bb09ce352e84690579c3a8852f13be12e49b49270eb8cef6 df2f0b3d1135f6410d0850dce7ae649fbf99beb4b708cfdd2253fcc407aa0e60 4268414d98a88c1b9b74d5e325bc9601908ffa3fb6460678eaa2a808c2bb18b1 a06e9718526c5226bc947fda16d2ed8d10c25dc3a04c5258ca6a1bf93efde209 e9bd5e2fe971b3782e7895a226890de8166f7f447e75b3866a3ac911203db0f4 99bba13467aa09d2a6db060179b677da1c2e7b27c4ab1c0033853086ecf645ac 3a93a4b51faedc8dacda324b72ae314c6c1c51e81925c38b50c2ea325ef68958 a8cc2c982fa2ec01545c353438b68f0e83a39b80ec035e5f658bd9f8f99ca235 54bff9f2cae95934611ddf17f5e76d3f2fd4674cbd94051120958569ee770dd6 1380ffe4c2ff25621869d266821ae5bb8a0c9efbbcf88debc58b38dc01f68485 f7d6b7c9848561f6aee87482ce6e1ed33d19c77962a2afa758523d20d900b20e 816827644583106216073270880caf48a4182aece6452af3ab407859c8fbfd72 5e11c8044595a79af88a06a231d8e2c89e1bd34c5f203f52a3a68da1783140b0 ba760a4a1fda5e32abbfb67aef57a2a98f04dd9c027b957e31081a3a1524de23 66fcf2500bfe213d304adb4adb60bc733c7cde4b7b0826bd00d8c383e9ea1a2a c5b114a7b6b9d0df7e3731bc6a9e453dcbf33d9d04a3c3bb860194893eadf7c0 78cd528f230f43b7aabf266c19a0ffcce839e02eb8139709953156a7f3bb0ff3 22a668e0153472b8a6fb7d62e8e2121accb6f1714a49cdfc829fd0a36c77c407 68461f17e2fb4c56d94e466afbae3f23988025434bb0e42494f7a9cdb76da34c 73729d8b7067b9e80ce697314fabec6dc5c0ad7e99cee31a3c50981dad8ef263 090bc609c4d003c392aedba5c12bb3e67e532947b7fbb69e03dcc1d803e1153c 68fcef80f7bf0f7701e175a262b5bced20ae76ed41aeaa90acb9f235377c297c 6204e2fc98c983ada5459ef49e2cba5dfe0cbd5753333ca0aab12387ef398808 b7420d4afcc792cb98df574d26775c73a85e0826506b5d0d7d0d2952f72045ea 4549d2d5da9901b84077f7145610120781417cb9e0a8a2b0364a457e3c169900 63be0d0eeded8bcdacb48c283b56d26a67a4bfe2ce37cf51567605ff74465804 c66df02f4381e7e71f1b049027114c705efffe9298dddfb4586941d591058d5a b75de7ac8dffd8ea383babc8ca99bf77469b87bcd113eb650d484e5f32c16125 1b50546bd18543f90d64a01503c715bc3bf3423d7319b329ab3a9ea1513ae4c1 bccae71f047d37a69bebd2d8526e0ebf0dbafa2c1026d2573e84105fe9ff7784 c6a09967d88a10e295bc53f8090dd0089f79b435df560f7edf2b93b9fcfa488d 1e836be489945ad1efce7dbc55bc208c97fcd199686e4a0c3580cef896eae3ed dd59e01e9bfd4494ed0c8880b30ac5b34215759037af78d2045ac05cfe253cc4 4179e0d6fc54ab733ed896464e611a7d4d94371dbcca068bbc1ea089844e4b5e 4d554feea77662f5992bd73f4aec44e685e001051e541b153ae97df85e58b480 7d518940b67695f26bfa4903a8febc36f4741edc266038a95d3b97fecdbc458d 0470746bac891ade6960c5bcaffcebde08e109d960cd993515e26db85238305f 4e01b39c45430a6c6ad42d44cac6029598fd6a0e69897ec8a191d9a8f33514e4 816ab8f4f1d25deea0adee595c82989e13234635e64a22c9498d7235139718dc 0fd7f4289caa8ef9fef81548a466052d5188865b51ed61cae460c7438ec13b49 22602ac52bc50e9dfc41c2050902699e8894536b755beacf 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (cross.dvi) @start /Fa 236[49 49 18[{}2 58.1154 /CMEX10 rf /Fb 135[33 7[31 6[22 34 78[35 25[{}5 41.511 /CMMI5 rf /Fc 255[55{}1 66.4176 /CMSY8 rf /Fd 138[41 25 4[34 43 4[24 105[{}5 66.4176 /CMMI8 rf /Fe 170[66 17[70 53[51 13[{}3 99.6264 /CMMI12 rf /Ff 173[42 82[{}1 58.1154 /MSBM7 rf /Fg 134[37 3[39 27 28 28 1[39 35 39 59 20 37 1[20 39 1[22 31 39 31 1[35 3[20 1[20 14[44 20[35 8[20 2[55 43[{}24 66.4176 /CMR8 rf /Fh 206[30 49[{}1 49.8132 /CMR6 rf /Fi 252[65 3[{}1 83.022 /MSAM10 rf /Fj 203[28 1[28 28 28 4[43 43[{}5 41.511 /CMR5 rf /Fk 192[45 14[18 40[45 6[45{}4 41.511 /CMSY5 rf /Fl 134[59 59 81 59 62 44 44 46 59 62 56 62 93 31 59 1[31 62 56 34 51 62 50 62 54 6[68 5[78 62 1[84 77 84 88 106 67 7[86 81 80 85 6[31 56 56 56 56 56 56 56 56 56 56 1[31 37 3[44 44 31 26[62 12[{}54 99.6264 /CMBX12 rf /Fm 207[31 48[{}1 41.511 /CMBX5 rf /Fn 140[30 2[42 1[42 1[21 7[42 33 1[37 27[49 18[38 38 38 48[{}11 58.1154 /CMBX7 rf /Fo 133[42 50 1[69 50 53 37 38 39 50 53 48 53 80 27 50 29 27 53 48 29 44 53 42 53 46 9[99 2[66 53 72 1[65 72 2[57 2[36 75 75 1[63 73 2[72 6[27 48 1[48 48 48 48 48 48 48 48 1[27 32 27 2[37 37 27 26[53 5[69 6[{}56 83.022 /CMBX10 rf /Fp 149[20 2[34 34 13[48 38[66 19 14[66 26[52 5[52{}9 58.1154 /CMSY7 rf /Fq 133[32 34 38 2[39 25 31 31 1[34 33 41 1[21 35 27 23 39 32 2[35 30 1[36 6[45 39 54 62 39 2[41 1[52 42 1[53 2[56 5[49 2[50 1[35 34 1[34 1[20 19[44 4[31 6[38 1[39 30 11[38 43 11[{}42 58.1154 /CMMI7 rf /Fr 173[60 3[60 10[60 67[{}3 83.022 /MSBM10 rf /Fs 142[83 12[120 83 46 7[46 1[120 7[88 12[73 73 73 73 14[73 73 28[61 61 50 50 14[38 38{}19 83.022 /CMEX10 rf /Ft 143[69 1[42 2[42 23 2[42 42 7[55 1[55 55 2[59 4[50 6[57 14[60 1[42 4[0 3[55 83 7[83 7[83 6[65 1[65 2[65 65 4[42 42 3[65 1[65 65 65 3[65 23 65{}32 83.022 /CMSY10 rf /Fu 129[42 3[39 41 47 59 40 48 30 39 37 37 42 1[50 1[25 43 34 29 48 40 41 39 43 36 36 44 6[57 48 69 78 48 57 49 51 63 66 53 63 67 81 57 71 46 36 69 65 53 61 69 59 63 62 44 42 65 42 65 23 23 18[54 4[39 52 54 52 49 1[36 47 43 47 36 1[50 48 2[39 3[37 43 47 53 11[{}76 83.022 /CMMI10 rf /Fv 134[71 71 2[75 52 53 55 1[75 67 75 112 37 2[37 75 67 41 61 75 60 75 65 4[69 7[94 1[100 2[101 1[128 81 2[50 105 106 1[88 2[96 102 6[37 67 67 67 67 67 67 67 67 67 67 2[45 37 9[69 34[{}46 119.552 /CMBX12 rf /Fw 134[33 1[45 1[37 23 28 29 2[35 38 56 18 1[21 21 35 2[32 35 32 32 35 13[38 5[61 1[52 7[49 8[21 35 7[35 36[39 12[{}26 58.1154 /CMTI7 rf /Fx 134[41 41 55 41 43 30 30 30 41 43 38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 3[21 38 21 47 2[79 2[55 1[57 1[52 60 58 70 48 60 1[28 58 60 50 1[59 55 54 58 7[38 1[38 2[38 38 38 38 38 1[21 26 21 2[30 30 21 4[38 21 18[64 1[43 45 11[{}64 74.7198 /CMR9 rf /Fy 139[34 35 36 14[39 49 43 31[67 65[{}7 74.7198 /CMBX9 rf /Fz 132[42 34 40 39 55 38 45 28 34 35 38 42 42 47 68 21 38 25 25 42 38 25 38 42 38 38 42 6[51 62 1[83 1[62 59 47 61 64 56 64 62 74 52 64 44 32 62 64 54 56 63 59 58 62 6[25 42 3[42 42 42 42 42 42 42 25 30 25 2[34 34 25 19[42 5[49 47 12[{}69 83.022 /CMTI10 rf /FA 129[33 3[30 35 35 47 35 37 26 26 26 35 37 33 37 55 19 1[21 19 37 33 21 30 37 30 37 33 11[49 1[37 48 51 45 51 49 60 41 1[34 24 49 1[43 2[47 46 1[51 2[51 2[19 1[33 33 1[33 33 33 33 33 33 33 19 22 19 51 1[26 26 19 19[33 33 6[39 4[47 6[{}64 58.1154 /CMR7 rf /FB 128[42 42 2[42 37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 25 23 46 42 25 37 46 37 46 42 2[42 23 42 23 51 62 62 85 62 62 60 46 61 65 57 65 62 76 52 65 43 30 62 65 54 57 63 60 59 62 1[39 1[65 1[23 23 42 42 42 42 42 42 42 42 42 42 42 23 28 23 65 1[32 32 23 4[42 23 13[42 42 3[69 46 46 48 60 3[60 1[55 58 1[69 52{}95 83.022 /CMR10 rf /FC 137[51 1[38 38 38 1[54 49 54 81 27 2[27 3[43 54 1[54 8[73 2[73 2[54 15[70 13[49 2[49 1[49 3[27 25[49 11[70 6[{}23 99.6264 /CMR12 rf /FD 139[47 57 59 1[72 72 79 115 3[43 72 65 43 65 72 65 1[72 16[95 9[92 28[57 57 43 19[72 19[{}21 143.462 /CMTI12 rf /FE 134[70 4[51 52 51 4[111 3[36 73 2[58 1[58 1[66 7[99 2[99 1[96 73 98 1[90 103 99 122 83 2[47 99 104 1[90 1[96 94 99 18[36 43 45[{}29 143.462 /CMR17 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop Black Black Black Black 622 739 a FE(THE)44 b(LEVEL)f(CR)l (OSSING)h(PR)l(OBLEM)g(IN)914 922 y(SEMI-CLASSICAL)h(ANAL)-11 b(YSIS)1195 1104 y(I.)43 b(The)g(symmetric)f(case)859 1287 y FD(\(to)50 b(app)-7 b(e)g(ar)48 b(in)j(the)e(Pr)-7 b(o)g(c)g(e)g(e)g(dings)47 b(of)1018 1469 y(F)-11 b(r)l(\023)-68 b(ed)l(\023)g(eric)49 b(Pham's)h(c)-7 b(ongr)g(ess\))1341 1760 y FC(Yv)m(es)34 b(Colin)f(de)g(V)-8 b(erdi)m(\022)-46 b(ere)1413 1955 y(Septem)m(b)s(er)34 b(25,)e(2002)930 2258 y FB(Pr)n(\023)-39 b(epublication)25 b(de)j(l'Institut)h(F)-7 b(ourier)26 b(n)2282 2228 y FA(0)2347 2258 y FB(574)h(\(2002\))838 2358 y Fz(http://www-fourier.ujf-gr)l(enoble.fr/pr)l(epublic)m (ations.h)q(tml)330 2812 y FA(Institut)22 b(F)-5 b(ourier,)20 b(Unit)n(\023)-31 b(e)22 b(mixte)f(de)g(rec)n(herc)n(he)f(CNRS-UJF)j (5582)330 2911 y(BP)f(74,)h(38402-Sain)n(t)f(Martin)g(d'H)n(\022)-31 b(eres)21 b(Cedex)g(\(F)-5 b(rance\))330 3011 y(yv)n(es.colin-de-v)n (erdiere@ujf-grenoble.f)o(r)330 3111 y(h)n (ttp://www-fourier.ujf-grenoble.fr/~)7 b(ycolv)n(er/)p Black Black 1661 3281 a Fy(Abstract)p Black Black 653 3407 a Fx(Our)34 b(goal)j(is)f(to)g(reco)n(v)n(er)f(and)g(extend)f(the) h(di\016cult)h(results)g(of)g(George)g(Hage-)538 3498 y(dorn)27 b(\(1994\))i(on)f(the)g(propagation)h(of)f(coheren)n(t)g (states)h(in)f(the)f(Born-Opp)r(enheimer)538 3589 y(appro)n(ximation)k (in)g(the)g(case)h(of)g(generic)g(crossings)h(of)f(eigen)n(v)l(alues)g (of)g(the)e(\(matrix)538 3680 y(v)l(alued\))20 b(classical)k (Hamiltonian.)33 b(This)22 b(problem,)h(going)f(bac)n(k)f(to)g(Landau)g (and)f(Zener)538 3772 y(in)28 b(the)g(thirties,)j(is)e(often)g(called)h (the)e(\\Mo)r(de)h(Con)n(v)n(ersion)h(Problem")g(b)n(y)d(ph)n(ysicists) 538 3863 y(and)f(o)r(ccurs)i(in)f(man)n(y)f(domains)h(of)h(ph)n(ysics)f (\(see)g(the)f(pap)r(er)h([23)q(])h(b)n(y)e(W.)h(Flynn)f(and)538 3954 y(R.)f(Littlejohn\).)653 4046 y(W)-6 b(e)19 b(w)n(an)n(t)i(to)f (obtain)g(a)h(geometrical)h(description)f(of)g(the)e(propagation)j(of)f (states)f(in)538 4137 y(the)f(framew)n(ork)i(of)f(semi-classical)j (analysis)e(and)e(WKB-Lagrangian)i(states.)34 b(It)19 b(turns)538 4228 y(out)28 b(that,)i(in)f(the)f(v)n(ery)g(b)r(eautiful)h (\(but)f(not)h(w)n(ell)g(kno)n(wn!\))44 b(pap)r(er)29 b([7])g(published)f(in)538 4320 y(1993,)23 b(P)n(eter)f(Braam)g(and)f (Hans)g(Duistermaat)h(found)f(that)g(there)g(is)g(a)h(formal)h(normal) 538 4411 y(form)j(for)g(this)f(problem.)35 b(A)25 b(formal)i(normal)f (form)g(for)g(the)f(disp)r(ersion)h(relation)h(w)n(ere)538 4502 y(already)j(founded)f(b)n(y)g(Arnold)h([3].)48 b(In)29 b(our)h(pap)r(er,)h(w)n(e)f(sho)n(w,)i(using)e(Nelson's)h(w)n(a)n(v)n (e)538 4594 y(op)r(erators)38 b(metho)r(d,)h(that,)h(in)c(the)h(h)n(yp) r(erb)r(olic)f(case,)41 b(their)c(normal)g(form)h(can)e(b)r(e)538 4685 y(extended)24 b(to)i(a)g(lo)r(cal)h(normal)g(form)f(in)g(the)f (phase)h(space.)653 4776 y(Then,)h(w)n(e)f(extend)g(this)g(classical)j (lo)r(cal)f(normal)f(form)g(to)g(the)f(complete)h(sym)n(b)r(ol,)538 4868 y(getting)h(a)g(microlo)r(cal)i(normal)f(form,)g(and)f(deriv)n(e)f (from)i(it)e(a)h(precise)h(geometric)g(de-)538 4959 y(scription)d(of)h (the)f(semi-classical)i(propagation)g(of)e(states)h(of)g(a)f(symmetric) h(system)f(of)538 5050 y(pseudo-di\013eren)n(tial)j(equations)g(near)g (a)g(generic)h(h)n(yp)r(erb)r(olic)f(co)r(dimension)h(3)f(singu-)538 5142 y(larit)n(y)23 b(of)i(the)e(c)n(haracteristic)i(set)f(\(de\014ned) e(b)n(y)h(the)g(so)h(called)h(\\disp)r(ersion)g(relation"\).)653 5233 y(W)-6 b(e)32 b(describ)r(e)g(in)g(a)h(sk)n(etc)n(h)n(y)e(w)n(a)n (y)h(the)g(elliptic)h(case.)55 b(The)33 b(complex)f(Hermitian)538 5324 y(case)26 b(will)h(b)r(e)f(w)n(ork)n(ed)f(out)h(in)f([10)r(].)330 5438 y Fw(Keywor)m(ds:)j FA(Mo)r(de)16 b(con)n(v)n(ersion,)h(p)r (olarization,)g(Born-Opp)r(enheimer)d(appro)n(ximation,)j(Maxw)n(ell)g (equations,)g(eigen-)330 5504 y(v)l(alues)i(crossing,)g (pseudo-di\013eren)n(tial)d(systems,)j(semi-classical)f(analysis,)h (Lagrangian)g(manifold,)e(propagation)h(of)330 5571 y(singularities,)j (coheren)n(t)f(states,)j(symplectic)c(spinors.)330 5670 y Fw(Mathematics)24 b(Subje)m(ct)g(Classi\014c)m(ation)i(1991:)31 b FA(35C20,)22 b(35Q40,)h(35S30)p Black 1809 5919 a FB(1)p Black eop %%Page: 2 2 2 1 bop Black Black 330 390 a Fv(In)l(tro)t(duction)330 572 y FB(Let)30 b(us)f(consider)g(a)g Fu(d)20 b Ft(\002)f Fu(d)30 b FB(self-adjoin)n(t)f(system)h(of)f(semi-classical)f (pseudo-di\013eren)n(tial)h(op-)330 672 y(erators)641 651 y Fs(b)621 672 y Fu(H)705 651 y(~)697 672 y(U)54 b FB(=)45 b(0)c(in)g Fr(R)1171 642 y Fq(n)1216 672 y FB(.)77 b(Man)n(y)41 b(examples)f(o)r(ccur)g(in)h(ph)n(ysics:)63 b(let)42 b(us)f(men)n(tion)g(the)330 771 y Fz(Born-Opp)l(enheimer)33 b(appr)l(oximation)e FB(in)f(molecular)e(ph)n(ysics)h(\(see)h([5)o(],)g ([14)o(],)g([15)o(],)h([37)o(])e(and)330 871 y([30)o(]\),)j(the)e Fz(Maxwel)t(l)k(e)l(quations)c FB(for)g(electromagnetic)f(w)n(a)n(v)n (es)f(in)j(a)f(non)g(homogeneous)e(and)330 971 y(anisotropic)21 b(medium)j(\(see)f([38)o(]\),)i(the)e Fz(pr)l(op)l(agation)28 b(of)e(elastic)g(waves)h(in)f(anisotr)l(opic)h(me)l(dia)330 1070 y FB(\(see)21 b([34)o(]\),)i(the)f Fz(pr)l(op)l(agation)k(of)f (waves)f(in)h(o)l(c)l(e)l(ans)c FB(\(see)g([33)o(])h(and)f([45)o(]\),)i (the)f Fz(spin-orbit)i(inter-)330 1170 y(action)k FB(\(see)e([24)o(])h (and,)g(for)f(a)h(global)e(and)i(geometrical)e(p)r(oin)n(t)i(of)g (view,)f([18)o(])h(and)g([19)o(]\).)37 b(The)330 1280 y(principal)26 b(sym)n(b)r(ol)h Fu(H)1028 1292 y FA(class)1193 1280 y FB(of)1306 1259 y Fs(b)1287 1280 y Fu(H)34 b FB(is)27 b(a)f(matrix)h(v)-5 b(alued)26 b(function)i(on)f(the)g(phase)f(space)h Fu(T)3165 1250 y Fq(?)3202 1280 y Fr(R)3262 1250 y Fq(n)3307 1280 y FB(,)330 1379 y(often)f(called)g(the)g Fz(disp)l(ersion)k (matrix)c FB(b)n(y)g(ph)n(ysicists.)36 b(The)26 b(ideal)f(generated)g (b)n(y)h(det\()p Fu(H)3159 1391 y FA(class)3298 1379 y FB(\))330 1479 y(is)h(called)h(the)g Fz(disp)l(ersion)j(r)l(elation)p FB(.)455 1579 y(Near)k(a)h Fz(generic)j(p)l(oint)e FB(of)f(the)h(phase) f(space)f(where)h(the)h(principal)f(sym)n(b)r(ol)g Fu(H)3100 1591 y FA(class)3274 1579 y FB(is)330 1678 y(not)25 b(in)n(v)n (ertible,)g(the)h(asso)r(ciated)d(eigenspace)h(k)n(er)o(\()p Fu(H)2012 1690 y FA(class)2151 1678 y FB(\))h(\(the)h Fz(p)l(olarization)k(bund)t(le)p FB(\))25 b(is)g(one)330 1778 y(dimensional)36 b(and)g(the)h(system)f(reduces)g(mo)r(d)h Fu(O)r FB(\()p Fu(h)2048 1748 y Fp(1)2119 1778 y FB(\))g(to)f(a)g (scalar)f(one.)63 b(The)37 b(principal)330 1878 y(part)29 b(of)h(the)g(solution)g(is)g(p)r(olarized)e(meaning)i(that)g(it)g(tak)n (es)f(v)-5 b(alues)30 b(in)n(to)f(the)i(p)r(olarization)330 1977 y(bundle.)36 b(F)-7 b(or)24 b(a)h(precise)f(description)g(of)g (the)h(WKB)g(states)f(in)h(this)g(case,)f(see)h(the)g(nice)g(pap)r(er) 330 2077 y([17)o(].)455 2176 y(An)h(in)n(teresting)f(problem,)g(often)h (called)f(the)h Fz(Mo)l(de)k(Conversion)d FB(problem)e(\(see)h([23)o (]\),)g(is)330 2276 y(to)g(describ)r(e)g(what)h(happ)r(ens)f(at)h(p)r (oin)n(ts)f(where)g(the)h(dimension)f(of)h(k)n(er)13 b Fu(H)2690 2288 y FA(class)2854 2276 y FB(jumps)27 b(due)g(to)330 2376 y(eigen)n(v)-5 b(alues)20 b(crossings)f(of)j(the)f(disp)r(ersion)g (matrix.)34 b(F)-7 b(or)21 b(the)g(Maxw)n(ell)g(equations,)h(the)f (\014b)r(ers)330 2475 y(of)26 b(the)h(zero)e(set)i(of)f(the)g(disp)r (ersion)g(relation)f Ft(f)p Fu(\030)i Ft(2)d Fr(R)2039 2445 y FA(3)2102 2475 y Ft(j)j FB(det\()p Fu(H)2368 2487 y FA(class)2506 2475 y FB(\)\()p Fu(x)2617 2487 y FA(0)2656 2475 y Fu(;)14 b(\030)t FB(\))23 b(=)g(0)p Ft(g)i FB(are)g(called)330 2575 y(the)34 b Fz(F)-6 b(r)l(esnel)36 b(surfac)l(es)f FB(whic)n(h)f(in)g(the)g(generic)f(case)h(turn)g(out)g(to)g(ha)n(v)n(e) f(4)g(singular)g(p)r(oin)n(ts)330 2675 y(\()p Fu(x)409 2687 y FA(0)447 2675 y Fu(;)14 b(\030)520 2687 y Fq(j)555 2675 y FB(\))28 b(where)f(the)h(k)n(ernel)e(of)i Fu(H)1406 2687 y FA(class)1544 2675 y FB(\()p Fu(x)1623 2687 y FA(0)1661 2675 y Fu(;)14 b(\030)1734 2687 y Fq(j)1769 2675 y FB(\))28 b(is)f(of)g(dimension)h(2)f(\(see)g([38)o(]\))h(and)f (hence)h(the)330 2774 y(p)r(olarization)h(bundle)i(is)f(no)g(more)g(a)f (bundle)i(there.)45 b(F)-7 b(or)30 b(the)h(elastic)e(w)n(a)n(v)n(es,)h (the)g(singular)330 2874 y(set)e(is)f(called)g Fz(ac)l(oustic)k(axis)d FB(in)f([34].)455 2973 y(Of)j(course)g(the)h(general)f(situation)h(is)f (v)n(ery)g(complicated)h(to)f(describ)r(e,)i(so)e(that)h(p)r(eople)330 3073 y(try)c(to)h(understand)f(the)h Fz(generic)g FB(case.)36 b(One)28 b(exp)r(ect)f(that)h(2)f(zero)g(eigen)n(v)-5 b(alues)26 b(cross)g(along)330 3173 y(a)c(submanifold)h(\006)f(of)h (the)g(phase)f(space)f(of)i(co)r(dimension)f(3)g(\(resp.)35 b(4\))22 b(in)h(the)g(real)e(symmetric)330 3272 y(\(resp.)34 b(complex)19 b(Hermitian\))h(case)f(after)h([46)o(])f(\(see)h(also)f ([9)o(]\).)35 b(But)20 b(not)g(all)f(submanifolds)h(of)f(a)330 3372 y(giv)n(en)f(co)r(dimension)g(are)g(equiv)-5 b(alen)n(t)18 b(in)h(a)f(symplectic)h(manifold,)h(ev)n(en)f(lo)r(cally:)31 b(restricted)18 b(to)330 3472 y(a)23 b(generic)g(manifold)h(of)f(co)r (dimension)g(3)h(a)f(symplectic)h(form)f(admits)h(a)f(k)n(ernel)g(of)g (dimension)330 3571 y(1,)38 b(while)f(a)f(generic)g(manifold)g(of)h(co) r(dimension)f(4)g(is)g(symplectic.)64 b(Near)36 b(a)g(p)r(oin)n(t)h (where)330 3671 y(dim\(k)n(er)13 b Fu(H)694 3683 y FA(class)833 3671 y FB(\))34 b(=)h(2,)g(the)g(system)f(splits)h(in)n(to)f(a)g (direct)h(sum)f(of)h(a)f(2)22 b Ft(\002)h FB(2)34 b(system)g(and)g(a) 330 3770 y(\()p Fu(d)13 b Ft(\000)g FB(2\))g Ft(\002)g FB(\()p Fu(d)g Ft(\000)g FB(2\))21 b(elliptic)k(system.)36 b(So)24 b(w)n(e)h(need)f(only)h(to)f(study)h(2)13 b Ft(\002)g FB(2)22 b(systems)i(near)g(p)r(oin)n(ts)330 3870 y(where)j(the)h(disp)r (ersion)f(matrix)g Fu(H)1443 3882 y FA(class)1609 3870 y FB(v)-5 b(anishes)27 b(in)h(a)f(generic)g(w)n(a)n(y)-7 b(.)455 3970 y(G.)27 b(Hagedorn)e(studied)i(this)h(problem)e(for)g(the) h(Born-Opp)r(enheimer)f(appro)n(ximation)f(in)330 4069 y(sev)n(eral)k(pap)r(ers)h(starting)f(with)i([29)o(])g(\(see)f(also)g ([31)o(])h(and)f([32)o(]\))h(b)n(y)f(the)h(so)f(called)g Fz(matching)330 4169 y(metho)l(d)55 b FB(whic)n(h)26 b(consists)g(in)g(giving)g(an)f(Ansatz)h(for)g(the)h(states)e(near)h (\006)g(and)g(to)g(matc)n(h)g(this)330 4269 y(Ansatz)h(with)h(the)g (WKB)f(Ansatz)g(in)h(some)f Fu(h)p Ft(\000)p FB(dep)r(enden)n(t)g (small)g(domain)g(around)f(\006.)37 b(The)330 4368 y(matc)n(hing)30 b(metho)r(d)g(is)h(v)n(ery)e(di\016cult)i(to)f(implemen)n(t)h(and)f (for)g(that)g(reason)f(it)h(is)h(tempting)330 4468 y(to)41 b(\014nd)g(another)f(metho)r(d)h(based)g(on)f(normal)g(forms)g(where)h (w)n(e)f(allo)n(w)g(b)r(oth)h(canonical)330 4567 y(di\013eomorphisms)27 b(in)h(the)g(phase)f(space)g(and)g(gauge)f(transforms)h(in)g Fr(C)2607 4537 y Fq(d)2646 4567 y FB(.)455 4667 y(In)35 b(the)h(pap)r(er)e([7],)j(P)n(eter)d(Braam)g(and)h(Hans)g(Duistermaat)g (found)g(a)g Fz(formal)j(normal)330 4767 y(form)30 b FB(for)f(the)g(principal)g(sym)n(b)r(ol)g(of)g(a)g(2)19 b Ft(\002)g FB(2)29 b(symmetric)g(system)g(near)f(a)h(generic)f (crossing)330 4866 y(of)37 b(the)h(eigen)n(v)-5 b(alues.)65 b(In)37 b(this)h(normal)e(form,)j(the)f(disp)r(ersion)e(matrix)h(is)g (linear)g(w.r.)65 b(to)330 4966 y(phase)28 b(space)f(co)r(ordinates)g (and)h(is)g(in)g(fact)h(closely)e(related)g(to)i(the)f(mo)r(del)g(in)n (tro)r(duced)g(\014rst)330 5066 y(b)n(y)f(Landau)g([39)o(])h(and)g (Zener)e([48)o(].)455 5165 y(In)g(the)g(presen)n(t)g(pap)r(er,)g(w)n(e) f(will)i(deriv)n(e,)e(in)i(the)f(h)n(yp)r(erb)r(olic)g(case,)f(a)h Fz(lo)l(c)l(al)j(normal)g(form)330 5265 y FB(for)36 b(the)g(principal)g (sym)n(b)r(ol.)62 b(Our)36 b(metho)r(d,)j(whic)n(h)d(is)g(quite)g (di\013eren)n(t)h(from)f(that)g(of)g([7],)330 5364 y(is)c(to)g(deriv)n (e)f(\014rst)h(a)g(normal)f(form)h(for)f(the)i(determinan)n(t)f(of)g (the)h(system)e(\(the)i Fz(disp)l(ersion)330 5464 y(r)l(elation)p FB(\),)i(whic)n(h)d(giv)n(es)f(the)i(classical)e(dynamics,)i(up)g(to)f (time)h(reparametrization,)e(using)330 5564 y(the)f(to)r(ol)e(of)i Fz(wave)i(op)l(er)l(ators)e FB(in)n(tro)r(duced)f(b)n(y)g(E.)g(Nelson)f ([43])h(in)g(his)g(pro)r(of)g(of)g(Stern)n(b)r(erg's)330 5663 y(linearization)i(theorem.)52 b(This)33 b(is)f(closely)g(related)g (to)h(Arnold's)f(result)g([3].)52 b(W)-7 b(e)33 b(can)g(then)p Black 1809 5919 a(2)p Black eop %%Page: 3 3 3 2 bop Black Black 330 390 a FB(pro)r(ceed)27 b(b)n(y)h(c)n(ho)r (osing)f(the)h(gauge)f(transform.)37 b(After)28 b(that,)h(the)f (semi-classical)e(microlo)r(cal)330 490 y(normal)h(form)g(is)g(easy)g (to)g(deriv)n(e.)455 589 y(F)-7 b(rom)18 b(this)g(normal)g(form,)i(w)n (e)e(can)g(easily)g(study)g(the)h(microlo)r(cal)e(solutions)h(of)h(our) e(system)330 689 y(follo)n(wing)23 b(the)g(same)g(kind)h(of)g(argumen)n (t)e(as)h(in)h([11)o(]:)35 b(the)24 b(solutions)f(of)g(the)h(normal)f (form)g(are)330 789 y(explicit)34 b(functions.)55 b(P)n(erforming)32 b(a)h(gauge)g(transform)f(and)i(a)f(F)-7 b(ourier)32 b(in)n(tegral)h(op)r(erator)330 888 y(giv)n(es)21 b(the)i(Mo)r(de)g (Con)n(v)n(ersion)d(rules.)35 b(This)22 b(w)n(a)n(y)g(w)n(e)g(deriv)n (e)f(geometric)h(constructions)f(of)i(the)330 988 y(principal)d(sym)n (b)r(ols)g(of)g(generic)g(Lagrangian)e(solutions)i(and)g(Hagedorn's)f (results)h([29)o(])h(for)f(the)330 1088 y(propagation)26 b(of)h(coheren)n(t)g(states.)37 b(W)-7 b(e)29 b(giv)n(e)e(an)g (explicit)h(description)f(of)h(the)g(transmission)330 1187 y(rules)40 b(for)g(the)h(principal)f(sym)n(b)r(ols.)75 b(These)40 b(rules)g(giv)n(e)g(the)h(\\Mo)r(de)f(Con)n(v)n(ersion".)73 b(W)-7 b(e)330 1287 y(describ)r(e)27 b(in)h(particular)e(the)i(follo)n (wing)f(solutions:)p Black 455 1453 a Ft(\017)p Black 41 w FB(If)d(the)h(incoming)e(state)h(is)h(a)e(WKB-Lagrangian)e(state)j (asso)r(ciated)f(to)h(one)g(eigen)n(v)-5 b(alue)538 1553 y(and)31 b(a)g Fz(generic)j(L)l(agr)l(angian)g(manifold)p FB(,)h(the)d(outgoing)e(state)h(corresp)r(onding)e(to)j(the)538 1652 y(other)27 b(eigen)n(v)-5 b(alue)26 b(is)i(a)f Fz(Gaussian)j(c)l (oher)l(ent)g(state)p FB(.)p Black 455 1818 a Ft(\017)p Black 41 w FB(If)21 b(the)h(incoming)e(state)h(is)g(a)g Fz(Gaussian)j(c)l(oher)l(ent)g(state)d FB(asso)r(ciated)f(to)h(one)g (eigen)n(v)-5 b(alue,)538 1918 y(the)37 b(outgoing)f(state)h(splits)g (in)n(to)g(2)f(parts:)55 b(the)38 b(part)e(corresp)r(onding)f(to)i(the) h(same)538 2017 y(eigen)n(v)-5 b(alue)28 b(is)h(a)f Fz(non)j(Gaussian)h (c)l(oher)l(ent)f(state)p FB(,)f(while)f(the)g(part)g(corresp)r(onding) e(to)538 2117 y(the)g(other)f(eigen)n(v)-5 b(alue)25 b(is)i(a)f Fz(Gaussian)k(c)l(oher)l(ent)f(state)p FB(.)36 b(This)27 b(case)f(allo)n(ws)f(to)i(reco)n(v)n(er)538 2217 y(Hagedorn's)f(results)h([29)o(].)330 2383 y(W)-7 b(e)28 b(giv)n(e)f(precise)f(geometrical)g(rules)h(for)h(the)g (computation)f(of)g(the)h(principal)g(sym)n(b)r(ols.)455 2482 y(An)h(App)r(endix)h(on)f Fz(semi-classic)l(al)k(c)l(oher)l(ent)e (states)e FB(has)f(b)r(een)i(written,)g(b)r(ecause)e(there)330 2582 y(are)d(sev)n(eral)g(de\014nitions)i(in)g(the)f(literature)g(and)h (w)n(e)f(ha)n(v)n(e)f(here)h(an)g(example)g(of)h(co)r(existence)330 2682 y(of)38 b(Gaussian)g(and)g(non)g(Gaussian)f(coheren)n(t)h(states.) 69 b(Moreo)n(v)n(er,)38 b(w)n(e)g(w)n(an)n(ted)g(to)g(clarify)330 2781 y(the)29 b(b)r(eha)n(viour)e(of)h(Gaussian)f(coheren)n(t)g(states) h(w.r.)39 b(to)28 b(F)-7 b(ourier)27 b(In)n(tegral)g(Op)r(erators.)37 b(The)330 2881 y(starting)j(p)r(oin)n(t)h(will)g(b)r(e)g(the)g(pap)r (er)g([28)o(])g(b)n(y)f(V.)i(Guillemin)f(\(see)g(also)f([6)o(]\):)64 b(w)n(e)41 b(giv)n(e)e(a)330 2980 y(short)19 b(description)g(of)g(the)h (construction)e(of)i(the)g(\\semi-classical")c(symplectic)k(spinors)e (whic)n(h)330 3080 y(are)31 b(easily)g(guessed)h(from)f(original)g (Guillemin's)i(\\homogeneous")c(symplectic)j(spinors)f(or)330 3180 y(Boutet's)c(\\Hermite)h(op)r(erators")d(\(see)i([6]\).)455 3279 y(It)k(seems)f(also)g(to)h(b)r(e)h(p)r(ossible)e(to)h(extend)g(to) g(this)h(case)e(the)h(results)g(of)g(P)-7 b(.)30 b(G)n(\023)-39 b(erard,)30 b(C.)330 3379 y(F)-7 b(ermanian-Kammerer)30 b(and)i(C.)h(Lasser)e(\([26)o(],)j([20)o(],)h([21)o(])d(and)h([22)o (]\))g(on)f(the)h(propagation)330 3479 y(of)28 b(the)h(asso)r(ciated)d (semi-classical)h(measures:)36 b(their)28 b(results)g(mainly)g(dep)r (end)h(on)e(a)h(normal)330 3578 y(form,)f(for)g(more)g(particular)f (Hamiltonians,)i(whic)n(h)f(is)h(v)n(ery)e(close)h(to)g(ours.)455 3678 y(More)f(general)g(t)n(yp)r(e)h(of)g(crossings)f(could)h(b)r(e)g (studied)h(using)f(the)h(same)e(to)r(ols:)36 b(the)28 b(main)330 3778 y(h)n(yp)r(othesis)k(is)f(the)i(h)n(yp)r(erb)r(olicit)n (y)e(of)h(the)h(transv)n(ersal)c(dynamics.)50 b(W)-7 b(e)32 b(describ)r(e)g(also)f(the)330 3877 y(elliptic)21 b(case)f(where)f(only)h(a)h(formal)e(normal)h(form)g(is)g(founded)h (whic)n(h)f(allo)n(ws)f(to)i(describ)r(e)f(the)330 3977 y(coheren)n(t)27 b(states)g(remaining)f(close)h(to)h(the)g(singular)e (part)h(of)h(the)g(c)n(haracteristic)d(manifold.)455 4076 y(Finally)-7 b(,)33 b(w)n(e)e(describ)r(e)h(brie\015y)f(the)i (case)e(of)h(a)f(complex)h(Hermitian)g(principal)f(sym)n(b)r(ol.)330 4176 y(This)d(case)e(will)i(b)r(e)g(the)g(sub)5 b(ject)28 b(of)f(another)g(publication)h([10)o(].)455 4276 y(Man)n(y)i(authors)h (ha)n(v)n(e)f(recen)n(tly)h(studied)g(this)h(problem:)44 b(a)31 b(\(non)h(complete\))f(list)h(is)f([4],)330 4375 y([17)o(],)d([23)o(],)g([26)o(],)g([27)o(],)g([22)o(],)f([29)o(],)h ([31)o(],)g([32)o(],)g([35)o(])g(and)f([44)o(].)330 4650 y Fv(1)135 b(The)44 b(general)i(setting)330 4845 y FB(Let)494 4824 y Fs(b)475 4845 y Fu(H)30 b FB(b)r(e)24 b(a)f Fu(d)10 b Ft(\002)g Fu(d)24 b FB(self-adjoin)n(t)f(system)h(of)f (\(semi-classical\))f(pseudo-di\013eren)n(tial)h(equations)330 4944 y(of)h(order)e(0)h(on)g Fr(R)870 4914 y Fq(n)915 4944 y FB(.)36 b(Our)23 b(study)h(will)g(b)r(e)g(microlo)r(cal)e(in)i Fu(T)2177 4914 y Fq(?)2214 4944 y Fr(R)2274 4914 y Fq(n)2319 4944 y FB(,)g(so)f(w)n(e)h(will)f(alw)n(a)n(ys)f(reduce)h(to)330 5044 y(some)29 b(neigh)n(b)r(ourho)r(o)r(d)f(of)h(the)h(origine.)41 b Fu(H)1729 5056 y Fq(class)1883 5044 y FB(,)30 b(the)g(principal)f (sym)n(b)r(ol)f(of)2830 5023 y Fs(b)2811 5044 y Fu(H)6 b FB(,)30 b(is)g(assumed)330 5143 y(to)d(b)r(e)h Fz(r)l(e)l(al)i(value) l(d)57 b FB(and)27 b(hence)h(symmetric.)36 b(W)-7 b(e)28 b(will)f(reform)n(ulate)f(Braam-Duistermaat's)330 5243 y(analysis)g(in)i([7])f(in)h(the)g(semi-classical)e(con)n(text.)455 5579 y Fo(Our)31 b(basic)h(assumptions)f(are:)p Black 1809 5919 a FB(3)p Black eop %%Page: 4 4 4 3 bop Black Black Black 422 390 a Fo(1.)p Black 41 w(If)32 b(E)698 402 y Fn(0)762 390 y FB(=)23 b Fo(k)m(erH)1055 402 y Fn(class)1210 390 y FB(\()p Fo(0)p FB(\))q Fo(,)31 b(w)m(e)h(ha)m(v)m(e)h(dim)e(E)1997 402 y Fn(0)2062 390 y FB(=)22 b Fo(2)p Black 422 555 a(2.)p Black 41 w(The)30 b(mapping)g(z)24 b Ft(!)f Fo(H)1368 567 y Fn(class)1523 555 y FB(\()p Fo(z)p FB(\))31 b Fo(is)f(transv)m(ersal)i(at)f(the)f(p)s (oin)m(t)g(0)h(to)f(the)h(co)s(di-)538 654 y(mension)f(3)h(submanifold) 1631 833 y(W)1730 845 y Fn(2)1795 833 y Ft(\032)23 b Fo(Sym)p FB(\()p Fr(R)2158 798 y Fn(d)2204 833 y FB(\))538 1011 y Fo(de\014ned)31 b(b)m(y)i(W)1101 1023 y Fn(2)1165 1011 y FB(=)23 b Ft(f)p Fo(A)p Ft(j)p Fo(dim)31 b(k)m(erA)24 b FB(=)e Fo(2)p Ft(g)o Fo(.)538 1143 y(This)45 b(condition)g(is)h (equiv)-5 b(alen)m(t)46 b(to)g Fu(\016)s Fo(z)23 b Ft(!)p Fu(<)g(\016)s Fo(H)2302 1155 y Fn(class)2456 1143 y Fu(:)p Ft(j)p Fu(:)h(>)2614 1158 y Fp(j)p Fn(E)2683 1166 y Fm(0)2768 1143 y Fo(is)45 b(a)i(surjectiv)538 1243 y(mapping.)p Black 422 1407 a(3.)p Black 41 w(If)28 b(p)23 b FB(=)g Fo(det)p FB(\()p Fo(H)1036 1419 y Fn(class)1191 1407 y FB(\))p Fo(,)29 b(the)f(Hamiltonian)f(v)m(ector)j(\014eld)d Ft(X)2537 1419 y Fn(p)2612 1407 y Fo(of)h(p)h(v)-5 b(anishes)27 b(at)i(0)538 1507 y(and)j(its)f(linearization)g(admits)g(a)i(pair)f(of) f(non)h(zero)g(real)g(eigen)m(v)-5 b(alues)30 b Ft(\006)p Fu(\025)p Fo(.)538 1639 y(It)39 b(implies)f(that)i(\006)23 b FB(=)f Ft(f)p Fo(z)p Ft(j)p Fo(dim)31 b(k)m(erH)1879 1651 y Fn(class)2058 1639 y FB(=)23 b Fo(2)p Ft(g)38 b Fo(is)h(a)h(submanifold)e(of)i(co)s(di-)538 1738 y(mension)29 b(3)h(of)h(T)1162 1708 y Fq(?)1200 1738 y Fr(R)1260 1708 y Fn(n)1337 1738 y Fo(on)g(whic)m(h)g(the)f(symplectic)h(form)f Fu(!)k Fo(admits)c(a)h(k)m(ernel)538 1838 y(\(the)g(c)m(haracterictic)k (foliation\))c(of)g(dimension)f(1.)455 2001 y FB(If)e Fu(d)23 b FB(=)f(2,)28 b(w)n(e)f(can)g(write)h Fu(H)1340 2013 y Fq(class)1521 2001 y FB(as)1338 2224 y Fu(H)1407 2236 y Fq(class)1584 2224 y FB(=)1671 2107 y Fs(\022)1774 2174 y Fu(q)21 b FB(+)d Fu(r)157 b(s)1845 2273 y(s)d(q)22 b Ft(\000)c Fu(r)2261 2107 y Fs(\023)3224 2224 y FB(\(1\))358 2448 y(Our)27 b(assumptions)f(can)i(b)r(e)g(rewritten)f(as)g(follo)n (ws:)455 2547 y(\(i\))h Fu(q)s FB(\(0)p Fu(;)14 b FB(0\))22 b(=)h Fu(r)r FB(\(0)p Fu(;)14 b FB(0\))23 b(=)g Fu(s)p FB(\(0)p Fu(;)14 b FB(0\))22 b(=)h(0,)455 2647 y(\(ii\))28 b(The)g(di\013eren)n(tials)f Fu(dq)s(;)41 b(dr)n(;)h(ds)28 b FB(are)f(linearly)g(indep)r(enden)n(t)h(at)f(the)h(origin,)455 2747 y(\(iii\))g(The)g(P)n(oisson)d(brac)n(k)n(ets)h(satisfy)h Ft(f)p Fu(q)s(;)14 b(r)r Ft(g)1871 2717 y FA(2)1927 2747 y FB(+)k Ft(f)p Fu(q)s(;)c(s)p Ft(g)2210 2717 y FA(2)2264 2747 y Ft(\000)k(f)p Fu(r)n(;)c(s)p Ft(g)2542 2717 y FA(2)2602 2747 y Fu(>)22 b FB(0.)455 2846 y(The)g(previous)g (assumptions)g(are)g(structurally)g(stable.)35 b(The)23 b(generic)e(case)h(includes)h(also)330 2946 y(the)28 b(elliptic)g(case)f(where)g(the)h(pair)f(of)g(non)h(zero)e(eigen)n(v)-5 b(alues)27 b(is)g(purely)g(imaginary)-7 b(,)26 b(see)i([7)o(].)455 3046 y(Prop)r(ert)n(y)34 b(\(2\))j(sa)n(ys)f(that)h(\006)f(is)h(a)f (smo)r(oth)h(submanifold)f(of)h(co)r(dimension)f(3.)64 b(Let)37 b(us)330 3145 y(denote)28 b(b)n(y)f Fu(M)36 b FB(the)28 b(linearization)e(of)i Ft(X)1602 3157 y Fq(p)1668 3145 y FB(at)g(the)g(origin.)455 3245 y(Because)23 b Fu(M)34 b FB(is)24 b(of)h(rank)f(3,)h Fu(M)33 b FB(admits)25 b(an)f(h)n(yp)r(erb)r(olic)h(blo)r(c)n(k)f(and)g(a)h(2)f(dimensional)g (non)330 3344 y(trivial)j(Jordan)f(blo)r(c)n(k)i(with)g(0)f(as)g(eigen) n(v)-5 b(alue)27 b(and)h(hence)f(the)h(follo)n(wing)f(linear)g (symplectic)330 3444 y(normal)g(form)g(at)g(eac)n(h)g(p)r(oin)n(t)h(of) f(\006:)1069 3817 y Fu(M)32 b FB(=)1269 3551 y Fs(0)1269 3697 y(B)1269 3747 y(B)1269 3796 y(B)1269 3846 y(B)1269 3899 y(@)1384 3551 y(\022)1486 3617 y Fu(\025)119 b FB(0)1490 3717 y(0)86 b Ft(\000)p Fu(\025)1772 3551 y Fs(\023)2081 3668 y FB(0)248 b(0)1588 3867 y(0)1916 3750 y Fs(\022)2019 3816 y FB(0)82 b(0)2019 3916 y(1)g(0)2226 3750 y Fs(\023)2371 3867 y FB(0)1588 4016 y(0)451 b(0)248 b(0)2454 3551 y Fs(1)2454 3697 y(C)2454 3747 y(C)2454 3796 y(C)2454 3846 y(C)2454 3899 y(A)2568 3817 y Fu(:)633 b FB(\(2\))330 4190 y(The)23 b(linear)f(v)n(ector)g(\014eld)i(de\014ned)f(b)n(y)g Fu(M)31 b FB(is)23 b(the)h(Hamiltonian)f(v)n(ector)e(\014eld)j(of)f (the)g(quadratic)330 4290 y(form)k Fu(\025x)621 4302 y FA(1)660 4290 y Fu(\030)696 4302 y FA(1)752 4290 y Ft(\000)845 4257 y FA(1)p 845 4271 34 4 v 845 4318 a(2)888 4290 y Fu(x)935 4260 y FA(2)935 4310 y(2)972 4290 y FB(.)38 b(In)28 b(general,)e(the)i(Jordan)f(blo)r(c)n(k)g(could)g(ha)n(v)n(e)g Ft(\006)p FB(1)g(as)g(en)n(tries,)g(but)i(here)330 4389 y(the)f(+)f(sign)g(is)h(forced)f(b)n(y)g(the)h(signature)f(\(+)p Fu(;)14 b Ft(\000)p Fu(;)g Ft(\000)p Fu(;)g FB(0)p Fu(;)g Ft(\001)g(\001)g(\001)25 b Fu(;)14 b FB(0\))28 b(of)f Fu(p)2500 4359 y Fp(00)2570 4389 y FB(at)g(the)h(p)r(oin)n(ts)g(of)g (\006.)330 4663 y Fv(2)135 b(Examples)330 4862 y Fl(2.1)112 b(Born-Opp)s(enheimer)40 b(appro)m(ximation)f(\(stationnary)f(case\)) 330 5015 y FB(If)1499 5094 y Fs(b)1480 5115 y Fu(H)30 b FB(=)1678 5094 y Fs(b)1666 5115 y Fu(S)24 b Ft(\012)18 b FB(Id)g(+)g Fu(V)h FB(\()p Fu(x)p FB(\))1045 b(\(3\))330 5272 y(where)576 5251 y Fs(b)565 5272 y Fu(S)28 b FB(=)22 b Ft(\000)p Fu(h)844 5242 y FA(2)881 5272 y FB(\001)950 5284 y Fq(g)996 5272 y Ft(\000)8 b Fu(E)27 b FB(is)22 b(the)h(free)f(stationnary)f(Sc)n(hr\177)-42 b(odinger)20 b(equation)i(in)h Fr(R)2898 5242 y Fq(n)2965 5272 y FB(and)f Fu(V)41 b FB(is)22 b(a)330 5372 y(symmetric)h Fu(d)9 b Ft(\002)g Fu(d)23 b FB(matrix)g(p)r(oten)n(tial)g(whic)n(h)f(admits)h (a)g(generic)f(crossing)f(of)i(t)n(w)n(o)f(eigen)n(v)-5 b(alues)330 5471 y(along)25 b(a)h(co)r(dimension)g(2)h(submanifold)f Fu(S)31 b FB(in)c Fr(R)1864 5441 y Fq(n)1909 5471 y FB(,)g(the)g (previous)e(assumptions)h(are)g(satis\014ed)330 5571 y(at)31 b(the)h(p)r(oin)n(t)f(\()p Fu(x)881 5583 y FA(0)919 5571 y Fu(;)14 b(\030)992 5583 y FA(0)1030 5571 y FB(\),)32 b(where)f Fu(x)1408 5583 y FA(0)1475 5571 y Ft(2)f Fu(S)36 b FB(and)31 b Fu(E)26 b Ft(\000)21 b(k)p Fu(\030)2063 5583 y FA(0)2100 5571 y Ft(k)2142 5541 y FA(2)2210 5571 y FB(is)31 b(the)h(degenerate)e(eigen)n(v)-5 b(alue)30 b(of)330 5670 y Fu(V)19 b FB(\()p Fu(x)476 5682 y FA(0)514 5670 y FB(\),)28 b(if)g(and)f(only)h(if)g(the)g(v)n(elo)r(cit)n(y)e(2)p Fu(\030)1620 5682 y FA(0)1657 5670 y Fu(@)1701 5682 y Fq(x)1771 5670 y FB(is)i(transv)n(ersal)d(to)i Fu(S)32 b FB(at)c(the)g(p)r(oin)n(t)g Fu(x)2969 5682 y FA(0)3006 5670 y FB(.)p Black 1809 5919 a(4)p Black eop %%Page: 5 5 5 4 bop Black Black 330 390 a Fl(2.2)112 b(Born-Opp)s(enheimer)27 b(appro)m(ximation)g(\(time)e(dep)s(enden)m(t)h(case\))330 543 y FB(W)-7 b(e)28 b(can)f(also)g(apply)g(our)g(results)g(to)g(the)h (time)g(dep)r(enden)n(t)h(Sc)n(hr\177)-42 b(odinger)26 b(equation)1466 705 y Fs(b)1447 726 y Fu(H)j FB(=)1645 705 y Fs(b)1633 726 y Fu(S)23 b Ft(\012)18 b FB(Id)h(+)f Fu(V)h FB(\()p Fu(x;)14 b(t)p FB(\))1011 b(\(4\))330 919 y(where)578 898 y Fs(b)566 919 y Fu(S)28 b FB(=)23 b Fu(ih@)854 931 y Fq(t)893 919 y Ft(\000)11 b Fu(h)1017 889 y FA(2)1053 919 y FB(\001)1122 931 y Fq(g)1185 919 y FB(and)23 b Fu(V)43 b FB(is)23 b(a)g(symmetric)h Fu(d)11 b Ft(\002)g Fu(d)23 b FB(matrix)g(p)r(oten)n(tial)g(whic)n(h)h(admits)f (a)330 1019 y(generic)d(crossing)g(of)h(t)n(w)n(o)g(eigen)n(v)-5 b(alues)20 b(along)g(a)h(co)r(dimension)g(2)g(manifold)g Fu(S)28 b Ft(\032)23 b Fr(R)6 b Ft(\002)g Fr(R)3085 989 y Fq(n)3129 1019 y FB(.)35 b(The)330 1118 y(previous)22 b(h)n(yp)r(othesis)g(are)g(satis\014ed)g(at)h(the)g(p)r(oin)n(t)g(\()p Fu(t)2017 1130 y FA(0)2054 1118 y Fu(;)14 b(\034)2127 1130 y FA(0)2165 1118 y Fu(;)g(x)2249 1130 y FA(0)2286 1118 y Fu(;)g(\030)2359 1130 y FA(0)2397 1118 y FB(\))23 b(if)g(\()p Fu(t)2585 1130 y FA(0)2623 1118 y Fu(;)14 b(x)2707 1130 y FA(0)2744 1118 y FB(\))24 b Ft(2)f Fu(S)5 b FB(,)24 b Fu(\034)3017 1130 y FA(0)3063 1118 y Ft(\000)9 b(k)p Fu(\030)3215 1130 y FA(0)3251 1118 y Ft(k)3293 1088 y FA(2)330 1218 y FB(is)32 b(the)h(degenerate)f(eigen)n(v)-5 b(alue)31 b(of)i Fu(V)19 b FB(\()p Fu(x)1634 1230 y FA(0)1672 1218 y Fu(;)14 b(t)1739 1230 y FA(0)1776 1218 y FB(\)\))31 b(=)g(0)h(and)h(the)g(v)n(ector)e(\014eld)i Ft(\000)p Fu(@)2904 1230 y Fq(t)2954 1218 y FB(+)22 b(2)p Fu(\030)3119 1230 y FA(0)3156 1218 y Fu(@)3200 1230 y Fq(x)3274 1218 y FB(is)330 1318 y(transv)n(ersal)j(to)j Fu(S)k FB(at)27 b(the)h(p)r(oin)n(t)g(\()p Fu(t)1459 1330 y FA(0)1497 1318 y Fu(;)14 b(x)1581 1330 y FA(0)1618 1318 y FB(\).)330 1550 y Fl(2.3)150 b(Adiabatic)38 b(limit)g(with)f(extra)g(parameters) 330 1703 y FB(This)24 b(example)g(is)g(v)n(ery)f(close)h(to)g(the)g (case)g(studied)g(in)h(our)e(pap)r(er)h([11)o(].)36 b(Let)24 b(us)h(consider)e(the)330 1803 y(follo)n(wing)k(adiabatic)f(ev)n (olution)h(problem:)1529 1968 y(1)p 1529 2005 42 4 v 1535 2081 a Fu(i)1591 1968 y(du)p 1591 2005 91 4 v 1594 2081 a(d\022)1714 2024 y FB(=)c Fu(A)p FB(\()p Fu(x;)14 b("\022)r FB(\))p Fu(u)330 2235 y FB(where)27 b Fu(A)p FB(\()p Fu(x;)14 b(t)p FB(\))29 b(is)e(a)h Fu(d)18 b Ft(\002)g Fu(d)28 b FB(real)f(symmetric)g(matrix.)455 2334 y(Here)d Fu(x)h FB(is)g(a)g(real)e(extra)h(parameter)g(close)g(to) h(0.)35 b(The)25 b(goal)f(is)g(to)h(get)g(uniform)f(estimates)330 2434 y(w.r.)41 b(to)29 b(the)g(small)g(parameters)f Fu(")g FB(and)h Fu(x)h FB(W)-7 b(e)29 b(can)g(transform)f(this)h(equation)g (in)n(to)g(a)f(semi-)330 2534 y(classical)e(problem:)37 b(b)n(y)27 b(putting)h Fu(t)23 b FB(=)g Fu("\022)r FB(,)k(w)n(e)h(get) 1556 2699 y Fu(")p 1556 2736 39 4 v 1561 2812 a(i)1614 2699 y(du)p 1614 2736 91 4 v 1623 2812 a(dt)1738 2755 y FB(=)23 b Fu(A)p FB(\()p Fu(x;)14 b(t)p FB(\))p Fu(u)330 2965 y FB(where)25 b Fu(")h FB(is)g(the)g(semi-classical)e(parameter.) 35 b(The)26 b(principal)g(sym)n(b)r(ol)f(is)h Fu(A)p FB(\()p Fu(x;)14 b(t)p FB(\))i Ft(\000)f Fu(\034)9 b FB(Id)q(.)36 b(The)330 3065 y(h)n(yp)r(othesis)f(are)f(ful\014lled)i (at)f(the)g(p)r(oin)n(t)h(\(0)p Fu(;)14 b(t)1823 3077 y FA(0)1860 3065 y Fu(;)g(\030)1933 3077 y FA(0)1970 3065 y Fu(;)g(\034)2043 3077 y FA(0)2081 3065 y FB(\))35 b(if)h(and)f(only)f(if)i(dim)14 b(k)n(er)o(\()p Fu(A)p FB(\(0)p Fu(;)g(t)3172 3077 y FA(0)3210 3065 y FB(\))23 b Ft(\000)330 3165 y Fu(\034)366 3177 y FA(0)404 3165 y FB(Id\))g(=)g(2)k(and)g(\()p Fu(x;)14 b(t;)g(\034)9 b FB(\))25 b Ft(!)e Fu(A)p FB(\()p Fu(x;)14 b(t)p FB(\))19 b Ft(\000)g Fu(\034)9 b FB(Id)28 b(is)f(transv)n(ersal)f(to)h Fu(W)2420 3177 y FA(2)2485 3165 y FB(at)h(that)g(p)r(oin)n(t.)330 3397 y Fl(2.4)112 b(Maxw)m(ell)39 b(equations)330 3550 y FB(W)-7 b(e)30 b(consider)f(the)h(stationnary)f(Maxw)n(ell)g (equations)g(for)g(an)g(electromagnetic)g(\014eld)h(inside)330 3650 y(a)35 b(non)h(homogeneous)e(and)h(non)h(isotropic)e(medium)j (\(see)e([38)o(]\).)62 b(In)36 b(this)g(case)e(the)i(semi-)330 3750 y(classical)23 b(regime)g(is)h(the)h(high)f(frequency)g(regime)f (and)h(the)g(corresp)r(onding)f(geometry)g(is)h(the)330 3849 y(geometrical)e(optic.)35 b(Let)23 b(us)h(giv)n(e)e(a)h Fz(diele)l(ctric)k(tensor)c Fu(")p FB(\()p Fu(x)p FB(\))h(\(a)f (Riemannian)g(metric)h(on)e Fr(R)3237 3819 y FA(3)3275 3849 y FB(\),)330 3949 y Fu(\026)h FB(the)h(magnetic)e(p)r(ermeabilit)n (y)h(and)g Fu(c)g FB(the)h(ligh)n(t)e(v)n(elo)r(cit)n(y)-7 b(,)24 b(w)n(e)e(get)h(the)h(follo)n(wing)e(disp)r(ersion)330 4048 y(matrix)27 b(\(see)h([38)o(]\):)1476 4192 y Fu(\026)p 1464 4229 74 4 v 1464 4305 a(c)1500 4281 y FA(2)1547 4248 y Fu(")p FB(\()p Fu(x)p FB(\))19 b Ft(\000)f(k)p Fu(\030)t Ft(k)1923 4213 y FA(2)1960 4248 y FB(Pro)5 b(j)2120 4268 y Fq(\030)2152 4251 y Fk(?)330 4425 y FB(Generically)32 b(\006)h(consists)g(of)g(4)g(branc)n(hes)e(\()p Fu(x;)14 b Ft(\006)p Fu(\030)1918 4437 y Fq(j)1954 4425 y FB(\()p Fu(x)p FB(\)\))p Fu(;)48 b(j)38 b FB(=)31 b(1)p Fu(;)14 b FB(2)p Fu(:)33 b FB(The)g(algebraic)e(surfaces)330 4525 y Fu(p)p FB(\()p Fu(x)451 4537 y FA(0)489 4525 y Fu(;)14 b(\030)t FB(\))25 b(=)g(0)j(are)g(called)g(the)h Fz(F)-6 b(r)l(esnel)31 b(surfac)l(es)p FB(.)41 b(It)29 b(is)f(pro)n(v)n(en)g(in)h([7)o(],)g(that)g(the)h(h)n(yp)r(erb)r(olic) 330 4624 y(case)d(as)g(w)n(ell)g(as)g(the)h(elliptic)g(case)f(can)g(o)r (ccur.)330 4857 y Fl(2.5)112 b(Acoustical)38 b(w)m(a)m(v)m(es)330 5010 y FB(W)-7 b(e)32 b(consider)f(the)h(propagation)e(of)h(acoustical) g(w)n(a)n(v)n(es)f(in)i(elastic)f(media.)49 b(The)32 b(disp)r(ersion)330 5110 y(matrix)27 b(is)h(giv)n(en)e(b)n(y:)1351 5209 y Fu(D)r FB(\()p Fu(x;)14 b(\030)t FB(\))24 b(=)f Fu(\032)p FB(\()p Fu(x)p FB(\)Id)c Ft(\000)f Fu(C)6 b FB(\()p Fu(x;)14 b(\030)t FB(\))330 5359 y(where)33 b Fu(\032)p FB(\()p Fu(x)p FB(\))g Fu(>)f FB(0)g(is)h(the)h(densit)n(y)f (and)g Fu(\030)j Ft(!)d Fu(C)6 b FB(\()p Fu(x;)14 b(\030)t FB(\),)36 b(the)d Fz(elastic)j(tensor)p FB(,)e(is)f(a)g(quadratic)330 5458 y(map)f(on)g Fr(R)699 5428 y FA(3)769 5458 y FB(with)h(v)-5 b(alues)32 b(in)g(the)h(p)r(ositiv)n(e)f(de\014nite)h(symmetric)f(3)21 b Ft(\002)g FB(3)32 b(matrices.)50 b(In)33 b(this)330 5558 y(case)c(they)h(are)e(at)i(most)f(16)g(singular)f(p)r(oin)n(ts)i (on)f(det\()p Fu(D)r FB(\()p Fu(x)2241 5570 y FA(0)2280 5558 y Fu(;)14 b(:)p FB(\)\))27 b(=)f(0)j(\(see)g([34]\).)43 b(They)29 b(can)330 5658 y(b)r(e)f(elliptic)g(or)f(h)n(yp)r(erb)r(olic) g(\(see)g([7]\).)p Black 1809 5919 a(5)p Black eop %%Page: 6 6 6 5 bop Black Black 330 390 a Fl(2.6)112 b(Oceanograph)m(y)330 543 y FB(The)31 b(mo)r(de)g(con)n(v)n(ersion)e(problem)h(has)h(also)f (b)r(een)h(considered)f(in)h(o)r(ceanograph)n(y)-7 b(,)29 b(see)i([33)o(],)330 643 y([45)o(].)330 875 y Fl(2.7)112 b(The)38 b(Landau-Zener)j(mo)s(del)330 1029 y FB(W)-7 b(e)28 b(denote)f(b)n(y)1494 1153 y Fs(c)1482 1174 y Fu(H)1551 1186 y FA(0)1611 1174 y FB(=)1699 1056 y Fs(\022)1802 1123 y Fu(D)1871 1135 y FA(1)1991 1123 y Fu(x)2038 1135 y FA(2)1812 1223 y Fu(x)1859 1235 y FA(2)1991 1223 y Fu(x)2038 1235 y FA(1)2117 1056 y Fs(\023)330 1384 y FB(with)h Fu(D)588 1396 y FA(1)648 1384 y FB(=)746 1351 y Fq(h)p 746 1365 39 4 v 754 1412 a(i)840 1351 y(@)p 805 1365 110 4 v 805 1412 a(@)t(x)882 1420 y Fj(1)951 1384 y FB(and)g(b)n(y)1493 1549 y Fu(H)1562 1561 y FA(0)1622 1549 y FB(=)1710 1432 y Fs(\022)1818 1499 y Fu(\030)1854 1511 y FA(1)1980 1499 y Fu(x)2027 1511 y FA(2)1812 1598 y Fu(x)1859 1610 y FA(2)1980 1598 y Fu(x)2027 1610 y FA(1)2106 1432 y Fs(\023)330 1748 y FB(its)h(W)-7 b(eyl)29 b(sym)n(b)r(ol.)40 b(Hyp)r(othesis)29 b(\(1\),)g(\(2\))g(and)g(\(3\))g (are)f(satis\014ed)g(at)h(the)g(p)r(oin)n(ts)g Fu(x)3003 1760 y FA(1)3066 1748 y FB(=)c Fu(x)3203 1760 y FA(2)3265 1748 y FB(=)330 1848 y Fu(\030)366 1860 y FA(1)427 1848 y FB(=)d(0.)455 1948 y(The)31 b(system)921 1927 y Fs(c)909 1948 y Fu(H)978 1960 y FA(0)1015 1948 y FB(,)i(whic)n(h)f(is)g(closely) f(related)g(to)g(the)i(case)e(computed)h(b)n(y)f(Landau)g(and)330 2047 y(Zener,)c(will)h(b)r(e)g(our)f(lo)r(cal)g(mo)r(del.)455 2147 y(It)k(will)h(b)r(e)f(usefull)h(to)f(denote)g(b)n(y)g Ft(X)1644 2159 y Fq(p)1714 2147 y FB(\(resp.)48 b Ft(X)2025 2159 y FA(0)2062 2147 y FB(\))32 b(the)f(Hamiltonian)h(v)n(ector)d (\014eld)j(of)f Fu(p)330 2247 y FB(\(resp.)37 b Fu(p)613 2259 y FA(0)673 2247 y FB(=)22 b Fu(x)807 2259 y FA(1)845 2247 y Fu(\030)881 2259 y FA(1)937 2247 y Ft(\000)c Fu(x)1067 2216 y FA(2)1067 2267 y(2)1105 2247 y FB(\).)37 b(W)-7 b(e)28 b(ha)n(v)n(e:)1287 2429 y Ft(X)1346 2441 y FA(0)1407 2429 y FB(=)23 b Fu(x)1542 2441 y FA(1)1579 2429 y Fu(@)1623 2441 y Fq(x)1661 2449 y Fj(1)1716 2429 y Ft(\000)18 b Fu(\030)1835 2441 y FA(1)1873 2429 y Fu(@)1917 2441 y Fq(\030)1947 2449 y Fj(1)2002 2429 y FB(+)g(2)p Fu(x)2174 2441 y FA(2)2211 2429 y Fu(@)2255 2441 y Fq(\030)2285 2449 y Fj(2)2350 2429 y Fu(:)330 2662 y Fl(2.8)112 b(Av)m(oided)38 b(crossings)330 2815 y FB(Let)c(us)f(assume)g(that)h(our)f(system)1533 2794 y(^)1511 2815 y Fu(H)7 b(u)33 b FB(=)f(0)h(dep)r(ends)h(on)g(a)f (real)g(parameter)f Fu(a)p FB(.)54 b(W)-7 b(e)34 b(can)330 2915 y(add)28 b Fu(a)h FB(as)e(another)h(co)r(ordinate)f(\(lik)n(e)h (some)g Fu(x)1823 2927 y Fq(n)p FA(+1)1953 2915 y FB(\))h(and)f(w)n(e)g (assume)f(that)i(the)g(new)f(system)330 3027 y(satis\014es)f(our)h(h)n (yp)r(othesis)g(\(1\),)g(\(2\))g(and)g(\(3\).)39 b(Then)29 b(w)n(e)f(get)g(the)g(normal)f(form)2930 3006 y Fs(c)2918 3027 y Fu(H)2987 3039 y FA(0)3053 3027 y FB(and)h(the)330 3126 y(op)r(erator)e(^)-43 b Fu(a)26 b FB(\(m)n(ultiplication)h(b)n(y)g Fu(a)p FB(\))g(comm)n(ute)f(with)h(it.)37 b(So)26 b(w)n(e)h(see)f(that) h(the)g(W)-7 b(eyl)27 b(sym)n(b)r(ol)330 3226 y(of)34 b(^)-43 b Fu(a)32 b FB(is)g(a)h(function)g(of)f(\()p Fu(x)1177 3238 y FA(2)1215 3226 y Fu(;)14 b(x)1299 3196 y Fp(0)1323 3226 y Fu(;)g(\030)1400 3196 y Fp(0)1423 3226 y FB(\).)52 b(If)33 b(w)n(e)g(assume)e(moreo)n(v)n(er)f(that)j Fu(@)5 b(a=@)g(x)2816 3238 y FA(2)2884 3226 y Ft(6)p FB(=)31 b(0,)i(w)n(e)f(can)330 3326 y(reco)n(v)n(er)25 b Fu(x)661 3338 y FA(2)726 3326 y FB(as)i(a)h(function)g(of)f(\()p Fu(a;)14 b(x)1477 3296 y Fp(0)1501 3326 y Fu(;)g(\030)1578 3296 y Fp(0)1601 3326 y FB(\))28 b(so)f(that)h(w)n(e)f(get)h(a)f (normal)g(form)1502 3543 y Fs(b)1482 3564 y Fu(H)1551 3576 y Fq(a)1614 3564 y FB(=)1702 3447 y Fs(\022)1829 3498 y(b)1815 3520 y Fu(\030)1851 3532 y FA(1)1982 3520 y Fu(P)2035 3532 y Fq(a)1805 3619 y Fu(P)1870 3589 y Fq(t)1858 3640 y(a)1986 3619 y Fu(x)2033 3631 y FA(1)2117 3447 y Fs(\023)330 3803 y FB(where)e Fu(P)621 3815 y Fq(a)686 3803 y FB(is)g(an)g Fu(a)p Ft(\000)p FB(dep)r(enden)n(t)g (pseudo-di\013eren)n(tial)f(op)r(erator)g(w.r.)35 b(to)25 b Fu(x)2730 3773 y Fp(0)2779 3803 y FB(only)-7 b(.)36 b(This)25 b(w)n(a)n(y)-7 b(,)330 3903 y(w)n(e)27 b(see)g(ho)n(w)g(to)h (reco)n(v)n(er)d(the)j(results)f(of)h([31)o(])f(and)h([32)o(].)330 4177 y Fv(3)177 b(Reduction)43 b(of)g(high)f(dimensional)i(systems)f (to)g(2)f(di-)532 4327 y(mensional)k(systems)330 4521 y FB(Let)33 b(us)h(consider)e(a)h Fu(d)22 b Ft(\002)g Fu(d)34 b FB(symmetric)f(matrix)f(of)i(pseudo-di\013eren)n(tial)e(op)r (erators)3107 4500 y Fs(b)3087 4521 y Fu(H)40 b FB(and)330 4621 y(assume)24 b(that)h(its)g(principal)g(sym)n(b)r(ol)f Fu(H)1598 4633 y Fq(class)1752 4621 y FB(\(0\))h(at)g(some)f(p)r(oin)n (t)h(0)g(is)g(singular)e(with)j(a)e(k)n(ernel)330 4720 y(of)31 b(dimension)h(2.)47 b(Then)32 b(it)g(is)f(w)n(ell)g(kno)n(wn)g (that)g(w)n(e)g(can)g(\014nd)h(an)f(in)n(v)n(ertible)g(matrix)f Fu(A)i FB(of)330 4820 y(pseudo-di\013eren)n(tial)c(op)r(erators)f(suc)n (h)h(that)h Fu(A)1824 4790 y Fq(t)1873 4799 y Fs(b)1854 4820 y Fu(H)7 b(A)29 b FB(splits)g(mo)r(d)g Fu(O)r FB(\()p Fu(h)2573 4790 y Fp(1)2644 4820 y FB(\))g(in)n(to)g(a)f(direct)h(sum) 330 4932 y(of)c(a)f(2)12 b Ft(\002)g FB(2)24 b(symmetric)g(system)1370 4911 y Fs(c)1358 4932 y Fu(H)1427 4944 y FA(1)1489 4932 y FB(whose)g(principal)g(sym)n(b)r(ol)g(v)-5 b(anishes)24 b(at)g(the)h(p)r(oin)n(t)g(0)f(and)330 5032 y(a)i(\()p Fu(d)16 b Ft(\000)g FB(2\))f Ft(\002)h FB(\()p Fu(d)g Ft(\000)f FB(2\))27 b(system)1297 5011 y Fs(c)1286 5032 y Fu(H)1355 5044 y FA(2)1418 5032 y FB(whic)n(h)g(is)f(in)n(v)n (ertible)f(at)h(the)h(p)r(oin)n(t)g(0)f(\(see)g(for)g(example)f([7])330 5132 y(and)i([17]\).)455 5231 y Fo(Hence,)k(w)m(e)g(will)g(w)m(ork)h (in)g(what)g(follo)m(ws)f(with)g(a)h FB(2)18 b Ft(\002)g FB(2)32 b Fo(system.)455 5331 y FB(W)-7 b(e)29 b(will)f(deriv)n(e)g(a)h (semi-classical)d(normal)i(form)g(in)h(the)g(follo)n(wing)f(w)n(a)n(y:) 38 b(w)n(e)28 b(\014rst)h(w)n(ork)330 5431 y(on)37 b(the)h(classical)e (lev)n(el)g(where)h(w)n(e)g(giv)n(e)g(a)f(re\014ned)i(v)n(ersion)d(of)j (the)f(Braam-Duistermaat)330 5530 y(normal)27 b(form.)36 b(W)-7 b(e)28 b(then)g(pro)r(ceed)f(on)g(the)h(semi-classical)e(lev)n (el.)p Black 1809 5919 a(6)p Black eop %%Page: 7 7 7 6 bop Black Black 330 390 a Fv(4)135 b(T)-11 b(ec)l(hnical)45 b(Lemmas)330 572 y FB(Our)30 b(canonical)g(co)r(ordinates)f(will)i(b)r (e)g(\()p Fu(x)1671 584 y FA(1)1709 572 y Fu(;)14 b(\030)1782 584 y FA(1)1819 572 y FB(;)g Fu(x)1903 584 y FA(2)1941 572 y Fu(;)g(\030)2014 584 y FA(2)2051 572 y FB(;)g Fu(x)2135 542 y Fp(0)2159 572 y Fu(;)g(\030)2236 542 y Fp(0)2259 572 y FB(\))32 b(with)f Fu(!)g FB(=)d Fu(d\030)2770 584 y FA(1)2828 572 y Ft(^)21 b Fu(dx)2994 584 y FA(1)3052 572 y FB(+)f Fu(d\030)3216 584 y FA(2)3275 572 y Ft(^)330 672 y Fu(dx)420 684 y FA(2)473 672 y FB(+)15 b Ft(\001)f(\001)g(\001)g FB(.)36 b(The)26 b(asso)r(ciated)f(P)n(oisson)f(brac)n(k)n(et)h(will)h (b)r(e)g(denoted)g(b)n(y)g Ft(f)p Fu(:;)14 b(:)p Ft(g)p FB(.)36 b(W)-7 b(e)26 b(will)g(denote)330 771 y(b)n(y)32 b Fu(Z)37 b FB(the)32 b(h)n(yp)r(erplane)f Ft(f)p Fu(x)1211 783 y FA(2)1279 771 y FB(=)e(0)p Ft(g)p FB(,)k(b)n(y)e Fu(Y)51 b FB(the)32 b(subspace)f Fu(Y)49 b FB(=)29 b Ft(f)p Fu(x)2509 783 y FA(1)2577 771 y FB(=)g Fu(\030)2707 783 y FA(1)2775 771 y FB(=)h(0)p Ft(g)h FB(and)g(b)n(y)h(\006)330 871 y(their)c(in)n(tersection)1203 971 y(\006)23 b(=)g Fu(Y)37 b Ft(\\)19 b Fu(Z)29 b FB(=)22 b Ft(f)p Fu(x)1795 983 y FA(1)1856 971 y FB(=)g Fu(\030)1979 983 y FA(1)2040 971 y FB(=)g Fu(x)2174 983 y FA(2)2235 971 y FB(=)h(0)p Ft(g)k Fu(:)330 1120 y FB(This)38 b(notation)g(could)g(seem)f(to)h(b)r (e)h(confusing,)h(but)f(this)f(\006)h(is)f(the)g(previous)f(\006)h(for) g(the)330 1220 y(Landau-Zener)26 b(mo)r(del.)455 1319 y(F)-7 b(or)30 b Fu(n)g Ft(2)g Fr(N)21 b Ft([)g(1)p FB(,)33 b Fu(f)38 b FB(=)29 b Fu(O)1304 1331 y Fq(V)1362 1319 y FB(\()p Fu(n)p FB(\))j(means)f(that)h Fu(f)40 b FB(is)31 b(of)h(of)f(order)f Fu(n)h FB(transv)n(ersally)e(to)j(the)330 1419 y(submanifold)23 b Fu(V)c FB(,)25 b(i.e.)35 b(the)24 b(T)-7 b(a)n(ylor)22 b(expansion)g(of)i Fu(f)32 b FB(starts)22 b(with)i(terms)g(of)f(degree)f Ft(\025)h Fu(n)g FB(along)330 1518 y Fu(V)c FB(.)455 1618 y(W)-7 b(e)28 b(will)f(need)h(the)g(follo)n (wing)f(Lemmas:)p Black 330 1801 a Fo(Lemma)32 b(1)p Black 41 w Fz(The)37 b(e)l(quation)f Ft(f)p Fu(X)r(;)14 b(x)1468 1813 y FA(1)1505 1801 y Fu(\030)1541 1813 y FA(1)1578 1801 y Ft(g)34 b FB(=)f Fu(R)k Fz(admits)f(a)h(smo)l(oth)f (solution)g Fu(X)42 b Fz(if)37 b(and)f(only)330 1900 y(if)c(the)f(T)-6 b(aylor)32 b(exp)l(ansion)g(of)g Fu(R)f Fz(admits)h(no)f(monomials)h FB(\()p Fu(x)2284 1912 y FA(1)2322 1900 y Fu(\030)2358 1912 y FA(1)2396 1900 y FB(\))2428 1870 y Fq(k)2469 1900 y Fz(.)42 b(The)32 b(same)f(r)l(esult) g(holds)330 2000 y(with)f(smo)l(oth)h(dep)l(endenc)l(e)f(of)h(p)l(ar)l (ameters.)455 2100 y(The)36 b(e)l(quation)f Ft(f)p Fu(X)r(;)14 b(x)1163 2112 y FA(1)1200 2100 y Fu(\030)1236 2112 y FA(1)1274 2100 y Ft(g)21 b FB(+)h Fu(Y)d(x)1538 2112 y FA(1)1576 2100 y Fu(\030)1612 2112 y FA(1)1682 2100 y FB(=)33 b Fu(R)j Fz(admits)g(a)f(smo)l(oth)h(solution)f FB(\()p Fu(X)r(;)14 b(Y)19 b FB(\))35 b Fz(if)h(and)330 2199 y(only)29 b(if)g Fu(R)g Fz(vanishes)g(at)f(the)g(origine.)40 b(The)29 b(same)g(r)l(esult)e(holds)j(with)e(smo)l(oth)h(dep)l(endenc)l (e)g(of)330 2299 y(p)l(ar)l(ameters.)330 2482 y(Pr)l(o)l(of.{)p Black Black 566 2648 a FB(The)g(\014rst)f(assertion)f(is)i(pro)n(v)n (en)e(in)i([13)o(].)40 b(The)29 b(second)f(one)g(is)g(a)h(trivial)f (conse-)538 2747 y(quence:)33 b(it)21 b(is)f(enough)g(to)h(c)n(ho)r (ose)e Fu(Y)39 b FB(so)20 b(that)h Fu(R)5 b Ft(\000)t Fu(Y)19 b(x)2229 2759 y FA(1)2266 2747 y Fu(\030)2302 2759 y FA(1)2361 2747 y FB(admits)h(no)h(monomials)538 2847 y(\()p Fu(x)617 2859 y FA(1)655 2847 y Fu(\030)691 2859 y FA(1)728 2847 y FB(\))760 2817 y Fq(k)829 2847 y FB(in)28 b(its)g(T)-7 b(a)n(ylor)25 b(expansion.)3265 3013 y Fi(\003)p Black 330 3196 a Fo(Lemma)32 b(2)p Black 41 w Fz(The)f(e)l(quation)1569 3295 y Fu(tU)1665 3261 y Fp(0)1656 3316 y Fq(x)1716 3295 y Ft(\000)18 b Fu(U)31 b FB(=)23 b Fu(R)30 b(;)1133 b FB(\(5\))330 3445 y Fz(wher)l(e)42 b Fu(R)h FB(=)g Fu(O)r FB(\()p Fu(t)917 3414 y Fp(1)988 3445 y FB(\))e Fz(is)h(a)f(c)l(omp)l(actly)h(supp)l(orte)l(d)f(smo)l (oth)h(function)e(of)i FB(\()p Fu(x;)14 b(t)p FB(\))p Fz(,)45 b(admits)d(a)330 3544 y(smo)l(oth)30 b(solution)g Fu(U)i FB(=)23 b Fu(O)r FB(\()p Fu(t)1230 3514 y Fp(1)1301 3544 y FB(\))p Fz(.)330 3727 y(Pr)l(o)l(of.{)p Black Black 565 3893 a FB(The)28 b(smo)r(oth)f(function)h Fu(U)37 b FB(de\014ned)28 b(b)n(y)1225 4130 y Fu(U)9 b FB(\()p Fu(x;)14 b(t)p FB(\))24 b(=)e Ft(\000)1659 4017 y Fs(Z)1742 4038 y FA(0)1705 4206 y Fp(\0001)1841 4130 y Fu(e)1880 4096 y Fq(u)1923 4130 y Fu(R)q FB(\()p Fu(x)d Ft(\000)f Fu(tu;)c(t)p FB(\))p Fu(du)538 4366 y FB(satis\014es)26 b(the)i(equation)f(\(5\))h(and)g(and)f(is)g(\015at)h(on)f Fu(t)c FB(=)g(0.)3265 4533 y Fi(\003)p Black 330 4715 a Fo(Lemma)32 b(3)p Black 41 w Fz(L)l(et)24 b Fu(p)938 4727 y FA(0)998 4715 y FB(=)f Fu(x)1133 4727 y FA(1)1171 4715 y Fu(\030)1207 4727 y FA(1)1252 4715 y Ft(\000)8 b Fu(x)1372 4685 y FA(2)1372 4736 y(2)1434 4715 y Fz(and)26 b Fu(\032)f Fz(a)g(given)h(smo)l(oth)f(function,)h(vanishing)h(on)e FB(\006)p Fz(,)h(ther)l(e)330 4815 y(exist)j(smo)l(oth)i(functions)e Fu(U)39 b Fz(and)30 b Fu(V)49 b Fz(such)29 b(that)1475 4997 y Ft(f)p Fu(U;)14 b(p)1653 5009 y FA(0)1689 4997 y Ft(g)k FB(+)g Fu(V)h(p)1941 5009 y FA(0)2001 4997 y FB(=)k Fu(\032)30 b(:)1039 b FB(\(6\))455 5180 y Fz(Mor)l(e)l(over,)35 b(if)f Fu(\032)c FB(=)f Fu(O)1163 5192 y FA(\006)1214 5180 y FB(\()p Fu(N)9 b FB(\))p Fz(,)35 b(we)f(c)l(an)f(cho)l(ose)h Fu(U)k FB(=)29 b Fu(O)2215 5192 y FA(\006)2267 5180 y FB(\()p Fu(N)9 b FB(\))34 b Fz(and)f Fu(V)49 b FB(=)28 b Fu(O)2858 5192 y FA(\006)2910 5180 y FB(\()p Fu(N)i Ft(\000)21 b FB(2\))p Fz(.)49 b(If)330 5280 y Fu(\032)23 b Ft(2)g Fu(O)537 5292 y Fq(Z)591 5280 y FB(\()p Ft(1)p FB(\))c Ft(\\)g Fu(O)894 5292 y Fq(Y)952 5280 y FB(\()p Fu(N)9 b FB(\))p Fz(,)30 b(we)g(c)l(an)g(cho)l(ose)h Fu(V)42 b FB(=)23 b(0)29 b Fz(and)h Fu(U)i Ft(2)23 b Fu(O)2326 5292 y Fq(Z)2380 5280 y FB(\()p Ft(1)p FB(\))c Ft(\\)g Fu(O)2683 5292 y Fq(Y)2741 5280 y FB(\()p Fu(N)9 b FB(\))p Fz(.)330 5462 y(Pr)l(o)l(of.{)p Black Black Black 1809 5919 a FB(7)p Black eop %%Page: 8 8 8 7 bop Black Black Black 637 390 a Ft(\017)p Black 41 w FB(W)-7 b(e)27 b(\014rst)g(solv)n(e)f(equation)g(\(6\))h(formally)f (with)h(resp)r(ect)g(to)g Fu(x)2654 402 y FA(2)2692 390 y FB(:)36 b(expanding)720 490 y(ev)n(erything)h(in)h(p)r(o)n(w)n(er)e (series)g(of)i Fu(x)1882 502 y FA(2)1920 490 y FB(,)i(namely)d Fu(U)49 b FB(=)2491 428 y Fs(P)2579 448 y Fp(1)2579 515 y Fq(j)s FA(=0)2712 490 y Fu(U)2769 502 y Fq(j)2803 490 y Fu(x)2850 450 y Fq(j)2850 512 y FA(2)2888 490 y FB(,)40 b Fu(V)59 b FB(=)720 550 y Fs(P)808 571 y Fp(1)808 638 y Fq(j)s FA(=0)941 613 y Fu(V)989 625 y Fq(j)1024 613 y Fu(x)1071 573 y Fq(j)1071 635 y FA(2)1140 613 y FB(and)30 b Fu(\032)f FB(=)1469 550 y Fs(P)1556 571 y Fp(1)1556 638 y Fq(j)s FA(=0)1689 613 y Fu(\032)1732 625 y Fq(j)1767 613 y Fu(x)1814 573 y Fq(j)1814 635 y FA(2)1852 613 y FB(,)j(w)n(e)e(get)h(the)g(follo)n(wing)f(equations)g(to)720 712 y(solv)n(e)d(for)g Fu(j)h FB(=)22 b(0)p Fu(;)14 b Ft(\001)g(\001)g(\001)f FB(:)901 930 y(\()p Fu(?j)5 b FB(\))28 b Ft(f)p Fu(U)1173 942 y Fq(j)1207 930 y Fu(;)14 b(x)1291 942 y FA(1)1328 930 y Fu(\030)1364 942 y FA(1)1402 930 y Ft(g)k FB(+)g Fu(V)1593 942 y Fq(j)1628 930 y Fu(x)1675 942 y FA(1)1713 930 y Fu(\030)1749 942 y FA(1)1810 930 y FB(=)k Fu(\032)1940 942 y Fq(j)1994 930 y FB(+)c(2)2129 873 y Fu(@)5 b(U)2235 885 y Fq(j)s Fp(\000)p FA(1)p 2128 911 226 4 v 2180 987 a Fu(@)g(\030)2265 999 y FA(2)2382 930 y FB(+)18 b Fu(V)2513 942 y Fq(j)s Fp(\000)p FA(2)2633 930 y FB(\(:=)23 b Fu(\033)2823 942 y Fq(j)2859 930 y FB(\))28 b Fu(;)720 1152 y FB(where)f Fu(U)1017 1164 y Fp(\000)p FA(1)1129 1152 y FB(=)c Fu(V)1265 1164 y Fp(\000)p FA(1)1377 1152 y FB(=)g Fu(V)1513 1164 y Fp(\000)p FA(2)1626 1152 y FB(:=)f(0.)37 b(W)-7 b(e)28 b(can)f(solv)n(e)f(\()p Fu(?j)5 b FB(\))28 b(if)g(and)g(only)f(if)1545 1331 y Fu(\033)1592 1343 y Fq(j)1627 1331 y FB(\(0)p Fu(;)14 b FB(0;)g Fu(x)1864 1343 y FA(2)1901 1331 y Fu(;)g(\030)1974 1343 y FA(2)2011 1331 y FB(;)g Fu(z)2091 1297 y Fp(0)2114 1331 y FB(\))23 b(=)g(0)720 1510 y(b)n(y)28 b(Lemma)f(1.)720 1625 y(The)k(condition)g Fu(\033)1309 1637 y Fq(j)1345 1625 y FB(\(0)p Fu(;)14 b FB(0;)g Fu(x)1582 1637 y FA(2)1618 1625 y Fu(;)g(\030)1691 1637 y FA(2)1729 1625 y FB(;)g Fu(z)1809 1595 y Fp(0)1831 1625 y FB(\))30 b(=)e(0)j(is)g(satis\014ed)f (for)h Fu(j)j FB(=)28 b(0)j(and)g(can)720 1725 y(b)r(e)g(a)5 b(justed)30 b(for)f Fu(j)j Ft(\025)27 b FB(1)j(b)n(y)g(the)g(c)n(hoice) g(of)g Fu(U)2158 1737 y Fq(j)s Fp(\000)p FA(1)2277 1725 y FB(\(0)p Fu(;)14 b FB(0;)g Fu(x)2514 1737 y FA(2)2551 1725 y Fu(;)g(\030)2624 1737 y FA(2)2662 1725 y FB(;)g Fu(z)2742 1695 y Fp(0)2764 1725 y FB(\))31 b(whic)n(h)f(is)720 1824 y(free)e(in)f(the)h(equation)f(\()p Fu(?)p FB(\()p Fu(j)d Ft(\000)18 b FB(1\)\).)720 1940 y(If)25 b Fu(\032)e FB(=)g Fu(O)1017 1952 y FA(\006)1069 1940 y FB(\()p Fu(N)9 b FB(\),)25 b(w)n(e)f(ha)n(v)n(e)f(for)h Fu(j)k Ft(\024)23 b Fu(N)9 b FB(,)25 b Fu(\032)2005 1952 y Fq(j)2063 1940 y FB(=)d Fu(O)2213 1952 y Fq(Y)2271 1940 y FB(\()p Fu(N)f Ft(\000)12 b Fu(j)5 b FB(\).)36 b(W)-7 b(e)25 b(can)f(c)n(ho)r(ose)720 2040 y Fu(U)777 2052 y Fq(j)835 2040 y FB(=)f Fu(O)986 2052 y Fq(Y)1043 2040 y FB(\()p Fu(N)g Ft(\000)13 b Fu(j)5 b FB(\))25 b(for)g Fu(j)j Ft(\024)22 b Fu(N)34 b FB(and)25 b Fu(V)1921 2052 y Fq(j)1980 2040 y FB(=)d Fu(O)2130 2052 y Fq(Y)2188 2040 y FB(\()p Fu(N)g Ft(\000)13 b Fu(j)19 b Ft(\000)13 b FB(2\))25 b(for)f Fu(j)k Ft(\024)23 b Fu(N)f Ft(\000)13 b FB(2.)720 2155 y(W)-7 b(e)28 b(no)n(w)f(can)g (assume)g(that)h Fu(\032)g FB(is)f(\015at)h(on)f Fu(x)2119 2167 y FA(2)2180 2155 y FB(=)c(0.)p Black 637 2286 a Ft(\017)p Black 41 w FB(W)-7 b(e)37 b(solv)n(e)f(no)n(w)g(equation)g (\(6\))h(in)g(p)r(o)n(w)n(er)e(series)h(w.r.)64 b(to)36 b(\()p Fu(x)2739 2298 y FA(1)2777 2286 y Fu(;)14 b(\030)2850 2298 y FA(1)2888 2286 y FB(\).)64 b(W)-7 b(e)720 2396 y(will)36 b(c)n(ho)r(ose)d Fu(V)55 b FB(=)35 b(0)g(and)g(expand)f Fu(U)45 b FB(=)2101 2333 y Fs(P)2202 2396 y Fu(U)2259 2408 y Fq(\013;\014)2367 2396 y FB(\()p Fu(x)2446 2408 y FA(2)2483 2396 y Fu(;)14 b(\030)2556 2408 y FA(2)2594 2396 y Fu(;)g Ft(\001)g(\001)g(\001)g FB(\))p Fu(x)2821 2365 y Fq(\013)2821 2416 y FA(1)2869 2396 y Fu(\030)2909 2356 y Fq(\014)2905 2418 y FA(1)2989 2396 y FB(and)720 2508 y(similarly)29 b Fu(\032)e FB(=)1223 2446 y Fs(P)1325 2508 y Fu(\032)1368 2520 y Fq(\013;\014)1475 2508 y FB(\()p Fu(x)1554 2520 y FA(2)1592 2508 y Fu(;)14 b(\030)1665 2520 y FA(2)1703 2508 y Fu(;)g Ft(\001)g(\001)g(\001)f FB(\))p Fu(x)1929 2478 y Fq(\013)1929 2528 y FA(1)1977 2508 y Fu(\030)2017 2468 y Fq(\014)2013 2530 y FA(1)2092 2508 y FB(with)30 b Fu(\032)2326 2520 y Fq(\013;\014)2461 2508 y FB(=)c Fu(O)r FB(\()p Fu(x)2696 2478 y Fp(1)2696 2528 y FA(2)2768 2508 y FB(\).)44 b(W)-7 b(e)30 b(get)720 2607 y(for)d Fu(\013)d Ft(6)p FB(=)e Fu(\014)t FB(:)1343 2746 y(\()p Fu(\013)d Ft(\000)f Fu(\014)t FB(\))p Fu(U)1670 2758 y Fq(\013;\014)1796 2746 y Ft(\000)g FB(2)p Fu(x)1968 2758 y FA(2)2016 2690 y Fu(@)5 b(U)2122 2702 y Fq(\013;\014)p 2016 2727 214 4 v 2061 2803 a Fu(@)g(\030)2146 2815 y FA(2)2262 2746 y FB(=)22 b Fu(\032)2392 2758 y Fq(\013;\014)3016 2746 y FB(\(7\))720 2932 y(and)28 b(for)f Fu(\013)c FB(=)g Fu(\014)t FB(:)1579 3070 y Ft(\000)p FB(2)p Fu(x)1733 3082 y FA(2)1780 3014 y Fu(@)5 b(U)1886 3026 y Fq(\013;\014)p 1780 3051 V 1825 3127 a Fu(@)g(\030)1910 3139 y FA(2)2026 3070 y FB(=)22 b Fu(\032)2156 3082 y Fq(\013;\014)3016 3070 y FB(\(8\))720 3257 y(Because)f Fu(\032)g FB(is)h(\015at)g(on)f Fu(x)1472 3269 y FA(2)1533 3257 y FB(=)h(0)g(it)g(can)f(b)r(e)h (divided)g(b)n(y)f Fu(x)2457 3269 y FA(2)2495 3257 y FB(,)i(so)e(that)h(equation)720 3357 y(\(8\))28 b(is)f(easy)g(to)h (solv)n(e.)720 3472 y(Equation)f(\(7\))h(can)f(b)r(e)h(solv)n(ed)e (using)i(Lemma)f(2.)720 3587 y(It)37 b(is)f(clear)g(from)g(the)h(pro)r (of)f(that,)j(if)e Fu(\032)h Ft(2)g Fu(O)2238 3599 y Fq(Y)2296 3587 y FB(\()p Fu(N)9 b FB(\))25 b Ft(\\)f Fu(O)2603 3599 y Fq(Z)2657 3587 y FB(\()p Ft(1)p FB(\),)40 b(w)n(e)c(can)720 3687 y(c)n(ho)r(ose)27 b Fu(U)k FB(=)23 b Fu(O)1223 3699 y Fq(Y)1281 3687 y FB(\()p Fu(N)9 b FB(\).)p Black 637 3818 a Ft(\017)p Black 41 w FB(W)-7 b(e)32 b(can)f(no)n(w)g(assume)g(that)h Fu(\032)g FB(is)f(\015at)h(on)f Fu(x)2155 3830 y FA(2)2222 3818 y FB(=)f(0)h(and)g(on)h Fu(x)2722 3830 y FA(1)2789 3818 y FB(=)d Fu(\030)2919 3830 y FA(1)2987 3818 y FB(=)g(0)720 3918 y(and)j(v)-5 b(anishes)31 b(outside)g(a)h(compact)f(set.)49 b(W)-7 b(e)32 b(tak)n(e)f Fu(V)49 b FB(=)29 b(0)i(and)h(need)g(to)720 4018 y(solv)n(e)e Ft(X)986 4030 y FA(0)1023 4018 y Fu(U)38 b FB(=)28 b Fu(\032)p FB(.)47 b(W)-7 b(e)31 b(\014rst)g(solv)n(e)e (formally)h(\(6\))h(along)f(the)h(h)n(yp)r(erplanes)720 4117 y Fu(x)767 4129 y FA(1)828 4117 y FB(=)23 b(0)i(and)h Fu(\030)1179 4129 y FA(1)1239 4117 y FB(=)d(0)i(as)g(in)h([13)o(])g (and)g(then)g(just)h(b)n(y)e(in)n(tegrating)g(along)f(the)720 4217 y(tra)5 b(jectories)26 b(from)h(the)h(diagonals)e Fu(x)1908 4229 y FA(1)1969 4217 y FB(=)c Ft(\006)p Fu(\030)2157 4229 y FA(1)2195 4217 y FB(.)720 4332 y(This)32 b(last)g(result)g (could)g(also)f(ha)n(v)n(e)g(b)r(een)h(deriv)n(ed)f(from)h(a)g (linearization)720 4432 y(of)c(Nelson)f(result)g(cited)h(in)g (subsection)f(6.1.)3265 4595 y Fi(\003)330 4869 y Fv(5)135 b(Other)45 b(Lemmas:)61 b(matrices)p Black 330 5051 a Fo(Lemma)32 b(4)p Black 41 w Fz(L)l(et)g Fu(R)e FB(=)e Fu(R)1153 5063 y FA(1)1211 5051 y FB(+)20 b Fu(iR)1388 5063 y FA(2)1454 5051 y FB(:)29 b Fu(T)1567 5020 y Fq(?)1604 5051 y Fr(R)1664 5020 y FA(2)1730 5051 y Ft(!)g FB(Herm\(2)20 b Ft(\002)h FB(2\))32 b Fz(such)h(that)g FB(\()p Fu(R)2789 5063 y FA(2)2827 5051 y FB(\))2859 5066 y Fp(j)p FA(\006)2959 5051 y FB(=)28 b(0)p Fz(,)34 b(ther)l(e)330 5150 y(exist)29 b(smo)l(oth)i(functions)e Fu(S)f FB(:)23 b Fu(T)1352 5120 y Fq(?)1389 5150 y Fr(R)1449 5120 y FA(2)1510 5150 y Ft(!)g Fr(R)29 b Fz(and)i Fu(A)23 b FB(:)g Fu(T)2059 5120 y Fq(?)2096 5150 y Fr(R)2156 5120 y FA(2)2217 5150 y Ft(!)g FB(Mat)2473 5162 y FA(2)2510 5150 y FB(\()p Fr(C)p FB(\))30 b Fz(such)g(that:)1289 5329 y Ft(f)p Fu(S;)14 b(H)1488 5341 y FA(0)1524 5329 y Ft(g)k FB(+)g Fu(A)1729 5295 y Fq(?)1768 5329 y Fu(H)1837 5341 y FA(0)1893 5329 y FB(+)g Fu(H)2045 5341 y FA(0)2082 5329 y Fu(A)23 b FB(=)g Fu(R)30 b(:)330 5508 y Fz(Pr)l(o)l(of.{)p Black Black Black 1809 5919 a FB(8)p Black eop %%Page: 9 9 9 8 bop Black Black Black 637 390 a Ft(\017)p Black 41 w FB(Splitting)29 b Fu(A)23 b FB(=)f Fu(A)1296 402 y FA(1)1352 390 y FB(+)c Fu(iA)1526 402 y FA(2)1564 390 y FB(,)27 b(w)n(e)h(get)f(the)h(equations)1370 566 y Ft(f)p Fu(S;)14 b(H)1569 578 y FA(0)1606 566 y Ft(g)k FB(+)g Fu(A)1811 532 y Fq(t)1811 586 y FA(1)1848 566 y Fu(H)1917 578 y FA(0)1973 566 y FB(+)g Fu(H)2125 578 y FA(0)2162 566 y Fu(A)2224 578 y FA(1)2285 566 y FB(=)k Fu(R)2435 578 y FA(1)3016 566 y FB(\(9\))720 741 y(where)27 b Fu(R)1023 753 y FA(1)1088 741 y FB(is)h(real)e(symmetric,)i(and)1527 917 y Ft(\000)p Fu(A)1654 883 y Fq(t)1654 937 y FA(2)1691 917 y Fu(H)1760 929 y FA(0)1816 917 y FB(+)18 b Fu(H)1968 929 y FA(0)2005 917 y Fu(A)2067 929 y FA(2)2128 917 y FB(=)k Fu(R)2278 929 y FA(2)2975 917 y FB(\(10\))720 1093 y(where)h Fu(R)1019 1105 y FA(2)1080 1093 y FB(is)g(real)f(and)h (an)n(tisymmetric.)35 b(Equation)22 b(\(10\))h(is)g(easily)g(solv)n (ed,)720 1192 y(using)k(the)h(h)n(yp)r(othesis)g(\()p Fu(R)1585 1204 y FA(2)1622 1192 y FB(\))1654 1207 y Fp(j)p FA(\006)1749 1192 y FB(=)22 b(0,)28 b(b)n(y)f(T)-7 b(a)n(ylor)26 b(form)n(ula.)p Black 637 1322 a Ft(\017)p Black 41 w FB(W)-7 b(e)29 b(\014rst)e(w)n(an)n(t)h(to)g(solv)n(e)e(equation)i (\(9\))g(formally)f(with)h(resp)r(ect)g(to)g Fu(x)2969 1334 y FA(2)3035 1322 y FB(b)n(y)720 1422 y(using)g(a)f(T)-7 b(a)n(ylor)26 b(expansion)h(with)h(resp)r(ect)g(to)f Fu(x)2276 1434 y FA(2)2314 1422 y FB(.)38 b(W)-7 b(e)28 b(get)f(the)i(follo)n(wing)720 1521 y(system)f(of)f(equations)1566 1695 y Ft(\000)1654 1662 y Fq(@)t(S)p 1641 1676 110 4 v 1641 1723 a(@)t(x)1718 1731 y Fj(1)1778 1695 y FB(+)18 b(2)p Fu(a\030)1983 1707 y FA(1)2153 1695 y FB(=)23 b Fu(T)2290 1707 y FA(1)1616 1772 y Fq(@)t(S)p 1607 1786 102 4 v 1607 1833 a(@)t(\030)1676 1841 y Fj(1)1737 1805 y FB(+)18 b(2)p Fu(dx)1952 1817 y FA(1)2153 1805 y FB(=)23 b Fu(T)2290 1817 y FA(2)1535 1885 y Fq(@)t(S)p 1526 1899 V 1526 1946 a(@)t(\030)1595 1954 y Fj(2)1656 1918 y FB(+)18 b Fu(cx)1822 1930 y FA(1)1878 1918 y FB(+)g Fu(b\030)2033 1930 y FA(1)2153 1918 y FB(=)23 b Fu(T)2290 1930 y FA(3)2975 1811 y FB(\(11\))720 2100 y(where)36 b Fu(T)1018 2112 y Fq(j)1088 2100 y FB(are)f(giv)n(en)g(and)h(the)g(unkno)n(wn)g(quan)n (tities)f(are)g Fu(a;)14 b(b;)g(c;)g(d)36 b FB(and)720 2210 y Fu(S)5 b FB(,)33 b(functions)f(of)g(\()p Fu(x)1372 2222 y FA(1)1410 2210 y Fu(;)14 b(\030)1483 2222 y FA(1)1520 2210 y Fu(;)g(\030)1593 2222 y FA(2)1631 2210 y Fu(;)g Ft(\001)g(\001)g(\001)g FB(\).)50 b(Here)31 b Fu(A)2146 2222 y FA(1)2214 2210 y FB(=)2309 2148 y Fs(P)2396 2235 y Fq(j)2445 2210 y Fu(A)2507 2222 y FA(1)p Fq(;j)2595 2210 y Fu(x)2642 2170 y Fq(j)2642 2232 y FA(2)2712 2210 y FB(and)h Fu(A)2940 2222 y FA(1)p Fq(;j)3058 2210 y FB(=)720 2258 y Fs(\022)823 2324 y Fu(a)87 b(b)827 2424 y(c)g(d)1034 2258 y Fs(\023)1096 2375 y FB(.)720 2535 y(W)-7 b(e)38 b(solv)n(e)f(the)h(t)n(w)n(o)f(\014rst)g(equations)g(b)n (y)h(c)n(ho)r(osing)e Fu(d)k FB(=)f(0)f(and)f Fu(a)h FB(suc)n(h)720 2635 y(that)i(the)g(compatibilit)n(y)g(condition,)i (whic)n(h)e(giv)n(e)f(an)g(equation)g(of)h(the)720 2734 y(form)c Fu(\030)961 2746 y FA(1)1022 2702 y Fq(@)t(a)p 1009 2716 V 1009 2763 a(@)t(\030)1078 2771 y Fj(1)1145 2734 y FB(+)23 b Fu(a)38 b FB(=)f Fu(r)r FB(,)i(is)d(satis\014ed.)63 b(Then)36 b(w)n(e)g(solv)n(e)f(the)i(last)f(one)g(on)720 2834 y Fu(x)767 2846 y FA(1)843 2834 y FB(=)h Fu(\030)981 2846 y FA(1)1056 2834 y FB(=)g(0)f(b)r(ecause,)j(in)d(the)h(t)n(w)n(o)f (\014rst)g(equations,)h(w)n(e)f(can)g(add)h(to)720 2933 y Fu(S)h FB(an)n(y)32 b(function)h(indep)r(enden)n(t)h(of)e(\()p Fu(x)1955 2945 y FA(1)1993 2933 y Fu(;)14 b(\030)2066 2945 y FA(1)2104 2933 y FB(\))33 b(and)f(w)n(e)h(c)n(ho)r(ose)e Fu(b)i FB(and)f Fu(c)h FB(b)n(y)720 3033 y(using)27 b(T)-7 b(a)n(ylor)26 b(form)n(ula.)p Black 637 3163 a Ft(\017)p Black 41 w FB(No)n(w)h(w)n(e)h(need)f(to)h(solv)n(e)e(equation)h(\(9\)) h(whic)n(h)f(w)n(e)h(expand)f(as)g(follo)n(ws)1191 3341 y(\()p Fu(a)p FB(\))220 b Ft(\000)1606 3308 y Fq(@)t(S)p 1593 3322 110 4 v 1593 3370 a(@)t(x)1670 3378 y Fj(1)1731 3341 y FB(+)18 b(2\()p Fu(a\030)1968 3353 y FA(1)2023 3341 y FB(+)g Fu(cx)2189 3353 y FA(2)2227 3341 y FB(\))220 b(=)22 b Fu(T)2627 3311 y Fp(0)2615 3362 y FA(1)1195 3451 y FB(\()p Fu(b)p FB(\))1569 3418 y Fq(@)t(S)p 1559 3432 102 4 v 1559 3480 a(@)t(\030)1628 3488 y Fj(1)1689 3451 y FB(+)c(2\()p Fu(dx)1936 3463 y FA(1)1993 3451 y FB(+)g Fu(bx)2159 3463 y FA(2)2196 3451 y FB(\))251 b(=)22 b Fu(T)2627 3421 y Fp(0)2615 3472 y FA(2)1194 3564 y FB(\()p Fu(c)p FB(\))1401 3531 y Fq(@)t(S)p 1392 3545 V 1392 3593 a(@)t(\030)1461 3601 y Fj(2)1522 3564 y FB(+)c Fu(cx)1688 3576 y FA(1)1744 3564 y FB(+)g Fu(b\030)1899 3576 y FA(1)1955 3564 y FB(+)g Fu(ax)2129 3576 y FA(2)2185 3564 y FB(+)g Fu(dx)2358 3576 y FA(2)2479 3564 y FB(=)k Fu(T)2627 3534 y Fp(0)2615 3585 y FA(3)2975 3457 y FB(\(12\))720 3751 y(with)38 b Fu(T)980 3721 y Fp(0)968 3772 y Fq(j)1040 3751 y FB(\015at)f(on)f Fu(x)1368 3763 y FA(2)1445 3751 y FB(=)j(0.)65 b(T)-7 b(aking)36 b(the)h(linear)g(com)n(bination)f Fu(x)2887 3763 y FA(1)2925 3751 y FB(\()p Fu(a)p FB(\))25 b(+)720 3850 y Fu(\030)756 3862 y FA(1)794 3850 y FB(\()p Fu(b)p FB(\))18 b Ft(\000)g FB(2)p Fu(x)1084 3862 y FA(2)1122 3850 y FB(\()p Fu(c)p FB(\))28 b(of)f(equations)g(\(a\),)h(\(b\),)g (\(c\))h(of)e(\(12\),)g(w)n(e)h(get)1345 4026 y(\()p Fu(d)p FB(\))56 b Ft(f)p Fu(S;)14 b(p)1680 4038 y FA(0)1717 4026 y Ft(g)k FB(+)g(2\()p Fu(a)g FB(+)g Fu(d)p FB(\))p Fu(p)2196 4038 y FA(0)2257 4026 y FB(=)k Fu(T)2405 3992 y Fp(00)2474 4026 y Fu(;)720 4201 y FB(with)h Fu(T)965 4171 y Fp(00)1030 4201 y FB(=)f Fu(O)1180 4213 y Fq(Z)1234 4201 y FB(\()p Ft(1)p FB(\),)i(whic)n(h)e(can)g(b)r(e)h(solv)n(ed)e (using)h(Lemma)h(3.)34 b(Moreo)n(v)n(er,)720 4301 y(w)n(e)23 b(can)h(c)n(ho)r(ose)e Fu(a)h FB(=)f Fu(d)i FB(=)e(0)h(and)h Fu(S)k FB(=)22 b Fu(O)2006 4313 y Fq(Z)2060 4301 y FB(\()p Ft(1)p FB(\).)36 b(W)-7 b(e)24 b(deduce)g Fu(b)f FB(and)g Fu(c)h FB(from)720 4401 y(equations)g(\(a\))h(and)g(\(b\).)37 b(No)n(w)24 b(equation)h(\(c\))g(is)g(ful\014lled)h(b)n(y)f(relation)f (\(d\).)3265 4561 y Fi(\003)p Black 330 4737 a Fo(Lemma)32 b(5)p Black 41 w Fz(We)f(de\014ne)f Fu(z)1191 4749 y FA(1)1253 4737 y FB(=)25 b(\()p Fu(x)1422 4749 y FA(1)1460 4737 y Fu(;)14 b(\030)1533 4749 y FA(1)1570 4737 y FB(\))p Fz(.)42 b(If)31 b Fu(L)24 b FB(:)h Fr(R)1946 4707 y FA(3)1946 4757 y Fq(z)1978 4765 y Fj(1)2010 4757 y Fq(;x)2068 4765 y Fj(2)2129 4737 y Ft(!)g FB(Sym)2396 4757 y FA(2)2434 4737 y FB(\()p Fr(R)p FB(\))31 b Fz(is)g(a)g(line)l(ar)g(map)h(such)330 4836 y(that)25 b FB(det\()p Fu(L)p FB(\()p Fu(z)770 4848 y FA(1)807 4836 y Fu(;)14 b(x)891 4848 y FA(2)929 4836 y FB(\)\))23 b(=)g Fu(x)1151 4848 y FA(1)1189 4836 y Fu(\030)1225 4848 y FA(1)1271 4836 y Ft(\000)8 b Fu(x)1391 4806 y FA(2)1391 4857 y(2)1428 4836 y Fz(,)26 b(ther)l(e)f(exists)g(a)g (c)l(onstant)g(invertible)h(matrix)f Fu(A)g Fz(such)g(that)330 4936 y Fu(A)392 4906 y Fq(t)421 4936 y Fu(L)p FB(\()p Fu(z)549 4948 y FA(1)586 4936 y Fu(;)14 b(x)670 4948 y FA(2)708 4936 y FB(\))p Fu(A)23 b FB(=)g Fu(H)982 4948 y FA(0)1019 4936 y FB(\()p Ft(\006)p Fu(z)1155 4948 y FA(1)1192 4936 y Fu(;)14 b(x)1276 4948 y FA(2)1314 4936 y FB(\))p Fz(.)330 5112 y(Pr)l(o)l(of.{)p Black Black 567 5272 a FB(W)-7 b(e)30 b(\014rst)f(restrict)f(to)i Fu(x)1324 5284 y FA(2)1387 5272 y FB(=)c(0.)41 b(W)-7 b(e)30 b(put)g Fu(L)25 b FB(=)h Fu(x)2103 5284 y FA(1)2141 5272 y Fu(q)2178 5284 y FA(1)2234 5272 y FB(+)20 b Fu(\030)2355 5284 y FA(1)2392 5272 y Fu(q)2429 5284 y FA(2)2486 5272 y FB(+)f Fu(x)2617 5284 y FA(2)2655 5272 y Fu(q)2692 5284 y FA(3)2759 5272 y FB(with)29 b(\014xed)538 5372 y(quadratic)e(forms)h Fu(q)1177 5384 y Fq(j)1212 5372 y FB(.)39 b(W)-7 b(e)28 b(ha)n(v)n(e)g(det\()p Fu(q)1794 5384 y FA(1)1831 5372 y FB(\))d(=)f(det\()p Fu(q)2161 5384 y FA(2)2199 5372 y FB(\))g(=)g(0)k(and)g Fu(q)2613 5384 y FA(1)2675 5372 y Ft(6)p FB(=)c(0)p Fu(;)41 b(q)2907 5384 y FA(2)2969 5372 y Ft(6)p FB(=)24 b(0.)538 5471 y(The)j(k)n(ernel)g(of)h Fu(q)1085 5483 y FA(1)1150 5471 y FB(is)g(generated)e(b)n(y)i Fu(V)1776 5483 y FA(1)1841 5471 y FB(and)g(the)g(k)n(ernel)f(of)h Fu(q)2523 5483 y FA(2)2588 5471 y FB(b)n(y)f Fu(V)2751 5483 y FA(2)2789 5471 y FB(.)38 b(\()p Fu(V)2930 5483 y FA(1)2968 5471 y Fu(;)14 b(V)3053 5483 y FA(2)3090 5471 y FB(\))538 5571 y(are)29 b(indep)r(enden)n(t)i(b)r(ecause)e Fu(q)1498 5583 y FA(1)1566 5571 y FB(and)h Fu(q)1767 5583 y FA(2)1834 5571 y FB(are)f(linearly)g(indep)r(enden)n(t)i(\(otherwise)538 5670 y(det\()p Fu(x)732 5682 y FA(1)770 5670 y Fu(q)807 5682 y FA(1)859 5670 y FB(+)15 b Fu(\030)975 5682 y FA(1)1013 5670 y Fu(q)1050 5682 y FA(2)1087 5670 y FB(\))24 b(=)e(0\).)36 b(W)-7 b(e)27 b(can)e(assume)h(that)g Fu(q)2156 5682 y FA(1)2193 5670 y FB(\()p Fu(V)2273 5682 y FA(2)2311 5670 y FB(\))e(=)e Fu(q)2491 5682 y FA(2)2529 5670 y FB(\()p Fu(V)2609 5682 y FA(1)2647 5670 y FB(\))h(=)g Ft(\006)p FB(1)i(\(b)r(oth)p Black 1809 5919 a(9)p Black eop %%Page: 10 10 10 9 bop Black Black 538 390 a FB(ha)n(v)n(e)24 b(the)j(same)e(sign)h (b)r(ecause)f(of)h(the)h(v)-5 b(alue)26 b(of)g(the)g(determinan)n(t)g (of)g Fu(L)p FB(\()p Fu(z)2920 402 y FA(1)2956 390 y Fu(;)14 b FB(0\)\).)538 490 y(Hence,)27 b(b)n(y)h(c)n(ho)r(osing)e(the) i(basis)f(\()p Fu(V)1687 502 y FA(2)1725 490 y Fu(;)14 b(V)1810 502 y FA(1)1847 490 y FB(\),)28 b(w)n(e)f(get)1342 722 y Fu(L)p FB(\()p Fu(z)1470 734 y FA(1)1507 722 y Fu(;)14 b FB(0\))23 b(=)f Ft(\006)1807 605 y Fs(\022)1909 672 y Fu(\030)1945 684 y FA(1)2087 672 y FB(0)1925 771 y(0)99 b Fu(x)2113 783 y FA(1)2192 605 y Fs(\023)2295 722 y Fu(:)662 955 y FB(W)-7 b(e)27 b(ha)n(v)n(e)e(no)n(w)h Fu(L)p FB(\()p Fu(z)1294 967 y FA(1)1330 955 y Fu(;)14 b(x)1414 967 y FA(2)1452 955 y FB(\))23 b(=)g Fu(H)1664 967 y FA(0)1701 955 y FB(\()p Ft(\006)p Fu(z)1837 967 y FA(1)1874 955 y Fu(;)14 b FB(0\))i(+)f Fu(x)2128 967 y FA(2)2166 955 y Fu(M)35 b FB(and)26 b(b)n(y)g(iden)n(ti\014cation)h (of)538 1054 y(the)f(determinan)n(ts)g(w)n(e)g(get)g Fu(L)p FB(\()p Fu(z)1565 1066 y FA(1)1602 1054 y Fu(;)14 b(x)1686 1066 y FA(2)1723 1054 y FB(\))24 b(=)e Fu(H)1935 1066 y FA(0)1973 1054 y FB(\()p Ft(\006)p Fu(z)2109 1066 y FA(1)2145 1054 y Fu(;)14 b Ft(\006)p Fu(x)2294 1066 y FA(2)2331 1054 y FB(\).)37 b(It)27 b(is)f(easy)g(to)g(c)n(hange)538 1154 y Ft(\000)p Fu(x)650 1166 y FA(2)714 1154 y FB(in)n(to)i(plus)g Fu(x)1106 1166 y FA(2)1171 1154 y FB(b)n(y)f(using)g(the)h(gauge)f (transform)f(\()p Fu(u;)14 b(v)s FB(\))23 b Ft(!)h FB(\()p Fu(u;)14 b Ft(\000)p Fu(v)s FB(\).)3265 1320 y Fi(\003)p Black 330 1503 a Fo(Lemma)32 b(6)p Black 41 w Fz(L)l(et)g Fu(H)j FB(=)28 b Fu(H)1170 1515 y FA(0)1228 1503 y FB(+)20 b Fu(O)1376 1515 y FA(\006)1428 1503 y FB(\(2\))33 b Fz(and)g(assume)g(that)g FB(det\()p Fu(H)7 b FB(\))29 b(=)f(det\()p Fu(H)2791 1515 y FA(0)2829 1503 y FB(\))p Fz(.)47 b(Then)34 b(ther)l(e)330 1602 y(exists)29 b(a)h(smo)l(oth)h (map)f Fu(x)24 b Ft(!)f Fu(A)p FB(\()p Fu(x)p FB(\))31 b Fz(de\014ne)l(d)f(in)g(some)g(neighb)l(ourho)l(o)l(d)i(of)e FB(\006)g Fz(such)g(that)1580 1785 y Fu(A)1642 1751 y Fq(t)1672 1785 y Fu(H)7 b(A)23 b FB(=)g Fu(H)1990 1797 y FA(0)2057 1785 y Fu(:)330 1968 y Fz(The)31 b(same)f(r)l(esult)f (holds)i(in)f(the)g(r)l(e)l(al)g(analytic)h(and)f(in)g(the)g(formal)h (series)f(settings.)330 2150 y(Pr)l(o)l(of.{)p Black Black 538 2316 a FB(W)-7 b(e)28 b(will)f(use)h(Moser's)e(path)i(metho)r (d.)p Black 614 2449 a(1.)p Black 41 w(Let)33 b(us)h(\014rst)e (construct)h(a)g(path)g Fu(H)1877 2461 y Fq(t)1906 2449 y Fu(;)47 b FB(0)32 b Ft(\024)g Fu(t)g Ft(\024)g FB(1)p Fu(;)h FB(from)g Fu(H)2675 2461 y FA(0)2745 2449 y FB(to)g Fu(H)40 b FB(with)720 2549 y(det)q(\()p Fu(H)937 2561 y Fq(t)966 2549 y FB(\))j(=)e(det)q(\()p Fu(H)1364 2561 y FA(0)1401 2549 y FB(\).)72 b(Let)39 b Fu(H)49 b FB(=)42 b Fu(H)1982 2561 y FA(0)2045 2549 y FB(+)26 b Fu(K)45 b FB(where)38 b Fu(K)48 b FB(=)42 b Fu(O)2792 2561 y FA(\006)2843 2549 y FB(\(2\))e(and)749 2627 y(~)720 2648 y Fu(H)789 2660 y Fq(t)842 2648 y FB(=)22 b Fu(H)998 2660 y FA(0)1036 2648 y FB(+)p Fu(tK)q(;)32 b FB(0)22 b Ft(\024)h Fu(t)g Ft(\024)g FB(1.)33 b(W)-7 b(e)19 b(ha)n(v)n(e)e (only)h(det)q(\()2314 2627 y(~)2286 2648 y Fu(H)2355 2660 y Fq(t)2384 2648 y FB(\))24 b(=)e(det)q(\()p Fu(H)2744 2660 y FA(0)2781 2648 y FB(\)+)p Fu(O)2941 2660 y FA(\006)2993 2648 y FB(\(3\).)720 2748 y(Using)j(the)h(Morse-Bott)e(Lemma)h(to)g (the)h(function)g(det\()2563 2727 y(~)2534 2748 y Fu(H)2603 2760 y Fq(t)2633 2748 y FB(\),)g(w)n(e)f(can)g(\014nd)720 2848 y(a)h(smo)r(oth)h(family)g(of)f(di\013eomorphisms)g Fu(')2097 2860 y Fq(t)2127 2848 y FB(\()p Fu(x;)14 b(\030)t FB(\))24 b(=)f(\()p Fu(x;)14 b(\030)t FB(\))j(+)f Fu(O)2776 2860 y FA(\006)2828 2848 y FB(\(2\))27 b(with)720 2947 y Fu(')774 2959 y FA(0)835 2947 y FB(=)22 b Fu(')976 2959 y FA(1)1037 2947 y FB(=)h Fu(I)7 b(d)28 b FB(suc)n(h)f(that)1478 3130 y(det\()1653 3109 y(~)1625 3130 y Fu(H)1694 3142 y Fq(t)1723 3130 y FB(\))19 b Ft(\016)f Fu(')1888 3142 y Fq(t)1941 3130 y FB(=)k(det)q(\()p Fu(H)2245 3142 y FA(0)2282 3130 y FB(\))28 b Fu(:)720 3313 y FB(W)-7 b(e)28 b(de\014ne)1479 3412 y Fu(H)1548 3424 y Fq(t)1577 3412 y FB(\()p Fu(x;)14 b(\030)t FB(\))25 b(=)1906 3391 y(~)1877 3412 y Fu(H)1946 3424 y Fq(t)1975 3412 y FB(\()p Fu(')2061 3424 y Fq(t)2091 3412 y FB(\()p Fu(x;)14 b(\030)t FB(\)\))29 b Fu(:)720 3562 y FB(W)-7 b(e)28 b(ha)n(v)n(e)f(no)n(w)g(det\()p Fu(H)1444 3574 y Fq(t)1473 3562 y FB(\))d(=)e(det)q(\()p Fu(H)1833 3574 y FA(0)1870 3562 y FB(\))28 b(and)g Fu(H)2161 3574 y Fq(t)2213 3562 y FB(=)23 b Fu(H)2370 3574 y FA(0)2425 3562 y FB(+)18 b Fu(O)2571 3574 y FA(\006)2623 3562 y FB(\(2\).)37 b(W)-7 b(e)28 b(put)1567 3794 y Fu(H)1636 3806 y Fq(t)1688 3794 y FB(=)1776 3677 y Fs(\022)1878 3743 y FB(\004)1933 3755 y FA(1)2067 3743 y Fu(X)2136 3755 y FA(2)1878 3843 y Fu(X)1947 3855 y FA(2)2067 3843 y Fu(X)2136 3855 y FA(1)2215 3677 y Fs(\023)720 4022 y FB(and)g(let)1439 4151 y Fu(D)1508 4163 y Fq(t)1560 4151 y FB(=)1673 4094 y Fu(d)p 1658 4132 74 4 v 1658 4208 a(dt)1741 4151 y(H)1810 4163 y Fq(t)1862 4151 y FB(=)23 b Ft(\000)2029 4034 y Fs(\022)2131 4100 y Fu(r)86 b(s)2131 4200 y(s)e(u)2343 4034 y Fs(\023)720 4350 y FB(F)-7 b(rom)27 b(det)q(\()p Fu(H)1155 4362 y Fq(t)1184 4350 y FB(\))d(=)e(det\()p Fu(H)1543 4362 y FA(0)1581 4350 y FB(\),)28 b(w)n(e)f(get)1508 4533 y Fu(u)p FB(\004)1611 4545 y FA(1)1666 4533 y FB(+)18 b Fu(r)r(X)1857 4545 y FA(1)1913 4533 y Ft(\000)g FB(2)p Fu(sX)2146 4545 y FA(2)2206 4533 y FB(=)23 b(0)639 b(\(13\))p Black 614 4732 a(2.)p Black 41 w(Let)28 b(us)f(solv)n(e)g(the)h(follo)n(wing)e (linear)h(equation:)1554 4914 y Fu(B)1621 4880 y Fq(t)1650 4914 y Fu(H)1719 4926 y Fq(t)1767 4914 y FB(+)18 b Fu(H)1919 4926 y Fq(t)1948 4914 y Fu(B)28 b FB(=)22 b Ft(\000)p Fu(D)2260 4926 y Fq(t)720 5139 y FB(with)33 b Fu(B)j FB(=)31 b Fu(O)1172 5151 y FA(\006)1224 5139 y FB(\(1\))i(and)f(T)-7 b(r\()p Fu(B)t FB(\))32 b(=)f(0.)52 b(W)-7 b(e)33 b(put)g Fu(B)j FB(=)2491 5022 y Fs(\022)2594 5088 y Fu(a)83 b(b)2594 5188 y(c)91 b Ft(\000)p Fu(a)2871 5022 y Fs(\023)2932 5139 y FB(.)52 b(W)-7 b(e)720 5283 y(get)28 b(the)g(follo)n(wing)e (system)h(of)h(equations:)1498 5461 y(2\()p Fu(a)p FB(\004)1671 5473 y FA(1)1727 5461 y FB(+)18 b Fu(cX)1915 5473 y FA(2)1952 5461 y FB(\))23 b(=)g Fu(r)106 b FB(\(1\))1498 5560 y(2\()p Fu(bX)1677 5572 y FA(2)1732 5560 y Ft(\000)18 b Fu(aX)1928 5572 y FA(1)1965 5560 y FB(\))23 b(=)g Fu(u)82 b FB(\(2\))1498 5660 y Fu(cX)1603 5672 y FA(1)1659 5660 y FB(+)18 b Fu(b)p FB(\004)1833 5672 y FA(1)1893 5660 y FB(=)k Fu(s)219 b FB(\(3\))p Black 1788 5919 a(10)p Black eop %%Page: 11 11 11 10 bop Black Black 720 390 a FB(F)-7 b(rom)27 b(equation)g(\(13\),)h (w)n(e)f(get)g(that)1465 568 y(\(\004)1552 580 y FA(1)1613 568 y FB(=)c Fu(X)1770 580 y FA(2)1830 568 y FB(=)g(0\))g Ft(\))g FB(\()p Fu(r)j FB(=)c(0\))720 746 y(and)1455 845 y(\()p Fu(X)1556 857 y FA(1)1616 845 y FB(=)h Fu(X)1773 857 y FA(2)1833 845 y FB(=)g(0\))f Ft(\))i FB(\()p Fu(u)e FB(=)h(0\))720 992 y(So)1219 1092 y Fu(r)j FB(=)c(2\()p Fu(a)p FB(\004)1542 1104 y FA(1)1598 1092 y FB(+)c Fu(cX)1786 1104 y FA(2)1823 1092 y FB(\))p Fu(;)42 b(u)22 b FB(=)h(2\()p Fu(b)2188 1057 y Fp(0)2211 1092 y Fu(X)2280 1104 y FA(2)2335 1092 y Ft(\000)18 b Fu(a)2462 1057 y Fp(0)2485 1092 y Fu(X)2554 1104 y FA(1)2592 1092 y FB(\))720 1238 y(Then)29 b(equation)g(\(13\))g(implies)g Fu(a)19 b Ft(\000)g Fu(a)1930 1208 y Fp(0)1979 1238 y FB(=)25 b Fu(!)s(X)2193 1250 y FA(2)2229 1238 y FB(,)30 b(so)e(w)n(e)h(can)g(c)n(hange)f Fu(a)2983 1208 y Fp(0)3035 1238 y FB(b)n(y)720 1338 y Fu(a)764 1308 y Fp(0)795 1338 y FB(+)8 b Fu(!)s(X)992 1350 y FA(2)1051 1338 y FB(and)22 b Fu(b)1243 1308 y Fp(0)1288 1338 y FB(to)g Fu(b)1420 1308 y Fp(0)1451 1338 y FB(+)8 b Fu(!)s(X)1648 1350 y FA(1)1706 1338 y FB(in)23 b(the)g(previous)e(equations.)34 b(Equation)21 b(\(3\))720 1437 y(is)32 b(then)g(ful\014lled)g(from)f(equation)g(\(13\).)48 b(All)32 b(previous)f(argumen)n(ts)f(w)n(ork)720 1537 y(smo)r(othly)d(with)i(resp)r(ect)e(to)g Fu(t)p FB(.)p Black 614 1668 a(3.)p Black 41 w(The)c(path)f(metho)r(d)h(w)n(orks)e (no)n(w)h(as)f(follo)n(ws:)34 b(w)n(e)22 b(try)g(to)g(\014nd)h Fu(A)2736 1680 y Fq(t)2788 1668 y FB(suc)n(h)f(that)720 1768 y Fu(A)782 1737 y Fq(t)782 1788 y(t)812 1768 y Fu(H)881 1780 y Fq(t)910 1768 y Fu(A)972 1780 y Fq(t)1025 1768 y FB(=)g Fu(H)1181 1780 y FA(0)1218 1768 y FB(.)36 b(T)-7 b(aking)23 b(the)h(deriv)-5 b(ativ)n(e)23 b(and)g(putting)2537 1735 y Fq(d)p 2525 1749 60 4 v 2525 1796 a(dt)2594 1768 y Fu(A)2656 1780 y Fq(t)2709 1768 y FB(=)g Fu(B)2860 1780 y Fq(t)2889 1768 y Fu(A)2951 1780 y Fq(t)2980 1768 y FB(,)i(w)n(e)720 1867 y(get:)1541 1967 y Fu(B)1608 1933 y Fq(t)1604 1987 y(t)1638 1967 y Fu(H)1707 1979 y Fq(t)1755 1967 y FB(+)18 b Fu(H)1907 1979 y Fq(t)1936 1967 y Fu(B)1999 1979 y Fq(t)2051 1967 y FB(=)23 b Ft(\000)p Fu(D)2273 1979 y Fq(t)720 2113 y FB(whic)n(h)28 b(w)n(e)f(ha)n(v)n(e)f (already)g(solv)n(ed)h(with)h(T)-7 b(r\()p Fu(B)2184 2125 y Fq(t)2213 2113 y FB(\))24 b(=)e(0..)3265 2276 y Fi(\003)330 2549 y Fv(6)135 b(The)44 b(classical)j(normal)e(form)330 2748 y Fl(6.1)112 b(Nelson's)38 b(result)330 2901 y FB(F)-7 b(or)29 b(con)n(v)n(enience,)f(w)n(e)i(recall)e(here)h(an)g(adapted)g (v)n(ersion)f(of)h(the)h(statemen)n(t)g(of)f(Theorem)f(8)330 3001 y(p.)37 b(46)27 b(of)g([43)o(]:)p Black 330 3163 a Fo(Theorem)k(1)p Black 42 w(\(Stern)m(b)s(erg's)g(theorem\))f Fz(L)l(et)f Fu(X)37 b Fz(b)l(e)30 b(a)g(smo)l(oth)h(ve)l(ctor)f (\014eld)g(on)g Fr(R)3088 3133 y Fq(s)3124 3163 y Fz(,)g(with)330 3262 y Fu(X)7 b FB(\(0\))28 b(=)g(0)p Fz(.)47 b(L)l(et)33 b Fu(X)963 3274 y FA(0)1000 3262 y Fu(x)c FB(=)f Fu(D)r(X)7 b FB(\(0\))p Fu(x)33 b Fz(b)l(e)g(the)g(line)l(ar)g(p)l(art)g(of)h Fu(X)39 b Fz(at)32 b(the)h(origin,)j(let)c Fu(U)9 b FB(\()p Fu(t)p FB(\))33 b Fz(and)330 3362 y Fu(U)387 3374 y FA(0)424 3362 y FB(\()p Fu(t)p FB(\))g Fz(b)l(e)f(the)g(\015ows)h(gener)l(ate)l (d)f(by)h Fu(X)39 b Fz(and)32 b Fu(X)1829 3374 y FA(0)1866 3362 y Fz(,)i(and)e(de\014ne)h Fu(X)g FB(=)28 b Fu(X)2597 3374 y FA(0)2654 3362 y FB(+)20 b Fu(X)2808 3374 y FA(1)2845 3362 y Fz(.)46 b(We)32 b(assume)330 3462 y(that)37 b Fu(X)576 3474 y FA(1)650 3462 y Fz(is)h(c)l(omp)l(actly)g(supp)l(orte)l (d.)62 b(Supp)l(ose)38 b(ther)l(e)f(is)h(a)f(line)l(ar)h(subsp)l(ac)l (e)g Fu(N)9 b Fz(,)39 b(invariant)330 3561 y(under)30 b Fu(X)636 3573 y FA(0)673 3561 y Fz(,)g(such)g(that)f Fu(X)1155 3573 y FA(1)1215 3561 y FB(=)23 b Fu(O)1366 3573 y Fq(N)1429 3561 y FB(\()p Ft(1)p FB(\))p Fz(.)455 3661 y(L)l(et)1068 3761 y Fu(E)28 b FB(=)23 b Ft(f)p Fu(x)g Ft(2)g Fr(R)1495 3726 y Fq(s)1560 3761 y Ft(j)91 b FB(lim)1627 3810 y Fq(t)p Fp(!)p FA(+)p Fp(1)1849 3761 y Ft(k)p Fu(U)1948 3773 y FA(0)1985 3761 y FB(\()p Fu(t)p FB(\))p Fu(x)19 b Ft(\000)f Fu(N)9 b Ft(k)23 b FB(=)f(0)p Ft(g)29 b Fu(:)330 3949 y Fz(Then,)35 b(for)f(al)t(l)g Fu(j)g Ft(2)c Fr(N)j Fz(and)g Fu(x)d Ft(2)f Fu(E)5 b Fz(,)34 b Fu(D)1601 3919 y Fq(j)1650 3949 y FB(\()q Fu(U)9 b FB(\()p Ft(\000)p Fu(t)p FB(\))p Fu(U)1965 3961 y FA(0)2001 3949 y FB(\()p Fu(t)p FB(\)\))15 b Fu(x)34 b Fz(c)l(onver)l(ges)f(as)g Fu(t)d Ft(!)f FB(+)p Ft(1)j Fz(and)i(the)330 4049 y(limit)e Fu(W)607 4061 y Fp(\000)664 4049 y FB(\()p Fu(x)p FB(\))g(\()p Fu(x)c Ft(2)f Fu(E)5 b FB(\))32 b Fz(has)g(a)h(smo)l(oth)f(extension)f Fu(G)h Fz(to)g Fr(R)2263 4019 y Fq(s)2330 4049 y Fz(such)g(that)f Fu(G)21 b Ft(\000)e FB(Id)27 b(=)f Fu(O)3119 4061 y Fq(N)3182 4049 y FB(\()p Ft(1)p FB(\))330 4149 y Fz(and)k(such)g(that)g FB(\()p Fu(G)947 4118 y Fp(\000)p FA(1)1037 4149 y FB(\))1069 4161 y Fq(?)1107 4149 y Fu(X)25 b Ft(\000)18 b Fu(X)1353 4161 y FA(0)1413 4149 y FB(=)k Fu(O)1563 4161 y Fq(E)1620 4149 y FB(\()p Ft(1)p FB(\))p Fz(.)330 4380 y Fl(6.2)112 b(Classical)39 b(normal)g(form)p Black 330 4533 a Fo(Theorem)31 b(2)p Black 42 w Fz(Assuming)21 b(hyp)l(othesis)k(\(i\),)f(\(ii\))g (and)f(\(iii\),)i(ther)l(e)e(exists)f(a)h(germ)f(of)i(c)l(anonic)l(al) 330 4633 y(tr)l(ansformation)40 b Fu(\037)g Fz(at)g(the)g(origin)h(and) f(a)g(germ)g(of)h(map)f FB(\()p Fu(x;)14 b(\030)t FB(\))42 b Ft(!)g Fu(A)p FB(\()p Fu(x;)14 b(\030)t FB(\))41 b Fz(wher)l(e)f Fu(A)i Ft(2)330 4733 y Fu(GL)p FB(\(2)p Fu(;)14 b Fr(R)p FB(\))29 b Fz(such)h(that)1404 4765 y Fs(\000)1442 4832 y Fu(A)1504 4798 y Fq(t)1533 4832 y Fu(H)1602 4844 y Fq(class)1756 4832 y Fu(A)1818 4765 y Fs(\001)1875 4832 y Ft(\016)18 b Fu(\037)23 b FB(=)f Fu(H)2166 4844 y FA(0)2233 4832 y Fu(:)926 b FB(\(14\))330 5010 y(The)34 b(normal)e(form)h(is)h Fz(lo)l(c)l(al)g FB(while)g(in)g([7)o(])g(it)g(w)n(as)e(only)h Fz(formal)i FB(along)d(the)i(co)r(dimension)f(3)330 5110 y(subspace)27 b(\006)c(=)g Ft(f)p Fu(x)937 5122 y FA(1)997 5110 y FB(=)f Fu(\030)1120 5122 y FA(1)1181 5110 y FB(=)h Fu(x)1316 5122 y FA(2)1376 5110 y FB(=)g(0)p Ft(g)p FB(.)330 5209 y Fz(Pr)l(o)l(of.{)p Black Black 571 5372 a FB(Let)34 b Fu(f)42 b FB(and)33 b Fu(g)j FB(germs)d(of)g(function)h(near)f(the)h (origin,)g(w)n(e)f(will)h(denote)f Fu(f)41 b Ft(\030)33 b Fu(g)538 5471 y FB(if)e(there)f(exists)h(a)f(\(germ)h(of)6 b(\))31 b(canonical)f(transformation)f Fu(\037)i FB(and)f(a)h(\(germ)f (of)6 b(\))538 5571 y(non)29 b(v)-5 b(anishing)29 b(p)r(ositiv)n(e)h (function)g Fu(e)f FB(suc)n(h)h(that)g Fu(f)e Ft(\016)19 b Fu(\037)27 b FB(=)f Fu(eg)s FB(.)43 b(Same)29 b(notation)538 5670 y(for)39 b(matrix)g(v)-5 b(alued)39 b(germs)g(b)n(y)g(allo)n(wing) f(gauge)g(transformations:)59 b(if)40 b Fu(H)r(;)14 b(K)p Black 1788 5919 a FB(11)p Black eop %%Page: 12 12 12 11 bop Black Black 538 390 a FB(are)33 b(germs)g(of)h(matrix)f(v)-5 b(alued)34 b(maps,)i(w)n(e)d(denote)h Fu(H)41 b Ft(\030)33 b Fu(K)40 b FB(if)34 b(there)g(exists)g(a)538 490 y(canonical)27 b(transformation)h Fu(\037)h FB(and)g(an)g(in)n(v)n(ertible)f(matrix)g (v)-5 b(alued)30 b(function)f Fu(A)538 589 y FB(suc)n(h)i(that)i Fu(H)28 b Ft(\016)21 b Fu(\037)30 b FB(=)g Fu(A)1313 559 y Fq(t)1343 589 y Fu(K)6 b(A)p FB(.)49 b(This)32 b(implies)h(det\()p Fu(H)7 b FB(\))31 b Ft(\030)f FB(det\()p Fu(K)6 b FB(\))32 b(as)g(germs)f(of)538 689 y(functions.)662 789 y(The)37 b(pro)r(of)f(splits)g(in)n(to)g(sev)n(eral)f(steps.)64 b(The)36 b(idea)h(is)f(to)g(start)g(\014nding)h(a)538 888 y(normal)19 b(form)i(for)f(the)h(ideal)g(generated)f(b)n(y)g(the)h (determinan)n(t)g Fu(p)g FB(\(the)g(disp)r(ersion)538 988 y(relation\).)p Black 614 1121 a(1.)p Black 41 w(Assuming)38 b(h)n(yp)r(othesis)g Fo(\(1\))p FB(,)j Fo(\(2\))d FB(and)g Fo(\(3\))p FB(,)j(w)n(e)d(pro)n(v)n(e)e(\014rst)i(that)g Fu(p)j Ft(\030)720 1220 y Fu(p)762 1232 y FA(0)818 1220 y FB(+)18 b Fu(O)964 1232 y FA(\006)1016 1220 y FB(\(3\).)720 1337 y(Let)30 b(us)g(denote)g(b)n(y)g Fu(A)1430 1349 y Fq(\033)1505 1337 y FB(the)g(linearized)f(v)n(ector)g(\014eld)h(of)g Ft(X)2616 1349 y Fq(p)2684 1337 y FB(at)g(the)g(p)r(oin)n(t)720 1436 y Fu(\033)38 b Ft(2)d FB(\006)g(and)f(b)n(y)h Ft(\006)p Fu(\025)p FB(\()p Fu(\033)s FB(\))p Fu(;)49 b(\025)p FB(\()p Fu(\033)s FB(\))36 b Fu(>)f FB(0)f(the)h(non)f(zero)g(eigen)n (v)-5 b(alues)33 b(of)h Fu(A)3054 1448 y Fq(\033)3099 1436 y FB(.)720 1536 y(Using)40 b(our)g(h)n(yp)r(othesis)g(on)g Fu(p)p FB(,)j(w)n(e)d(c)n(ho)r(ose)f(v)n(ectors)g Fu(e)2530 1548 y FA(2)2567 1536 y Fu(;)14 b(f)2645 1548 y FA(2)2726 1536 y Ft(2)45 b Fu(T)2875 1548 y Fq(\033)2919 1536 y Fu(T)2980 1506 y Fq(?)3017 1536 y Fr(R)3077 1506 y Fq(n)720 1636 y FB(so)31 b(that)i Fu(!)s FB(\()p Fu(f)1139 1648 y FA(2)1175 1636 y Fu(;)14 b(e)1251 1648 y FA(2)1288 1636 y FB(\))31 b(=)f(1)p Fu(;)45 b(Af)1659 1648 y FA(2)1726 1636 y FB(=)30 b(0)p Fu(;)46 b(Ae)2033 1648 y FA(2)2100 1636 y FB(=)30 b Fu(\025)p FB(\()p Fu(\033)s FB(\))p Fu(f)2398 1648 y FA(2)2436 1636 y FB(.)50 b(There)31 b(exist)h(lo)r(cal)720 1735 y(co)r(ordinates)18 b(\()p Fu(\030)1221 1747 y FA(2)1258 1735 y Fu(;)c(x)1342 1705 y Fp(0)1366 1735 y Fu(;)g(\030)1443 1705 y Fp(0)1466 1735 y FB(\))20 b(on)e(\006)h(so)f(that)h Fu(f)2008 1747 y FA(2)2068 1735 y FB(=)k Fu(@)2200 1747 y Fq(\030)2230 1755 y Fj(2)2286 1735 y FB(and)c Fu(!)2491 1750 y Fp(j)p FA(\006)2585 1735 y FB(=)j Fu(d\030)2755 1705 y Fp(0)2780 1735 y Ft(^)q Fu(dx)2926 1705 y Fp(0)2950 1735 y FB(.)34 b(W)-7 b(e)720 1835 y(extend)28 b(these)h(co)r(ordinates)d(to)i Fu(T)1796 1847 y FA(\006)1847 1835 y Fu(T)1908 1805 y Fq(?)1945 1835 y Fr(R)2005 1805 y Fq(n)2079 1835 y FB(b)n(y)g(c)n(ho)r (osing)e Fu(e)2571 1847 y FA(1)2608 1835 y Fu(;)14 b(f)2686 1847 y FA(1)2747 1835 y Ft(2)24 b Fu(T)2875 1847 y Fq(\033)2919 1835 y Fu(T)2980 1805 y Fq(?)3017 1835 y Fr(R)3077 1805 y Fq(n)720 1934 y FB(so)30 b(that)i Fu(A)1071 1946 y Fq(\033)1116 1934 y Fu(e)1155 1946 y FA(1)1220 1934 y FB(=)c Fu(\025)p FB(\()p Fu(\033)s FB(\))p Fu(e)1514 1946 y FA(1)1552 1934 y FB(,)k Fu(A)1669 1946 y Fq(\033)1714 1934 y Fu(f)1755 1946 y FA(1)1821 1934 y FB(=)c Ft(\000)p Fu(\025)p FB(\()p Fu(\033)s FB(\))p Fu(f)2182 1946 y FA(1)2251 1934 y FB(and)i Fu(!)i FB(=)c Fu(f)2642 1904 y Fq(?)2633 1955 y FA(1)2700 1934 y Ft(^)21 b Fu(e)2815 1904 y Fq(?)2815 1955 y FA(1)2873 1934 y FB(+)g Fu(f)3009 1904 y Fq(?)3000 1955 y FA(2)3067 1934 y Ft(^)720 2034 y Fu(e)759 2004 y Fq(?)759 2055 y FA(2)821 2034 y FB(+)j Fu(d\030)993 2004 y Fp(0)1041 2034 y Ft(^)h Fu(dx)1211 2004 y Fp(0)1235 2034 y FB(.)63 b(Applying)37 b(W)-7 b(einstein's)36 b(theorem)g(\([47])g(Theo.)63 b(4.1.\),)720 2134 y(these)31 b(co)r(ordinates)e(can)g(b)r(e)i(extended)g(to)f (symplectic)g(co)r(ordinates)f(near)720 2233 y(\006.)37 b(W)-7 b(e)28 b(ha)n(v)n(e)f(then)h(clearly)e Fu(p)d FB(=)g Fu(\025)p FB(\()p Fu(\033)s FB(\)\()p Fu(x)2023 2245 y FA(1)2062 2233 y Fu(\030)2098 2245 y FA(1)2154 2233 y Ft(\000)18 b Fu(x)2284 2203 y FA(2)2284 2254 y(2)2322 2233 y FB(\))g(+)g Fu(O)2518 2245 y FA(\006)2570 2233 y FB(\(3\).)720 2350 y(W)-7 b(e)31 b(remark)e(for)h(later)g(use)h(that) g Fu(x)1857 2362 y FA(2)1925 2350 y FB(is)g(uniquely)g(de\014ned)g(up)g (to)f Ft(\006)g FB(mo)r(d)720 2449 y Fu(O)783 2461 y FA(\006)835 2449 y FB(\(2\))e(\(lo)r(ok)f(at)g(the)h(Hamiltonian)g(v)n (ector)e(\014eld)i(of)g Fu(x)2474 2461 y FA(2)2539 2449 y FB(on)f(\006\).)720 2565 y(W)-7 b(e)31 b(remark)e(for)h(later)g(use)h (that)g Fu(x)1857 2577 y FA(2)1925 2565 y FB(is)g(uniquely)g(de\014ned) g(up)g(to)f Ft(\006)g FB(mo)r(d)720 2665 y Fu(O)783 2677 y FA(\006)835 2665 y FB(\(2\).)p Black 614 2798 a(2.)p Black 41 w(Using)40 b(Lemma)g(3)g(in)g(order)f(to)h(solv)n(e)f(the)h (homological)e(equation,)43 b(w)n(e)720 2897 y(pro)n(v)n(e)37 b(that)h Fu(p)j Ft(\030)f Fu(p)1375 2909 y FA(0)1438 2897 y FB(+)25 b Fu(O)1591 2909 y FA(\006)1643 2897 y FB(\()p Ft(1)p FB(\):)59 b(if)38 b(w)n(e)g(assume)g Fu(p)i FB(=)h Fu(p)2619 2909 y FA(0)2681 2897 y FB(+)25 b Fu(r)2808 2909 y Fq(N)2910 2897 y FB(where)720 2997 y Fu(r)757 3009 y Fq(N)844 2997 y FB(=)d Fu(O)994 3009 y FA(\006)1046 2997 y FB(\()p Fu(N)9 b FB(\))27 b(and)f Fu(N)32 b Ft(\025)22 b FB(3,)k(w)n(e)g(use)g Fu(\037)1965 3009 y Fq(N)2055 2997 y FB(whic)n(h)g(is)g(the)h(time)f(1)g(\015o)n(w)g(of)g(an)720 3097 y(Hamiltonian)g Fu(U)32 b FB(=)22 b Fu(O)1435 3109 y FA(\006)1487 3097 y FB(\()p Fu(N)9 b FB(\))26 b(and)g Fu(e)d FB(=)g(1)14 b(+)h Fu(V)44 b FB(with)27 b Fu(V)42 b FB(=)22 b Fu(O)2619 3109 y FA(\006)2671 3097 y FB(\()p Fu(N)i Ft(\000)15 b FB(2\).)36 b(W)-7 b(e)720 3196 y(solv)n(e)1539 3296 y Ft(f)p Fu(U;)14 b(p)1717 3308 y FA(0)1753 3296 y Ft(g)k FB(+)g Fu(V)h(p)2005 3308 y FA(0)2065 3296 y FB(=)j Fu(r)2189 3308 y Fq(N)2281 3296 y Fu(;)720 3445 y FB(w)n(e)33 b(get)h(a)f(remainder)g(term)g Fu(r)1708 3457 y Fq(N)6 b FA(+1)1889 3445 y FB(=)32 b Fu(O)2049 3457 y FA(\006)2101 3445 y FB(\()p Fu(N)g FB(+)22 b(1\))33 b(and)h(w)n(e)f(pro)r(ceed)g(b)n(y)720 3545 y(induction.)1121 3515 y FA(1)p Black 614 3678 a FB(3.)p Black 41 w(W)-7 b(e)25 b(w)n(an)n(t)e(to)h(pro)n(v)n(e)e(that)i Fu(p)f Ft(\030)g Fu(p)1748 3690 y FA(0)1796 3678 y FB(+)11 b Fu(O)1935 3690 y Fq(Y)1992 3678 y FB(\()p Ft(1)p FB(\).)37 b(W)-7 b(e)24 b(ha)n(v)n(e)f(already)f Fu(p)h FB(=)g Fu(p)3010 3690 y FA(0)3058 3678 y FB(+)720 3778 y Fu(O)783 3790 y FA(\006)835 3778 y FB(\()p Ft(1)p FB(\).)37 b(Let)26 b Fu( )g FB(:)e Fu(T)1377 3747 y Fq(?)1414 3778 y Fr(R)1474 3747 y Fq(n)1542 3778 y Ft(!)f FB([0)p Fu(;)14 b FB(1])25 b(a)h(function)g(whic)n(h)g(is)g(homogeneous)f(of)720 3877 y(degree)18 b(0)h(w.r.)34 b(to)19 b(\()p Fu(x)1376 3889 y FA(1)1414 3877 y Fu(;)14 b(\030)1487 3889 y FA(1)1524 3877 y Fu(;)g(x)1608 3889 y FA(2)1646 3877 y FB(\),)21 b(v)-5 b(anishes)19 b(in)h(a)e(conical)h(neigh)n(b)r(ourho)r(o)r(d)57 b(of)720 3977 y(the)26 b(cone)e Fu(p)1089 3989 y FA(0)1149 3977 y FB(=)f(0,)i(is)g(1)g(in)g(some)g(conical)f(neigh)n(b)r(ourho)r (o)r(d)74 b(of)25 b Fu(Y)44 b FB(and)25 b(the)720 4076 y(restriction)31 b(of)h(whic)n(h)g(to)g(the)g(unit)h(sphere)e(is)h(smo) r(oth.)50 b(W)-7 b(e)32 b(de\014ne)g Fu(e)g FB(as)720 4176 y(follo)n(ws)27 b(:)1560 4276 y Fu(e)c FB(=)g(\(1)18 b Ft(\000)g Fu( )s FB(\))h(+)f Fu( )2161 4219 y(p)p 2143 4257 80 4 v 2143 4333 a(p)2185 4345 y FA(0)2259 4276 y Fu(:)720 4464 y FB(One)28 b(can)g(c)n(hec)n(k)g(that)g Fu(e)g FB(is)h(smo)r(oth)f(and)g(non)g(v)-5 b(anishing)28 b(near)f(\006)i(and)f(w)n(e)720 4564 y(ha)n(v)n(e)f Fu(p)22 b FB(=)h Fu(ep)1145 4576 y FA(0)1200 4564 y FB(+)18 b Fu(O)1346 4576 y Fq(Y)1404 4564 y FB(\()p Ft(1)p FB(\).)p Black 614 4697 a(4.)p Black 41 w(W)-7 b(e)25 b(use)g(Nelson's)f (theorem)h(8)f(\(p.)36 b(46)24 b(of)h([43)o(]\))g(\(see)g(also)f (subsection)g(6.1\):)p Black 792 4830 a Ft(\017)p Black 41 w FB(With)1099 4800 y Fp(00)1142 4830 y Fu(X)1218 4800 y Fp(00)1211 4850 y FA(0)1298 4830 y FB(=)39 b Ft(X)1461 4842 y Fq(p)1495 4850 y Fj(0)1532 4830 y FB(,)1594 4800 y Fp(00)1637 4830 y Fu(X)1713 4800 y Fp(00)1793 4830 y FB(=)g Ft(X)1956 4842 y Fq(p)1994 4830 y FB(,)h(where)c Fu(p)25 b Ft(\000)f Fu(p)2504 4842 y FA(0)2580 4830 y FB(=)38 b Fu(O)2746 4842 y Fq(Y)2804 4830 y FB(\()p Ft(1)p FB(\))g(and)875 4929 y Fu(p)28 b Ft(\000)f Fu(p)1079 4941 y FA(0)1158 4929 y FB(compactly)40 b(supp)r(orted,)45 b(and)2176 4899 y Fp(00)2219 4929 y Fu(N)2295 4899 y Fp(00)2383 4929 y FB(=)g Fu(Y)19 b FB(.)78 b(W)-7 b(e)42 b(get)f Fu(p)46 b Ft(\030)875 5029 y Fu(p)917 5041 y FA(0)973 5029 y FB(+)18 b Fu(O)1119 5044 y Fp(f)p Fq(x)1191 5052 y Fj(1)1223 5044 y FA(=0)p Fp(g)1346 5029 y FB(\()p Ft(1)p FB(\).)p Black 792 5145 a Ft(\017)p Black 41 w FB(With)1091 5115 y Fp(00)1134 5145 y Fu(X)1210 5115 y Fp(00)1203 5166 y FA(0)1277 5145 y FB(=)25 b Ft(\000X)1491 5157 y Fq(p)1525 5165 y Fj(0)1561 5145 y FB(,)1614 5115 y Fp(00)1656 5145 y Fu(X)1732 5115 y Fp(00)1800 5145 y FB(=)g Ft(\000X)2014 5157 y Fq(p)2052 5145 y FB(,)k(where)g Fu(p)19 b Ft(\000)g Fu(p)2533 5157 y FA(0)2595 5145 y FB(=)25 b Fu(O)2748 5160 y Fp(f)p Fq(x)2820 5168 y Fj(1)2853 5160 y FA(=0)p Fp(g)2975 5145 y FB(\()p Ft(1)p FB(\))875 5245 y(and)34 b Fu(p)22 b Ft(\000)g Fu(p)1236 5257 y FA(0)1306 5245 y FB(compactly)33 b(supp)r(orted,)i(and)2299 5215 y Fp(00)2342 5245 y Fu(N)2418 5215 y Fp(00)2493 5245 y FB(=)d Ft(f)p Fu(x)2679 5257 y FA(1)2749 5245 y FB(=)h(0)p Ft(g)p FB(.)53 b(W)-7 b(e)875 5345 y(get)28 b(conjugacy)e(of)i(\015o)n(ws.)p Black 330 5414 1200 4 v 422 5467 a Fh(1)457 5491 y Fg(Let)c(us)g(remark)f(that)i(the)g (conclusion)f(of)g(this)f(step)h(is)f(already)h(a)g(corollary)f(of)h (the)g(main)g(result)f(of)h([7].)p Black Black 1788 5919 a FB(12)p Black eop %%Page: 13 13 13 12 bop Black Black Black 614 390 a FB(5.)p Black 41 w(W)-7 b(e)33 b(sho)n(w)f(that)h(b)n(y)f(gauge)g(transform)f Fu(H)2080 402 y Fq(class)2265 390 y Ft(\030)g Fu(H)2430 402 y FA(0)2490 390 y FB(+)21 b Fu(O)2639 402 y FA(\006)2691 390 y FB(\(2\).)52 b(This)33 b(is)720 490 y(based)27 b(on)h(Lemma)f(5.)720 606 y(W)-7 b(e)23 b(can)f(assume)g(the)h(plus)g (sign)f(in)h(the)g(normal)f(form)g(of)h(Lemma)f(5)h(b)n(y)f(us-)720 706 y(ing)c(the)h(canonical)e(transformation)g(\()p Fu(z)1966 718 y FA(1)2003 706 y Fu(;)d(x)2087 718 y FA(2)2125 706 y Fu(;)g(\030)2198 718 y FA(2)2235 706 y Fu(;)g(x)2319 676 y Fp(0)2343 706 y Fu(;)g(\030)2420 676 y Fp(0)2443 706 y FB(\))23 b Ft(!)h FB(\()p Ft(\006)p Fu(z)2741 718 y FA(1)2777 706 y Fu(;)14 b(x)2861 718 y FA(2)2899 706 y Fu(;)g(\030)2972 718 y FA(2)3009 706 y Fu(;)g(x)3093 676 y Fp(0)3117 706 y Fu(;)g(\030)3194 676 y Fp(0)3217 706 y FB(\).)p Black 614 839 a(6.)p Black 41 w(W)-7 b(e)28 b(no)n(w)f(apply)g(Lemma)h(6.)3265 1005 y Fi(\003)455 1104 y FB(F)-7 b(rom)36 b(the)h(previous)f(normal)g(form,)j(w)n(e)d (can)g(deduce)h(some)g(geometrical)e(prop)r(erties:)330 1204 y(the)25 b(dynamics)f(of)g Ft(X)37 b FB(admits)24 b(the)h(co)r(dimension)f(3)g(submanifold)g(\006)g(as)g(a)g(singular)f (manifold,)330 1303 y(\006)37 b(admits)h(smo)r(oth)f(unstable)g (\(resp.)65 b(stable\))38 b(manifold)f(\006)2320 1315 y Fp(\000)2413 1303 y FB(\(resp.)66 b(\006)2743 1315 y FA(+)2798 1303 y FB(\))38 b(whic)n(h)f(are)f(of)330 1403 y(co)r(dimension)27 b(2)g(and)h(b)r(oth)g(included)g(in)n(to)f(a)g (smo)r(oth)h(co)r(dimension)f(1)g(in)n(v)-5 b(arian)n(t)27 b(manifold.)330 1678 y Fv(7)135 b(The)44 b(semi-classical)j(normal)f (form)330 1859 y FB(W)-7 b(e)28 b(ha)n(v)n(e)e(the)i(follo)n(wing)f (normal)g(form:)p Black 330 2026 a Fo(Theorem)k(3)p Black 42 w Fz(Under)21 b(the)h(assumptions)g(\(i\),)i(\(ii\))e(and)h (\(iii\),)i(ther)l(e)c(exists)h(a)g(F)-6 b(ourier)22 b(inte)l(gr)l(al)330 2125 y(op)l(er)l(ator,)40 b(micr)l(olo)l(c)l(al)t (ly)g(unitary,)f Fu(U)9 b Fz(,)39 b(a)e(symb)l(ol)h(of)g(or)l(der)g FB(0)e Fz(denote)l(d)i(by)f Fu(A)2865 2137 y Fq(h)2944 2125 y FB(:)g Fu(T)3065 2095 y Fq(?)3102 2125 y Fu(R)3166 2095 y Fq(n)3247 2125 y Ft(!)330 2225 y Fu(GL)p FB(\(2)p Fu(;)14 b Fr(C)p FB(\))29 b(\(a)f(gauge)e(transform\),)j Fz(and)h(a)g(r)l(e)l(al)g(value)l(d)h(symb)l(ol)f(denote)l(d)1374 2474 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))23 b Ft(\030)1672 2370 y Fp(1)1645 2395 y Fs(X)1648 2572 y Fq(j)s FA(=0)1779 2474 y Fu(\015)1822 2486 y Fq(j)1857 2474 y FB(\()p Fu(\030)1925 2486 y FA(2)1963 2474 y Fu(;)14 b(x)2047 2440 y Fp(0)2070 2474 y Fu(;)g(\030)2147 2440 y Fp(0)2171 2474 y FB(\))p Fu(h)2251 2440 y Fq(j)330 2745 y FB(\(called)28 b(the)g(minimal)f (gap\))i Fz(such)h(that:)879 2978 y Fu(U)945 2943 y Fq(?)994 2957 y Fs(c)983 2978 y Fu(A)1045 2990 y Fq(h)1089 2915 y(?)1146 2957 y Fs(b)1127 2978 y Fu(H)1214 2957 y Fs(c)1202 2978 y Fu(A)1264 2990 y Fq(h)1308 2978 y Fu(U)i FB(=)1496 2957 y Fs(c)1484 2978 y Fu(H)1553 2990 y FA(0)1609 2978 y FB(+)18 b Fu(ih)1788 2951 y Fs(d)1769 2978 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))1942 2860 y Fs(\022)2077 2927 y FB(0)115 b(1)2045 3027 y Ft(\000)p FB(1)82 b(0)2317 2860 y Fs(\023)2396 2978 y FB(+)19 b Fu(O)r FB(\()p Fu(h)2625 2943 y Fp(1)2696 2978 y FB(\))30 b Fu(:)455 3229 y Fz(If)g(the)g (subprincip)l(al)h(symb)l(ol)g(of)1528 3208 y Fs(b)1508 3229 y Fu(H)37 b Fz(vanishes,)31 b Fu(\015)2013 3241 y FA(0)2050 3229 y FB(\()p Fu(\030)2118 3241 y FA(2)2156 3229 y Fu(;)14 b(x)2240 3199 y Fp(0)2264 3229 y Fu(;)g(\030)2341 3199 y Fp(0)2364 3229 y FB(\))23 b(=)g(0)p Fz(.)330 3395 y(Pr)l(o)l(of.{)p Black Black 559 3561 a FB(First)d(using)h(the)g (classical)f(normal)g(form)g(of)h(Theorem)g(2)f(and)h(Egoro)n(v)d (theorem,)538 3660 y(w)n(e)24 b(reduce)h(the)h(system)f(to)1443 3639 y Fs(c)1431 3660 y Fu(H)1500 3672 y FA(0)1551 3660 y FB(+)14 b Fu(h)1693 3639 y Fs(b)1678 3660 y Fu(R)26 b FB(where)2020 3639 y Fs(b)2004 3660 y Fu(R)g FB(is)f(self-adjoin)n(t) g(of)h(order)d(0.)36 b(W)-7 b(e)538 3760 y(normalize)26 b(the)i(next)g(terms)f(\(transp)r(ort)g(equations\))g(b)n(y)g(using)h (Lemma)f(4.)662 3870 y(Let)k(assume)g(that)g(sub\()1465 3849 y Fs(b)1445 3870 y Fu(H)7 b FB(\))29 b(=)g(0.)47 b(It)31 b(is)g(not)g(di\016cult)h(to)f(sho)n(w)f(that,)i(if)g(w)n(e)538 3980 y(c)n(ho)r(ose)817 3959 y Fs(b)797 3980 y Fu(A)24 b FB(so)f(that)h(its)g(subprincipal)f(sym)n(b)r(ol)h(v)-5 b(anishes,)24 b(the)g(samething)f(is)h(true)538 4080 y(for)682 4059 y Fs(b)662 4080 y Fu(A)724 4050 y Fq(?)782 4059 y Fs(b)763 4080 y Fu(H)858 4059 y Fs(b)838 4080 y Fu(A)q FB(.)36 b(It)26 b(is)f(enough)f(then)i(to)f(c)n(ho)r(ose)f Fu(U)34 b FB(so)25 b(that)h(its)f(principal)g(sym)n(b)r(ol)g(is)538 4179 y(constan)n(t)h(to)i(get)f(the)h(fact)g(that)g Fu(\015)1642 4191 y FA(0)1707 4179 y FB(v)-5 b(anishes.)3265 4345 y Fi(\003)330 4620 y Fv(8)135 b(Microlo)t(cal)71 b(description)g(of)g (the)f(solutions)i(of)f(the)532 4769 y(normal)45 b(form)330 4951 y FB(W)-7 b(e)33 b(will)f(assume)f(in)i(this)f(section)g(that)1685 4925 y Fs(d)1665 4951 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))30 b(=)h(0.)50 b(The)32 b(result)g(can)g(b)r(e)g(extended)h(to)f(the)330 5069 y(general)25 b(case)h(using)h(the)g(fact)g(that)1512 5042 y Fs(d)1491 5069 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))27 b(comm)n(utes)g(with)h Fs(c)-84 b Fu(x)2303 5081 y FA(1)2368 5069 y FB(and)2542 5047 y Fs(b)2529 5069 y Fu(\030)2565 5081 y FA(1)2602 5069 y FB(.)37 b(If)27 b(the)h(subprincipal)330 5169 y(sym)n(b)r(ols)f(v)-5 b(anish,)27 b(the)h(form)n(ulae)f(b)r(elo)n (w)g(for)g(the)h(principal)f(sym)n(b)r(ols)g(are)g(still)h(v)-5 b(alid.)p Black 1788 5919 a(13)p Black eop %%Page: 14 14 14 13 bop Black Black 330 390 a Fl(8.1)112 b(Some)38 b(notations)330 543 y FB(W)-7 b(e)38 b(will)g(giv)n(e)e(some)h (notations)g(for)g(the)h(Hamiltonian)2219 522 y Fs(b)2200 543 y Fu(H)7 b FB(.)66 b(All)38 b(geometric)e(sets)i(de\014ned)330 643 y(b)r(elo)n(w)27 b(are)g(preserv)n(ed)f(b)n(y)h(canonical)f (transformations)g(and)i(b)n(y)f(gauge)f(transforms.)455 743 y Fu(C)36 b FB(will)29 b(denote)h(the)g(c)n(haracteristic)e (manifold)i Fu(p)2024 713 y Fp(\000)p FA(1)2112 743 y FB(\(0\))g(where)f Fu(p)h FB(is)g(the)g(determinan)n(t)f(of)330 842 y Fu(H)399 854 y FA(class)537 842 y FB(.)42 b(W)-7 b(e)29 b(ha)n(v)n(e)f Fu(C)k FB(=)25 b(\006)20 b Ft([)g Fu(C)1334 854 y FA(+)1408 842 y Ft([)g Fu(C)1542 854 y Fp(\000)1628 842 y FB(whic)n(h)29 b(is)g(a)g(disjoin)n(t)g(union)g (where)g Fu(C)2853 854 y FA(+)2937 842 y FB(\(resp.)41 b Fu(C)3241 854 y Fp(\000)3298 842 y FB(\))330 942 y(is)32 b(de\014ned)h(b)n(y)f(the)g(fact)g(that)h(b)r(oth)g(eigen)n(v)-5 b(alues)31 b(of)h Fu(H)2132 954 y FA(class)2302 942 y FB(close)f(to)i(0)e(are)g Fu(\025)2876 954 y Fp(\000)2964 942 y FB(=)f(0)g Fu(<)g(\025)3274 954 y FA(+)330 1042 y FB(\(resp.)49 b Fu(\025)631 1054 y Fp(\000)717 1042 y Fu(<)29 b(\025)859 1054 y FA(+)944 1042 y FB(=)h(0\).)48 b(W)-7 b(e)32 b(will)g(also)f(de\014ne)h(\006)1967 1054 y FA(+)2051 1042 y Ft(\032)e Fu(C)38 b FB(\(resp.)48 b(\006)2555 1054 y Fp(\000)2641 1042 y Ft(\032)29 b Fu(C)6 b FB(\))32 b(as)f(the)h(stable)330 1141 y(\(resp.)37 b(unstable\))27 b(manifolds)h(of)f(\006)h(for)f(the)h(dynamics)f Fu(\036)2180 1153 y Fq(t)2237 1141 y FB(of)h Ft(X)2391 1153 y Fq(p)2430 1141 y FB(.)455 1241 y(W)-7 b(e)30 b(will)g(denote)g (b)n(y)g Fu(W)12 b(F)1290 1253 y Fq(h)1333 1241 y FB(\()p Fu(u)1413 1253 y Fq(h)1456 1241 y FB(\))31 b(the)f Fz(semi-classic)l (al)k(wave)f(fr)l(ont)f(set)62 b FB(or)29 b Fz(micr)l(osupp)l(ort)330 1340 y FB(or)f Fz(fr)l(e)l(quency)j(set)e FB(of)f(the)i(family)f Fu(u)1472 1352 y Fq(h)1514 1340 y FB(.)41 b(W)-7 b(e)29 b(will)g(write)g Fu(u)2142 1352 y Fq(h)2209 1340 y FB(=)c(0)j(or)g Fu(u)2520 1352 y Fq(h)2588 1340 y FB(=)d(0\()p Fu(h)2800 1310 y Fp(1)2869 1340 y FB(\))30 b(in)f(\012)g(where)330 1440 y(\012)f(is)f(an)g(op)r(en)h(set)g(in)g Fu(T)1105 1410 y Fq(?)1142 1440 y Fr(R)1202 1410 y Fq(n)1275 1440 y FB(if)g Fu(W)12 b(F)1494 1452 y Fq(h)1537 1440 y FB(\()p Fu(u)1617 1452 y Fq(h)1660 1440 y FB(\))19 b Ft(\\)f FB(\012)23 b(=)g Ft(;)p FB(.)455 1550 y(If)554 1529 y Fu(~)546 1550 y(U)44 b FB(a)36 b(microlo)r(cal)e(solution)h(of)1576 1529 y Fs(b)1557 1550 y Fu(H)1641 1529 y(~)1632 1550 y(U)46 b FB(=)36 b(0)f(in)h(\012,)i(an)e(op)r(en)f(neigh)n(b)r(ourho)r (o)r(d)g(of)h(some)330 1650 y(p)r(oin)n(t)28 b Fu(z)586 1662 y FA(0)646 1650 y Ft(2)23 b FB(\006,)28 b(w)n(e)f(will)h(denote)f (b)n(y)p Black 455 1816 a Ft(\017)p Black 546 1795 a Fu(~)538 1816 y(U)604 1780 y FA(+)595 1839 y Fq(in)691 1816 y FB(the)h(restriction)e(of)1334 1795 y Fu(~)1326 1816 y(U)36 b FB(to)28 b(some)f(neigh)n(b)r(ourho)r(o)r(d)f(of)i Fu(C)2450 1828 y FA(+)2524 1816 y Ft(\\)18 b FB(\006)2657 1828 y FA(+)p Black 455 1994 a Ft(\017)p Black 546 1973 a Fu(~)538 1994 y(U)604 1958 y Fp(\000)595 2017 y Fq(in)691 1994 y FB(the)28 b(restriction)e(of)1334 1973 y Fu(~)1326 1994 y(U)36 b FB(to)28 b(some)f(neigh)n(b)r(ourho)r(o)r(d)f(of)i Fu(C)2450 2006 y Fp(\000)2525 1994 y Ft(\\)18 b FB(\006)2658 2006 y Fp(\000)p Black 455 2172 a Ft(\017)p Black 546 2151 a Fu(~)538 2172 y(U)604 2137 y FA(+)595 2193 y Fq(out)723 2172 y FB(the)28 b(restriction)f(of)1366 2151 y Fu(~)1358 2172 y(U)37 b FB(to)27 b(some)g(neigh)n(b)r(ourho)r(o)r(d)g(of)g Fu(C)2482 2184 y Fp(\000)2557 2172 y Ft(\\)19 b FB(\006)2691 2184 y FA(+)p Black 455 2348 a Ft(\017)p Black 546 2327 a Fu(~)538 2348 y(U)604 2312 y Fp(\000)595 2368 y Fq(out)723 2348 y FB(the)28 b(restriction)f(of)1366 2327 y Fu(~)1358 2348 y(U)37 b FB(to)27 b(some)g(neigh)n(b)r(ourho)r(o)r(d)g(of)g Fu(C)2482 2360 y FA(+)2556 2348 y Ft(\\)19 b FB(\006)2690 2360 y Fp(\000)455 2523 y FB(W)-7 b(e)28 b(will)f(concen)n(trate)g(on)g (solutions)g(whose)g(comp)r(onen)n(t)2339 2502 y Fu(~)2331 2523 y(U)2397 2487 y Fp(\000)2388 2546 y Fq(in)2484 2523 y FB(v)-5 b(anishes.)455 2623 y(W)e(e)28 b(will)f(also)g(use)g(a)g (partial)g(F)-7 b(ourier)27 b(transform)f(w.r.)37 b(to)27 b Fu(x)2394 2635 y FA(1)2432 2623 y FB(:)869 2843 y Fs(b)-49 b Fu(u)o FB(\()p Fu(\030)981 2855 y FA(1)1019 2843 y Fu(;)14 b(x)1103 2855 y FA(2)1141 2843 y Fu(;)g(x)1225 2809 y Fp(0)1248 2843 y FB(\))24 b(=)e(\(2)p Fu(\031)s(h)p FB(\))1595 2809 y Fp(\000)1657 2786 y Fj(1)p 1657 2795 29 3 v 1657 2829 a(2)1714 2730 y Fs(Z)1760 2919 y Ff(R)1820 2843 y Fu(e)1859 2809 y Fp(\000)p Fq(ix)1972 2817 y Fj(1)2004 2809 y Fq(\030)2034 2817 y Fj(1)2066 2809 y Fq(=h)2143 2843 y Fu(u)p FB(\()p Fu(x)2270 2855 y FA(1)2308 2843 y Fu(;)14 b(x)2392 2855 y FA(2)2430 2843 y Fu(;)g(x)2514 2809 y Fp(0)2537 2843 y FB(\))p Ft(j)p Fu(dx)2682 2855 y FA(1)2720 2843 y Ft(j)28 b Fu(:)p Black Black Black 1190 4395 a @beginspecial @setspecial %%BeginDocument: class.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: class.pstex %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Thu Sep 19 09:12:41 2002 %%For: ycolver@mozart (Yves Colin De Verdiere) %%Orientation: Portrait %%BoundingBox: 0 0 203 156 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -26.0 163.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 3712 m -1000 -1000 l 4808 -1000 l 4808 3712 l cp clip 0.06000 0.06000 sc % Polyline 7.500 slw n 1580 395 m 2405 390 l 2930 865 l 2825 1490 l 1585 1480 l 1590 1475 l cp gs col7 0.95 shd ef gr gs col7 s gr % Polyline n 525 1510 m 1575 1505 l 1575 2565 l 1080 2585 l 525 2095 l cp gs col7 0.95 shd ef gr gs col7 s gr % Polyline n 1575 300 m 1575 2700 l gs col0 s gr % Polyline n 450 1500 m 2925 1500 l gs col0 s gr % Polyline n 1500 825 m 1575 975 l 1650 825 l gs col0 s gr % Polyline n 2025 1425 m 2175 1500 l 2025 1575 l gs col0 s gr % Polyline n 1510 2115 m 1575 1990 l 1640 2110 l gs col0 s gr % Polyline n 1180 1415 m 1060 1495 l 1150 1585 l gs col0 s gr $F2psEnd rs %%EndDocument @endspecial 1759 4239 a Fe(U)1835 4198 y Fg(+)1825 4262 y Fd(out)2059 3902 y Fe(U)2135 3861 y Fc(\000)2125 3924 y Fd(out)1234 3714 y Fe(U)1310 3673 y Fc(\000)1300 3740 y Fd(in)1571 3339 y Fe(U)1647 3298 y Fg(+)1637 3365 y Fd(in)1371 4064 y Fe(C)1441 4079 y Fc(\000)2141 3492 y Fe(C)2211 3507 y Fg(+)1724 3854 y FC(\006)1659 3179 y(\006)1729 3194 y Fg(+)2414 3822 y FC(\006)2484 3837 y Fc(\000)p Black 1218 4578 a FB(Figure)f(1:)36 b(the)28 b(microlo)r(cal)e(solutions)p Black Black 330 4971 a Fl(8.2)112 b(Sp)s(ecial)39 b(solution)330 5124 y FB(W)-7 b(e)30 b(will)f(build)h(a)f(sp)r(ecial)g(solution)f(of)i(the)f(mo)r (del)h(problem)e(whic)n(h)i(will)f(allo)n(w)f(to)h(describ)r(e)330 5223 y(all)e(microlo)r(cal)g(solutions)f(of)1298 5202 y Fs(c)1286 5223 y Fu(H)1355 5235 y FA(0)1400 5202 y Fu(~)1392 5223 y(U)32 b FB(=)23 b(0)k(near)g(\006.)455 5323 y(Let)g(us)h(consider)e(the)i(solution)1609 5514 y Fu(~)1601 5535 y(U)1658 5547 y FA(0)1718 5535 y FB(=)1806 5418 y Fs(\022)1909 5484 y Fu(u)1911 5584 y(v)1998 5418 y Fs(\023)3182 5535 y FB(\(15\))p Black 1788 5919 a(14)p Black eop %%Page: 15 15 15 14 bop Black Black 330 390 a FB(of)28 b(the)g(mo)r(del)f(equation:) 1562 484 y Fu(D)1631 496 y FA(1)1668 484 y Fu(u)18 b FB(+)g Fu(x)1864 496 y FA(2)1902 484 y Fu(v)26 b FB(=)d(0)1573 584 y Fu(x)1620 596 y FA(2)1658 584 y Fu(u)18 b FB(+)g Fu(x)1854 596 y FA(1)1891 584 y Fu(v)27 b FB(=)22 b(0)3182 535 y(\(16\))330 723 y(giv)n(en)27 b(b)n(y)p Black 455 879 a Ft(\017)p Black 546 858 a Fu(~)538 879 y(U)604 844 y FA(+)595 900 y Fq(out)695 879 y FB(:)884 1092 y Fu(u)p FB(\()p Fu(x)1011 1104 y FA(1)1049 1092 y Fu(;)14 b(x)1133 1104 y FA(2)1171 1092 y FB(\))23 b(=)f Ft(\000)p Fu(i)1407 996 y Fs(q)p 1490 996 94 4 v 1500 1059 a FA(2)p Fq(\031)p 1500 1073 75 4 v 1517 1120 a(h)1584 1092 y Fu(Y)c FB(\()p Fu(x)1729 1104 y FA(1)1767 1092 y FB(\))p Fu(x)1846 1104 y FA(2)1898 1000 y Fs(\020)1948 1092 y FB(\000\(1)g(+)g Fu(i)2214 1050 y Fq(x)2252 1024 y Fj(2)2252 1066 y(2)p 2213 1073 71 4 v 2229 1120 a Fq(h)2293 1092 y FB(\))2325 1000 y Fs(\021)2375 1017 y Fp(\000)p FA(1)2478 1092 y Fu(e)2527 1025 y Fb(x)2560 1008 y Fj(2)2560 1043 y(2)p 2527 1049 66 3 v 2542 1082 a Fb(h)2602 1062 y FA(\()p Fq(i)12 b FA(log)2770 1031 y Fb(x)2803 1043 y Fj(1)p 2770 1049 V 2785 1082 a Fb(h)2845 1062 y Fp(\000)2907 1039 y Fb(\031)p 2907 1048 36 3 v 2911 1082 a Fj(2)2953 1062 y FA(\))1485 1216 y Fu(v)s FB(\()p Fu(x)1607 1228 y FA(1)1645 1216 y Fu(;)i(x)1729 1228 y FA(2)1767 1216 y FB(\))23 b(=)g Ft(\000)1985 1182 y Fq(x)2023 1190 y Fj(2)p 1984 1197 71 4 v 1984 1244 a Fq(x)2022 1252 y Fj(1)2064 1216 y Fu(u)p FB(\()p Fu(x)2191 1228 y FA(1)2229 1216 y Fu(;)14 b(x)2313 1228 y FA(2)2350 1216 y FB(\))3182 1137 y(\(17\))538 1390 y(where)39 b Fu(Y)59 b FB(is)41 b(the)f(Hea)n(viside)g(function)h(and)f(\000)g(the)h(Gamma)f(function.) 76 b(Previous)538 1489 y(form)n(ulae)18 b(de\014ne)i Fu(u)f FB(as)g(a)h(distribution)f(asso)r(ciated)g(with)h(a)f(lo)r (cally)g(in)n(tegrable)g(function)538 1589 y(and)27 b Fu(v)k FB(outside)c Fu(x)1103 1601 y FA(1)1164 1589 y FB(=)c(0.)538 1720 y(The)g(precise)f(de\014nition)i(of)f(the)g (distribution)g Fu(v)k FB(is)c(giv)n(en)f(b)r(elo)n(w)h(in)g(term)h(of) f(its)g(partial)538 1819 y(F)-7 b(ourier)26 b(transform.)p Black 455 1981 a Ft(\017)p Black 546 1960 a Fu(~)538 1981 y(U)604 1945 y FA(+)595 2004 y Fq(in)663 1981 y FB(:)36 b(the)25 b Fu(h)p FB(-F)-7 b(ourier)24 b(transforms)j Fs(b)-49 b Fu(u)25 b FB(\(resp.)37 b Fs(b)-47 b Fu(v)s FB(\))26 b(with)g(resp)r(ect)f(to)g Fu(x)2664 1993 y FA(1)2701 1981 y FB(,)h(of)g Fu(u)f FB(\(resp.)35 b Fu(v)s FB(\))26 b(at)538 2080 y(the)i(non)f(zero)f(v)-5 b(alues)28 b(of)f Fu(\030)1395 2092 y FA(1)1460 2080 y FB(are)g(giv)n(en,)g(for)g Fu(\030)2002 2092 y Fn(1)2067 2080 y Fu(>)c Fo(0)p FB(,)k(b)n(y:)1455 2301 y Fs(b)-49 b Fu(u)p FB(\()p Fu(\030)1568 2313 y FA(1)1606 2301 y Fu(;)14 b(x)1690 2313 y FA(2)1727 2301 y FB(\))24 b(=)e Ft(\000)1945 2267 y Fq(x)1983 2275 y Fj(2)p 1945 2282 V 1949 2330 a Fq(\030)1979 2338 y Fj(1)2025 2301 y Fu(e)2064 2271 y Fp(\000)2132 2248 y Fb(i)p 2125 2257 35 3 v 2125 2291 a(h)2170 2271 y Fq(x)2208 2246 y Fj(2)2208 2287 y(2)2251 2271 y FA(log)12 b Fq(\030)2378 2279 y Fj(1)1533 2423 y Fs(b)-47 b Fu(v)s FB(\()p Fu(\030)1643 2435 y FA(1)1681 2423 y Fu(;)14 b(x)1765 2435 y FA(2)1803 2423 y FB(\))23 b(=)g Fu(e)1985 2393 y Fp(\000)2052 2370 y Fb(i)p 2046 2379 V 2046 2413 a(h)2090 2393 y Fq(x)2128 2368 y Fj(2)2128 2409 y(2)2172 2393 y FA(log)12 b Fq(\030)2299 2401 y Fj(1)3182 2357 y FB(\(18\))p Black 455 2615 a Ft(\017)p Black 546 2594 a Fu(~)538 2615 y(U)604 2579 y Fp(\000)595 2635 y Fq(out)695 2615 y FB(:)37 b(for)28 b Fu(\030)919 2627 y Fn(1)984 2615 y Fu(<)22 b Fo(0)p FB(,)28 b(b)n(y:)1342 2797 y Fs(b)-49 b Fu(u)o FB(\()p Fu(\030)1454 2809 y FA(1)1492 2797 y Fu(;)14 b(x)1576 2809 y FA(2)1614 2797 y FB(\))23 b(=)1783 2763 y Fq(x)1821 2771 y Fj(2)p 1767 2778 103 4 v 1767 2826 a Fp(j)p Fq(\030)1817 2834 y Fj(1)1849 2826 y Fp(j)1879 2797 y Fu(e)1918 2767 y Fp(\000)1979 2745 y Fb(\031)p 1979 2754 36 3 v 1980 2787 a(h)2025 2767 y Fq(x)2063 2742 y Fj(2)2063 2783 y(2)2099 2797 y Fu(e)2138 2767 y Fp(\000)2206 2745 y Fb(i)p 2200 2754 35 3 v 2200 2787 a(h)2244 2767 y Fq(x)2282 2742 y Fj(2)2282 2783 y(2)2325 2767 y FA(log)13 b Fp(j)p Fq(\030)2473 2775 y Fj(1)2505 2767 y Fp(j)1403 2922 y Fs(b)-47 b Fu(v)s FB(\()p Fu(\030)1513 2934 y FA(1)1551 2922 y Fu(;)14 b(x)1635 2934 y FA(2)1672 2922 y FB(\))24 b(=)e Fu(e)1854 2892 y Fp(\000)1916 2870 y Fb(\031)p 1916 2879 36 3 v 1917 2912 a(h)1962 2892 y Fq(x)2000 2867 y Fj(2)2000 2909 y(2)2036 2922 y Fu(e)2075 2892 y Fp(\000)2143 2870 y Fb(i)p 2137 2879 35 3 v 2137 2912 a(h)2181 2892 y Fq(x)2219 2867 y Fj(2)2219 2909 y(2)2262 2892 y FA(log)13 b Fp(j)p Fq(\030)2410 2900 y Fj(1)2442 2892 y Fp(j)3182 2854 y FB(\(19\))538 3120 y(The)40 b(partial)g(F)-7 b(ourier)39 b(transform)g(of)h Fu(v)k FB(is)c(the)h(distribution)g (asso)r(ciated)e(with)i(the)538 3220 y(lo)r(cally)26 b(in)n(tegrable)h(function)h(giv)n(en)f(b)n(y)g(the)h(previous)f(form)n (ulae.)330 3376 y(One)e(get)f(easily)g(other)h(solutions)f(supp)r (orted)g(b)n(y)h Fu(x)1970 3388 y FA(1)2031 3376 y Ft(\025)d FB(0)j(b)n(y)f(m)n(ultiplying)h(the)h(previous)d(one)330 3476 y(b)n(y)k(an)h(arbitrary)d(function)j(of)g(\()p Fu(x)1413 3488 y FA(2)1451 3476 y Fu(;)14 b Ft(\001)g(\001)g(\001)27 b Fu(;)14 b(x)1696 3488 y Fq(n)1742 3476 y FB(\).)p Black 330 3665 a Fo(Remark)32 b(1)p Black 41 w Fz(:)e(if)938 3639 y Fs(d)918 3665 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))30 b Fz(do)l(es)g(not)f(vanish,)j(our)d(system)h(is)g(r)l(eplac)l(e)l(d)h (by)1572 3835 y Fu(D)1641 3847 y FA(1)1678 3835 y Fu(u)18 b FB(+)g Fu(P)12 b(v)26 b FB(=)d(0)1564 3935 y Fu(P)1629 3905 y Fq(?)1667 3935 y Fu(u)18 b FB(+)g Fu(x)1863 3947 y FA(1)1901 3935 y Fu(v)26 b FB(=)d(0)3182 3886 y(\(20\))330 4133 y Fz(wher)l(e)29 b Fu(P)34 b FB(=)23 b Fu(x)785 4145 y FA(2)837 4133 y FB(+)14 b Fu(ih)1012 4107 y Fs(d)993 4133 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))27 b Fz(c)l(ommutes)g(with)j Fs(c)-84 b Fu(x)1790 4145 y FA(1)1855 4133 y Fz(and)2028 4112 y Fs(b)2015 4133 y Fu(\030)2051 4145 y FA(1)2088 4133 y Fz(.)38 b(We)28 b(c)l(an)g(do)h(the)f(same)g(c)l(alculations)330 4233 y(wher)l(e)i Fu(x)611 4245 y FA(2)678 4233 y Fz(is)f(r)l(eplac)l (e)l(d)i(at)e(some)h(plac)l(es)g(by)g Fu(P)12 b Fz(,)30 b(at)f(other)h(plac)l(es)g(by)g Fu(P)2589 4203 y Fq(?)2627 4233 y Fz(,)f(and)h Fu(x)2889 4203 y FA(2)2889 4254 y(2)2956 4233 y Fz(is)g(r)l(eplac)l(e)l(d)330 4333 y(by)j Fu(P)506 4303 y Fq(?)544 4333 y Fu(P)44 b Fz(or)32 b(by)h Fu(P)12 b(P)991 4303 y Fq(?)1029 4333 y Fz(.)46 b(We)32 b(get)h(the)f(same)h (kind)g(of)g(formulae)g(fr)l(om)g(which)h(we)e(c)l(an)g(de)l(duc)l(e) 330 4432 y(that)i(the)g(r)l(esults)f(describ)l(e)l(d)j(b)l(elow)f(also) g(holds)g(in)f(this)g(c)l(ase)h(with)g(the)f(same)g(rules)g(for)h(the) 330 4546 y(princip)l(al)d(symb)l(ols)e(if)h(the)f(princip)l(al)h(symb)l (ol)g(of)1929 4519 y Fs(d)1909 4546 y Fu(\015)5 b FB(\()p Fu(h)p FB(\))29 b Fz(vanish.)455 4645 y FB(If)f Ft(j)p Fu(x)608 4657 y FA(2)645 4645 y Ft(j)23 b Fu(>>)844 4574 y Ft(p)p 913 4574 48 4 v 71 x Fu(h)k FB(and)h Fu(x)1197 4657 y FA(1)1258 4645 y Ft(\025)22 b Fu(c)h(>)g FB(0,)k(w)n(e)g(get) 1105 4866 y Fu(u)p FB(\()p Fu(x)1232 4878 y FA(1)1270 4866 y Fu(;)14 b(x)1354 4878 y FA(2)1391 4866 y FB(\))24 b(=)e Fu(u)1582 4878 y Fq(W)9 b(K)t(B)1770 4866 y FB(\()p Fu(x)1849 4878 y FA(1)1887 4866 y Fu(;)14 b(x)1971 4878 y FA(2)2009 4866 y FB(\))2055 4749 y Fs(\022)2116 4866 y FB(1)k(+)g Fu(O)r FB(\()2385 4810 y Fu(h)p 2366 4847 85 4 v 2366 4923 a(x)2413 4894 y FA(2)2413 4945 y(2)2461 4866 y FB(\))2493 4749 y Fs(\023)330 5087 y FB(where,)27 b(b)n(y)g(using)h(Stirling's)f(form)n(ula)g(\([1)o(])h(p)g(257\):)964 5336 y Fu(u)1012 5348 y Fq(W)9 b(K)t(B)1200 5336 y FB(\()p Fu(x)1279 5348 y FA(1)1317 5336 y Fu(;)14 b(x)1401 5348 y FA(2)1438 5336 y FB(\))24 b(=)e Ft(\000)p FB(sign)o(\()p Fu(x)1868 5348 y FA(2)1906 5336 y FB(\))p Fu(e)1977 5302 y Fq(i)2011 5279 y Fb(\031)p 2011 5288 36 3 v 2015 5322 a Fj(4)2061 5336 y Fu(e)2100 5272 y Fp(\000)2167 5249 y Fb(i)p 2161 5258 35 3 v 2161 5292 a(h)2206 5272 y Fq(x)2244 5247 y Fj(2)2244 5288 y(2)2276 5190 y Fa(\022)2325 5272 y FA(log)2432 5235 y Fb(x)2465 5218 y Fj(2)2465 5253 y(2)p 2432 5259 66 3 v 2432 5292 a Fb(x)2465 5304 y Fj(1)2507 5272 y Fp(\000)p FA(1)2592 5190 y Fa(\023)2673 5336 y Fu(:)486 b FB(\(21\))455 5507 y(More)26 b(precisely)1249 5655 y Fu(u)p FB(\()p Fu(x)1376 5667 y FA(1)1413 5655 y Fu(;)14 b(x)1497 5667 y FA(2)1535 5655 y FB(\))23 b(=)g Fu(u)1726 5667 y Fq(W)9 b(K)t(B)1914 5655 y FB(\()p Fu(x)1993 5667 y FA(1)2031 5655 y Fu(;)14 b(x)2115 5667 y FA(2)2153 5655 y FB(\))p Fu( )s FB(\()2284 5599 y Fu(x)2331 5569 y FA(2)2331 5619 y(2)p 2284 5636 85 4 v 2303 5712 a Fu(h)2379 5655 y FB(\))p Black 1788 5919 a(15)p Black eop %%Page: 16 16 16 15 bop Black Black 330 390 a FB(where)26 b Fu( )j FB(is)d(the)g(smo)r(oth)g(function)h(on)f(]0)p Fu(;)14 b FB(+)p Ft(1)p FB([,)25 b(con)n(tin)n(uous)g(at)h(0,)g(whose)g(limit)h (at)f(in\014nit)n(y)330 490 y(is)h(1,)h(giv)n(en)f(b)n(y:)1422 627 y Fu( )s FB(\()p Fu(x)p FB(\))e(=)1777 571 y(\000)p 1712 608 182 4 v 1712 684 a(\000)1764 696 y Fq(S)s(tir)1903 627 y FB(\(1)19 b(+)f Fu(ix)p FB(\))28 b Fu(:)330 802 y FB(Moreo)n(v)n(er,)d(w)n(e)i(can)g(c)n(hec)n(k)g(that)1111 1016 y Ft(j)p Fu(u)p FB(\()p Fu(x)1261 1028 y FA(1)1299 1016 y Fu(;)14 b(x)1383 1028 y FA(2)1420 1016 y FB(\))p Ft(j)1475 982 y FA(2)1536 1016 y FB(=)22 b Ft(j)p Fu( )s FB(\()1745 960 y Fu(x)1792 930 y FA(2)1792 981 y(2)p 1746 997 85 4 v 1764 1073 a Fu(h)1840 1016 y FB(\))p Ft(j)1895 982 y FA(2)1956 1016 y FB(=)h(1)18 b Ft(\000)g Fu(e)2226 982 y Fp(\000)p FA(2)p Fq(\031)r(x)2390 957 y Fj(2)2390 998 y(2)2421 982 y Fq(=h)2526 1016 y Fu(:)330 1264 y Fl(8.3)112 b(Microlo)s(cal)38 b(solutions)330 1417 y FB(In)30 b(this)g(section,)g(w)n(e)f(will)h(describ)r(e)g(all)f (microlo)r(cal)g(solutions)g(of)2486 1396 y Fs(c)2474 1417 y Fu(H)2543 1429 y FA(0)2589 1396 y Fu(~)2581 1417 y(U)35 b FB(=)26 b(0)k(for)f(whic)n(h)3213 1396 y Fu(~)3205 1417 y(U)3271 1382 y Fp(\000)3262 1440 y Fq(in)330 1529 y FB(v)-5 b(anishes)27 b(using)g(our)g(previous)g(solution)1674 1508 y Fu(~)1666 1529 y(U)1723 1541 y FA(0)1760 1529 y FB(.)455 1628 y(W)-7 b(e)28 b(get)f(the:)p Black 330 1781 a Fo(Theorem)k(4)p Black 42 w Fz(L)l(et)976 1760 y Fu(~)968 1781 y(U)38 b Fz(b)l(e)30 b(a)g(micr)l(olo)l(c)l(al)i (solution)e(ne)l(ar)g(the)g(origine)h(of)2659 1760 y Fs(c)2647 1781 y Fu(H)2716 1793 y FA(0)2762 1760 y Fu(~)2753 1781 y(U)h FB(=)23 b(0)p Fz(,)30 b(i.e.)1440 1946 y Fu(W)12 b(F)1583 1958 y Fq(h)1626 1946 y FB(\()1670 1925 y Fs(c)1658 1946 y Fu(H)1727 1958 y FA(0)1773 1925 y Fu(~)1765 1946 y(U)d FB(\))18 b Ft(\\)h FB(\012)k(=)g Ft(;)29 b Fu(;)330 2121 y Fz(wher)l(e)h FB(\012)g Fz(is)g(a)g(neighb)l(ourho)l(o)l(d)i(of) f(the)f(origine.)40 b(L)l(et)29 b(us)g(assume)h(mor)l(e)l(over)h(that) 2982 2100 y Fu(~)2974 2121 y(U)3040 2086 y Fp(\000)3031 2145 y Fq(in)3123 2121 y FB(=)22 b(0)p Fz(.)455 2221 y(Then,)30 b(if)h Fu(')831 2233 y Fq(h)874 2221 y FB(\()p Fu(x)953 2233 y FA(2)991 2221 y Fu(;)14 b(x)1075 2191 y Fp(0)1099 2221 y FB(\))23 b(=)h Fs(b)-47 b Fu(v)s FB(\()p Fu(\030)1353 2233 y FA(1)1414 2221 y FB(=)23 b(1)p Fu(;)14 b(x)1628 2233 y FA(2)1665 2221 y Fu(;)g(x)1749 2191 y Fp(0)1772 2221 y FB(\))p Fz(,)31 b(we)f(have)1526 2375 y Fu(~)1518 2396 y(U)i FB(=)22 b Fu(')1748 2408 y Fq(h)1791 2396 y FB(\()p Fu(x)1870 2408 y FA(2)1908 2396 y Fu(;)14 b(x)1992 2362 y Fp(0)2016 2396 y FB(\))2056 2375 y Fu(~)2048 2396 y(U)2105 2408 y FA(0)330 2562 y Fz(micr)l(olo)l(c)l(al)t(ly)32 b(ne)l(ar)e(the)g(origin.)330 2714 y FB(The)e(pro)r(of)f(is)g(an)g (extension)h(of)f(an)g(argumen)n(t)g(giv)n(en)g(in)h([12)o(])f(\(Prop.) 36 b(17\).)455 2814 y(All)25 b(microlo)r(cal)g(solutions)f(near)h(\006) g(are)g(sums)g(of)g(the)h(previous)f(one's)f(and)i(a)f(similar)f(one) 330 2913 y(whose)j(ingoing)f(part)i(is)1137 2892 y Fu(~)1129 2913 y(U)1195 2878 y Fp(\000)1186 2937 y Fq(in)1254 2913 y FB(,)g(i.e.)1456 2892 y Fu(~)1448 2913 y(U)1514 2878 y FA(+)1505 2937 y Fq(in)1597 2913 y FB(=)22 b(0.)330 3185 y Fv(9)135 b(Lagrangian)46 b(states)330 3383 y Fl(9.1)112 b(Qualitativ)m(e)39 b(description)330 3545 y FB(W)-7 b(e)37 b(w)n(an)n(t)e(to)h(describ)r(e)g(solutions)f(for)h(whic)n(h) 1878 3524 y Fu(~)1870 3545 y(U)1936 3510 y Fp(\000)1927 3568 y Fq(in)2031 3545 y FB(v)-5 b(anishes)36 b(while)2599 3524 y Fu(~)2591 3545 y(U)2657 3510 y FA(+)2648 3568 y Fq(in)2753 3545 y FB(is)g(a)g(Lagrangian)330 3645 y(state)28 b(asso)r(ciated)f(to)i(a)f(germ)f(of)i(Lagrangian)d(manifold)i(\003) 2245 3609 y FA(+)2245 3668 y Fq(in)2338 3645 y Ft(\032)c Fu(T)2488 3615 y Fq(?)2525 3645 y Fr(R)2585 3615 y Fq(n)2659 3645 y FB(whic)n(h)k(is)h(con)n(tained)330 3744 y(in)k Fu(C)491 3756 y FA(+)579 3744 y FB(near)e(some)h(p)r(oin)n(t)g Fu(z)j Ft(2)c Fu(C)1421 3756 y FA(+)1498 3744 y Ft(\\)22 b FB(\006)1635 3756 y FA(+)1690 3744 y FB(.)51 b(W)-7 b(e)33 b(will)g(assume)e(that)i(\003)2608 3709 y FA(+)2608 3767 y Fq(in)2709 3744 y FB(and)f(\006)2935 3756 y FA(+)3023 3744 y FB(in)n(tersect)330 3844 y(transv)n(ersally)i(inside)i Fu(C)1136 3814 y FA(+)1192 3844 y FB(.)63 b(Their)36 b(in)n(tersection)f(is)h(then)h(an)f(isotropic)f(manifold)i Fu(W)3170 3808 y FA(+)3158 3867 y Fq(in)3263 3844 y FB(of)330 3944 y(dimension)28 b Fu(n)18 b Ft(\000)g FB(1.)36 b(W)-7 b(e)28 b(will)g(denote)g(b)n(y)1289 4109 y Fu(W)1367 4121 y FA(0)1428 4109 y FB(=)22 b Ft(f)47 b FB(lim)1557 4159 y Fq(t)p Fp(!)p FA(+)p Fp(1)1779 4109 y Fu(\036)1828 4121 y Fq(t)1858 4109 y FB(\()p Fu(z)t FB(\))p Ft(j)p Fu(z)26 b Ft(2)e Fu(W)2222 4074 y FA(+)2210 4132 y Fq(in)2279 4109 y Ft(g)j Fu(:)330 4306 y(W)408 4318 y FA(0)485 4306 y FB(is)40 b(an)f(isotropic)g(submanifold)g(of)h(\006)f(of)h(dimension) f Fu(n)27 b Ft(\000)f FB(2)39 b(transv)n(ersal)e(to)i(the)h(one)330 4406 y(dimensional)35 b(n)n(ull)h(foliation)f(\004)h(of)g(\006.)61 b(W)-7 b(e)36 b(will)g(also)f(denote)h(b)n(y)f Fu(W)2618 4370 y Fp(\000)2606 4426 y Fq(out)2744 4406 y Ft(\032)h FB(\006)2905 4375 y FA(+)2984 4406 y Ft(\\)25 b Fu(C)3123 4418 y Fp(\000)3215 4406 y FB(the)330 4505 y(isotropic)h(submanifold)i (of)g(dimension)f Fu(n)18 b Ft(\000)g FB(1)1162 4671 y Fu(W)1252 4635 y Fp(\000)1240 4691 y Fq(out)1365 4671 y FB(=)k Ft(f)p Fu(z)t Ft(j)60 b FB(lim)1574 4720 y Fq(t)p Fp(!)p FA(+)p Fp(1)1795 4671 y Fu(\036)1844 4683 y Fq(t)1874 4671 y FB(\()p Fu(z)t FB(\))23 b Ft(2)g Fu(W)2160 4683 y FA(0)2198 4671 y Ft(g)18 b(\\)h Fu(C)2391 4683 y Fp(\000)2475 4671 y Fu(:)p Black 330 4893 a Fo(Theorem)31 b(5)p Black 42 w Fz(L)l(et)973 4872 y Fu(~)965 4893 y(U)1031 4858 y FA(+)1022 4916 y Fq(in)1113 4893 y Ft(2)24 b Fu(I)1235 4863 y FA(0)1272 4893 y FB(\(\003)1362 4858 y FA(+)1362 4916 y Fq(in)1431 4893 y FB(\))i Fz(b)l(e)h(a)g(micr)l(olo)l(c)l(al)h (solution)f(of)2462 4872 y Fs(c)2450 4893 y Fu(H)2519 4905 y FA(0)2565 4872 y Fu(~)2557 4893 y(U)2623 4858 y FA(+)2614 4916 y Fq(in)2705 4893 y FB(=)c(0)p Fz(.)37 b(Ther)l(e)27 b(exists)330 5008 y(an)36 b(unique)f(micr)l(olo)l(c)l(al) i(solution)e(of)1559 4987 y Fs(c)1548 5008 y Fu(H)1617 5020 y FA(0)1662 4987 y Fu(~)1654 5008 y(U)42 b FB(=)33 b(0)i Fz(in)g(some)h(neighb)l(ourho)l(o)l(d)i(of)e FB(\006)f Fz(such)h(that)338 5086 y Fu(~)330 5107 y(U)396 5072 y Fp(\000)387 5131 y Fq(in)485 5107 y Fz(vanishes.)455 5207 y(We)29 b(have)i(the)f(fol)t(lowing)i(qualitative)f(description)h (of)f(this)f(solution:)p Black 454 5359 a Ft(\017)p Black 42 w Fz(The)37 b(\015ow-out)g FB(\003)1100 5329 y Fp(0)1159 5359 y Ft(\032)e Fu(C)1318 5371 y FA(+)1411 5359 y Fz(of)i FB(\003)1573 5324 y FA(+)1573 5383 y Fq(in)1665 5359 y Ft(n)23 b FB(\006)1790 5371 y FA(+)1882 5359 y Fz(by)38 b Fu(\036)2047 5371 y Fq(t)2113 5359 y Fz(is)g(a)f(smo)l(oth)g(L)l(agr) l(angian)h(manifold)538 5471 y(whose)c(closur)l(e)h(is)f(singular)g (along)h FB(\006)1766 5483 y Fp(\000)1843 5471 y Ft(\\)22 b Fu(C)1979 5483 y FA(+)2034 5471 y Fz(.)2118 5450 y Fu(~)2110 5471 y(U)42 b Fz(is)35 b(a)f(L)l(agr)l(angian)h(distribution) f(of)538 5571 y(or)l(der)d FB(0)e Fz(on)i FB(\003)1006 5541 y Fp(0)1029 5571 y Fz(.)40 b(Its)29 b(princip)l(al)k(symb)l(ol)e (do)l(es)f(not)g(extend)g(c)l(ontinuously)g(\(in)g(gener)l(al\))538 5670 y(along)g FB(\006)818 5682 y Fp(\000)893 5670 y Ft(\\)18 b Fu(C)1025 5682 y FA(+)1111 5670 y Fz(although)31 b FB(\003)1500 5640 y Fp(0)1552 5670 y Fz(is)f Fu(C)1706 5640 y FA(1)1774 5670 y Fz(\(but)f(not)g Fu(C)2159 5640 y FA(2)2196 5670 y Fz(\).)p Black 1788 5919 a FB(16)p Black eop %%Page: 17 17 17 16 bop Black Black Black 454 390 a Ft(\017)p Black 42 w Fz(A)n(long)26 b Fu(C)831 402 y Fp(\000)888 390 y Fz(,)949 369 y Fu(~)941 390 y(U)31 b FB(=)1125 369 y Fu(~)1117 390 y(U)1183 355 y Fp(\000)1174 411 y Fq(out)1302 390 y Fz(is)c(a)g(Gaussian)h(state)e(of)i(or)l(der)2334 358 y FA(1)p 2334 372 34 4 v 2334 419 a(2)2404 390 y Fz(asso)l(ciate)l(d)h(to)d(the)h(isotr)l(opic)538 499 y(manifold)k Fu(W)971 463 y Fp(\000)959 519 y Fq(out)1091 499 y Fz(and)f(a)g(p)l(ositive)h(L)l(agr)l(angian)g(manifold)h FB(\003)2456 463 y Fp(\000)2456 519 y Fq(out)2557 499 y Fz(.)330 656 y(Pr)l(o)l(of.{)p Black Black 565 801 a FB(It)27 b(is)h(of)f(course)f(enough)g(to)h(pro)n(v)n(e)f(the)i (theorem)e(for)h(the)h(mo)r(del.)36 b(In)28 b(this)f(case)546 880 y Fu(~)538 901 y(U)36 b FB(=)26 b Fu(')796 880 y(~)776 901 y(U)833 913 y FA(0)901 901 y FB(where)j Fu(')p FB(\()p Fu(x)1276 913 y FA(2)1315 901 y Fu(;)14 b(x)1399 870 y Fp(0)1422 901 y FB(\))31 b(is)f(an)n(y)f(Lagrangian)e(state)j(w.r.)44 b(to)30 b(the)h(v)-5 b(ariables)538 1000 y(\()p Fu(x)617 1012 y FA(2)655 1000 y Fu(;)14 b(x)739 970 y Fp(0)762 1000 y FB(\).)36 b(The)24 b(theorem)f(follo)n(ws)g(directly)h(b)n(y)f (examination)g(of)h(the)g(expressions)538 1110 y(of)640 1089 y Fu(~)632 1110 y(U)689 1122 y FA(0)754 1110 y FB(giv)n(en)i(b)n (y)i(Theorem)f(4.)3265 1255 y Fi(\003)330 1483 y Fl(9.2)112 b(Principal)38 b(sym)m(b)s(ols)330 1636 y FB(W)-7 b(e)29 b(will)h(no)n(w)e(describ)r(e)h(a)f(construction)g(of)h(the)h (Lagrangian)c(manifold)j(\003)2757 1601 y Fp(\000)2757 1657 y Fq(out)2887 1636 y FB(as)f(w)n(ell)h(as)f(of)330 1745 y(the)g(principal)f(sym)n(b)r(ol)g(of)1206 1724 y Fu(~)1198 1745 y(U)1264 1710 y Fp(\000)1255 1766 y Fq(out)1356 1745 y FB(.)330 1957 y Fo(9.2.1)94 b(Logarithmic)31 b(maps)330 2110 y FB(Let)h Fu(X)37 b FB(b)r(e)32 b(a)f(\014xed)h (\014nite)g(dimensional)f(complex)g(v)n(ector)f(space)g(and)i Fu(G)2699 2122 y Fq(n)2776 2110 y FB(the)f(Grassmann)330 2210 y(manifold)36 b(of)h(its)g(complex)f(subspaces)f(of)h(dimension)h Fu(n)p FB(.)63 b(W)-7 b(e)37 b(will)g(sa)n(y)e(that)i(a)f(map)g Fu(F)50 b FB(:)330 2309 y(])17 b Ft(\000)g Fu(a;)d FB(0[)p Ft(!)22 b Fu(G)768 2321 y Fq(n)840 2309 y FB(is)27 b Fz(lo)l(garithmic)i FB(if)f(there)e(exist)h(maps)g Fu(f)2093 2321 y Fq(j)2150 2309 y FB(:])17 b Ft(\000)g Fu(a;)d FB(0[)p Ft(!)22 b Fu(X)r(;)41 b(j)28 b FB(=)23 b(1)p Fu(;)14 b Ft(\001)g(\001)g(\001)27 b Fu(;)14 b(n)p FB(,)26 b(suc)n(h)330 2409 y(that)35 b Fu(f)558 2421 y Fq(j)592 2409 y FB(\()p Fu(u)p FB(\))g(=)e Fu(e)876 2421 y Fq(j)925 2409 y FB(log)14 b Ft(j)p Fu(u)p Ft(j)23 b FB(+)f Fu(g)1290 2421 y Fq(j)1325 2409 y FB(\()p Fu(u)p FB(\))34 b(with)h Fu(g)1707 2421 y Fq(j)1776 2409 y FB(smo)r(oth)f(at)g(0)g(and)g Fu(F)12 b FB(\()p Fu(u)p FB(\))35 b(is)f(the)h(v)n(ector)e(space)330 2508 y(freely)g(generated)f(b)n(y)h(the)h Fu(f)1257 2520 y Fq(j)1292 2508 y FB(\()p Fu(u)p FB(\)'s.)54 b(Suc)n(h)33 b(a)g(mapping)g Fu(F)45 b FB(admits)34 b(a)f(formal)f(extension)h(to) 330 2608 y Fu(u)23 b(>)f FB(0)i(de\014ned)g(b)n(y)g Fu(f)989 2620 y Fq(j)1023 2608 y FB(\()p Fu(u)p FB(\))f(=)g Fu(e)1285 2620 y Fq(j)1320 2608 y FB(\(log)14 b Fu(u)d FB(+)g Fu(i\031)s FB(\))g(+)g Fu(g)1846 2620 y Fq(j)1880 2608 y FB(\()p Fu(u)p FB(\).)36 b(This)24 b(extension,)g(called)f(the)i Fz(c)l(anonic)l(al)330 2708 y(extension)37 b(of)i Fu(F)12 b FB(,)39 b(is)d(indep)r(enden)n(t)h(of)f(the)h(c)n(hoice)e(of)i(the)f (basis)g(as)f(w)n(ell)i(as)e(in)n(v)-5 b(arian)n(t)35 b(b)n(y)330 2807 y(increasing)26 b(di\013eomorphisms)h Fu( )k FB(in)d Fu(u)f FB(suc)n(h)g(that)h Fu( )s FB(\(0\))23 b(=)g(0.)330 3019 y Fo(9.2.2)94 b(The)32 b(transmission)e(rule)h(for)h (the)g(Lagrangian)h(manifold)330 3172 y FB(W)-7 b(e)29 b(will)g(c)n(ho)r(ose)e(a)h(tra)5 b(jectory)27 b Fu(\015)1398 3184 y FA(+)1453 3172 y FB(\()p Fu(t)p FB(\))p Fu(;)44 b(t)24 b Ft(2)p FB(])p Fu(t)1776 3184 y FA(0)1814 3172 y Fu(;)14 b FB(+)p Ft(1)p FB([)p Fu(;)28 b FB(of)h Ft(X)2228 3184 y Fq(p)2295 3172 y FB(con)n(tained)f(in)h(\003)2828 3136 y FA(+)2828 3195 y Fq(in)2916 3172 y Ft(\\)19 b FB(\006)3050 3142 y FA(+)3105 3172 y FB(.)40 b(This)330 3272 y(tra)5 b(jectory)36 b(admits)i(an)g(unique)g(prolongation)e Fu(\015)1955 3284 y Fp(\000)2049 3272 y FB(as)h(another)g(tra)5 b(jectory)37 b(con)n(tained)g(in)330 3371 y Fu(C)395 3341 y Fp(\000)471 3371 y Ft(\\)20 b FB(\006)606 3341 y FA(+)690 3371 y FB(so)28 b(that)i(the)f(closure)f(of)h(their)g(union) g(is)g(a)g(smo)r(oth)g(arc)f(denote)h(b)n(y)g Fu(\015)5 b FB(\()p Fu(u)p FB(\))29 b(with)g Fu(u)330 3471 y FB(close)e(to)g(0.) 37 b(W)-7 b(e)28 b(will)g(assume)e(that)p Black 455 3616 a Ft(\017)p Black 41 w FB(If)i Fu(u)22 b(<)h FB(0,)k Fu(\015)5 b FB(\()p Fu(u)p FB(\))23 b(=)f Fu(\015)1184 3628 y FA(+)1240 3616 y FB(\()p Fu(u)p FB(\))h Ft(2)g Fu(C)1518 3586 y FA(+)p Black 455 3772 a Ft(\017)p Black 41 w Fu(\015)5 b FB(\(0\))22 b Ft(2)i FB(\006)p Black 455 3928 a Ft(\017)p Black 41 w FB(If)k Fu(u)22 b(>)h FB(0,)k Fu(\015)5 b FB(\()p Fu(u)p FB(\))23 b(=)f Fu(\015)1184 3940 y Fp(\000)1240 3928 y FB(\()p Fu(u)p FB(\))i Ft(2)f Fu(C)1519 3898 y Fp(\000)455 4073 y FB(It)29 b(is)f(clear)g(that)h Fu(W)1101 4038 y Fp(\000)1089 4094 y Fq(out)1220 4073 y FB(is)g(foliated)g(b)n(y)f(the)h(tra)5 b(jectories)27 b Fu(\015)2345 4085 y Fp(\000)2402 4073 y FB(.)40 b(So)29 b(it)g(is)g(enough)f(to)h(mak)n(e)330 4173 y(our)e(constructions)f (along)h(an)n(y)g Fu(\015)5 b FB(.)455 4272 y(W)-7 b(e)28 b(will)f(denote)h(b)n(y)f Fu(L)1194 4284 y FA(+)1249 4272 y FB(\()p Fu(u)p FB(\))h(the)g(tangen)n(t)f(plane)g(of)h(\003)2208 4237 y FA(+)2208 4296 y Fq(in)2304 4272 y FB(at)f(the)h(p)r(oin)n(t)g Fu(\015)5 b FB(\()p Fu(u)p FB(\))p Fu(;)41 b(u)23 b(<)f FB(0.)455 4372 y(Similarly)32 b Fu(L)870 4384 y Fp(\000)926 4372 y FB(\()p Fu(u)p FB(\))h(will)h(b)r(e)g(the)f(complex)g (Lagrangian)e(plane)i(tangen)n(t)g(to)g(\003)2973 4337 y Fp(\000)2973 4392 y Fq(out)3107 4372 y FB(at)h(the)330 4472 y(p)r(oin)n(t)28 b Fu(\015)5 b FB(\()p Fu(u)p FB(\))p Fu(;)41 b(u)23 b(>)f FB(0.)455 4571 y Fu(L)512 4583 y FA(+)566 4571 y FB(\()p Fu(u)p FB(\))28 b(is)f(logarithmic)g(in)h(the)g (sense)f(of)g(the)h(previous)f(section.)p Black 330 4717 a Fo(Prop)s(osition)j(1)p Black 41 w Fu(L)992 4729 y Fp(\000)1048 4717 y FB(\()p Fu(u)p FB(\))p Fu(;)43 b(u)22 b(>)h FB(0)p Fu(;)28 b Fz(is)h(uniquely)g(de\014ne)l(d)g(by)g(its)f (formal)i(exp)l(ansion)f(which)i(is)330 4816 y(the)f(c)l(anonic)l(al)h (extension)e(of)i Fu(L)1355 4828 y FA(+)1409 4816 y FB(\()p Fu(u)p FB(\))f Fz(and)g(its)g(invarianc)l(e)h(by)g(the)e(line)l (arization)j(of)e Fu(\036)3104 4828 y Fq(t)3134 4816 y Fz(.)330 5028 y Fo(9.2.3)94 b(The)32 b(transmission)e(rule)h(for)h (the)g(principal)g(sym)m(b)s(ol)330 5181 y FB(Both)27 b(limits)h(of)g Fu(L)919 5193 y Fp(\006)975 5181 y FB(\()p Fu(u)p FB(\))f(as)g Fu(u)c Ft(!)g FB(0)k(agree)1058 5381 y Fu(L)1115 5393 y FA(0)1175 5381 y FB(:=)59 b(lim)1285 5439 y Fq(u)p Fp(!)p FA(0)1423 5423 y Fk(\007)1487 5381 y Fu(L)1544 5393 y Fp(\006)1599 5381 y FB(\()p Fu(u)p FB(\))24 b(=)e Fu(T)12 b(W)1961 5393 y FA(0)2016 5381 y Ft(\010)18 b FB(\004)p Ft(\010)23 b Fu(<)2340 5325 y(d\015)p 2340 5362 91 4 v 2340 5438 a(du)2464 5381 y(>)50 b(:)330 5571 y FB(The)26 b(follo)n(wing)f(Prop)r(osition)f(describ)r (es)h(the)h(transmission)f(rules)g(for)g(the)h(principal)g(sym)n(b)r (ol)330 5670 y(whic)n(h)i(is)f(an)g(half)h(densit)n(y)f(on)h Fu(L)1389 5682 y Fp(\006)1444 5670 y FB(\()p Fu(u)p FB(\).)p Black 1788 5919 a(17)p Black eop %%Page: 18 18 18 17 bop Black Black Black 330 390 a Fo(Prop)s(osition)30 b(2)p Black 41 w Fz(We)g(have)656 534 y FB(lim)621 592 y Fq(u)p Fp(!)p FA(0)759 575 y Fj(+)806 534 y FB(\(log)14 b Ft(j)p Fu(u)p Ft(j)p FB(\))1095 477 y Fj(1)p 1095 486 29 3 v 1095 519 a(2)1138 534 y Fu(\033)s FB(\()p Fu(\015)1263 546 y Fp(\000)1319 534 y FB(\()p Fu(u)p FB(\)\))24 b(=)59 b(lim)1575 592 y Fq(u)p Fp(!)p FA(0)1713 575 y Fk(\000)1762 534 y FB(\(log)15 b Ft(j)p Fu(u)p Ft(j)p FB(\))2052 477 y Fj(1)p 2051 486 V 2051 519 a(2)2094 534 y Fu(\033)s FB(\()p Fu(\015)2219 546 y FA(+)2275 534 y FB(\()p Fu(u)p FB(\)\))23 b(=)g Fu(\033)2577 546 y FA(0)2637 534 y Ft(2)h FB(\012)2786 477 y Fj(1)p 2786 486 V 2786 519 a(2)2828 534 y FB(\()p Fu(L)2917 546 y FA(0)2954 534 y FB(\))30 b Fu(:)330 714 y FB(Once)d(giv)n(en)g(the)g(transp)r(ort)g(equation)g (\(see)g(for)g(example)g([17)o(]\),)h(one)f(can)g(c)n(hec)n(k)g(that)g (there)330 814 y(exists)22 b(unique)h Fu(\033)866 826 y Fp(\006)922 814 y FB(\()p Fu(u)p FB(\))g(whic)n(h)f(satisfy)g(the)h (transp)r(ort)e(equation)h(and)g(suc)n(h)g(that)g(the)h(previous)330 914 y(rule)40 b(holds.)75 b(So)40 b(w)n(e)h(ha)n(v)n(e)e(really)g (describ)r(ed)i(the)f(transmission)g(rule)g(for)g(the)h(principal)330 1013 y(sym)n(b)r(ol.)330 1281 y Fv(10)135 b(Gaussian)68 b(states:)106 b(\\the)68 b(dromadery)g(b)t(ecomes)g(a)599 1431 y(camel")330 1612 y FB(In)28 b(this)g(section,)f(w)n(e)g(will)h (use)f(the)h(de\014nitions)g(of)g(the)g(App)r(endix.)330 1838 y Fl(10.1)112 b(Mo)s(del)39 b(problem)330 1991 y FB(In)21 b(order)e(to)h(reco)n(v)n(er)e(Hagedorn's)g(results,)k(one)e (\014rst)g(has)f(to)i(c)n(ho)r(ose)e(an)h(incoming)g(tra)5 b(jectory)330 2091 y Fu(\015)378 2055 y FA(+)373 2114 y Fq(in)465 2091 y Ft(\032)22 b Fu(C)611 2103 y FA(+)685 2091 y Ft(\\)d FB(\006)819 2103 y FA(+)902 2091 y FB(of)27 b(the)h(v)n(ector)f(\014eld)h Ft(X)1628 2103 y Fq(p)1666 2091 y FB(.)37 b(W)-7 b(e)28 b(can)f(assume)g(that)h Fu(\015)2536 2055 y FA(+)2531 2114 y Fq(in)2600 2091 y FB(\(+)p Ft(1)p FB(\))23 b(=)g Fu(\015)2966 2103 y Fp(1)3059 2091 y Ft(2)g FB(\006.)455 2191 y(W)-7 b(e)28 b(ha)n(v)n(e)e(t)n(w)n(o)h(outgoing)f(tra)5 b(jectories)p Black 455 2325 a Ft(\017)p Black 41 w Fu(\015)586 2290 y FA(+)581 2346 y Fq(out)705 2325 y Ft(\032)22 b Fu(C)851 2337 y FA(+)925 2325 y Ft(\\)d FB(\006)1059 2337 y Fp(\000)1143 2325 y FB(so)27 b(that)h Fu(\015)1473 2290 y FA(+)1468 2346 y Fq(out)1569 2325 y FB(\()p Ft(\0001)p FB(\))23 b(=)g Fu(\015)1935 2337 y Fp(1)p Black 455 2476 a Ft(\017)p Black 41 w Fu(\015)586 2440 y Fp(\000)581 2496 y Fq(out)705 2476 y Ft(\032)f Fu(C)851 2488 y Fp(\000)926 2476 y Ft(\\)d FB(\006)1060 2488 y FA(+)1143 2476 y FB(so)27 b(that)h Fu(\015)1473 2440 y Fp(\000)1468 2496 y Fq(out)1569 2476 y FB(\(+)p Ft(1)p FB(\))23 b(=)g Fu(\015)1935 2488 y Fp(1)2005 2476 y FB(.)p Black 330 2629 a Fo(Theorem)31 b(6)p Black 42 w Fz(L)l(et)973 2608 y Fu(~)965 2629 y(U)1031 2593 y FA(+)1022 2652 y Fq(in)1116 2629 y Fz(b)l(e)c(a)g(Gaussian)g (state)f(of)h(or)l(der)h FB(0)e Fz(b)l(ase)l(d)h(on)f(the)h(isotr)l (opic)h(manifold)330 2741 y Fu(\015)378 2705 y FA(+)373 2764 y Fq(in)471 2741 y Fz(and)j(assume)931 2720 y Fu(~)923 2741 y(U)989 2705 y Fp(\000)980 2764 y Fq(in)1072 2741 y FB(=)22 b(0)p Fz(.)455 2853 y(Then)30 b(the)g(micr)l(olo)l(c)l(al)h (solution)f(ne)l(ar)g Fu(\033)1749 2865 y FA(0)1816 2853 y Fz(of)1933 2832 y Fs(b)1914 2853 y Fu(H)1998 2832 y(~)1990 2853 y(U)i FB(=)22 b(0)29 b Fz(satis\014es)p Black 454 2988 a Ft(\017)p Black 546 2967 a Fu(~)538 2988 y(U)604 2952 y Fp(\000)595 3008 y Fq(out)725 2988 y Fz(is)h(a)g Fo(Gaussian)i(state)e Fz(of)g(or)l(der)h FB(0)e Fz(asso)l(ciate)l(d)i (to)f Fu(\015)2449 2952 y Fp(\000)2444 3008 y Fq(out)p Black 454 3147 a Ft(\017)p Black 546 3127 a Fu(~)538 3147 y(U)604 3112 y FA(+)595 3168 y Fq(out)725 3147 y Fz(is)g Fo(non)i(Gaussian)d Fz(symple)l(ctic)i(spinor)g(of)g(or)l(der)f FB(0)f Fz(asso)l(ciate)l(d)j(to)d Fu(\015)2983 3112 y FA(+)2978 3168 y Fq(out)3080 3147 y Fz(.)330 3291 y(Pr)l(o)l(of.{)p Black Black 569 3426 a FB(W)-7 b(e)33 b(lo)r(ok)e(at)g(our)g(mo)r(del)h (problem.)49 b(W)-7 b(e)33 b(c)n(ho)r(ose)d Fu(\015)2240 3390 y FA(+)2235 3449 y Fq(in)2304 3426 y FB(\()p Fu(t)p FB(\))g(=)g(\(0)p Fu(;)14 b(e)2673 3396 y Fp(\000)p Fq(t)2753 3426 y FB(;)g(0)p Fu(;)g FB(0;)g(0)p Fu(;)g FB(0\).)538 3525 y(W)-7 b(e)28 b(ha)n(v)n(e)e Fu(\015)920 3490 y FA(+)915 3546 y Fq(out)1016 3525 y FB(\()p Fu(t)p FB(\))e(=)e(\()p Fu(e)1292 3495 y Fq(t)1322 3525 y Fu(;)14 b FB(0;)g(0)p Fu(;)g FB(0;)g(0)p Fu(;)g FB(0\))25 b(and)i Fu(\015)1983 3490 y Fp(\000)1978 3546 y Fq(out)2079 3525 y FB(\()p Fu(t)p FB(\))d(=)f(\(0)p Fu(;)14 b Ft(\000)p Fu(e)2500 3495 y Fp(\000)p Fq(t)2580 3525 y FB(;)g(0)p Fu(;)g FB(0;)g(0)p Fu(;)g FB(0\).)662 3625 y(A)28 b(t)n(ypical)f(\\Gaussian)f(state")h(is) h(giv)n(en)e(b)n(y)1394 3783 y Fu(~)1386 3804 y(U)1452 3769 y FA(+)1443 3827 y Fq(in)1535 3804 y FB(=)c Fu(')p FB(\()p Fu(x)1755 3816 y FA(2)1794 3804 y Fu(;)14 b(x)1878 3770 y Fp(0)1901 3804 y FB(\))1947 3712 y Fs(\020)2005 3783 y Fu(~)1997 3804 y(U)2054 3816 y FA(0)2091 3712 y Fs(\021)2140 3729 y FA(+)2140 3862 y Fq(in)2251 3804 y Fu(;)538 3972 y FB(where)1229 4072 y Fu(')p FB(\()p Fu(x)1362 4084 y FA(2)1400 4072 y Fu(;)g(x)1484 4037 y Fp(0)1508 4072 y FB(\))23 b(=)g Fu(Ah)1761 4037 y Fp(\000)p FA(\()p Fq(n)p Fp(\000)p FA(1\))p Fq(=)p FA(2)2062 4072 y Fu(e)2101 4037 y Fq(Q)p FA(\()p Fq(x)2217 4045 y Fj(2)2249 4037 y Fq(;x)2307 4012 y Fk(0)2328 4037 y FA(\))p Fq(=h)538 4198 y FB(with)28 b Fu(Q)22 b FB(=)h Fu(Q)969 4210 y FA(1)1024 4198 y FB(+)18 b Fu(iQ)1202 4210 y FA(2)1266 4198 y FB(and)28 b Fu(Q)1494 4210 y FA(1)1554 4198 y Fu(<<)22 b FB(0.)p Black 637 4331 a Ft(\017)p Black 41 w FB(F)-7 b(rom)36 b(the)g(explicit)g(form)n(ulae,)i(w)n(e)d(get)h (that)2248 4310 y Fu(~)2240 4331 y(U)2306 4296 y FA(+)2297 4352 y Fq(out)2434 4331 y FB(is)g(a)g(coheren)n(t)f(state)720 4431 y(asso)r(ciated)26 b(to)i Fu(\015)1265 4395 y FA(+)1260 4451 y Fq(out)1361 4431 y FB(.)37 b(The)28 b(sym)n(b)r(ol)f(of)g Fu(u)2018 4395 y FA(+)2018 4451 y Fq(out)2147 4431 y FB(is)1169 4590 y Fu(Ae)1270 4555 y Fq(Q)p FA(\()p Fq(X)1402 4563 y Fj(2)1435 4555 y Fq(;X)1514 4530 y Fk(0)1536 4555 y FA(\))1567 4590 y Fu(X)1636 4602 y FA(2)1673 4590 y FB(\000\(1)18 b(+)g Fu(iX)2005 4555 y FA(2)1998 4610 y(2)2041 4590 y FB(\))2073 4555 y Fp(\000)p FA(1)2162 4590 y Fu(e)2201 4555 y Fq(X)2260 4530 y Fj(2)2255 4572 y(2)2292 4555 y FA(\()p Fq(i)12 b FA(log)2460 4524 y Fb(x)2493 4536 y Fj(1)p 2460 4542 66 3 v 2476 4575 a Fb(h)2535 4555 y Fp(\000)2597 4533 y Fb(\031)p 2597 4542 36 3 v 2601 4575 a Fj(2)2643 4555 y FA(\))720 4733 y FB(apart)18 b(from)g(trivial)g(factors.)33 b(The)18 b(\000)h(factor)e (prev)n(en)n(t)h Fu(u)2455 4698 y FA(+)2455 4754 y Fq(out)2574 4733 y FB(to)h(b)r(e)f(Gaussian.)720 4841 y(W)-7 b(e)28 b(ha)n(v)n(e:)933 4985 y Ft(j)p Fu(\033)s FB(\()p Fu(u)1086 4949 y FA(+)1086 5005 y Fq(out)1188 4985 y FB(\)\()p Fu(X)1321 4997 y FA(2)1358 4985 y Fu(;)14 b(X)1471 4951 y Fp(0)1494 4985 y FB(\))p Ft(j)1549 4951 y FA(2)1610 4985 y FB(=)22 b Ft(j)p Fu(A)p Ft(j)1805 4951 y FA(2)1843 4985 y Fu(e)1882 4951 y FA(2)p Fq(Q)1967 4959 y Fj(1)1999 4951 y FA(\()p Fq(X)2079 4959 y Fj(2)2112 4951 y Fq(;X)2191 4926 y Fk(0)2213 4951 y FA(\))2243 4985 y FB(\(1)d Ft(\000)f Fu(e)2458 4951 y Fp(\000)p FA(2)p Fq(\031)r(X)2643 4926 y Fj(2)2638 4967 y(2)2679 4985 y FB(\))28 b Fu(;)213 b FB(\(22\))720 5128 y(hence)28 b(a)f(dromadery!)720 5237 y(The)35 b(rules)g(for)g(the)g(sym)n(b)r(ol)g(along)f Fu(\015)1959 5207 y Fq(out)1954 5257 y Fp(\000)2095 5237 y FB(are)g(the)h(same)g(as)f(for)h(the)g(La-)720 5336 y(grangian)26 b(states.)3265 5471 y Fi(\003)455 5571 y FB(It)d(remains)f(to)h(describ)r(e)g(the)h(rules)e(for)h(the)h (principal)e(sym)n(b)r(ol)h(of)g(the)h(symplectic)f(spinor)330 5670 y(asso)r(ciated)j(to)i Fu(\015)875 5640 y Fq(out)870 5691 y FA(+)976 5670 y FB(.)p Black 1788 5919 a(18)p Black eop %%Page: 19 19 19 18 bop Black Black Black Black Black 846 1247 a @beginspecial @setspecial %%BeginDocument: drom.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: drom.pstex %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Fri Sep 20 14:38:17 2002 %%For: ycolver@mozart (Yves Colin De Verdiere) %%Orientation: Portrait %%BoundingBox: 0 0 266 113 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 1.0000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -30.0 135.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /endash 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 3248 m -1000 -1000 l 5933 -1000 l 5933 3248 l cp clip 0.06000 0.06000 sc % Polyline 7.500 slw [60] 0 sd n 794 2235 m 1484 2235 l 1484 1627 l 794 1627 l cp gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 3599 1005 m 4289 1005 l 4289 397 l 3599 397 l cp gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 3509 2183 m 4199 2183 l 4199 1575 l 3509 1575 l cp gs col0 s gr [] 0 sd % Polyline n 518 1590 m 520 1590 l 525 1590 l 534 1590 l 549 1591 l 569 1591 l 595 1592 l 627 1592 l 665 1593 l 707 1594 l 754 1594 l 803 1595 l 855 1595 l 908 1595 l 961 1595 l 1014 1595 l 1065 1595 l 1115 1595 l 1163 1594 l 1209 1593 l 1252 1591 l 1294 1590 l 1333 1588 l 1370 1585 l 1405 1583 l 1439 1579 l 1472 1576 l 1503 1572 l 1533 1568 l 1562 1563 l 1591 1558 l 1619 1553 l 1647 1546 l 1674 1540 l 1702 1533 l 1730 1526 l 1758 1518 l 1786 1510 l 1815 1501 l 1844 1492 l 1873 1482 l 1903 1472 l 1933 1461 l 1964 1451 l 1995 1439 l 2026 1428 l 2058 1416 l 2090 1405 l 2123 1393 l 2155 1381 l 2188 1369 l 2221 1357 l 2255 1345 l 2288 1333 l 2321 1322 l 2355 1310 l 2388 1299 l 2422 1288 l 2456 1278 l 2490 1267 l 2524 1257 l 2558 1247 l 2593 1238 l 2629 1229 l 2659 1221 l 2691 1214 l 2723 1206 l 2756 1199 l 2790 1192 l 2826 1185 l 2863 1178 l 2902 1171 l 2942 1164 l 2985 1157 l 3029 1149 l 3076 1142 l 3126 1134 l 3178 1127 l 3232 1119 l 3288 1111 l 3347 1103 l 3408 1095 l 3471 1086 l 3535 1078 l 3600 1070 l 3664 1061 l 3729 1053 l 3792 1046 l 3852 1038 l 3910 1031 l 3963 1024 l 4011 1019 l 4054 1013 l 4091 1009 l 4122 1005 l 4147 1002 l 4165 1000 l 4178 999 l 4187 998 l 4191 997 l 4193 997 l gs col0 s gr % Polyline n 2175 1372 m 2177 1372 l 2182 1371 l 2190 1370 l 2203 1369 l 2222 1367 l 2246 1364 l 2275 1361 l 2309 1358 l 2347 1354 l 2388 1351 l 2431 1347 l 2476 1343 l 2522 1340 l 2567 1336 l 2612 1333 l 2656 1331 l 2698 1329 l 2739 1327 l 2778 1326 l 2816 1326 l 2853 1326 l 2888 1327 l 2922 1328 l 2956 1330 l 2989 1332 l 3022 1336 l 3055 1339 l 3088 1343 l 3121 1348 l 3149 1353 l 3178 1358 l 3207 1363 l 3237 1369 l 3268 1376 l 3299 1383 l 3332 1391 l 3367 1399 l 3402 1408 l 3440 1418 l 3479 1429 l 3520 1441 l 3563 1453 l 3608 1466 l 3655 1480 l 3705 1495 l 3755 1511 l 3807 1527 l 3861 1544 l 3914 1561 l 3968 1578 l 4021 1595 l 4073 1612 l 4122 1628 l 4168 1643 l 4211 1656 l 4249 1669 l 4282 1680 l 4309 1689 l 4331 1696 l 4348 1702 l 4360 1706 l 4367 1708 l 4371 1709 l 4373 1710 l gs col0 s gr % Polyline n 3600 982 m 3603 982 l 3609 981 l 3620 979 l 3635 977 l 3654 973 l 3675 969 l 3697 963 l 3720 956 l 3741 948 l 3760 939 l 3778 929 l 3793 917 l 3807 904 l 3819 889 l 3829 872 l 3839 853 l 3847 831 l 3854 809 l 3861 785 l 3867 760 l 3872 732 l 3877 703 l 3882 673 l 3887 642 l 3891 611 l 3895 580 l 3899 550 l 3902 521 l 3906 493 l 3909 468 l 3912 445 l 3914 426 l 3917 409 l 3920 396 l 3922 387 l 3925 381 l 3927 380 l 3930 382 l 3933 388 l 3937 398 l 3940 412 l 3944 429 l 3949 450 l 3953 473 l 3958 499 l 3964 527 l 3970 556 l 3976 587 l 3983 619 l 3989 650 l 3997 682 l 4004 712 l 4012 741 l 4019 769 l 4028 794 l 4036 818 l 4045 840 l 4055 861 l 4066 880 l 4078 897 l 4091 911 l 4106 923 l 4122 934 l 4141 943 l 4161 951 l 4183 957 l 4206 963 l 4229 967 l 4251 970 l 4270 972 l 4285 974 l 4296 975 l 4302 975 l 4305 975 l gs col0 s gr % Polyline n 795 2228 m 797 2228 l 802 2226 l 810 2224 l 821 2221 l 834 2216 l 849 2210 l 863 2202 l 877 2193 l 891 2183 l 903 2171 l 914 2157 l 924 2141 l 933 2123 l 942 2101 l 951 2077 l 958 2055 l 965 2031 l 972 2006 l 980 1979 l 988 1950 l 995 1920 l 1004 1889 l 1012 1858 l 1020 1827 l 1029 1796 l 1038 1767 l 1046 1740 l 1055 1715 l 1064 1692 l 1072 1673 l 1081 1657 l 1089 1644 l 1097 1635 l 1106 1629 l 1114 1628 l 1122 1630 l 1130 1635 l 1138 1644 l 1146 1655 l 1155 1670 l 1164 1687 l 1173 1707 l 1183 1729 l 1192 1754 l 1202 1780 l 1212 1807 l 1222 1835 l 1232 1864 l 1242 1893 l 1251 1922 l 1261 1951 l 1270 1978 l 1279 2004 l 1288 2029 l 1296 2052 l 1304 2074 l 1313 2094 l 1324 2118 l 1335 2139 l 1346 2158 l 1358 2173 l 1371 2186 l 1385 2198 l 1400 2207 l 1416 2215 l 1432 2222 l 1448 2227 l 1463 2231 l 1475 2234 l 1484 2235 l 1490 2236 l 1492 2236 l gs col0 s gr % Polyline n 3472 2192 m 3474 2191 l 3479 2190 l 3488 2186 l 3498 2181 l 3510 2175 l 3522 2167 l 3534 2157 l 3544 2146 l 3553 2133 l 3561 2119 l 3568 2102 l 3574 2081 l 3580 2058 l 3584 2037 l 3588 2014 l 3591 1990 l 3595 1963 l 3599 1935 l 3603 1907 l 3606 1877 l 3610 1848 l 3614 1819 l 3617 1792 l 3621 1766 l 3624 1743 l 3628 1723 l 3631 1706 l 3634 1692 l 3638 1682 l 3641 1676 l 3645 1674 l 3648 1676 l 3652 1682 l 3656 1692 l 3660 1706 l 3665 1723 l 3669 1743 l 3675 1766 l 3680 1792 l 3687 1819 l 3693 1848 l 3699 1877 l 3706 1906 l 3713 1934 l 3721 1962 l 3728 1988 l 3736 2013 l 3744 2035 l 3752 2055 l 3757 2066 l 3762 2076 l 3767 2085 l 3772 2094 l 3777 2102 l 3783 2109 l 3789 2116 l 3795 2122 l 3801 2128 l 3807 2132 l 3813 2136 l 3819 2140 l 3826 2142 l 3832 2144 l 3839 2145 l 3845 2145 l 3852 2145 l 3858 2143 l 3864 2141 l 3870 2139 l 3876 2135 l 3882 2131 l 3888 2126 l 3893 2120 l 3899 2114 l 3904 2107 l 3909 2099 l 3913 2091 l 3918 2082 l 3922 2072 l 3926 2062 l 3930 2052 l 3936 2031 l 3941 2009 l 3947 1984 l 3952 1958 l 3956 1931 l 3960 1902 l 3964 1873 l 3968 1844 l 3972 1815 l 3975 1788 l 3978 1762 l 3981 1739 l 3984 1719 l 3987 1701 l 3989 1687 l 3992 1677 l 3995 1670 l 3998 1668 l 4002 1669 l 4005 1675 l 4010 1684 l 4014 1696 l 4019 1713 l 4024 1732 l 4030 1754 l 4036 1778 l 4042 1804 l 4048 1832 l 4055 1860 l 4062 1888 l 4068 1916 l 4075 1943 l 4082 1968 l 4089 1992 l 4096 2014 l 4102 2034 l 4110 2054 l 4118 2072 l 4127 2087 l 4136 2101 l 4147 2113 l 4158 2124 l 4171 2133 l 4185 2142 l 4199 2149 l 4213 2156 l 4226 2161 l 4237 2165 l 4245 2167 l 4250 2168 l 4252 2169 l gs col0 s gr $F2psEnd rs %%EndDocument @endspecial 1122 851 a Fe(\015)1178 809 y Fg(+)1173 876 y Fd(in)1954 663 y Fe(\015)2010 622 y Fc(\000)2005 686 y Fd(out)2491 858 y Fe(\015)2547 817 y Fg(+)2542 881 y Fd(out)p Black 865 1430 a FB(Figure)27 b(2:)37 b(the)28 b(squares)e(of)h(the)h(mo)r(dulus)g(of)g(the)g(solutions)p Black Black 330 1715 a Fv(11)135 b(The)44 b(elliptic)j(case)330 1897 y FB(If)28 b(w)n(e)f(replace)g(in)h(our)f(assumptions)f(of)i (section)f(1)g(the)h(condition)g Fo(\(3\))f FB(b)n(y)h Fo(\(4\))455 1997 y(4.)41 b(The)30 b(linearization)f(of)h Ft(X)1475 2009 y Fq(p)1543 1997 y Fo(admits)f(a)h(non)g(zero)g(pair)g (of)g(purely)g(imaginary)330 2096 y(eigen)m(v)-5 b(alues)30 b Ft(\006)p Fu(i\026)p Fo(.)455 2196 y FB(and)d(\(iii\))h(b)n(y)g (\(iv\):)1155 2342 y(\()p Fo(iv)q FB(\))56 b Ft(f)p Fo(q)p Fu(;)14 b Fo(r)p Ft(g)1563 2307 y Fn(2)1623 2342 y FB(+)k Ft(f)p Fo(q)p Fu(;)c Fo(s)p Ft(g)1915 2307 y Fn(2)1974 2342 y Ft(\000)k(f)p Fo(r)p Fu(;)c Fo(s)p Ft(g)2255 2307 y Fn(2)2319 2342 y Fu(<)23 b Fo(0)k Fu(;)330 2487 y FB(w)n(e)j(get)g (that)g(the)h(semi-simple)f(factor)f(is)h(no)n(w)g(elliptic.)45 b(As)30 b(already)f(observ)n(ed)g(in)h([7],)h(this)330 2587 y(case)21 b(o)r(ccurs)g(in)h(Maxw)n(ell)e(equations)h(as)g(w)n (ell)h(as)f(in)h(propagation)d(of)j(w)n(a)n(v)n(es)e(in)i(elastic)f (media.)455 2687 y(On)28 b(the)h(lev)n(el)f(of)h(formal)f(series)g (expansions,)f(the)i(same)g(results)f(holds,)g(but)i(w)n(e)e(can)g(no) 330 2786 y(more)f(use)g(Stern)n(b)r(erg's)g(theorem.)455 2886 y(W)-7 b(e)28 b(get)f(the:)p Black 330 3022 a Fo(Theorem)k(7)p Black 42 w Fz(Assuming)j(hyp)l(othesis)k Fo(\(1\),)i(\(2\))c Fz(and)g Fo(\(4\))p Fz(,)h(The)l(or)l(em)f(3)g(r)l(emains)g(true)f(on) 330 3122 y(the)30 b(level)h(of)f(formal)h(series)g(tr)l(ansversal)t(ly) g(to)e FB(\006)23 b(=)g Ft(f)p Fu(x)2096 3134 y FA(1)2156 3122 y FB(=)g Fu(\030)2280 3134 y FA(1)2341 3122 y FB(=)f Fu(\030)2464 3134 y FA(2)2525 3122 y FB(=)g(0)p Ft(g)29 b Fz(with)1318 3317 y Fu(H)1387 3329 y FA(0)1447 3317 y FB(=)1535 3200 y Fs(\022)1637 3267 y Fu(\030)1673 3279 y FA(2)1729 3267 y Ft(\000)18 b Fu(x)1859 3279 y FA(1)1980 3267 y Fu(\030)2016 3279 y FA(1)1637 3366 y Fu(\030)1673 3378 y FA(1)1980 3366 y Fu(\030)2016 3378 y FA(2)2072 3366 y FB(+)g Fu(x)2202 3378 y FA(1)2281 3200 y Fs(\023)455 3508 y FB(W)-7 b(e)28 b(can)f(describ)r(e)g(easily)g(the)h(solutions)f (of)g(the)h(mo)r(del)g(system)1579 3678 y Fs(c)1567 3699 y Fu(H)1636 3711 y FA(0)1688 3582 y Fs(\022)1790 3649 y Fu(u)1790 3748 y(v)1879 3582 y Fs(\023)1963 3699 y FB(=)23 b(0)330 3890 y(b)n(y)32 b(using)h(the)g(unkno)n(wn)f(functions) h Fu(w)1603 3902 y Fp(\006)1692 3890 y FB(=)e Fu(u)21 b Ft(\006)h Fu(iv)s FB(.)52 b(W)-7 b(e)33 b(get)g(the)g(follo)n(wing)e (equation)i(for)330 3990 y Fu(w)389 4002 y FA(+)445 3990 y FB(:)1312 4141 y(\(2\012)18 b(+)g Fu(h)p FB(\))p Fu(w)1686 4153 y FA(+)1760 4141 y FB(+)g Fu(h)1891 4107 y FA(2)1962 4085 y Fu(@)2011 4055 y FA(2)p 1938 4122 134 4 v 1938 4198 a Fu(@)5 b(x)2034 4169 y FA(2)2034 4220 y(2)2082 4141 y Fu(w)2141 4153 y FA(+)2219 4141 y FB(=)23 b(0)330 4324 y(where)j(\012)d(=)g Ft(\000)p Fu(h)853 4294 y FA(2)890 4324 y Fu(@)939 4294 y FA(2)934 4344 y Fq(x)972 4352 y Fj(1)1025 4324 y FB(+)17 b Fu(x)1154 4294 y FA(2)1154 4344 y(1)1219 4324 y FB(is)27 b(an)g(harmonic)f(oscillator.)34 b(The)28 b(formal)e(normal)g(form)g(su\016ces)330 4423 y(to)i(describ)r(e)g(microlo)r(cal)f(solutions)h(whose)f(microsupp)r (ort)h(is)g(\006;)h(it)g(is)f(enough)g(to)g(dev)n(elopp)330 4523 y(the)g(v)-5 b(alue)27 b(of)h Fu(w)841 4535 y FA(+)924 4523 y FB(at)g Fu(x)1073 4535 y FA(2)1133 4523 y FB(=)23 b(0)k(using)h(the)g(basis)e(of)i(eigenfunctions)f(of)h(\012.)330 4791 y Fv(12)135 b(The)44 b(Hermitian)j(case)330 4973 y FB(The)19 b(same)g(metho)r(d)h(can)f(b)r(e)g(applied)g(to)h(other)e (kinds)h(of)h(generic)e(eigen)n(v)-5 b(alues)18 b(crossings.)32 b(The)330 5073 y(main)20 b(h)n(yp)r(othesis)f(in)h(order)f(to)h(get)f (a)h(microlo)r(cal)e(normal)h(form)g(is)h Fz(tr)l(ansversal)j(hyp)l (erb)l(olicity)p FB(,)330 5172 y(namely)31 b(the)i(linearized)e (Hamiltonian)g(v)n(ector)g(\014eld)h(should)f(ha)n(v)n(e)g(h)n(yp)r (erb)r(olic)g(blo)r(c)n(ks)g(and)330 5272 y(Jordan)f(blo)r(c)n(ks)g (with)i(0)f(as)f(eigen)n(v)-5 b(alue)30 b(only)-7 b(.)48 b(W)-7 b(e)31 b(giv)n(e)g(b)r(elo)n(w)f(a)h(sk)n(etc)n(h)n(y)f(presen)n (tation)g(of)330 5372 y(the)e(Hermitian)g(case)e(whic)n(h)i(will)g(the) g(ob)5 b(ject)27 b(of)h([10)o(].)455 5471 y(In)21 b(the)h(Hermitian)g (case,)g(b)r(ecause)f(of)h(the)g(signature)e(\(+)p Fu(;)14 b Ft(\000)p Fu(;)g Ft(\000)p Fu(;)g Ft(\000)p Fu(;)g FB(0)p Fu(;)g Ft(\001)g(\001)g(\001)25 b Fu(;)14 b FB(0\))22 b(of)f Fu(p)3057 5441 y Fp(00)3099 5471 y FB(,)i(there)330 5571 y(are)28 b(only)g(4)h(cases.)40 b(W)-7 b(e)29 b(will)g(classify)f (according)g(the)h(corank)e(of)i Fu(!)2498 5586 y Fp(j)p FA(\006)2598 5571 y FB(whic)n(h)g(is)g(assumed)f(to)330 5670 y(b)r(e)g(lo)r(cally)f(constan)n(t:)p Black 1788 5919 a(19)p Black eop %%Page: 20 20 20 19 bop Black Black 330 390 a Fl(12.1)112 b(Corank)38 b FC(0)p Fl(:)50 b(the)37 b(generic)h(case)g(\(elliptic-h)m(yp)s(erb)s (olic\))330 543 y FB(The)27 b(singular)f(stratum)h(\006)g(of)g(the)g(c) n(haracteristic)e(manifold)i(is)g(symplectic.)37 b(The)27 b(lineariza-)330 643 y(tion)h(of)f Ft(X)654 655 y Fq(p)720 643 y FB(do)h(admit)g(t)n(w)n(o)e(pairs)h(of)h(non)f(v)-5 b(anishing)27 b(eigen)n(v)-5 b(alues)27 b(\()p Ft(\006)p Fu(\025;)14 b Ft(\006)p Fu(i\026)p FB(\).)455 743 y(W)-7 b(e)31 b(get)f(mo)r(duli)h(in)g(the)g(normal)e(form:)43 b(w)n(e)30 b(cannot)g(reduce)g(b)r(oth)i(semi-simple)e(blo)r(c)n(ks)330 842 y(using)d(our)g(equiv)-5 b(alence)27 b(relation.)36 b(W)-7 b(e)28 b(do)f(not)h(kno)n(w)e(some)h(ph)n(ysical)g(example)g(of) h(this)f(last)330 942 y(case.)36 b(The)28 b(normal)e(form)i(should)f(b) r(e:)417 1154 y Fu(H)486 1166 y FA(0)546 1154 y FB(=)634 1037 y Fs(\022)737 1103 y Fu(\030)773 1115 y FA(1)1948 1103 y Fu(a)p FB(\()p Fu(x)2071 1115 y FA(1)2109 1103 y Fu(\030)2145 1115 y FA(1)2182 1103 y Fu(;)14 b(x)2266 1073 y FA(2)2322 1103 y FB(+)k Fu(\030)2445 1073 y FA(2)2483 1103 y Fu(;)c(x)2567 1073 y Fp(0)2590 1103 y Fu(;)g(\030)2667 1073 y Fp(0)2691 1103 y FB(\)\()p Fu(x)2802 1115 y FA(2)2858 1103 y Ft(\006)k Fu(i\030)3006 1115 y FA(2)3043 1103 y FB(\))737 1203 y Fu(a)p FB(\()p Fu(x)860 1215 y FA(1)897 1203 y Fu(\030)933 1215 y FA(1)971 1203 y Fu(;)c(x)1055 1173 y FA(2)1111 1203 y FB(+)k Fu(\030)1234 1173 y FA(2)1272 1203 y Fu(;)c(x)1356 1173 y Fp(0)1379 1203 y Fu(;)g(\030)1456 1173 y Fp(0)1479 1203 y FB(\)\()p Fu(x)1590 1215 y FA(2)1647 1203 y Ft(\007)k Fu(i\030)1795 1215 y FA(2)1832 1203 y FB(\))84 b Fu(x)1995 1215 y FA(1)3117 1037 y Fs(\023)3220 1154 y Fu(;)330 1386 y FB(where)27 b Fu(a)p FB(\()p Fu(\034)5 b(;)14 b(x)771 1356 y Fp(0)795 1386 y Fu(;)g(\030)872 1356 y Fp(0)895 1386 y FB(\))28 b(is)g(a)f(smo)r(oth)g Fu(>)c FB(0)k(function.)455 1486 y(Both)d(cases)g(\()p Ft(\006)p FB(\))h(are)f(not)h(equiv)-5 b(alen)n(t:)36 b(the)25 b(op)r(en)g(cones)f Fu(C)2341 1498 y Fp(\006)2423 1486 y FB(whic)n(h)h(corresp)r(ond)e(resp)r(ec-)330 1586 y(tiv)n(ely)36 b(to)g Fu(\025)725 1598 y Fp(\000)819 1586 y FB(=)h(0)g Fu(<)g(\025)1150 1598 y FA(+)1242 1586 y FB(\()p Fu(\025)1322 1598 y Fp(\000)1416 1586 y Fu(<)g(\025)1566 1598 y FA(+)1659 1586 y FB(=)g(0\))f(are)f(w)n(ell)h(de\014ned)h(near)e (\006.)63 b(Morse)35 b(indices)330 1685 y(di\013ers)26 b(b)n(y)g(1)g(on)g(those)g(cones.)36 b(Moreo)n(v)n(er,)24 b(b)r(oth)j(cones)f(are)f(orien)n(ted)h(b)n(y)g Fu(p)c(>)h FB(0.)36 b(Hence)27 b(the)330 1785 y(p)r(olarization)g(bundle)i(ha)n(v) n(e)f(a)g(w)n(ell)g(de\014ned)h(\014rst)f(Chern)h(class)e(on)i Fu(C)2576 1797 y FA(+)2660 1785 y FB(and)f(b)r(oth)h(signes)f(in)330 1884 y(the)g(normal)f(form)g(giv)n(es)f(b)r(oth)i(signes)f(in)h(the)g (Chern)f(class.)455 1984 y(In)j(the)g(case)f(of)h(2)f(degrees)g(of)g (freedom)h(and)g(analytic)f(data,)h(the)g(normal)f(form)g(for)h(the)330 2084 y(disp)r(ersion)35 b(relation)h(has)f(b)r(een)i(pro)n(v)n(ed)d(to) i(b)r(e)h(con)n(v)n(ergen)n(t)c(b)n(y)j(Moser)f([42)o(].)63 b(The)36 b(mo)r(del)330 2183 y(problem)27 b(is)h(studied)g(in)f([20].) 330 2416 y Fl(12.2)112 b(Corank)38 b(2:)50 b(the)38 b(h)m(yp)s(erb)s (olic)g(case)330 2569 y FB(The)25 b(singular)e(manifold)i(is)g(not)g (symplectic)g(and)f(the)i(linearization)d(of)i Ft(X)2704 2581 y Fq(p)2768 2569 y FB(admits)f(one)h(pair)330 2669 y(of)j(real)e(non)i(v)-5 b(anishing)27 b(eigen)n(v)-5 b(alues.)1246 2897 y Fu(H)1315 2909 y FA(0)1375 2897 y FB(=)1463 2780 y Fs(\022)1565 2846 y Fu(\030)1601 2858 y FA(1)1948 2846 y Fu(x)1995 2858 y FA(2)2051 2846 y FB(+)18 b Fu(ix)2210 2858 y FA(3)1565 2946 y Fu(x)1612 2958 y FA(2)1668 2946 y Ft(\000)g Fu(ix)1827 2958 y FA(3)1948 2946 y Fu(x)1995 2958 y FA(1)2289 2780 y Fs(\023)2391 2897 y Fu(:)330 3092 y FB(This)40 b(normal)f(form)h(is)f(lo)r(cal)h(as) f(in)h(our)f(previous)g(result.)74 b(W)-7 b(e)40 b(get)g(this)g(mo)r (del)g(in)h(the)330 3191 y(Born-Opp)r(enheimer)26 b(appro)n(ximation)g (with)i(magnetic)f(\014eld.)330 3424 y Fl(12.3)112 b(Corank)38 b(2:)50 b(the)38 b(elliptic)f(case)330 3577 y FB(The)25 b(singular)e(manifold)i(is)g(not)g(symplectic)g(and)f(the)i (linearization)d(of)i Ft(X)2704 3589 y Fq(p)2768 3577 y FB(admits)f(one)h(pair)330 3676 y(of)j(purely)f(imaginary)f(non)h(v) -5 b(anishing)27 b(eigen)n(v)-5 b(alues.)455 3776 y(W)e(e)35 b(get)f(a)g(normal)g(form)g(whic)n(h)h(is)g(only)f(formal)g(as)g(b)r (efore.)58 b(This)35 b(mo)r(del)g(is)f(used)h(in)330 3876 y(the)g(example)g(of)f(spin-orbit)g(in)n(teraction)g(\([18])h(and) f([19)o(]\).)59 b(It)36 b(leads)e(to)g(transition)h(of)f(an)330 3975 y(eigenstate)27 b(from)g(one)g(band)h(to)f(another)g(one.)1257 4204 y Fu(H)1326 4216 y FA(0)1386 4204 y FB(=)1474 4087 y Fs(\022)1576 4153 y Fu(x)1623 4165 y FA(1)1948 4153 y Fu(x)1995 4165 y FA(3)2051 4153 y FB(+)18 b Fu(i\030)2199 4165 y FA(3)1576 4253 y Fu(x)1623 4265 y FA(3)1679 4253 y Ft(\000)h Fu(i\030)1828 4265 y FA(3)1948 4253 y Fu(x)1995 4265 y FA(2)2278 4087 y Fs(\023)2380 4204 y Fu(:)330 4476 y Fl(12.4)112 b(Corank)38 b(4:)50 b(the)38 b(in)m(v)m(olutiv)m(e)g (case)330 4629 y FB(The)23 b(singular)f(manifold)h(is)g(in)n(v)n (olutiv)n(e.)35 b(A)23 b(similar)f(case)h(has)f(b)r(een)i(studied)f(b)n (y)g(Melrose)f(and)330 4729 y(Uhlmann)28 b(in)g([41)o(].)330 5004 y Fv(13)135 b(Bifurcations)330 5185 y FB(It)24 b(w)n(ould)f(b)r(e) i(in)n(teresting)e(to)g(describ)r(e)h(generic)f(bifurcations)g(whic)n (h)g(ma)n(y)g(o)r(ccur)h(at)f(least)h(for)330 5285 y(three)j(reasons:)p Black 431 5451 a(1.)p Black 42 w(The)c(condition)h Fo(2.)35 b FB(is)23 b(no)g(more)g(satis\014ed)h(at)f(some)g(p)r(oin)n(ts.)36 b(This)23 b(imply)h(a)f(singularit)n(y)538 5551 y(of)k(the)h(manifold)g (\006.)p Black 1788 5919 a(20)p Black eop %%Page: 21 21 21 20 bop Black Black Black 431 390 a FB(2.)p Black 42 w(There)23 b(is)i(a)e(c)n(hange)h(in)g(the)h(normal)e(form)h(in)n(v)n (olv)n(ed.)35 b(F)-7 b(or)23 b(example)h(in)h(the)f(symmetric)538 490 y(case,)i(ho)n(w)h(do)h(w)n(e)f(pass)g(generically)f(from)h(the)h (h)n(yp)r(erb)r(olic)f(to)h(the)f(elliptic)i(case?)p Black 431 655 a(3.)p Black 42 w(F)-7 b(or)38 b(a)g Fu(d)26 b Ft(\002)f Fu(d)39 b FB(system)f(with)h Fu(d)j Ft(\025)f FB(3,)g(there)d(exists)g(triply)h(and)f(more)g(degenerated)538 754 y(eigen)n(v)-5 b(alue)26 b(of)i(the)g(classical)e(Hamiltonian)h(at) h(some)f(p)r(oin)n(ts.)330 1028 y Fv(14)135 b(App)t(endix:)64 b(coheren)l(t)49 b(states,)h(symplectic)e(spinors)599 1178 y(and)d(Gaussian)g(states)330 1376 y Fl(14.1)112 b(De\014nitions)330 1530 y FB(A)32 b(\(semi-classical\))d Fz(c)l(oher)l(ent)34 b(state)d FB(is,)h(roughly)d(sp)r(eaking,)j(a)e (semi-classical)g(state)h(whose)330 1629 y(microsupp)r(ort)d(is)g(an)h (isotropic)e(submanifold)i Fu(K)34 b FB(of)29 b(the)g(cotangen)n(t)f (space.)39 b(It)29 b(is)g(desirable)330 1729 y(to)c(describ)r(e)g(nice) h(families)f(of)g(coheren)n(t)g(states)g(for)f(whic)n(h)i(a)f (so-called)f Fz(symb)l(olic)29 b(c)l(alculus)c FB(is)330 1828 y(a)n(v)-5 b(ailable.)33 b(Of)19 b(course,)h(suc)n(h)g(families)f (should)h(b)r(e)g(in)n(v)-5 b(arian)n(t)18 b(b)n(y)h(F)-7 b(ourier)19 b(In)n(tegral)f(Op)r(erators.)455 1928 y(There)h(are)g(at)h (least)g(3)f(a)n(v)-5 b(ailable)19 b(theories)g(of)h(coheren)n(t)f (states)h(whic)n(h)g(are)f(closely)g(related:)p Black 431 2092 a(1.)p Black 42 w(\(Semi-classical\))h Fz(F)-6 b(ourier)25 b(Inte)l(gr)l(al)f(Op)l(er)l(ators)h(with)g(c)l(omplex)g (phase)g(functions)d FB(stud-)538 2191 y(ied)27 b(b)n(y)h(Melin)g(and)f (Sj\177)-42 b(ostrand)27 b([40)o(].)p Black 431 2356 a(2.)p Black 42 w(\(Semi-classical\))17 b Fz(Symple)l(ctic)22 b(Spinors)d FB(studied)g(b)n(y)f(Boutet)g(de)h(Mon)n(v)n(el)e(and)i (Guillemin)538 2456 y([28)o(])27 b(and)h([6)o(],)g(see)f(also)g([36)o (].)p Black 431 2621 a(3.)p Black 42 w(Hagedorn's)f Fz(Semi-classic)l (al)31 b(Wave)f(Packets)f FB([29)o(])f(or)e Fz(Gaussian)31 b(states)p FB(..)455 2785 y(The)g(\014rst)g(t)n(w)n(o)g(theories)f(are) g(b)r(etter)i(adapted)f(to)g(the)h(con)n(text)f(of)g(microlo)r(cal)f (analysis)330 2884 y(b)r(eing)e(in)n(v)-5 b(arian)n(t)27 b(b)n(y)h(F)-7 b(ourier)28 b(In)n(tegral)f(Op)r(erators.)36 b(W)-7 b(e)29 b(will)f(use)h(the)f(second)g(one)g(in)g(what)330 2984 y(follo)n(ws:)61 b(w)n(e)40 b(will)g(\014rst)g(giv)n(e)f(the)h (de\014nition)h(of)f(the)h Fz(semi-classic)l(al)i(symple)l(ctic)f (spinors)330 3084 y FB(follo)n(wing)34 b(closely)h([28)o(].)61 b(Then)36 b(w)n(e)f(will)g(de\014ne)h(a)f(subset)h(of)f(it,)j(the)e (so-called)e Fz(Gaussian)330 3183 y(states)p FB(,)29 b(asso)r(ciated)f(to)h(some)g(jet)g(of)g(order)f Ft(1)h FB(of)g(p)r(ositiv)n(e)g(complex)g(Lagrangian)d(manifold)330 3283 y(con)n(taining)h Fu(K)6 b FB(;)27 b(they)h(are)f(v)n(ery)g(close) g(to)g(Hagedorn's)f(semi-classical)g(w)n(a)n(v)n(e)g(pac)n(k)n(ets.)37 b(After)330 3382 y(that,)32 b(w)n(e)e(will)h(de\014ne)g(the)g (principal)f(sym)n(b)r(ols)g(of)h(these)f(ob)5 b(jects.)46 b(All)31 b(our)f(discussion)g(will)330 3482 y(b)r(e)e(\(micro-\)lo)r (cal)e(ev)n(en)i(if)g(it)g(is)f(not)h(alw)n(a)n(ys)d(sp)r(eci\014ed.)p Black 330 3662 a Fo(De\014nition)31 b(1)p Black Black 165 w Ft(\017)p Black 42 w Fz(L)l(et)e Fu(K)1287 3674 y FA(0)1354 3662 y Fz(b)l(e)g(the)h(isotr)l(opic)i(submanifold)f(of)g Fu(T)2551 3632 y Fq(?)2588 3662 y FB(\()p Fr(R)2680 3632 y Fq(k)2680 3682 y(x)2741 3662 y Ft(\010)18 b Fr(R)2884 3632 y Fq(n)p Fp(\000)p Fq(k)2884 3682 y(y)3018 3662 y FB(\))30 b Fz(de\014ne)l(d)538 3762 y(by)1417 3861 y Fu(K)1488 3873 y FA(0)1548 3861 y FB(=)22 b Ft(f)p FB(\()p Fu(x;)14 b FB(0;)g(0)p Fu(;)g FB(0\))29 b Ft(j)h Fu(x)23 b Ft(2)h Fr(R)2316 3827 y Fq(k)2356 3861 y Ft(g)30 b Fu(:)538 4042 y Fz(We)44 b(wil)t(l)i(say)f(that)f Fu(a)p FB(\()p Fu(x;)14 b(Y)5 b(;)14 b(h)p FB(\))51 b Ft(2)f Fu(C)1771 4011 y Fp(1)1841 4042 y FB(\()p Fr(R)1933 4011 y Fq(k)1933 4062 y(x)2004 4042 y Ft(\010)29 b Fr(R)2158 4006 y Fq(n)p Fp(\000)p Fq(k)2158 4066 y(Y)2292 4042 y FB(\))45 b Fz(is)g(a)f FB(sym)n(b)r(ol)g Fz(in)h FB(\006)3037 4011 y Fq(l)3062 4042 y FB(\()p Fu(K)3165 4054 y FA(0)3202 4042 y FB(\))g Fz(if)538 4150 y Fu(a)p FB(\()p Fu(x;)14 b(:;)g(h)p FB(\))23 b Ft(2)h(S)6 b FB(\()p Fr(R)1088 4120 y Fq(n)p Fp(\000)p Fq(k)1222 4150 y FB(\))22 b Fz(and,)i(for)e(al) t(l)g(semi-norms)f Fu(N)30 b Fz(of)22 b(the)g(Schwartz)g(sp)l(ac)l(e)f Ft(S)6 b FB(\()p Fr(R)3146 4115 y Fq(n)p Fp(\000)p Fq(k)3146 4174 y(Y)3281 4150 y FB(\))p Fz(,)538 4250 y(and)30 b(al)t(l)h Fu(")22 b(>)h FB(0)p Fz(,)30 b(we)g(have:)1617 4349 y Fu(N)9 b FB(\()p Fu(a)p FB(\))23 b(=)g Fu(O)r FB(\()p Fu(h)2057 4315 y Fq(l)p FA(+)p Fq(")2165 4349 y FB(\))30 b Fu(;)538 4497 y Fz(uniformly)g(on)g(c)l(omp)l(acts)g(in)g Fr(R)1551 4467 y Fq(k)1551 4518 y(x)1593 4497 y Fz(.)p Black 454 4662 a Ft(\017)p Black 42 w Fz(A)f FB(classical)e(sym)n(b)r (ol)i Fz(in)h FB(\006)1397 4632 y Fq(l)1422 4662 y FB(\()p Fu(K)1525 4674 y FA(0)1562 4662 y FB(\))h Fz(is)f(a)g(symb)l(ol)h (which)g(admits)g(an)f(asymptotic)h(exp)l(an-)538 4787 y(sion)j Fu(a)p FB(\()p Fu(x;)14 b(Y)5 b(;)14 b(h)p FB(\))30 b Ft(\030)f Fu(h)1222 4756 y Fq(l)1261 4694 y Fs(\020)1311 4724 y(P)1399 4745 y Fp(1)1399 4811 y Fq(j)s FA(=0)1531 4787 y Fu(h)1579 4756 y Fq(j)s(=)p FA(2)1681 4787 y Fu(a)1725 4799 y Fq(j)1760 4787 y FB(\()p Fu(x;)14 b(Y)20 b FB(\))1976 4694 y Fs(\021)2025 4787 y Fz(.)50 b(We)34 b(wil)t(l)h(denote)f(by)g FB(\006)2857 4756 y Fq(l)2857 4810 y FA(class)2995 4787 y FB(\()p Fu(K)3098 4799 y FA(0)3135 4787 y FB(\))g Fz(this)538 4886 y(sp)l(ac)l(e.)p Black 454 5051 a Ft(\017)p Black 42 w Fz(A)39 b FB(symplectic)h(spinor)f Fz(\(r)l(esp.)70 b FB(classical)38 b(symplectic)h(spinor)p Fz(\))g Fu(u)2691 5063 y Fq(h)2734 5051 y FB(\()p Fu(x;)14 b(y)s FB(\))40 b Fz(of)i(or)l(der)f Fu(l)538 5151 y Fz(asso)l(ciate)l(d)30 b(with)g(the)g(isotr)l(opic)h(manifold)g Fu(K)1995 5163 y FA(0)2055 5151 y FB(=)22 b Ft(f)p FB(\()p Fu(x;)14 b FB(0;)g(0)p Fu(;)g FB(0\))p Ft(g)22 b(\032)g Fu(T)2744 5121 y Fq(?)2782 5151 y FB(\()p Fr(R)2874 5121 y Fq(k)2874 5171 y(x)2933 5151 y Ft(\010)17 b Fr(R)3075 5121 y Fq(n)p Fp(\000)p Fq(k)3075 5171 y(y)3209 5151 y FB(\))30 b Fz(is)538 5250 y(de\014ne)l(d)g(by:)1327 5367 y Fu(u)1375 5379 y Fq(h)1418 5367 y FB(\()p Fu(x;)14 b(y)s FB(\))23 b(=)g Fu(h)1769 5332 y Fp(\000)p FA(\()p Fq(n)p Fp(\000)p Fq(k)q FA(\))p Fq(=)p FA(2)2073 5367 y Fu(a)p FB(\()p Fu(x;)2280 5311 y(y)p 2244 5348 118 4 v 2244 5364 a Ft(p)p 2313 5364 48 4 v 71 x Fu(h)2371 5367 y(;)14 b(h)p FB(\))30 b Fu(;)538 5571 y Fz(wher)l(e)g Fu(a)24 b Ft(2)g FB(\006)979 5541 y Fq(l)1004 5571 y FB(\()p Fu(K)1107 5583 y FA(0)1144 5571 y FB(\))31 b Fz(\(r)l(esp.)39 b Fu(a)24 b Ft(2)g FB(\006)1657 5541 y Fq(l)1657 5594 y FA(class)1795 5571 y FB(\()p Fu(K)1898 5583 y FA(0)1935 5571 y FB(\))p Fz(\).)40 b(We)30 b(wil)t(l)h(denote)g Fu(a)23 b Ft(2)h Fu(S)5 b(S)2898 5541 y Fq(l)2923 5571 y FB(\()p Fu(K)3026 5583 y FA(0)3063 5571 y FB(\))30 b Fz(\(r)l(esp.)538 5670 y Fu(a)23 b Ft(2)g Fu(S)5 b(S)795 5640 y Fq(l)790 5694 y(class)943 5670 y FB(\()p Fu(K)1046 5682 y FA(0)1083 5670 y FB(\))p Fz(\).)p Black 1788 5919 a FB(21)p Black eop %%Page: 22 22 22 21 bop Black Black Black 454 390 a Ft(\017)p Black 42 w Fz(If)33 b Fu(K)39 b Fz(is)34 b(an)g(isotr)l(opic)h(submanifold)g (of)f Fu(T)1922 360 y Fq(?)1960 390 y Fr(R)2020 360 y Fq(n)2098 390 y Fz(and)g Fu(\037)g Fz(a)g(c)l(anonic)l(al)g(tr)l (ansformation)538 490 y(such)c(that)g Fu(\037)p FB(\()p Fu(K)1052 502 y FA(0)1089 490 y FB(\))25 b(=)e Fu(K)6 b Fz(,)31 b(we)f(cho)l(ose)i(an)e(el)t(liptic)i(FIO)f(of)g(or)l(der)g FB(0)f Fz(say)h Fu(A)f Fz(and)h(de\014ne)538 589 y Fu(S)5 b(S)650 559 y Fq(l)674 589 y FB(\()p Fu(K)h FB(\))24 b(=)e Fu(A)p FB(\()p Fu(S)5 b(S)1132 559 y Fq(l)1158 589 y FB(\()p Fu(K)1261 601 y FA(0)1298 589 y FB(\)\))30 b Fz(\(r)l(esp.)39 b Fu(S)5 b(S)1747 559 y Fq(l)1742 613 y(class)1895 589 y FB(\()p Fu(K)h FB(\))23 b(=)g Fu(A)p FB(\()p Fu(S)5 b(S)2353 559 y Fq(l)2348 613 y(class)2502 589 y FB(\()p Fu(K)2605 601 y FA(0)2642 589 y FB(\)\))p Fz(\).)p Black 330 768 a Fo(Remark)32 b(2)p Black 41 w Fz(:if)i Fu(K)39 b Fz(is)33 b(a)h(L)l(agr)l(angian)g(submanifold,)i (symple)l(ctic)e(spinors)g(asso)l(ciate)l(d)g(with)330 868 y Fu(K)h Fz(ar)l(e)30 b(exactly)g(the)g(L)l(agrnagian)h(states)f (\(WKB-Maslov)h(states\).)455 968 y FB(The)h(pro)r(of)g(of)h(the)g (coherence)f(of)h(the)g(previous)e(de\014nition)i(is)g(an)f(easy)g (adaptation)g(of)330 1067 y(Guillemin's)26 b(argumen)n(t)d(in)i([28])g (\(see)f(also)g([6]\).)36 b(It)25 b(is)g(clear)f(that,)i(if)f Fu(u)2576 1079 y Fq(h)2642 1067 y Ft(2)e Fu(S)5 b(S)2832 1037 y Fq(l)2857 1067 y FB(\()p Fu(K)h FB(\),)26 b(w)n(e)e(ha)n(v)n(e) 330 1167 y Fu(W)12 b(F)473 1179 y Fq(h)516 1167 y FB(\()p Fu(u)596 1179 y Fq(h)639 1167 y FB(\))24 b Ft(\032)e Fu(K)6 b FB(.)455 1266 y(An)29 b(example)g(whic)n(h)g(is)g(useful)g(in) g(our)g(pap)r(er)f(is)h Fu(a)p FB(\()p Fu(x;)14 b(Y)5 b(;)14 b(h)p FB(\))26 b(=)f Fu(a)2539 1278 y FA(0)2576 1266 y FB(\()p Fu(x;)14 b(Y)20 b FB(\))p Fu(e)2831 1236 y Fq(iP)9 b FA(\()p Fq(Y)15 b FA(\))c(log)h Fq(h)3191 1266 y FB(\(see)330 1366 y(form)n(ula)32 b(\(22\)\))g(where)g Fu(a)1141 1378 y FA(0)1211 1366 y FB(is)h(in)g(the)g(Sc)n(h)n(w)n(artz) e(class)g(w.r.)52 b(to)32 b Fu(Y)52 b FB(and)32 b Fu(P)45 b FB(is)32 b(a)g(real)g(v)-5 b(alued)330 1466 y(p)r(olynomial.)p Black 330 1629 a Fo(De\014nition)31 b(2)p Black 41 w Fz(A)36 b(p)l(ositive)i(formal)g(L)l(agr)l(angian)f(manifold)h(along)f Fu(K)42 b Fz(is)37 b(a)g(jet)f(of)h(in\014nite)330 1728 y(or)l(der)d(of)f(c)l(omplex)g(L)l(agr)l(angian)h(manifold)h(along)e Fu(K)39 b Fz(whose)33 b(line)l(ar)h(p)l(art)f(is)g(a)g(p)l(ositive)h(L) l(a-)330 1828 y(gr)l(angian)d(subsp)l(ac)l(e)f(of)g FB(\(\()p Fu(T)12 b(K)6 b FB(\))1335 1798 y Fq(o)1372 1828 y Fu(=T)12 b(K)6 b FB(\))16 b Ft(\012)i Fr(C)p Fz(.)455 1928 y(If)29 b Fu(K)f FB(=)23 b Fu(K)799 1940 y FA(0)836 1928 y Fz(,)29 b FB(\003)23 b(=)g(\003)1117 1940 y Fq(')1193 1928 y Fz(is)29 b(de\014ne)l(d)h(by)f(a)g(formal)i(series)e Fu(')p FB(\()p Fu(x;)14 b(y)s FB(\))24 b(=)2594 1865 y Fs(P)2682 1886 y Fp(1)2682 1952 y Fq(j)s FA(=2)2814 1928 y Fu(')2868 1940 y Fq(j)2904 1928 y FB(\()p Fu(x;)14 b(y)s FB(\))29 b Fz(wher)l(e)330 2027 y Fu(')384 2039 y Fq(j)419 2027 y FB(\()p Fu(x;)14 b(y)s FB(\))38 b Fz(is)f(homo)l (gene)l(ous)g(of)h(de)l(gr)l(e)l(e)f Fu(j)k Fz(w.r.)60 b(to)37 b Fu(y)i Fz(and)e Ft(=)p Fu(')2353 2039 y FA(2)2391 2027 y FB(\()p Fu(x;)14 b(:)p FB(\))38 b Fz(is)f(a)g(strictly)g(p)l (ositive)330 2127 y(quadr)l(atic)31 b(form.)p Black 330 2306 a Fo(De\014nition)g(3)p Black 41 w Fz(A)f FB(Gaussian)c(state)k Fz(of)g(or)l(der)h Fu(l)g Fz(asso)l(ciate)l(d)g(to)f FB(\()p Fu(K)2482 2318 y FA(0)2519 2306 y Fu(;)14 b FB(\003)2614 2318 y Fq(')2661 2306 y FB(\))30 b Fz(is)g(de\014ne)l(d)g(by)1329 2495 y Fu(u)1377 2507 y Fq(h)1420 2495 y FB(\()p Fu(x;)14 b(y)s FB(\))24 b(=)e Fu(a)1767 2507 y Fq(h)1810 2495 y FB(\()p Fu(x;)14 b(y)s FB(\))p Fu(e)2041 2461 y Fq(i')p FA(\()p Fq(x;y)r FA(\))p Fq(=h)330 2674 y Fz(wher)l(e)30 b Fu(a)g Fz(is)g(a)g(classic)l(al)i(symb)l(ol)e(of)h(or)l(der)f Fu(l)20 b Ft(\000)e FB(\()p Fu(n)h Ft(\000)f Fu(k)s FB(\))p Fu(=)p FB(2)p Fz(.)455 2773 y(We)29 b(wil)t(l)i(denote)g(by)f Fu(GS)1257 2743 y Fq(l)1282 2773 y FB(\()p Fu(K)1385 2785 y FA(0)1422 2773 y Fu(;)14 b FB(\003)1517 2785 y Fq(')1565 2773 y FB(\))30 b Fz(the)g(c)l(orr)l(esp)l(onding)h(sp)l(ac)l (e.)455 2873 y(We)e(c)l(an)h(de\014ne)g Fu(GS)1121 2843 y Fq(l)1146 2873 y FB(\()p Fu(K)q(;)14 b FB(\003\))30 b Fz(using)g(F)-6 b(ourier)30 b(inte)l(gr)l(al)g(op)l(er)l(ators.)p Black 330 3052 a Fo(Prop)s(osition)g(3)p Black 41 w Fz(A)i(Gaussian)i (state)e(is)g(a)h(symple)l(ctic)h(spinor.)47 b(If)33 b Fu(u)27 b Ft(2)i Fu(GS)2833 3022 y FA(0)2870 3052 y FB(\()p Fu(K)2973 3064 y FA(0)3010 3052 y Fu(;)14 b FB(\003)3105 3064 y Fq(')3152 3052 y FB(\))p Fz(,)34 b(its)330 3151 y(total)d(symb)l(ol)g(is)882 3089 y Fs(P)970 3110 y Fp(1)970 3176 y Fq(j)s FA(=0)1103 3151 y Fu(A)1165 3163 y Fq(j)1200 3151 y FB(\()p Fu(x;)14 b(Y)19 b FB(\))p Fu(h)1463 3121 y Fq(j)s(=)p FA(2)1566 3151 y Fu(e)1605 3121 y Fq(i')1672 3129 y Fj(2)1704 3121 y FA(\()p Fq(x;Y)13 b FA(\))1901 3151 y Fz(wher)l(e)32 b Fu(A)2199 3163 y Fq(j)2234 3151 y FB(\()p Fu(x;)14 b(Y)19 b FB(\))31 b Fz(is)g(a)g(p)l(olynomial)i(in)e Fu(Y)49 b Fz(of)330 3251 y(de)l(gr)l(e)l(e)30 b(less)g(than)g FB(3)p Fu(j)k Fz(and)c(c)l(onversely.)330 3430 y(R)l(emark:)37 b FB(the)28 b(\\3)p Fu(j)5 b FB(")27 b(can)g(already)f(b)r(e)i(seen)f (in)h(the)g(form)n(ula)f(\(3.2\))g(in)h([16)o(].)330 3662 y Fl(14.2)150 b(Principal)38 b(sym)m(b)s(ols)330 3815 y Fo(14.2.1)93 b(Symplectic)32 b(spinors)330 3968 y FB(W)-7 b(e)28 b(will)g(no)n(w)f(de\014ne)h(the)g(principal)f(sym)n (b)r(ol)g(of)g(a)h(symplectic)f(spinor)g(follo)n(wing)g([28)o(].)455 4068 y(Let)39 b Fu(K)44 b FB(b)r(e)c(a)f Fu(k)s Ft(\000)p FB(dimensional)f(isotropic)g(submanifold)h(of)g Fu(T)2511 4038 y Fq(?)2548 4068 y Fr(R)2608 4038 y Fq(n)2653 4068 y FB(.)72 b(W)-7 b(e)39 b(will)h(assume)330 4167 y(as)g(in)h([28])g (that)g Fu(K)46 b FB(is)41 b(equipp)r(ed)h(with)f(a)g(metalinear)f (structure.)76 b(The)41 b(v)n(ector)f(bundle)330 4267 y Fu(E)28 b FB(=)23 b Fu(T)12 b(K)645 4237 y Fq(o)680 4267 y Fu(=T)g(K)32 b FB(of)27 b(dimension)h(2\()p Fu(n)17 b Ft(\000)h Fu(k)s FB(\))28 b(o)n(v)n(er)d Fu(K)33 b FB(is)28 b(symplectic.)37 b(W)-7 b(e)27 b(will)h(assume)f(that)h(it)330 4367 y(is)21 b(equipp)r(ed)g(with)g(a)f(metaplectic)h(structure.)34 b(It)22 b(implies)f(that)g(eac)n(h)e(Lagrangian)g(subbundle)330 4466 y(is)27 b(equipp)r(ed)h(with)f(a)g(metalinear)g(structure.)36 b(W)-7 b(e)27 b(assume)g(also)f(that)h Fr(R)2658 4436 y Fq(n)2731 4466 y FB(is)g(equipp)r(ed)h(with)330 4566 y(the)g(standard)f(metalinear)f(structure.)455 4666 y(W)-7 b(e)38 b(w)n(an)n(t)f(to)g(de\014ne)h(the)h(principal)e(sym)n(b)r(ol)g (of)h(a)f(semi-classical)f(symplectic)i(spinor)330 4765 y(whic)n(h)c(is)g(a)g(half)g(form:)49 b Fu(u)1199 4777 y Fq(h)1242 4765 y FB(\()p Fu(x;)14 b(y)s FB(\))1434 4702 y Ft(p)p 1504 4702 178 4 v 1504 4765 a Fu(dxdy)s FB(.)56 b(W)-7 b(e)35 b(start)e(with)i(a)f(direct)f(sum)i(decomp)r (osition)330 4865 y Fu(E)d FB(=)27 b Fu(L)20 b Ft(\010)g Fu(L)734 4835 y Fp(0)787 4865 y FB(of)30 b Fu(E)35 b FB(in)n(to)30 b(a)f(sum)i(of)f(2)g(transv)n(ersal)d(Lagrangian)h (subbundles.)44 b(The)31 b(sym)n(b)r(ol)330 4964 y Fu(\033)s FB(\()p Fu(u)460 4976 y Fq(h)503 4964 y FB(\))37 b(of)f Fu(u)723 4976 y Fq(h)802 4964 y FB(will)h(b)r(e)g(an)f(elemen)n(t)g([)p Fu(a)1596 4976 y Fq(h)1639 4964 y FB(\()p Fu(x;)14 b(Y)20 b FB(\)])1878 4894 y Ft(p)p 1947 4894 206 4 v 70 x Fu(dxd)5 b(Y)56 b FB(where)36 b Fu(x)i Ft(2)g Fu(K)6 b FB(,)38 b Fu(Y)56 b Ft(2)38 b Fu(L)e FB(and)h(the)330 5073 y(equiv)-5 b(alen)n(t)26 b(class)f([)p Fu(:)p FB(])h(is)f(in)i(\006)1248 5043 y FA(0)1285 5073 y FB(\()p Fu(L)p FB(\))p Fu(=)p FB(\006)1518 5020 y Fj(1)p 1517 5029 29 3 v 1517 5063 a(2)1560 5073 y FB(\()p Fu(L)p FB(\).)36 b(W)-7 b(e)26 b(use)g(a)f(lo)r(cal)h(trivialisation)e(of)i Fu(L)g FB(in)g(order)e(to) 330 5172 y(get)f(functions)g(of)g(\()p Fu(x;)14 b(Y)20 b FB(\).)36 b(If)23 b Fu(K)29 b FB(=)22 b Fu(K)1518 5184 y FA(0)1555 5172 y FB(,)i Fu(u)f FB(=)f Fu(h)1808 5142 y Fp(\000)p FA(\()p Fq(n)p Fp(\000)p Fq(k)q FA(\))p Fq(=)p FA(2)2113 5172 y Fu(a)2157 5184 y Fq(h)2200 5172 y FB(\()p Fu(x;)14 b(y)s(=)2402 5102 y Ft(p)p 2471 5102 48 4 v 70 x Fu(h)p FB(\))2551 5110 y Ft(p)p 2620 5110 178 4 v 62 x Fu(dxdy)t(;)23 b(L)f FB(=)h(0)10 b Ft(\010)g Fr(R)3198 5142 y Fq(n)p Fp(\000)p Fq(k)330 5272 y FB(and)27 b Fu(L)548 5242 y Fp(0)594 5272 y FB(=)c(0)18 b Ft(\010)g FB(\()p Fr(R)917 5242 y Fq(n)p Fp(\000)p Fq(k)1051 5272 y FB(\))1083 5242 y Fq(?)1121 5272 y FB(,)28 b(w)n(e)f(ha)n(v)n(e)g Fu(\033)s FB(\()p Fu(u)1616 5284 y Fq(h)1659 5272 y FB(\))c(=)g([)p Fu(a)p FB(\()p Fu(x;)14 b(Y)19 b FB(\)])2107 5201 y Ft(p)p 2177 5201 206 4 v 2177 5272 a Fu(dxd)5 b(Y)19 b FB(.)455 5372 y(It)32 b(is)h(no)n(w)f(enough)g(to)g(sa)n(y)g(what)g(is)h(the)g (transformation)e(rule)h(for)g(the)h(sym)n(b)r(ol)f(under)330 5471 y(the)f(action)e(of)i(an)f(elliptic)h(F)-7 b(ourier)29 b(In)n(tegral)g(Op)r(erator)f(of)j(order)e(0:)41 b(the)31 b(canonical)e(trans-)330 5571 y(formation)i Fu(\037)h FB(suc)n(h)f(that)h Fu(\037)p FB(\()p Fu(K)1329 5583 y FA(0)1366 5571 y FB(\))e(=)f Fu(K)38 b FB(transforms)30 b(the)i Fu(K)2267 5583 y FA(0)2304 5571 y FB(-bundles)f Fu(L)2697 5583 y FA(0)2755 5571 y Ft(\010)21 b Fu(L)2898 5541 y Fp(0)2898 5591 y FA(0)2965 5571 y Ft(\032)29 b Fu(E)3120 5583 y FA(0)3189 5571 y FB(in)n(to)330 5670 y(the)e Fu(K)6 b FB(-bundles)25 b Fu(L)15 b Ft(\010)g Fu(L)1088 5640 y Fp(0)1134 5670 y Ft(\032)23 b Fu(E)5 b FB(.)36 b(It)27 b(acts)e(in)i(a)f(natural)f(w)n(a)n(y)g(on)h (principal)f(sym)n(b)r(ols)h(using)g(the)p Black 1788 5919 a(22)p Black eop %%Page: 23 23 23 22 bop Black Black 330 390 a FB(metaplectic)27 b(represen)n(tation)e (asso)r(ciated)g(to)i(the)g(linear)f(part)g(of)h Fu(\037)p FB(.)37 b(The)27 b(sym)n(b)r(ol)f(of)h Fu(A)p FB(\()p Fu(u)3255 402 y Fq(h)3298 390 y FB(\))330 490 y(using)f(this)g(natural) g(action)f(is)h(just)h(obtained)f(b)n(y)g(m)n(ultiplication)g(b)n(y)g (the)h(principal)f(sym)n(b)r(ol)330 589 y(of)i(the)g(F)-7 b(ourier)26 b(In)n(tegral)g(Op)r(erator.)455 689 y(It)d(remains)e(to)i (sp)r(eak)f(ab)r(out)g(the)h Fz(tr)l(ansp)l(ort)i(e)l(quation:)35 b FB(w)n(e)23 b(assume)f(that)h Fu(P)34 b FB(is)23 b(a)f(pseudo-)330 789 y(di\013eren)n(tial)31 b(op)r(erator)f(whose)h(principal)g(sym)n(b) r(ol)g Fu(p)g FB(v)-5 b(anishes)31 b(on)g Fu(K)37 b FB(and)31 b(suc)n(h)g(that)h Ft(X)3204 801 y Fq(p)3274 789 y FB(is)330 888 y(tangen)n(t)f(to)g Fu(K)6 b FB(.)48 b(If)31 b Fu(u)1023 900 y Fq(h)1095 888 y Ft(2)f FB(\006)1240 858 y FA(0)1277 888 y FB(\()p Fu(K)6 b FB(\),)32 b Fu(P)12 b(u)1586 900 y Fq(h)1658 888 y Ft(2)30 b FB(\006)1803 858 y FA(1)1840 888 y FB(\()p Fu(K)6 b FB(\))31 b(and)g(its)h(principal)f(sym)n(b)r(ol) g(is)g(giv)n(en)f(b)n(y)330 988 y(the)e(familiar)f(form)n(ula)1218 1188 y Fu(\033)s FB(\()p Fu(P)12 b(u)p FB(\))23 b(=)1566 1131 y(1)p 1566 1169 42 4 v 1572 1245 a Fu(i)1617 1188 y Ft(L)1674 1200 y Fp(X)1722 1208 y Fb(p)1761 1188 y Fu(\033)s FB(\()p Fu(u)p FB(\))c(+)f(sub\()p Fu(P)12 b FB(\))p Fu(\033)s FB(\()p Fu(u)p FB(\))330 1397 y(where)27 b(one)g(need)h(to)f(in)n(terpret)h(prop)r(erly)e(as)h(in)h([28)o(])g (the)g(Lie)f(deriv)-5 b(ativ)n(e!)455 1497 y(In)28 b(the)h(matrix)f (case,)g(w)n(e)h(need)f(a)g(natural)g(extension)g(of)h(the)g(calculus)f (of)h([17)o(].)40 b(F)-7 b(or)28 b(the)330 1596 y(standard)23 b(examples)h(\(Born-Opp)r(enheimer)f(or)g(adiabatic)h(cases\),)g(it)g (is)g(enough)g(to)g(consider)330 1696 y(the)k(canonical)e(connexion)h (on)g(the)h(p)r(olarization)f(bundle.)330 1911 y Fo(14.2.2)93 b(Gaussian)32 b(states)330 2065 y FB(The)37 b(case)e(of)i(Gaussian)e (states)h(is)h(easier)e(to)h(describ)r(e:)55 b(the)37 b(principal)f(sym)n(b)r(ol)g(is)g(just)h(a)330 2164 y(half)k(form)f(on) g(the)h(bundle)h(of)e(Lagrangian)e(spaces)i Fu(J)2155 2176 y FA(1)2192 2164 y FB(\(\003\))h(o)n(v)n(er)e Fu(K)6 b FB(.)75 b(If)41 b Fu(K)50 b FB(=)45 b Fu(K)3119 2176 y FA(0)3196 2164 y FB(and)330 2264 y(\003)f(=)g(\003)599 2276 y Fq(')647 2264 y FB(.)75 b Fu(J)791 2276 y FA(1)828 2264 y FB(\(\003\))45 b(=)f Ft(f)p FB(\()p Fu(x;)14 b FB(0;)g Fu(y)s(;)g(@)5 b(')1525 2276 y FA(2)1561 2264 y FB(\()p Fu(x;)14 b(y)s FB(\))p Fu(=@)5 b(y)s FB(\))p Ft(g)40 b FB(and,)j(if)e(w)n(e)f(denote)h(b)n(y)f Fu(\031)48 b FB(:)c Fu(J)3043 2276 y FA(1)3080 2264 y FB(\(\003\))h Ft(!)330 2363 y Fu(T)379 2375 y Fq(K)435 2383 y Fj(0)471 2363 y Fr(R)531 2333 y Fq(n)602 2363 y FB(the)26 b(canonical)f(pro)5 b(jection,)25 b(the)i(principal)e(sym)n(b)r(ol)h(of)g Fu(a)2428 2375 y Fq(h)2471 2363 y FB(\()p Fu(x;)14 b(y)s FB(\))p Fu(e)2702 2333 y Fq(i')p FA(\()p Fq(x;y)r FA(\))p Fq(=h)2991 2301 y Ft(p)p 3060 2301 270 4 v 62 x Fu(dx)19 b Ft(^)g Fu(dy)330 2463 y FB(is)27 b Fu(\031)463 2433 y Fq(?)502 2463 y FB(\()p Fu(a)578 2475 y FA(0)615 2463 y FB(\()p Fu(x;)14 b FB(0\))805 2400 y Ft(p)p 875 2400 V 875 2463 a Fu(dx)19 b Ft(^)g Fu(dy)s FB(\).)330 2737 y Fv(References)p Black 372 2919 a FB([1])p Black 41 w(M.)40 b(Abramo)n(witz)g(and)g(I.)h(Stegun,)78 b(Handb)r(o)r(ok)40 b(of)h(mathematical)f(functions)h(with)501 3019 y(form)n(ulas,)i (graphs,)h(and)d(mathematical)g(tables.)78 b Fz(Dover)43 b(Public)l(ation)h(Inc.,)i(N.Y.,)501 3119 y FB(\(1970)26 b(\).)p Black 372 3284 a([2])p Black 41 w(V.)i(Arnold,)36 b(Singularities)27 b(of)g(Caustics)g(and)h(W)-7 b(a)n(v)n(e)27 b(F)-7 b(ron)n(ts.)36 b Fz(Kluwer)27 b FB(\(1990\).)p Black 372 3450 a([3])p Black 41 w(V.)19 b(Arnold,)24 b(On)18 b(the)h(in)n(terior)f(scattering)f(of)i(w)n(a)n(v)n(es,)g (de\014ned)g(b)n(y)f(h)n(yp)r(erb)r(olic)h(v)-5 b(ariational)501 3549 y(principles.)36 b Fz(J.)30 b(Ge)l(om.)h(Phys.,)e FB(5:305-315)24 b(\(1988\).)p Black 372 3715 a([4])p Black 41 w(J.E.)g(Avron)f(and)i(A.)g(Gordon,)31 b(Born-Opp)r(enheimer) 23 b(w)n(a)n(v)n(e)g(function)i(near)f(lev)n(el)g(cross-)501 3814 y(ing.)36 b Fz(Phys.)31 b(R)l(ev.)f(A)p FB(,)e(62-06254,)c(2000.)p Black 372 3980 a([5])p Black 41 w(M.)39 b(Born)g(und)h(R.)g(Opp)r (enheimer,)75 b(Z)r(\177)-44 b(ur)39 b(Quan)n(ten)n(theorie)f(der)h (Molek)n(eln.)72 b Fz(A)n(nnal.)501 4079 y(Phys.,)29 b FB(84:457-484,)24 b(1927.)p Black 372 4245 a([6])p Black 41 w(L.)29 b(Boutet)g(de)g(Mon)n(v)n(el)f(and)g(V.)i(Guillemin,) 42 b(The)29 b(Sp)r(ectral)g(Theory)e(of)i(T)-7 b(o)r(eplitz)30 b(Op-)501 4345 y(erators.)35 b Fz(Princ)l(eton)30 b(Univ.)g(Pr)l(ess)e FB(\(1981\).)p Black 372 4510 a([7])p Black 41 w(P)-7 b(.)28 b(Braam)f(and)i(H.)g(Duistermaat,)40 b(Normal)28 b(forms)g(of)h(real)f(symmetric)g(systems)h(with)501 4610 y(m)n(ultiplicit)n(y)-7 b(.)37 b Fz(Indag.)31 b(Math.,)g(N.S.)p FB(,)d(4\(4\):407-421,)d(1993.)p Black 372 4775 a([8])p Black 41 w(Y.)31 b(Colin)f(de)h(V)-7 b(erdi)n(\022)-39 b(ere,)45 b(Singular)30 b(Lagrangian)e(manifolds)j(and)f (semi-classical)f(anal-)501 4875 y(ysis.)52 b Fz(Pr)n(\023)-40 b(epublic)l(ation)36 b(Institut)d(F)-6 b(ourier)35 b(no)g(534)h (\(2001\),)h(Duke)e(Math.)h(Journal)e(\(to)501 4975 y(app)l(e)l(ar\))p FB(.)p Black 372 5140 a([9])p Black 41 w(Y.)28 b(Colin)f(de)h(V)-7 b(erdi)n(\022)-39 b(ere,)35 b(Sp)r(ectres)27 b(de)h(Graphes.)36 b Fz(So)l(c.)30 b(Math.)h(F)-6 b(r.,)29 b FB(1998.)p Black 330 5306 a([10])p Black 41 w(Y.)g(Colin)h(de)f(V)-7 b(erdi)n(\022)-39 b(ere,)41 b(The)29 b(lev)n(el)g(crossing)f(problem)h (in)g(semi-classical)f(analysis)g(I)r(I.)501 5405 y(The)f(Hermitian)h (case.)36 b Fz(In)29 b(pr)l(ep)l(ar)l(ation,)h FB(2002.)p Black 330 5571 a([11])p Black 41 w(Y.)21 b(Colin)g(de)h(V)-7 b(erdi)n(\022)-39 b(ere,)21 b(M.)g(Lom)n(bardi)f(and)i(J.)f(P)n(ollet,) 27 b(The)21 b(microlo)r(cal)f(Landau-Zener)501 5670 y(form)n(ula.)35 b Fz(A)n(nnales)30 b(de)g(l'IHP)h(\(Physique)g(th)n(\023)-40 b(eorique\))p FB(,)28 b(71:95-127,)c(1999.)p Black 1788 5919 a(23)p Black eop %%Page: 24 24 24 23 bop Black Black Black 330 390 a FB([12])p Black 41 w(Y.)22 b(Colin)g(de)g(V)-7 b(erdi)n(\022)-39 b(ere)21 b(et)h(B.)g(P)n(arisse,)27 b(Equilibre)22 b(instable)g(en)g(r)n(\023) -39 b(egime)20 b(semi-classique)h(:)501 490 y(I-Concen)n(tration)k (microlo)r(cale.)36 b Fz(Commun.)30 b(in)g(PDE)p FB(,)e(19:1535-1563,) 22 b(1994.)p Black 330 656 a([13])p Black 41 w(Y.)j(Colin)g(de)g(V)-7 b(erdi)n(\022)-39 b(ere)24 b(et)h(J.)g(V)-7 b(ey)g(,)33 b(Le)25 b(lemme)h(de)f(Morse)f(iso)r(c)n(hore.)31 b Fz(T)-6 b(op)l(olo)l(gy)p FB(,)28 b(18:283-)501 756 y(293,)e(1979.)p Black 330 922 a([14])p Black 41 w(J.-M.)f(Com)n(b)r(es,)34 b(On)25 b(the)h(Born-Opp)r(enheimer)f(appro)n(ximation,)32 b Fz(International)c(Sym-)501 1021 y(p)l(osium)36 b(on)g(Mathematic)l (al)i(Pr)l(oblems)f(in)f(The)l(or)l(etic)l(al)i(Physics)f(\(Kyoto)g (Univ.,)h(Ky-)501 1121 y(oto\),)30 b(L)l(e)l(ctur)l(e)f(Notes)h(in)f (Phys.,)h FB(39:467{471,)23 b(1975.)p Black 330 1287 a([15])p Black 41 w(J.-M.)41 b(Com)n(b)r(es)g(and)g(R.)g(Seiler,)81 b(Sp)r(ectral)41 b(prop)r(erties)g(of)g(atomic)g(and)g(molecular)501 1386 y(systems,)24 b Fz(Quantum)c(dynamics)k(of)f(mole)l(cules)f(\(Pr)l (o)l(c.)h(NA)-6 b(TO)22 b(A)l(dv.)g(Study)g(Inst.,)i(Univ.)501 1486 y(Cambridge\),)30 b FB(435{482,)24 b(1979.)p Black 330 1652 a([16])p Black 41 w(M.)d(Com)n(b)r(escure)g(and)g(D.)i(Rob)r (ert,)28 b(Semiclassical)20 b(spreading)g(of)i(quan)n(tum)f(w)n(a)n(v)n (e)f(pac)n(k-)501 1752 y(ets)i(and)g(applications)g(near)f(unstable)i (\014xed)f(p)r(oin)n(ts)h(of)f(the)h(classical)e(\015o)n(w.)27 b Fz(Asymptotic)501 1851 y(A)n(nalysis)p FB(,)h(14:377-404,)c(1997.)p Black 330 2017 a([17])p Black 41 w(C.)j(Emmric)n(h)f(and)h(A.)h(W)-7 b(einstein,)37 b(Geometry)26 b(of)h(the)h(transp)r(ort)e(Equation)g(in) i(Multi-)501 2117 y(comp)r(onen)n(t)e(WKB)f(Appro)n(ximations.)34 b Fz(Commun.)28 b(Math.)i(Phys.)p FB(,)e(176:701-711,)22 b(1996.)p Black 330 2283 a([18])p Black 41 w(F.)34 b(F)-7 b(aure)33 b(and)g(B.)h(Zhilinskii,)57 b(T)-7 b(op)r(ological)32 b(Chern)h(Indices)h(in)g(Molecular)e(Sp)r(ectra.)501 2383 y Fz(Phys.)f(R)l(ev.)f(L)l(etters,)d FB(85:960-963,)d(2000.)p Black 330 2549 a([19])p Black 41 w(F.)33 b(F)-7 b(aure)33 b(and)g(B.)g(Zhilinskii,)54 b(T)-7 b(op)r(ological)32 b(prop)r(erties)g(of)h(the)h(Born-Opp)r(enheimer)501 2648 y(appro)n(ximation)h(and)i(implications)f(for)h(the)g(exact)g(sp)r (ectrum.)64 b Fz(L)l(ett.)38 b(Math.)i(Phys.,)501 2748 y FB(55:219-239,)23 b(2001.)p Black 330 2914 a([20])p Black 41 w(C.)67 b(F)-7 b(ermanian-Kammerer,)161 b(A)67 b(non-comm)n(utativ)n(e)f(Landau-Zener)f(form)n(ula.)501 3014 y Fz(Pr)n(\023)-40 b(epublic)l(ation)31 b(Universit)n(\023)-40 b(e)30 b(de)h(Cer)l(gy-Pontoise,)e FB(01/02:1-34,)24 b(2002.)p Black 330 3180 a([21])p Black 41 w(C.)32 b(F)-7 b(ermanian-Kammerer,)48 b(Une)33 b(form)n(ule)e(de)i(Landau-Zener)d(p)r (our)i(un)g(croisemen)n(t)501 3279 y(de)22 b(co)r(dimension)h(2.)28 b Fz(S)n(\023)-40 b(eminair)l(e)26 b(Equations)g(aux)f(d)n(\023)-40 b(eriv)n(\023)g(ees)26 b(p)l(artiel)t(les,)j(Ec)l(ole)d(Polyte)l(ch-) 501 3379 y(nique.)i FB(Exp)r(os)n(\023)-39 b(e)25 b(XXI,)k(9/04/2002.)p Black 330 3545 a([22])p Black 41 w(C.)35 b(F)-7 b(ermanian-Kammerer)33 b(and)i(C.)g(Lasser,)60 b(Wigner)35 b(measures)f(and)h(co)r(dimension) 501 3645 y(t)n(w)n(o)26 b(crossings.)35 b Fz(pr)l(eprint)30 b(mp-ar)l(c,)f FB(02-186,)c(2002.)p Black 330 3811 a([23])p Black 41 w(W.)36 b(Flynn)h(and)f(R.)h(Littlejohn,)65 b(Normal)35 b(forms)h(for)g(linear)f(mo)r(de)h(con)n(v)n(ersion)e(and) 501 3910 y(Landau-Zener)40 b(transitions)g(in)i(one)g(dimension.)78 b Fz(A)n(nn.)43 b(Physics)p FB(,)k(234\(2\):334-403,)501 4010 y(1994.)p Black 330 4176 a([24])p Black 41 w(W.)22 b(Flynn)h(and)f(R.)g(Littlejohn,)30 b(Semi-classical)21 b(theory)g(of)h(spin-orbit)g(coupling,)29 b Fz(Phys.)501 4276 y(R)l(ev.)h(A,)d FB(45:7697-7717,)c(1992.)p Black 330 4442 a([25])p Black 41 w(G.)f(F)-7 b(olland,)28 b(Harmonic)21 b(Analysis)g(on)h(Phase)e(Space.)27 b Fz(Princ)l(eton)e(Univ.)g(Pr)l (ess,)e FB(\(1989\).)p Black 330 4608 a([26])p Black 41 w(P)-7 b(.)28 b(G)n(\023)-39 b(erard)27 b(et)i(C.)g(F)-7 b(ermanian-Kammerer,)38 b(Mesures)28 b(semi-classiques)f(et)i (croisemen)n(t)501 4707 y(de)e(mo)r(des.)37 b Fz(Bul)t(l.)31 b(So)l(c.)f(Math.)h(F)-6 b(r.,)29 b FB(130:123-168,)23 b(2002.)p Black 330 4873 a([27])p Black 41 w(P)-7 b(.)42 b(G)n(\023)-39 b(erard)40 b(et)j(C.)g(F)-7 b(ermanian-Kammerer,)83 b(A)43 b(Landau-Zener)e(form)n(ula)g(for)i(non-)501 4973 y(degenerated)26 b(in)n(v)n(olutiv)n(e)h(co)r(dimension)g(3)g (crossings,)35 b Fz(Pr)l(eprint,)28 b FB(sept.)g(2002.)p Black 330 5139 a([28])p Black 41 w(V.)47 b(Guillemin,)100 b(Symplectic)47 b(spinors)e(and)i(PDE,)94 b Fz(G)n(\023)-40 b(eom)n(\023)g(etrie)48 b(Symple)l(ctique)g(et)501 5239 y(Physique)31 b(math)n(\023)-40 b(ematique.)29 b FB(Coll.)e(CNRS)h (Aix-en-Pro)n(v)n(ence)d(\(1974\).)p Black 330 5405 a([29])p Black 41 w(G.)19 b(Hagedorn,)24 b(Molecular)18 b(Propagation)f(through) i(Electron)f(Energy)g(Lev)n(el)h(Crossings.)501 5504 y Fz(Memoirs)31 b(of)f(the)g(AMS)p FB(,)e(536)e(\(1994\).)p Black 1788 5919 a(24)p Black eop %%Page: 25 25 25 24 bop Black Black Black 330 390 a FB([30])p Black 41 w(G.)53 b(Hagedorn,)119 b(Higher)53 b(Order)f(Corrections)g(to)h (the)h(Time-Dep)r(enden)n(t)g(Born-)501 490 y(Opp)r(enheimer)28 b(Appro)n(ximation)g(I:)h(Smo)r(oth)g(P)n(oten)n(tials.)38 b Fz(A)n(nn.)31 b(Math.,)g FB(124:571-590,)501 589 y(1986.)p Black 330 756 a([31])p Black 41 w(G.)26 b(Hagedorn)e(and)h(A.)h(Jo)n(y) n(e,)33 b(Landau-Zener)24 b(T)-7 b(ransitions)24 b(through)h(small)g (Electronic)501 855 y(Eigen)n(v)-5 b(alues)23 b(Gaps)h(in)h(the)f (Born-Opp)r(enheimer)g(Appro)n(ximation.)30 b Fz(A)n(nnales)d(de)g (l'IHP)501 955 y(\(Physique)k(th)n(\023)-40 b(eorique\),)29 b FB(68:85{134,)24 b(1998.)p Black 330 1121 a([32])p Black 41 w(G.)36 b(Hagedorn)e(and)i(A.)g(Jo)n(y)n(e,)62 b(Molecular)34 b(Propapagation)f(through)i(small)h(a)n(v)n(oided)501 1220 y(Crossings)25 b(of)j(Electron)e(Energy)g(Lev)n(els.)36 b Fz(R)l(ev.)30 b(Math.)h(Phys.,)f FB(11:41{101,)24 b(1999.)p Black 330 1386 a([33])p Black 41 w(R.)32 b(Halb)r(erg,)52 b(Lo)r(calized)32 b(coupling)f(b)r(et)n(w)n(een)i(surface-)e(and)h(b)r (ottom-in)n(tensi\014ed)h(\015o)n(w)501 1486 y(o)n(v)n(er)25 b(top)r(ograph)n(y)-7 b(.)35 b Fz(J.)30 b(Phys.)h(Oc)l(e)l(ano)l(gr.,)e FB(27:977-999,)24 b(1997.)p Black 330 1652 a([34])p Black 41 w(P)-7 b(.)27 b(Holm,)37 b(Generic)27 b(elastic)g(Media.)37 b Fz(Physic)l(a)31 b(Scripta,)e FB(44:122-127,)24 b(1992.)p Black 330 1818 a([35])p Black 41 w(N.)h(Kaidi)f(et)h(M.)g(Rouleux,)32 b(F)-7 b(orme)24 b(normale)g(d'un)h(hamiltonien)g(\022)-42 b(a)24 b(deux)h(niv)n(eaux)f(pr)n(\022)-39 b(es)501 1918 y(d'un)37 b(p)r(oin)n(t)g(de)g(branc)n(hemen)n(t)f(\(limite)h (semi-classique\).)63 b Fz(C.)39 b(R.)g(A)l(c)l(ad.)f(Sci.)h(Paris,)501 2017 y(S)n(\023)-40 b(er.)30 b(I,)e FB(317\(4\):359-364,)23 b(1993.)p Black 330 2183 a([36])p Black 50 w(M.)28 b(Karasev)d(and)j (Y.)g(V)-7 b(orob)5 b(jev,)35 b(In)n(tegral)27 b(represen)n(tations)e (o)n(v)n(er)h(isotropic)h(subman-)501 2283 y(ifolds)g(and)h(equations)e (of)i(zero)e(curv)-5 b(ature.)36 b Fz(A)l(dv.)31 b(Math.,)e FB(135:220-286,)23 b(1998.)p Black 330 2449 a([37])p Black 41 w(M.)33 b(Klein,)h(A.)g(Martinez,)f(R.)h(Seiler)e(and)h(X.)h (W)-7 b(ang,)88 b(On)33 b(the)g(Born)f(Opp)r(enheimer)501 2549 y(Appro)n(ximation)26 b(of)h(W)-7 b(a)n(v)n(e)27 b(Op)r(erators)e(in)j(Molecular)e(Scattering)h(Theory)-7 b(.)36 b Fz(Commun.)501 2648 y(Math.)31 b(Phys.,)e FB(143:607-639,)23 b(1992.)p Black 330 2814 a([38])p Black 41 w(M.)35 b(Kline)f(and)g(I.)h (Ka)n(y)-7 b(,)35 b(Electromagnetic)e(theory)h(and)g(geometrical)f (optics.)58 b Fz(Inter-)501 2914 y(scienc)l(e)30 b(publishers,)f FB(1965.)p Black 330 3080 a([39])p Black 41 w(L.)e(Landau,)64 b(Collected)27 b(pap)r(ers)g(of)h(L.)g(Landau.)36 b Fz(Per)l(gamon)30 b(Pr)l(ess)e FB(\(1965\).)p Black 330 3246 a([40])p Black 41 w(A.)35 b(Melin)g(and)g(J.)g(Sj\177)-42 b(ostrand,)60 b(F)-7 b(ourier)34 b(In)n(tegral)f(Op)r(erators)g(with)j(complex)e(v)-5 b(alued)501 3346 y(phase)27 b(functions.)37 b Fz(L)l(e)l(ctur)l(e)29 b(Notes)g(in)h(Math)h(no)e(459)g FB(\(1975\).)p Black 330 3512 a([41])p Black 41 w(R.)e(Melrose)e(and)i(G.)g(Uhlmann,)36 b(Microlo)r(cal)25 b(structure)h(of)h(in)n(v)n(olutiv)n(e)f(conical)g (refrac-)501 3611 y(tion.)37 b Fz(Duke)29 b(Math.)i(J.,)d FB(46:571-582,)c(1979.)p Black 330 3778 a([42])p Black 41 w(J.)e(Moser,)27 b(On)22 b(the)h(generalization)d(of)i(a)f(theorem)h (of)g(Liap)r(ouno\013.)28 b Fz(Comm.)d(Pur)l(e)g(Appl.)501 3877 y(Math.,)k FB(11:257-271,)24 b(1958.)p Black 330 4043 a([43])p Black 41 w(E.)j(Nelson,)64 b(T)-7 b(opics)27 b(in)h(dynamics,)f(I:)h(Flo)n(ws.)36 b Fz(Princ)l(eton)30 b(Univ.)g(Pr)l(ess)e FB(\(1969\).)p Black 330 4209 a([44])p Black 41 w(P)-7 b(.)35 b(P)n(ettersson,)96 b(WKB)35 b(expansions)f(for) h(systems)g(of)g(Sc)n(hr\177)-42 b(odinger)33 b(op)r(erators)h(with)501 4309 y(crossing)25 b(eigen)n(v)-5 b(alues.)36 b Fz(Asymptotic)30 b(A)n(nal.,)f FB(14:1-48,)c(1997.)p Black 330 4475 a([45])p Black 41 w(J.)31 b(V)-7 b(anneste,)51 b(Mo)r(de)32 b(Con)n(v)n(ersion)e (for)h(Rossb)n(y)g(W)-7 b(a)n(v)n(es)31 b(o)n(v)n(er)f(T)-7 b(op)r(ograph)n(y)g(.)48 b Fz(J.)34 b(Phys.)501 4575 y(Oc)l(e)l(ano)l(gr.,)28 b FB(31:1922-1925,)23 b(2001.)p Black 330 4741 a([46])p Black 41 w(J.)37 b(v)n(on)g(Neumann)h(und)g(E.) f(Wigner,)1819 4720 y(\177)1808 4741 y(Ub)r(er)h(das)f(V)-7 b(erhalten)38 b(v)n(on)f(Eigen)n(w)n(erten)f(b)r(ei)501 4840 y(adiabatisc)n(hen)26 b(Prozessen.)35 b Fz(Phys.)c(Zeit.,)e FB(30:467-470,)23 b(1929.)p Black 330 5006 a([47])p Black 41 w(A.)29 b(W)-7 b(einstein,)40 b(Symplectic)29 b(manifolds)f(and)g (their)h(Lagrangian)c(submanifolds.)39 b Fz(A)l(dv.)501 5106 y(Math.)p FB(,)29 b(6:329{346,)24 b(1971.)p Black 330 5272 a([48])p Black 41 w(C.)37 b(Zener,)66 b(Non-adiabatic)36 b(crossing)f(of)i(energy)f(lev)n(els.)65 b Fz(Pr)l(o)l(c.)39 b(R)l(oy.)g(So)l(c.)g(L)l(ond.)g FB(,)501 5372 y(137:696{702,)23 b(1932.)p Black 1788 5919 a(25)p Black eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0209250815915--