%!PS-Adobe-3.0
%%Title: (no38.1_7)
%%Version: 1 2
%%Creator: (Penta Systems International Inc.)
%%CreationDate: (D:19990513091232)
%%DocumentData: Clean7Bit
%%LanguageLevel: 2
%%BoundingBox: 0 0 612 792
%%Pages: 7
%%DocumentProcessColors: (atend)
%%DocumentNeededResources: (atend)
%%DocumentSuppliedResources:
%%+ procset (Adobe Acrobat - PDF operators) 1.2 0
%%+ procset (Adobe Acrobat - type operators) 1.2 0
%%+ procset (Adobe Acrobat - general image support) 1.2 0
%%+ procset (Adobe Acrobat - monochrome image support) 1.2 0
%%EndComments
%%BeginDefaults
%%EndDefaults
%%BeginProlog
%%EndProlog
%%BeginSetup
%%BeginResource: l2check
%%Copyright: Copyright 1993 Adobe Systems Incorporated. All Rights Reserved.
systemdict /languagelevel known
{ systemdict /languagelevel get 1 eq }
{ true }
ifelse
{
initgraphics /Helvetica findfont 18 scalefont setfont
72 600 moveto (Error: Your printer driver needs to be configured) dup show
72 580 moveto (for printing to a PostScript Language Level 1 printer.) dup show
exch = =
/Helvetica-Bold findfont 16 scalefont setfont
72 520 moveto (Windows and Unix) show
/Times-Roman findfont 16 scalefont setfont
72 500 moveto (Select ªLanguage Level 1º in the PostScript options section) show
72 480 moveto (of the Acrobat print dialog.) show
/Helvetica-Bold findfont 16 scalefont setfont
72 440 moveto (Macintosh) show
/Times-Roman findfont 16 scalefont setfont
72 420 moveto (In the Chooser, select your printer driver.) show
72 400 moveto (Then select your printer and click the Setup button.) show
72 380 moveto (Follow any on-screen dialogs that may appear.) show
showpage
quit
}
if
%%EndResource
/currentpacking where{pop currentpacking true setpacking}if
%%BeginResource: procset pdfvars
%%Copyright: Copyright 1987-1999 Adobe Systems Incorporated. All Rights Reserved.
%%Version: 4.0 2
%%Title: definition of dictionary of variables used by PDF & PDFText procsets
userdict /PDF 160 dict put
userdict /PDFVars 86 dict dup begin put
/_save 0 def
/_cshow 0 def
/InitAll 0 def
/TermAll 0 def
/DocInitAll 0 def
/DocTermAll 0 def
/_lp /none def
/_doClip 0 def
/sfc 0 def
/_sfcs 0 def
/_sfc 0 def
/ssc 0 def
/_sscs 0 def
/_ssc 0 def
/_fcs 0 def
/_scs 0 def
/_fp 0 def
/_sp 0 def
/AGM_MAX_CS_COMPONENTS 10 def
/_fillColors [ 0 1 AGM_MAX_CS_COMPONENTS { array } for ] def
/_strokeColors [ 0 1 AGM_MAX_CS_COMPONENTS { array } for ] def
/_fc null def
/_sc null def
/DefaultGray [/DeviceGray] def
/DefaultRGB [/DeviceRGB] def
/DefaultCMYK [/DeviceCMYK] def
/_inT false def
/_tr -1 def
/_rise 0 def
/_ax 0 def
/_cx 0 def
/_ld 0 def
/_tm matrix def
/_ctm matrix def
/_mtx matrix def
/_hy (-) def
/_fScl 0 def
/_hs 1 def
/_pdfEncodings 2 array def
/_baselineadj 0 def
/_fTzero false def
/_Tj 0 def
/_italMtx [1 0 .212557 1 0 0] def
/_italMtx_WMode1 [1 -.212557 0 1 0 0] def
/_italMtxType0 [1 0 .1062785 1 0 0] def
/_italMtx_WMode1Type0 [1 -.1062785 0 1 0 0] def
/_basefont 0 def
/_basefonto 0 def
/_pdf_oldCIDInit null def
/_pdf_FontDirectory 30 dict def
/_categories 10 dict def
/_sa? true def
/_op? false def
/_OP? false def
/_opmode 0 def
/_ColorSep5044? false def
/_tmpcolr? [] def
/_tmpop? {} def
/_processColors 0 def
/_defaulttransfer currenttransfer def
/_defaultflatness currentflat def
/_defaulthalftone null def
/_defaultcolortransfer null def
/_defaultblackgeneration null def
/_defaultundercolorremoval null def
/_defaultcolortransfer null def
end
%%EndResource
PDFVars begin PDF begin
%%BeginResource: procset pdfutil
%%Copyright: Copyright 1993-1999 Adobe Systems Incorporated. All Rights Reserved.
%%Version: 4.0 2
%%Title: Basic utilities used by other PDF procsets
/bd {bind def} bind def
/ld {load def} bd
/bld {
dup length dict begin
{ null def } forall
bind
end
def
} bd
/dd { PDFVars 3 1 roll put } bd
/xdd { exch dd } bd
/Level2?
systemdict /languagelevel known
{ systemdict /languagelevel get 2 ge } { false } ifelse
def
/Level3?
systemdict /languagelevel known
{systemdict /languagelevel get 3 eq } { false } ifelse
def
/getifknown {
2 copy known { get true } { pop pop false } ifelse
} bd
/here {
currentdict exch getifknown
} bd
/isdefined? { where { pop true } { false } ifelse } bd
/StartLoad { dup dup not { /_save save dd } if } bd
/EndLoad { if not { _save restore } if } bd
%%EndResource
%%BeginResource: procset pdf
%%Version: 4.0 3
%%Copyright: Copyright 1998-1999 Adobe Systems Incorporated. All Rights Reserved.
%%Title: General operators for PDF, common to all Language Levels.
[/b/B/b*/B*/BDC/BI/BMC/BT/BX/c/cm/cs/CS/d/d0/d1/Do/DP/EI/EMC/ET/EX/f/f*/g/G/gs
/h/i/j/J/k/K/l/m/M/MP/n/q/Q/re/rg/RG/ri/s/S/sc/SC/scn/SCN/sg/Tc/Td/TD/Tf/Tj/TJ
/TL/Tm/Tr/Ts/Tw/Tz/T*/v/w/W/W*/y/'/"
/applyInterpFunc/applystitchFunc/domainClip/EF/encodeInput/gsDI/ilp/icl
/initgs/int/limit/PS/rangeClip/RC/rf/makePat/csfamily 
/? /! /| /: /+ /GetGlyphDirectory
] {null def} bind forall
/v { currentpoint 6 2 roll c } bd
/y { 2 copy c } bd
/h/closepath ld
/d/setdash ld
/j/setlinejoin ld
/J/setlinecap ld
/M/setmiterlimit ld
/w/setlinewidth ld
/i {
dup 0 eq { pop _defaultflatness } if
setflat
} bd
/gsDI {
begin
/OP here { /_OP? xdd } if
/op here { /_op? xdd }
{ /OP here { /_op? xdd } if }
ifelse
/OPM here { /_opmode xdd } if
/Font here { aload pop Tf } if
/LW here { w } if
/LC here { J } if
/LJ here { j } if
/ML here { M } if
/D here { aload pop d } if
end
} bd
/ilp { /_lp /none dd } bd
/icl { /_doClip 0 dd } bd
/W { /_doClip 1 dd } bd
/W* { /_doClip 2 dd } bd
/n {
{{} {clip} {eoclip}} _doClip get exec
icl
newpath
} bd
/s { h S } bd
/B { q f Q S } bd
/B* { q f* Q S } bd
/b { h B } bd
/b* { h B* } bd
/q/save ld
/Q { restore ilp } bd
/GetCSFamily {
dup type /arraytype eq {0 get} if
} bd
/GetCompsDict
11 dict begin
/DeviceGray { pop 1 } bd
/DeviceRGB { pop 3 } bd
/DeviceCMYK { pop 4 } bd
/CIEBasedA { pop 1 } bd
/CIEBasedABC { pop 3 } bd
/CIEBasedDEF { pop 3 } bd
/CIEBasedDEFG { pop 4 } bd
/DeviceN { 1 get length } bd
/Separation { pop 1 } bd
/Indexed { pop 1 } bd
/Pattern { pop 0 } bd
currentdict
end
def
/GetComps {
GetCompsDict
1 index GetCSFamily
get exec
} bd
/cs
{
dup _fcs eq
{ pop }
{ dup /_fcs xdd
GetComps
_fillColors exch get
/_fc xdd
/_fp null dd
} ifelse
} bd
/CS
{
dup _scs eq
{ pop }
{ dup /_scs xdd GetComps _strokeColors exch get /_sc xdd /_sp null dd }
ifelse
} bd
/sc {
_fc astore pop
ilp
} bd
/SC {
_sc astore pop
ilp
} bd
/g { DefaultGray cs sc } bd
/rg { DefaultRGB cs sc } bd
/k { DefaultCMYK cs sc } bd
/G { DefaultGray CS SC } bd
/RG { DefaultRGB CS SC } bd
/K { DefaultCMYK CS SC } bd
/cm { _mtx astore concat } bd
/re {
4 2 roll m
1 index 0 rlineto
0 exch rlineto
neg 0 rlineto
h
} bd
/RC/rectclip ld
/EF/execform ld
/PS { cvx exec } bd
/initgs {
/DefaultGray [/DeviceGray] dd
/DefaultRGB [/DeviceRGB] dd
/DefaultCMYK [/DeviceCMYK] dd
0 g 0 G
[] 0 d
0 j
0 J
10 M
1 w
true setSA
/_op? false dd
/_OP? false dd
/_opmode 0 dd
/_defaulttransfer load settransfer
0 i
/RelativeColorimetric ri
newpath
} bd
/int {
dup 2 index sub 3 index 5 index sub div 6 -2 roll sub mul
exch pop add exch pop
} bd
/limit {
dup 2 index le { exch } if pop
dup 2 index ge { exch } if pop
} bd
/domainClip {
Domain aload pop 3 2 roll
limit
} [/Domain] bld
/applyInterpFunc {
0 1 DimOut 1 sub
{
dup C0 exch get exch
dup C1 exch get exch
3 1 roll
1 index sub
3 index
N exp mul add
exch
currentdict /Range_lo known
{
dup Range_lo exch get exch
Range_hi exch get
3 2 roll limit
}
{
pop
}
ifelse
exch
} for
pop
} [/DimOut /C0 /C1 /N /Range_lo /Range_hi] bld
/encodeInput {
NumParts 1 sub
0 1 2 index
{
dup Bounds exch get
2 index gt
{ exit }
{ dup
3 index eq
{ exit }
{ pop } ifelse
} ifelse
} for
3 2 roll pop
dup Bounds exch get exch
dup 1 add Bounds exch get exch
2 mul
dup Encode exch get exch
1 add Encode exch get
int
} [/NumParts /Bounds /Encode] bld
/rangeClip {
exch dup Range_lo exch get
exch Range_hi exch get
3 2 roll
limit
} [/Range_lo /Range_hi] bld
/applyStitchFunc {
Functions exch get exec
currentdict /Range_lo known {
0 1 DimOut 1 sub {
DimOut 1 add -1 roll
rangeClip
} for
} if
} [/Functions /Range_lo /DimOut] bld
%%EndResource
%%BeginResource: procset pdflev2
%%Version: 4.0 5
%%Copyright: Copyright 1987-1999 Adobe Systems Incorporated. All Rights Reserved.
%%LanguageLevel: 2
%%Title: PDF operators, with code specific for Level 2
/_defaulthalftone currenthalftone dd
/_defaultblackgeneration currentblackgeneration dd
/_defaultundercolorremoval currentundercolorremoval dd
/_defaultcolortransfer [currentcolortransfer] dd
/initialize {
_defaulthalftone sethalftone
/_defaultblackgeneration load setblackgeneration
/_defaultundercolorremoval load setundercolorremoval
_defaultcolortransfer aload pop setcolortransfer
false setoverprint
<</MaxFormItem 0>> setuserparams
} bd
/terminate { } bd
/m/moveto ld
/l/lineto ld
/c/curveto ld
/setSA/setstrokeadjust ld
/defineRes/defineresource ld
/findRes/findresource ld
currentglobal
true systemdict /setglobal get exec
[/Function /ExtGState /Form /Shading /FunctionDictionary /MadePattern /PatternPrototype /DataSource]
{ /Generic /Category findresource dup length dict copy /Category defineresource pop }
forall
systemdict /setglobal get exec
/ri
{
/findcolorrendering isdefined?
{
mark exch
findcolorrendering
counttomark 2 eq
{ type /booleantype eq
{ dup type /nametype eq
{ dup /ColorRendering resourcestatus
{ pop pop
dup /DefaultColorRendering ne
{
/ColorRendering findresource
setcolorrendering
} if
} if
} if
} if
} if
cleartomark
}
{ pop
} ifelse
} bd
/_sfcs {_fcs setcolorspace} bind dd
/_sscs {_scs setcolorspace} bind dd
/_sfc
{
_fc aload pop
_fp null eq
{ setcolor }
{ _fp setpattern }
ifelse
} bind dd
/_ssc
{
_sc aload pop
_sp null eq { setcolor} { _sp setpattern } ifelse
} bind dd
/scn {
dup type /dicttype eq
{ dup /_fp xdd
/PaintType get 1 eq
{ /_fc _fillColors 0 get dd ilp }
{ /_fc _fillColors
_fcs 1 get
GetComps get dd
sc
}
ifelse
}
{ sc }
ifelse
} bd
/SCN {
dup type /dicttype eq
{ dup /_sp xdd
/PaintType get 1 eq
{ /_sc _strokeColors 0 get dd ilp }
{ /_sc _strokeColors _scs 1 get GetComps get dd
SC
}
ifelse
}
{ SC }
ifelse
} bd
/gs
{
begin
/SA here { setstrokeadjust } if
/BG here { setblackgeneration } if
/UCR here { setundercolorremoval } if
/FL here { i } if
/RI here { ri } if
/TR here
{
dup xcheck
{ settransfer }
{ aload pop setcolortransfer }
ifelse
} if
/sethalftonephase isdefined? { /HTP here { sethalftonephase } if } if
/HT here { sethalftone } if
currentdict gsDI
end
} bd
/sfc {
_op? setoverprint
_lp /fill ne {
_sfcs
_sfc
/_lp /fill dd
} if
} dd
/ssc {
_OP? setoverprint
_lp /stroke ne {
_sscs
_ssc
/_lp /stroke dd
} if
} dd
/f {
{ { sfc fill }
{gsave sfc fill grestore clip newpath icl ilp}
{gsave sfc fill grestore eoclip newpath icl ilp}
} _doClip get exec
} bd
/f* {
{ { sfc eofill }
{gsave sfc eofill grestore clip newpath icl ilp}
{gsave sfc eofill grestore eoclip newpath icl ilp}
} _doClip get exec
} bd
/S {
{ { ssc stroke }
{gsave ssc stroke grestore clip newpath icl ilp}
{gsave ssc stroke grestore eoclip newpath icl ilp}
} _doClip get exec
} bd
/rf {
{ { sfc rectfill }
{gsave sfc rectfill grestore clip newpath icl ilp}
{gsave sfc rectfill grestore eoclip newpath icl ilp}
} _doClip get exec
} bd
/knownColorants? {
pop false
} bd
/makePat {
gsave
dup /Matrix get concat
matrix makepattern
grestore
/MadePattern defineRes pop
} bd
%%EndResource
%%BeginResource: procset pdftext
%%Version: 4.0 2
%%Copyright: Copyright 1987-1998 Adobe Systems Incorporated. All Rights Reserved.
%%Title: Text operators for PDF
PDF /PDFText 75 dict dup begin put
/docinitialize
{
/resourcestatus where {
pop
/CIDParams /ProcSet resourcestatus {
pop pop
false /CIDParams /ProcSet findresource /SetBuildCompatible get exec
} if
} if
PDF begin
PDFText /_pdfDefineIdentity-H known
{ PDFText /_pdfDefineIdentity-H get exec}
if
end
} bd
/initialize {
PDFText begin
/_intT false dd
0 Tr
} bd
/terminate { end } bd
/_safeput
{
Level2? not
{
2 index load dup dup length exch maxlength ge
{ dup length 5 add dict copy
3 index xdd
}
{ pop }
ifelse
}
if
3 -1 roll load 3 1 roll put
}
bd
/pdf_has_composefont? systemdict /composefont known def
/CopyFont {
{
1 index /FID ne 2 index /UniqueID ne and
{ def } { pop pop } ifelse
} forall
} bd
/Type0CopyFont
{
exch
dup length dict
begin
CopyFont
[
exch
FDepVector
{
dup /FontType get 0 eq
{
1 index Type0CopyFont
/_pdfType0 exch definefont
}
{
/_pdfBaseFont exch
2 index exec
}
ifelse
exch
}
forall
pop
]
/FDepVector exch def
currentdict
end
} bd
/cHexEncoding
[/c00/c01/c02/c03/c04/c05/c06/c07/c08/c09/c0A/c0B/c0C/c0D/c0E/c0F/c10/c11/c12
/c13/c14/c15/c16/c17/c18/c19/c1A/c1B/c1C/c1D/c1E/c1F/c20/c21/c22/c23/c24/c25
/c26/c27/c28/c29/c2A/c2B/c2C/c2D/c2E/c2F/c30/c31/c32/c33/c34/c35/c36/c37/c38
/c39/c3A/c3B/c3C/c3D/c3E/c3F/c40/c41/c42/c43/c44/c45/c46/c47/c48/c49/c4A/c4B
/c4C/c4D/c4E/c4F/c50/c51/c52/c53/c54/c55/c56/c57/c58/c59/c5A/c5B/c5C/c5D/c5E
/c5F/c60/c61/c62/c63/c64/c65/c66/c67/c68/c69/c6A/c6B/c6C/c6D/c6E/c6F/c70/c71
/c72/c73/c74/c75/c76/c77/c78/c79/c7A/c7B/c7C/c7D/c7E/c7F/c80/c81/c82/c83/c84
/c85/c86/c87/c88/c89/c8A/c8B/c8C/c8D/c8E/c8F/c90/c91/c92/c93/c94/c95/c96/c97
/c98/c99/c9A/c9B/c9C/c9D/c9E/c9F/cA0/cA1/cA2/cA3/cA4/cA5/cA6/cA7/cA8/cA9/cAA
/cAB/cAC/cAD/cAE/cAF/cB0/cB1/cB2/cB3/cB4/cB5/cB6/cB7/cB8/cB9/cBA/cBB/cBC/cBD
/cBE/cBF/cC0/cC1/cC2/cC3/cC4/cC5/cC6/cC7/cC8/cC9/cCA/cCB/cCC/cCD/cCE/cCF/cD0
/cD1/cD2/cD3/cD4/cD5/cD6/cD7/cD8/cD9/cDA/cDB/cDC/cDD/cDE/cDF/cE0/cE1/cE2/cE3
/cE4/cE5/cE6/cE7/cE8/cE9/cEA/cEB/cEC/cED/cEE/cEF/cF0/cF1/cF2/cF3/cF4/cF5/cF6
/cF7/cF8/cF9/cFA/cFB/cFC/cFD/cFE/cFF] def
/modEnc {
/_enc xdd
/_icode 0 dd
counttomark 1 sub -1 0
{
index
dup type /nametype eq
{
_enc _icode 3 -1 roll put
_icode 1 add
}
if
/_icode xdd
} for
cleartomark
_enc
} bd
/trEnc {
/_enc xdd
255 -1 0 {
exch dup -1 eq
{ pop /.notdef }
{ Encoding exch get }
ifelse
_enc 3 1 roll put
} for
pop
_enc
} bd
/TE {
/_i xdd
StandardEncoding 256 array copy modEnc
_pdfEncodings exch _i exch put
} bd
/TZ
{
/_usePDFEncoding xdd
findfont
dup length 6 add dict
begin
{
1 index /FID ne { def } { pop pop } ifelse
} forall
/pdf_origFontName FontName def
/FontName exch def
_usePDFEncoding 0 ge
{
/Encoding _pdfEncodings _usePDFEncoding get def
pop
}
{
_usePDFEncoding -1 eq
{
counttomark 0 eq
{ pop }
{
Encoding 256 array copy
modEnc /Encoding exch def
}
ifelse
}
{
256 array
trEnc /Encoding exch def
}
ifelse
}
ifelse
pdf_EuroProcSet pdf_origFontName known
{
pdf_origFontName pdf_AddEuroGlyphProc
} if
FontName currentdict
end
definefont pop
}
bd
/Level2?
systemdict /languagelevel known
{systemdict /languagelevel get 2 ge}
{false}
ifelse
def
Level2?
{
/_pdfFontStatus
{
currentglobal exch
/Font resourcestatus
{pop pop true}
{false}
ifelse
exch setglobal
} bd
}
{
/_pdfFontStatusString 50 string def
_pdfFontStatusString 0 (fonts/) putinterval
/_pdfFontStatus
{
FontDirectory 1 index known
{ pop true }
{
_pdfFontStatusString 6 42 getinterval
cvs length 6 add
_pdfFontStatusString exch 0 exch getinterval
{ status } stopped
{pop false}
{
{ pop pop pop pop true}
{ false }
ifelse
}
ifelse
}
ifelse
} bd
}
ifelse
Level2?
{
/_pdfCIDFontStatus
{
/CIDFont /Category resourcestatus
{
pop pop
/CIDFont resourcestatus
{pop pop true}
{false}
ifelse
}
{ pop false }
ifelse
} bd
}
if
/_pdfString100 100 string def
/_pdfComposeFontName
{
dup length 1 eq
{
0 get
1 index
type /nametype eq
{
_pdfString100 cvs
length dup dup _pdfString100 exch (-) putinterval
_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
2 index exch cvs length
add 1 add _pdfString100 exch 0 exch getinterval
exch pop
true
}
{
pop pop
false
}
ifelse
}
{
false
}
ifelse
dup {exch cvn exch} if
} bd
/_pdfConcatNames
{
exch
_pdfString100 cvs
length dup dup _pdfString100 exch (-) putinterval
_pdfString100 exch 1 add dup _pdfString100 length exch sub getinterval
3 -1 roll exch cvs length
add 1 add _pdfString100 exch 0 exch getinterval
cvn
} bind def
/_pdfTextTempString 50 string def
/_pdfRegOrderingArray [(Adobe-Japan1) (Adobe-CNS1) (Adobe-Korea1) (Adobe-GB1)] def
/_pdf_CheckSupplements
{
1 index _pdfTextTempString cvs
false
_pdfRegOrderingArray
{
2 index exch
anchorsearch
{ pop pop pop true exit}
{ pop }
ifelse
}
forall
exch pop
{
/CIDFont findresource
/CIDSystemInfo get /Supplement get
exch /CMap findresource
/CIDSystemInfo get
dup type /dicttype eq
{/Supplement get}
{pop 0 }
ifelse
ge
}
{ pop pop true }
ifelse
} bind def
pdf_has_composefont?
{
/_pdfComposeFont
{
2 copy _pdfComposeFontName not
{
2 index
}
if
(pdf) exch _pdfConcatNames
dup _pdfFontStatus
{ dup findfont 5 2 roll pop pop pop true}
{
4 1 roll
1 index /CMap resourcestatus
{
pop pop
true
}
{false}
ifelse
1 index true exch
{
_pdfCIDFontStatus not
{pop false exit}
if
}
forall
and
{
1 index 1 index 0 get _pdf_CheckSupplements
{
3 -1 roll pop
2 index 3 1 roll
composefont true
}
{
pop pop exch pop false
}
ifelse
}
{
_pdfComposeFontName
{
dup _pdfFontStatus
{
exch pop
1 index exch
findfont definefont true
}
{
pop exch pop
false
}
ifelse
}
{
exch pop
false
}
ifelse
}
ifelse
{ true }
{
dup _pdfFontStatus
{ dup findfont true }
{ pop false }
ifelse
}
ifelse
}
ifelse
} bd
}
{
/_pdfComposeFont
{
_pdfComposeFontName not
{
dup
}
if
dup
_pdfFontStatus
{exch pop dup findfont true}
{
1 index
dup type /nametype eq
{pop}
{cvn}
ifelse
eq
{pop false}
{
dup _pdfFontStatus
{dup findfont true}
{pop false}
ifelse
}
ifelse
}
ifelse
} bd
}
ifelse
/_pdfStyleDicts 4 dict dup begin
/Adobe-Japan1 4 dict dup begin
Level2?
{
/Serif
/HeiseiMin-W3-83pv-RKSJ-H _pdfFontStatus
{/HeiseiMin-W3}
{
/HeiseiMin-W3 _pdfCIDFontStatus
{/HeiseiMin-W3}
{/Ryumin-Light}
ifelse
}
ifelse
def
/SansSerif
/HeiseiKakuGo-W5-83pv-RKSJ-H _pdfFontStatus
{/HeiseiKakuGo-W5}
{
/HeiseiKakuGo-W5 _pdfCIDFontStatus
{/HeiseiKakuGo-W5}
{/GothicBBB-Medium}
ifelse
}
ifelse
def
/HeiseiMaruGo-W4-83pv-RKSJ-H _pdfFontStatus
{/HeiseiMaruGo-W4}
{
/HeiseiMaruGo-W4 _pdfCIDFontStatus
{/HeiseiMaruGo-W4}
{
/Jun101-Light-RKSJ-H _pdfFontStatus
{ /Jun101-Light }
{ SansSerif }
ifelse
}
ifelse
}
ifelse
/RoundSansSerif exch def
/Default Serif def
}
{
/Serif /Ryumin-Light def
/SansSerif /GothicBBB-Medium def
{
(fonts/Jun101-Light-83pv-RKSJ-H) status
}stopped
{pop}{
{ pop pop pop pop /Jun101-Light }
{ SansSerif }
ifelse
/RoundSansSerif exch def
}ifelse
/Default Serif def
}
ifelse
end
def
/Adobe-Korea1 4 dict dup begin
/Serif /HYSMyeongJo-Medium def
/SansSerif /HYGoThic-Medium def
/RoundSansSerif SansSerif def
/Default Serif def
end
def
/Adobe-GB1 4 dict dup begin
/Serif /STSong-Light def
/SansSerif /STHeiti-Regular def
/RoundSansSerif SansSerif def
/Default Serif def
end
def
/Adobe-CNS1 4 dict dup begin
/Serif /MKai-Medium def
/SansSerif /MHei-Medium def
/RoundSansSerif SansSerif def
/Default Serif def
end
def
end
def
/TZzero
{
/_fyAdj xdd
/_wmode xdd
/_styleArr xdd
/_regOrdering xdd
3 copy
_pdfComposeFont
{
5 2 roll pop pop pop
}
{
[
0 1 _styleArr length 1 sub
{
_styleArr exch get
_pdfStyleDicts _regOrdering 2 copy known
{
get
exch 2 copy known not
{ pop /Default }
if
get
}
{
pop pop pop /Unknown
}
ifelse
}
for
]
exch pop
2 index 3 1 roll
_pdfComposeFont
{3 -1 roll pop}
{
findfont dup /FontName get exch
}
ifelse
}
ifelse
dup /WMode 2 copy known
{ get _wmode ne }
{ pop pop _wmode 1 eq}
ifelse
_fyAdj 0 ne or
{
exch _wmode _pdfConcatNames _fyAdj _pdfConcatNames
dup _pdfFontStatus
{ exch pop dup findfont false}
{ exch true }
ifelse
}
{
dup /FontType get 0 ne
}
ifelse
{
dup /FontType get 3 eq _wmode 1 eq and
{
_pdfVerticalRomanT3Font dup length 10 add dict copy
begin
/_basefont exch
dup length 3 add dict
begin
{1 index /FID ne {def}{pop pop} ifelse }
forall
/Encoding Encoding dup length array copy
dup 16#27 /quotesingle put
dup 16#60 /grave put
_regOrdering /Adobe-Japan1 eq
{dup 16#5c /yen put dup 16#a5 /yen put dup 16#b4 /yen put}
if
def
FontName
currentdict
end
definefont
def
/Encoding _basefont /Encoding get def
/_fauxfont true def
}
{
dup length 3 add dict
begin
{1 index /FID ne {def}{pop pop} ifelse }
forall
FontType 0 ne
{
/Encoding Encoding dup length array copy
dup 16#27 /quotesingle put
dup 16#60 /grave put
_regOrdering /Adobe-Japan1 eq
{dup 16#5c /yen put}
if
def
/_fauxfont true def
} if
} ifelse
/WMode _wmode def
/BaseLineAdj _fyAdj def
dup dup /FontName exch def
currentdict
end
definefont pop
}
{
pop
}
ifelse
/_pdf_FontDirectory 3 1 roll _safeput
}
bd
/swj {
dup 4 1 roll
dup length exch stringwidth
exch 5 -1 roll 3 index mul add
4 1 roll 3 1 roll mul add
6 2 roll /_cnt 0 dd
{1 index eq {/_cnt _cnt 1 add dd} if} forall pop
exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop
} bd
/jss {
4 1 roll
{
pop pop
(0) exch 2 copy 0 exch put
gsave
exch false charpath currentpoint
5 index setmatrix stroke
3 -1 roll
32 eq
{
moveto
5 index 5 index rmoveto currentpoint
}
if
grestore
moveto
2 copy rmoveto
} exch cshow
6 {pop} repeat
} def
/jsfTzero {
{
pop pop
(0) exch 2 copy 0 exch put
exch show
32 eq
{
4 index 4 index rmoveto
}
if
2 copy rmoveto
} exch cshow
5 {pop} repeat
} def
/jsp
{
{
pop pop
(0) exch 2 copy 0 exch put
32 eq
dup {currentfont /Encoding get dup length 33 ge 
{32 get /space eq and}{pop}ifelse
}if
{ exch 5 index 5 index 5 index 5 -1 roll widthshow }
{ false charpath }
ifelse
2 copy rmoveto
} exch cshow
5 {pop} repeat
} bd
/trj { _cx 0 fWModeProc 32 _ax 0 fWModeProc 6 5 roll } bd
/pjsf { trj sfc fawidthshowProc } bd
/pjss { trj _ctm ssc jss } bd
/pjsc { trj jsp } bd
/_Tjdef [
/pjsf load
/pjss load
{
dup
currentpoint 3 2 roll
pjsf
newpath moveto
pjss
} bind
{
trj swj rmoveto
} bind
{
dup currentpoint 4 2 roll gsave
pjsf
grestore 3 1 roll moveto
pjsc
} bind
{
dup currentpoint 4 2 roll
currentpoint gsave newpath moveto
pjss
grestore 3 1 roll moveto
pjsc
} bind
{
dup currentpoint 4 2 roll gsave
dup currentpoint 3 2 roll
pjsf
newpath moveto
pjss
grestore 3 1 roll moveto
pjsc
} bind
/pjsc load
] def
/BT
{
/_inT true dd
_ctm currentmatrix pop matrix _tm copy pop
0 _rise _baselineadj add translate _hs 1 scale
0 0 moveto
} bd
/ET
{
/_inT false dd
_tr 3 gt {clip} if
_ctm setmatrix newpath
} bd
/Tr {
_inT { _tr 3 le {currentpoint newpath moveto} if } if
dup /_tr xdd
_Tjdef exch get /_Tj xdd
} bd
/Tj {
userdict /$$copystring 2 index put
_Tj
} bd
/iTm { _ctm setmatrix _tm concat 0 _rise _baselineadj add translate _hs 1 scale } bd
/Tm { _tm astore pop iTm 0 0 moveto } bd
/Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } bd
/TD { dup /_ld xdd Td } bd
/_nullProc {} bd
/Tf {
dup 1000 div /_fScl xdd
_pdf_FontDirectory 2 index 2 copy known
{get exch 3 -1 roll pop}
{pop pop}
ifelse
Level2?
{ selectfont }
{ exch findfont exch scalefont setfont}
ifelse
currentfont dup
/_nullProc exch
/WMode known
{
1 index /WMode get 1 eq
{pop /exch}
if
}
if
load /fWModeProc xdd
dup
/FontType get 0 eq dup _cx 0 ne and
{ /jsfTzero }
{ /awidthshow }
ifelse
load /fawidthshowProc xdd
/_fTzero xdd
dup /BaseLineAdj known
{ dup /BaseLineAdj get _fScl mul }
{ 0 }
ifelse
/_baselineadj xdd
dup /_pdfT3Font known
{ 0 }
{_tr}
ifelse
_Tjdef exch get /_Tj xdd
_intT
{currentpoint iTm moveto}
if
pop
} bd
/TL { neg /_ld xdd } bd
/Tw {
/_cx xdd
_cx 0 ne _fTzero and
{ /jsfTzero }
{ /awidthshow }
ifelse
load /fawidthshowProc xdd
} bd
/Tc { /_ax xdd } bd
/Ts { /_rise xdd currentpoint iTm moveto } bd
/Tz { 100 div /_hs xdd iTm } bd
/Tk { exch pop _fScl mul neg 0 fWModeProc rmoveto } bd
/T* { 0 _ld Td } bd
/' { T* Tj } bd
/" { exch Tc exch Tw ' } bd
/TJ {
{
dup type /stringtype eq
{ Tj }
{ 0 exch Tk }
ifelse
} forall
} bd
/T- { _hy Tj } bd
/d0/setcharwidth ld
/d1 { setcachedevice /sfc{}dd /ssc{}dd } bd
/nND {{/.notdef} repeat} bd
/T3Defs {
/BuildChar
{
1 index /Encoding get exch get
1 index /BuildGlyph get exec
}
def
/BuildGlyph {
exch begin
GlyphProcs exch get exec
end
} def
/_pdfT3Font true def
} bd
/_pdfBoldRomanWidthProc
{
stringwidth 1 index 0 ne { exch .03 add exch }if setcharwidth
0 0
} bd
/_pdfType0WidthProc
{
dup stringwidth 0 0 moveto
2 index true charpath pathbbox
0 -1
7 index 2 div .88
setcachedevice2
pop
0 0
} bd
/_pdfType0WMode1WidthProc
{
dup stringwidth
pop 2 div neg -0.88
2 copy
moveto
0 -1
5 -1 roll true charpath pathbbox
setcachedevice
} bd
/_pdfBoldBaseFont
11 dict begin
/FontType 3 def
/FontMatrix[1 0 0 1 0 0]def
/FontBBox[0 0 1 1]def
/Encoding cHexEncoding def
/_setwidthProc /_pdfBoldRomanWidthProc load def
/_bcstr1 1 string def
/BuildChar
{
exch begin
_basefont setfont
_bcstr1 dup 0 4 -1 roll put
dup
_setwidthProc
3 copy
moveto
show
_basefonto setfont
moveto
show
end
}bd
currentdict
end
def
pdf_has_composefont?
{
/_pdfBoldBaseCIDFont
11 dict begin
/CIDFontType 1 def
/CIDFontName /_pdfBoldBaseCIDFont def
/FontMatrix[1 0 0 1 0 0]def
/FontBBox[0 0 1 1]def
/_setwidthProc /_pdfType0WidthProc load def
/_bcstr2 2 string def
/BuildGlyph
{
exch begin
_basefont setfont
_bcstr2 1 2 index 256 mod put
_bcstr2 0 3 -1 roll 256 idiv put
_bcstr2 dup _setwidthProc
3 copy
moveto
show
_basefonto setfont
moveto
show
end
}bd
currentdict
end
def
/_pdfDefineIdentity-H
{
/Identity-H /CMap resourcestatus
{
pop pop
}
{
/CIDInit/ProcSet findresource begin 12 dict begin
begincmap
/CIDSystemInfo
3 dict begin
/Registry (Adobe) def
/Ordering (Identity) def
/Supplement 0 def
currentdict
end
def
/CMapName /Identity-H def
/CMapVersion 1 def
/CMapType 1 def
1 begincodespacerange
<0000> <ffff>
endcodespacerange
1 begincidrange
<0000> <ffff> 0
endcidrange
endcmap
CMapName currentdict/CMap defineresource pop
end
end
} ifelse
} def
} if
/_pdfVerticalRomanT3Font
10 dict begin
/FontType 3 def
/FontMatrix[1 0 0 1 0 0]def
/FontBBox[0 0 1 1]def
/_bcstr1 1 string def
/BuildChar
{
exch begin
_basefont setfont
_bcstr1 dup 0 4 -1 roll put
dup
_pdfType0WidthProc
moveto
show
end
}bd
currentdict
end
def
/MakeBoldFont
{
dup /ct_SyntheticBold known
{
dup length 3 add dict begin
CopyFont
/ct_StrokeWidth .03 0 FontMatrix idtransform pop def
/ct_SyntheticBold true def
currentdict
end
definefont
}
{
dup dup length 3 add dict
begin
CopyFont
/PaintType 2 def
/StrokeWidth .03 0 FontMatrix idtransform pop def
/dummybold currentdict
end
definefont
dup /FontType get dup 9 ge exch 11 le and
{
_pdfBoldBaseCIDFont
dup length 3 add dict copy begin
dup /CIDSystemInfo get /CIDSystemInfo exch def
/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
/_basefont exch def
/_Type0Identity /Identity-H 3 -1 roll [ exch ] composefont
/_basefonto exch def
currentdict
end
/CIDFont defineresource
}
{
_pdfBoldBaseFont
dup length 3 add dict copy begin
/_basefont exch def
/_basefonto exch def
currentdict
end
definefont
}
ifelse
}
ifelse
} bd
/MakeBold {
1 index
_pdf_FontDirectory 2 index 2 copy known
{get}
{exch pop}
ifelse
findfont
dup
/FontType get 0 eq
{
dup /WMode known {dup /WMode get 1 eq }{false} ifelse
version length 4 ge
and
{version 0 4 getinterval cvi 2015 ge }
{true}
ifelse
{/_pdfType0WidthProc}
{/_pdfType0WMode1WidthProc}
ifelse
_pdfBoldBaseFont /_setwidthProc 3 -1 roll load put
{MakeBoldFont} Type0CopyFont definefont
}
{
dup /_fauxfont known not 1 index /SubstMaster known not and
{
_pdfBoldBaseFont /_setwidthProc /_pdfBoldRomanWidthProc load put
MakeBoldFont
}
{
2 index 2 index eq
{ exch pop }
{
dup length dict begin
CopyFont
currentdict
end
definefont
}
ifelse
}
ifelse
}
ifelse
pop pop
dup /dummybold ne
{/_pdf_FontDirectory exch dup _safeput }
{ pop }
ifelse
}bd
/MakeItalic {
_pdf_FontDirectory exch 2 copy known
{get}
{exch pop}
ifelse
dup findfont
dup /FontInfo 2 copy known
{
get
/ItalicAngle 2 copy known
{get 0 eq }
{ pop pop true}
ifelse
}
{ pop pop true}
ifelse
{
exch pop
dup /FontType get 0 eq Level2? not and
{ dup /FMapType get 6 eq }
{ false }
ifelse
{
dup /WMode 2 copy known
{
get 1 eq
{ _italMtx_WMode1Type0 }
{ _italMtxType0 }
ifelse
}
{ pop pop _italMtxType0 }
ifelse
}
{
dup /WMode 2 copy known
{
get 1 eq
{ _italMtx_WMode1 }
{ _italMtx }
ifelse
}
{ pop pop _italMtx }
ifelse
}
ifelse
makefont
dup /FontType get 42 eq Level2? not or
{
dup length dict begin
CopyFont
currentdict
end
}
if
1 index exch
definefont pop
/_pdf_FontDirectory exch dup _safeput
}
{
pop
2 copy ne
{
/_pdf_FontDirectory 3 1 roll _safeput
}
{ pop pop }
ifelse
}
ifelse
}bd
/MakeBoldItalic {
/dummybold exch
MakeBold
/dummybold
MakeItalic
}bd
Level2?
{
/pdf_CopyDict
{1 index length add dict copy}
def
}
{
/pdf_CopyDict
{
1 index length add dict
1 index wcheck
{ copy }
{ begin
{def} forall
currentdict
end
}
ifelse
}
def
}
ifelse
/pdf_AddEuroGlyphProc
{
currentdict /CharStrings known
{
CharStrings /Euro known not
{
dup
/CharStrings
CharStrings 1 pdf_CopyDict
begin
/Euro pdf_EuroProcSet 4 -1 roll get def
currentdict
end
def
/pdf_PSBuildGlyph /pdf_PSBuildGlyph load def
/pdf_PathOps /pdf_PathOps load def
/Symbol eq
{
/Encoding Encoding dup length array copy
dup 160 /Euro put def
}
if
}
{ pop
}
ifelse
}
{ pop
}
ifelse
}
def
/pdf_PathOps 4 dict dup begin
/m {moveto} def
/l {lineto} def
/c {curveto} def
/cp {closepath} def
end
def
/pdf_PSBuildGlyph
{
gsave
8 -1 roll pop
7 1 roll
currentdict /PaintType 2 copy known {get 2 eq}{pop pop false} ifelse
dup 9 1 roll
{
currentdict /StrokeWidth 2 copy known
{
get 2 div
5 1 roll
4 -1 roll 4 index sub
4 1 roll
3 -1 roll 4 index sub
3 1 roll
exch 4 index add exch
4 index add
5 -1 roll pop
}
{
pop pop
}
ifelse
}
if
setcachedevice
pdf_PathOps begin
exec
end
{
currentdict /StrokeWidth 2 copy known
{ get }
{ pop pop 0 }
ifelse
setlinewidth stroke
}
{
fill
}
ifelse
grestore
} def
/pdf_EuroProcSet 13 dict def
pdf_EuroProcSet
begin
/Courier-Bold
{
600 0 6 -12 585 612
{
385 274 m
180 274 l
179 283 179 293 179 303 c
179 310 179 316 180 323 c
398 323 l
423 404 l
197 404 l
219 477 273 520 357 520 c
409 520 466 490 487 454 c
487 389 l
579 389 l
579 612 l
487 612 l
487 560 l
449 595 394 612 349 612 c
222 612 130 529 98 404 c
31 404 l
6 323 l
86 323 l
86 304 l
86 294 86 284 87 274 c
31 274 l
6 193 l
99 193 l
129 77 211 -12 359 -12 c
398 -12 509 8 585 77 c
529 145 l
497 123 436 80 356 80 c
285 80 227 122 198 193 c
360 193 l
cp
600 0 m
}
pdf_PSBuildGlyph
} def
/Courier-BoldOblique /Courier-Bold load def
/Courier
{
600 0 17 -12 578 584
{
17 204 m
97 204 l
126 81 214 -12 361 -12 c
440 -12 517 17 578 62 c
554 109 l
501 70 434 43 366 43 c
266 43 184 101 154 204 c
380 204 l
400 259 l
144 259 l
144 270 143 281 143 292 c
143 299 143 307 144 314 c
418 314 l
438 369 l
153 369 l
177 464 249 529 345 529 c
415 529 484 503 522 463 c
522 391 l
576 391 l
576 584 l
522 584 l
522 531 l
473 566 420 584 348 584 c
216 584 122 490 95 369 c
37 369 l
17 314 l
87 314 l
87 297 l
87 284 88 272 89 259 c
37 259 l
cp
600 0 m
}
pdf_PSBuildGlyph
} def
/Courier-Oblique /Courier load def
/Helvetica
{
556 0 24 -19 541 703
{
541 628 m
510 669 442 703 354 703 c
201 703 117 607 101 444 c
50 444 l
25 372 l
97 372 l
97 301 l
49 301 l
24 229 l
103 229 l
124 67 209 -19 350 -19 c
435 -19 501 25 509 32 c
509 131 l
492 105 417 60 343 60 c
267 60 204 127 197 229 c
406 229 l
430 301 l
191 301 l
191 372 l
455 372 l
479 444 l
194 444 l
201 531 245 624 348 624 c
433 624 484 583 509 534 c
cp
556 0 m
}
pdf_PSBuildGlyph
} def
/Helvetica-Oblique /Helvetica load def
/Helvetica-Bold
{
556 0 12 -19 563 710
{
563 621 m
537 659 463 710 363 710 c
216 710 125 620 101 462 c
51 462 l
12 367 l
92 367 l
92 346 l
92 337 93 328 93 319 c
52 319 l
12 224 l
102 224 l
131 58 228 -19 363 -19 c
417 -19 471 -12 517 18 c
517 146 l
481 115 426 93 363 93 c
283 93 254 166 246 224 c
398 224 l
438 319 l
236 319 l
236 367 l
457 367 l
497 462 l
244 462 l
259 552 298 598 363 598 c
425 598 464 570 486 547 c
507 526 513 517 517 509 c
cp
556 0 m
}
pdf_PSBuildGlyph
} def
/Helvetica-BoldOblique /Helvetica-Bold load def
/Symbol
{
750 0 20 -12 714 685
{
714 581 m
650 645 560 685 465 685 c
304 685 165 580 128 432 c
50 432 l
20 369 l
116 369 l
115 356 115 347 115 337 c
115 328 115 319 116 306 c
50 306 l
20 243 l
128 243 l
165 97 300 -12 465 -12 c
560 -12 635 25 685 65 c
685 155 l
633 91 551 51 465 51 c
340 51 238 131 199 243 c
555 243 l
585 306 l
184 306 l
183 317 182 326 182 336 c
182 346 183 356 184 369 c
614 369 l 644 432 l
199 432 l
233 540 340 622 465 622 c
555 622 636 580 685 520 c
cp
750 0 m
}
pdf_PSBuildGlyph
} def
/Times-Bold
{
500 0 16 -14 478 700
{
367 308 m
224 308 l
224 368 l
375 368 l
380 414 l
225 414 l
230 589 257 653 315 653 c
402 653 431 521 444 457 c
473 457 l
473 698 l
444 697 l
441 679 437 662 418 662 c
393 662 365 700 310 700 c
211 700 97 597 73 414 c
21 414 l
16 368 l
69 368 l
69 359 68 350 68 341 c
68 330 68 319 69 308 c
21 308 l
16 262 l
73 262 l
91 119 161 -14 301 -14 c
380 -14 443 50 478 116 c
448 136 l
415 84 382 40 323 40 c
262 40 231 77 225 262 c
362 262 l
cp
500 0 m
}
pdf_PSBuildGlyph
} def
/Times-BoldItalic
{
500 0 9 -20 542 686
{
542 686 m
518 686 l
513 673 507 660 495 660 c
475 660 457 683 384 683 c
285 683 170 584 122 430 c
58 430 l
34 369 l
105 369 l
101 354 92 328 90 312 c
34 312 l
9 251 l
86 251 l
85 238 84 223 84 207 c
84 112 117 -14 272 -14 c
326 -14 349 9 381 9 c
393 9 393 -10 394 -20 c
420 -20 l
461 148 l
429 148 l
416 109 362 15 292 15 c
227 15 197 55 197 128 c
197 162 204 203 216 251 c
378 251 l
402 312 l
227 312 l
229 325 236 356 241 369 c
425 369 l
450 430 l
255 430 l
257 435 264 458 274 488 c
298 561 337 654 394 654 c
437 654 484 621 484 530 c
484 516 l
516 516 l
cp
500 0 m
}
pdf_PSBuildGlyph
} def
/Times-Italic
{
500 0 23 -10 595 692
{
399 317 m
196 317 l
199 340 203 363 209 386 c
429 386 l
444 424 l
219 424 l
246 514 307 648 418 648 c
448 648 471 638 492 616 c
529 576 524 529 527 479 c
549 475 l
595 687 l
570 687 l
562 674 558 664 542 664 c
518 664 474 692 423 692 c
275 692 162 551 116 424 c
67 424 l
53 386 l
104 386 l
98 363 93 340 90 317 c
37 317 l
23 279 l
86 279 l
85 266 85 253 85 240 c
85 118 137 -10 277 -10 c
370 -10 436 58 488 128 c
466 149 l
424 101 375 48 307 48 c
212 48 190 160 190 234 c
190 249 191 264 192 279 c
384 279 l
cp
500 0 m
}
pdf_PSBuildGlyph
} def
/Times-Roman
{
500 0 10 -12 484 692
{
347 298 m
171 298 l
170 310 170 322 170 335 c
170 362 l
362 362 l
374 403 l
172 403 l
184 580 244 642 308 642 c
380 642 434 574 457 457 c
481 462 l
474 691 l
449 691 l
433 670 429 657 410 657 c
394 657 360 692 299 692 c
204 692 94 604 73 403 c
22 403 l
10 362 l
70 362 l
69 352 69 341 69 330 c
69 319 69 308 70 298 c
22 298 l
10 257 l
73 257 l
97 57 216 -12 295 -12 c
364 -12 427 25 484 123 c
458 142 l
425 101 384 37 316 37 c
256 37 189 84 173 257 c
335 257 l
cp
500 0 m
}
pdf_PSBuildGlyph
} def
end
currentdict readonly pop end
%%EndResource
PDFText begin
[39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis
/Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute
/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde
/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex
/udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef
/guillemotleft/guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide
/.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright
/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand
/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex
/Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex
/Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla
/hungarumlaut/ogonek/caron
0 TE
[1/dotlessi/caron 39/quotesingle 96/grave 
127/bullet/Euro/bullet/quotesinglbase/florin/quotedblbase/ellipsis
/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE
/bullet/Zcaron/bullet/bullet/quoteleft/quoteright/quotedblleft
/quotedblright/bullet/endash/emdash/tilde/trademark/scaron
/guilsinglright/oe/bullet/zcaron/Ydieresis/space/exclamdown/cent/sterling
/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine
/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus
/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla
/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters
/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash
/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave
/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde
/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute
/ucircumflex/udieresis/yacute/thorn/ydieresis
1 TE
end
%%BeginResource: pdfimage.prc
%%Copyright: Copyright 1987-1993 Adobe Systems Incorporated. All Rights Reserved.
PDF /PDFImage 38 dict put
PDF /PDFIVars 20 dict put
PDF /PDFImage get begin
/initialize { PDFImage begin } bd
/terminate { end } bd
/nulldict 0 dict def
/gv { PDFIVars exch get } bd
/pv { PDFIVars 3 1 roll put } bd
/BI { save /savelevel exch pv mark } bd
/EI { /savelevel gv restore } bd
end
%%EndResource
%%BeginResource: pdfimg2.prc
%%Version: 4.0 4
%%Copyright: Copyright 1987-1993 Adobe Systems Incorporated. All Rights Reserved.
PDF /PDFImage get begin
Level2? StartLoad {
/ID {
5 counttomark 2 idiv
dup 3 1 roll add
dict begin
{ def } repeat
cleartomark
currentdict
end
begin
/ImageType here { pop } { /ImageType 1 def } ifelse
/ImageMatrix [ Width 0 0 Height neg 0 Height ] def
/ImageMask here { not } { true } ifelse
{ /ImageMask false def } if
ImageMask not { ColorSpace setcolorspace } if
/Intent here { ri } if
SLBApplies?
{ ApplySLB }
{
mark
/DataSource here { } { currentfile } ifelse
/Filter here {
dup type /arraytype eq { length } { pop 1 } ifelse
1 sub 0 1 3 -1 roll {
/DecodeParms here {
dup type /arraytype eq {
1 index get
} if
dup null eq { pop } { exch } ifelse
} if
Filter dup type /arraytype eq
{ exch get } { exch pop } ifelse
filter
dup
} for
} if
/DataSource exch def
currentdict /ImageMask here not {false} if
{ sfc imagemask } { image } ifelse
counttomark
{ dup status
dup currentfile ne and
{ dup flushfile closefile }
{ pop }
ifelse
}
repeat
pop
}ifelse
end
} [/Width /Height /ImageMask /ColorSpace /Filter] bld
/SLBApplies?
{
{
languagelevel 3 lt {stop} if
currentsystemparams /SourceListBypass known not {stop} if
currentsystemparams /SourceListBypass get not {stop} if
currentdict /Filter known not {stop} if
Filter /CCITTFaxDecode ne {stop} if
currentdict /DecodeParms known not {stop} if
DecodeParms /K known not {stop} if
DecodeParms /K get -1 ne {stop} if
} stopped not
} [/DecodeParms] bld
/ApplySLB
{
{
/UncompressedLength
Width
DecodeParms /EncodedByteAlign getifknown
{ { 7 add 3 bitshift } if } if
Height mul def
/DataSource dup here { } {currentfile} ifelse
5 dict begin
/Filter Filter def
/DecodeParms DecodeParms def
/Intent 3 def
/AsyncRead false def
/CloseSource false def
currentdict end /ReusableStreamDecode filter def
currentdict /ImageMask here not {false} if
{ sfc imagemask } { image } ifelse
} exec
} [/Width /DecodeParms /Height] bld
currentdict readonly pop
} EndLoad
end
%%EndResource
%%BeginResource: pdfasc.prc
%%Version: 4.0 2
%%Copyright: Copyright 1992-1997 Adobe Systems Incorporated. All Rights Reserved.
/AS {
9 dict begin
/shrink? xdd
/Pury xdd
/Purx xdd
/Plly xdd
/Pllx xdd
gsave newpath clippath pathbbox newpath grestore
/Dury xdd
/Durx xdd
/Dlly xdd
/Dllx xdd
Durx Dllx sub Dury Dlly sub
Pury Plly sub div exch Purx Pllx sub div
2 copy gt { exch } if pop
Durx Dllx add 2 div Dury Dlly add 2 div translate
shrink? { dup scale } { pop } ifelse
Purx Pllx add -2 div Pury Plly add -2 div translate
end
} [/shrink? /Pury /Purx /Plly /Pllx /Durx /Dury /Dllx /Dlly]
bld
%%EndResource
currentdict readonly pop
end end
/currentpacking where {pop setpacking}if
PDFVars/DocInitAll{[ PDFText]{/docinitialize get exec}forall }put
PDFVars/InitAll{[PDF PDFText PDFImage]{/initialize get exec}forall initgs}put
PDFVars/TermAll{[PDFImage PDFText PDF]{/terminate get exec}forall}put
PDFVars begin PDF begin
PDFVars/DocInitAll get exec PDFVars/InitAll get exec
/N13 <<
/SA false 
/OP false 
>> /ExtGState defineRes pop
%%IncludeResource Times-Bold
[/N12/Times-Bold -1 TZ
%%IncludeResource Symbol
[/N11/Symbol -1 TZ
%%IncludeResource Times-Italic
[/N10/Times-Italic -1 TZ
%%IncludeResource Times-Roman
[/N9/Times-Roman -1 TZ
%%BeginResource: file Pscript_CFF PSVER
userdict/ct_CffDict 6 dict put ct_CffDict begin/F0Subr{systemdict/internaldict
known{1183615869 systemdict/internaldict get exec/FlxProc known{save true}{
false}ifelse}{userdict/internaldict known not{userdict/internaldict{count 0 eq
{/internaldict errordict/invalidaccess get exec}if dup type/integertype ne{
/internaldict errordict/invalidaccess get exec}if dup 1183615869 eq{pop 0}{
/internaldict errordict/invalidaccess get exec}ifelse}dup 14 get 1 25 dict put
bind executeonly put}if 1183615869 userdict/internaldict get exec/FlxProc
known{save true}{false}ifelse}ifelse[systemdict/internaldict known not{100
dict/begin cvx/mtx matrix/def cvx}if systemdict/currentpacking known{
currentpacking true setpacking}if{systemdict/internaldict known{1183615869
systemdict/internaldict get exec dup/$FlxDict known not{dup dup length exch
maxlength eq{pop userdict dup/$FlxDict known not{100 dict begin/mtx matrix def
dup/$FlxDict currentdict put end}if}{100 dict begin/mtx matrix def dup
/$FlxDict currentdict put end}ifelse}if/$FlxDict get begin}if grestore/exdef{
exch def}def/dmin exch abs 100 div def/epX exdef/epY exdef/c4y2 exdef/c4x2
exdef/c4y1 exdef/c4x1 exdef/c4y0 exdef/c4x0 exdef/c3y2 exdef/c3x2 exdef/c3y1
exdef/c3x1 exdef/c3y0 exdef/c3x0 exdef/c1y2 exdef/c1x2 exdef/c2x2 c4x2 def
/c2y2 c4y2 def/yflag c1y2 c3y2 sub abs c1x2 c3x2 sub abs gt def/PickCoords{{
c1x0 c1y0 c1x1 c1y1 c1x2 c1y2 c2x0 c2y0 c2x1 c2y1 c2x2 c2y2}{c3x0 c3y0 c3x1
c3y1 c3x2 c3y2 c4x0 c4y0 c4x1 c4y1 c4x2 c4y2}ifelse/y5 exdef/x5 exdef/y4 exdef
/x4 exdef/y3 exdef/x3 exdef/y2 exdef/x2 exdef/y1 exdef/x1 exdef/y0 exdef/x0
exdef}def mtx currentmatrix pop mtx 0 get abs 1e-05 lt mtx 3 get abs 1e-05 lt
or{/flipXY -1 def}{mtx 1 get abs 1e-05 lt mtx 2 get abs 1e-05 lt or{/flipXY 1
def}{/flipXY 0 def}ifelse}ifelse/erosion 1 def systemdict/internaldict known{
1183615869 systemdict/internaldict get exec dup/erosion known{/erosion get
/erosion exch def}{pop}ifelse}if yflag{flipXY 0 eq c3y2 c4y2 eq or{false
PickCoords}{/shrink c3y2 c4y2 eq{0}{c1y2 c4y2 sub c3y2 c4y2 sub div abs}ifelse
def/yshrink{c4y2 sub shrink mul c4y2 add}def/c1y0 c3y0 yshrink def/c1y1 c3y1
yshrink def/c2y0 c4y0 yshrink def/c2y1 c4y1 yshrink def/c1x0 c3x0 def/c1x1
c3x1 def/c2x0 c4x0 def/c2x1 c4x1 def/dY 0 c3y2 c1y2 sub round dtransform
flipXY 1 eq{exch}if pop abs def dY dmin lt PickCoords y2 c1y2 sub abs .001 gt{
c1x2 c1y2 transform flipXY 1 eq{exch}if/cx exch def/cy exch def/dY 0 y2 c1y2
sub round dtransform flipXY 1 eq{exch}if pop def dY round dup 0 ne{/dY exdef}{
pop dY 0 lt{-1}{1}ifelse/dY exdef}ifelse/erode PaintType 2 ne erosion .5 ge
and def erode{/cy cy .5 sub def}if/ey cy dY add def/ey ey ceiling ey sub ey
floor add def erode{/ey ey .5 add def}if ey cx flipXY 1 eq{exch}if itransform
exch pop y2 sub/eShift exch def/y1 y1 eShift add def/y2 y2 eShift add def/y3
y3 eShift add def}if}ifelse}{flipXY 0 eq c3x2 c4x2 eq or{false PickCoords}{
/shrink c3x2 c4x2 eq{0}{c1x2 c4x2 sub c3x2 c4x2 sub div abs}ifelse def/xshrink
{c4x2 sub shrink mul c4x2 add}def/c1x0 c3x0 xshrink def/c1x1 c3x1 xshrink def
/c2x0 c4x0 xshrink def/c2x1 c4x1 xshrink def/c1y0 c3y0 def/c1y1 c3y1 def/c2y0
c4y0 def/c2y1 c4y1 def/dX c3x2 c1x2 sub round 0 dtransform flipXY -1 eq{exch}
if pop abs def dX dmin lt PickCoords x2 c1x2 sub abs .001 gt{c1x2 c1y2
transform flipXY -1 eq{exch}if/cy exch def/cx exch def/dX x2 c1x2 sub round 0
dtransform flipXY -1 eq{exch}if pop def dX round dup 0 ne{/dX exdef}{pop dX 0
lt{-1}{1}ifelse/dX exdef}ifelse/erode PaintType 2 ne erosion .5 ge and def
erode{/cx cx .5 sub def}if/ex cx dX add def/ex ex ceiling ex sub ex floor add
def erode{/ex ex .5 add def}if ex cy flipXY -1 eq{exch}if itransform pop x2
sub/eShift exch def/x1 x1 eShift add def/x2 x2 eShift add def/x3 x3 eShift add
def}if}ifelse}ifelse x2 x5 eq y2 y5 eq or{x5 y5 lineto}{x0 y0 x1 y1 x2 y2
curveto x3 y3 x4 y4 x5 y5 curveto}ifelse epY epX}systemdict/currentpacking
known{exch setpacking}if/exec cvx/end cvx]cvx executeonly exch{pop true exch
restore}{systemdict/internaldict known not{1183615869 userdict/internaldict
get exec exch/FlxProc exch put true}{1183615869 systemdict/internaldict get
exec dup length exch maxlength eq{false}{1183615869 systemdict/internaldict
get exec exch/FlxProc exch put true}ifelse}ifelse}ifelse{systemdict
/internaldict known{1183615869 systemdict/internaldict get exec/FlxProc get
exec}{1183615869 userdict/internaldict get exec/FlxProc get exec}ifelse}if}
executeonly def/F1Subr{gsave currentpoint newpath moveto}bind def/F2Subr{
currentpoint grestore gsave currentpoint newpath moveto}bind def/HSSubr{
systemdict/internaldict known not{pop 3}{1183615869 systemdict/internaldict
get exec dup/startlock known{/startlock get exec}{dup/strtlck known{/strtlck
get exec}{pop 3}ifelse}ifelse}ifelse}bind def end
%%EndResource
%%BeginResource: font CGKPBN+MathematicalPi-Six
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1990 Adobe Systems Incorporated.  All Rights Reserved.) def
/version (001.000) def
/FullName (Mathematical Pi 6) def
/FamilyName (Mathematical Pi) def
/BaseFontName (MathematicalPi-Six) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGKPBN+MathematicalPi-Six def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { 0 -188 990 742 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 27 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -18 0 713 731 ] def
/OtherBlues [ -188 -188 ] def
/StdHW [ 42 ] def
/StdVW [ 42 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
5.25 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
42 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 4 dict dup begin
/.notdef 9 -| 68CCB9B776D66C9B0D |-
/H11938 171 -| 68CCB9B776D819D31FDBC0FC4ED6F0D413DC44E8904B5EBFEF8592680CF84DB0BFC73046
762E7C2AD0A0B95FF874343CE4DD868D77BFE2BC2B053000C8FD64A893D3C605
41F28E712D099420E3021E5ED5EAE48CB0686100C760BD4B1B4B51BBCEC0F964
19DAFBA644DE2364F3A7BF9CEEB57AE8C7E15CF45F8F0FD4FD186C8481AF6CAE
C273423FEEAF80BA2CBD4F615B37E94D9C563FE0EB005DDB985F0A66EA8F06FD
74664FB0BC7B9E |-
/H11946 70 -| 68CCB9B776D8503AE9A7AF0D114310248C17CDB9A67ECC79898CC425EEFFC5E543D57113
7C7BE0D50143BF92B21049879E6256919C656AC5831E43B407CC4E0D0B45CF5F
43EE |-
/H17040 50 -| 68CCB9B776D8AAC7D69197CC1DB726C0854324DE304EAC961393E4210BD36A974C72F44D
095F2A87643DA4382CA658B4A4AB |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGKPBN+MathematicalPi-Six findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGKPBN+MathematicalPi-Six findfont /Encoding get
dup 0 /.notdef put
dup 82 /H11938 put
dup 90 /H11946 put
dup 104 /H17040 put
pop
%%EndResource
[/N8/CGKPBN+MathematicalPi-Six -1 TZ
%%BeginResource: font CGKGDN+Universal-NewswithCommPi
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1988 Adobe Systems Incorporated.  All Rights Reserved.) def
/version (001.000) def
/FullName (Universal News w. Commercial Pi 97) def
/FamilyName (Universal) def
/BaseFontName (Universal-NewswithCommPi) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGKGDN+Universal-NewswithCommPi def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -7 -227 989 764 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 26 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ 0 0 757 757 ] def
/OtherBlues [ -227 -227 ] def
/StdVW [ 48 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
6 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
48 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D64E6B38 |-
/H11541 51 -| 68CCB9B776D603E1D8F9AA9115D171D54A4AF7E2F9BA979AF3A7B025B5BC96ED96473C78
CD9C863B81D6F9D6A89F12D67425D3 |-
/H17015 194 -| 68CCB9B776D8AAC7224FCDB603ACB4FF9A44CC4EE2185E478B3C6FF2AB138216BB07DADA
CD9FC166011A3D4DC82D78C82AB744696F38857909DD563FD93F177A9A2B895A
4B8C2A41FB17D1C8755D5E0F2730680FA960906C07AC89BD319B6B916D6A0701
88D6C554DB153C2C0C09D456C87D87345D1F9FD432C129B4839C1A81FE2C4241
96B5B00C595C8C4351AA08B66CFE18D43FED37C052E5985674FB8EB8A71991AD
EA687C187AA48644B6EB44747840995F91F1091E07B240532305A8C5D832 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGKGDN+Universal-NewswithCommPi findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGKGDN+Universal-NewswithCommPi findfont /Encoding get
dup 0 /.notdef put
dup 42 /H11541 put
dup 113 /H17015 put
pop
%%EndResource
[/N7/CGKGDN+Universal-NewswithCommPi -1 TZ
%%BeginResource: font CGNFLA+GreekSlanted
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Created 1992 pjs modified April 96) def
/version (001.000) def
/FullName (GreekSlanted) def
/FamilyName (GreekSlanted) def
/BaseFontName (GreekSlanted) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGNFLA+GreekSlanted def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -9 -225 922 767 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -20 0 431 443 690 722 725 726 ] def
/StdHW [ 19 ] def
/StdVW [ 108 ] def
/StemSnapH [ 19 22 ] def
/StemSnapV [ 103 108 ] def
/BlueScale 0.031 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
13.5 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
108 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D64E6B38 |-
/V 172 -| 68CCB9B776D819D31FA2CB7078542195355BD12843475E735CE8F12036D85CACC098DE31
9FF5D9CFAF064D0A8066ADD203B8F559257FC274698A19CECBE233156F77DEF2
2F77AD61BF7E61B9F23F67056882B29431500E25FA63BCAAEACB13516A18F49E
26A30C40A42CC7AB4AEA03F5337B3BC016925E6A3C067A16953869B2111F8BB9
6E02483505512ABE23ED958E6540AFDC137C015510508E7BCF085AFD8A6FC5CB
F70E48C2F299BD22 |-
/d 154 -| 68CCB9B776D921E191846EF14DB165BAFAB13CE501E640C6C955AEA6533D3A62188AD00B
8F6A470AD1AFCF1A19CDDBBB1C4B2D4AAED266A302D6F580A75ACDEBF6A64AD3
75319DC0A7ACBFBE4A888F1D8D8A1057E6D2CB0897B61A28307B8F35C2560934
EA027D6994F639473DA2CBD85C684E43003255C09E9E53B5B7059E4619AFB3E4
905038F214AD078069D7988DE635170373ACCCF64FEB |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGNFLA+GreekSlanted findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGNFLA+GreekSlanted findfont /Encoding get
dup 0 /.notdef put
dup 86 /V put
dup 100 /d put
pop
%%EndResource
[/N22/CGNFLA+GreekSlanted -1 TZ
%%BeginResource: font CGMCAE+LucidaMath-Extension
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice ( Copyright (c) 1990 Adobe Systems Incorporated, All Rights Reserved.Lucida is a registered trademark of Bigelow & Holmes.) def
/version (001.000) def
/FullName (Lucida Math Extension) def
/FamilyName (Lucida Math) def
/BaseFontName (LucidaMath-Extension) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -30 def
/UnderlineThickness 60 def
end def
/FontName /CGMCAE+LucidaMath-Extension def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { 0 -2741 1398 849 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 25 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -18 0 723 741 530 542 ] def
/StdVW [ 72 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
9 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
72 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 2 dict dup begin
/.notdef 9 -| 68CCB9B776D622E6D5 |-
/radicalBig 70 -| 68CCB9B776D83C1A7BABF49DC3D3751A0A0FB2C18DD20ADFDAC240D50EDDA941D19D4EB5
E104FE205D3D9F00EDDD67E3950B9375FCF632F78F4D5D9567D3729EF9D91829
DE4D |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGMCAE+LucidaMath-Extension findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGMCAE+LucidaMath-Extension findfont /Encoding get
dup 0 /.notdef put
dup 113 /radicalBig put
pop
%%EndResource
[/N5/CGMCAE+LucidaMath-Extension -1 TZ
%%BeginResource: font CGOCMK+LucidaMath-Symbol
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice ( Copyright (c) 1990 Adobe Systems Incorporated, All Rights Reserved.Lucida is a registered trademark of Bigelow & Holmes.) def
/version (001.000) def
/FullName (Lucida Math Symbol) def
/FamilyName (Lucida Math) def
/BaseFontName (LucidaMath-Symbol) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -30 def
/UnderlineThickness 60 def
end def
/FontName /CGOCMK+LucidaMath-Symbol def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -70 -940 1414 855 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 25 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -18 0 723 741 530 542 ] def
/StdVW [ 96 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
12 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
96 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D622E6D5 |-
/reflexsubset 80 -| 68CCB9B776D872AF7FE8C6EFEDB735B9FA1A28D1E6D2219C20568974D5A02F9345D9B590
5B6A5B2EF22C8AF7EC2F850BA31D464BE8C31A7D576A568686E635CFE0963774
F23DCED9971941976C77BF5E |-
/reflexsuperset 79 -| 68CCB9B776D872AF7FE8C6EFEDB735B9FA1A764107440A0F566741248F1C1A280D2037EE
36E4D17CC3D2D2EA0A29C4FB1BE5FAFA6866A4FE904942514B8548CBDD32DC30
C4632A60B05385D91CD2B0 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGOCMK+LucidaMath-Symbol findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGOCMK+LucidaMath-Symbol findfont /Encoding get
dup 0 /.notdef put
dup 181 /reflexsubset put
dup 182 /reflexsuperset put
pop
%%EndResource
[/N20/CGOCMK+LucidaMath-Symbol -1 TZ
%%BeginResource: font CGLFBM+TapSymbol
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Created 1993 pjs for TAPSCO, Inc.) def
/version (001.000) def
/FullName (TapSymbol) def
/FamilyName (TapSymbol) def
/BaseFontName (TapSymbol) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGLFBM+TapSymbol def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -28 -954 1317 898 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -19 0 449 464 686 701 712 717 ] def
/StdHW [ 48 ] def
/StdVW [ 48 ] def
/StemSnapH [ 48 ] def
/StemSnapV [ 48 ] def
/BlueScale 0.046 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
6 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
48 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 9 dict dup begin
/.notdef 9 -| 68CCB9B776D9C5247D |-
/slash 55 -| 68CCB9B776D8D0632D0FFB86A0DA5A4438450F6AE8E7E402C1204910DE45A203C05B1879
8BD47598107046031EF4EA53D1C415D1C8313A |-
/zero 26 -| 68CCB9B776D8D0635108B049FF5E17598DF48E7E43D0873835B2 |-
/one 66 -| 68CCB9B776D8D0632D0FFB8892E11D8ABB6F09C3BE15E75B15143AC0BACA4CB0C420EE6F
CEECF84497E4A76F8C962D978F596522FC2DC3B584D3BD1E00AB0E3373F7 |-
/Aring 43 -| 68CCB9B776D8D06351D431EA67E20C297755C9BB91A4CC723155622E2245E958BDE94F77
D54347DCD1A8B1 |-
/uacute 38 -| 68CCB9B776D880E17448EED14A8C1F5F258A85910AED7902BD6912810D5E13A0691588E3
7022 |-
/degree 57 -| 68CCB9B776D880E138CECA424451BBA8F827F321545F3A849D869FF617072E8C62A807B2
27E19009FC769ACCA0C9B6A4E76CB7E99AC4D97834 |-
/cent 57 -| 68CCB9B776D880E138CECA4FB0673A767B90966EF363B73B333ED9EEEF2E68DFEB7BAF63
6ED9D2156770E458F5E2E81CD34194B619E214ED29 |-
/radical 85 -| 68CCB9B776D8D0632D2B8C247597F71AB3D106A727131BA95DF715B20D0D3F382C8FA15B
D71572E0574C059C31ECAC5764557893475EA66C9FCD6F5560974A55A31D084A
0D616A5C29757D6594C8990912BF2B0401 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGLFBM+TapSymbol findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGLFBM+TapSymbol findfont /Encoding get
dup 0 /.notdef put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 129 /Aring put
dup 156 /uacute put
dup 161 /degree put
dup 162 /cent put
dup 195 /radical put
pop
%%EndResource
[ 0 /NUL 9 /HT/LF 13 /CR 127 /DEL/Adieresis
/N4/CGLFBM+TapSymbol -1 TZ
%%BeginResource: font CGNLHN+SymTap
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Created 1994 pjs for TAPSCO, Inc. v1.4) def
/version (001.000) def
/FullName (SymTap) def
/FamilyName (SymTap) def
/BaseFontName (SymTap) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGNLHN+SymTap def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -1 -234 1665 1000 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 432 476 716 750 800 805 ] def
/StdHW [ 48 ] def
/StdVW [ 48 ] def
/StemSnapH [ 48 ] def
/StemSnapV [ 48 ] def
/BlueScale 0.023 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
6 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
48 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D9C5247D |-
/Eacute 27 -| 68CCB9B776D9C52484ECB12F38C37E6F56463448E1811392AD1D12 |-
/sterling 167 -| 68CCB9B776D96329D8A6CC80E825B5CABCA43530655EF1F71641518C363027F1A67B7AED
A6933003788BB7CB9761DACFB76659CE47EA0111CC5700F20454AC2F5ECBF5A8
DD329C6025117FC96777092DBA555062035326802B26DC917EE0F6FD8CCD0692
112016F01D02C0C9ABD357A5FEA74D91692E8B3615EECB1ED776A318790EEA6A
C21A7B4F53111A1C00DB69626E68F04CE169C492FF3D729ACA7E6F8F4CE29F46
68F7A9 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGNLHN+SymTap findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGNLHN+SymTap findfont /Encoding get
dup 0 /.notdef put
dup 131 /Eacute put
dup 163 /sterling put
pop
%%EndResource
[ 0 /NUL 9 /HT/LF 13 /CR 127 /DEL/Adieresis
/N19/CGNLHN+SymTap -1 TZ
%%BeginResource: font CGLKOK+MathematicalPi-Four
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1990 Adobe Systems Incorporated.  All Rights Reserved.) def
/version (001.000) def
/FullName (Mathematical Pi 4) def
/FamilyName (Mathematical Pi) def
/BaseFontName (MathematicalPi-Four) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGLKOK+MathematicalPi-Four def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -26 -240 928 773 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 27 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -16 0 704 720 ] def
/OtherBlues [ -210 -210 ] def
/StdHW [ 38 ] def
/StdVW [ 146 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
18.25 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
146 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 5 dict dup begin
/.notdef 9 -| 68CCB9B776D66C9B0D |-
/H20666 67 -| 68CCB9B776D8AAC7D6E1192400DA15C495583DEFEE37A246A0BBDDD5114C6606F63747D1
2BB7448A338D98565DDB6B3CAF0BEB506BFC5B852AD15B93A3006E51417681 |-
/H20667 69 -| 68CCB9B776D8AAC7D6E1192400DA15DA320990601813644A744CEC1C982B307903212AE8
90CD7C13DBD62CC9553A1217A2AC8F6648BFF8CB5DC2741B38A83ED5A4BB73CD
B6 |-
/H20668 69 -| 68CCB9B776D8AAC728130854F9BF87DB203910E3D24171A9224A5CB217C2E3F5D4F00061
A57E18962008FE79EF97DB874D0519D8E062A0285C9B7FCD7B36037D5E2321DD
4D |-
/H20669 71 -| 68CCB9B776D8AAC7FDE0D127A052945CF5A9AA682445E8AF9CB17DC659287587BB9F27E7
B20747D057A3EB3F2B8F981B83998F945A080441DA8D72DF33F7404461A5093F
CDB080 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGLKOK+MathematicalPi-Four findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGLKOK+MathematicalPi-Four findfont /Encoding get
dup 0 /.notdef put
dup 44 /H20666 put
dup 46 /H20667 put
dup 60 /H20668 put
dup 62 /H20669 put
pop
%%EndResource
[/N6/CGLKOK+MathematicalPi-Four -1 TZ
%%BeginResource: font CGOOIG+MathematicalPi-Three
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1990 Adobe Systems Incorporated.  All Rights Reserved.) def
/version (001.000) def
/FullName (Mathematical Pi 3) def
/FamilyName (Mathematical Pi) def
/BaseFontName (MathematicalPi-Three) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGOOIG+MathematicalPi-Three def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -27 -292 1023 981 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 27 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ 0 0 759 759 981 981 ] def
/OtherBlues [ -292 -292 ] def
/StdHW [ 46 ] def
/StdVW [ 46 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
5.75 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
46 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 12 dict dup begin
/.notdef 9 -| 68CCB9B776D66C9B0D |-
/H20898 72 -| 68CCB9B776D69093BC3ED2B8DB95F535B8785AB80328EF02B9F76DA429AFEAF3A74A7BD3
88848A664B8E0431A1B1F3F45C9835CC47186CC5996C911DF5D73C9D8BC2F1B9
86854DED |-
/H20899 72 -| 68CCB9B776D69093BC3ED2B8DB95F535E8B918AD430882F17D4B49C9F2D649F11D6AD72D
F6FC831A73E7D14E373135889C1D28B8F0ACBB44BAE77F0CDDC85E11D3598FA4
EBA9D545 |-
/H20900 47 -| 68CCB9B776D69093BC3EB62595C722C0C03D4C4D7D1A5B9A959B9A4ABEF0BC1B0FC1B3CF
EBEDBB7980422E4D9E30FD |-
/H20901 49 -| 68CCB9B776D69093BC3EB62595C722C085D4D65F3BE662BFCCDC5AE84B2B0DA615F802A9
7A37BFF92900B6B5145BEB47C0 |-
/H20902 128 -| 68CCB9B776D69093BC3EB62595C722C0A89BA2AEF88DB1286F1632ECA3D134C3FEC5CC1A
08CF776FFF3DC23876981552AA4B475D854DB4366501EE6A3EE9CFBF64B32C15
35416C01EE1F463D3455CC31266077EBEA379AE2CF0F518CD68D81111F7B73E3
39778C85CD42D1489CA50E6CE45A01AD30122867F0954EA894A14C66 |-
/H20874 61 -| 68CCB9B776D69093BC3C6B7F4A2E8F4B531C68967C31CD6A8734A83A4A39D4BBCDF2F8B5
06C2B5493616D721E8695097B9E2883FB0814130BDBABD6DD6 |-
/H20875 42 -| 68CCB9B776D69093BC3C0A3FD6D1A3E6DC76C1324DA7C0716ACE91B97BF9266D870FF8CE
BC5674267FC3 |-
/H20876 44 -| 68CCB9B776D69093BC3C0A3FD6D1A3E6EBE81224AEEE42767E2C3121C1512176580732F7
91ED0DC986DE0513 |-
/H20877 139 -| 68CCB9B776D69093BC3C06050857418654D0F6E76C00941A2D08AC3964944531D80FA2C6
C605C3BC081F3C77D4EF387DCD373302EA3B76E8C2EC37A45B052C215228FC66
6232ED78A9EFE6A566321E8249339E9C3B4403E634F39210FC96E4DA3B391680
010A52F6C7B41ACEA403DDB0166CF52E4695F897069C71289ED35F454C73400D
584069C92A2FB5 |-
/H20878 144 -| 68CCB9B776D69093BC3C06050857418654D0F6E74468FA6892E2DC221666A64C587F318C
964B0D416B104B044BE0E6165A02380EE45E6656952AAA99D020DA3DD602E706
20A4AA8AB894C341A1949334B4753C3C822970C11EA3D90556E501C0AE2FC40F
FC624FBEF1DDE482B56268FEE56C4032204D867715E0750F2BCA84589D8E067F
23AE19CAEB00721D7A1393DE |-
/H20873 61 -| 68CCB9B776D69093BC3C6B7F4A6FBE02C19C05B994E30AFD1C79706DF9C87AD7603DBBFF
5E693776FA1A755456FA4710B94DCB16DEA373FF8A3A8606B4 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGOOIG+MathematicalPi-Three findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGOOIG+MathematicalPi-Three findfont /Encoding get
dup 0 /.notdef put
dup 49 /H20898 put
dup 50 /H20899 put
dup 51 /H20900 put
dup 52 /H20901 put
dup 53 /H20902 put
dup 68 /H20874 put
dup 70 /H20875 put
dup 71 /H20876 put
dup 72 /H20877 put
dup 74 /H20878 put
dup 83 /H20873 put
pop
%%EndResource
[/N21/CGOOIG+MathematicalPi-Three -1 TZ
%%BeginResource: font CHFBOH+MathTechnicalP04
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice () def
/version (001.001) def
/FullName (MathTechnicalP04) def
/FamilyName (MathTechnicalP04) def
/BaseFontName (MathTechnicalP04) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -264 def
/UnderlineThickness 0 def
end def
/FontName /CHFBOH+MathTechnicalP04 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -2 -265 985 803 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 737 742 749 759 762 763 ] def
/StdHW [ 45 ] def
/StdVW [ 45 ] def
/StemSnapH [ 45 71 98 129 ] 
 systemdict /internaldict known
{1183615869 systemdict /internaldict get exec
/StemSnapLength 2 copy known {get 4 lt} {pop pop true} ifelse}
{true} ifelse {pop [45 129]} if def
/StemSnapV [ 21 45 59 70 ] 
 systemdict /internaldict known
{1183615869 systemdict /internaldict get exec
/StemSnapLength 2 copy known {get 4 lt} {pop pop true} ifelse}
{true} ifelse {pop [45 70]} if def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
5.625 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
45 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D64E6B38 |-
/quotedbl 23 -| 68CCB9B776D9C5248B0F744D84109B85CD9CFC045C6DBC |-
/a 8 -| 68CCB9B776AA6A61 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CHFBOH+MathTechnicalP04 findfont /Encoding get
dup 0 /.notdef put
pop
end
/CHFBOH+MathTechnicalP04 findfont /Encoding get
dup 0 /.notdef put
dup 34 /quotedbl put
dup 97 /a put
pop
%%EndResource
[/N36/CHFBOH+MathTechnicalP04 -1 TZ
%%BeginResource: font CHDPLL+TapscoPiAccents
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (©1992 Benjamin Graphics. All rights reserved.) def
/version (001.000) def
/FullName (TapscoPiAccents) def
/FamilyName (TapscoPiAccents) def
/BaseFontName (TapscoPiAccents) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CHDPLL+TapscoPiAccents def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -500 -315 500 1056 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 400 405 833 877 880 956 ] def
/StdHW [ 50 ] def
/StdVW [ 50 ] def
/StemSnapH [ 37 50 ] def
/StemSnapV [ 50 106 ] def
/BlueScale 0.023 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
6.25 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
50 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 3 dict dup begin
/.notdef 9 -| 68CCB9B776D9C5247D |-
/P 37 -| 68CCB9B776AA6A98D3A5A751698D09810E1ECD5CA95692EE3EDD8F7F3CFD0A75AAF99EFE
5D |-
/V 25 -| 68CCB9B776AA6A97CA3CAF378EFFA5C71DAB5FEF8052265A42 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CHDPLL+TapscoPiAccents findfont /Encoding get
dup 0 /.notdef put
pop
end
/CHDPLL+TapscoPiAccents findfont /Encoding get
dup 0 /.notdef put
dup 80 /P put
dup 86 /V put
pop
%%EndResource
[ 0 /NUL 9 /HT/LF 13 /CR 127 /DEL/Adieresis
/N32/CHDPLL+TapscoPiAccents -1 TZ
%%BeginResource: font CHCPJE+TapArrows
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Created 1993 pjs for TAPSCO, Inc.) def
/version (001.000) def
/FullName (TapArrows) def
/FamilyName (TapArrows) def
/BaseFontName (TapArrows) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CHCPJE+TapArrows def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -114 -205 1108 819 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 28 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 409 439 558 602 605 795 ] def
/StdHW [ 48 ] def
/StdVW [ 48 ] def
/StemSnapH [ 48 ] def
/StemSnapV [ 48 ] def
/BlueScale 0.023 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
6 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
48 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 2 dict dup begin
/.notdef 9 -| 68CCB9B776D9C5247D |-
/x 80 -| 68CCB9B776D8D06351D431EA67E20C297755C90FC6A5C055FBB1153A8CFD873993FADB4A
81D8A87AF3A76597364D4E7644B0ADC80D7AC8FF0C4EF81790BC17C9AC8D1D49
771AFE14B934FFAA0AD6ABC9 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CHCPJE+TapArrows findfont /Encoding get
dup 0 /.notdef put
pop
end
/CHCPJE+TapArrows findfont /Encoding get
dup 0 /.notdef put
dup 120 /x put
pop
%%EndResource
[ 0 /NUL 9 /HT/LF 13 /CR 127 /DEL/Adieresis
/N28/CHCPJE+TapArrows -1 TZ
%%BeginResource: font CHCIPO+ATGoudySans-Medium
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1990 Adobe Systems Incorporated.  All rights reserved.ITC Goudy Sans is a registered trademark of International Typeface Corporation.) def
/version (1.0) def
/FullName (AT Goudy Sans Medium) def
/FamilyName (ATGoudySans) def
/BaseFontName (ATGoudySans-Medium) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -90 def
/UnderlineThickness 50 def
end def
/FontName /CHCIPO+ATGoudySans-Medium def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -44 -286 1093 954 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 27 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 690 700 482 492 638 648 738 738 ] def
/OtherBlues [ 254 258 -202 -192 ] def
/StdHW [ 70 ] def
/StdVW [ 90 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
11.25 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
90 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 2 dict dup begin
/.notdef 9 -| 68CCB9B776D648822A |-
/periodcentered 47 -| 68CCB9B776D9C5248407957CB4726865180C957DFA9D236DC95F31EDCE916FFC950B2F7C
2646C6E16E2A96809BC017 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CHCIPO+ATGoudySans-Medium findfont /Encoding get
dup 0 /.notdef put
pop
end
/CHCIPO+ATGoudySans-Medium findfont /Encoding get
dup 0 /.notdef put
dup 180 /periodcentered put
pop
%%EndResource
[/N27/CHCIPO+ATGoudySans-Medium -1 TZ
%%BeginResource: font CGOIKI+Universal-GreekwithMathPi
ct_CffDict begin
15 dict begin
/FontInfo 15 dict dup begin
/Notice (Copyright (c) 1988 Adobe Systems Incorporated.  All Rights Reserved.) def
/version (001.000) def
/FullName (Universal Greek w. Math Pi 169) def
/FamilyName (Universal) def
/BaseFontName (Universal-GreekwithMathPi) def
/Weight (Medium) def
/ItalicAngle 0 def
/isFixedPitch false  def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end def
/FontName /CGOIKI+Universal-GreekwithMathPi def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ] def
/FontBBox { -30 -240 1012 815 } def
/StrokeWidth 0 def
currentdict end
systemdict begin
dup /Private 26 dict dup begin
/-|{string currentfile exch readhexstring pop}executeonly def
/|-{def}executeonly def
/|{put}executeonly def
/BlueValues [ -10 0 712 722 425 435 640 650 815 815 ] def
/OtherBlues [ -240 -240 ] def
/StdVW [ 90 ] def
/BlueScale 0.039625 def
/BlueShift 7 def
/BlueFuzz 1 def
/ForceBold false  def
/ForceBoldThreshold 0 def
/LanguageGroup 0 def
/ExpansionFactor 0.06 def
/initialRandomSeed 0 def
/lenIV 4 def
/MinFeature {16 16} def
/password 5839 def
/Erode{
11.25 dup 3 -1 roll 0.1 mul exch 0.5 sub mul cvi sub dup mul
90 0 dtransform dup mul exch dup mul add
le{pop pop 1.0 1.0}{pop pop 0.0 1.5}ifelse}def
/OtherSubrs [
{ct_CffDict/F0Subr get exec}executeonly{ct_CffDict/F1Subr get exec}executeonly{ct_CffDict/F2Subr get exec}executeonly{ct_CffDict/HSSubr get exec}executeonly] |-
/Subrs 5  array
dup 0 15 -| 68CCB9B7733DBF957B5C4F6827AC8A |
dup 1 9 -| 68CCB9B776ADDED836 |
dup 2 9 -| 68CCB9B776AC088F04 |
dup 3 5 -| 68CCB9B7F6 |
dup 4 13 -| 68CCB9B7733AC657EC3EB6EC2F |
|-
2 index /CharStrings 2 dict dup begin
/.notdef 9 -| 68CCB9B776D64E6B38 |-
/H20858 85 -| 68CCB9B776D8503AE9C9197B52AEC6B622642EDA1B8810B5B9FC6480E22E68BC8E34ADBB
D8618A19AA1A1D64729F68C4F3C7F8A017A5288D8AF8C4325E7CF21F4B3D61D6
78C1C3B2328A529883826E2A1EE6B98AA4 |-
end
end
put
put
dup/FontName get exch definefont pop
end
/CGOIKI+Universal-GreekwithMathPi findfont /Encoding get
dup 0 /.notdef put
pop
end
/CGOIKI+Universal-GreekwithMathPi findfont /Encoding get
dup 0 /.notdef put
dup 40 /H20858 put
pop
%%EndResource
[/N18/CGOIKI+Universal-GreekwithMathPi -1 TZ
PDFVars/TermAll get exec end end

%%EndSetup
%%Page: 1 1
%%BeginPageSetup
userdict /pgsave save put
PDFVars begin PDF begin PDFVars/InitAll get exec
0 0 612 792 true PDF begin PDFVars begin AS end end
%%EndPageSetup
0 0 612 792 RC
1 g
/N13 /ExtGState findRes gsDI

119.54899 67.24598 370.60099 -23.90998 rf
119.54899 119.54899 370.60099 -14.94398 rf
119.54899 99.62399 370.60099 -19.92498 rf
119.54899 725.26298 370.60099 -547.93199 rf
119.54899 159.39799 370.60099 -39.84999 rf
BT
/N9 1 Tf
8.26899 0 0 8.06999 138.12899 47.32099 Tm
0 Tc
(/)Tj [-247 ]TJ (3907)Tj [-343 ]TJ (no38)Tj [-349 ]TJ (Mp)Tj [-1000 ]TJ (1)Tj [-1000 ]TJ (Monday)Tj [-337 ]TJ (Mar)Tj [-343 ]TJ (08)Tj [-349 ]TJ (03:24)Tj [-349 ]TJ (PM)Tj [-1000 ]TJ (INF\261MOR)Tj [-1000 ]TJ (no38)Tj 
0 g
19.90948 7.09878 TD
0 Tw
(1)Tj 
9.25918 -1.97529 TD
(0364-765X/99/2401/0001/$05.00)Tj 
6.17698 0 0 6.07699 280.93998 80.69499 Tm
(Copyright)Tj 
/N7 1 Tf
5.97698 0 0 5.97698 307.73799 80.69499 Tm
(q)Tj 
/N9 1 Tf
6.17698 0 0 6.07699 314.51298 80.69499 Tm
(1999,)Tj [-298 ]TJ (Institute)Tj [-274 ]TJ (for)Tj [-298 ]TJ (Operations)Tj [-274 ]TJ (Research)Tj [-290 ]TJ (and)Tj [-298 ]TJ (the)Tj [-290 ]TJ (Management)Tj [-290 ]TJ (Sciences)Tj 
-31.56449 104.75408 TD
(MATHEMATICS)Tj [-452 ]TJ (OF)Tj [-492 ]TJ (OPERATIONS)Tj [-444 ]TJ (RESEARCH)Tj 
0 -1.31149 TD
(Vol.)Tj [-492 ]TJ (24,)Tj [-500 ]TJ (No.)Tj [-500 ]TJ (1,)Tj [-500 ]TJ (February)Tj [-484 ]TJ (1999)Tj 
/N10 1 Tf
T*
(Printed)Tj [-484 ]TJ (in)Tj [-500 ]TJ (U.S.A.)Tj 
/N9 1 Tf
11.85499 0 0 11.65599 141.76499 677.44299 Tm
(ON)Tj [-496 ]TJ (A)Tj [-496 ]TJ (REPRESENTATION)Tj [-466 ]TJ (OF)Tj [-496 ]TJ (THE)Tj [-492 ]TJ (MATCHING)Tj [-479 ]TJ (POLYTOPE)Tj 
6.72268 -1.02558 TD
(VIA)Tj [-496 ]TJ (SEMIDEFINITE)Tj [-475 ]TJ (LIFTINGS)Tj 
9.26499 0 0 9.06599 214.53999 643.57099 Tm
(TAMON)Tj [-495 ]TJ (STEPHEN)Tj 
7.17298 0 0 6.67498 298.17399 643.57099 Tm
(AND)Tj 
9.26499 0 0 9.06599 318.19799 643.57099 Tm
(LEVENT)Tj [-484 ]TJ (TUNC)Tj 
6.59689 0 TD
0.16398 Tc
(\313E)Tj [164 ]TJ (L)Tj 
8.26899 0 0 8.06999 159.99598 625.63899 Tm
0 Tc
(We)Tj [-211 ]TJ (consider)Tj [-217 ]TJ (the)Tj [-211 ]TJ (relaxation)Tj [-211 ]TJ (of)Tj [-211 ]TJ (the)Tj [-205 ]TJ (matching)Tj [-211 ]TJ (polytope)Tj [-205 ]TJ (de\256ned)Tj [-205 ]TJ (by)Tj [-205 ]TJ (the)Tj [-199 ]TJ (non-negativity)Tj [-193 ]TJ (and)Tj [-187 ]TJ (degree)Tj 
-2 -1.23458 TD
(constraints.)Tj [-253 ]TJ (We)Tj [-247 ]TJ (prove)Tj [-247 ]TJ (that)Tj [-253 ]TJ (given)Tj [-253 ]TJ (an)Tj [-253 ]TJ (undirected)Tj [-247 ]TJ (graph)Tj [-247 ]TJ (on)Tj 
/N10 1 Tf
22.65649 0 TD
(n)Tj 
/N9 1 Tf
0.74708 0 TD
(nodes)Tj [-241 ]TJ (and)Tj [-241 ]TJ (the)Tj [-229 ]TJ (corresponding)Tj [-223 ]TJ (relaxation)Tj 
-23.40359 -1.23458 TD
(of)Tj [-295 ]TJ (the)Tj [-289 ]TJ (matching)Tj [-295 ]TJ (polytope,)Tj 
/N11 1 Tf
7.96998 0 0 7.96998 231.875 605.71398 Tm
(\353)Tj 
/N10 1 Tf
8.26899 0 0 8.06999 235.70999 605.71398 Tm
(n)Tj 
/N9 1 Tf
0.59638 0 TD
0.09599 Tc
(/2)Tj 
/N11 1 Tf
7.96998 0 0 7.96998 248.70999 605.71398 Tm
0 Tc
(\373)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 254.18998 605.71398 Tm
(iterations)Tj [-283 ]TJ (of)Tj [-289 ]TJ (the)Tj [-283 ]TJ (Lova)Tj 
8.30119 0 TD
(\302)Tj [-53 ]TJ (sz-Schrijver)Tj [-283 ]TJ (semide\256nite)Tj [-265 ]TJ (lifting)Tj [-259 ]TJ (procedure)Tj 
-21.69268 -1.23458 TD
(are)Tj [-301 ]TJ (needed)Tj [-307 ]TJ (to)Tj [-307 ]TJ (obtain)Tj [-307 ]TJ (the)Tj [-307 ]TJ (matching)Tj [-307 ]TJ (polytope,)Tj [-301 ]TJ (in)Tj [-307 ]TJ (the)Tj [-301 ]TJ (worst)Tj [-301 ]TJ (case.)Tj [-301 ]TJ (We)Tj [-301 ]TJ (show)Tj [-301 ]TJ (that)Tj 
/N11 1 Tf
7.96998 0 0 7.96998 403.72599 595.75199 Tm
(\353)Tj 
/N10 1 Tf
8.26899 0 0 8.06999 407.56199 595.75199 Tm
(n)Tj 
/N9 1 Tf
0.59638 0 TD
0.09599 Tc
(/2)Tj 
/N11 1 Tf
7.96998 0 0 7.96998 420.51298 595.75199 Tm
0 Tc
(\373)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 426.14199 595.75199 Tm
(iterations)Tj [-301 ]TJ (of)Tj 
-34.18669 -1.23458 TD
(the)Tj [-295 ]TJ (procedure)Tj [-277 ]TJ (always)Tj [-277 ]TJ (suf\256ce.)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 559.88699 Tm
(1.)Tj [-1000 ]TJ (Introduction.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 214.04199 559.88699 Tm
(In)Tj [-269 ]TJ (integer)Tj [-269 ]TJ (programming,)Tj [-269 ]TJ (given)Tj [-264 ]TJ (a)Tj [-264 ]TJ (polyhedron)Tj [-264 ]TJ (in)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 412.64299 559.88699 Tm
(R)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 420.81098 563.87199 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 425.04499 559.88699 Tm
(,)Tj [-260 ]TJ (w)Tj [0 ]TJ (e)Tj [-260 ]TJ (are)Tj [-255 ]TJ (usually)Tj 
-29.48548 -1.17649 TD
(interested)Tj [-236 ]TJ (in)Tj [-236 ]TJ (obtaining)Tj [-236 ]TJ (a)Tj [-236 ]TJ (description)Tj [-236 ]TJ (of)Tj 
/N10 1 Tf
15.57688 0 TD
(P)Tj 
6.47599 0 0 5.97698 287.26599 546.43798 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 291.79798 547.93199 Tm
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 294.68699 547.93199 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 304.99798 547.93199 Tm
(conv)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.47129 0 TD
(P)Tj 
/N6 1 Tf
9.96199 0 0 9.96199 339.31898 547.93199 Tm
(>)Tj 
/N8 1 Tf
1.06988 0 TD
(Z)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 357.64999 551.91699 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 361.88398 547.93199 Tm
(\))Tj [-231 ]TJ (i)Tj [0 ]TJ (n)Tj [-226 ]TJ (terms)Tj [-221 ]TJ (of)Tj [-221 ]TJ (linear)Tj [-207 ]TJ (inequalities.)Tj 
-23.38938 -1.17649 TD
(There)Tj [-312 ]TJ (has)Tj [-312 ]TJ (been)Tj [-312 ]TJ (a)Tj [-317 ]TJ (considerable)Tj [-312 ]TJ (amount)Tj [-308 ]TJ (of)Tj [-312 ]TJ (work)Tj [-312 ]TJ (in)Tj [-312 ]TJ (this)Tj [-308 ]TJ (area.)Tj [-312 ]TJ (Recently,)Tj [-308 ]TJ (an)Tj [-308 ]TJ (intriguing)Tj [-288 ]TJ (pro-)Tj 
T*
(cedure)Tj [-308 ]TJ (was)Tj [-308 ]TJ (described)Tj [-308 ]TJ (by)Tj [-308 ]TJ (Lova)Tj 
11.95188 0 TD
(\302)Tj [-52 ]TJ (s)Tj [0 ]TJ (z)Tj [-308 ]TJ (and)Tj [-308 ]TJ (Schrijver)Tj [-308 ]TJ (\()Tj [-96 ]TJ (1991)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-308 ]TJ (Their)Tj [-308 ]TJ (procedure)Tj [-298 ]TJ (takes)Tj [-298 ]TJ (as)Tj [-303 ]TJ (input)Tj [-298 ]TJ (a)Tj 
-11.95188 -1.17649 TD
(polyhedron)Tj [-385 ]TJ (and)Tj [-385 ]TJ (using)Tj [-385 ]TJ (the)Tj [-385 ]TJ (cone)Tj [-385 ]TJ (of)Tj [-385 ]TJ (symmetric)Tj [-380 ]TJ (positive)Tj [-380 ]TJ (semide\256nite)Tj [-370 ]TJ (matrices,)Tj [-356 ]TJ (delivers)Tj [-346 ]TJ (a)Tj 
T*
(description)Tj [-279 ]TJ (of)Tj [-279 ]TJ (the)Tj [-279 ]TJ (convex)Tj [-279 ]TJ (hull)Tj [-274 ]TJ (of)Tj [-279 ]TJ (integer)Tj [-274 ]TJ (points)Tj [-269 ]TJ (in)Tj [-274 ]TJ (the)Tj [-274 ]TJ (original)Tj [-264 ]TJ (polyhedron.)Tj [-264 ]TJ (Each)Tj [-260 ]TJ (iteration)Tj 
T*
(of)Tj [-332 ]TJ (the)Tj [-327 ]TJ (procedure)Tj [-322 ]TJ (consists)Tj [-322 ]TJ (of)Tj [-322 ]TJ (one)Tj [-327 ]TJ (``semide\256nite)Tj [-327 ]TJ (lifting'')Tj [-322 ]TJ (and)Tj [-322 ]TJ (one)Tj [-322 ]TJ (``projection.'')Tj [-308 ]TJ (The)Tj [-312 ]TJ (pro-)Tj 
T*
(cedure)Tj [-293 ]TJ (requires)Tj [-284 ]TJ (at)Tj [-293 ]TJ (most)Tj 
/N10 1 Tf
9.70669 0 TD
(d)Tj 
/N9 1 Tf
0.79809 0 TD
(iterations.)Tj 
-9.50479 -1.17649 TD
(Lova)Tj 
1.66828 0 TD
(\302)Tj [-54 ]TJ (s)Tj [0 ]TJ (z)Tj [-303 ]TJ (and)Tj [-303 ]TJ (Schrijver)Tj [-303 ]TJ (illustrate)Tj [-303 ]TJ (their)Tj [-298 ]TJ (procedure)Tj [-298 ]TJ (on)Tj [-298 ]TJ (the)Tj [-298 ]TJ (stable)Tj [-298 ]TJ (set)Tj [-298 ]TJ (problem.)Tj [-293 ]TJ (One)Tj [-293 ]TJ (of)Tj [-284 ]TJ (their)Tj 
-2.66828 -1.17649 TD
(impressive)Tj [-341 ]TJ (results)Tj [-341 ]TJ (is)Tj [-341 ]TJ (that)Tj [-341 ]TJ (only)Tj [-346 ]TJ (one)Tj [-341 ]TJ (iteration)Tj [-346 ]TJ (of)Tj [-346 ]TJ (the)Tj [-346 ]TJ (procedure)Tj [-346 ]TJ (applied)Tj [-341 ]TJ (to)Tj [-341 ]TJ (the)Tj [-341 ]TJ (basic)Tj [-327 ]TJ (linear)Tj 
T*
(programming)Tj [-308 ]TJ (relaxation)Tj [-303 ]TJ (of)Tj [-308 ]TJ (the)Tj [-303 ]TJ (stable)Tj [-303 ]TJ (set)Tj [-303 ]TJ (problem)Tj [-298 ]TJ (\()Tj [-96 ]TJ (only)Tj [-298 ]TJ (edge)Tj [-303 ]TJ (inequalities)Tj [-284 ]TJ (and)Tj [-288 ]TJ (non-nega-)Tj 
T*
(tivity)Tj [-437 ]TJ (constraints)Tj [-96 ]TJ (\))Tj [-96 ]TJ (,)Tj [-437 ]TJ (delivers)Tj [-433 ]TJ (a)Tj [-437 ]TJ (description)Tj [-433 ]TJ (of)Tj [-433 ]TJ (a)Tj [-433 ]TJ (convex)Tj [-433 ]TJ (set)Tj [-428 ]TJ (for)Tj [-433 ]TJ (which)Tj [-428 ]TJ (many)Tj [-428 ]TJ (interesting)Tj 
T*
(classes)Tj [-322 ]TJ (of)Tj [-327 ]TJ (inequalities)Tj [-322 ]TJ (such)Tj [-322 ]TJ (as)Tj [-317 ]TJ (odd)Tj [-322 ]TJ (hole,)Tj [-322 ]TJ (odd)Tj [-322 ]TJ (anti-hole,)Tj [-322 ]TJ (and)Tj [-322 ]TJ (clique)Tj [-317 ]TJ (inequalities)Tj [-303 ]TJ (are)Tj [-308 ]TJ (valid.)Tj 
T*
(Moreover,)Tj [-375 ]TJ (any)Tj [-375 ]TJ (linear)Tj [-370 ]TJ (function)Tj [-375 ]TJ (can)Tj [-370 ]TJ (be)Tj [-375 ]TJ (approximately)Tj [-370 ]TJ (optimized)Tj [-365 ]TJ (over)Tj [-365 ]TJ (this)Tj [-361 ]TJ (convex)Tj [-365 ]TJ (set)Tj [-351 ]TJ (in)Tj 
T*
(polynomial)Tj [-284 ]TJ (time.)Tj 
1 -1.17649 TD
(Lova)Tj 
1.66828 0 TD
(\302)Tj [-54 ]TJ (s)Tj [0 ]TJ (z)Tj [-298 ]TJ (and)Tj [-298 ]TJ (Schrijver)Tj [-298 ]TJ (ask)Tj [-298 ]TJ (the)Tj [-293 ]TJ (question)Tj [-293 ]TJ (of)Tj [-288 ]TJ (how)Tj [-293 ]TJ (many)Tj [-293 ]TJ (iterations)Tj [-284 ]TJ (of)Tj [-288 ]TJ (the)Tj [-279 ]TJ (procedure)Tj [-279 ]TJ (would)Tj 
-2.66828 -1.17649 TD
(be)Tj [-255 ]TJ (needed)Tj [-255 ]TJ (to)Tj [-250 ]TJ (obtain)Tj [-250 ]TJ (a)Tj [-250 ]TJ (description)Tj [-250 ]TJ (of)Tj [-245 ]TJ (the)Tj [-250 ]TJ (convex)Tj [-245 ]TJ (hull)Tj [-240 ]TJ (of)Tj [-245 ]TJ (the)Tj [-240 ]TJ (incidence)Tj [-236 ]TJ (vectors)Tj [-240 ]TJ (of)Tj [-231 ]TJ (stable)Tj [-221 ]TJ (sets)Tj 
T*
(in)Tj [-312 ]TJ (a)Tj [-308 ]TJ (line)Tj [-303 ]TJ (graph.)Tj [-312 ]TJ (Or)Tj [-308 ]TJ (equivalently,)Tj [-308 ]TJ (how)Tj [-308 ]TJ (many)Tj [-308 ]TJ (iterations)Tj [-298 ]TJ (of)Tj [-308 ]TJ (the)Tj [-303 ]TJ (procedure)Tj [-298 ]TJ (would)Tj [-303 ]TJ (be)Tj [-308 ]TJ (needed)Tj 
T*
(to)Tj [-269 ]TJ (get)Tj [-264 ]TJ (the)Tj [-264 ]TJ (convex)Tj [-264 ]TJ (hull)Tj [-260 ]TJ (of)Tj [-264 ]TJ (the)Tj [-264 ]TJ (incidence)Tj [-260 ]TJ (vectors)Tj [-260 ]TJ (of)Tj [-264 ]TJ (matchings)Tj [-255 ]TJ (in)Tj [-260 ]TJ (an)Tj [-255 ]TJ (undirected)Tj [-250 ]TJ (graph,)Tj [-250 ]TJ (if)Tj [-240 ]TJ (we)Tj 
T*
(start)Tj [-327 ]TJ (the)Tj [-327 ]TJ (procedure)Tj [-327 ]TJ (with)Tj [-327 ]TJ (the)Tj [-327 ]TJ (polytope)Tj [-327 ]TJ (de\256ned)Tj [-327 ]TJ (by)Tj [-327 ]TJ (the)Tj [-327 ]TJ (non-negativity)Tj [-322 ]TJ (and)Tj [-322 ]TJ (the)Tj [-317 ]TJ (degree)Tj [-322 ]TJ (con-)Tj 
T*
(straints.)Tj [-409 ]TJ (The)Tj [-409 ]TJ (same)Tj [-409 ]TJ (problem)Tj [-404 ]TJ (is)Tj [-404 ]TJ (also)Tj [-409 ]TJ (mentioned)Tj [-404 ]TJ (in)Tj [-404 ]TJ (the)Tj [-399 ]TJ (recent)Tj [-399 ]TJ (survey)Tj [-404 ]TJ (paper)Tj [-404 ]TJ (of)Tj [-409 ]TJ (Goemans)Tj 
T*
0.09599 Tc
(\(1)Tj [96 ]TJ (9)Tj [96 ]TJ (9)Tj [96 ]TJ (7\).)Tj 
1 -1.17649 TD
0 Tc
(In)Tj [-298 ]TJ (this)Tj [-293 ]TJ (paper,)Tj [-298 ]TJ (we)Tj [-288 ]TJ (prove)Tj [-293 ]TJ (that)Tj [-293 ]TJ (for)Tj [-293 ]TJ (a)Tj [-293 ]TJ (clique)Tj [-288 ]TJ (on)Tj [-293 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
18.60569 0 TD
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 330.89999 296.87998 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 341.85899 296.87998 Tm
(1)Tj [-96 ]TJ (\))Tj [-293 ]TJ (nodes,)Tj [-288 ]TJ (at)Tj [-284 ]TJ (least)Tj 
/N10 1 Tf
7.21638 0 TD
(n)Tj 
/N9 1 Tf
0.78369 0 TD
(iterations)Tj [-269 ]TJ (of)Tj [-274 ]TJ (the)Tj 
-29.45669 -1.17649 TD
(procedure)Tj [-399 ]TJ (are)Tj [-399 ]TJ (needed)Tj [-399 ]TJ (to)Tj [-399 ]TJ (obtain)Tj [-399 ]TJ (the)Tj [-399 ]TJ (underlying)Tj [-399 ]TJ (matching)Tj [-394 ]TJ (polytope.)Tj [-389 ]TJ (Moreover,)Tj [-389 ]TJ (it)Tj [-385 ]TJ (easily)Tj 
T*
(follows)Tj [-341 ]TJ (from)Tj [-341 ]TJ (a)Tj [-346 ]TJ (result)Tj [-346 ]TJ (of)Tj [-341 ]TJ (Lova)Tj 
11.82688 0 TD
(\302)Tj [-54 ]TJ (s)Tj [0 ]TJ (z)Tj [-346 ]TJ (and)Tj [-346 ]TJ (Schrijver)Tj [-346 ]TJ (that)Tj [-337 ]TJ (for)Tj [-341 ]TJ (an)Tj [-346 ]TJ (undirected)Tj [-341 ]TJ (graph)Tj [-341 ]TJ (on)Tj 
/N10 1 Tf
20.52398 0 TD
(n)Tj 
/N9 1 Tf
0.84129 0 TD
(nodes,)Tj 
/N11 1 Tf
9.96199 0 0 9.96199 119.54899 261.01499 Tm
(\353)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 124.33099 261.01499 Tm
(n)Tj 
/N9 1 Tf
0.59619 0 TD
0.09599 Tc
(/2)Tj 
/N11 1 Tf
9.96199 0 0 9.96199 140.56898 261.01499 Tm
0 Tc
(\373)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 147.04499 261.01499 Tm
(iterations)Tj [-255 ]TJ (of)Tj [-260 ]TJ (the)Tj [-255 ]TJ (procedure)Tj [-260 ]TJ (suf\256ce)Tj [-255 ]TJ (in)Tj [-260 ]TJ (the)Tj [-250 ]TJ (worst)Tj [-250 ]TJ (case.)Tj [-255 ]TJ (Note)Tj [-255 ]TJ (that)Tj [-245 ]TJ (for)Tj [-245 ]TJ (the)Tj [-250 ]TJ (clique)Tj [-245 ]TJ (on)Tj [-240 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
32.61529 0 TD
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 249.05999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.40699 249.05999 Tm
(1)Tj [-96 ]TJ (\))Tj [-284 ]TJ (nodes,)Tj [-279 ]TJ (the)Tj [-279 ]TJ (corresponding)Tj [-279 ]TJ (matching)Tj [-279 ]TJ (polytope)Tj [-274 ]TJ (has)Tj [-269 ]TJ (dimension)Tj 
/N10 1 Tf
25.38949 0 TD
(d)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 401.43499 249.05999 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 412.14498 249.05999 Tm
(n)Tj 
/N9 1 Tf
0.59609 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.93278 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 435.95498 249.05999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 446.66398 249.05999 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-264 ]TJ (There-)Tj 
-31.57209 -1.17649 TD
(fore,)Tj [-308 ]TJ (our)Tj [-303 ]TJ (results)Tj [-303 ]TJ (show)Tj [-308 ]TJ (that)Tj [-303 ]TJ (the)Tj [-308 ]TJ (number)Tj [-308 ]TJ (of)Tj [-303 ]TJ (iterations)Tj [-298 ]TJ (of)Tj [-303 ]TJ (the)Tj [-303 ]TJ (Lova)Tj 
25.31719 0 TD
(\302)Tj [-51 ]TJ (sz-Schrijver)Tj [-293 ]TJ (procedure)Tj [-288 ]TJ (is)Tj 
-25.31719 -1.17649 TD
(roughly)Tj [-2582 ]TJ (on)Tj [-298 ]TJ (matching)Tj [-284 ]TJ (problems,)Tj [-284 ]TJ (in)Tj [-293 ]TJ (the)Tj [-293 ]TJ (worst)Tj [-288 ]TJ (case.)Tj 
3.83169 1.12748 TD
(_)Tj 
0.0625 0 TD
(___)Tj 
/N5 1 Tf
6.47599 0 0 6.47599 154.81498 235.11299 Tm
(q)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 160.24499 225.14999 Tm
(d)Tj 
/N9 1 Tf
0.59619 0 TD
0.09599 Tc
(/2)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 194.06799 Tm
0 Tc
(2.)Tj [-1000 ]TJ (Matching)Tj [-300 ]TJ (polytope.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 240.24299 194.06799 Tm
(Let)Tj 
/N10 1 Tf
1.62979 0 TD
(G)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 267.68998 194.06799 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 278.69799 194.06799 Tm
(\()Tj 
/N10 1 Tf
0.33169 0 TD
(V)Tj 
/N9 1 Tf
0.61048 0 TD
(,)Tj 
/N10 1 Tf
0.54818 0 TD
(E)Tj 
/N9 1 Tf
0.70669 0 TD
(\))Tj [-298 ]TJ (denote)Tj [-293 ]TJ (an)Tj [-298 ]TJ (undirected)Tj [-293 ]TJ (graph)Tj [-293 ]TJ (with)Tj [-288 ]TJ (node)Tj [-288 ]TJ (set)Tj 
/N10 1 Tf
17.60089 0 TD
(V)Tj 
/N9 1 Tf
-35.15859 -1.17649 TD
(and)Tj [-298 ]TJ (edge)Tj [-293 ]TJ (set)Tj 
/N10 1 Tf
5.32209 0 TD
(E)Tj 
/N9 1 Tf
0.70669 0 TD
(.)Tj [-298 ]TJ (De\256ne)Tj 
8.26899 0 0 8.06999 119.54899 149.43598 Tm
(Received)Tj [-277 ]TJ (July)Tj [-289 ]TJ (22,)Tj [-295 ]TJ (1997;)Tj [-289 ]TJ (revised)Tj [-283 ]TJ (May)Tj [-289 ]TJ (11,)Tj [-289 ]TJ (1998.)Tj 
/N10 1 Tf
0 -1.23458 TD
(AMS)Tj [-295 ]TJ (1991)Tj [-295 ]TJ (subject)Tj [-283 ]TJ (classi\256cation.)Tj 
/N9 1 Tf
13.44578 0 TD
(Primary:)Tj [-283 ]TJ (90C10,)Tj [-289 ]TJ (90C27.)Tj 
/N10 1 Tf
-13.44578 -1.23458 TD
(OR/MS)Tj [-289 ]TJ (subject)Tj [-283 ]TJ (classi\256cation.)Tj 
/N9 1 Tf
12.14459 0 TD
(Primary:)Tj [-283 ]TJ (Programming/Semide\256nite,)Tj [-259 ]TJ (Programming/Integer.)Tj 
/N10 1 Tf
-12.14459 -1.23458 TD
(Key)Tj [-283 ]TJ (words.)Tj 
/N9 1 Tf
4.81329 0 TD
(Matching)Tj [-283 ]TJ (polytope,)Tj [-283 ]TJ (semide\256nite)Tj [-277 ]TJ (lifting,)Tj [-283 ]TJ (semide\256nite)Tj [-277 ]TJ (programming,)Tj [-277 ]TJ (integer)Tj [-289 ]TJ (programming.)Tj 
ET
PDFVars/TermAll get exec end end
userdict /pgsave get restore
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1 g
/N13 /ExtGState findRes gsDI

119.54899 725.26298 370.60099 -19.92498 rf
119.54899 67.24598 370.60099 -23.90998 rf
119.54899 705.33799 370.60099 -621.65399 rf
BT
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 717.29299 Tm
0 g
0 Tc
0 Tw
(2)Tj 
7.17298 0 0 6.67498 249.45698 717.29299 Tm
0.06898 Tc
(T.)Tj [-500 ]TJ (STEPHEN)Tj [-459 ]TJ (AND)Tj [-486 ]TJ (L.)Tj [-493 ]TJ (TUNC)Tj 
13.61819 0 TD
0.23399 Tc
(\313E)Tj [165 ]TJ (L)Tj 
8.26899 0 0 8.06999 140.12098 47.32099 Tm
1 g
0.05999 Tc
(/)Tj [-247 ]TJ (3907)Tj [-494 ]TJ (no38)Tj [-500 ]TJ (Mp)Tj [-1000 ]TJ (2)Tj [-1000 ]TJ (Monday)Tj [-488 ]TJ (Mar)Tj [-494 ]TJ (08)Tj [-500 ]TJ (03:24)Tj [-500 ]TJ (PM)Tj [-1000 ]TJ (INF\261MOR)Tj [-1000 ]TJ (no38)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 270.72799 697.36799 Tm
0 g
0 Tc
(E)Tj 
10.36099 0 0 10.16198 197.75399 693.38299 Tm
(P)Tj 
/N9 1 Tf
0.70669 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
0.28799 Tc
(\):)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 227.24198 693.38299 Tm
0 Tc
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 238.15098 693.38299 Tm
({)Tj 
/N10 1 Tf
0.57209 0 TD
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 251.64999 693.38299 Tm
(\303)Tj 
/N8 1 Tf
1.09489 0 TD
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 277.65199 693.38299 Tm
(:)Tj 
/N10 1 Tf
0.56239 0 TD
(x)Tj 
/N9 1 Tf
0.53849 0 TD
(\()Tj 
/N22 1 Tf
9.96199 0 0 9.96199 293.49198 693.38299 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 299.16999 693.38299 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 303.60398 693.38299 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 308.68499 693.38299 Tm
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 319.54399 693.38299 Tm
0 Tc
(\241)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 331.25 693.38299 Tm
(1,)Tj 
/N11 1 Tf
9.96199 0 0 9.96199 342.00799 693.38299 Tm
(")Tj 
/N19 1 Tf
0.70999 0 TD
(\243)Tj 
/N4 1 Tf
0.71009 0 TD
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 367.06498 693.38299 Tm
(V)Tj 
/N9 1 Tf
0.61048 0 TD
(,)Tj 
/N10 1 Tf
0.53849 0 TD
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 386.54098 693.38299 Tm
(\242)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 398.24699 693.38299 Tm
0.09599 Tc
(0}.)Tj 
-26.89898 -2.46078 TD
0 Tc
(In)Tj [-245 ]TJ (the)Tj [-245 ]TJ (above,)Tj 
/N22 1 Tf
9.96199 0 0 9.96199 175.78698 668.37699 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 181.46398 668.37699 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 185.89799 668.37699 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 190.97898 668.37699 Tm
(\))Tj [-240 ]TJ (i)Tj [0 ]TJ (s)Tj [-240 ]TJ (the)Tj [-245 ]TJ (set)Tj [-236 ]TJ (of)Tj [-240 ]TJ (edges)Tj [-240 ]TJ (in)Tj 
/N10 1 Tf
8.90379 0 TD
(E)Tj 
/N9 1 Tf
0.85099 0 TD
(that)Tj [-240 ]TJ (are)Tj [-240 ]TJ (incident)Tj [-231 ]TJ (on)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 373.83898 668.37699 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 377.92399 668.37699 Tm
(;)Tj [-236 ]TJ (for)Tj 
/N10 1 Tf
1.91349 0 TD
(S)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 405.36898 668.37699 Tm
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 414.03698 668.37699 Tm
(E)Tj 
/N9 1 Tf
0.71148 0 TD
(,)Tj 
/N10 1 Tf
0.48078 0 TD
(x)Tj 
/N9 1 Tf
0.53849 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(S)Tj 
/N9 1 Tf
0.59629 0 TD
(\))Tj [-226 ]TJ (represents)Tj 
/N18 1 Tf
9.96199 0 0 9.96199 119.54899 656.42298 Tm
(\()Tj 
/N10 1 Tf
6.47599 0 0 5.97698 126.17399 654.92799 Tm
(j)Tj 
/N4 1 Tf
0.47689 0 TD
(\303)Tj 
/N10 1 Tf
0.89219 0 TD
(S)Tj 
10.36099 0 0 10.16198 141.71499 656.42298 Tm
(x)Tj 
6.47599 0 0 5.97698 146.34698 654.92799 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 149.13699 656.42298 Tm
(.)Tj [-332 ]TJ (For)Tj 
/N10 1 Tf
2.30279 0 TD
(S)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 181.61499 656.42298 Tm
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 191.32798 656.42298 Tm
(V)Tj 
/N9 1 Tf
0.61048 0 TD
(,)Tj 
/N10 1 Tf
0.58178 0 TD
(E)Tj 
/N9 1 Tf
0.71148 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(S)Tj 
/N9 1 Tf
0.59619 0 TD
(\))Tj [-332 ]TJ (refers)Tj [-322 ]TJ (to)Tj [-332 ]TJ (the)Tj [-322 ]TJ (set)Tj [-322 ]TJ (of)Tj [-332 ]TJ (edges)Tj [-327 ]TJ (in)Tj 
/N10 1 Tf
12.22119 0 TD
(E)Tj 
/N9 1 Tf
0.94219 0 TD
(with)Tj [-327 ]TJ (both)Tj [-327 ]TJ (endpoints)Tj [-322 ]TJ (in)Tj 
/N10 1 Tf
9.52409 0 TD
(S)Tj 
/N9 1 Tf
0.59609 0 TD
(.)Tj [-327 ]TJ (Then)Tj 
-33.13929 -1.17649 TD
(the)Tj 
/N10 1 Tf
1.51438 0 TD
(matching)Tj [-288 ]TJ (polytope)Tj 
/N9 1 Tf
7.74038 0 TD
(associated)Tj [-274 ]TJ (with)Tj 
/N10 1 Tf
6.45188 0 TD
(G)Tj 
/N9 1 Tf
1.01919 0 TD
(is)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 356.15599 623.44599 Tm
(E)Tj 
10.36099 0 0 10.16198 241.03999 619.46099 Tm
(P)Tj 
/N9 1 Tf
0.91349 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
0.28799 Tc
(\):)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 272.67098 619.46099 Tm
0 Tc
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 283.57899 619.46099 Tm
(conv)Tj [-96 ]TJ ({)Tj 
/N10 1 Tf
2.61059 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(\))Tj 
/N6 1 Tf
9.96199 0 0 9.96199 337.27598 619.46099 Tm
(>)Tj 
/N8 1 Tf
1.13009 0 TD
(Z)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 361.08699 619.46099 Tm
0.09599 Tc
(}.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 247.36599 617.96699 Tm
0 Tc
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 594.35598 Tm
(Edmonds)Tj [-293 ]TJ (\()Tj [-96 ]TJ (1965)Tj [-96 ]TJ (\))Tj [-293 ]TJ (proved)Tj [-298 ]TJ (that)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 281.28799 569.25199 Tm
(\203)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 287.26599 569.25199 Tm
(S)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 292.44499 569.25199 Tm
(\203)Tj 
/N4 1 Tf
0.79998 0 TD
(0)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 311.32499 569.25199 Tm
(1)Tj 
ET
281.28799 565.76499 35.21699 -0.49798 rf
BT
/N10 1 Tf
10.36099 0 0 10.16198 132.94799 562.27799 Tm
(P)Tj 
/N9 1 Tf
0.91349 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 161.73999 562.27799 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 179.82099 562.27799 Tm
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 187.39299 562.27799 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 198.30198 562.27799 Tm
(P)Tj 
/N9 1 Tf
0.70658 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
0.28799 Tc
(\):)Tj 
/N10 1 Tf
1.18258 0 TD
0 Tc
(x)Tj 
/N9 1 Tf
0.53858 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(E)Tj 
/N9 1 Tf
0.70669 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(S)Tj 
/N9 1 Tf
0.59619 0 TD
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 269.58299 562.27799 Tm
0 Tc
(\241)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 319.49398 562.27799 Tm
(,)Tj [-288 ]TJ (for)Tj [-288 ]TJ (all)Tj 
/N10 1 Tf
3.26919 0 TD
(S)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 361.53399 562.27799 Tm
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 370.80099 562.27799 Tm
(V)Tj 
/N9 1 Tf
0.89889 0 TD
(such)Tj [-288 ]TJ (that)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 420.46199 562.27799 Tm
(\203)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 426.43998 562.27799 Tm
(S)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 431.62098 562.27799 Tm
(\203)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 439.59098 562.27799 Tm
(is)Tj [-288 ]TJ (odd)Tj [-981 ]TJ (.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 139.27398 560.78399 Tm
(I)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 172.64799 559.78698 Tm
10.29199 Tc
(HJ)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 296.28099 555.30398 Tm
0 Tc
(2)Tj 
-16.05758 -2.47059 TD
(Instead)Tj [-288 ]TJ (of)Tj 
/N10 1 Tf
4.30279 0 TD
(P)Tj 
/N9 1 Tf
0.71159 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(\))Tj [-293 ]TJ (and)Tj 
/N10 1 Tf
2.36538 0 TD
(P)Tj 
6.47599 0 0 5.97698 225.59899 528.70498 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 228.73699 530.19898 Tm
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(\))Tj [-96 ]TJ (,)Tj [-293 ]TJ (we)Tj [-298 ]TJ (will)Tj [-284 ]TJ (deal)Tj [-293 ]TJ (with)Tj [-288 ]TJ (the)Tj [-293 ]TJ (related)Tj [-284 ]TJ (cones)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 253.69198 509.07899 Tm
(E)Tj 
/N6 1 Tf
0.60778 0 TD
(<)Tj 
/N9 1 Tf
0.83079 0 TD
0.09899 Tc
({0})Tj 
/N10 1 Tf
10.36099 0 0 10.16198 198.05299 505.09399 Tm
0 Tc
(P)Tj 
/N9 1 Tf
0.89889 0 TD
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 210.20698 505.09399 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 221.11499 505.09399 Tm
({)Tj 
/N10 1 Tf
0.57199 0 TD
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 234.61499 505.09399 Tm
(\303)Tj 
/N8 1 Tf
1.09498 0 TD
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 273.71699 505.09399 Tm
(:)Tj 
/N10 1 Tf
0.5625 0 TD
(x)Tj 
/N9 1 Tf
0.53849 0 TD
(\()Tj 
/N22 1 Tf
9.96199 0 0 9.96199 289.55599 505.09399 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 295.23599 505.09399 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 299.66799 505.09399 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 304.74899 505.09399 Tm
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 315.60798 505.09399 Tm
0 Tc
(\241)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 327.31399 505.09399 Tm
(x)Tj 
/N9 1 Tf
0.85099 0 TD
(,)Tj 
/N11 1 Tf
9.96199 0 0 9.96199 341.70999 505.09399 Tm
(")Tj 
/N19 1 Tf
0.70999 0 TD
(\243)Tj 
/N4 1 Tf
0.70999 0 TD
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 366.76499 505.09399 Tm
(V)Tj 
/N9 1 Tf
0.61068 0 TD
(,)Tj 
/N10 1 Tf
0.53849 0 TD
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 386.24198 505.09399 Tm
(\242)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 397.94799 505.09399 Tm
0.09599 Tc
(0},)Tj 
6.47599 0 0 5.97698 331.89599 503.59899 Tm
0 Tc
(0)Tj 
/N10 1 Tf
-0.16918 -3.28349 TD
(E)Tj 
/N6 1 Tf
0.60778 0 TD
(<)Tj 
/N9 1 Tf
0.83059 0 TD
0.09899 Tc
({0})Tj 
/N10 1 Tf
10.36099 0 0 10.16198 251.84899 479.98699 Tm
0 Tc
(P)Tj 
/N9 1 Tf
1.10569 0 TD
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 266.14498 479.98699 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 277.05398 479.98699 Tm
(conv)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.46629 0 TD
(P)Tj 
/N6 1 Tf
9.96199 0 0 9.96199 311.92298 479.98699 Tm
(>)Tj 
/N8 1 Tf
1.12989 0 TD
(Z)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 351.82099 479.98699 Tm
0.09599 Tc
(\).)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 258.17498 478.49299 Tm
0 Tc
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 454.88299 Tm
(We)Tj [-274 ]TJ (suppressed)Tj [-274 ]TJ (the)Tj [-274 ]TJ (reference)Tj [-269 ]TJ (to)Tj [-274 ]TJ (the)Tj [-264 ]TJ (graph)Tj 
/N10 1 Tf
16.88929 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(,)Tj [-269 ]TJ (since)Tj [-269 ]TJ (for)Tj [-269 ]TJ (the)Tj [-264 ]TJ (most)Tj [-260 ]TJ (part)Tj [-260 ]TJ (of)Tj [-264 ]TJ (the)Tj [-264 ]TJ (paper,)Tj [-260 ]TJ (we)Tj [-250 ]TJ (will)Tj 
-17.70658 -1.17649 TD
(deal)Tj [-389 ]TJ (only)Tj [-394 ]TJ (with)Tj [-394 ]TJ (cliques)Tj [-385 ]TJ (on)Tj [-389 ]TJ (an)Tj [-394 ]TJ (odd)Tj [-394 ]TJ (number)Tj [-385 ]TJ (of)Tj [-394 ]TJ (nodes.)Tj [-389 ]TJ (From)Tj [-385 ]TJ (now)Tj [-394 ]TJ (on,)Tj 
/N10 1 Tf
28.18739 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.93269 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 437.19999 442.92799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 449.20399 442.92799 Tm
0.09599 Tc
(1\),)Tj 
/N10 1 Tf
1.66839 0 TD
0 Tc
(P)Tj 
6.47599 0 0 5.97698 472.81498 441.43399 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 476.00299 442.92799 Tm
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 430.97299 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.55699 430.97299 Tm
(1)Tj [-96 ]TJ (\))Tj [-298 ]TJ (refer)Tj [-298 ]TJ (to)Tj [-298 ]TJ (the)Tj [-298 ]TJ (cones)Tj 
/N10 1 Tf
8.57688 0 TD
(P)Tj 
/N9 1 Tf
0.90869 0 TD
(and)Tj 
/N10 1 Tf
1.74038 0 TD
(P)Tj 
6.47599 0 0 5.97698 253.19299 429.47898 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 258.42399 430.97299 Tm
(de\256ned)Tj [-298 ]TJ (by)Tj [-303 ]TJ (the)Tj [-298 ]TJ (clique)Tj [-293 ]TJ (on)Tj [-298 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
11.02888 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 380.41398 430.97299 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 391.47299 430.97299 Tm
(1)Tj [-96 ]TJ (\))Tj [-303 ]TJ (nodes.)Tj [-298 ]TJ (We)Tj [-298 ]TJ (will)Tj [-288 ]TJ (refer)Tj 
-26.24519 -1.17649 TD
(to)Tj [-298 ]TJ (the)Tj [-288 ]TJ (edge)Tj [-298 ]TJ (set)Tj [-288 ]TJ (of)Tj [-293 ]TJ (a)Tj [-298 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
8.96629 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 220.11898 419.01899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 231.12799 419.01899 Tm
(1)Tj [-96 ]TJ (\))Tj [-298 ]TJ (clique)Tj [-288 ]TJ (as)Tj 
/N10 1 Tf
5.08169 0 TD
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 290.10499 417.52398 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79978 0 TD
(1)Tj 
10.36099 0 0 10.16198 305.64498 419.01899 Tm
(.)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 393.91198 Tm
(3.)Tj [-1000 ]TJ (Lova)Tj 
3.5 0 TD
(\302)Tj [-84 ]TJ (sz-Schrijver)Tj [-365 ]TJ (procedure.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 280.19299 393.91198 Tm
(We)Tj [-361 ]TJ (present)Tj [-356 ]TJ (a)Tj [-361 ]TJ (brief)Tj [-361 ]TJ (description)Tj [-356 ]TJ (of)Tj [-351 ]TJ (one)Tj [-361 ]TJ (of)Tj [-361 ]TJ (the)Tj [-356 ]TJ (pro-)Tj 
-15.50479 -1.17649 TD
(cedures)Tj [-312 ]TJ (proposed)Tj [-317 ]TJ (by)Tj [-317 ]TJ (Lova)Tj 
10.33648 0 TD
(\302)Tj [-52 ]TJ (s)Tj [0 ]TJ (z)Tj [-317 ]TJ (and)Tj [-317 ]TJ (Schrijver.)Tj [-317 ]TJ (Let)Tj 
/N10 1 Tf
9.17298 0 TD
(K)Tj 
/N6 1 Tf
9.96199 0 0 9.96199 331.84799 381.95698 Tm
(,)Tj 
/N8 1 Tf
1.15998 0 TD
(R)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 351.62298 385.94198 Tm
(d)Tj 
/N4 1 Tf
0.5 0 TD
(/)Tj 
/N9 1 Tf
0.89228 0 TD
(1)Tj 
10.36099 0 0 10.16198 367.16299 381.95698 Tm
(denote)Tj [-312 ]TJ (a)Tj [-322 ]TJ (polyhedral)Tj [-312 ]TJ (cone)Tj [-317 ]TJ (ob-)Tj 
-23.89889 -1.17649 TD
(tained)Tj [-260 ]TJ (from)Tj [-255 ]TJ (a)Tj [-255 ]TJ (polyhedron)Tj [-260 ]TJ (in)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 238.20098 370.00299 Tm
(R)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 246.36999 373.98799 Tm
(d)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 252.29798 370.00299 Tm
(via)Tj [-260 ]TJ (homogenization)Tj [-255 ]TJ (using)Tj [-255 ]TJ (the)Tj [-245 ]TJ (new)Tj [-250 ]TJ (variable)Tj 
/N10 1 Tf
17.45188 0 TD
(x)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 437.74699 368.50799 Tm
(0)Tj 
10.36099 0 0 10.16198 441.98098 370.00299 Tm
(.)Tj 
/N10 1 Tf
0.49519 0 TD
(K)Tj 
6.47599 0 0 5.97698 453.98699 368.50799 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 458.61898 370.00299 Tm
(denotes)Tj 
-32.72599 -1.17649 TD
(the)Tj [-418 ]TJ (cone)Tj [-423 ]TJ (generated)Tj [-423 ]TJ (by)Tj [-423 ]TJ (all)Tj [-418 ]TJ (0-1)Tj [-423 ]TJ (vectors)Tj [-418 ]TJ (of)Tj 
/N10 1 Tf
17.41819 0 TD
(K)Tj 
/N9 1 Tf
0.76449 0 TD
(.)Tj [-423 ]TJ (The)Tj [-423 ]TJ (cone)Tj [-418 ]TJ (generated)Tj [-418 ]TJ (by)Tj [-418 ]TJ (all)Tj [-418 ]TJ (0-1)Tj [-418 ]TJ (vectors)Tj 
/N10 1 Tf
17.14408 0 TD
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 346.09298 Tm
(\303)Tj 
/N8 1 Tf
1.10499 0 TD
(R)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 138.72599 350.07798 Tm
(d)Tj 
/N4 1 Tf
0.5 0 TD
(/)Tj 
/N9 1 Tf
0.89228 0 TD
(1)Tj 
10.36099 0 0 10.16198 154.06799 346.09298 Tm
(with)Tj 
/N10 1 Tf
2.06729 0 TD
(x)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 180.06999 344.59799 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 186.39599 346.09298 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 197.40399 346.09298 Tm
(1)Tj [-298 ]TJ (i)Tj [0 ]TJ (s)Tj [-288 ]TJ (called)Tj 
/N10 1 Tf
4.42799 0 TD
(Q)Tj 
/N9 1 Tf
0.81729 0 TD
(.)Tj 
-11.75959 -1.17649 TD
(Now,)Tj [-288 ]TJ (we)Tj [-288 ]TJ (de\256ne)Tj [-279 ]TJ (the)Tj [-284 ]TJ (lifting)Tj [-284 ]TJ (and)Tj [-284 ]TJ (projection)Tj [-279 ]TJ (operations.)Tj [-279 ]TJ (In)Tj [-279 ]TJ (what)Tj [-279 ]TJ (follows,)Tj 
/N10 1 Tf
28.50479 0 TD
(e)Tj 
6.47599 0 0 5.97698 429.87799 332.64399 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 434.45999 334.13798 Tm
(is)Tj [-264 ]TJ (the)Tj 
/N10 1 Tf
2.41828 0 TD
(j)Tj 
/N9 1 Tf
0.37489 0 TD
(th)Tj [-260 ]TJ (unit)Tj 
-33.18739 -1.17649 TD
(vector)Tj [-279 ]TJ (and)Tj 
/N10 1 Tf
4.5 0 TD
(e)Tj 
/N9 1 Tf
0.72119 0 TD
(is)Tj [-274 ]TJ (the)Tj [-279 ]TJ (vector)Tj [-274 ]TJ (of)Tj [-279 ]TJ (all)Tj [-274 ]TJ (ones.)Tj [-279 ]TJ (The)Tj [-274 ]TJ (sizes)Tj [-269 ]TJ (of)Tj 
/N10 1 Tf
15.11059 0 TD
(e)Tj 
/N9 1 Tf
0.71618 0 TD
(and)Tj 
/N10 1 Tf
1.71638 0 TD
(e)Tj 
6.47599 0 0 5.97698 359.99099 320.68899 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 364.62399 322.18299 Tm
(will)Tj [-269 ]TJ (be)Tj [-269 ]TJ (clear)Tj [-264 ]TJ (from)Tj [-260 ]TJ (the)Tj [-260 ]TJ (context.)Tj 
/N10 1 Tf
-23.65379 -1.17649 TD
(K)Tj 
/N9 1 Tf
0.75959 0 TD
(*,)Tj 
/N10 1 Tf
1.04809 0 TD
(Q)Tj 
/N9 1 Tf
0.81729 0 TD
(*)Tj [-298 ]TJ (are)Tj [-293 ]TJ (the)Tj [-288 ]TJ (dual)Tj [-293 ]TJ (cones)Tj [-293 ]TJ (of)Tj 
/N10 1 Tf
9.53849 0 TD
(K)Tj 
/N9 1 Tf
0.96148 0 TD
(and)Tj 
/N10 1 Tf
1.74038 0 TD
(Q)Tj 
/N9 1 Tf
1.01919 0 TD
(under)Tj [-298 ]TJ (the)Tj [-288 ]TJ (standard)Tj [-288 ]TJ (Euclidean)Tj [-284 ]TJ (inner-product.)Tj [-284 ]TJ (e.g.,)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 286.41899 289.10899 Tm
(d)Tj 
/N4 1 Tf
0.5 0 TD
(/)Tj 
/N9 1 Tf
0.89219 0 TD
(1)Tj 
/N10 1 Tf
2.26168 0 TD
(T)Tj 
10.36099 0 0 10.16198 224.65199 285.12399 Tm
(K)Tj 
/N9 1 Tf
0.75949 0 TD
0.28799 Tc
(*:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 243.53099 285.12399 Tm
0 Tc
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 254.43899 285.12399 Tm
({)Tj 
/N10 1 Tf
0.57218 0 TD
(s)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 267.34098 285.12399 Tm
(\303)Tj 
/N8 1 Tf
1.09489 0 TD
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 298.67199 285.12399 Tm
(:)Tj 
/N10 1 Tf
0.5625 0 TD
0.44099 Tc
(xs)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 320.63999 285.12399 Tm
0 Tc
(\242)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 332.34599 285.12399 Tm
(0,)Tj 
/N11 1 Tf
9.96199 0 0 9.96199 343.10398 285.12399 Tm
(")Tj 
/N10 1 Tf
10.36099 0 0 10.16198 351.17498 285.12399 Tm
(x)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 358.74598 285.12399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 369.65399 285.12399 Tm
(K)Tj 
/N9 1 Tf
0.75968 0 TD
0.09599 Tc
(}.)Tj 
-23.89898 -1.82348 TD
0 Tc
(D)Tj 
7.96998 0 0 7.47198 137.37998 266.59399 Tm
(EFINITION)Tj 
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8.26899 0 0 8.06999 203.92999 83.68399 Tm
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(F)Tj 
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(IGURE)Tj 
8.26899 0 0 8.06999 230.33099 83.68399 Tm
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15.51199 0 TD
(k)Tj 
/N4 1 Tf
7.96998 0 0 7.96998 364.67298 83.68399 Tm
(/)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 373.44099 83.68399 Tm
(3)Tj [-96 ]TJ (\))Tj [-295 ]TJ (clique.)Tj 
6.47599 0 0 5.97698 279.89399 697.36799 Tm
(2)Tj 
/N10 1 Tf
10.39228 0 TD
(d)Tj 
10.36099 0 0 10.16198 217.03099 693.38299 Tm
(K)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 226.89399 693.38299 Tm
(\266)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 236.15899 693.38299 Tm
(N)Tj 
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(\()Tj 
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(K)Tj 
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(\))Tj 
/N20 1 Tf
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(\266)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 272.02198 693.38299 Tm
(N)Tj 
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(\()Tj 
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0.42779 0 TD
(K)Tj 
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(\))Tj 
/N20 1 Tf
9.96199 0 0 9.96199 302.85699 693.38299 Tm
(\266)Tj 
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(\264\264\264)Tj 
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(\266)Tj 
/N10 1 Tf
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(N)Tj 
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(\()Tj 
/N10 1 Tf
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(K)Tj 
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0.75959 0 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 370.15199 693.38299 Tm
(\201)Tj 
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(K)Tj 
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6.47599 0 0 5.97698 387.93499 691.88899 Tm
(I)Tj 
10.36099 0 0 10.16198 119.54899 668.07798 Tm
(and)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 280.54098 646.75898 Tm
(2)Tj 
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10.68449 0 TD
(d)Tj 
10.36099 0 0 10.16198 212.54798 642.77398 Tm
(K)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 222.41099 642.77398 Tm
(\266)Tj 
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10.36099 0 0 10.16198 231.67599 642.77398 Tm
(N)Tj 
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1.25479 0 TD
(\()Tj 
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0.42788 0 TD
(K)Tj 
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(\))Tj 
/N20 1 Tf
9.96199 0 0 9.96199 263.40499 642.77398 Tm
(\266)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 272.67098 642.77398 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(K)Tj 
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0.75959 0 TD
(\))Tj 
/N20 1 Tf
9.96199 0 0 9.96199 305.39599 642.77398 Tm
(\266)Tj 
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0.93009 0 TD
(\264\264\264)Tj 
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1.79998 0 TD
(\266)Tj 
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10.36099 0 0 10.16198 341.85899 642.77398 Tm
(N)Tj 
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1.35108 0 TD
(\()Tj 
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0.42779 0 TD
(K)Tj 
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0.75959 0 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 374.58599 642.77398 Tm
(\201)Tj 
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(K)Tj 
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(.)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 238.54998 641.27999 Tm
5.68998 Tc
(//)Tj [-4199 ]TJ (/)Tj 
/N10 1 Tf
23.75379 0 TD
0 Tc
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 617.46899 Tm
(Lova)Tj 
1.66828 0 TD
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(\()Tj [-96 ]TJ (iii)Tj 
/N7 1 Tf
9.96199 0 0 9.96199 143.95698 605.51399 Tm
(*)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 148.28999 605.51399 Tm
(\))Tj 
/N10 1 Tf
0.83169 0 TD
(Ye)Tj 
6.47599 0 0 5.97698 167.26799 604.01899 Tm
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 172.94699 605.51399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 183.95498 605.51399 Tm
(K)Tj 
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0.96148 0 TD
(for)Tj [-293 ]TJ (all)Tj 
/N10 1 Tf
2.75009 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 228.33799 605.51399 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 239.34698 605.51399 Tm
0.25 Tc
({)Tj [154 ]TJ (0)Tj [250 ]TJ (,)Tj [-43 ]TJ (1)Tj [250 ]TJ (,)Tj [-48 ]TJ (...,)Tj 
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4.71629 0 TD
0 Tc
(d)Tj 
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0.59619 0 TD
(})Tj [-293 ]TJ (and)Tj 
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2.51429 0 TD
(Y)Tj 
/N9 1 Tf
0.75009 0 TD
(\()Tj 
/N10 1 Tf
0.52389 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 338.27198 604.01899 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 344.49899 605.51399 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 355.50799 605.51399 Tm
(e)Tj 
6.47599 0 0 5.97698 360.09098 604.01899 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 363.87699 605.51399 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 370.40098 605.51399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 381.40998 605.51399 Tm
(K)Tj 
/N9 1 Tf
0.96148 0 TD
(for)Tj [-293 ]TJ (all)Tj 
/N10 1 Tf
2.75 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 425.79199 605.51399 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 436.80099 605.51399 Tm
0.25 Tc
({)Tj [250 ]TJ (1)Tj [250 ]TJ (,)Tj [-43 ]TJ (...,)Tj 
/N10 1 Tf
3.57209 0 TD
0 Tc
(d)Tj 
/N9 1 Tf
0.59609 0 TD
0.09599 Tc
(}.)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 580.10998 Tm
0 Tc
(4.)Tj [-1000 ]TJ (Construction)Tj [-265 ]TJ (of)Tj [-260 ]TJ (fractional)Tj [-255 ]TJ (points)Tj [-255 ]TJ (for)Tj [-255 ]TJ (semide\256nite)Tj [-245 ]TJ (liftings.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 399.78999 580.10998 Tm
(We)Tj [-245 ]TJ (turn)Tj [-245 ]TJ (to)Tj [-240 ]TJ (the)Tj [-231 ]TJ (match-)Tj 
-27.04798 -1.17649 TD
(ing)Tj [-231 ]TJ (polytope)Tj 
/N10 1 Tf
5.23559 0 TD
(P)Tj 
6.47599 0 0 5.97698 180.11999 566.65998 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 184.65299 568.15499 Tm
(and)Tj [-231 ]TJ (its)Tj [-221 ]TJ (relaxation)Tj 
/N10 1 Tf
7.06239 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
(.)Tj [-226 ]TJ (Consider)Tj [-216 ]TJ (the)Tj [-216 ]TJ (matching)Tj [-221 ]TJ (polytope)Tj [-216 ]TJ (of)Tj [-216 ]TJ (a)Tj [-212 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
16.03858 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 438.14498 568.15499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 448.30799 568.15499 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (-clique.)Tj 
-31.73078 -1.17649 TD
(Let)Tj [-245 ]TJ (Inc)Tj [-96 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
3.87979 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 166.91999 556.19999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 177.42999 556.19999 Tm
(1)Tj [-96 ]TJ (\))Tj [-250 ]TJ (denote)Tj [-245 ]TJ (the)Tj [-250 ]TJ (set)Tj [-245 ]TJ (of)Tj [-250 ]TJ (all)Tj [-245 ]TJ (pairs)Tj [-240 ]TJ ({)Tj 
/N10 1 Tf
12.00959 0 TD
(i)Tj 
/N9 1 Tf
0.37019 0 TD
(,)Tj 
/N10 1 Tf
0.49519 0 TD
(j)Tj 
/N9 1 Tf
0.37489 0 TD
0.09599 Tc
(},)Tj 
/N10 1 Tf
1.07209 0 TD
0 Tc
(i)Tj 
/N28 1 Tf
9.96199 0 0 9.96199 331.19999 556.19999 Tm
(x)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 341.66099 556.19999 Tm
(j)Tj 
/N9 1 Tf
0.51919 0 TD
(such)Tj [-245 ]TJ (that)Tj [-236 ]TJ (the)Tj [-240 ]TJ (edges)Tj 
/N10 1 Tf
7.78849 0 TD
(i)Tj 
/N9 1 Tf
0.375 0 TD
(,)Tj 
/N10 1 Tf
0.48548 0 TD
(j)Tj 
/N9 1 Tf
0.50968 0 TD
(are)Tj [-226 ]TJ (incident)Tj 
-31.11538 -1.17649 TD
(on)Tj [-298 ]TJ (the)Tj [-293 ]TJ (same)Tj [-288 ]TJ (node)Tj [-298 ]TJ (of)Tj [-293 ]TJ (the)Tj [-293 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
10.96629 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 240.84098 544.24499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 251.84899 544.24499 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (-clique.)Tj 
-11.76919 -1.17649 TD
(Given)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 158.25299 532.28999 Tm
(\243)Tj 
/N4 1 Tf
0.71998 0 TD
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 224.00498 532.28999 Tm
(for)Tj 
/N10 1 Tf
1.46148 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 245.07499 532.28999 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 256.08299 532.28999 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 262.40899 530.79598 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79249 0 TD
(3)Tj 
10.36099 0 0 10.16198 279.94299 532.28999 Tm
(we)Tj [-293 ]TJ (de\256ne)Tj 
/N10 1 Tf
4.19699 0 TD
(w)Tj 
6.47599 0 0 5.97698 331.34899 536.27499 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 334.13798 532.28999 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 338.57199 532.28999 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 343.65299 532.28999 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 350.12899 532.28999 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 405.76799 532.28999 Tm
(as)Tj [-293 ]TJ (follows.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 184.60299 536.27499 Tm
(E)Tj 
/N6 1 Tf
2.46919 0 TD
(<)Tj 
/N9 1 Tf
0.93058 0 TD
0.09899 Tc
({0})Tj 
/N10 1 Tf
25.12319 0 TD
0 Tc
(E)Tj 
/N6 1 Tf
2.46919 0 TD
(<)Tj 
/N9 1 Tf
0.93058 0 TD
0.09899 Tc
({0})Tj 
5.17999 0 0 4.78199 189.03698 535.07998 Tm
0 Tc
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44209 0 TD
(/)Tj 
/N9 1 Tf
0.78869 0 TD
(1)Tj 
33.92289 0 TD
(2)Tj 
/N10 1 Tf
0.50019 0 TD
(k)Tj 
/N4 1 Tf
0.44209 0 TD
(/)Tj 
/N9 1 Tf
0.78849 0 TD
(3)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 176.43399 532.28999 Tm
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 218.32499 532.28999 Tm
(,)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 361.13699 532.28999 Tm
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 268.38598 506.88598 Tm
1.12998 Tc
(1i)Tj [1130 ]TJ (f)Tj 
/N10 1 Tf
2.52398 0 TD
0 Tc
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 300.36599 506.88598 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 311.27499 506.88598 Tm
0.28799 Tc
(0o)Tj [288 ]TJ (r)Tj 
/N10 1 Tf
1.90859 0 TD
0 Tc
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 336.87799 506.88598 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 347.78698 506.88598 Tm
(i)Tj 
/N9 1 Tf
0.27398 0 TD
(;)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 228.28698 492.93899 Tm
(i)Tj 
10.36099 0 0 10.16198 220.41799 488.95399 Tm
(w)Tj 
/N9 1 Tf
1.02879 0 TD
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 235.50999 488.95399 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 240.59199 488.95399 Tm
0.28799 Tc
(\):)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 249.85699 488.95399 Tm
0 Tc
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 268.38598 488.95399 Tm
1.12998 Tc
(0i)Tj [1130 ]TJ (f)Tj [842 ]TJ ({)Tj 
/N10 1 Tf
3.09629 0 TD
0 Tc
(i)Tj 
/N9 1 Tf
0.37019 0 TD
(,)Tj 
/N10 1 Tf
0.53839 0 TD
(j)Tj 
/N9 1 Tf
0.37019 0 TD
(})Tj 
/N4 1 Tf
9.96199 0 0 9.96199 321.63598 488.95399 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 332.54399 488.95399 Tm
0.09599 Tc
(I)Tj [96 ]TJ (n)Tj [96 ]TJ (c\(2)Tj 
/N10 1 Tf
2.29818 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 363.92498 488.95399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 374.83499 488.95399 Tm
0.09599 Tc
(3\);)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 228.28698 487.45899 Tm
0 Tc
(j)Tj 
/N21 1 Tf
29.88699 0 0 43.03799 260.76599 477.39799 Tm
(5)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 268.38598 471.02099 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 285.27299 471.02099 Tm
(otherwise.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 272.47198 469.52699 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 444.12298 Tm
(Note)Tj [-212 ]TJ (that)Tj [-202 ]TJ (\256xing)Tj [-207 ]TJ (any)Tj [-207 ]TJ (edge)Tj 
/N10 1 Tf
10.13938 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 229.58399 444.12298 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 239.64599 444.12298 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 245.97099 442.62799 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44628 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 261.46299 444.12298 Tm
(,)Tj [-207 ]TJ (throwing)Tj [-207 ]TJ (away)Tj [-202 ]TJ (all)Tj [-202 ]TJ (the)Tj [-197 ]TJ (edges)Tj [-197 ]TJ (incident)Tj [-192 ]TJ (on)Tj [-192 ]TJ (some)Tj [-183 ]TJ (endpoint)Tj 
-13.69709 -1.17649 TD
(of)Tj 
/N10 1 Tf
1.12979 0 TD
(i)Tj 
/N9 1 Tf
0.37489 0 TD
(,)Tj [-293 ]TJ (uniquely)Tj [-288 ]TJ (identi\256es)Tj [-279 ]TJ (a)Tj [-293 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
9.94239 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 245.82199 432.16799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 256.82998 432.16799 Tm
(1)Tj [-96 ]TJ (\))Tj [-293 ]TJ (clique.)Tj [-288 ]TJ (Figure)Tj [-288 ]TJ (1)Tj [-298 ]TJ (represents)Tj [-279 ]TJ (the)Tj [-293 ]TJ (vector)Tj 
/N10 1 Tf
16.53849 0 TD
(w)Tj 
6.47599 0 0 5.97698 436.10398 436.15299 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 438.89299 432.16799 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 443.32699 432.16799 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 448.40798 432.16799 Tm
(\))Tj [-288 ]TJ (for)Tj 
-13.375 -2.5 TD
(1)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 263.40499 399.29199 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 270.47898 399.29199 Tm
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 273.31799 399.29199 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 343.65299 399.29199 Tm
(.)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 284.22599 396.80099 Tm
1.57998 Tc
(SD)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 291.39999 391.81999 Tm
0.09599 Tc
(\(1/\(2)Tj 
/N10 1 Tf
2.32199 0 TD
0 Tc
(k)Tj 
/N9 1 Tf
0.53858 0 TD
0.09599 Tc
(\)\))Tj 
/N10 1 Tf
0.75949 0 TD
0 Tc
(e)Tj 
/N9 1 Tf
-20.20658 -2.5 TD
(When)Tj [-298 ]TJ (we)Tj [-293 ]TJ (refer)Tj [-293 ]TJ (to)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 196.15899 366.41598 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 200.24398 366.41598 Tm
(,)Tj [-298 ]TJ (i)Tj [0 ]TJ (t)Tj [-288 ]TJ (will)Tj [-288 ]TJ (be)Tj [-293 ]TJ (clear)Tj [-288 ]TJ (from)Tj [-293 ]TJ (the)Tj [-293 ]TJ (context)Tj [-284 ]TJ (what)Tj [-293 ]TJ (the)Tj [-293 ]TJ (corresponding)Tj 
/N10 1 Tf
23.44219 0 TD
(k)Tj 
/N9 1 Tf
0.74049 0 TD
(is.)Tj 
-30.97119 -1.84298 TD
(L)Tj 
7.96998 0 0 7.47198 136.23599 347.68798 Tm
(EMMA)Tj 
10.36099 0 0 10.16198 166.02198 347.68798 Tm
(4.1.)Tj 
/N10 1 Tf
2.59619 0 TD
(Let)Tj [-279 ]TJ (r)Tj [-279 ]TJ (b)Tj [0 ]TJ (e)Tj [-284 ]TJ (a)Tj [-284 ]TJ (nonnegative)Tj [-284 ]TJ (integer)Tj 
/N9 1 Tf
12.33659 0 TD
(.)Tj 
/N10 1 Tf
0.53369 0 TD
(If)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 335.48399 347.68798 Tm
(\243)Tj 
/N4 1 Tf
0.69999 0 TD
4.68998 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 407.90998 347.68798 Tm
0.09599 Tc
(1\)\))Tj 
/N10 1 Tf
1.63938 0 TD
0 Tc
(and)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 443.32699 347.68798 Tm
(\243)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 447.41099 346.19299 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 453.53799 347.68798 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 464.34698 347.68798 Tm
(1)Tj 
/N10 1 Tf
0.77389 0 TD
(then)Tj 
6.47599 0 0 5.97698 361.83399 351.67298 Tm
(r)Tj 
10.36099 0 0 10.16198 353.96299 347.68798 Tm
(N)Tj 
/N9 1 Tf
1.35108 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 361.83399 346.19299 Tm
(/)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 119.54899 335.73298 Tm
(w)Tj 
6.47599 0 0 5.97698 127.41899 339.71798 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.20899 335.73298 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 134.69198 335.73298 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 139.77198 335.73298 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 146.24798 335.73298 Tm
4.72999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 212.29899 335.73298 Tm
0.09599 Tc
(3\)\))Tj 
/N10 1 Tf
1.84619 0 TD
0 Tc
(for)Tj [-288 ]TJ (every)Tj [-288 ]TJ (i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 277.84999 335.73298 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 288.85998 335.73298 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 295.18499 334.23899 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44628 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 310.67698 335.73298 Tm
(.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 166.12298 339.71798 Tm
(r)Tj 
10.36099 0 0 10.16198 158.25299 335.73298 Tm
(N)Tj 
/N9 1 Tf
1.35089 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09498 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 166.12298 334.23899 Tm
(/)Tj 
ET
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1 g
/N13 /ExtGState findRes gsDI

119.54899 725.26298 370.60099 -19.92498 rf
119.54899 67.24598 370.60099 -23.90998 rf
119.54899 705.33799 370.60099 -621.65399 rf
BT
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 717.29299 Tm
0 g
0 Tc
0 Tw
(4)Tj 
7.17298 0 0 6.67498 249.45698 717.29299 Tm
0.06898 Tc
(T.)Tj [-500 ]TJ (STEPHEN)Tj [-459 ]TJ (AND)Tj [-486 ]TJ (L.)Tj [-493 ]TJ (TUNC)Tj 
13.61819 0 TD
0.23399 Tc
(\313E)Tj [165 ]TJ (L)Tj 
8.26899 0 0 8.06999 140.12098 47.32099 Tm
1 g
0.05999 Tc
(/)Tj [-247 ]TJ (3907)Tj [-494 ]TJ (no38)Tj [-500 ]TJ (Mp)Tj [-1000 ]TJ (4)Tj [-1000 ]TJ (Monday)Tj [-488 ]TJ (Mar)Tj [-494 ]TJ (08)Tj [-500 ]TJ (03:24)Tj [-500 ]TJ (PM)Tj [-1000 ]TJ (INF\261MOR)Tj [-1000 ]TJ (no38)Tj 
10.36099 0 0 10.16198 129.90998 693.38299 Tm
0 g
0 Tc
(P)Tj 
7.96998 0 0 7.47198 135.63699 693.38299 Tm
(ROOF)Tj 
10.36099 0 0 10.16198 157.90399 693.38299 Tm
(.)Tj [-1000 ]TJ (W)Tj [0 ]TJ (e)Tj [-245 ]TJ (prove)Tj [-250 ]TJ (the)Tj [-250 ]TJ (statement)Tj [-240 ]TJ (by)Tj [-245 ]TJ (induction)Tj [-245 ]TJ (on)Tj 
/N10 1 Tf
17.46629 0 TD
(r)Tj 
/N9 1 Tf
0.48568 0 TD
(.)Tj [-240 ]TJ (For)Tj 
/N10 1 Tf
2.12019 0 TD
(r)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 372.34498 693.38299 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 382.75498 693.38299 Tm
(0,)Tj [-240 ]TJ (consider)Tj [-231 ]TJ (the)Tj [-226 ]TJ (constraints)Tj 
-25.40379 -1.17649 TD
(de\256ning)Tj 
/N10 1 Tf
3.54798 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.93269 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 180.71699 681.42799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 191.47698 681.42799 Tm
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-274 ]TJ (Setting)Tj 
/N10 1 Tf
4.65859 0 TD
(x)Tj 
6.47599 0 0 5.97698 244.32798 679.93399 Tm
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 249.95599 681.42799 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 260.71598 681.42799 Tm
(1)Tj [-274 ]TJ (for)Tj [-274 ]TJ (some)Tj 
/N10 1 Tf
4.60089 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 314.06498 681.42799 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 324.82299 681.42799 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 331.14898 679.93399 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79249 0 TD
(3)Tj 
10.36099 0 0 10.16198 348.48399 681.42799 Tm
(forces)Tj 
/N10 1 Tf
2.70678 0 TD
(x)Tj 
6.47599 0 0 5.97698 381.11099 679.93399 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 385.69299 681.42799 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 396.40299 681.42799 Tm
(0)Tj [-269 ]TJ (for)Tj [-269 ]TJ (all)Tj 
/N10 1 Tf
3.47129 0 TD
(j)Tj 
/N9 1 Tf
0.53849 0 TD
(such)Tj [-264 ]TJ (that)Tj [-250 ]TJ ({)Tj 
/N10 1 Tf
4.42309 0 TD
(i)Tj 
/N9 1 Tf
0.375 0 TD
(,)Tj 
/N10 1 Tf
-35.52879 -1.17649 TD
(j)Tj 
/N9 1 Tf
0.37019 0 TD
(})Tj 
/N4 1 Tf
9.96199 0 0 9.96199 131.40299 669.47299 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 142.41198 669.47299 Tm
0.09599 Tc
(I)Tj [96 ]TJ (n)Tj [96 ]TJ (c\(2)Tj 
/N10 1 Tf
2.30279 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 173.94398 669.47299 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 184.95098 669.47299 Tm
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-298 ]TJ (The)Tj [-298 ]TJ (remaining)Tj [-293 ]TJ (variables)Tj [-293 ]TJ (have)Tj [-293 ]TJ (precisely)Tj [-288 ]TJ (the)Tj [-284 ]TJ (same)Tj [-279 ]TJ (constraints)Tj [-264 ]TJ (on)Tj [-269 ]TJ (them)Tj 
-6.31239 -1.17649 TD
(as)Tj [-293 ]TJ (those)Tj [-293 ]TJ (de\256ning)Tj 
/N10 1 Tf
7.10099 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 217.67799 657.51799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 228.63699 657.51799 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-293 ]TJ (Thus,)Tj [-293 ]TJ (for)Tj [-293 ]TJ (every)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 312.42098 657.51799 Tm
(\243)Tj 
/N4 1 Tf
0.71499 0 TD
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 330.50299 657.51799 Tm
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 355.05899 657.51799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 365.96899 657.51799 Tm
(1)Tj [-96 ]TJ (\))Tj [-288 ]TJ (and)Tj [-288 ]TJ (every)Tj 
/N10 1 Tf
5.45669 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 428.33299 657.51799 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 439.24099 657.51799 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 445.56799 656.02398 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44599 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 461.05899 657.51799 Tm
(,)Tj 
/N10 1 Tf
0.52879 0 TD
(w)Tj 
6.47599 0 0 5.97698 474.45899 661.50299 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 477.24798 657.51799 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 481.73098 657.51799 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 486.81199 657.51799 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 645.56399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 132.20098 645.56399 Tm
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 158.45199 645.56399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 171.10398 645.56399 Tm
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-457 ]TJ (The)Tj [-457 ]TJ (induction)Tj [-457 ]TJ (hypothesis)Tj [-447 ]TJ (is)Tj [-447 ]TJ (that)Tj [-447 ]TJ (if)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 345.44599 645.56399 Tm
(\243)Tj 
/N4 1 Tf
0.88499 0 TD
5.05999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 425.24499 645.56399 Tm
0 Tc
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-452 ]TJ (then)Tj 
/N10 1 Tf
3.98548 0 TD
(w)Tj 
6.47599 0 0 5.97698 474.45899 649.54798 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 477.24798 645.56399 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 481.68199 645.56399 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 486.76298 645.56399 Tm
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 375.68199 649.54798 Tm
(r)Tj 
10.36099 0 0 10.16198 367.81199 645.56399 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 375.68199 644.06898 Tm
(/)Tj 
9.96199 0 0 9.96199 119.54899 633.60899 Tm
4.72999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 185.59999 633.60899 Tm
0 Tc
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-298 ]TJ (for)Tj [-293 ]TJ (every)Tj 
/N10 1 Tf
5.63449 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 249.90699 633.60899 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 260.91398 633.60899 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 267.24099 632.11399 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44599 0 TD
(/)Tj 
/N9 1 Tf
0.80018 0 TD
(3)Tj 
10.36099 0 0 10.16198 282.78298 633.60899 Tm
(.)Tj [-293 ]TJ (Suppose)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 326.51799 633.60899 Tm
(\243)Tj 
/N4 1 Tf
0.71488 0 TD
5.35998 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 405.91799 633.60899 Tm
0.09599 Tc
(1\)\).)Tj [-197 ]TJ (S)Tj [96 ]TJ (o)Tj [96 ]TJ (,)Tj 
3.59199 0 TD
0 Tc
(there)Tj [-279 ]TJ (exists)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 139.42399 637.59399 Tm
(r)Tj 
33.02308 0 TD
(r)Tj 
/N4 1 Tf
0.48458 0 TD
(/)Tj 
/N9 1 Tf
0.79209 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 131.55299 633.60899 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
16.78199 Tc
(kN)Tj 
/N9 1 Tf
19.19219 0 TD
0 Tc
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 139.42399 632.11399 Tm
(/)Tj 
33.02308 0 TD
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 621.65399 Tm
(a)Tj [-437 ]TJ (symmetric,)Tj [-433 ]TJ (positive)Tj [-428 ]TJ (semide\256nite)Tj [-428 ]TJ (real)Tj [-433 ]TJ (matrix,)Tj 
/N10 1 Tf
19.91819 0 TD
(Y)Tj 
/N9 1 Tf
0.64898 0 TD
(,)Tj [-428 ]TJ (such)Tj [-428 ]TJ (that)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 383.05398 621.65399 Tm
(\243)Tj 
/N4 1 Tf
0.85488 0 TD
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 403.92599 621.65399 Tm
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 414.28599 620.15899 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 421.95599 621.65399 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 434.31098 621.65399 Tm
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.37489 0 TD
(Y)Tj 
/N9 1 Tf
0.75009 0 TD
0.09599 Tc
(\),)Tj 
/N10 1 Tf
1.09609 0 TD
0 Tc
(Ye)Tj 
6.47599 0 0 5.97698 488.40699 620.15899 Tm
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 609.69898 Tm
4.90998 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 188.28898 609.69898 Tm
0 Tc
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-385 ]TJ (for)Tj [-380 ]TJ (all)Tj 
/N10 1 Tf
4.66828 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 243.47999 609.69898 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 255.38598 609.69898 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 261.71199 608.20498 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79978 0 TD
(1)Tj 
/N6 1 Tf
9.96199 0 0 9.96199 280.24099 609.69898 Tm
(<)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 292.49598 609.69898 Tm
0.09599 Tc
({0},)Tj 
/N10 1 Tf
2.38449 0 TD
0 Tc
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\()Tj 
/N10 1 Tf
0.52879 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 334.98599 608.20498 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 342.20799 609.69898 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 354.11399 609.69898 Tm
(e)Tj 
6.47599 0 0 5.97698 358.69499 608.20498 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 362.53099 609.69898 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 369.95399 609.69898 Tm
4.91999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 438.84399 609.69898 Tm
0 Tc
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-389 ]TJ (for)Tj [-385 ]TJ (all)Tj 
/N10 1 Tf
4.67779 0 TD
(i)Tj 
6.47599 0 0 5.97698 140.31999 613.68399 Tm
(r)Tj 
38.68449 0 TD
(r)Tj 
10.36099 0 0 10.16198 132.44999 609.69898 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
20.31999 Tc
(kN)Tj 
/N9 1 Tf
22.11538 0 TD
0 Tc
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 140.31999 608.20498 Tm
(/)Tj 
38.68449 0 TD
(/)Tj 
9.96199 0 0 9.96199 119.54899 597.74398 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 130.55699 597.74398 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 136.88198 596.25 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.43859 0 TD
(/)Tj 
/N9 1 Tf
0.79998 0 TD
(1)Tj 
10.36099 0 0 10.16198 152.375 597.74398 Tm
(.)Tj [-293 ]TJ (Note)Tj [-293 ]TJ (that)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 355.20799 578.51699 Tm
(T)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 345.89498 576.62298 Tm
(V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 286.26998 574.53199 Tm
(1)Tj [-2519 ]TJ (Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
5.48078 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj 
/N10 1 Tf
-10.33178 -0.73529 TD
(Y)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 252.44599 567.05999 Tm
(\201)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 263.35598 564.56898 Tm
3.23498 Tc
(FG)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 298.87199 561.67898 Tm
3.83999 Tc
(VV)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 270.52799 559.58799 Tm
0 Tc
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.46148 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj 
/N10 1 Tf
2.94709 0 TD
(Y)Tj 
/N9 1 Tf
-20.72589 -2.28428 TD
(for)Tj [-298 ]TJ (some)Tj 
/N10 1 Tf
3.86048 0 TD
(Y)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 162.48699 538.46798 Tm
(V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 166.32199 536.37599 Tm
(.)Tj [-293 ]TJ (For)Tj [-293 ]TJ (the)Tj [-293 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
4.66828 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 222.36099 536.37599 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 233.36898 536.37599 Tm
(3)Tj [-96 ]TJ (\))Tj [-293 ]TJ (clique)Tj [-288 ]TJ (we)Tj [-293 ]TJ (de\256ne)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 385.09599 517.14698 Tm
(T)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 375.78199 515.25498 Tm
(V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 253.59298 513.16198 Tm
(1)Tj [-4038 ]TJ (1)Tj [-2519 ]TJ (0)Tj [-1000 ]TJ (Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
11.51919 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 385.09599 505.19299 Tm
(T)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 375.78199 503.29998 Tm
(V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 253.59298 501.20799 Tm
(1)Tj [-4038 ]TJ (1)Tj [-2519 ]TJ (0)Tj [-1000 ]TJ (Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
11.51919 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj 
/N10 1 Tf
10.36099 0 0 10.46099 209.65899 497.42199 Tm
(\304)Tj 
10.36099 0 0 10.16198 208.51298 495.23098 Tm
(Y)Tj 
/N9 1 Tf
0.84129 0 TD
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 220.06799 495.23098 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 398.54499 495.23098 Tm
(.)Tj 
-13.99029 -0.58819 TD
4.03799 Tc
(00)Tj [1519 ]TJ (0)Tj [1298 ]TJ (0)Tj 
/N21 1 Tf
26.69898 0 0 38.45498 230.97799 486.16499 Tm
5.72198 Tc
(34)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 266.19499 479.39099 Tm
4.71998 Tc
(VV)Tj [-680 ]TJ (V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 237.85198 477.29899 Tm
0 Tc
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.46148 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj [-1000 ]TJ (Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
3.79319 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
1 Tc
(\)0)Tj 
/N10 1 Tf
4.44709 0 TD
0 Tc
(Y)Tj 
/N9 1 Tf
-23.61048 -2.27459 TD
(Without)Tj [-394 ]TJ (loss)Tj [-389 ]TJ (of)Tj [-394 ]TJ (generality,)Tj [-394 ]TJ (we)Tj [-389 ]TJ (assumed)Tj 
/N10 1 Tf
16.875 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 301.31298 454.18499 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 313.31698 454.18499 Tm
(1;)Tj [-389 ]TJ (in)Tj [-394 ]TJ (the)Tj [-385 ]TJ (above,)Tj [-394 ]TJ (the)Tj [-389 ]TJ (block)Tj [-389 ]TJ (matrices)Tj [-380 ]TJ (of)Tj [-380 ]TJ (0s)Tj 
-18.70188 -1.17649 TD
(correspond)Tj [-288 ]TJ (to)Tj [-298 ]TJ (the)Tj [-288 ]TJ (edges)Tj 
/N10 1 Tf
9.88459 0 TD
(j)Tj 
/N9 1 Tf
0.57209 0 TD
(in)Tj 
/N10 1 Tf
1.07199 0 TD
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 245.32398 440.73599 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44599 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 262.85798 442.22999 Tm
(such)Tj [-293 ]TJ (that)Tj [-288 ]TJ ({)Tj 
/N10 1 Tf
4.49029 0 TD
(i)Tj 
/N9 1 Tf
0.37509 0 TD
(,)Tj 
/N10 1 Tf
0.53839 0 TD
(j)Tj 
/N9 1 Tf
0.37509 0 TD
(})Tj 
/N4 1 Tf
9.96199 0 0 9.96199 330.70199 442.22999 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 341.70999 442.22999 Tm
0.09599 Tc
(I)Tj [96 ]TJ (n)Tj [96 ]TJ (c\(2)Tj 
/N10 1 Tf
2.30288 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 373.19099 442.22999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 384.19898 442.22999 Tm
0.09599 Tc
(3\).)Tj 
-24.54319 -1.17649 TD
0 Tc
(It)Tj [-293 ]TJ (is)Tj [-293 ]TJ (clear)Tj [-298 ]TJ (by)Tj [-298 ]TJ (construction)Tj [-293 ]TJ (that)Tj 
/N10 1 Tf
12.42779 0 TD
(Y)Tj 
0.11059 0.20599 TD
(\304)Tj 
/N9 1 Tf
0.73568 -0.20599 TD
(is)Tj [-288 ]TJ (symmetric)Tj [-288 ]TJ (and)Tj [-288 ]TJ (that)Tj 
/N10 1 Tf
8.98548 0 TD
(w)Tj 
6.47599 0 0 5.97698 368.40899 434.25999 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 371.24798 430.27499 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 375.68199 430.27499 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 380.76298 430.27499 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 387.13899 430.27499 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 397.99798 430.27499 Tm
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 408.35798 428.78099 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 414.53498 430.27499 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 425.34498 430.27499 Tm
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.37489 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj [-96 ]TJ (.)Tj [-264 ]TJ (Next,)Tj 
-32.63449 -1.17649 TD
(we)Tj [-332 ]TJ (note)Tj [-332 ]TJ (that)Tj [-327 ]TJ (every)Tj [-332 ]TJ (principal)Tj [-327 ]TJ (submatrix)Tj [-327 ]TJ (of)Tj 
/N10 1 Tf
17.30288 0 TD
(Y)Tj 
0.11529 0.20599 TD
(\304)Tj 
/N9 1 Tf
0.76919 -0.20599 TD
(either)Tj [-327 ]TJ (has)Tj [-322 ]TJ (zero)Tj [-327 ]TJ (determinant)Tj [-322 ]TJ (or)Tj [-327 ]TJ (is)Tj [-322 ]TJ (equal)Tj [-317 ]TJ (to)Tj [-327 ]TJ (a)Tj 
-18.18739 -1.17649 TD
(principal)Tj [-231 ]TJ (submatrix)Tj [-231 ]TJ (of)Tj 
/N10 1 Tf
9.07679 0 TD
(Y)Tj 
/N9 1 Tf
0.78369 0 TD
(and)Tj [-231 ]TJ (hence)Tj [-231 ]TJ (have)Tj [-231 ]TJ (nonnegative)Tj [-221 ]TJ (determinant.)Tj [-221 ]TJ (Therefore,)Tj 
/N10 1 Tf
21.12019 0 TD
(Y)Tj 
0.11529 0.20599 TD
(\304)Tj 
/N9 1 Tf
0.65388 -0.20599 TD
(is)Tj [-202 ]TJ (positive)Tj 
-31.75 -1.17649 TD
(semide\256nite.)Tj 
1 -1.17649 TD
(Since)Tj 
/N10 1 Tf
2.54798 0 TD
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 166.67098 380.96099 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 173.29598 382.45599 Tm
4.79998 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 240.39299 382.45599 Tm
0.09599 Tc
(1\)\),)Tj [-236 ]TJ (b)Tj [96 ]TJ (y)Tj 
3.36769 0 TD
0 Tc
(induction)Tj [-327 ]TJ (hypothesis,)Tj 
/N10 1 Tf
8.95919 0 TD
(Y)Tj 
0.11538 0.20599 TD
(\304)Tj 
0.44059 -0.20599 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 378.47099 380.96099 Tm
(0)Tj 
10.36099 0 0 10.16198 382.70498 382.45599 Tm
(,)Tj 
/N10 1 Tf
0.57218 0 TD
(Y)Tj 
0.11529 0.20599 TD
(\304)Tj 
0.44068 -0.20599 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 398.99398 380.96099 Tm
(1)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 405.56898 382.45599 Tm
4.78999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 472.51599 382.45599 Tm
0.09599 Tc
(3\)\).)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 193.46998 386.44099 Tm
0 Tc
(r)Tj 
35.84619 0 TD
(r)Tj 
10.36099 0 0 10.16198 185.59999 382.45599 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
18.54598 Tc
(kN)Tj 
/N9 1 Tf
20.34138 0 TD
0 Tc
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 193.46998 380.96099 Tm
(/)Tj 
35.84619 0 TD
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 370.50099 Tm
(Clearly,)Tj [-370 ]TJ (0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 165.47499 370.50099 Tm
4.87998 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 233.76699 370.50099 Tm
0.09599 Tc
(3\)\).)Tj [-274 ]TJ (I)Tj [96 ]TJ (f)Tj [-274 ]TJ (\()Tj 
/N10 1 Tf
3.44239 0 TD
0 Tc
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 279.79399 369.00599 Tm
(0)Tj 
10.36099 0 0 10.16198 284.02799 370.50099 Tm
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 288.11199 369.00599 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 293.74099 370.50099 Tm
(\234)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 306.34399 370.50099 Tm
(0,)Tj [-375 ]TJ (then)Tj [-370 ]TJ (we)Tj [-375 ]TJ (have)Tj 
7.01599 0 TD
0.09599 Tc
(\(1/\()Tj 
/N10 1 Tf
1.72918 0 TD
0 Tc
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 407.31298 369.00599 Tm
(0)Tj 
10.36099 0 0 10.16198 411.54699 370.50099 Tm
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 415.68099 369.00599 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 418.12199 370.50099 Tm
(\))Tj 
/N10 1 Tf
0.33158 0 TD
(Ye)Tj 
6.47599 0 0 5.97698 431.91899 369.00599 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 437.49798 370.50099 Tm
(\303)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 186.04798 374.48599 Tm
(r)Tj 
42.00749 0 TD
(r)Tj 
10.36099 0 0 10.16198 178.17799 370.50099 Tm
(N)Tj 
/N9 1 Tf
1.35089 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
22.39698 Tc
(kN)Tj 
/N9 1 Tf
24.19229 0 TD
0 Tc
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 186.04798 369.00599 Tm
(/)Tj 
42.00749 0 TD
(/)Tj 
9.96199 0 0 9.96199 119.54899 358.54598 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 131.50399 358.54598 Tm
0.09599 Tc
(1\)\).)Tj 
2.09379 0 TD
0 Tc
(Thus,)Tj [-385 ]TJ (by)Tj [-389 ]TJ (the)Tj [-385 ]TJ (induction)Tj [-385 ]TJ (hypothesis,)Tj 
14.70489 0 TD
0.09599 Tc
(\(1/\()Tj 
/N10 1 Tf
1.73019 0 TD
0 Tc
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 333.83999 357.05099 Tm
(0)Tj 
10.36099 0 0 10.16198 338.07398 358.54598 Tm
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 342.15798 357.05099 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 344.64898 358.54598 Tm
(\))Tj 
/N10 1 Tf
0.42779 0 TD
(Y)Tj 
0.11549 0.20599 TD
(\304)Tj 
0.44049 -0.20599 TD
(e)Tj 
6.47599 0 0 5.97698 359.44198 357.05099 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 365.17098 358.54598 Tm
4.89999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 433.81298 358.54598 Tm
0.09599 Tc
(3\)\).)Tj [-284 ]TJ (I)Tj [96 ]TJ (f)Tj [-289 ]TJ (\()Tj 
/N10 1 Tf
3.46629 0 TD
0 Tc
(Ye)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 480.08699 357.05099 Tm
(0)Tj 
10.36099 0 0 10.16198 484.32099 358.54598 Tm
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 488.45498 357.05099 Tm
(j)Tj 
-15.87678 0.91668 TD
(r)Tj 
10.36099 0 0 10.16198 377.77398 358.54598 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 385.64498 357.05099 Tm
(/)Tj 
9.96199 0 0 9.96199 119.54899 346.59098 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.70698 346.59098 Tm
(0)Tj [-312 ]TJ (\()Tj [-96 ]TJ (that)Tj [-308 ]TJ (is,)Tj [-312 ]TJ (Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
6.64898 0 TD
(Y)Tj 
/N9 1 Tf
0.74989 0 TD
(\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 211.45199 345.09698 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 216.48298 346.59098 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 227.64099 346.59098 Tm
(0)Tj [-96 ]TJ (\))Tj [-312 ]TJ (then)Tj 
/N10 1 Tf
3.27879 0 TD
(Ye)Tj 
6.47599 0 0 5.97698 271.97399 345.09698 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 277.00399 346.59098 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 288.16198 346.59098 Tm
(0,)Tj [-312 ]TJ (since)Tj 
/N10 1 Tf
3.42779 0 TD
(Y)Tj 
/N9 1 Tf
0.86538 0 TD
(is)Tj [-308 ]TJ (symmetric)Tj [-298 ]TJ (positive)Tj [-298 ]TJ (semide\256nite.)Tj [-274 ]TJ (In)Tj 
-20.56719 -1.17649 TD
(this)Tj [-389 ]TJ (case,)Tj [-394 ]TJ (we)Tj [-389 ]TJ (again)Tj [-394 ]TJ (have)Tj 
/N10 1 Tf
10.59118 0 TD
(Y)Tj 
0.11068 0.20599 TD
(\304)Tj 
0.44529 -0.20599 TD
(e)Tj 
6.47599 0 0 5.97698 239.64599 333.14199 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 245.52299 334.63598 Tm
4.92999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 314.56298 334.63598 Tm
0 Tc
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-394 ]TJ (A)Tj [-394 ]TJ (similar)Tj [-394 ]TJ (argument)Tj [-385 ]TJ (applies)Tj [-380 ]TJ (to)Tj 
/N10 1 Tf
14.92309 0 TD
(Y)Tj 
/N9 1 Tf
0.75 0 TD
(\()Tj 
/N10 1 Tf
0.52398 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 486.96099 333.14199 Tm
(0)Tj 
/N10 1 Tf
-34.06909 0.91668 TD
(r)Tj 
10.36099 0 0 10.16198 258.47399 334.63598 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 266.34498 333.14199 Tm
(/)Tj 
9.96199 0 0 9.96199 119.54899 322.68099 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 130.90499 322.68099 Tm
(e)Tj 
6.47599 0 0 5.97698 135.48899 321.18699 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 137.92898 322.68099 Tm
(\))Tj [-332 ]TJ (showing)Tj [-332 ]TJ (that)Tj 
/N10 1 Tf
6.21148 0 TD
(Y)Tj 
0.11538 0.20599 TD
(\304)Tj 
/N9 1 Tf
0.63459 -0.20599 TD
(\()Tj 
/N10 1 Tf
0.52398 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 220.06799 321.18699 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 226.74398 322.68099 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 238.10099 322.68099 Tm
(e)Tj 
6.47599 0 0 5.97698 242.73298 321.18699 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 245.17498 322.68099 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 252.04899 322.68099 Tm
4.80999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 319.29499 322.68099 Tm
0.09599 Tc
(3\)\).)Tj [-236 ]TJ (W)Tj [96 ]TJ (e)Tj 
3.76049 0 TD
0 Tc
(proved)Tj [-332 ]TJ (that)Tj 
/N10 1 Tf
4.93659 0 TD
(Y)Tj 
0.11529 0.20599 TD
(\304)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 418.61999 322.68099 Tm
(\303)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 272.37098 326.66598 Tm
28.28799 Tc
(rr)Tj 
10.36099 0 0 10.16198 264.50199 322.68099 Tm
0 Tc
(N)Tj 
/N9 1 Tf
1.35089 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09498 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
12.21598 Tc
(kM)Tj 
/N9 1 Tf
14.08169 0 TD
0 Tc
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(N)Tj 
/N9 1 Tf
1.35108 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09498 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 272.37098 321.18699 Tm
25.03599 Tc
(//)Tj [22985 ]TJ (/)Tj 
9.96199 0 0 9.96199 119.54899 310.72599 Tm
0 Tc
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.55699 310.72599 Tm
0.09599 Tc
(1\)\)\).)Tj 
2.43159 0 TD
0 Tc
(Therefore,)Tj 
/N10 1 Tf
4.47698 0 TD
(w)Tj 
6.47599 0 0 5.97698 210.05699 314.71099 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 212.84599 310.72599 Tm
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 217.27999 310.72599 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 222.36099 310.72599 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 228.83599 310.72599 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 239.84498 310.72599 Tm
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.46618 0 TD
(Y)Tj 
0.11549 0.20599 TD
(\304)Tj 
/N9 1 Tf
0.63459 -0.20599 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 279.59399 310.72599 Tm
5.36999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 352.02099 310.72599 Tm
0.09599 Tc
(3\)\).)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 380.06599 310.72599 Tm
0 Tc
(h)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 299.46998 314.71099 Tm
(r)Tj 
/N4 1 Tf
0.48458 0 TD
(/)Tj 
/N9 1 Tf
0.79219 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 291.59899 310.72599 Tm
(N)Tj 
/N9 1 Tf
1.96618 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 299.46998 309.23199 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 298.77099 Tm
(From)Tj [-293 ]TJ (now)Tj [-298 ]TJ (on,)Tj [-298 ]TJ (we)Tj [-293 ]TJ (set)Tj 
17.36538 -2.75489 TD
(1)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 266.04499 258.82199 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 273.11799 258.82199 Tm
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 275.95799 258.82199 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 341.01199 258.82199 Tm
(.)Tj 
/N21 1 Tf
24.90599 0 0 35.86499 286.86698 250.85299 Tm
1.60998 Tc
(12)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 292.39599 246.86799 Tm
0.09599 Tc
(\(1/\()Tj [96 ]TJ (2)Tj 
/N10 1 Tf
2.22589 0 TD
0 Tc
(k)Tj 
/N9 1 Tf
0.44239 0 TD
0.09599 Tc
(\)\))Tj 
/N10 1 Tf
0.75949 0 TD
0 Tc
(e)Tj 
/N9 1 Tf
-20.11048 -2.86268 TD
(Based)Tj [-409 ]TJ (on)Tj [-409 ]TJ (the)Tj [-409 ]TJ (point)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 206.07199 217.77799 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 214.39099 217.77799 Tm
(and)Tj [-409 ]TJ (Lemma)Tj [-409 ]TJ (4.1,)Tj [-409 ]TJ (we)Tj [-409 ]TJ (de\256ne)Tj [-409 ]TJ (a)Tj [-404 ]TJ (matrix)Tj 
/N10 1 Tf
15.51429 0 TD
(Y)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 385.04699 217.77799 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 481.58099 217.77799 Tm
(as)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 405.26899 221.76298 Tm
(E)Tj 
/N6 1 Tf
2.46939 0 TD
(<)Tj 
/N9 1 Tf
0.93058 0 TD
0.09899 Tc
({0})Tj 
/N4 1 Tf
1.75379 0 TD
0 Tc
(1)Tj 
/N10 1 Tf
0.89248 0 TD
(E)Tj 
/N6 1 Tf
2.39219 0 TD
(<)Tj 
/N9 1 Tf
0.93089 0 TD
0.09899 Tc
({0})Tj 
5.17999 0 0 4.78199 409.70399 220.56698 Tm
0 Tc
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44209 0 TD
(/)Tj 
/N9 1 Tf
0.78869 0 TD
5.23098 Tc
(32)Tj 
/N10 1 Tf
6.23059 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
0.44248 0 TD
(/)Tj 
/N9 1 Tf
0.78829 0 TD
(3)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 397.10099 217.77799 Tm
(R)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 205.82299 Tm
(follows.)Tj 
14.57688 -2.27459 TD
(1)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 298.47399 179.72099 Tm
(i)Tj 
ET
258.77299 179.22299 28.84098 -0.49798 rf
BT
10.36099 0 0 10.16198 228.93598 175.73599 Tm
-0.00299 Tc
(Ye)Tj 
/N9 1 Tf
1.55288 0 TD
0 Tc
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 247.86499 175.73599 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 290.60299 175.73599 Tm
(w)Tj 
/N9 1 Tf
1.02868 0 TD
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 305.69599 175.73599 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 310.77699 175.73599 Tm
(\))Tj [-1000 ]TJ (for)Tj 
/N10 1 Tf
2.78359 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 345.44599 175.73599 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 356.35499 175.73599 Tm
(E)Tj 
/N9 1 Tf
2.10089 0 TD
(,)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 239.24598 174.24099 Tm
(i)Tj 
/N9 1 Tf
19.06149 0 TD
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.43849 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 258.77299 168.76199 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 271.52398 168.76199 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 282.43399 168.76199 Tm
(2)Tj 
3.49029 -2.27439 TD
(1)Tj 
-8.67779 -0.04899 TD
17.08198 Tc
(12)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 254.28999 142.16299 Tm
0 Tc
(i)Tj 
ET
219.12298 141.66499 24.30799 -0.49798 rf
399.04299 141.66499 28.84199 -0.49798 rf
BT
10.36099 0 0 10.16198 162.13798 138.17799 Tm
-0.00299 Tc
(Ye)Tj 
/N9 1 Tf
1.59619 0 TD
0 Tc
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 181.51499 138.17799 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 246.41999 138.17799 Tm
(w)Tj 
/N9 1 Tf
1.02879 0 TD
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 261.51298 138.17799 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 266.59399 138.17799 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 273.01899 138.17799 Tm
8.07998 Tc
(\201\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 430.87399 138.17799 Tm
-0.00299 Tc
(Ye)Tj 
/N9 1 Tf
1.36048 0 TD
0 Tc
(.)Tj 
/N11 1 Tf
11.95498 0 0 11.95498 199.99499 137.18199 Tm
14.33699 Tc
(\345\345)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 172.44898 136.68399 Tm
0 Tc
(0)Tj 
/N10 1 Tf
41.5 0 TD
(i)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 283.92799 135.68798 Tm
2.22799 Tc
(SD)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 223.55499 135.18998 Tm
0 Tc
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.43859 0 TD
(/)Tj 
/N9 1 Tf
0.79219 0 TD
(3)Tj 
10.36099 0 0 10.16198 219.12298 131.20498 Tm
1.58699 Tc
(\(\))Tj [-13528 ]TJ (2)Tj 
/N10 1 Tf
17.86538 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 411.79598 131.20498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 422.70399 131.20498 Tm
(3)Tj 
-12.70179 -0.04899 TD
0.09599 Tc
(\(1/\()Tj [96 ]TJ (2)Tj 
/N10 1 Tf
2.22599 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 321.73599 130.70698 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 332.64399 130.70698 Tm
(2\))Tj [-192 ]TJ (\))Tj 
/N10 1 Tf
1.35589 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 229.53298 129.70999 Tm
(2)Tj 
/N10 1 Tf
-5.73078 -0.25 TD
(i)Tj 
/N4 1 Tf
0.37709 0 TD
(\303)Tj 
/N10 1 Tf
0.89219 0 TD
25.90499 Tc
(Ei)Tj 
/N4 1 Tf
26.89248 0 TD
0 Tc
(\303)Tj 
/N10 1 Tf
0.89228 0 TD
(E)Tj 
/N9 1 Tf
5.17999 0 0 4.78199 204.57798 127.02099 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44229 0 TD
(/)Tj 
/N9 1 Tf
0.78849 0 TD
(3)Tj 
33 0 TD
(2)Tj 
/N10 1 Tf
0.49978 0 TD
(k)Tj 
/N4 1 Tf
0.44248 0 TD
(/)Tj 
/N9 1 Tf
0.78849 0 TD
(3)Tj 
10.36099 0 0 10.16198 119.54899 107.59399 Tm
(It)Tj [-365 ]TJ (is)Tj [-365 ]TJ (clear)Tj [-370 ]TJ (by)Tj [-370 ]TJ (the)Tj [-365 ]TJ (de\256nition)Tj [-365 ]TJ (of)Tj 
/N10 1 Tf
12.67309 0 TD
(Y)Tj 
/N9 1 Tf
0.91828 0 TD
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0.50009 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 302.80699 474.40998 Tm
(0)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 313.71499 474.40998 Tm
(1)Tj 
ET
279.74299 470.92298 49.46398 -0.49798 rf
BT
10.36099 0 0 10.16198 339.56799 467.43598 Tm
(otherwise.)Tj 
-5.77398 -0.68629 TD
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N9 1 Tf
0.53849 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 307.68899 460.46199 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 318.59698 460.46199 Tm
0.09599 Tc
(1\))Tj 
-18.21139 -3.46089 TD
0 Tc
(For)Tj [-341 ]TJ (each)Tj 
/N10 1 Tf
3.89898 0 TD
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 176.68299 425.29399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 188.18899 425.29399 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 194.51599 423.79899 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44599 0 TD
(/)Tj 
/N9 1 Tf
0.79249 0 TD
(3)Tj 
10.36099 0 0 10.16198 212.54798 425.29399 Tm
(consider)Tj [-341 ]TJ (all)Tj 
/N10 1 Tf
5.06719 0 TD
(l)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 271.42599 425.29399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 282.88198 425.29399 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 289.20698 423.79899 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44628 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
10.36099 0 0 10.16198 307.23899 425.29399 Tm
(such)Tj [-341 ]TJ (that)Tj [-341 ]TJ ({)Tj 
/N10 1 Tf
4.59129 0 TD
(i)Tj 
/N9 1 Tf
0.375 0 TD
(,)Tj 
/N10 1 Tf
0.59138 0 TD
(l)Tj 
/N9 1 Tf
0.47109 0 TD
(})Tj 
/N4 1 Tf
9.96199 0 0 9.96199 378.17298 425.29399 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 389.62899 425.29399 Tm
0.09599 Tc
(I)Tj [96 ]TJ (n)Tj [96 ]TJ (c\(2)Tj 
/N10 1 Tf
2.30279 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 421.60899 425.29399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 433.06599 425.29399 Tm
(3)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-346 ]TJ (There)Tj [-341 ]TJ (are)Tj 
-30.25959 -1.17649 TD
0.09599 Tc
(2\(2)Tj 
/N10 1 Tf
1.52398 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 143.00999 413.33898 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 154.01899 413.33898 Tm
(1)Tj [-96 ]TJ (\))Tj [-298 ]TJ (such)Tj 
/N10 1 Tf
3.35099 0 TD
(l)Tj 
/N9 1 Tf
0.37019 0 TD
(.)Tj [-298 ]TJ (W)Tj [0 ]TJ (e)Tj [-293 ]TJ (have)Tj 
0.02888 -2.57829 TD
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 205.62298 387.13899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 216.53298 387.13899 Tm
13.5 Tc
(21)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 397.5 384.14999 Tm
0 Tc
(l)Tj 
ET
192.87199 383.65199 28.84098 -0.49798 rf
341.75898 383.65199 44.88198 -0.49798 rf
BT
10.36099 0 0 10.16198 224.70199 380.16499 Tm
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\()Tj 
/N10 1 Tf
0.52398 0 TD
(e)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 248.66099 380.16499 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 259.56898 380.16499 Tm
(e)Tj 
/N9 1 Tf
0.80778 0 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 274.36299 380.16499 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 389.62899 380.16499 Tm
(w)Tj 
/N9 1 Tf
1.02879 0 TD
(\()Tj 
/N19 1 Tf
9.96199 0 0 9.96199 404.72299 380.16499 Tm
(\243)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 409.80299 380.16499 Tm
0.09599 Tc
(\),)Tj 
/N11 1 Tf
11.95498 0 0 11.95498 307.73799 379.16899 Tm
0 Tc
(\345)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 242.43499 378.67098 Tm
(0)Tj 
/N10 1 Tf
3.35369 0 TD
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 192.87199 373.19198 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 205.62298 373.19198 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 216.53298 373.19198 Tm
0.09599 Tc
(1)Tj [-11491 ]TJ (2\(2)Tj 
/N10 1 Tf
13.61048 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 365.12199 373.19198 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 376.03099 373.19198 Tm
0.09599 Tc
(1\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 285.27299 370.20298 Tm
0 Tc
(l)Tj 
/N9 1 Tf
0.27679 0 TD
0.09899 Tc
(:{)Tj 
/N10 1 Tf
0.95399 0 TD
0 Tc
(i)Tj 
/N9 1 Tf
0.27679 0 TD
(,)Tj 
/N10 1 Tf
0.24629 0 TD
(l)Tj 
/N9 1 Tf
0.37689 0 TD
(})Tj 
/N4 1 Tf
0.67689 0 TD
(\303)Tj 
/N9 1 Tf
0.89219 0 TD
-0.00099 Tc
(Inc)Tj [-95 ]TJ (\()Tj [-99 ]TJ (2)Tj 
/N10 1 Tf
2.30018 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
0.43849 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
0.09999 Tc
(3\))Tj 
10.36099 0 0 10.16198 119.54899 346.98899 Tm
0 Tc
(and)Tj [-442 ]TJ (thus)Tj 
/N10 1 Tf
3.99038 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\()Tj 
/N10 1 Tf
0.52879 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 178.67599 345.49499 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 186.49598 346.98899 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 198.99899 346.98899 Tm
(e)Tj 
6.47599 0 0 5.97698 203.58198 345.49499 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 207.36599 346.98899 Tm
(\))Tj [-437 ]TJ (i)Tj [0 ]TJ (s)Tj [-437 ]TJ (a)Tj [-437 ]TJ (nonnegative)Tj [-442 ]TJ (linear)Tj [-442 ]TJ (combination)Tj [-437 ]TJ (of)Tj [-437 ]TJ (elements)Tj [-423 ]TJ (of)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 451.99398 350.97399 Tm
(k)Tj 
/N4 1 Tf
0.43829 0 TD
(0)Tj 
/N9 1 Tf
0.79249 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 444.12298 346.98899 Tm
(N)Tj 
/N9 1 Tf
1.93759 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 451.99398 345.49499 Tm
(/)Tj 
9.96199 0 0 9.96199 119.54899 335.03498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.55699 335.03498 Tm
0.09599 Tc
(3\)\).)Tj 
2.00239 0 TD
0 Tc
(Therefore,)Tj 
/N10 1 Tf
4.47828 0 TD
(Y)Tj 
/N9 1 Tf
0.75 0 TD
(\()Tj 
/N10 1 Tf
0.52398 0 TD
(e)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 215.48699 333.53999 Tm
(0)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 221.76298 335.03498 Tm
(0)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 232.76998 335.03498 Tm
(e)Tj 
6.47599 0 0 5.97698 237.40399 333.53999 Tm
(i)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 241.18998 335.03498 Tm
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 247.66499 335.03498 Tm
5.33999 Tc
(\303/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 319.79299 335.03498 Tm
0.09599 Tc
(3\)\).)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 267.53898 339.01998 Tm
0 Tc
(k)Tj 
/N4 1 Tf
0.43849 0 TD
(0)Tj 
/N9 1 Tf
0.79229 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 259.66899 335.03498 Tm
(N)Tj 
/N9 1 Tf
1.9375 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 267.53898 333.53999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 323.07998 Tm
(Next,)Tj [-365 ]TJ (we)Tj [-365 ]TJ (prove)Tj [-365 ]TJ (that)Tj 
/N10 1 Tf
8.59129 0 TD
(Y)Tj 
/N9 1 Tf
0.91828 0 TD
(is)Tj [-361 ]TJ (positive)Tj [-361 ]TJ (semide\256nite)Tj [-356 ]TJ (by)Tj [-356 ]TJ (identifying)Tj [-356 ]TJ (its)Tj [-346 ]TJ (eigenvalues)Tj [-346 ]TJ (and)Tj [-341 ]TJ (the)Tj 
-10.50959 -1.17649 TD
(corresponding)Tj [-288 ]TJ (eigenspaces.)Tj [-274 ]TJ (For)Tj [-293 ]TJ (convenience)Tj [-288 ]TJ (we)Tj [-293 ]TJ (scale)Tj 
/N10 1 Tf
22.01919 0 TD
(Y)Tj 
/N9 1 Tf
0.85099 0 TD
(and)Tj [-293 ]TJ (work)Tj [-298 ]TJ (with)Tj 
/N32 1 Tf
9.96199 0 2.11799 9.96199 267.53898 287.01699 Tm
(P)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 264.70098 284.92498 Tm
(Y)Tj 
/N9 1 Tf
0.84129 0 TD
(:)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 276.25599 284.92498 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 287.16598 284.92498 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N9 1 Tf
0.53839 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 315.10998 284.92498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 326.01998 284.92498 Tm
0.09599 Tc
(2\))Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(Y)Tj 
/N9 1 Tf
0.64898 0 TD
(.)Tj 
-21.50469 -2.57839 TD
(The)Tj [-327 ]TJ (eigenvalues)Tj [-322 ]TJ (of)Tj 
/N10 1 Tf
8.08169 0 TD
(Y)Tj 
0.11538 0.20579 TD
(\303)Tj 
/N9 1 Tf
0.76919 -0.20579 TD
(are)Tj [-322 ]TJ (\()Tj [-96 ]TJ (6)Tj 
/N10 1 Tf
2.47119 0 TD
(k)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 243.62998 262.70899 Tm
(2)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 250.25498 258.72399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 261.56199 258.72399 Tm
(7)Tj 
/N10 1 Tf
0.50009 0 TD
(k)Tj 
/N9 1 Tf
0.54319 0 TD
0.09599 Tc
(\),)Tj [-231 ]TJ (\(2)Tj 
/N10 1 Tf
1.93278 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 300.36599 258.72399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 311.72299 258.72399 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (,)Tj [-332 ]TJ (and)Tj [-332 ]TJ (0)Tj [-332 ]TJ (with)Tj [-327 ]TJ (the)Tj [-327 ]TJ (ranks)Tj [-322 ]TJ (of)Tj [-327 ]TJ (corresponding)Tj 
-18.54798 -1.17649 TD
(eigenspaces)Tj [-303 ]TJ (1,)Tj 
/N10 1 Tf
6.13938 0 TD
(k)Tj 
/N9 1 Tf
0.53849 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.93258 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 206.17199 246.76899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 217.32899 246.76899 Tm
0.09599 Tc
(3\),)Tj [-216 ]TJ (a)Tj [96 ]TJ (n)Tj [96 ]TJ (d)Tj [-216 ]TJ (\(2)Tj 
/N10 1 Tf
4.27409 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 269.38198 246.76899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 280.54098 246.76899 Tm
(3)Tj [-96 ]TJ (\))Tj [-312 ]TJ (respectively.)Tj [-303 ]TJ (The)Tj [-303 ]TJ (eigenvector)Tj [-298 ]TJ (corresponding)Tj [-288 ]TJ (to)Tj 
-15.53849 -1.17649 TD
(the)Tj [-293 ]TJ (eigenvalue)Tj [-284 ]TJ (\()Tj [-96 ]TJ (6)Tj 
/N10 1 Tf
7.05758 0 TD
(k)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 198.25199 238.79899 Tm
(2)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 204.57798 234.81399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 215.58499 234.81399 Tm
(7)Tj 
/N10 1 Tf
0.50009 0 TD
(k)Tj 
/N9 1 Tf
0.54328 0 TD
0.29299 Tc
(\)i)Tj [293 ]TJ (s)Tj 
5.90869 -2.57849 TD
0 Tc
(2)Tj 
/N10 1 Tf
0.49989 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 300.36599 208.61199 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 311.27499 208.61199 Tm
(2)Tj 
1.48078 -0.73529 TD
(.)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 280.44198 198.64898 Tm
1.10499 Tc
(SD)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 299.71899 193.66799 Tm
0 Tc
(e)Tj 
/N9 1 Tf
-17.38938 -2.58808 TD
(The)Tj [-332 ]TJ (eigenspace)Tj [-327 ]TJ (for)Tj [-327 ]TJ (the)Tj [-327 ]TJ (eigenvalue)Tj [-327 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
15.22599 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 285.27299 167.36799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 296.58099 167.36799 Tm
(1)Tj [-96 ]TJ (\))Tj [-327 ]TJ (is)Tj [-322 ]TJ (spanned)Tj [-327 ]TJ (by)Tj [-332 ]TJ (the)Tj [-322 ]TJ (signed)Tj [-327 ]TJ (incidence)Tj [-312 ]TJ (vectors)Tj 
-17.08648 -1.17649 TD
(of)Tj [-322 ]TJ (even)Tj [-322 ]TJ (cycles)Tj [-312 ]TJ (where)Tj [-317 ]TJ (the)Tj [-312 ]TJ (signing)Tj [-317 ]TJ (forces)Tj [-312 ]TJ (any)Tj [-317 ]TJ (two)Tj [-317 ]TJ (consecutive)Tj [-312 ]TJ (edges)Tj [-312 ]TJ (of)Tj [-317 ]TJ (the)Tj [-312 ]TJ (cycle)Tj [-308 ]TJ (to)Tj [-317 ]TJ (have)Tj 
T*
(the)Tj [-293 ]TJ (opposite)Tj [-293 ]TJ (sign)Tj [-298 ]TJ (\()Tj [-96 ]TJ (w)Tj [0 ]TJ (e)Tj [-298 ]TJ (set)Tj [-293 ]TJ (the)Tj [-298 ]TJ (0th)Tj [-298 ]TJ (component)Tj [-293 ]TJ (to)Tj [-298 ]TJ (0)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-298 ]TJ (We)Tj [-298 ]TJ (claim)Tj [-293 ]TJ (that)Tj [-293 ]TJ (there)Tj [-298 ]TJ (are)Tj [-293 ]TJ (at)Tj [-288 ]TJ (least)Tj 
/N10 1 Tf
33.86048 0 TD
(k)Tj 
/N9 1 Tf
0.53858 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 131.50399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 130.15798 131.50399 Tm
(3)Tj [-96 ]TJ (\))Tj [-260 ]TJ (linearly)Tj [-255 ]TJ (independent)Tj [-250 ]TJ (such)Tj [-255 ]TJ (vectors.)Tj [-255 ]TJ (Take)Tj [-250 ]TJ (a)Tj [-255 ]TJ (simple)Tj [-245 ]TJ (cycle)Tj 
/N10 1 Tf
23.33169 0 TD
(C)Tj 
/N9 1 Tf
0.91349 0 TD
(on)Tj [-250 ]TJ (all)Tj [-245 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
3.42799 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 424 131.50399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 434.45999 131.50399 Tm
(3)Tj [-96 ]TJ (\))Tj [-245 ]TJ (nodes.)Tj [-231 ]TJ (For)Tj 
-30.39419 -1.17649 TD
(every)Tj [-269 ]TJ (edge)Tj 
/N10 1 Tf
4.64419 0 TD
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 173.29598 119.54899 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 184.00599 119.54899 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 190.33198 118.05398 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
/N36 1 Tf
9.96199 0 0 9.96199 205.82299 119.54899 Tm
(")Tj 
/N10 1 Tf
10.36099 0 0 10.16198 211.80099 119.54899 Tm
(C)Tj 
/N9 1 Tf
0.76438 0 TD
(,)Tj 
/N10 1 Tf
0.51429 0 TD
(C)Tj 
/N6 1 Tf
9.96199 0 0 9.96199 234.66398 119.54899 Tm
(<)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 245.67298 119.54899 Tm
({)Tj 
/N10 1 Tf
0.67309 0 TD
(j)Tj 
/N9 1 Tf
0.375 0 TD
(})Tj [-260 ]TJ (has)Tj [-260 ]TJ (one)Tj [-264 ]TJ (odd)Tj [-264 ]TJ (and)Tj [-264 ]TJ (one)Tj [-264 ]TJ (even)Tj [-260 ]TJ (cycle)Tj [-255 ]TJ (containing)Tj 
/N10 1 Tf
18.21139 0 TD
(j)Tj 
/N9 1 Tf
0.375 0 TD
(.)Tj [-250 ]TJ (For)Tj [-245 ]TJ (each)Tj 
/N10 1 Tf
-31.80758 -1.17649 TD
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 125.62599 107.59399 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 136.78399 107.59399 Tm
(E)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 143.10899 106.09999 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44628 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
/N36 1 Tf
9.96199 0 0 9.96199 158.60099 107.59399 Tm
(")Tj 
/N10 1 Tf
10.36099 0 0 10.16198 164.57899 107.59399 Tm
(C)Tj 
/N9 1 Tf
0.76429 0 TD
(,)Tj [-312 ]TJ (consider)Tj [-312 ]TJ (the)Tj [-312 ]TJ (signed)Tj [-312 ]TJ (incidence)Tj [-308 ]TJ (vectors)Tj [-303 ]TJ (of)Tj [-308 ]TJ (the)Tj [-308 ]TJ (even)Tj [-308 ]TJ (cycle)Tj [-303 ]TJ (containing)Tj [-298 ]TJ (edge)Tj 
/N10 1 Tf
30.03849 0 TD
(j)Tj 
/N9 1 Tf
0.37509 0 TD
(.)Tj 
-35.52398 -1.17649 TD
(These)Tj [-288 ]TJ (vectors)Tj [-279 ]TJ (are)Tj [-284 ]TJ (linearly)Tj [-284 ]TJ (independent)Tj [-279 ]TJ (\()Tj [-96 ]TJ (since)Tj [-274 ]TJ (each)Tj 
/N10 1 Tf
20.72119 0 TD
(j)Tj 
/N9 1 Tf
0.55288 0 TD
(appears)Tj [-274 ]TJ (only)Tj [-279 ]TJ (in)Tj [-274 ]TJ (one)Tj [-269 ]TJ (such)Tj [-274 ]TJ (cycle)Tj [-96 ]TJ (\))Tj [-260 ]TJ (and)Tj 
-21.27398 -1.17649 TD
(there)Tj [-293 ]TJ (are)Tj 
ET
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119.54899 67.24598 370.60099 -23.90998 rf
119.54899 705.33799 370.60099 -621.65399 rf
BT
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 717.29299 Tm
0 g
0 Tc
0 Tw
(6)Tj 
7.17298 0 0 6.67498 249.45698 717.29299 Tm
0.06898 Tc
(T.)Tj [-500 ]TJ (STEPHEN)Tj [-459 ]TJ (AND)Tj [-486 ]TJ (L.)Tj [-493 ]TJ (TUNC)Tj 
13.61819 0 TD
0.23399 Tc
(\313E)Tj [165 ]TJ (L)Tj 
8.26899 0 0 8.06999 140.12098 47.32099 Tm
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0.05999 Tc
(/)Tj [-247 ]TJ (3907)Tj [-494 ]TJ (no38)Tj [-500 ]TJ (Mp)Tj [-1000 ]TJ (6)Tj [-1000 ]TJ (Monday)Tj [-488 ]TJ (Mar)Tj [-494 ]TJ (08)Tj [-500 ]TJ (03:24)Tj [-500 ]TJ (PM)Tj [-1000 ]TJ (INF\261MOR)Tj [-1000 ]TJ (no38)Tj 
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0 Tc
(2)Tj 
/N10 1 Tf
0.50009 0 TD
(k)Tj 
/N4 1 Tf
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(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 259.66899 693.38299 Tm
(3)Tj 
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/N10 1 Tf
0.92779 0 TD
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(k)Tj 
/N4 1 Tf
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(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 314.01499 685.91099 Tm
0.09599 Tc
(3\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 326.61698 685.91099 Tm
0 Tc
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 337.52499 685.91099 Tm
(k)Tj 
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/N10 1 Tf
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0 Tc
(k)Tj 
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(/)Tj 
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(3\))Tj 
/N21 1 Tf
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1.10499 Tc
(SD)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 247.81498 678.43899 Tm
0 Tc
(2)Tj 
-12.37979 -2.55879 TD
(of)Tj [-269 ]TJ (them.)Tj [-269 ]TJ (Next,)Tj [-269 ]TJ (we)Tj [-260 ]TJ (identify)Tj [-264 ]TJ (the)Tj [-264 ]TJ (eigenspace)Tj [-264 ]TJ (of)Tj [-260 ]TJ (the)Tj [-260 ]TJ (eigenvalue)Tj [-260 ]TJ (0.)Tj [-260 ]TJ (Fix)Tj [-260 ]TJ (a)Tj [-255 ]TJ (node)Tj 
/N10 1 Tf
29.69219 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 432.36799 650.94299 Tm
(1)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 438.24499 652.43798 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 448.80599 652.43798 Tm
(V)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 455.13198 650.94299 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44619 0 TD
(/)Tj 
/N9 1 Tf
0.79219 0 TD
(3)Tj 
10.36099 0 0 10.16198 470.62298 652.43798 Tm
(.)Tj [-250 ]TJ (For)Tj 
-33.88449 -1.17649 TD
(each)Tj 
/N10 1 Tf
2.19229 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 147.44398 638.98799 Tm
(2)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 154.41699 640.48298 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 166.12298 640.48298 Tm
(V)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 172.44898 638.98799 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.43849 0 TD
(/)Tj 
/N9 1 Tf
0.79978 0 TD
(3)Tj 
/N36 1 Tf
9.96199 0 0 9.96199 187.93998 640.48298 Tm
(")Tj 
/N9 1 Tf
10.36099 0 0 10.16198 194.91299 640.48298 Tm
({)Tj 
/N10 1 Tf
0.57688 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 206.07199 638.98799 Tm
(1)Tj 
10.36099 0 0 10.16198 210.30599 640.48298 Tm
(})Tj [-96 ]TJ (,)Tj [-361 ]TJ (consider)Tj [-361 ]TJ (the)Tj [-361 ]TJ (complete)Tj [-356 ]TJ (bipartite)Tj [-356 ]TJ (graph)Tj [-356 ]TJ (whose)Tj [-351 ]TJ (bipartition)Tj [-341 ]TJ (is)Tj [-337 ]TJ ({)Tj 
/N10 1 Tf
25.85099 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 483.32499 638.98799 Tm
(1)Tj 
10.36099 0 0 10.16198 487.55899 640.48298 Tm
(,)Tj 
/N10 1 Tf
-35.51908 -1.17649 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 124.72898 627.03399 Tm
(2)Tj 
10.36099 0 0 10.16198 128.96299 628.52799 Tm
0.09599 Tc
(},)Tj 
/N10 1 Tf
1.11538 0 TD
0 Tc
(V)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 146.84498 627.03399 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
0.44628 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(3)Tj 
/N36 1 Tf
9.96199 0 0 9.96199 162.33699 628.52799 Tm
(")Tj 
/N9 1 Tf
10.36099 0 0 10.16198 169.31098 628.52799 Tm
({)Tj 
/N10 1 Tf
0.57688 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 180.46798 627.03399 Tm
(1)Tj 
10.36099 0 0 10.16198 184.70199 628.52799 Tm
(,)Tj 
/N10 1 Tf
0.54339 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 195.51199 627.03399 Tm
(2)Tj 
10.36099 0 0 10.16198 199.74598 628.52799 Tm
(})Tj [-96 ]TJ (.)Tj [-288 ]TJ (Assign)Tj [-288 ]TJ (weight)Tj [-284 ]TJ (1)Tj [-288 ]TJ (t)Tj [0 ]TJ (o)Tj [-288 ]TJ (every)Tj [-288 ]TJ (edge)Tj [-284 ]TJ (incident)Tj [-279 ]TJ (on)Tj 
/N10 1 Tf
18.50959 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 396.70298 627.03399 Tm
(1)Tj 
10.36099 0 0 10.16198 400.93699 628.52799 Tm
(,)Tj [-284 ]TJ (assign)Tj [-279 ]TJ (weight)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 466.23999 628.52799 Tm
(0)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 474.15998 628.52799 Tm
0.26899 Tc
(1t)Tj [269 ]TJ (o)Tj 
-34.22599 -1.17649 TD
0 Tc
(every)Tj [-356 ]TJ (edge)Tj [-356 ]TJ (incident)Tj [-356 ]TJ (on)Tj 
/N10 1 Tf
9.74989 0 TD
(h)Tj 
/N9 1 Tf
6.47599 0 0 5.97698 225.74798 615.07899 Tm
(2)Tj 
10.36099 0 0 10.16198 232.67199 616.57299 Tm
(in)Tj [-351 ]TJ (this)Tj [-346 ]TJ (bipartite)Tj [-351 ]TJ (graph.)Tj [-351 ]TJ (De\256ne)Tj [-351 ]TJ (the)Tj [-351 ]TJ (0th)Tj [-351 ]TJ (entry)Tj [-346 ]TJ (and)Tj [-346 ]TJ (all)Tj [-341 ]TJ (the)Tj [-346 ]TJ (other)Tj 
-10.91828 -1.17649 TD
(entries)Tj [-274 ]TJ (to)Tj [-274 ]TJ (be)Tj [-274 ]TJ (0.)Tj [-274 ]TJ (Such)Tj [-274 ]TJ (a)Tj [-269 ]TJ (vector)Tj [-274 ]TJ (is)Tj [-269 ]TJ (in)Tj [-274 ]TJ (the)Tj [-274 ]TJ (eigenspace)Tj [-264 ]TJ (corresponding)Tj [-269 ]TJ (to)Tj [-269 ]TJ (the)Tj [-260 ]TJ (eigenvalue)Tj [-255 ]TJ (0.)Tj [-260 ]TJ (It)Tj [-255 ]TJ (is)Tj 
T*
(easy)Tj [-293 ]TJ (to)Tj [-293 ]TJ (check)Tj [-293 ]TJ (that)Tj [-288 ]TJ (these)Tj [-288 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
10.82688 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 239.34698 592.66299 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 250.35499 592.66299 Tm
(2)Tj [-96 ]TJ (\))Tj [-298 ]TJ (vectors)Tj [-284 ]TJ (are)Tj [-293 ]TJ (linearly)Tj [-284 ]TJ (independent.)Tj [-284 ]TJ (Finally,)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 276.50498 566.65998 Tm
(0)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 285.42298 566.65998 Tm
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 302.60798 566.65998 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 313.51699 566.65998 Tm
0.09599 Tc
(3\)/2)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 269.33299 556.69799 Tm
2.10099 Tc
(SD)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 302.50698 551.71699 Tm
0 Tc
(e)Tj 
/N9 1 Tf
-17.65859 -2.55868 TD
(is)Tj [-332 ]TJ (also)Tj [-336 ]TJ (a)Tj [-332 ]TJ (vector)Tj [-337 ]TJ (in)Tj [-337 ]TJ (the)Tj [-332 ]TJ (eigenspace)Tj [-332 ]TJ (de\256ned)Tj [-332 ]TJ (by)Tj [-332 ]TJ (the)Tj [-332 ]TJ (eigenvalue)Tj [-327 ]TJ (0.)Tj [-332 ]TJ (So,)Tj [-332 ]TJ (we)Tj [-327 ]TJ (have)Tj [-332 ]TJ (at)Tj [-327 ]TJ (least)Tj [-322 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
35.32679 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 119.54899 513.76098 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 131.55299 513.76098 Tm
(3)Tj [-96 ]TJ (\))Tj [-394 ]TJ (linearly)Tj [-394 ]TJ (independent)Tj [-389 ]TJ (vectors)Tj [-385 ]TJ (in)Tj [-394 ]TJ (the)Tj [-385 ]TJ (eigenspace)Tj [-389 ]TJ (of)Tj [-389 ]TJ (0.)Tj [-389 ]TJ (Since)Tj [-385 ]TJ (the)Tj [-385 ]TJ (sum)Tj [-389 ]TJ (of)Tj [-389 ]TJ (the)Tj [-389 ]TJ (lower)Tj 
-1.15869 -1.17649 TD
(bounds)Tj [-240 ]TJ (we)Tj [-240 ]TJ (proved)Tj [-240 ]TJ (for)Tj [-240 ]TJ (the)Tj [-240 ]TJ (eigenspaces)Tj [-236 ]TJ (equals)Tj [-231 ]TJ (the)Tj [-236 ]TJ (order)Tj [-236 ]TJ (of)Tj [-236 ]TJ (the)Tj [-231 ]TJ (matrix)Tj 
/N10 1 Tf
27.38449 0 TD
(Y)Tj 
0.11068 0.20579 TD
(\303)Tj 
/N9 1 Tf
0.53839 -0.20579 TD
(,)Tj [-226 ]TJ (w)Tj [0 ]TJ (e)Tj [-226 ]TJ (have)Tj [-216 ]TJ (identi\256ed)Tj 
-28.03359 -1.17649 TD
(all)Tj [-298 ]TJ (eigenvalues)Tj [-303 ]TJ (of)Tj 
/N10 1 Tf
7.45188 0 TD
(Y)Tj 
0.11048 0.20579 TD
(\303)Tj 
/N9 1 Tf
0.53858 -0.20579 TD
(.)Tj [-303 ]TJ (Since)Tj [-293 ]TJ (each)Tj [-298 ]TJ (of)Tj [-298 ]TJ (the)Tj [-298 ]TJ (three)Tj [-293 ]TJ (eigenvalues)Tj [-293 ]TJ (is)Tj [-293 ]TJ (nonnegative,)Tj 
/N10 1 Tf
21.55279 0 TD
(Y)Tj 
0.11549 0.20579 TD
(\303)Tj 
/N9 1 Tf
0.53849 -0.20579 TD
(,)Tj [-298 ]TJ (and)Tj [-298 ]TJ (hence)Tj 
/N10 1 Tf
4.90859 0 TD
(Y)Tj 
/N9 1 Tf
-35.21629 -1.17649 TD
(is)Tj [-293 ]TJ (positive)Tj [-279 ]TJ (semide\256nite.)Tj [-269 ]TJ (We)Tj [-293 ]TJ (proved)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 291.10099 455.87899 Tm
(k)Tj 
/N4 1 Tf
0.43829 0 TD
(0)Tj 
/N9 1 Tf
0.79249 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 244.42698 451.89498 Tm
(Y)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 253.14498 451.89498 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 264.05198 451.89498 Tm
(M)Tj 
/N9 1 Tf
1.42318 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(N)Tj 
/N9 1 Tf
1.93759 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 332.24598 451.89498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 343.15499 451.89498 Tm
0.09599 Tc
(3\)\)\),)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 272.67098 450.39999 Tm
2.05099 Tc
(//)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 425.89299 Tm
0 Tc
(which)Tj [-293 ]TJ (implies)Tj [-279 ]TJ (that)Tj 
15.90368 -2.56869 TD
(1)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 338.42298 396.30299 Tm
(k)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 207.61499 392.31799 Tm
(Diag)Tj [-96 ]TJ (\()Tj 
/N10 1 Tf
2.36549 0 TD
(Y)Tj 
/N9 1 Tf
0.74519 0 TD
(\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 246.27099 392.31799 Tm
6.56999 Tc
(\201\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 330.55099 392.31799 Tm
0 Tc
(N)Tj 
/N9 1 Tf
1.35108 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 373.48899 392.31799 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 384.39898 392.31799 Tm
0.09599 Tc
(3\)\).)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 338.42298 390.82398 Tm
0 Tc
(/)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 257.17799 389.82798 Tm
1.68899 Tc
(SD)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 264.35198 384.84698 Tm
0 Tc
(e)Tj 
/N9 1 Tf
0.44229 0 TD
(/\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
1.20188 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 288.95799 384.84698 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 299.86799 384.84698 Tm
0.09599 Tc
(2\))Tj 
-17.40379 -2.56849 TD
0 Tc
(This)Tj [-293 ]TJ (completes)Tj [-274 ]TJ (the)Tj [-293 ]TJ (induction.)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 253.64299 358.74598 Tm
(h)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 332.64399 Tm
(5.)Tj [-1000 ]TJ (Analysis)Tj [-225 ]TJ (of)Tj [-225 ]TJ (the)Tj [-225 ]TJ (Lova)Tj 
9.95498 0 TD
(\302)Tj [-82 ]TJ (sz-Schrijver)Tj [-215 ]TJ (procedure)Tj [-215 ]TJ (for)Tj [-210 ]TJ (the)Tj [-210 ]TJ (matching)Tj [-210 ]TJ (problem.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 453.18998 332.64399 Tm
(We)Tj [-187 ]TJ (sum-)Tj 
-32.20188 -1.17649 TD
(marize)Tj [-288 ]TJ (the)Tj [-288 ]TJ (consequences)Tj [-284 ]TJ (of)Tj [-298 ]TJ (the)Tj [-288 ]TJ (above)Tj [-298 ]TJ (construction)Tj [-274 ]TJ (in)Tj [-293 ]TJ (the)Tj [-293 ]TJ (next)Tj [-293 ]TJ (theorem.)Tj 
1 -1.87249 TD
(T)Tj 
7.96998 0 0 7.47198 136.23599 301.66099 Tm
(HEOREM)Tj 
10.36099 0 0 10.16198 174.88999 301.66099 Tm
(5.1.)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 201.73899 279.54499 Tm
(n)Tj 
/N4 1 Tf
0.5 0 TD
(0)Tj 
/N9 1 Tf
0.79219 0 TD
(1)Tj 
/N10 1 Tf
22.00779 0 TD
(n)Tj 
10.36099 0 0 10.16198 193.86799 275.55999 Tm
(N)Tj 
/N9 1 Tf
1.97589 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 243.87998 275.55999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 254.78799 275.55999 Tm
0.09599 Tc
(1\)\))Tj 
/N6 1 Tf
9.96199 0 0 9.96199 271.82398 275.55999 Tm
0 Tc
(.)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 283.08099 275.55999 Tm
(P)Tj 
/N9 1 Tf
0.91349 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 310.32899 275.55999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 321.23799 275.55999 Tm
0.09599 Tc
(1\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 333.83999 275.55999 Tm
0 Tc
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 344.74798 275.55999 Tm
(N)Tj 
/N9 1 Tf
1.35108 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 388.28498 275.55999 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 399.19299 275.55999 Tm
0.09599 Tc
(1\)\).)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 201.73899 274.06599 Tm
0 Tc
(/)Tj 
/N10 1 Tf
13.53849 0 TD
(I)Tj 
/N4 1 Tf
9.76148 0 TD
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 256.53199 Tm
(P)Tj 
7.96998 0 0 7.47198 135.63699 256.53199 Tm
(ROOF)Tj 
10.36099 0 0 10.16198 157.90399 256.53199 Tm
(.)Tj [-1000 ]TJ (B)Tj [0 ]TJ (y)Tj [-279 ]TJ (Lemma)Tj [-288 ]TJ (4.2,)Tj 
7.13459 -2.56858 TD
(1)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 272.76998 226.94299 Tm
(n)Tj 
/N4 1 Tf
0.5 0 TD
(0)Tj 
/N9 1 Tf
0.79249 0 TD
(1)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 199.89498 222.95899 Tm
(\243)Tj 
/N4 1 Tf
0.71009 0 TD
3.92498 Tc
(\201\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 264.89898 222.95899 Tm
0 Tc
(N)Tj 
/N9 1 Tf
1.97608 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 314.91099 222.95899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 325.81898 222.95899 Tm
0.09599 Tc
(1\)\),)Tj [-904 ]TJ (f)Tj [96 ]TJ (o)Tj [96 ]TJ (r)Tj [-192 ]TJ (a)Tj [96 ]TJ (l)Tj [96 ]TJ (l)Tj 
/N10 1 Tf
5.43269 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 390.27699 222.95899 Tm
(\242)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 401.98298 222.95899 Tm
(1.)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 272.76998 221.46398 Tm
(/)Tj 
/N21 1 Tf
27.89498 0 0 27.89498 217.87799 220.46798 Tm
0.74398 Tc
(SD)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 225.04998 215.48699 Tm
0 Tc
(e)Tj 
/N9 1 Tf
0.44239 0 TD
(/2)Tj 
/N10 1 Tf
0.77398 0 TD
(n)Tj 
/N9 1 Tf
-11.39898 -2.56858 TD
(Since)Tj 
17.58639 -2.56869 TD
(2)Tj 
/N10 1 Tf
0.50009 0 TD
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 315.10998 163.28298 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 326.01998 163.28298 Tm
(1)Tj 
ET
301.75999 159.79598 29.43998 -0.49798 rf
BT
/N19 1 Tf
9.96199 0 0 9.96199 281.98498 156.30899 Tm
(\243)Tj 
/N4 1 Tf
0.89009 0 TD
3.55499 Tc
(\201\234)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 345.89498 156.30899 Tm
0 Tc
(n)Tj 
/N9 1 Tf
0.59609 0 TD
(,)Tj 
/N11 1 Tf
11.95498 0 0 11.95498 262.70799 155.31298 Tm
(\345)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 286.06898 154.81498 Tm
(j)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 313.86399 149.33499 Tm
(2)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 254.98799 146.34698 Tm
(j)Tj 
/N4 1 Tf
0.37678 0 TD
(\303)Tj 
/N10 1 Tf
0.89248 0 TD
(E)Tj 
/N9 1 Tf
5.17999 0 0 4.78199 267.14099 145.15199 Tm
(2)Tj 
/N10 1 Tf
0.50019 0 TD
(n)Tj 
/N4 1 Tf
0.5 0 TD
(/)Tj 
/N9 1 Tf
0.78849 0 TD
(1)Tj 
10.36099 0 0 10.16198 119.54899 123.23498 Tm
(the)Tj [-260 ]TJ (maximum)Tj [-264 ]TJ (cardinality)Tj [-264 ]TJ (of)Tj [-264 ]TJ (any)Tj [-260 ]TJ (matching)Tj [-260 ]TJ (in)Tj [-260 ]TJ (the)Tj [-255 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
20.56719 0 TD
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 340.51399 123.23498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 351.125 123.23498 Tm
(1)Tj [-96 ]TJ (\))Tj [-260 ]TJ (clique,)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 394.01298 123.23498 Tm
(\243)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 412.29399 123.23498 Tm
(P)Tj 
6.47599 0 0 5.97698 418.61999 121.74099 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 421.75799 123.23498 Tm
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 439.19198 123.23498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 449.70199 123.23498 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (.)Tj [-245 ]TJ (Using)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 400.33898 123.23498 Tm
(\303)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 402.92898 123.23498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 111.27999 Tm
(Theorem)Tj [-293 ]TJ (3.1,)Tj [-298 ]TJ (we)Tj [-293 ]TJ (have)Tj [-293 ]TJ (the)Tj [-293 ]TJ (strict)Tj [-279 ]TJ (inclusion.)Tj [-279 ]TJ (For)Tj [-298 ]TJ (the)Tj [-288 ]TJ (equality,)Tj [-284 ]TJ (note)Tj [-293 ]TJ (that)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 308.98298 89.16398 Tm
(n)Tj 
10.36099 0 0 10.16198 241.08999 85.17898 Tm
(P)Tj 
/N9 1 Tf
0.91349 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92779 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 268.33699 85.17898 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 279.24499 85.17898 Tm
0.09599 Tc
(1\))Tj 
/N20 1 Tf
9.96199 0 0 9.96199 291.84899 85.17898 Tm
0 Tc
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 301.11399 85.17898 Tm
(N)Tj 
/N9 1 Tf
1.35089 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 344.64898 85.17898 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 355.55699 85.17898 Tm
0.09599 Tc
(1\)\))Tj 
/N10 1 Tf
6.47599 0 0 5.97698 247.41598 83.68399 Tm
0 Tc
(I)Tj 
/N4 1 Tf
9.50749 0 TD
(/)Tj 
ET
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1 g
/N13 /ExtGState findRes gsDI

119.54899 725.26298 370.60099 -19.92498 rf
119.54899 67.24598 370.60099 -23.90998 rf
119.54899 705.33799 370.60099 -621.65399 rf
BT
/N9 1 Tf
10.36099 0 0 10.16198 484.96899 717.29299 Tm
0 g
0 Tc
0 Tw
(7)Tj 
7.17298 0 0 6.67498 200.04499 717.29299 Tm
0.06898 Tc
(MATCHING)Tj [-466 ]TJ (POLYTOPE)Tj [-459 ]TJ (VIA)Tj [-480 ]TJ (SEMIDEFINITIVE)Tj [-424 ]TJ (LIFTINGS)Tj 
8.26899 0 0 8.06999 140.12098 47.32099 Tm
1 g
0.05999 Tc
(/)Tj [-247 ]TJ (3907)Tj [-494 ]TJ (no38)Tj [-500 ]TJ (Mp)Tj [-1000 ]TJ (7)Tj [-1000 ]TJ (Monday)Tj [-488 ]TJ (Mar)Tj [-494 ]TJ (08)Tj [-500 ]TJ (03:24)Tj [-500 ]TJ (PM)Tj [-1000 ]TJ (INF\261MOR)Tj [-1000 ]TJ (no38)Tj 
10.36099 0 0 10.16198 119.54899 693.38299 Tm
0 g
0 Tc
(again)Tj [-327 ]TJ (by)Tj [-327 ]TJ (Theorem)Tj [-322 ]TJ (3.1.)Tj [-332 ]TJ (For)Tj [-327 ]TJ (the)Tj [-327 ]TJ (converse,)Tj [-327 ]TJ (we)Tj [-322 ]TJ (apply)Tj [-327 ]TJ (Lemma)Tj [-327 ]TJ (1.5)Tj [-327 ]TJ (of)Tj [-327 ]TJ (Lova)Tj 
28.80279 0 TD
(\302)Tj [-53 ]TJ (s)Tj [0 ]TJ (z)Tj [-327 ]TJ (and)Tj [-327 ]TJ (Schrijver)Tj 
-28.80279 -1.17649 TD
(\()Tj [-96 ]TJ (1991)Tj [-96 ]TJ (\))Tj [-298 ]TJ (i)Tj [0 ]TJ (n)Tj [-293 ]TJ (a)Tj [0 ]TJ (n)Tj [-298 ]TJ (induction.)Tj [-284 ]TJ (We)Tj [-293 ]TJ (will)Tj [-288 ]TJ (prove)Tj [-293 ]TJ (that)Tj [-288 ]TJ (the)Tj [-293 ]TJ (inequality)Tj 
/N10 1 Tf
14.80769 -2.35289 TD
(x)Tj 
/N9 1 Tf
0.53849 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(E)Tj 
/N9 1 Tf
0.70669 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(S)Tj 
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0.59609 0 TD
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 311.77299 657.51799 Tm
0 Tc
(\241)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 323.47898 657.51799 Tm
-0.00399 Tc
(lx)Tj 
/N9 1 Tf
1.12489 0 TD
0 Tc
(,)Tj 
6.47599 0 0 5.97698 330.89999 656.02398 Tm
(0)Tj 
10.36099 0 0 10.16198 119.54899 633.60899 Tm
(where)Tj 
/N10 1 Tf
2.76438 0 TD
(S)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 156.75799 633.60899 Tm
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 166.42199 633.60899 Tm
(V)Tj 
/N9 1 Tf
0.61048 0 TD
(,)Tj [-332 ]TJ (has)Tj [-322 ]TJ (cardinality)Tj [-327 ]TJ (\()Tj [-96 ]TJ (2)Tj 
/N10 1 Tf
7.76928 0 TD
(l)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 259.47099 633.60899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 270.77699 633.60899 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (,)Tj [-327 ]TJ (is)Tj [-322 ]TJ (valid)Tj [-327 ]TJ (for)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 383.15399 633.60899 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 394.51098 633.60899 Tm
0.09599 Tc
(1\)\).)Tj [-236 ]TJ (I)Tj [96 ]TJ (t)Tj [-231 ]TJ (c)Tj [96 ]TJ (a)Tj [96 ]TJ (n)Tj [-231 ]TJ (b)Tj [96 ]TJ (e)Tj 
5.95959 0 TD
0 Tc
(checked)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 346.09298 637.59399 Tm
(l)Tj 
10.36099 0 0 10.16198 338.22299 633.60899 Tm
(N)Tj 
/N9 1 Tf
1.35089 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 346.09298 632.11399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 621.65399 Tm
(by)Tj [-284 ]TJ (direct)Tj [-279 ]TJ (computation)Tj [-284 ]TJ (that)Tj [-274 ]TJ (the)Tj [-279 ]TJ (statement)Tj [-274 ]TJ (is)Tj [-274 ]TJ (true)Tj [-274 ]TJ (for)Tj 
/N10 1 Tf
20.71629 0 TD
(l)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 339.91699 621.65399 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 350.72499 621.65399 Tm
(1.)Tj [-279 ]TJ (For)Tj 
/N10 1 Tf
2.69229 0 TD
(l)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 384.29998 621.65399 Tm
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 395.05799 621.65399 Tm
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 402.48098 621.65399 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 413.23899 621.65399 Tm
(1,)Tj [-274 ]TJ (note)Tj [-269 ]TJ (that)Tj [-260 ]TJ (setting)Tj 
-28.34609 -1.17649 TD
(any)Tj [-365 ]TJ (edge)Tj [-361 ]TJ (variable)Tj 
/N10 1 Tf
7.63938 0 TD
(x)Tj 
6.47599 0 0 5.97698 203.28298 608.20498 Tm
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 208.86099 609.69898 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 220.56698 609.69898 Tm
(1,)Tj [-370 ]TJ (forces)Tj 
/N10 1 Tf
3.92318 0 TD
(x)Tj 
6.47599 0 0 5.97698 265.84698 608.20498 Tm
(i)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 272.42199 609.69898 Tm
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 284.17698 609.69898 Tm
(0)Tj [-370 ]TJ (for)Tj [-370 ]TJ (all)Tj 
/N10 1 Tf
3.76429 0 TD
(i)Tj 
/N9 1 Tf
0.64428 0 TD
(such)Tj [-365 ]TJ (that)Tj [-361 ]TJ ({)Tj 
/N10 1 Tf
4.63449 0 TD
(i)Tj 
/N9 1 Tf
0.37509 0 TD
(,)Tj 
/N10 1 Tf
0.61538 0 TD
(j)Tj 
/N9 1 Tf
0.375 0 TD
(})Tj 
/N4 1 Tf
9.96199 0 0 9.96199 400.73799 609.69898 Tm
(\303)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 412.44299 609.69898 Tm
0.09599 Tc
(I)Tj [96 ]TJ (n)Tj [96 ]TJ (c\(2)Tj 
/N10 1 Tf
2.29798 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 445.26998 609.69898 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 457.02499 609.69898 Tm
0.09599 Tc
(1\).)Tj [-269 ]TJ (T)Tj [96 ]TJ (h)Tj [96 ]TJ (e)Tj 
-32.57209 -1.17649 TD
0 Tc
(resulting)Tj [-279 ]TJ (inequality)Tj [-279 ]TJ (is)Tj 
/N10 1 Tf
14.46629 -2.35289 TD
(x)Tj 
/N9 1 Tf
0.53839 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(E)Tj 
/N9 1 Tf
0.70669 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(S)Tj 
/N7 1 Tf
9.96199 0 0 9.96199 297.37799 573.83399 Tm
(*)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 301.65998 573.83399 Tm
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 312.51998 573.83399 Tm
0 Tc
(\241)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 324.22599 573.83399 Tm
0.09399 Tc
(kx)Tj 
/N9 1 Tf
1.38929 0 TD
0 Tc
(,)Tj 
6.47599 0 0 5.97698 334.38699 572.33999 Tm
(0)Tj 
10.36099 0 0 10.16198 119.54899 549.92498 Tm
(where)Tj 
/N10 1 Tf
2.95188 0 TD
(S)Tj 
/N7 1 Tf
9.96199 0 0 9.96199 156.30899 549.92498 Tm
(*)Tj 
/N20 1 Tf
0.86509 0 TD
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 176.53399 549.92498 Tm
(S)Tj 
/N9 1 Tf
1.01438 0 TD
(with)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 210.80398 549.92498 Tm
(\203)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 216.78199 549.92498 Tm
(S)Tj 
/N7 1 Tf
9.96199 0 0 9.96199 222.95899 549.92498 Tm
(*)Tj 
/N19 1 Tf
0.32998 0 TD
(\203)Tj 
/N4 1 Tf
1.03498 0 TD
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 249.80699 549.92498 Tm
(2)Tj 
/N10 1 Tf
0.5 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 264.89898 549.92498 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 278.14999 549.92498 Tm
(1.)Tj [-514 ]TJ (By)Tj [-519 ]TJ (induction,)Tj [-514 ]TJ (the)Tj [-514 ]TJ (last)Tj [-510 ]TJ (inequality)Tj [-505 ]TJ (is)Tj [-500 ]TJ (valid)Tj [-500 ]TJ (for)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 165.57499 537.96998 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 176.98098 537.96998 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-337 ]TJ (for)Tj [-332 ]TJ (any)Tj [-337 ]TJ (choice)Tj [-332 ]TJ (of)Tj 
/N10 1 Tf
9.08178 0 TD
(j)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 277.40299 537.96998 Tm
(\303)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 288.85998 537.96998 Tm
(E)Tj 
/N9 1 Tf
0.70658 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(S)Tj 
/N9 1 Tf
0.59619 0 TD
(\))Tj [-96 ]TJ (.)Tj [-341 ]TJ (Therefore,)Tj [-337 ]TJ (by)Tj [-336 ]TJ (Lemma)Tj [-337 ]TJ (1.5)Tj [-337 ]TJ (of)Tj [-337 ]TJ (Lova)Tj 
14.70658 0 TD
(\302)Tj [-48 ]TJ (s)Tj [0 ]TJ (z)Tj [-332 ]TJ (and)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 128.41398 541.95498 Tm
(k)Tj 
10.36099 0 0 10.16198 120.54499 537.96998 Tm
(N)Tj 
/N9 1 Tf
1.35099 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92788 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 128.41398 536.47499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 119.54899 526.01499 Tm
(Schrijver)Tj [-284 ]TJ (\()Tj [-96 ]TJ (1991)Tj [-96 ]TJ (\))Tj [-96 ]TJ (,)Tj 
/N10 1 Tf
13.32688 -2.35289 TD
(x)Tj 
/N9 1 Tf
0.53849 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(E)Tj 
/N9 1 Tf
0.70678 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(S)Tj 
/N9 1 Tf
0.59609 0 TD
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 296.42999 502.10499 Tm
0 Tc
(\241)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 308.13598 502.10499 Tm
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 320.14199 502.10499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 331.04998 502.10499 Tm
0.09599 Tc
(1\))Tj 
/N10 1 Tf
1.02409 0 TD
0 Tc
(x)Tj 
/N9 1 Tf
0.85089 0 TD
(,)Tj 
6.47599 0 0 5.97698 346.24198 500.61099 Tm
(0)Tj 
10.36099 0 0 10.16198 119.54899 478.19499 Tm
(is)Tj [-293 ]TJ (valid)Tj [-288 ]TJ (for)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 220.01998 478.19499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 231.02699 478.19499 Tm
(1)Tj [-96 ]TJ (\))Tj [-96 ]TJ (\))Tj [-298 ]TJ (for)Tj [-293 ]TJ (any)Tj 
/N10 1 Tf
4.85578 0 TD
(S)Tj 
/N20 1 Tf
9.96199 0 0 9.96199 289.60699 478.19499 Tm
(\265)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 298.97198 478.19499 Tm
(V)Tj 
/N9 1 Tf
0.90859 0 TD
(such)Tj [-293 ]TJ (that)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 348.93299 478.19499 Tm
(\203)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 354.90998 478.19499 Tm
(S)Tj 
/N19 1 Tf
9.96199 0 0 9.96199 360.09098 478.19499 Tm
(\203)Tj 
/N4 1 Tf
0.80989 0 TD
(\201)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 379.16899 478.19499 Tm
(2)Tj 
/N10 1 Tf
0.49989 0 TD
(k)Tj 
/N4 1 Tf
9.96199 0 0 9.96199 392.01998 478.19499 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 403.02799 478.19499 Tm
(3.)Tj 
/N8 1 Tf
9.96199 0 0 9.96199 421.15998 478.19499 Tm
(h)Tj 
/N10 1 Tf
6.47599 0 0 5.97698 177.18099 482.17999 Tm
(k)Tj 
/N4 1 Tf
0.43849 0 TD
(/)Tj 
/N9 1 Tf
0.79229 0 TD
(1)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 169.31098 478.19499 Tm
(N)Tj 
/N9 1 Tf
1.9375 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(P)Tj 
/N9 1 Tf
0.70658 0 TD
0.09599 Tc
(\(2)Tj 
/N10 1 Tf
0.92799 0 TD
0 Tc
(n)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 177.18099 476.70098 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 466.23999 Tm
(Note)Tj [-226 ]TJ (that)Tj [-221 ]TJ (the)Tj [-226 ]TJ (second)Tj [-226 ]TJ (part)Tj [-221 ]TJ (of)Tj [-221 ]TJ (the)Tj [-216 ]TJ (above)Tj [-221 ]TJ (proof)Tj [-216 ]TJ (applies)Tj [-216 ]TJ (to)Tj [-221 ]TJ (any)Tj [-216 ]TJ (undirected)Tj [-211 ]TJ (graph)Tj 
/N10 1 Tf
30.23069 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
(,)Tj [-207 ]TJ (yielding)Tj 
/N11 1 Tf
6.47599 0 0 5.97698 259.71998 446.31599 Tm
(\353)Tj 
/N19 1 Tf
0.37678 0 TD
(\203)Tj 
/N10 1 Tf
0.5 0 TD
(V)Tj 
/N19 1 Tf
0.80769 0 TD
(\203)Tj 
/N9 1 Tf
0.5 0 TD
0.09899 Tc
(/2)Tj 
/N11 1 Tf
0.97709 0 TD
0 Tc
(\373)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 251.20098 442.33099 Tm
(N)Tj 
/N9 1 Tf
3.12989 0 TD
(\()Tj 
/N10 1 Tf
0.42779 0 TD
(P)Tj 
/N9 1 Tf
0.70678 0 TD
(\()Tj 
/N10 1 Tf
0.42788 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
0.09599 Tc
(\)\))Tj 
/N4 1 Tf
9.96199 0 0 9.96199 319.14498 442.33099 Tm
0 Tc
(\201)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 330.05299 442.33099 Tm
(P)Tj 
/N9 1 Tf
0.91349 0 TD
(\()Tj 
/N10 1 Tf
0.42799 0 TD
(G)Tj 
/N9 1 Tf
0.81729 0 TD
0.09599 Tc
(\).)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 259.07099 440.83599 Tm
0 Tc
(/)Tj 
/N10 1 Tf
11.93849 0 TD
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 129.90998 418.42098 Tm
(Consider)Tj [-351 ]TJ (the)Tj [-351 ]TJ (general)Tj [-351 ]TJ (setting)Tj [-351 ]TJ (of)Tj [-351 ]TJ (0-1)Tj [-351 ]TJ (integer)Tj [-351 ]TJ (programming)Tj [-351 ]TJ (problems.)Tj [-346 ]TJ (If)Tj 
/N10 1 Tf
28.96629 0 TD
(P)Tj 
/N9 1 Tf
0.95678 0 TD
(and)Tj 
/N10 1 Tf
1.79328 0 TD
(P)Tj 
6.47599 0 0 5.97698 464.84599 416.92599 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 470.62298 418.42098 Tm
(have)Tj 
-33.88449 -1.17649 TD
(dimension)Tj 
/N10 1 Tf
4.46629 0 TD
(d)Tj 
/N9 1 Tf
0.59609 0 TD
(,)Tj [-303 ]TJ (then)Tj [-303 ]TJ (to)Tj [-303 ]TJ (obtain)Tj 
/N10 1 Tf
6.46159 0 TD
(P)Tj 
6.47599 0 0 5.97698 245.27398 404.97198 Tm
(I)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 250.55398 406.46598 Tm
(from)Tj 
/N10 1 Tf
2.24029 0 TD
(P)Tj 
/N9 1 Tf
0.70669 0 TD
(,)Tj [-303 ]TJ (a)Tj [0 ]TJ (t)Tj [-298 ]TJ (least)Tj [-3263 ]TJ (iterations)Tj [-288 ]TJ (of)Tj [-293 ]TJ (the)Tj [-288 ]TJ (Lova)Tj 
14.99038 0 TD
(\302)Tj [-47 ]TJ (sz-Schrijver)Tj 
-9.75959 1.12748 TD
(_)Tj 
0.19229 0 TD
(_)Tj 
/N5 1 Tf
6.47599 0 0 6.47599 330.85099 416.42799 Tm
(q)Tj 
/N22 1 Tf
9.96199 0 0 9.96199 319.24499 406.46598 Tm
(V)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 326.41699 406.46598 Tm
(\()Tj 
/N10 1 Tf
0.95188 0 TD
(d)Tj 
/N9 1 Tf
0.69239 0 TD
(\))Tj 
/N10 1 Tf
-21.61059 -1.17649 TD
(N)Tj 
/N4 1 Tf
6.47599 0 0 5.97698 126.42298 393.01699 Tm
(/)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 134.54199 394.51098 Tm
(procedure)Tj [-288 ]TJ (is)Tj [-284 ]TJ (needed)Tj [-288 ]TJ (in)Tj [-288 ]TJ (the)Tj [-284 ]TJ (worst)Tj [-279 ]TJ (case.)Tj [-284 ]TJ (For)Tj [-284 ]TJ (the)Tj [-279 ]TJ (matching)Tj [-279 ]TJ (problem)Tj [-3333 ]TJ (iterations)Tj [-245 ]TJ (of)Tj 
28.10089 1.12748 TD
(_)Tj 
0.19229 0 TD
(_)Tj 
/N5 1 Tf
6.47599 0 0 6.47599 421.25999 404.47299 Tm
(q)Tj 
/N10 1 Tf
10.36099 0 0 10.16198 408.35798 394.51098 Tm
(O)Tj 
/N9 1 Tf
0.81729 0 TD
(\()Tj 
/N10 1 Tf
0.95188 0 TD
(d)Tj 
/N9 1 Tf
0.69239 0 TD
(\))Tj 
-30.33648 -1.17649 TD
(the)Tj [-293 ]TJ (procedure)Tj [-293 ]TJ (suf\256ce.)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 129.51098 358.64599 Tm
(Acknowledgements.)Tj 
/N9 1 Tf
10.36099 0 0 10.16198 224.40299 358.64599 Tm
(Research)Tj [-308 ]TJ (of)Tj [-308 ]TJ (the)Tj [-303 ]TJ (\256rst)Tj [-303 ]TJ (author)Tj [-298 ]TJ (was)Tj [-303 ]TJ (supported)Tj [-303 ]TJ (in)Tj [-303 ]TJ (part)Tj [-298 ]TJ (by)Tj [-303 ]TJ (a)Tj [-308 ]TJ (summer)Tj 
-10.12019 -1.17649 TD
(research)Tj [-327 ]TJ (award)Tj [-322 ]TJ (from)Tj [-317 ]TJ (Faculty)Tj [-322 ]TJ (of)Tj [-322 ]TJ (Mathematics,)Tj [-317 ]TJ (University)Tj [-317 ]TJ (of)Tj [-317 ]TJ (Waterloo)Tj [-312 ]TJ (and)Tj [-317 ]TJ (by)Tj [-317 ]TJ (a)Tj [-312 ]TJ (research)Tj 
T*
(grant)Tj [-361 ]TJ (form)Tj [-361 ]TJ (NSERC)Tj [-361 ]TJ (of)Tj [-365 ]TJ (Canada.)Tj [-365 ]TJ (The)Tj [-365 ]TJ (second)Tj [-365 ]TJ (author's)Tj [-361 ]TJ (research)Tj [-361 ]TJ (was)Tj [-356 ]TJ (supported)Tj [-361 ]TJ (in)Tj [-361 ]TJ (part)Tj [-356 ]TJ (by)Tj 
T*
(research)Tj [-288 ]TJ (grants)Tj [-284 ]TJ (from)Tj [-293 ]TJ (NSERC)Tj [-288 ]TJ (of)Tj [-293 ]TJ (Canada.)Tj 
/N12 1 Tf
9.96199 0 0 10.16198 281.78599 304.84899 Tm
(References)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 119.54899 290.90199 Tm
(Edmonds,)Tj [-253 ]TJ (J.)Tj [-253 ]TJ (1965.)Tj [-247 ]TJ (Maximum)Tj [-253 ]TJ (matching)Tj [-253 ]TJ (and)Tj [-253 ]TJ (a)Tj [-247 ]TJ (polyhedron)Tj [-253 ]TJ (with)Tj [-247 ]TJ (0,1-vertices.)Tj 
/N10 1 Tf
30.56608 0 TD
(J)Tj 
/N9 1 Tf
0.53628 0 TD
(.)Tj 
/N10 1 Tf
0.49398 0 TD
(Res)Tj 
/N9 1 Tf
1.53608 0 TD
(.)Tj 
/N10 1 Tf
0.48779 0 TD
(Nat)Tj 
/N9 1 Tf
1.54219 0 TD
(.)Tj 
/N10 1 Tf
0.48789 0 TD
(Bureau)Tj [-229 ]TJ (of)Tj [-229 ]TJ (Standards-B)Tj 
/N12 1 Tf
7.96998 0 0 8.06999 143.45899 280.93998 Tm
(69B)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 159.14898 280.93998 Tm
(125)Tj [-96 ]TJ (\261)Tj [-96 ]TJ (130.)Tj 
-4.78919 -1.23458 TD
(Goemans,)Tj [-277 ]TJ (M.)Tj [-289 ]TJ (X.)Tj [-289 ]TJ (1997.)Tj [-289 ]TJ (Semide\256nite)Tj [-277 ]TJ (programming)Tj [-283 ]TJ (in)Tj [-295 ]TJ (combinatorial)Tj [-277 ]TJ (optimization.)Tj 
/N10 1 Tf
33.07818 0 TD
(Math)Tj 
/N9 1 Tf
2.20478 0 TD
(.)Tj 
/N10 1 Tf
0.54229 0 TD
(Prog)Tj 
/N9 1 Tf
2.09638 0 TD
(.)Tj 
/N12 1 Tf
7.96998 0 0 8.06999 437.54899 270.97698 Tm
(79)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 447.95799 270.97698 Tm
(143)Tj [-96 ]TJ (\261)Tj [-96 ]TJ (161.)Tj 
-39.71669 -1.23458 TD
(Lova)Tj 
1.66868 0 TD
(\302)Tj [-53 ]TJ (sz,)Tj [-374 ]TJ (L.,)Tj [-367 ]TJ (A.)Tj [-374 ]TJ (Schrijver)Tj [-367 ]TJ (1991.)Tj [-374 ]TJ (Cones)Tj [-374 ]TJ (of)Tj [-367 ]TJ (matrices)Tj [-367 ]TJ (and)Tj [-367 ]TJ (set-functions)Tj [-367 ]TJ (and)Tj [-367 ]TJ (0-1)Tj [-367 ]TJ (optimization.)Tj 
/N10 1 Tf
35.67469 0 TD
(SIAM)Tj [-367 ]TJ (J)Tj 
/N9 1 Tf
3.18669 0 TD
(.)Tj 
/N10 1 Tf
0.60839 0 TD
(Optim)Tj 
/N9 1 Tf
2.59638 0 TD
(.)Tj 
/N12 1 Tf
7.96998 0 0 8.06999 486.16499 261.01499 Tm
(1)Tj 
/N9 1 Tf
8.26899 0 0 8.06999 143.45899 251.05299 Tm
(166)Tj [-96 ]TJ (\261)Tj [-96 ]TJ (190.)Tj 
-1.89158 -2.96299 TD
(Tamon)Tj [-337 ]TJ (Stephen:)Tj [-337 ]TJ (Department)Tj [-331 ]TJ (of)Tj [-325 ]TJ (Mathematics,)Tj [-325 ]TJ (University)Tj [-331 ]TJ (of)Tj [-331 ]TJ (Michigan,)Tj [-319 ]TJ (2072)Tj [-331 ]TJ (East)Tj [-319 ]TJ (Hall,)Tj [-319 ]TJ (525)Tj [-331 ]TJ (East)Tj [-319 ]TJ (University)Tj 
-1 -1.23458 TD
(Avenue,)Tj [-283 ]TJ (Ann)Tj [-289 ]TJ (Arbor,)Tj [-283 ]TJ (Michigan)Tj [-283 ]TJ (48109-1109;)Tj [-289 ]TJ (e-mail:)Tj [-283 ]TJ (tamon@umich.edu)Tj 
1 -1.23458 TD
(Levent)Tj [-307 ]TJ (Tunc)Tj 
4.75299 0 TD
(\313)Tj [-53 ]TJ (el:)Tj [-301 ]TJ (Department)Tj [-301 ]TJ (of)Tj [-301 ]TJ (Combinatorics)Tj [-301 ]TJ (and)Tj [-301 ]TJ (Optimization,)Tj [-295 ]TJ (Faculty)Tj [-295 ]TJ (of)Tj [-301 ]TJ (Mathematics,)Tj [-289 ]TJ (University)Tj [-283 ]TJ (of)Tj [-283 ]TJ (Wa-)Tj 
-5.75299 -1.23458 TD
(terloo,)Tj [-289 ]TJ (Waterloo,)Tj [-277 ]TJ (Ontario)Tj [-277 ]TJ (N2L)Tj [-289 ]TJ (3G1,)Tj [-289 ]TJ (Canada;)Tj [-277 ]TJ (e-mail:)Tj [-283 ]TJ (ltuncel@math.uwaterloo.ca)Tj 
ET
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